Finite Group Databasebeta

← #14968390

Subgroups — #14968390

Order 2816.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077007C211yesmaximal, characteristic
2#13076997C211yesmaximal, characteristic, complemented
3#13076498C211yesmaximal, characteristic, complemented
4#13076491C211yesmaximal, characteristic
5#13076435C211yesmaximal, characteristic, complemented
6#13076414C211yesmaximal, characteristic, complemented
7#13076397C211yesmaximal, characteristic, complemented
8#13076372C211yesmaximal, characteristic, complemented
9#13076355C211yesmaximal, characteristic
10#13076355C211yesmaximal, characteristic
11#13076121C211yesmaximal, characteristic
12#13076121C211yesmaximal, characteristic
13#13076104C211yesmaximal, characteristic, complemented
14#13076015C211yesmaximal, characteristic, complemented
15#13075976C211yesmaximal, characteristic
16#13075969C211yesmaximal, characteristic, complemented
17#13075913C211yesmaximal, characteristic
18#13074704C211yesmaximal, characteristic, complemented
19#13074635C211yesmaximal, characteristic
20#13074315C211yesmaximal, characteristic
21#13074266C211yesmaximal, characteristic, complemented
22#13074194C211yesmaximal, characteristic
23#13074115C211yesmaximal, characteristic
24#13074056C211yesmaximal, characteristic, complemented
25#13073804C211yesmaximal, characteristic, complemented
26#13073496C211yesmaximal, characteristic, complemented
27#13073476C211yesmaximal, characteristic
28#13071416C211yesmaximal, characteristic, complemented
29#13071220C211yesmaximal, characteristic
30#13071089C211yesmaximal, characteristic, complemented
31C11×#2793C211yesmaximal, characteristic
32C2×#66943C2211yescharacteristic
33C2×#66940C2211yescharacteristic
34C2×#66930C2211yescharacteristic
35C11×#400C2211yescharacteristic
36C11×#398C2211yescharacteristic
37C11×#397C2211yescharacteristic
38C11×#397C2211yescharacteristic
39C11×#396C2211yescharacteristic
40C11×#396C2211yescharacteristic
41C11×#388C2211yescharacteristic
42C11×#388C2211yescharacteristic
43C11×#388C2211yescharacteristic
44C11×#387C2211yescharacteristic
45C11×#387C2211yescharacteristic
46C11×#387C2211yescharacteristic
47C11×#387C2211yescharacteristic
48C11×#387C2211yescharacteristic
49C11×#384C2211yescharacteristic
50#10622599C2211yescharacteristic
51#10622599C2211yescharacteristic
52#10622597C2211yescharacteristic
53#10622597C2211yescharacteristic
54#10622597C2211yescharacteristic
55#10622596C2211yescharacteristic
56#10622595C2211yescharacteristic
57#10622595C2211yescharacteristic
58#10622595C2211yescharacteristic
59#10622595C2211yescharacteristic
60#10622595C2211yescharacteristic
61#10622594C2211yescharacteristic
62#10622594C2211yescharacteristic
63#10622594C2211yescharacteristic
64#10622594C2211yescharacteristic
65#10622594C2211yescharacteristic
66#10622594C2211yescharacteristic
67#10622593C2211yescharacteristic
68#10622593C2211yescharacteristic
69#10622593C2211yescharacteristic
70#10622593C2211yescharacteristic
71#10622593C2211yescharacteristic
72#10622593C2211yescharacteristic
73#10622592C2211yescharacteristic
74#10622592C2211yescharacteristic
75#10622592C2211yescharacteristic
76#10622591C2211yescharacteristic
77#10622591C2211yescharacteristic
78#10622591C2211yescharacteristic
79#10622591C2211yescharacteristic
80#10622590C2211yescharacteristic
81#10622589C2211yescharacteristic
82C4⋊C4×Dic11C2211yescharacteristic
83C4⋊C4×Dic11C2211yescharacteristic
84#10622587C2211yescharacteristic
85#10622587C2211yescharacteristic
86#10622586C2211yescharacteristic
87#10622585C2211yescharacteristic
88#10622585C2211yescharacteristic
89#10622585C2211yescharacteristic
90#10622585C2211yescharacteristic
91#10622585C2211yescharacteristic
92#10622566C2211yescharacteristic
93#10622566C2211yescharacteristic
94#10622565C2211yescharacteristic
95#10622565C2211yescharacteristic
96#10622564C2211yescharacteristic
97#10622564C2211yescharacteristic
98#10622564C2211yescharacteristic
99#10622564C2211yescharacteristic
100#10622564C2211yescharacteristic
101#10622562C2211yescharacteristic
102#10622560C2211yescharacteristic
103#10622560C2211yescharacteristic
104#10622560C2211yescharacteristic
105#10622559C2211yescharacteristic
106#10622559C2211yescharacteristic
107#10622559C2211yescharacteristic
108#10622559C2211yescharacteristic
109#10622558C2211yescharacteristic
110#10622558C2211yescharacteristic
111#10622558C2211yescharacteristic
112#10622557C2211yescharacteristic
113#10622557C2211yescharacteristic
114#10622557C2211yescharacteristic
115#10622557C2211yescharacteristic
116#10622557C2211yescharacteristic
117#10622555C2211yescharacteristic
118#10622555C2211yescharacteristic
119C4×C4⋊Dic11C2211yescharacteristic
120#10622546C2211yescharacteristic
121#10622546C2211yescharacteristic
122#10622546C2211yescharacteristic
123#10622546C2211yescharacteristic
124#10622546C2211yescharacteristic
125#10622546C2211yescharacteristic
126#10622546C2211yescharacteristic
127C4×Dic11⋊C4C2211yescharacteristic
128C42×Dic11C2211yescharacteristic
129#10622542C2211yescharacteristic
130#10622542C2211yescharacteristic
131C11⋊#401C2211yescharacteristic
132C11⋊#401C2211yescharacteristic
133#10622273C2211yescharacteristic
134#10622273C2211yescharacteristic
135#10622272C2211yescharacteristic
136#10622272C2211yescharacteristic
137#10622271C2211yescharacteristic
138#10622271C2211yescharacteristic
139#10622271C2211yescharacteristic
140#10622271C2211yescharacteristic
141#10622271C2211yescharacteristic
142#10622270C2211yescharacteristic
143#10622269C2211yescharacteristic
144#10622269C2211yescharacteristic
145#10622268C2211yescharacteristic
146#10622268C2211yescharacteristic
147#10622268C2211yescharacteristic
148#10622267C2211yescharacteristic
149#10622267C2211yescharacteristic
150#10622267C2211yescharacteristic
151#10622267C2211yescharacteristic
152#10622267C2211yescharacteristic
153#10622266C2211yescharacteristic
154#10622266C2211yescharacteristic
155#10622266C2211yescharacteristic
156#10622265C2211yescharacteristic
157#10622265C2211yescharacteristic
158#10622265C2211yescharacteristic
159#10622265C2211yescharacteristic
160#10622265C2211yescharacteristic
161#10622265C2211yescharacteristic
162#10622265C2211yescharacteristic
163#10622265C2211yescharacteristic
164#10622265C2211yescharacteristic
165#10622264C2211yescharacteristic
166#10622264C2211yescharacteristic
167#10622264C2211yescharacteristic
168#10622264C2211yescharacteristic
169#10622264C2211yescharacteristic
170#10622263C2211yescharacteristic
171#10622262C2211yescharacteristic
172#10622262C2211yescharacteristic
173#10622261C2211yescharacteristic
174#10622261C2211yescharacteristic
175#10622260C2211yescharacteristic
176#10622260C2211yescharacteristic
177#10622260C2211yescharacteristic
178#10622260C2211yescharacteristic
179#10622259C2211yescharacteristic
180#10622259C2211yescharacteristic
181#10622259C2211yescharacteristic
182#10622259C2211yescharacteristic
183#10622259C2211yescharacteristic
184#10622259C2211yescharacteristic
185#10622259C2211yescharacteristic
186#10622259C2211yescharacteristic
187C23×Dic11C2311yescharacteristic
188C22×Dic22C2311yescharacteristic
189C22×Dic22C2311yescharacteristic
190C22×Dic22C2311yescharacteristic
191C2×C11×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
203C2×C11×C22⋊C4C2311yescharacteristic
204C2×C11×C22⋊C4C2311yescharacteristic
205C2×C11×C22⋊C4C2311yescharacteristic
206C2×C11×C22⋊C4C2311yescharacteristic
207C2×C11×C22⋊C4C2311yescharacteristic
208C2×C11×C22⋊C4C2311yescharacteristic
209C2×C42×C11C2311yescharacteristic
210C2×C42×C11C2311yescharacteristic
211C2×C42×C11C2311yescharacteristic
212C2×C22⋊Dic11C2311yescharacteristic
213C2×C22⋊Dic11C2311yescharacteristic
214C2×C22⋊Dic11C2311yescharacteristic
215C2×C22⋊Dic11C2311yescharacteristic
216C2×C22⋊Dic11C2311yescharacteristic
217C2×C22⋊Dic11C2311yescharacteristic
218C2×C22⋊Dic11C2311yescharacteristic
219C2×C4⋊Dic11C2311yescharacteristic
220C2×C4⋊Dic11C2311yescharacteristic
221C2×C4⋊Dic11C2311yescharacteristic
222C2×C4⋊Dic11C2311yescharacteristic
223C2×C4⋊Dic11C2311yescharacteristic
224C2×C4⋊Dic11C2311yescharacteristic
225C2×C4⋊Dic11C2311yescharacteristic
226C2×C4⋊Dic11C2311yescharacteristic
227C2×Dic11⋊C4C2311yescharacteristic
228C2×Dic11⋊C4C2311yescharacteristic
229C2×Dic11⋊C4C2311yescharacteristic
230C2×Dic11⋊C4C2311yescharacteristic
231C2×Dic11⋊C4C2311yescharacteristic
232C2×Dic11⋊C4C2311yescharacteristic
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×C4×Dic11C2311yescharacteristic
254C2×C4×Dic11C2311yescharacteristic
255C2×C4×Dic11C2311yescharacteristic
256C2×C4×Dic11C2311yescharacteristic
257C2×C4×Dic11C2311yescharacteristic
258C2×C4×Dic11C2311yescharacteristic
259C2×C4×Dic11C2311yescharacteristic
260C2×C4×Dic11C2311yescharacteristic
261C2×C4×Dic11C2311yescharacteristic
262C2×C4×Dic11C2311yescharacteristic
263C2×C4×Dic11C2311yescharacteristic
264C2×C4×Dic11C2311yescharacteristic
265C2×C4×Dic11C2311yescharacteristic
266C2×C4×Dic11C2311yescharacteristic
267C2×C4×Dic11C2311yescharacteristic
268#66943—24no—
269#66940—24no—
270#66930—24no—
271C11×#95C2311yescharacteristic
272C11×#95C2311yescharacteristic
273C11×#95C2311yescharacteristic
274C11×#95C2311yescharacteristic
275C11×#95C2311yescharacteristic
276C11×#95C2311yescharacteristic
277C11×#95C2311yescharacteristic
278C11×#95C2311yescharacteristic
279C11×#95C2311yescharacteristic
280C11×#95C2311yescharacteristic
281C11×#95C2311yescharacteristic
282C11×#95C2311yescharacteristic
283C11×#95C2311yescharacteristic
284C11×#95C2311yescharacteristic
285C11⋊#95C2311yescharacteristic
286C11⋊#95C2311yescharacteristic
287C11⋊#95C2311yescharacteristic
288C11⋊#95C2311yescharacteristic
289C11⋊#95C2311yescharacteristic
290C11⋊#95C2311yescharacteristic
291C11⋊#95C2311yescharacteristic
292C11⋊#95C2311yescharacteristic
293C11⋊#95C2311yescharacteristic
294C11⋊#95C2311yescharacteristic
295C11⋊#95C2311yescharacteristic
296C11⋊#95C2311yescharacteristic
297C11⋊#95C2311yescharacteristic
298C11⋊#95C2311yescharacteristic
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
345#37001—111nomaximal, Sylow
346C24×C11C2411yescharacteristic
347C22×C4×C11C2411yescharacteristic
348C22×C4×C11C2411yescharacteristic
349C22×C4×C11C2411yescharacteristic
350C22×C4×C11C2411yescharacteristic
351C22×C4×C11C2411yescharacteristic
352C22×C4×C11C2411yescharacteristic
353C22×C4×C11C2411yescharacteristic
354C22×C4×C11C2411yescharacteristic
355C22×C4×C11C2411yescharacteristic
356C22×C4×C11C2411yescharacteristic
357C22×C4×C11C2411yescharacteristic
358C22×C4×C11C2411yescharacteristic
359C22×C4×C11C2411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C22×Dic11—22no—
362C22×Dic11—41no—
363C22×Dic11—41no—
364C22×Dic11C2411yescharacteristic
365C22×Dic11C2411yescharacteristic
366C22×Dic11C2411yescharacteristic
367C22×Dic11C2411yescharacteristic
368C22×Dic11C2411yescharacteristic
369C22×Dic11C2411yescharacteristic
370C22×Dic11C2411yescharacteristic
371C22×Dic11C2411yescharacteristic
372C22×Dic11C2411yescharacteristic
373C22×Dic11C2411yescharacteristic
374C22×Dic11C2411yescharacteristic
375C22×Dic11C2411yescharacteristic
376C22×Dic11C2411yescharacteristic
377C22×Dic11C2411yescharacteristic
378C22×Dic11C2411yescharacteristic
379C22×Dic11C2411yescharacteristic
380C2×Dic22—22no—
381C2×Dic22—22no—
382C2×Dic22—22no—
383C2×Dic22—41no—
384C2×Dic22—41no—
385C2×Dic22—41no—
386C2×Dic22—41no—
387C2×Dic22—41no—
388C2×Dic22—41no—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—41no—
392C11×C4⋊C4—41no—
393C11×C4⋊C4—41no—
394C11×C4⋊C4—41no—
395C11×C4⋊C4—41no—
396C11×C4⋊C4—41no—
397C11×C4⋊C4—41no—
398C11×C4⋊C4—41no—
399C11×C4⋊C4—41no—
400C11×C22⋊C4—22no—
401C11×C22⋊C4—41no—
402C11×C22⋊C4—41no—
403C11×C22⋊C4—41no—
404C11×C22⋊C4—41no—
405C11×C22⋊C4—41no—
406C11×C22⋊C4—41no—
407C42×C11—41no—
408C42×C11—41no—
409C42×C11—41no—
410C22⋊Dic11—22no—
411C22⋊Dic11—22no—
412C22⋊Dic11—22no—
413C22⋊Dic11—41no—
414C22⋊Dic11—41no—
415C22⋊Dic11—41no—
416C22⋊Dic11—41no—
417C4⋊Dic11—22no—
418C4⋊Dic11—22no—
419C4⋊Dic11—22no—
420C4⋊Dic11—22no—
421C4⋊Dic11—41no—
422C4⋊Dic11—41no—
423C4⋊Dic11—41no—
424C4⋊Dic11—41no—
425Dic11⋊C4—22no—
426Dic11⋊C4—22no—
427Dic11⋊C4—22no—
428Dic11⋊C4—22no—
429Dic11⋊C4—22no—
430Dic11⋊C4—22no—
431Dic11⋊C4—22no—
432Dic11⋊C4—22no—
433Dic11⋊C4—22no—
434Dic11⋊C4—41no—
435Dic11⋊C4—41no—
436Dic11⋊C4—41no—
437Dic11⋊C4—41no—
438Dic11⋊C4—41no—
439Dic11⋊C4—41no—
440Dic11⋊C4—41no—
441Dic11⋊C4—41no—
442Dic11⋊C4—41no—
443Dic11⋊C4—41no—
444Dic11⋊C4—41no—
445Dic11⋊C4—41no—
446Dic11⋊C4—41no—
447Dic11⋊C4—41no—
448Dic11⋊C4—41no—
449Dic11⋊C4—41no—
450Dic11⋊C4—41no—
451C4×Dic11—22no—
452C4×Dic11—22no—
453C4×Dic11—22no—
454C4×Dic11—22no—
455C4×Dic11—22no—
456C4×Dic11—41no—
457C4×Dic11—41no—
458C4×Dic11—41no—
459C4×Dic11—41no—
460C4×Dic11—41no—
461C4×Dic11—41no—
462C4×Dic11—41no—
463C4×Dic11—41no—
464C4×Dic11—41no—
465C4×Dic11#4114yes—
466#2866—111no—
467#2863—111no—
468#2799—111no—
469#2798—111no—
470#2794—111no—
471#2793D1111yescharacteristic
472#2792—111no—
473#2791—111no—
474#2789—111no—
475#2788—111no—
476#2788—111no—
477#2770—111no—
478#2770—111no—
479#2769—111no—
480#2762—111no—
481#2759—111no—
482#2758—111no—
483#2754—111no—
484#2655—111no—
485#2650—111no—
486#2611—111no—
487#2605—111no—
488#2599—111no—
489#2594—111no—
490#2588—111no—
491#2565—111no—
492#2533—111no—
493#2532—111no—
494#2336—111no—
495#2314—111no—
496#2295—111no—
497C23×C11—21no—
498C23×C11—21no—
499C23×C11—21no—
500C23×C11—21no—
501C23×C11—21no—
502C23×C11—21no—
503C23×C11—21no—
504C23×C11C2511yescharacteristic
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—21no—
517C2×C4×C11—21no—
518C2×C4×C11—21no—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
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×C11C2×#4112yes—
547C2×Dic11—21no—
548C2×Dic11—21no—
549C2×Dic11—21no—
550C2×Dic11—21no—
551C2×Dic11—21no—
552C2×Dic11—21no—
553C2×Dic11—21no—
554C2×Dic11—21no—
555C2×Dic11—21no—
556C2×Dic11—21no—
557C2×Dic11—21no—
558C2×Dic11—21no—
559C2×Dic11—21no—
560C2×Dic11—21no—
561C2×Dic11—21no—
562C2×Dic11—21no—
563C2×Dic11—21no—
564C2×Dic11—21no—
565C2×Dic11—21no—
566C2×Dic11—21no—
567C2×Dic11—21no—
568C2×Dic11—21no—
569C2×Dic11—21no—
570C2×Dic11—21no—
571C2×Dic11—21no—
572C2×Dic11—21no—
573C2×Dic11—21no—
574C2×Dic11—21no—
575C2×Dic11—21no—
576C2×Dic11—21no—
577C2×Dic11—21no—
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—44no—
592C2×Dic11C2×#4112yes—
593C2×Dic11C2×#4112yes—
594C2×Dic112−1+412yes—
595C2×Dic112−1+412yes—
596Dic22—44no—
597Dic22—82no—
598Dic22—82no—
599C2×#125—111no—
600C2×C4×Q8—111no—
601C2×#117—111no—
602#401—111no—
603#401—111no—
604#400—111no—
605#400—111no—
606#400—111no—
607#400—111no—
608#400—111no—
609#400—111no—
610#400—111no—
611#400—111no—
612#400—111no—
613#400—111no—
614#400—111no—
615#400—111no—
616#400—111no—
617#400—111no—
618#400—111no—
619#400—111no—
620#400C2×D1111yescharacteristic
621#399—111no—
622#398—111no—
623#398—111no—
624#398—111no—
625#398—111no—
626#398—111no—
627#398—111no—
628#398—111no—
629#398—111no—
630#398—111no—
631#398—111no—
632#398—111no—
633#398C2×D1111yescharacteristic
634#397—111no—
635#397—111no—
636#397—111no—
637#397—111no—
638#397C2×D1111yescharacteristic
639#397C2×D1111yescharacteristic
640#396C2×D1111yescharacteristic
641#396C2×D1111yescharacteristic
642#395—111no—
643#395—111no—
644#395—111no—
645#395—111no—
646#395—111no—
647#393—111no—
648#393—111no—
649#393—111no—
650#391—111no—
651#391—111no—
652#391—111no—
653#391—111no—
654#391—111no—
655#391—111no—
656#391—111no—
657#391—111no—
658#391—111no—
659#391—111no—
660#391—111no—
661#391—111no—
662#389—111no—
663#389—111no—
664#389—111no—
665#389—111no—
666#389—111no—
667#389—111no—
668#389—111no—
669#389—111no—
670#389—111no—
671#389—111no—
672#388—111no—
673#388—111no—
674#388—111no—
675#388—111no—
676#388—111no—
677#388—111no—
678#388—111no—
679#388—111no—
680#388—111no—
681#388—111no—
682#388—111no—
683#388—111no—
684#388—111no—
685#388C2×D1111yescharacteristic
686#388C2×D1111yescharacteristic
687#388C2×D1111yescharacteristic
688#387—111no—
689#387—111no—
690#387—111no—
691#387—111no—
692#387—111no—
693#387—111no—
694#387—111no—
695#387—111no—
696#387—111no—
697#387—111no—
698#387—111no—
699#387—111no—
700#387—111no—
701#387—111no—
702#387—111no—
703#387—111no—
704#387—111no—
705#387—111no—
706#387—111no—
707#387—111no—
708#387—111no—
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#387C2×D1111yescharacteristic
726#387C2×D1111yescharacteristic
727#387C2×D1111yescharacteristic
728#387C2×D1111yescharacteristic
729#387C2×D1111yescharacteristic
730#385—111no—
731#385—111no—
732#385—111no—
733#385—111no—
734#384—111no—
735#384C2×D1111yescharacteristic
736#383—111no—
737#383—111no—
738#383—111no—
739#383—111no—
740#383—111no—
741#382—111no—
742#382—111no—
743#380—111no—
744#380—111no—
745C4×C4⋊C4—111no—
746C4×C4⋊C4—111no—
747C4×C4⋊C4—111no—
748C4×C4⋊C4—111no—
749C4×C4⋊C4—111no—
750C4×C4⋊C4—111no—
751#376—111no—
752#376—111no—
753C43—111no—
754C22×C11—41no—
755C22×C11—41no—
756C22×C11—41no—
757C22×C11—41no—
758C22×C11—41no—
759C22×C11—41no—
760C22×C11—41no—
761C22×C11C22×#4111yescharacteristic
762C22×C11C2×2−1+411yescharacteristic
763C22×C11C2×2−1+411yescharacteristic
764C22×C11#58511yescharacteristic
765C22×C11#58511yescharacteristic
766C22×C11#58511yescharacteristic
767C22×C11#58511yescharacteristic
768C4×C11—22no—
769C4×C11—41no—
770C4×C11—41no—
771C4×C11—41no—
772C4×C11—41no—
773C4×C11—41no—
774C4×C11—41no—
775C4×C11—41no—
776C4×C11—41no—
777C4×C11—41no—
778C4×C11—41no—
779C4×C11—41no—
780C4×C11—41no—
781C4×C11—41no—
782Dic11—22no—
783Dic11—22no—
784Dic11—22no—
785Dic11—22no—
786Dic11—41no—
787Dic11—41no—
788Dic11—41no—
789Dic11—41no—
790Dic11—41no—
791Dic11—41no—
792Dic11—41no—
793Dic11—41no—
794Dic11—41no—
795Dic11—41no—
796Dic11—41no—
797Dic11—41no—
798C22×Q8—111no—
799C22×Q8—111no—
800C22×Q8—111no—
801C23×C4—111no—
802#125—224no—
803C4×Q8—224no—
804#117—224no—
805C2×C4⋊C4—111no—
806C2×C4⋊C4—111no—
807C2×C4⋊C4—111no—
808C2×C4⋊C4—111no—
809C2×C4⋊C4—111no—
810C2×C4⋊C4—111no—
811C2×C4⋊C4—111no—
812C2×C4⋊C4—111no—
813C2×C4⋊C4—111no—
814C2×C4⋊C4—111no—
815C2×C4⋊C4—111no—
816C2×C4⋊C4—111no—
817C2×C4⋊C4—111no—
818C2×C4⋊C4—111no—
819C2×C4⋊C4—111no—
820C2×C4⋊C4—111no—
821C2×C4⋊C4—111no—
822C2×C4⋊C4—111no—
823C2×C4⋊C4—111no—
824C2×C4⋊C4—111no—
825C2×C4⋊C4—111no—
826C2×C4⋊C4—111no—
827C2×C4⋊C4—111no—
828C2×C4⋊C4—111no—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4—111no—
833C2×C4⋊C4—111no—
834C2×C4⋊C4—111no—
835C2×C4⋊C4—111no—
836C2×C4⋊C4—111no—
837C2×C4⋊C4—111no—
838C2×C4⋊C4—111no—
839C2×C4⋊C4C22×D1111yescharacteristic
840C2×C4⋊C4C22×D1111yescharacteristic
841C2×C4⋊C4C22×D1111yescharacteristic
842C2×C4⋊C4C22×D1111yescharacteristic
843C2×C4⋊C4C22×D1111yescharacteristic
844C2×C4⋊C4C22×D1111yescharacteristic
845C2×C4⋊C4C22×D1111yescharacteristic
846C2×C4⋊C4C22×D1111yescharacteristic
847C2×C4⋊C4C22×D1111yescharacteristic
848C2×C4⋊C4C22×D1111yescharacteristic
849C2×C4⋊C4C22×D1111yescharacteristic
850C2×C22⋊C4—111no—
851C2×C22⋊C4—111no—
852C2×C22⋊C4—111no—
853C2×C22⋊C4—111no—
854C2×C22⋊C4—111no—
855C2×C22⋊C4—111no—
856C2×C22⋊C4—111no—
857C2×C22⋊C4C22×D1111yescharacteristic
858C2×C22⋊C4C22×D1111yescharacteristic
859C2×C22⋊C4C22×D1111yescharacteristic
860C2×C22⋊C4C22×D1111yescharacteristic
861C2×C22⋊C4C22×D1111yescharacteristic
862C2×C22⋊C4C22×D1111yescharacteristic
863C2×C22⋊C4C22×D1111yescharacteristic
864C2×C42—111no—
865C2×C42—111no—
866C2×C42—111no—
867C2×C42—111no—
868C2×C42—111no—
869C2×C42—111no—
870C2×C42—111no—
871C2×C42—111no—
872C2×C42—111no—
873C2×C42—111no—
874C2×C42—111no—
875C2×C42—111no—
876C2×C42—111no—
877C2×C42—111no—
878C2×C42—111no—
879C2×C42C22×D1111yescharacteristic
880C2×C42C22×D1111yescharacteristic
881C2×C42C22×D1111yescharacteristic
882#95—111no—
883#95—111no—
884#95—111no—
885#95—111no—
886#95—111no—
887#95—111no—
888#95—111no—
889#95—111no—
890#95—111no—
891#95—111no—
892#95—111no—
893#95—111no—
894#95—111no—
895#95—111no—
896#95—111no—
897#95—111no—
898#95—111no—
899#95—111no—
900#95—111no—
901#95—111no—
902#95—111no—
903#95—111no—
904#95—111no—
905#95—111no—
906#95—111no—
907#95—111no—
908#95—111no—
909#95—111no—
910#95—111no—
911#95—111no—
912#95—111no—
913#95—111no—
914#95—111no—
915#95—111no—
916#95—111no—
917#95—111no—
918#95—111no—
919#95—111no—
920#95—111no—
921#95—111no—
922#95—111no—
923#95—111no—
924#95—111no—
925#95—111no—
926#95—111no—
927#95—111no—
928#95—111no—
929#95—111no—
930#95—111no—
931#95—111no—
932#95—111no—
933#95—111no—
934#95—111no—
935#95—111no—
936#95—111no—
937#95—111no—
938#95—111no—
939#95—111no—
940#95—111no—
941#95—111no—
942#95C22×D1111yescharacteristic
943#95C22×D1111yescharacteristic
944#95C22×D1111yescharacteristic
945#95C22×D1111yescharacteristic
946#95C22×D1111yescharacteristic
947#95C22×D1111yescharacteristic
948#95C22×D1111yescharacteristic
949#95C22×D1111yescharacteristic
950#95C22×D1111yescharacteristic
951#95C22×D1111yescharacteristic
952#95C22×D1111yescharacteristic
953#95C22×D1111yescharacteristic
954#95C22×D1111yescharacteristic
955#95C22×D1111yescharacteristic
956C2×C11—81no—
957C2×C11#345511yescharacteristic
958C2×C11#349511yescharacteristic
959C2×C11#350711yescharacteristic
960C2×C11#355511yescharacteristic
961C2×C11#356411yescharacteristic
962C2×C11#356511yescharacteristic
963C2×C11#356611yescharacteristic
964C24C23×D1111yescharacteristic
965C2×Q8—222no—
966C2×Q8—222no—
967C2×Q8—222no—
968C2×Q8—441no—
969C2×Q8—441no—
970C2×Q8—441no—
971C2×Q8—441no—
972C2×Q8—441no—
973C2×Q8—441no—
974C22×C4—111no—
975C22×C4—111no—
976C22×C4—111no—
977C22×C4—111no—
978C22×C4—111no—
979C22×C4—111no—
980C22×C4—111no—
981C22×C4—111no—
982C22×C4—111no—
983C22×C4—111no—
984C22×C4—111no—
985C22×C4—111no—
986C22×C4—111no—
987C22×C4—111no—
988C22×C4—111no—
989C22×C4—111no—
990C22×C4—222no—
991C22×C4—441no—
992C22×C4—441no—
993C22×C4C23×D1111yescharacteristic
994C22×C4C23×D1111yescharacteristic
995C22×C4C23×D1111yescharacteristic
996C22×C4C23×D1111yescharacteristic
997C22×C4C23×D1111yescharacteristic
998C22×C4C23×D1111yescharacteristic
999C22×C4C23×D1111yescharacteristic
1000C22×C4C23×D1111yescharacteristic
1001C22×C4C23×D1111yescharacteristic
1002C22×C4C23×D1111yescharacteristic
1003C22×C4C23×D1111yescharacteristic
1004C22×C4C23×D1111yescharacteristic
1005C22×C4C23×D1111yescharacteristic
1006C22×C4C23×D1111yescharacteristic
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—222no—
1019C4⋊C4—222no—
1020C4⋊C4—222no—
1021C4⋊C4—222no—
1022C4⋊C4—222no—
1023C4⋊C4—222no—
1024C4⋊C4—222no—
1025C4⋊C4—222no—
1026C4⋊C4—222no—
1027C4⋊C4—222no—
1028C4⋊C4—222no—
1029C4⋊C4—222no—
1030C4⋊C4—222no—
1031C4⋊C4—441no—
1032C4⋊C4—441no—
1033C4⋊C4—441no—
1034C4⋊C4—441no—
1035C4⋊C4—441no—
1036C4⋊C4—441no—
1037C4⋊C4—441no—
1038C4⋊C4—441no—
1039C4⋊C4—441no—
1040C4⋊C4—441no—
1041C4⋊C4—441no—
1042C4⋊C4—441no—
1043C4⋊C4—441no—
1044C4⋊C4—441no—
1045C4⋊C4—441no—
1046C4⋊C4—441no—
1047C4⋊C4—441no—
1048C4⋊C4—441no—
1049C4⋊C4—441no—
1050C4⋊C4—441no—
1051C4⋊C4—441no—
1052C22⋊C4—22no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—222no—
1060C22⋊C4—222no—
1061C22⋊C4—222no—
1062C22⋊C4—441no—
1063C22⋊C4—441no—
1064C22⋊C4—441no—
1065C22⋊C4—441no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—114no—
1070C42—222no—
1071C42—222no—
1072C42—222no—
1073C42—222no—
1074C42—222no—
1075C42—441no—
1076C42—441no—
1077C42—441no—
1078C42—441no—
1079C42—441no—
1080C42—441no—
1081C42—441no—
1082C42—441no—
1083C42—441no—
1084C11#3700111yescharacteristic, complemented, Sylow
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23C24×D1111yescharacteristic
1093Q8—444no—
1094Q8—882no—
1095Q8—882no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—112no—
1138C2×C4—112no—
1139C2×C4—112no—
1140C2×C4—112no—
1141C2×C4—221no—
1142C2×C4—221no—
1143C2×C4—221no—
1144C2×C4—221no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—221no—
1148C2×C4—221no—
1149C2×C4—221no—
1150C2×C4—221no—
1151C2×C4—221no—
1152C2×C4—221no—
1153C2×C4—221no—
1154C2×C4—221no—
1155C2×C4—221no—
1156C2×C4—221no—
1157C2×C4—221no—
1158C2×C4—221no—
1159C2×C4—221no—
1160C2×C4—221no—
1161C2×C4—221no—
1162C2×C4—221no—
1163C2×C4—221no—
1164C2×C4—221no—
1165C2×C4—221no—
1166C2×C4—221no—
1167C2×C4—221no—
1168C2×C4—221no—
1169C2×C4—221no—
1170C2×C4—221no—
1171C2×C4—221no—
1172C2×C4—221no—
1173C2×C4—221no—
1174C2×C4—221no—
1175C2×C4—221no—
1176C2×C4—221no—
1177C2×C4—221no—
1178C2×C4—221no—
1179C2×C4—221no—
1180C2×C4—221no—
1181C2×C4—221no—
1182C2×C4—221no—
1183C2×C4—221no—
1184C2×C4—221no—
1185C2×C4—444no—
1186C2×C4#41×D1112yes—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22C2×#41×D1111yescharacteristic
1195C22#1062345311yescharacteristic
1196C22#1062345311yescharacteristic
1197C22#1062345511yescharacteristic
1198C22#1062345511yescharacteristic
1199C22D11×2−1+411yescharacteristic
1200C22D11×2−1+411yescharacteristic
1201C4—22no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—222no—
1216C4—222no—
1217C4—222no—
1218C4—222no—
1219C4—441no—
1220C4—441no—
1221C4—441no—
1222C4—441no—
1223C4—441no—
1224C4—441no—
1225C4—441no—
1226C4—441no—
1227C4—441no—
1228C4—441no—
1229C4—441no—
1230C4—441no—
1231C2—81no—
1232C2#1308200011yescharacteristic
1233C2#1308235911yescharacteristic
1234C2#1308247711yescharacteristic
1235C2#1308309511yescharacteristic
1236C2#1308323311yescharacteristic
1237C2#1308324811yescharacteristic
1238C2#1308329311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2793C2
prime radicalC24×C11C24
hypercenter#2793D11
hypocenterC11#37001
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2793

Complements

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

NH ≅ G/Ntype
2. #13076997C2semidirect
3. #13076498C2semidirect
5. #13076435C2semidirect
6. #13076414C2semidirect
7. #13076397C2semidirect
8. #13076372C2semidirect
13. #13076104C2semidirect
14. #13076015C2semidirect
16. #13075969C2semidirect
18. #13074704C2semidirect
21. #13074266C2semidirect
24. #13074056C2semidirect
25. #13073804C2semidirect
26. #13073496C2semidirect
28. #13071416C2semidirect
30. #13071089C2semidirect
1084. C11#37001semidirect

Maximal subgroups

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

subgroupindex
#130770072
#130769972
#130764982
#130764912
#130764352
#130764142
#130763972
#130763722
#130763552
#130761212
#130761042
#130760152
#130759762
#130759692
#130759132
#130747042
#130746352
#130743152
#130742662
#130741942
#130741152
#130740562
#130738042
#130734962
#130734762
#130714162
#130712202
#130710892
C11×#27932
#3700111