Finite Group Databasebeta

← #15617146

Subgroups — #15617146

Order 2816.

1634 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076606C211yesmaximal, characteristic, complemented
2#13075571C211yesmaximal, characteristic, complemented
3#13075569C211yesmaximal, characteristic, complemented
4#13075564C211yesmaximal, characteristic, complemented
5#13074020C211yesmaximal, characteristic, complemented
6#13074019C211yesmaximal, characteristic, complemented
7#13074018C211yesmaximal, characteristic, complemented
8#13074016C211yesmaximal, characteristic, complemented
9#13074011C211yesmaximal, characteristic, complemented
10#13074006C211yesmaximal, characteristic, complemented
11#13072828C211yesmaximal, characteristic
12#13072828C211yesmaximal, characteristic
13#13072827C211yesmaximal, characteristic
14#13072826C211yesmaximal, characteristic
15#13072825C211yesmaximal, characteristic
16#13072793C211yesmaximal, characteristic
17#13072791C211yesmaximal, characteristic
18#13072788C211yesmaximal, characteristic
19#13072788C211yesmaximal, characteristic
20#13072786C211yesmaximal, characteristic
21#13072784C211yesmaximal, characteristic
22#13071717C211yesmaximal, characteristic, complemented
23#13071715C211yesmaximal, characteristic, complemented
24#13071713C211yesmaximal, characteristic, complemented
25#13071712C211yesmaximal, characteristic, complemented
26#13071707C211yesmaximal, characteristic, complemented
27#13071707C211yesmaximal, characteristic, complemented
28#13071098C211yesmaximal, characteristic
29#13071095C211yesmaximal, characteristic
30#13071095C211yesmaximal, characteristic
31C11×#2478C211yesmaximal, characteristic
32C2×C11×#126C2211yescharacteristic
33C2×C11×#117C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C2×#66943C2211yescharacteristic
37C2×#66942C2211yescharacteristic
38C2×#66942C2211yescharacteristic
39C2×#66942C2211yescharacteristic
40C2×#66942C2211yescharacteristic
41C2×#66932C2211yescharacteristic
42C2×#66930C2211yescharacteristic
43C2×#66930C2211yescharacteristic
44C2×#66930C2211yescharacteristic
45C2×#66930C2211yescharacteristic
46C2×#66923C2211yescharacteristic
47C11×#398C2211yescharacteristic
48C11×#398C2211yescharacteristic
49C11×#397C2211yescharacteristic
50C11×#397C2211yescharacteristic
51C11×#389C2211yescharacteristic
52C11×#389C2211yescharacteristic
53C11×#388C2211yescharacteristic
54C11×#387C2211yescharacteristic
55C11×#387C2211yescharacteristic
56C11×#387C2211yescharacteristic
57C11×#385C2211yescharacteristic
58C11×#385C2211yescharacteristic
59C4×C11×C4⋊C4C2211yescharacteristic
60#10622823C2211yescharacteristic
61#10622823C2211yescharacteristic
62#10622599C2211yescharacteristic
63#10622597C2211yescharacteristic
64#10622597C2211yescharacteristic
65#10622597C2211yescharacteristic
66#10622597C2211yescharacteristic
67#10622596C2211yescharacteristic
68#10622596C2211yescharacteristic
69#10622594C2211yescharacteristic
70#10622594C2211yescharacteristic
71#10622594C2211yescharacteristic
72#10622593C2211yescharacteristic
73#10622593C2211yescharacteristic
74#10622593C2211yescharacteristic
75#10622591C2211yescharacteristic
76#10622591C2211yescharacteristic
77#10622591C2211yescharacteristic
78#10622591C2211yescharacteristic
79#10622591C2211yescharacteristic
80#10622591C2211yescharacteristic
81C4⋊C4×Dic11C2211yescharacteristic
82C4⋊C4×Dic11C2211yescharacteristic
83C4⋊C4×Dic11C2211yescharacteristic
84C4⋊C4×Dic11C2211yescharacteristic
85C4⋊C4×Dic11C2211yescharacteristic
86C4⋊C4×Dic11C2211yescharacteristic
87#10622586C2211yescharacteristic
88#10622586C2211yescharacteristic
89#10622586C2211yescharacteristic
90#10622586C2211yescharacteristic
91#10622586C2211yescharacteristic
92#10622586C2211yescharacteristic
93#10622586C2211yescharacteristic
94#10622586C2211yescharacteristic
95#10622586C2211yescharacteristic
96#10622585C2211yescharacteristic
97#10622585C2211yescharacteristic
98#10622585C2211yescharacteristic
99#10622585C2211yescharacteristic
100#10622585C2211yescharacteristic
101#10622585C2211yescharacteristic
102#10622585C2211yescharacteristic
103#10622585C2211yescharacteristic
104#10622585C2211yescharacteristic
105#10622565C2211yescharacteristic
106#10622565C2211yescharacteristic
107#10622565C2211yescharacteristic
108#10622565C2211yescharacteristic
109#10622564C2211yescharacteristic
110#10622564C2211yescharacteristic
111#10622564C2211yescharacteristic
112#10622563C2211yescharacteristic
113#10622563C2211yescharacteristic
114#10622561C2211yescharacteristic
115#10622561C2211yescharacteristic
116#10622559C2211yescharacteristic
117#10622559C2211yescharacteristic
118#10622559C2211yescharacteristic
119#10622559C2211yescharacteristic
120#10622559C2211yescharacteristic
121#10622559C2211yescharacteristic
122#10622558C2211yescharacteristic
123#10622557C2211yescharacteristic
124C4×C4⋊Dic11C2211yescharacteristic
125#10622546C2211yescharacteristic
126#10622546C2211yescharacteristic
127#10622546C2211yescharacteristic
128#10622546C2211yescharacteristic
129#10622546C2211yescharacteristic
130C4×Dic11⋊C4C2211yescharacteristic
131C4×Dic11⋊C4C2211yescharacteristic
132C4×Dic11⋊C4C2211yescharacteristic
133C4×Dic11⋊C4C2211yescharacteristic
134C4×Dic11⋊C4C2211yescharacteristic
135C4×Dic11⋊C4C2211yescharacteristic
136C4×Dic11⋊C4C2211yescharacteristic
137C4×Dic11⋊C4C2211yescharacteristic
138#10622541C2211yescharacteristic
139#10622274C2211yescharacteristic
140#10622273C2211yescharacteristic
141#10622272C2211yescharacteristic
142#10622271C2211yescharacteristic
143#10622271C2211yescharacteristic
144#10622271C2211yescharacteristic
145#10622270C2211yescharacteristic
146#10622270C2211yescharacteristic
147#10622270C2211yescharacteristic
148#10622270C2211yescharacteristic
149#10622270C2211yescharacteristic
150#10622270C2211yescharacteristic
151#10622268C2211yescharacteristic
152#10622268C2211yescharacteristic
153#10622268C2211yescharacteristic
154#10622268C2211yescharacteristic
155#10622268C2211yescharacteristic
156#10622268C2211yescharacteristic
157#10622267C2211yescharacteristic
158#10622267C2211yescharacteristic
159#10622267C2211yescharacteristic
160#10622267C2211yescharacteristic
161#10622266C2211yescharacteristic
162#10622266C2211yescharacteristic
163#10622266C2211yescharacteristic
164#10622266C2211yescharacteristic
165#10622265C2211yescharacteristic
166#10622265C2211yescharacteristic
167#10622265C2211yescharacteristic
168#10622265C2211yescharacteristic
169#10622265C2211yescharacteristic
170#10622262C2211yescharacteristic
171#10622262C2211yescharacteristic
172#10622262C2211yescharacteristic
173#10622262C2211yescharacteristic
174#10622262C2211yescharacteristic
175#10622262C2211yescharacteristic
176#10622262C2211yescharacteristic
177#10622262C2211yescharacteristic
178#10622260C2211yescharacteristic
179#10622260C2211yescharacteristic
180#10622260C2211yescharacteristic
181#10622260C2211yescharacteristic
182#10622260C2211yescharacteristic
183#10622260C2211yescharacteristic
184#10622260C2211yescharacteristic
185#10622260C2211yescharacteristic
186#10622260C2211yescharacteristic
187C23×C4×C11C2311yescharacteristic
188C23×Dic11C2311yescharacteristic
189C23×Dic11C2311yescharacteristic
190C11×#126—42no—
191C11×#117—42no—
192C2×C11×C4⋊C4C2311yescharacteristic
193C2×C11×C4⋊C4C2311yescharacteristic
194C2×C11×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
202C2×C11×C4⋊C4C2311yescharacteristic
203C2×C11×C4⋊C4C2311yescharacteristic
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2311yescharacteristic
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C11×C22⋊C4C2311yescharacteristic
208C2×C11×C22⋊C4C2311yescharacteristic
209C2×C11×C22⋊C4C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C42×C11C2311yescharacteristic
213C2×C42×C11C2311yescharacteristic
214C2×C22⋊Dic11C2311yescharacteristic
215C2×C22⋊Dic11C2311yescharacteristic
216C2×C22⋊Dic11C2311yescharacteristic
217C2×C22⋊Dic11C2311yescharacteristic
218C2×C22⋊Dic11C2311yescharacteristic
219C2×C22⋊Dic11C2311yescharacteristic
220#66979—24no—
221C2×C4⋊Dic11C2311yescharacteristic
222C2×C4⋊Dic11C2311yescharacteristic
223C2×C4⋊Dic11C2311yescharacteristic
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×Dic11⋊C4C2311yescharacteristic
234C2×Dic11⋊C4C2311yescharacteristic
235C2×Dic11⋊C4C2311yescharacteristic
236C2×Dic11⋊C4C2311yescharacteristic
237C2×Dic11⋊C4C2311yescharacteristic
238C2×Dic11⋊C4C2311yescharacteristic
239C2×Dic11⋊C4C2311yescharacteristic
240C2×Dic11⋊C4C2311yescharacteristic
241C2×Dic11⋊C4C2311yescharacteristic
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×Dic11⋊C4C2311yescharacteristic
267C2×Dic11⋊C4C2311yescharacteristic
268C2×Dic11⋊C4C2311yescharacteristic
269C2×C4×Dic11—42no—
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
289C2×C4×Dic11C2311yescharacteristic
290#66943—24no—
291#66942—24no—
292#66942—24no—
293#66942—24no—
294#66942—24no—
295#66932—42no—
296#66930—24no—
297#66930—24no—
298#66930—42no—
299#66930—42no—
300#66923—24no—
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
355C11⋊#95C2311yescharacteristic
356C11⋊#95C2311yescharacteristic
357#60049—111nomaximal, Sylow
358C24×C11C2411yescharacteristic
359C22×C4×C11—22no—
360C22×C4×C11—22no—
361C22×C4×C11—22no—
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×C4×C11C2411yescharacteristic
375C22×C4×C11C2411yescharacteristic
376C22×Dic11—22no—
377C22×Dic11—22no—
378C22×Dic11—22no—
379C22×Dic11—22no—
380C22×Dic11—22no—
381C22×Dic11—22no—
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
396C22×Dic11C2411yescharacteristic
397C22×Dic11C2411yescharacteristic
398C11×C4⋊C4—22no—
399C11×C4⋊C4—22no—
400C11×C4⋊C4—22no—
401C11×C4⋊C4—22no—
402C11×C4⋊C4—22no—
403C11×C4⋊C4—22no—
404C11×C4⋊C4—22no—
405C11×C4⋊C4—41no—
406C11×C4⋊C4—41no—
407C11×C4⋊C4—41no—
408C11×C4⋊C4—41no—
409C11×C4⋊C4—41no—
410C11×C22⋊C4—22no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C42×C11—22no—
417C42×C11—41no—
418C42×C11—41no—
419C42×C11—41no—
420C22⋊Dic11—22no—
421C22⋊Dic11—22no—
422C22⋊Dic11—22no—
423C22⋊Dic11—22no—
424C22⋊Dic11—22no—
425C22⋊Dic11—22no—
426C4⋊Dic11—22no—
427C4⋊Dic11—22no—
428C4⋊Dic11—22no—
429C4⋊Dic11—22no—
430C4⋊Dic11—22no—
431C4⋊Dic11—22no—
432C4⋊Dic11—22no—
433C4⋊Dic11—22no—
434C4⋊Dic11—22no—
435C4⋊Dic11—22no—
436C4⋊Dic11—41no—
437C4⋊Dic11#4114yes—
438Dic11⋊C4—22no—
439Dic11⋊C4—22no—
440Dic11⋊C4—22no—
441Dic11⋊C4—22no—
442Dic11⋊C4—22no—
443Dic11⋊C4—22no—
444Dic11⋊C4—22no—
445Dic11⋊C4—22no—
446Dic11⋊C4—22no—
447Dic11⋊C4—22no—
448Dic11⋊C4—22no—
449Dic11⋊C4—22no—
450Dic11⋊C4—22no—
451Dic11⋊C4—22no—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
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—41no—
467Dic11⋊C4—41no—
468Dic11⋊C4—41no—
469Dic11⋊C4—41no—
470Dic11⋊C4—41no—
471Dic11⋊C4—41no—
472Dic11⋊C4#4114yes—
473Dic11⋊C4#4114yes—
474C4×Dic11—22no—
475C4×Dic11—22no—
476C4×Dic11—22no—
477C4×Dic11—22no—
478C4×Dic11—22no—
479C4×Dic11—22no—
480C4×Dic11—22no—
481C4×Dic11—22no—
482C4×Dic11—22no—
483C4×Dic11—22no—
484C4×Dic11—22no—
485C4×Dic11—41no—
486C4×Dic11—41no—
487C4×Dic11—41no—
488C4×Dic11—41no—
489C4×Dic11—41no—
490C4×Dic11—41no—
491C4×Dic11—41no—
492C4×Dic11—41no—
493C4×Dic11—41no—
494#2810—111no—
495#2726—111no—
496#2726—111no—
497#2726—111no—
498#2585—111no—
499#2585—111no—
500#2585—111no—
501#2585—111no—
502#2585—111no—
503#2585—111no—
504#2478—111no—
505#2478—111no—
506#2478—111no—
507#2478—111no—
508#2478—111no—
509#2478D1111yescharacteristic
510#2475—111no—
511#2475—111no—
512#2475—111no—
513#2475—111no—
514#2475—111no—
515#2475—111no—
516#2370—111no—
517#2370—111no—
518#2370—111no—
519#2370—111no—
520#2370—111no—
521#2370—111no—
522#2296—111no—
523#2296—111no—
524#2296—111no—
525C23×C11—21no—
526C23×C11—21no—
527C23×C11—21no—
528C23×C11—21no—
529C23×C11—21no—
530C23×C11—21no—
531C23×C11H(5,𝔽2)12yes—
532C23×C11C2511yescharacteristic
533C2×C4×C11—28no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—21no—
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—21no—
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×C11C2×#4112yes—
573C2×C4×C11C2×#4112yes—
574C2×C4×C11C2×#4112yes—
575C2×C4×C112−1+412yes—
576C2×Dic11—28no—
577C2×Dic11—28no—
578C2×Dic11—21no—
579C2×Dic11—21no—
580C2×Dic11—21no—
581C2×Dic11—21no—
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×Dic11C2×#4112yes—
619C2×Dic11C2×#4112yes—
620C2×Dic11C2×#4112yes—
621C2×Dic11C2×#4112yes—
622C2×Dic11C2×#4112yes—
623C2×Dic11C2×#4112yes—
624C2×Dic112−1+412yes—
625C2×Dic112−1+412yes—
626C2×#126—111no—
627C2×#126C2×D1111yescharacteristic
628C2×#125—111no—
629C2×#125—111no—
630C2×#125—111no—
631C2×#125—111no—
632C2×#125—111no—
633C2×#125—111no—
634C2×#117—111no—
635C2×#117—111no—
636C2×#117—111no—
637C2×#117—111no—
638C2×#117—111no—
639C2×#117C2×D1111yescharacteristic
640C22×C42—111no—
641#400—111no—
642#400—111no—
643#400—111no—
644#400—111no—
645#400—111no—
646#400—111no—
647#398—111no—
648#398—111no—
649#398—111no—
650#398—111no—
651#398—111no—
652#398—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#398C2×D1111yescharacteristic
664#398C2×D1111yescharacteristic
665#397—111no—
666#397—111no—
667#397—111no—
668#397—111no—
669#397C2×D1111yescharacteristic
670#397C2×D1111yescharacteristic
671#396—111no—
672#396—111no—
673#389—111no—
674#389—111no—
675#389—111no—
676#389—111no—
677#389—111no—
678#389—111no—
679#389—111no—
680#389—111no—
681#389—111no—
682#389—111no—
683#389—111no—
684#389—111no—
685#389—111no—
686#389—111no—
687#389—111no—
688#389—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#389C2×D1111yescharacteristic
702#389C2×D1111yescharacteristic
703#388—111no—
704#388—111no—
705#388—111no—
706#388—111no—
707#388—111no—
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#387—111no—
738#387—111no—
739#387—111no—
740#387—111no—
741#387—111no—
742#387C2×D1111yescharacteristic
743#387C2×D1111yescharacteristic
744#387C2×D1111yescharacteristic
745#385—111no—
746#385—111no—
747#385—111no—
748#385—111no—
749#385—111no—
750#385—111no—
751#385—111no—
752#385—111no—
753#385—111no—
754#385—111no—
755#385C2×D1111yescharacteristic
756#385C2×D1111yescharacteristic
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⋊C4—111no—
774C4×C4⋊C4—111no—
775C4×C4⋊C4—111no—
776C4×C4⋊C4—111no—
777C4×C4⋊C4—111no—
778C4×C4⋊C4—111no—
779C4×C4⋊C4—111no—
780C4×C4⋊C4C2×D1111yescharacteristic
781C22×C11—22no—
782C22×C11—22no—
783C22×C11—22no—
784C22×C11—41no—
785C22×C11—41no—
786C22×C11—41no—
787C22×C11—41no—
788C22×C11C22×#4111yescharacteristic
789C22×C11C22×#4111yescharacteristic
790C22×C11C22×#4111yescharacteristic
791C22×C11C2×H(5,𝔽2)11yescharacteristic
792C22×C11C2×2−1+411yescharacteristic
793C22×C11C2×2−1+411yescharacteristic
794C22×C11C2×2−1+411yescharacteristic
795C4×C11—22no—
796C4×C11—22no—
797C4×C11—22no—
798C4×C11—22no—
799C4×C11—41no—
800C4×C11—41no—
801C4×C11—41no—
802C4×C11—41no—
803C4×C11—41no—
804C4×C11—41no—
805C4×C11—41no—
806C4×C11—41no—
807C4×C11—41no—
808C4×C11—41no—
809Dic11—22no—
810Dic11—22no—
811Dic11—22no—
812Dic11—22no—
813Dic11—22no—
814Dic11—22no—
815Dic11—22no—
816Dic11—22no—
817Dic11—41no—
818Dic11—41no—
819Dic11—41no—
820Dic11—41no—
821Dic11—41no—
822Dic11—41no—
823Dic11—41no—
824Dic11—41no—
825C23×C4—111no—
826C23×C4—111no—
827C23×C4C22×D1111yescharacteristic
828#126—42no—
829#126—442no—
830#125—224no—
831#125—224no—
832#125—224no—
833#125—224no—
834#125—224no—
835#125—224no—
836#117—42no—
837#117—224no—
838#117—224no—
839#117—224no—
840#117—442no—
841#117—442no—
842C2×C4⋊C4—111no—
843C2×C4⋊C4—111no—
844C2×C4⋊C4—111no—
845C2×C4⋊C4—111no—
846C2×C4⋊C4—111no—
847C2×C4⋊C4—111no—
848C2×C4⋊C4—111no—
849C2×C4⋊C4—111no—
850C2×C4⋊C4—111no—
851C2×C4⋊C4—111no—
852C2×C4⋊C4—111no—
853C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
891C2×C4⋊C4C22×D1111yescharacteristic
892C2×C4⋊C4C22×D1111yescharacteristic
893C2×C4⋊C4C22×D1111yescharacteristic
894C2×C4⋊C4C22×D1111yescharacteristic
895C2×C4⋊C4C22×D1111yescharacteristic
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—442no—
935C2×C42C22×D1111yescharacteristic
936C2×C42C22×D1111yescharacteristic
937C2×C42C22×D1111yescharacteristic
938C2×C42C22×D1111yescharacteristic
939#95—111no—
940#95—111no—
941#95—111no—
942#95—111no—
943#95—111no—
944#95—111no—
945#95—111no—
946#95—111no—
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#95C22×D1111yescharacteristic
984#95C22×D1111yescharacteristic
985#95C22×D1111yescharacteristic
986#95C22×D1111yescharacteristic
987#95C22×D1111yescharacteristic
988#95C22×D1111yescharacteristic
989#95C22×D1111yescharacteristic
990#95C22×D1111yescharacteristic
991#95C22×D1111yescharacteristic
992#95C22×D1111yescharacteristic
993#95C22×D1111yescharacteristic
994#95C22×D1111yescharacteristic
995C2×C11—42no—
996C2×C11#348211yescharacteristic
997C2×C11#348211yescharacteristic
998C2×C11#348211yescharacteristic
999C2×C11#349211yescharacteristic
1000C2×C11#349211yescharacteristic
1001C2×C11#349211yescharacteristic
1002C2×C11#355611yescharacteristic
1003C24C23×D1111yescharacteristic
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—111no—
1008C22×C4—111no—
1009C22×C4—111no—
1010C22×C4—111no—
1011C22×C4—111no—
1012C22×C4—111no—
1013C22×C4—111no—
1014C22×C4—111no—
1015C22×C4—111no—
1016C22×C4—111no—
1017C22×C4—111no—
1018C22×C4—111no—
1019C22×C4—111no—
1020C22×C4—111no—
1021C22×C4—111no—
1022C22×C4—111no—
1023C22×C4—222no—
1024C22×C4—222no—
1025C22×C4—222no—
1026C22×C4—222no—
1027C22×C4—222no—
1028C22×C4—222no—
1029C22×C4C23×D1111yescharacteristic
1030C22×C4C23×D1111yescharacteristic
1031C22×C4C23×D1111yescharacteristic
1032C22×C4C23×D1111yescharacteristic
1033C22×C4C23×D1111yescharacteristic
1034C22×C4C23×D1111yescharacteristic
1035C22×C4C23×D1111yescharacteristic
1036C22×C4C23×D1111yescharacteristic
1037C22×C4C23×D1111yescharacteristic
1038C22×C4C23×D1111yescharacteristic
1039C22×C4C23×D1111yescharacteristic
1040C22×C4C23×D1111yescharacteristic
1041C22×C4C23×D1111yescharacteristic
1042C22×C4C23×D1111yescharacteristic
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—114no—
1056C4⋊C4—114no—
1057C4⋊C4—114no—
1058C4⋊C4—222no—
1059C4⋊C4—222no—
1060C4⋊C4—222no—
1061C4⋊C4—222no—
1062C4⋊C4—222no—
1063C4⋊C4—222no—
1064C4⋊C4—222no—
1065C4⋊C4—222no—
1066C4⋊C4—222no—
1067C4⋊C4—222no—
1068C4⋊C4—222no—
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—441no—
1097C4⋊C4—441no—
1098C4⋊C4—441no—
1099C4⋊C4—441no—
1100C4⋊C4—441no—
1101C4⋊C4—441no—
1102C4⋊C4—441no—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—22no—
1106C22⋊C4—22no—
1107C22⋊C4—22no—
1108C22⋊C4—22no—
1109C22⋊C4—222no—
1110C22⋊C4—222no—
1111C22⋊C4—222no—
1112C22⋊C4—222no—
1113C22⋊C4—222no—
1114C22⋊C4—222no—
1115C42—22no—
1116C42—41no—
1117C42—41no—
1118C42—41no—
1119C42—222no—
1120C42—222no—
1121C42—222no—
1122C42—222no—
1123C42—222no—
1124C42—222no—
1125C42—222no—
1126C42—222no—
1127C42—222no—
1128C42—222no—
1129C42—222no—
1130C42—441no—
1131C42—441no—
1132C42—441no—
1133C42—441no—
1134C42—441no—
1135C42—441no—
1136C42—441no—
1137C42—441no—
1138C42—441no—
1139C11#6004911yescharacteristic, complemented, Sylow
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23#6703712yes—
1147C23C24×D1111yescharacteristic
1148C2×C4—28no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
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—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—112no—
1188C2×C4—112no—
1189C2×C4—112no—
1190C2×C4—112no—
1191C2×C4—112no—
1192C2×C4—112no—
1193C2×C4—112no—
1194C2×C4—112no—
1195C2×C4—228no—
1196C2×C4—228no—
1197C2×C4—221no—
1198C2×C4—221no—
1199C2×C4—221no—
1200C2×C4—221no—
1201C2×C4—221no—
1202C2×C4—221no—
1203C2×C4—221no—
1204C2×C4—221no—
1205C2×C4—221no—
1206C2×C4—221no—
1207C2×C4—221no—
1208C2×C4—221no—
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#41×D1112yes—
1238C2×C4#41×D1112yes—
1239C2×C4#41×D1112yes—
1240C2×C4#6704312yes—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22C2×#6703711yescharacteristic
1249C22C2×#41×D1111yescharacteristic
1250C22C2×#41×D1111yescharacteristic
1251C22C2×#41×D1111yescharacteristic
1252C22C2×#6704311yescharacteristic
1253C22D11×2−1+411yescharacteristic
1254C22D11×2−1+411yescharacteristic
1255C4—22no—
1256C4—22no—
1257C4—22no—
1258C4—22no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—222no—
1270C4—222no—
1271C4—222no—
1272C4—222no—
1273C4—222no—
1274C4—222no—
1275C4—222no—
1276C4—222no—
1277C4—441no—
1278C4—441no—
1279C4—441no—
1280C4—441no—
1281C4—441no—
1282C4—441no—
1283C4—441no—
1284C4—441no—
1285C2—42no—
1286C2#1308222911yescharacteristic
1287C2#1308223011yescharacteristic
1288C2#1308223511yescharacteristic
1289C2#1308231711yescharacteristic
1290C2#1308231811yescharacteristic
1291C2#1308231811yescharacteristic
1292C2#1308310911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2478C2
prime radicalC24×C11C24
hypercenter#2478D11
hypocenterC11#60049
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2478

Complements

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

NH ≅ G/Ntype
1. #13076606C2semidirect
2. #13075571C2semidirect
3. #13075569C2semidirect
4. #13075564C2semidirect
5. #13074020C2semidirect
6. #13074019C2semidirect
7. #13074018C2semidirect
8. #13074016C2semidirect
9. #13074011C2semidirect
10. #13074006C2semidirect
22. #13071717C2semidirect
23. #13071715C2semidirect
24. #13071713C2semidirect
25. #13071712C2semidirect
26. #13071707C2semidirect
27. #13071707C2semidirect
1139. C11#60049semidirect

Maximal subgroups

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

subgroupindex
#130766062
#130755712
#130755692
#130755642
#130740202
#130740192
#130740182
#130740162
#130740112
#130740062
#130728282
#130728272
#130728262
#130728252
#130727932
#130727912
#130727882
#130727862
#130727842
#130717172
#130717152
#130717132
#130717122
#130717072
#130710982
#130710952
C11×#24782
#6004911