Finite Group Databasebeta

← #14924855

Subgroups — #14924855

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074026C211yesmaximal, characteristic, complemented
2#13074024C211yesmaximal, characteristic, complemented
3#13074011C211yesmaximal, characteristic, complemented
4#13074009C211yesmaximal, characteristic, complemented
5#13073897C211yesmaximal, characteristic
6#13073889C211yesmaximal, characteristic
7#13073707C211yesmaximal, characteristic
8#13073699C211yesmaximal, characteristic
9#13073339C211yesmaximal, characteristic
10#13073331C211yesmaximal, characteristic
11#13073311C211yesmaximal, characteristic, complemented
12#13073303C211yesmaximal, characteristic, complemented
13#13072642C211yesmaximal, characteristic
14#13072634C211yesmaximal, characteristic
15#13072605C211yesmaximal, characteristic, complemented
16#13072597C211yesmaximal, characteristic, complemented
17#13071910C211yesmaximal, characteristic, complemented
18#13071910C211yesmaximal, characteristic, complemented
19#13071890C211yesmaximal, characteristic
20#13071890C211yesmaximal, characteristic
21C4×#66943C211yesmaximal, characteristic, complemented
22C4×#66943C211yesmaximal, characteristic, complemented
23C4×#66931C211yesmaximal, characteristic
24C4×#66931C211yesmaximal, characteristic
25#13071114C211yesmaximal, characteristic
26#13071093C211yesmaximal, characteristic, complemented
27#13071088C211yesmaximal, characteristic, complemented
28#13071088C211yesmaximal, characteristic, complemented
29C42×Dic22C211yesmaximal, characteristic, complemented
30#117×Dic11C211yesmaximal, characteristic
31C11×#2298C211yesmaximal, characteristic
32C2×C11×#117C2211yescharacteristic
33C2×#66979C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66943C2211yescharacteristic
36C2×#66943C2211yescharacteristic
37C2×#66931C2211yescharacteristic
38C2×#66931C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C2×C4×Dic22C2211yescharacteristic
41C2×C4×Dic22C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#388C2211yescharacteristic
46C11×#388C2211yescharacteristic
47C11×#388C2211yescharacteristic
48C11×#388C2211yescharacteristic
49C11×#387C2211yescharacteristic
50C11×#387C2211yescharacteristic
51C11×#387C2211yescharacteristic
52C11×#387C2211yescharacteristic
53C4×C11×C4⋊C4C2211yescharacteristic
54C4×C11×C4⋊C4C2211yescharacteristic
55C4×C11×C22⋊C4C2211yescharacteristic
56C4×C11×C22⋊C4C2211yescharacteristic
57C11×#376C2211yescharacteristic
58C43×C11C2211yescharacteristic
59C4×C22⋊Dic11C2211yescharacteristic
60C4×C22⋊Dic11C2211yescharacteristic
61#10622598C2211yescharacteristic
62#10622598C2211yescharacteristic
63#10622597C2211yescharacteristic
64#10622597C2211yescharacteristic
65#10622597C2211yescharacteristic
66#10622597C2211yescharacteristic
67#10622594C2211yescharacteristic
68#10622594C2211yescharacteristic
69#10622594C2211yescharacteristic
70#10622594C2211yescharacteristic
71#10622592C2211yescharacteristic
72#10622592C2211yescharacteristic
73#10622592C2211yescharacteristic
74#10622592C2211yescharacteristic
75#10622590C2211yescharacteristic
76#10622590C2211yescharacteristic
77C4⋊C4×Dic11C2211yescharacteristic
78C4⋊C4×Dic11C2211yescharacteristic
79C4⋊C4×Dic11C2211yescharacteristic
80C4⋊C4×Dic11C2211yescharacteristic
81#10622586C2211yescharacteristic
82#10622586C2211yescharacteristic
83#10622564C2211yescharacteristic
84#10622564C2211yescharacteristic
85#10622564C2211yescharacteristic
86#10622564C2211yescharacteristic
87#10622563C2211yescharacteristic
88#10622563C2211yescharacteristic
89#10622562C2211yescharacteristic
90#10622562C2211yescharacteristic
91#10622561C2211yescharacteristic
92#10622561C2211yescharacteristic
93#10622561C2211yescharacteristic
94#10622561C2211yescharacteristic
95#10622560C2211yescharacteristic
96#10622560C2211yescharacteristic
97#10622559C2211yescharacteristic
98#10622559C2211yescharacteristic
99#10622555C2211yescharacteristic
100#10622555C2211yescharacteristic
101C22⋊C4×Dic11C2211yescharacteristic
102C22⋊C4×Dic11C2211yescharacteristic
103C22⋊C4×Dic11C2211yescharacteristic
104C22⋊C4×Dic11C2211yescharacteristic
105C4×C4⋊Dic11C2211yescharacteristic
106C4×C4⋊Dic11C2211yescharacteristic
107C4×C4⋊Dic11C2211yescharacteristic
108C4×C4⋊Dic11C2211yescharacteristic
109C4×C4⋊Dic11C2211yescharacteristic
110C4×C4⋊Dic11C2211yescharacteristic
111C4×C4⋊Dic11C2211yescharacteristic
112C4×C4⋊Dic11C2211yescharacteristic
113#10622546C2211yescharacteristic
114#10622546C2211yescharacteristic
115#10622546C2211yescharacteristic
116#10622546C2211yescharacteristic
117#10622545C2211yescharacteristic
118#10622545C2211yescharacteristic
119#10622545C2211yescharacteristic
120C4×Dic11⋊C4C2211yescharacteristic
121C4×Dic11⋊C4C2211yescharacteristic
122C4×Dic11⋊C4C2211yescharacteristic
123C4×Dic11⋊C4C2211yescharacteristic
124C4×Dic11⋊C4C2211yescharacteristic
125C4×Dic11⋊C4C2211yescharacteristic
126C4×Dic11⋊C4C2211yescharacteristic
127C4×Dic11⋊C4C2211yescharacteristic
128C4×Dic11⋊C4C2211yescharacteristic
129C4×Dic11⋊C4C2211yescharacteristic
130C4×Dic11⋊C4C2211yescharacteristic
131C4×Dic11⋊C4C2211yescharacteristic
132C42×Dic11C2211yescharacteristic
133C42×Dic11C2211yescharacteristic
134C42×Dic11C2211yescharacteristic
135#10622542C2211yescharacteristic
136#10622542C2211yescharacteristic
137#10622541C2211yescharacteristic
138#10622541C2211yescharacteristic
139#10622274C2211yescharacteristic
140#10622274C2211yescharacteristic
141#10622273C2211yescharacteristic
142#10622273C2211yescharacteristic
143#10622270C2211yescharacteristic
144#10622270C2211yescharacteristic
145#10622270C2211yescharacteristic
146#10622270C2211yescharacteristic
147#10622270C2211yescharacteristic
148#10622270C2211yescharacteristic
149#10622269C2211yescharacteristic
150#10622269C2211yescharacteristic
151#10622269C2211yescharacteristic
152#10622269C2211yescharacteristic
153#10622269C2211yescharacteristic
154#10622269C2211yescharacteristic
155#10622268C2211yescharacteristic
156#10622268C2211yescharacteristic
157#10622268C2211yescharacteristic
158#10622268C2211yescharacteristic
159#10622268C2211yescharacteristic
160#10622268C2211yescharacteristic
161#10622268C2211yescharacteristic
162#10622268C2211yescharacteristic
163#10622268C2211yescharacteristic
164#10622268C2211yescharacteristic
165#10622267C2211yescharacteristic
166#10622267C2211yescharacteristic
167#10622267C2211yescharacteristic
168#10622267C2211yescharacteristic
169#10622267C2211yescharacteristic
170#10622267C2211yescharacteristic
171#10622267C2211yescharacteristic
172#10622267C2211yescharacteristic
173#10622267C2211yescharacteristic
174#10622267C2211yescharacteristic
175#10622260C2211yescharacteristic
176#10622260C2211yescharacteristic
177#10622260C2211yescharacteristic
178#10622260C2211yescharacteristic
179#10622260C2211yescharacteristic
180#10622260C2211yescharacteristic
181#10622259C2211yescharacteristic
182#10622259C2211yescharacteristic
183#10622259C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C23×C4×C11C2311yescharacteristic
188C23×Dic11C2311yescharacteristic
189C23×Dic11C2311yescharacteristic
190C22×Dic22C2311yescharacteristic
191C22×Dic22C2311yescharacteristic
192C22×Dic22C2311yescharacteristic
193C22×Dic22C2311yescharacteristic
194C11×#117Q818yescomplemented
195C2×C11×C4⋊C4C2311yescharacteristic
196C2×C11×C4⋊C4C2311yescharacteristic
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C4⋊C4C2311yescharacteristic
199C2×C11×C4⋊C4C2311yescharacteristic
200C2×C11×C4⋊C4C2311yescharacteristic
201C2×C11×C22⋊C4C2311yescharacteristic
202C2×C11×C22⋊C4C2311yescharacteristic
203C2×C11×C22⋊C4C2311yescharacteristic
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2311yescharacteristic
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C42×C11C2311yescharacteristic
208C2×C42×C11C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C42×C11C2311yescharacteristic
215C2×C42×C11C2311yescharacteristic
216C2×C42×C11C2311yescharacteristic
217C2×C22⋊Dic11C2311yescharacteristic
218C2×C22⋊Dic11C2311yescharacteristic
219C2×C22⋊Dic11C2311yescharacteristic
220C2×C22⋊Dic11C2311yescharacteristic
221C2×C22⋊Dic11C2311yescharacteristic
222C2×C22⋊Dic11C2311yescharacteristic
223#66979—24no—
224C2×C4⋊Dic11C2311yescharacteristic
225C2×C4⋊Dic11C2311yescharacteristic
226C2×C4⋊Dic11C2311yescharacteristic
227C2×C4⋊Dic11C2311yescharacteristic
228C2×C4⋊Dic11C2311yescharacteristic
229C2×C4⋊Dic11C2311yescharacteristic
230C2×C4⋊Dic11C2311yescharacteristic
231C2×C4⋊Dic11C2311yescharacteristic
232C2×C4⋊Dic11C2311yescharacteristic
233C2×C4⋊Dic11C2311yescharacteristic
234C2×C4⋊Dic11C2311yescharacteristic
235C2×C4⋊Dic11C2311yescharacteristic
236C2×C4⋊Dic11C2311yescharacteristic
237C2×C4⋊Dic11C2311yescharacteristic
238C2×C4⋊Dic11C2311yescharacteristic
239C2×C4⋊Dic11C2311yescharacteristic
240C2×C4⋊Dic11C2311yescharacteristic
241C2×C4⋊Dic11C2311yescharacteristic
242C2×Dic11⋊C4C2311yescharacteristic
243C2×Dic11⋊C4C2311yescharacteristic
244C2×Dic11⋊C4C2311yescharacteristic
245C2×Dic11⋊C4C2311yescharacteristic
246C2×Dic11⋊C4C2311yescharacteristic
247C2×Dic11⋊C4C2311yescharacteristic
248C2×Dic11⋊C4C2311yescharacteristic
249C2×Dic11⋊C4C2311yescharacteristic
250C2×Dic11⋊C4C2311yescharacteristic
251C2×Dic11⋊C4C2311yescharacteristic
252C2×Dic11⋊C4C2311yescharacteristic
253C2×Dic11⋊C4C2311yescharacteristic
254C2×Dic11⋊C4C2311yescharacteristic
255C2×Dic11⋊C4C2311yescharacteristic
256C2×Dic11⋊C4C2311yescharacteristic
257C2×Dic11⋊C4C2311yescharacteristic
258C2×Dic11⋊C4C2311yescharacteristic
259C2×Dic11⋊C4C2311yescharacteristic
260C2×Dic11⋊C4C2311yescharacteristic
261C2×Dic11⋊C4C2311yescharacteristic
262C2×Dic11⋊C4C2311yescharacteristic
263C2×Dic11⋊C4C2311yescharacteristic
264C2×Dic11⋊C4C2311yescharacteristic
265C2×Dic11⋊C4C2311yescharacteristic
266C2×C4×Dic11—24no—
267C2×C4×Dic11C2311yescharacteristic
268C2×C4×Dic11C2311yescharacteristic
269C2×C4×Dic11C2311yescharacteristic
270C2×C4×Dic11C2311yescharacteristic
271C2×C4×Dic11C2311yescharacteristic
272C2×C4×Dic11C2311yescharacteristic
273C2×C4×Dic11C2311yescharacteristic
274C2×C4×Dic11C2311yescharacteristic
275C2×C4×Dic11C2311yescharacteristic
276C2×C4×Dic11C2311yescharacteristic
277C2×C4×Dic11C2311yescharacteristic
278C2×C4×Dic11C2311yescharacteristic
279C2×C4×Dic11C2311yescharacteristic
280C2×C4×Dic11C2311yescharacteristic
281C2×C4×Dic11C2311yescharacteristic
282C2×C4×Dic11C2311yescharacteristic
283C2×C4×Dic11C2311yescharacteristic
284C2×C4×Dic11C2311yescharacteristic
285C2×C4×Dic11C2311yescharacteristic
286C2×C4×Dic11C2311yescharacteristic
287C2×C4×Dic11C2311yescharacteristic
288C2×C4×Dic11C2311yescharacteristic
289#66943—24no—
290#66943—24no—
291#66931—24no—
292#66931—24no—
293C4×Dic22—24no—
294C4×Dic22—24no—
295C4×Dic22—24no—
296C4×Dic22—24no—
297C4×Dic22—24no—
298C4×Dic22—24no—
299C11×#95C2311yescharacteristic
300C11×#95C2311yescharacteristic
301C11×#95C2311yescharacteristic
302C11×#95C2311yescharacteristic
303C11×#95C2311yescharacteristic
304C11×#95C2311yescharacteristic
305C11×#95C2311yescharacteristic
306C11×#95C2311yescharacteristic
307C11×#95C2311yescharacteristic
308C11×#95C2311yescharacteristic
309C11×#95C2311yescharacteristic
310C11×#95C2311yescharacteristic
311C11⋊#95C2311yescharacteristic
312C11⋊#95C2311yescharacteristic
313C11⋊#95C2311yescharacteristic
314C11⋊#95C2311yescharacteristic
315C11⋊#95C2311yescharacteristic
316C11⋊#95C2311yescharacteristic
317C11⋊#95C2311yescharacteristic
318C11⋊#95C2311yescharacteristic
319C11⋊#95C2311yescharacteristic
320C11⋊#95C2311yescharacteristic
321C11⋊#95C2311yescharacteristic
322C11⋊#95C2311yescharacteristic
323C11⋊#95C2311yescharacteristic
324C11⋊#95C2311yescharacteristic
325C11⋊#95C2311yescharacteristic
326C11⋊#95C2311yescharacteristic
327C11⋊#95C2311yescharacteristic
328C11⋊#95C2311yescharacteristic
329C11⋊#95C2311yescharacteristic
330C11⋊#95C2311yescharacteristic
331C11⋊#95C2311yescharacteristic
332C11⋊#95C2311yescharacteristic
333C11⋊#95C2311yescharacteristic
334C11⋊#95C2311yescharacteristic
335C11⋊#95C2311yescharacteristic
336C11⋊#95C2311yescharacteristic
337C11⋊#95C2311yescharacteristic
338C11⋊#95C2311yescharacteristic
339C11⋊#95C2311yescharacteristic
340C11⋊#95C2311yescharacteristic
341C11⋊#95C2311yescharacteristic
342C11⋊#95C2311yescharacteristic
343C11⋊#95C2311yescharacteristic
344C11⋊#95C2311yescharacteristic
345C11⋊#95C2311yescharacteristic
346C11⋊#95C2311yescharacteristic
347C11⋊#95C2311yescharacteristic
348C11⋊#95C2311yescharacteristic
349C11⋊#95C2311yescharacteristic
350C11⋊#95C2311yescharacteristic
351C11⋊#95C2311yescharacteristic
352C11⋊#95C2311yescharacteristic
353C11⋊#95C2311yescharacteristic
354C11⋊#95C2311yescharacteristic
355#34882—111nomaximal, Sylow
356C24×C11C2411yescharacteristic
357C22×C4×C11—22no—
358C22×C4×C11—22no—
359C22×C4×C11C2×Q814yes—
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2411yescharacteristic
362C22×C4×C11C2411yescharacteristic
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2411yescharacteristic
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C22×C4×C11C2411yescharacteristic
370C22×C4×C11C2411yescharacteristic
371C22×C4×C11C2411yescharacteristic
372C22×C4×C11C2411yescharacteristic
373C22×C4×C11C2411yescharacteristic
374C22×Dic11—22no—
375C22×Dic11—22no—
376C22×Dic11—22no—
377C22×Dic11—22no—
378C22×Dic11—41no—
379C22×Dic11—41no—
380C22×Dic11C2411yescharacteristic
381C22×Dic11C2411yescharacteristic
382C22×Dic11C2411yescharacteristic
383C22×Dic11C2411yescharacteristic
384C22×Dic11C2411yescharacteristic
385C22×Dic11C2411yescharacteristic
386C22×Dic11C2411yescharacteristic
387C22×Dic11C2411yescharacteristic
388C22×Dic11C2411yescharacteristic
389C22×Dic11C2411yescharacteristic
390C22×Dic11C2411yescharacteristic
391C22×Dic11C2411yescharacteristic
392C22×Dic11C2411yescharacteristic
393C22×Dic11C2411yescharacteristic
394C22×Dic11C2411yescharacteristic
395C22×Dic11C2411yescharacteristic
396C2×Dic22—22no—
397C2×Dic22—22no—
398C2×Dic22—22no—
399C2×Dic22—22no—
400C2×Dic22—22no—
401C2×Dic22—22no—
402C2×Dic22—22no—
403C2×Dic22—22no—
404C2×Dic22—41no—
405C2×Dic22—41no—
406C2×Dic22—41no—
407C2×Dic22—41no—
408C11×C4⋊C4—22no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4—41no—
411C11×C4⋊C4—41no—
412C11×C4⋊C4C2×Q814yes—
413C11×C4⋊C4C2×Q814yes—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—41no—
417C11×C22⋊C4—41no—
418C11×C22⋊C4C2×Q814yes—
419C11×C22⋊C4C2×Q814yes—
420C42×C11—22no—
421C42×C11—22no—
422C42×C11—22no—
423C42×C11—22no—
424C42×C11—22no—
425C42×C11—22no—
426C42×C11—41no—
427C42×C11—41no—
428C42×C11C2×Q814yes—
429C42×C11C2×Q814yes—
430C22⋊Dic11—22no—
431C22⋊Dic11—22no—
432C22⋊Dic11—22no—
433C22⋊Dic11—22no—
434C22⋊Dic11—41no—
435C22⋊Dic11—41no—
436C4⋊Dic11—22no—
437C4⋊Dic11—22no—
438C4⋊Dic11—22no—
439C4⋊Dic11—22no—
440C4⋊Dic11—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11—22no—
443C4⋊Dic11—22no—
444C4⋊Dic11—22no—
445C4⋊Dic11—22no—
446C4⋊Dic11—22no—
447C4⋊Dic11—22no—
448C4⋊Dic11—22no—
449C4⋊Dic11—41no—
450C4⋊Dic11—41no—
451C4⋊Dic11—41no—
452C4⋊Dic11—41no—
453C4⋊Dic11#4114yes—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463Dic11⋊C4—22no—
464Dic11⋊C4—22no—
465Dic11⋊C4—22no—
466Dic11⋊C4—22no—
467Dic11⋊C4—22no—
468Dic11⋊C4—22no—
469Dic11⋊C4—22no—
470Dic11⋊C4—22no—
471Dic11⋊C4—41no—
472Dic11⋊C4—41no—
473Dic11⋊C4—41no—
474Dic11⋊C4—41no—
475Dic11⋊C4—41no—
476Dic11⋊C4—41no—
477Dic11⋊C4#4114yes—
478C4×Dic11—22no—
479C4×Dic11—22no—
480C4×Dic11—22no—
481C4×Dic11—22no—
482C4×Dic11—22no—
483C4×Dic11—22no—
484C4×Dic11—22no—
485C4×Dic11—22no—
486C4×Dic11—22no—
487C4×Dic11—22no—
488C4×Dic11—22no—
489C4×Dic11—22no—
490C4×Dic11—22no—
491C4×Dic11—22no—
492C4×Dic11—41no—
493C4×Dic11—41no—
494C4×Dic11—41no—
495C4×Dic11—41no—
496C4×Dic11—41no—
497C4×Dic11—41no—
498C4×Dic11#4114yes—
499C4×Dic11#4114yes—
500#2586—111no—
501#2586—111no—
502#2585—111no—
503#2585—111no—
504#2574—111no—
505#2574—111no—
506#2556—111no—
507#2556—111no—
508#2522—111no—
509#2522—111no—
510#2520—111no—
511#2520—111no—
512#2465—111no—
513#2465—111no—
514#2462—111no—
515#2462—111no—
516#2399—111no—
517#2399—111no—
518#2396—111no—
519#2396—111no—
520C4×#125—111no—
521C4×#125—111no—
522C4×C22⋊Q8—111no—
523C4×C22⋊Q8—111no—
524#2298—111no—
525#2298D1111yescharacteristic
526#2295—111no—
527#2295—111no—
528#2295—111no—
529C42×Q8—111no—
530C4×#117—111no—
531C23×C11—21no—
532C23×C11—21no—
533C23×C11—21no—
534C23×C11—21no—
535C23×C11—21no—
536C23×C11—21no—
537C23×C11C22×Q812yes—
538C23×C11C2511yescharacteristic
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—21no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—28no—
554C2×C4×C11—21no—
555C2×C4×C11—21no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—21no—
561C2×C4×C11—21no—
562C2×C4×C11—21no—
563C2×C4×C11—21no—
564C2×C4×C11—21no—
565C2×C4×C11—21no—
566C2×C4×C11—21no—
567C2×C4×C11—21no—
568C2×C4×C11—21no—
569C2×C4×C11—21no—
570C2×C4×C11—21no—
571C2×C4×C11—21no—
572C2×C4×C11C22×Q812yes—
573C2×C4×C11C22×Q812yes—
574C2×C4×C11C22×Q812yes—
575C2×C4×C11C22×Q812yes—
576C2×C4×C11C22×Q812yes—
577C2×C4×C11C22×Q812yes—
578C2×C4×C11C2×#4112yes—
579C2×C4×C11C2×#4112yes—
580C2×C4×C11C2×#4112yes—
581C2×C4×C11C2×#4112yes—
582C2×Dic11—21no—
583C2×Dic11—21no—
584C2×Dic11—21no—
585C2×Dic11—21no—
586C2×Dic11—21no—
587C2×Dic11—21no—
588C2×Dic11—21no—
589C2×Dic11—21no—
590C2×Dic11—21no—
591C2×Dic11—21no—
592C2×Dic11—21no—
593C2×Dic11—21no—
594C2×Dic11—21no—
595C2×Dic11—21no—
596C2×Dic11—21no—
597C2×Dic11—21no—
598C2×Dic11—21no—
599C2×Dic11—21no—
600C2×Dic11—21no—
601C2×Dic11—21no—
602C2×Dic11—21no—
603C2×Dic11—21no—
604C2×Dic11—21no—
605C2×Dic11—21no—
606C2×Dic11—21no—
607C2×Dic11—21no—
608C2×Dic11—21no—
609C2×Dic11—21no—
610C2×Dic11—21no—
611C2×Dic11—21no—
612C2×Dic11—21no—
613C2×Dic11—21no—
614C2×Dic11—21no—
615C2×Dic11—21no—
616C2×Dic11—21no—
617C2×Dic11—21no—
618C2×Dic11—21no—
619C2×Dic11—21no—
620C2×Dic11—21no—
621C2×Dic11—21no—
622C2×Dic11—44no—
623C2×Dic11—44no—
624C2×Dic11C2×#4112yes—
625C2×Dic11C2×#4112yes—
626C2×Dic11C2×#4112yes—
627C2×Dic11C2×#4112yes—
628C2×Dic11C2×#4112yes—
629C2×Dic11C2×#4112yes—
630C2×Dic11C2×#4112yes—
631C2×Dic11C2×#4112yes—
632Dic22—28no—
633Dic22—44no—
634Dic22—44no—
635Dic22—44no—
636C2×#125—111no—
637C2×#125—111no—
638C2×C22⋊Q8—111no—
639C2×C22⋊Q8—111no—
640C2×C4×Q8—111no—
641C2×C4×Q8—111no—
642C2×C4×Q8—111no—
643C2×C4×Q8—111no—
644C2×C4×Q8—111no—
645C2×C4×Q8—111no—
646C2×#117—111no—
647C2×#117C2×D1111yescharacteristic
648C22×C42—111no—
649#400—111no—
650#400—111no—
651#399—111no—
652#399—111no—
653#398—111no—
654#398—111no—
655#398—111no—
656#398—111no—
657#398—111no—
658#398—111no—
659#398—111no—
660#398—111no—
661#398—111no—
662#398—111no—
663#398—111no—
664#398—111no—
665#396—111no—
666#396—111no—
667#396—111no—
668#396—111no—
669#395—111no—
670#395—111no—
671#395—111no—
672#395—111no—
673#395—111no—
674#395—111no—
675#395—111no—
676#395—111no—
677#395—111no—
678#395—111no—
679#393—111no—
680#393—111no—
681#391—111no—
682#391—111no—
683#391—111no—
684#391—111no—
685#391—111no—
686#391—111no—
687#391—111no—
688#391—111no—
689#389—111no—
690#389—111no—
691#389—111no—
692#389—111no—
693#389—111no—
694#389—111no—
695#389—111no—
696#389—111no—
697#389—111no—
698#389—111no—
699#389—111no—
700#389—111no—
701#388—111no—
702#388—111no—
703#388—111no—
704#388—111no—
705#388C2×D1111yescharacteristic
706#388C2×D1111yescharacteristic
707#388C2×D1111yescharacteristic
708#388C2×D1111yescharacteristic
709#387—111no—
710#387—111no—
711#387—111no—
712#387—111no—
713#387—111no—
714#387—111no—
715#387—111no—
716#387—111no—
717#387—111no—
718#387—111no—
719#387—111no—
720#387—111no—
721#387—111no—
722#387—111no—
723#387—111no—
724#387—111no—
725#387—111no—
726#387—111no—
727#387—111no—
728#387—111no—
729#387—111no—
730#387—111no—
731#387—111no—
732#387—111no—
733#387—111no—
734#387—111no—
735#387—111no—
736#387—111no—
737#387C2×D1111yescharacteristic
738#387C2×D1111yescharacteristic
739#387C2×D1111yescharacteristic
740#387C2×D1111yescharacteristic
741#385—111no—
742#385—111no—
743#385—111no—
744#385—111no—
745#382—111no—
746#382—111no—
747#380—111no—
748#380—111no—
749C4×C4⋊C4—111no—
750C4×C4⋊C4—111no—
751C4×C4⋊C4—111no—
752C4×C4⋊C4—111no—
753C4×C4⋊C4—111no—
754C4×C4⋊C4—111no—
755C4×C4⋊C4—111no—
756C4×C4⋊C4—111no—
757C4×C4⋊C4—111no—
758C4×C4⋊C4—111no—
759C4×C4⋊C4—111no—
760C4×C4⋊C4—111no—
761C4×C4⋊C4—111no—
762C4×C4⋊C4—111no—
763C4×C4⋊C4—111no—
764C4×C4⋊C4—111no—
765C4×C4⋊C4—111no—
766C4×C4⋊C4—111no—
767C4×C4⋊C4—111no—
768C4×C4⋊C4—111no—
769C4×C4⋊C4—111no—
770C4×C4⋊C4—111no—
771C4×C4⋊C4—111no—
772C4×C4⋊C4—111no—
773C4×C4⋊C4C2×D1111yescharacteristic
774C4×C4⋊C4C2×D1111yescharacteristic
775C4×C22⋊C4—111no—
776C4×C22⋊C4—111no—
777C4×C22⋊C4—111no—
778C4×C22⋊C4—111no—
779C4×C22⋊C4—111no—
780C4×C22⋊C4—111no—
781C4×C22⋊C4C2×D1111yescharacteristic
782C4×C22⋊C4C2×D1111yescharacteristic
783#376—111no—
784#376—111no—
785#376—111no—
786#376C2×D1111yescharacteristic
787C43—111no—
788C43—111no—
789C43—111no—
790C43C2×D1111yescharacteristic
791C22×C11—22no—
792C22×C11—22no—
793C22×C11—22no—
794C22×C11—41no—
795C22×C11—41no—
796C22×C11—41no—
797C22×C11—41no—
798C22×C11C23×Q811yescharacteristic
799C22×C11C22×#4111yescharacteristic
800C22×C11C22×#4111yescharacteristic
801C22×C11C22×#4111yescharacteristic
802C22×C11C22×#4111yescharacteristic
803C22×C11#58511yescharacteristic
804C22×C11#58511yescharacteristic
805C4×C11—22no—
806C4×C11—22no—
807C4×C11—22no—
808C4×C11—22no—
809C4×C11—22no—
810C4×C11—22no—
811C4×C11—22no—
812C4×C11—41no—
813C4×C11—41no—
814C4×C11—41no—
815C4×C11—41no—
816C4×C11—41no—
817C4×C11—41no—
818C4×C11#53314yes—
819Dic11—22no—
820Dic11—22no—
821Dic11—22no—
822Dic11—22no—
823Dic11—22no—
824Dic11—22no—
825Dic11—22no—
826Dic11—22no—
827Dic11—41no—
828Dic11—41no—
829Dic11—41no—
830Dic11—41no—
831Dic11—41no—
832Dic11—41no—
833Dic11—41no—
834Dic11—41no—
835C22×Q8—111no—
836C22×Q8—111no—
837C22×Q8—111no—
838C22×Q8—111no—
839C23×C4—111no—
840C23×C4—111no—
841C23×C4C22×D1111yescharacteristic
842#125—224no—
843#125—224no—
844C22⋊Q8—224no—
845C22⋊Q8—224no—
846C4×Q8—224no—
847C4×Q8—224no—
848C4×Q8—224no—
849C4×Q8—224no—
850C4×Q8—224no—
851C4×Q8—224no—
852#117—224no—
853#117Dic2218yescomplemented
854C2×C4⋊C4—111no—
855C2×C4⋊C4—111no—
856C2×C4⋊C4—111no—
857C2×C4⋊C4—111no—
858C2×C4⋊C4—111no—
859C2×C4⋊C4—111no—
860C2×C4⋊C4—111no—
861C2×C4⋊C4—111no—
862C2×C4⋊C4—111no—
863C2×C4⋊C4—111no—
864C2×C4⋊C4—111no—
865C2×C4⋊C4—111no—
866C2×C4⋊C4—111no—
867C2×C4⋊C4—111no—
868C2×C4⋊C4—111no—
869C2×C4⋊C4—111no—
870C2×C4⋊C4—111no—
871C2×C4⋊C4—111no—
872C2×C4⋊C4—111no—
873C2×C4⋊C4—111no—
874C2×C4⋊C4—111no—
875C2×C4⋊C4—111no—
876C2×C4⋊C4—111no—
877C2×C4⋊C4—111no—
878C2×C4⋊C4—111no—
879C2×C4⋊C4—111no—
880C2×C4⋊C4—111no—
881C2×C4⋊C4—111no—
882C2×C4⋊C4—111no—
883C2×C4⋊C4—111no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4—111no—
886C2×C4⋊C4—111no—
887C2×C4⋊C4—111no—
888C2×C4⋊C4—111no—
889C2×C4⋊C4—111no—
890C2×C4⋊C4—111no—
891C2×C4⋊C4—111no—
892C2×C4⋊C4—111no—
893C2×C4⋊C4—111no—
894C2×C4⋊C4—111no—
895C2×C4⋊C4—111no—
896C2×C4⋊C4C22×D1111yescharacteristic
897C2×C4⋊C4C22×D1111yescharacteristic
898C2×C4⋊C4C22×D1111yescharacteristic
899C2×C4⋊C4C22×D1111yescharacteristic
900C2×C4⋊C4C22×D1111yescharacteristic
901C2×C4⋊C4C22×D1111yescharacteristic
902C2×C22⋊C4—111no—
903C2×C22⋊C4—111no—
904C2×C22⋊C4—111no—
905C2×C22⋊C4—111no—
906C2×C22⋊C4—111no—
907C2×C22⋊C4—111no—
908C2×C22⋊C4C22×D1111yescharacteristic
909C2×C22⋊C4C22×D1111yescharacteristic
910C2×C22⋊C4C22×D1111yescharacteristic
911C2×C22⋊C4C22×D1111yescharacteristic
912C2×C22⋊C4C22×D1111yescharacteristic
913C2×C22⋊C4C22×D1111yescharacteristic
914C2×C42—111no—
915C2×C42—111no—
916C2×C42—111no—
917C2×C42—111no—
918C2×C42—111no—
919C2×C42—111no—
920C2×C42—111no—
921C2×C42—111no—
922C2×C42—111no—
923C2×C42—111no—
924C2×C42—111no—
925C2×C42—111no—
926C2×C42—111no—
927C2×C42—111no—
928C2×C42—111no—
929C2×C42—111no—
930C2×C42—111no—
931C2×C42—111no—
932C2×C42—111no—
933C2×C42—111no—
934C2×C42—111no—
935C2×C42—111no—
936C2×C42—224no—
937C2×C42C22×D1111yescharacteristic
938C2×C42C22×D1111yescharacteristic
939C2×C42C22×D1111yescharacteristic
940C2×C42C22×D1111yescharacteristic
941C2×C42C22×D1111yescharacteristic
942C2×C42C22×D1111yescharacteristic
943C2×C42C22×D1111yescharacteristic
944C2×C42C22×D1111yescharacteristic
945C2×C42C22×D1111yescharacteristic
946C2×C42C22×D1111yescharacteristic
947#95—111no—
948#95—111no—
949#95—111no—
950#95—111no—
951#95—111no—
952#95—111no—
953#95—111no—
954#95—111no—
955#95—111no—
956#95—111no—
957#95—111no—
958#95—111no—
959#95—111no—
960#95—111no—
961#95—111no—
962#95—111no—
963#95—111no—
964#95—111no—
965#95—111no—
966#95—111no—
967#95—111no—
968#95—111no—
969#95—111no—
970#95—111no—
971#95—111no—
972#95—111no—
973#95—111no—
974#95—111no—
975#95—111no—
976#95—111no—
977#95—111no—
978#95—111no—
979#95—111no—
980#95—111no—
981#95—111no—
982#95—111no—
983#95—111no—
984#95—111no—
985#95—111no—
986#95—111no—
987#95—111no—
988#95—111no—
989#95—111no—
990#95—111no—
991#95C22×D1111yescharacteristic
992#95C22×D1111yescharacteristic
993#95C22×D1111yescharacteristic
994#95C22×D1111yescharacteristic
995#95C22×D1111yescharacteristic
996#95C22×D1111yescharacteristic
997#95C22×D1111yescharacteristic
998#95C22×D1111yescharacteristic
999#95C22×D1111yescharacteristic
1000#95C22×D1111yescharacteristic
1001#95C22×D1111yescharacteristic
1002#95C22×D1111yescharacteristic
1003C2×C11—42no—
1004C2×C11C2×#53311yescharacteristic
1005C2×C11#344411yescharacteristic
1006C2×C11#345511yescharacteristic
1007C2×C11#347511yescharacteristic
1008C2×C11#347511yescharacteristic
1009C2×C11Q8×#4111yescharacteristic
1010C2×C11Q8×#4111yescharacteristic
1011C24C23×D1111yescharacteristic
1012C2×Q8—222no—
1013C2×Q8—222no—
1014C2×Q8—222no—
1015C2×Q8—222no—
1016C2×Q8—222no—
1017C2×Q8—222no—
1018C2×Q8—222no—
1019C2×Q8—222no—
1020C2×Q8—441no—
1021C2×Q8—441no—
1022C2×Q8—441no—
1023C2×Q8—441no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—111no—
1027C22×C4—111no—
1028C22×C4—111no—
1029C22×C4—111no—
1030C22×C4—111no—
1031C22×C4—111no—
1032C22×C4—111no—
1033C22×C4—111no—
1034C22×C4—111no—
1035C22×C4—111no—
1036C22×C4—111no—
1037C22×C4—111no—
1038C22×C4—111no—
1039C22×C4—111no—
1040C22×C4—111no—
1041C22×C4—111no—
1042C22×C4—222no—
1043C22×C4—222no—
1044C22×C4—222no—
1045C22×C4—222no—
1046C22×C4—441no—
1047C22×C4—441no—
1048C22×C4C2×Dic2214yes—
1049C22×C4C23×D1111yescharacteristic
1050C22×C4C23×D1111yescharacteristic
1051C22×C4C23×D1111yescharacteristic
1052C22×C4C23×D1111yescharacteristic
1053C22×C4C23×D1111yescharacteristic
1054C22×C4C23×D1111yescharacteristic
1055C22×C4C23×D1111yescharacteristic
1056C22×C4C23×D1111yescharacteristic
1057C22×C4C23×D1111yescharacteristic
1058C22×C4C23×D1111yescharacteristic
1059C22×C4C23×D1111yescharacteristic
1060C22×C4C23×D1111yescharacteristic
1061C22×C4C23×D1111yescharacteristic
1062C22×C4C23×D1111yescharacteristic
1063C4⋊C4—22no—
1064C4⋊C4—22no—
1065C4⋊C4—41no—
1066C4⋊C4—41no—
1067C4⋊C4—114no—
1068C4⋊C4—114no—
1069C4⋊C4—222no—
1070C4⋊C4—222no—
1071C4⋊C4—222no—
1072C4⋊C4—222no—
1073C4⋊C4—222no—
1074C4⋊C4—222no—
1075C4⋊C4—222no—
1076C4⋊C4—222no—
1077C4⋊C4—222no—
1078C4⋊C4—222no—
1079C4⋊C4—222no—
1080C4⋊C4—222no—
1081C4⋊C4—222no—
1082C4⋊C4—222no—
1083C4⋊C4—222no—
1084C4⋊C4—222no—
1085C4⋊C4—222no—
1086C4⋊C4—222no—
1087C4⋊C4—222no—
1088C4⋊C4—222no—
1089C4⋊C4—222no—
1090C4⋊C4—222no—
1091C4⋊C4—222no—
1092C4⋊C4—222no—
1093C4⋊C4—222no—
1094C4⋊C4—222no—
1095C4⋊C4—222no—
1096C4⋊C4—222no—
1097C4⋊C4—222no—
1098C4⋊C4—222no—
1099C4⋊C4—441no—
1100C4⋊C4—441no—
1101C4⋊C4—441no—
1102C4⋊C4—441no—
1103C4⋊C4—441no—
1104C4⋊C4—441no—
1105C4⋊C4—441no—
1106C4⋊C4—441no—
1107C4⋊C4—441no—
1108C4⋊C4—441no—
1109C4⋊C4C2×Dic2214yes—
1110C4⋊C4C2×Dic2214yes—
1111C22⋊C4—22no—
1112C22⋊C4—22no—
1113C22⋊C4—41no—
1114C22⋊C4—41no—
1115C22⋊C4—222no—
1116C22⋊C4—222no—
1117C22⋊C4—222no—
1118C22⋊C4—222no—
1119C22⋊C4—441no—
1120C22⋊C4—441no—
1121C22⋊C4C2×Dic2214yes—
1122C22⋊C4C2×Dic2214yes—
1123C42—22no—
1124C42—22no—
1125C42—22no—
1126C42—22no—
1127C42—22no—
1128C42—22no—
1129C42—41no—
1130C42—41no—
1131C42—114no—
1132C42—114no—
1133C42—222no—
1134C42—222no—
1135C42—222no—
1136C42—222no—
1137C42—222no—
1138C42—222no—
1139C42—222no—
1140C42—222no—
1141C42—222no—
1142C42—222no—
1143C42—222no—
1144C42—222no—
1145C42—222no—
1146C42—222no—
1147C42—441no—
1148C42—441no—
1149C42—441no—
1150C42—441no—
1151C42—441no—
1152C42—441no—
1153C42C2×Dic2214yes—
1154C42C2×Dic2214yes—
1155C11#3488211yescharacteristic, complemented, Sylow
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23C22×Dic2212yes—
1163C23C24×D1111yescharacteristic
1164Q8—228no—
1165Q8—444no—
1166Q8—444no—
1167Q8—444no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—28no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—112no—
1202C2×C4—112no—
1203C2×C4—112no—
1204C2×C4—112no—
1205C2×C4—112no—
1206C2×C4—112no—
1207C2×C4—112no—
1208C2×C4—112no—
1209C2×C4—221no—
1210C2×C4—221no—
1211C2×C4—221no—
1212C2×C4—221no—
1213C2×C4—221no—
1214C2×C4—221no—
1215C2×C4—221no—
1216C2×C4—221no—
1217C2×C4—221no—
1218C2×C4—221no—
1219C2×C4—221no—
1220C2×C4—221no—
1221C2×C4—221no—
1222C2×C4—221no—
1223C2×C4—221no—
1224C2×C4—221no—
1225C2×C4—221no—
1226C2×C4—221no—
1227C2×C4—221no—
1228C2×C4—221no—
1229C2×C4—221no—
1230C2×C4—221no—
1231C2×C4—221no—
1232C2×C4—221no—
1233C2×C4—221no—
1234C2×C4—221no—
1235C2×C4—221no—
1236C2×C4—221no—
1237C2×C4—221no—
1238C2×C4—221no—
1239C2×C4—221no—
1240C2×C4—221no—
1241C2×C4—221no—
1242C2×C4—221no—
1243C2×C4—221no—
1244C2×C4—221no—
1245C2×C4—221no—
1246C2×C4—221no—
1247C2×C4—221no—
1248C2×C4—221no—
1249C2×C4—444no—
1250C2×C4—444no—
1251C2×C4C22×Dic2212yes—
1252C2×C4C22×Dic2212yes—
1253C2×C4C22×Dic2212yes—
1254C2×C4C22×Dic2212yes—
1255C2×C4C22×Dic2212yes—
1256C2×C4C22×Dic2212yes—
1257C2×C4#41×D1112yes—
1258C2×C4#41×D1112yes—
1259C2×C4#41×D1112yes—
1260C2×C4#41×D1112yes—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22C23×Dic2211yescharacteristic
1269C22C2×#41×D1111yescharacteristic
1270C22C2×#41×D1111yescharacteristic
1271C22C2×#41×D1111yescharacteristic
1272C22C2×#41×D1111yescharacteristic
1273C22#1062345311yescharacteristic
1274C22#1062345311yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—22no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—222no—
1289C4—222no—
1290C4—222no—
1291C4—222no—
1292C4—222no—
1293C4—222no—
1294C4—222no—
1295C4—222no—
1296C4—441no—
1297C4—441no—
1298C4—441no—
1299C4—441no—
1300C4—441no—
1301C4—441no—
1302C4—441no—
1303C4—441no—
1304C4#1062304814yes—
1305C2—42no—
1306C2C2×#1062304811yescharacteristic
1307C2#1308191011yescharacteristic
1308C2#1308199911yescharacteristic
1309C2#1308216811yescharacteristic
1310C2#1308217211yescharacteristic
1311C2#41×Dic2211yescharacteristic
1312C2#41×Dic2211yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2298C2
prime radicalC24×C11C24
hypercenter#2298D11
hypocenterC11#34882
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2298

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13074026C2semidirect
2. #13074024C2semidirect
3. #13074011C2semidirect
4. #13074009C2semidirect
11. #13073311C2semidirect
12. #13073303C2semidirect
15. #13072605C2semidirect
16. #13072597C2semidirect
17. #13071910C2semidirect
18. #13071910C2semidirect
21. C4×#66943C2semidirect
22. C4×#66943C2semidirect
26. #13071093C2semidirect
27. #13071088C2semidirect
28. #13071088C2semidirect
29. C42×Dic22C2semidirect
194. C11×#117Q8semidirect
853. #117Dic22semidirect
1155. C11#34882semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130740262
#130740242
#130740112
#130740092
#130738972
#130738892
#130737072
#130736992
#130733392
#130733312
#130733112
#130733032
#130726422
#130726342
#130726052
#130725972
#130719102
#130718902
C4×#669432
C4×#669312
#130711142
#130710932
#130710882
C42×Dic222
#117×Dic112
C11×#22982
#3488211