Finite Group Databasebeta

← #14927167

Subgroups — #14927167

Order 2816.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077002C211yesmaximal, characteristic, complemented
2#13076980C211yesmaximal, characteristic, complemented
3#13076946C211yesmaximal, characteristic, complemented
4#13076921C211yesmaximal, characteristic, complemented
5#13074689C212yesmaximal, complemented
6#13074624C212yesmaximal, complemented
7#13073879C212yesmaximal, complemented
8#13073660C212yesmaximal, complemented
9#13073154C211yesmaximal, characteristic, complemented
10#13073107C211yesmaximal, characteristic, complemented
11#13073028C211yesmaximal, characteristic, complemented
12#13072931C211yesmaximal, characteristic, complemented
13#13072878C212yesmaximal, complemented
14#13072354C212yesmaximal, complemented
15#13072336C211yesmaximal, characteristic, complemented
16#13072102C211yesmaximal, characteristic, complemented
17#13072059C211yesmaximal, characteristic
18#13071313C212yesmaximal, complemented
19#13071251C212yesmaximal, complemented
20C4×#66991C211yesmaximal, characteristic, complemented
21D11×#389C211yesmaximal, characteristic, complemented
22C4×#66946C211yesmaximal, characteristic, complemented
23C11×#2454C211yesmaximal, characteristic, complemented
24C2×C11×#125C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×#66991C2211yescharacteristic
27C2×#66991C2211yescharacteristic
28C2×C4×C22⋊D11C2212yes—
29C2×#66946C2211yescharacteristic
30C2×#66946C2211yescharacteristic
31C2×C4⋊C4×D11C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×C4⋊C4×D11C2212yes—
34C2×#66937C2212yes—
35C2×#66936C2212yes—
36C2×#66932C2212yes—
37C2×C4×D44C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C42×D11C2211yescharacteristic
40C11×#399C2212yes—
41C11×#396C2212yes—
42C11×#390C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#389C2211yescharacteristic
45C11×#389C2211yescharacteristic
46C11×#385C2212yes—
47C11×#380C2212yes—
48C4×C11×C4⋊C4C2211yescharacteristic
49#10622834C2211yescharacteristic
50#10622834C2211yescharacteristic
51#10622826C2212yes—
52#10622824C2212yes—
53C4×C22⋊Dic11C2212yes—
54#10622606C2212yes—
55#10622605C2212yes—
56#10622602C2212yes—
57#10622602C2212yes—
58#10622602C2212yes—
59#10622602C2212yes—
60#10622600C2211yescharacteristic
61#10622600C2211yescharacteristic
62#10622600C2211yescharacteristic
63#10622600C2211yescharacteristic
64#10622600C2212yes—
65#10622599C2212yes—
66#10622598C2211yescharacteristic
67#10622598C2211yescharacteristic
68#10622597C2212yes—
69#10622595C2212yes—
70#10622594C2212yes—
71#10622593C2212yes—
72#10622591C2212yes—
73#10622591C2212yes—
74#10622591C2212yes—
75#10622591C2212yes—
76#10622590C2211yescharacteristic
77#10622590C2211yescharacteristic
78C4⋊C4×Dic11C2211yescharacteristic
79C4⋊C4×Dic11C2211yescharacteristic
80#10622586C2211yescharacteristic
81#10622586C2211yescharacteristic
82#10622585C2212yes—
83#10622572C2212yes—
84#10622572C2212yes—
85#10622569C2212yes—
86#10622569C2212yes—
87#10622569C2212yes—
88#10622569C2212yes—
89#10622569C2212yes—
90#10622565C2212yes—
91#10622565C2212yes—
92#10622565C2212yes—
93#10622564C2212yes—
94#10622564C2212yes—
95#10622561C2212yes—
96#10622558C2212yes—
97#10622558C2212yes—
98#10622557C2212yes—
99#10622557C2212yes—
100C4×(C2×D11)⋊C4C2211yescharacteristic
101C4×(C2×D11)⋊C4C2211yescharacteristic
102#10622549C2211yescharacteristic
103C4×C4⋊Dic11C2211yescharacteristic
104C42×Dic11C2211yescharacteristic
105#10622541C2211yescharacteristic
106#10622541C2211yescharacteristic
107#10622541C2211yescharacteristic
108#10622541C2211yescharacteristic
109#10622283C2212yes—
110#10622279C2211yescharacteristic
111#10622279C2211yescharacteristic
112#10622279C2211yescharacteristic
113#10622279C2211yescharacteristic
114#10622278C2212yes—
115D11×#95C2212yes—
116#10622273C2212yes—
117#10622271C2212yes—
118#10622266C2212yes—
119#10622265C2212yes—
120#10622264C2212yes—
121#10622263C2212yes—
122#10622260C2212yes—
123C22×D4×C11C2311yescharacteristic
124C23×C4×C11C2312yes—
125C22×C22⋊D11C2312yes—
126C22×C22⋊D11C2312yes—
127C22×D44C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2312yes—
134C22×C4×D11C2312yes—
135C22×C4×D11C2311yescharacteristic
136C11×#125—42no—
137C4×D4×C11—42no—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2311yescharacteristic
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161#66991—24no—
162#66991—42no—
163C4×C22⋊D11—28no—
164C2×(C2×D11)⋊C4C2311yescharacteristic
165C2×(C2×D11)⋊C4C2311yescharacteristic
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2311yescharacteristic
168C2×(C2×D11)⋊C4C2311yescharacteristic
169C2×(C2×D11)⋊C4C2311yescharacteristic
170C2×(C2×D11)⋊C4C2311yescharacteristic
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2311yescharacteristic
200#66946—24no—
201#66946—24no—
202C4⋊C4×D11—24no—
203C4⋊C4×D11—44no—
204C4⋊C4×D11—42no—
205#66937—28no—
206#66936—44no—
207#66932—44no—
208C4×D44—24no—
209C42×D11—42no—
210C42×D11—42no—
211C11×#95C2312yes—
212C11×#95C2311yescharacteristic
213C11×#95C2312yes—
214C11×#95C2311yescharacteristic
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2311yescharacteristic
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238#35029—111nomaximal, Sylow
239C24×C11C2412yes—
240C23×D11C2411yescharacteristic
241C23×D11C2411yescharacteristic
242C2×D4×C11—22no—
243C2×D4×C11—22no—
244C2×D4×C11—22no—
245C22×C4×C11—24no—
246C22×C4×C11—42no—
247C22×C4×C11—42no—
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2412yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11—24no—
259C2×C22⋊D11—24no—
260C2×C22⋊D11—24no—
261C2×C22⋊D11—24no—
262C2×C22⋊D11—42no—
263C2×C22⋊D11—42no—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2411yescharacteristic
266C22×Dic11C2412yes—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2411yescharacteristic
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2411yescharacteristic
274C2×D44—22no—
275C2×D44—22no—
276C2×D44#4114yes—
277C2×C4×D11—22no—
278C2×C4×D11—22no—
279C2×C4×D11—22no—
280C2×C4×D11—24no—
281C2×C4×D11—22no—
282C2×C4×D11—22no—
283C2×C4×D11—24no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—22no—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×C4×D11—41no—
290C2×C4×D11—41no—
291C2×C4×D11—41no—
292C2×C4×D11—41no—
293C2×C4×D11—42no—
294C2×C4×D11—41no—
295C2×C4×D11—41no—
296C2×C4×D11—42no—
297C2×C4×D11—42no—
298C2×C4×D11—42no—
299C2×C4×D11#4114yes—
300C2×C4×D11#4114yes—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—22no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—42no—
307C11×C4⋊C4—42no—
308C11×C4⋊C4—42no—
309C11×C4⋊C4—42no—
310C11×C22⋊C4—24no—
311C11×C22⋊C4—42no—
312C11×C22⋊C4—42no—
313C11×C22⋊C4—42no—
314C11×C22⋊C4—42no—
315C42×C11—22no—
316C42×C11—22no—
317C42×C11—22no—
318C22⋊Dic11—24no—
319C22⋊Dic11—24no—
320C22⋊Dic11—24no—
321C22⋊Dic11—42no—
322C22⋊Dic11—42no—
323C22⋊Dic11—42no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—42no—
333(C2×D11)⋊C4—42no—
334C4⋊Dic11—22no—
335C4⋊Dic11—24no—
336C4⋊Dic11—22no—
337C4⋊Dic11—22no—
338C4⋊Dic11—22no—
339C4⋊Dic11—22no—
340C4⋊Dic11—42no—
341Dic11⋊C4—24no—
342Dic11⋊C4—24no—
343Dic11⋊C4—24no—
344Dic11⋊C4—24no—
345Dic11⋊C4—42no—
346Dic11⋊C4—42no—
347Dic11⋊C4—42no—
348Dic11⋊C4—42no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—22no—
352C4×Dic11—24no—
353C4×Dic11—22no—
354C4×Dic11—22no—
355C4×Dic11—41no—
356C4×Dic11—41no—
357C4×Dic11—41no—
358C4×Dic11—41no—
359C4×Dic11—41no—
360#2864—111no—
361#2860—111no—
362#2854—111no—
363#2851—111no—
364#2654—112no—
365#2649—112no—
366#2573—112no—
367#2553—112no—
368#2508—111no—
369#2504—111no—
370#2495—111no—
371#2487—111no—
372#2481—112no—
373#2454D1111yescharacteristic, complemented
374#2443—112no—
375#2442—111no—
376#2420—111no—
377#2416—111no—
378#2325—112no—
379#2318—112no—
380C4×#121—111no—
381C2×#389—111no—
382C42×D4—111no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11C2511yescharacteristic
391C22×D11—21no—
392C22×D11—21no—
393C22×D11—21no—
394C22×D11—21no—
395C22×D11—21no—
396C22×D11—21no—
397C22×D11—21no—
398C22×D11—21no—
399C22×D11—21no—
400C22×D11—21no—
401C22×D11C2×#4112yes—
402C22×D11C2×#4112yes—
403C22×D11C2×#4112yes—
404C22×D11C2×#4112yes—
405D4×C11—44no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—21no—
413C2×C4×C11—22no—
414C2×C4×C11—21no—
415C2×C4×C11—21no—
416C2×C4×C11—21no—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—21no—
428C2×C4×C11—22no—
429C2×C4×C11—21no—
430C2×C4×C11—22no—
431C2×C4×C11—84no—
432C2×C4×C11C2×#4112yes—
433C2×C4×C11C2×#4112yes—
434C2×C4×C11C2×#4112yes—
435C2×C4×C11H(5,𝔽2)12yes—
436C2×C4×C112−1+412yes—
437C22⋊D11—48no—
438C22⋊D11—84no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—22no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—22no—
449C2×Dic11—22no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—21no—
453C2×Dic11—22no—
454C2×Dic11—21no—
455C2×Dic11—21no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—21no—
461C2×Dic11—21no—
462C2×Dic11—22no—
463C2×Dic11—21no—
464C2×Dic11—21no—
465C2×Dic11—22no—
466C2×Dic11C2×#4112yes—
467C2×Dic11C2×#4112yes—
468C2×Dic11H(5,𝔽2)12yes—
469D44—28no—
470C4×D11—28no—
471C4×D11—44no—
472C4×D11—44no—
473C4×D11—44no—
474C4×D11—44no—
475C4×D11—48no—
476C4×D11—44no—
477C4×D11—84no—
478C2×#126—112no—
479C2×#125C2×D1111yescharacteristic
480C2×#123—112no—
481C2×#121—111no—
482C2×#121—111no—
483C2×#121—112no—
484C2×C4×D4—112no—
485C2×C4×D4—111no—
486C2×C4×D4—111no—
487C2×C4×D4—111no—
488C2×C4×D4C2×D1111yescharacteristic
489C22×C4⋊C4—111no—
490C22×C4⋊C4—111no—
491C22×C4⋊C4—112no—
492C22×C42—111no—
493C22×C42—111no—
494#400—112no—
495#400—112no—
496#400—112no—
497#400—112no—
498#399—112no—
499#399C2×D1112yes—
500#398—112no—
501#398—112no—
502#397—112no—
503#397—112no—
504#397—112no—
505#397—112no—
506#396—112no—
507#396C2×D1112yes—
508#394—112no—
509#394—112no—
510#390—111no—
511#390—111no—
512#390C2×D1111yescharacteristic
513#390C2×D1111yescharacteristic
514#389—111no—
515#389—111no—
516#389—111no—
517#389—111no—
518#389—112no—
519#389—111no—
520#389—111no—
521#389—111no—
522#389—111no—
523#389—112no—
524#389C2×D1111yescharacteristic
525#389C2×D1111yescharacteristic
526#388—112no—
527#388—112no—
528#388—112no—
529#388—112no—
530#388—112no—
531#388—112no—
532#388—112no—
533#387—112no—
534#387—112no—
535#387—112no—
536#387—112no—
537#387—112no—
538#387—112no—
539#387—112no—
540#386—112no—
541#386—112no—
542#386—112no—
543#386—112no—
544#386—112no—
545#386—112no—
546#386—112no—
547#385—112no—
548#385—112no—
549#385—112no—
550#385—112no—
551#385C2×D1112yes—
552#383—112no—
553#382—111no—
554#382—111no—
555#382—111no—
556#382—112no—
557#381—112no—
558#380—112no—
559#380—111no—
560#380—111no—
561#380—111no—
562#380—111no—
563#380C2×D1112yes—
564C4×C4⋊C4—111no—
565C4×C4⋊C4—111no—
566C4×C4⋊C4—111no—
567C4×C4⋊C4C2×D1111yescharacteristic
568C4×C22⋊C4—112no—
569C4×C22⋊C4—111no—
570C4×C22⋊C4—111no—
571C4×C22⋊C4—111no—
572C4×C22⋊C4—111no—
573C4×C22⋊C4—111no—
574C4×C22⋊C4—111no—
575C2×#95—112no—
576C43—111no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11C22×#4111yescharacteristic
585C22×C11C22×#4111yescharacteristic
586C22×C11C22×#4111yescharacteristic
587C22×C11C2×H(5,𝔽2)11yescharacteristic
588C22×C11C2×H(5,𝔽2)11yescharacteristic
589C22×C11C2×2−1+411yescharacteristic
590C22×C11#58511yescharacteristic
591C2×D11—22no—
592C2×D11—22no—
593C2×D11—22no—
594C2×D11—22no—
595C2×D11—22no—
596C2×D11—22no—
597C2×D11—22no—
598C2×D11—22no—
599C2×D11—22no—
600C2×D11—41no—
601C2×D11—41no—
602C2×D11—41no—
603C2×D11—41no—
604C2×D11#52914yes—
605C4×C11—22no—
606C4×C11—22no—
607C4×C11—41no—
608C4×C11—42no—
609C4×C11—42no—
610C4×C11—41no—
611C4×C11—41no—
612C4×C11—41no—
613C4×C11—42no—
614C4×C11#53914yes—
615Dic11—22no—
616Dic11—22no—
617Dic11—22no—
618Dic11—42no—
619Dic11—41no—
620Dic11—42no—
621Dic11—41no—
622Dic11—42no—
623Dic11—41no—
624Dic11—42no—
625C22×D4—112no—
626C22×D4—112no—
627C22×D4—111no—
628C22×D4C22×D1111yescharacteristic
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—112no—
635C23×C4—112no—
636C23×C4—111no—
637C23×C4C22×D1112yes—
638#126—444no—
639#125—42no—
640#123—444no—
641#121—228no—
642#121—224no—
643#121—442no—
644C4×D4—42no—
645C4×D4—224no—
646C4×D4—224no—
647C4×D4—224no—
648C4×D4—228no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—112no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—112no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—112no—
656C2×C4⋊C4—111no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—111no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—112no—
662C2×C4⋊C4—112no—
663C2×C4⋊C4—112no—
664C2×C4⋊C4—224no—
665C2×C4⋊C4—442no—
666C2×C4⋊C4—444no—
667C2×C4⋊C4C22×D1111yescharacteristic
668C2×C4⋊C4C22×D1111yescharacteristic
669C2×C4⋊C4C22×D1111yescharacteristic
670C2×C4⋊C4C22×D1111yescharacteristic
671C2×C4⋊C4C22×D1111yescharacteristic
672C2×C4⋊C4C22×D1112yes—
673C2×C4⋊C4C22×D1112yes—
674C2×C4⋊C4C22×D1112yes—
675C2×C4⋊C4C22×D1112yes—
676C2×C22⋊C4—112no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—112no—
679C2×C22⋊C4—111no—
680C2×C22⋊C4—111no—
681C2×C22⋊C4—111no—
682C2×C22⋊C4—111no—
683C2×C22⋊C4—111no—
684C2×C22⋊C4—111no—
685C2×C22⋊C4—112no—
686C2×C22⋊C4—112no—
687C2×C22⋊C4—112no—
688C2×C22⋊C4—112no—
689C2×C22⋊C4—112no—
690C2×C22⋊C4—112no—
691C2×C22⋊C4—112no—
692C2×C22⋊C4C22×D1112yes—
693C2×C22⋊C4C22×D1112yes—
694C2×C22⋊C4C22×D1112yes—
695C2×C22⋊C4C22×D1112yes—
696C2×C22⋊C4C22×D1112yes—
697C2×C42—111no—
698C2×C42—111no—
699C2×C42—112no—
700C2×C42—111no—
701C2×C42—111no—
702C2×C42—111no—
703C2×C42—111no—
704C2×C42—111no—
705C2×C42—111no—
706C2×C42—111no—
707C2×C42—111no—
708C2×C42—442no—
709C2×C42—442no—
710C2×C42C22×D1111yescharacteristic
711C2×C42C22×D1111yescharacteristic
712C2×C42C22×D1111yescharacteristic
713#95—112no—
714#95—112no—
715#95—112no—
716#95—111no—
717#95—111no—
718#95—111no—
719#95—111no—
720#95—112no—
721#95—112no—
722#95—112no—
723#95—112no—
724#95—112no—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95—112no—
730#95—112no—
731#95—112no—
732#95—112no—
733#95—112no—
734#95—112no—
735#95—112no—
736#95C22×D1112yes—
737#95C22×D1111yescharacteristic
738#95C22×D1111yescharacteristic
739#95C22×D1112yes—
740C2×C11—82no—
741C2×C11C2×#52911yescharacteristic
742C2×C11C2×#53911yescharacteristic
743C2×C11#346011yescharacteristic
744C2×C11#350511yescharacteristic
745C2×C11#351111yescharacteristic
746C2×C11#351511yescharacteristic
747C2×C11#351911yescharacteristic
748D11—24no—
749D11—42no—
750C24—111no—
751C24—111no—
752C24C23×D1112yes—
753C2×D4—22no—
754C2×D4—22no—
755C2×D4—22no—
756C2×D4—114no—
757C2×D4—222no—
758C2×D4—222no—
759C2×D4—224no—
760C2×D4—224no—
761C2×D4—224no—
762C2×D4—224no—
763C2×D4—442no—
764C2×D4—442no—
765C22×C4—24no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—111no—
769C22×C4—111no—
770C22×C4—111no—
771C22×C4—114no—
772C22×C4—114no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—112no—
776C22×C4—111no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—112no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—224no—
784C22×C4—222no—
785C22×C4—222no—
786C22×C4—224no—
787C22×C4—222no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—441no—
793C22×C4—441no—
794C22×C4—441no—
795C22×C4—441no—
796C22×C4—442no—
797C22×C4—441no—
798C22×C4—441no—
799C22×C4—442no—
800C22×C4—442no—
801C22×C4—442no—
802C22×C4C23×D1111yescharacteristic
803C22×C4C23×D1112yes—
804C22×C4C23×D1112yes—
805C22×C4C23×D1111yescharacteristic
806C22×C4C23×D1111yescharacteristic
807C22×C4C23×D1112yes—
808C22×C4C23×D1111yescharacteristic
809C22×C4C23×D1111yescharacteristic
810C22×C4C23×D1111yescharacteristic
811C22×C4C23×D1111yescharacteristic
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—42no—
821C4⋊C4—224no—
822C4⋊C4—224no—
823C4⋊C4—224no—
824C4⋊C4—224no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4—222no—
828C4⋊C4—222no—
829C4⋊C4—224no—
830C4⋊C4—222no—
831C4⋊C4—442no—
832C4⋊C4—442no—
833C4⋊C4—442no—
834C4⋊C4—442no—
835C4⋊C4—442no—
836C22⋊C4—24no—
837C22⋊C4—42no—
838C22⋊C4—42no—
839C22⋊C4—42no—
840C22⋊C4—42no—
841C22⋊C4—222no—
842C22⋊C4—222no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—222no—
846C22⋊C4—224no—
847C22⋊C4—224no—
848C22⋊C4—224no—
849C22⋊C4—224no—
850C22⋊C4—224no—
851C22⋊C4—222no—
852C22⋊C4—442no—
853C22⋊C4—442no—
854C22⋊C4—442no—
855C22⋊C4—442no—
856C22⋊C4—442no—
857C42—22no—
858C42—22no—
859C42—22no—
860C42—222no—
861C42—222no—
862C42—222no—
863C42—222no—
864C42—222no—
865C42—224no—
866C42—441no—
867C42—441no—
868C42—441no—
869C42—441no—
870C42—441no—
871C11#3502911yescharacteristic, complemented, Sylow
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—112no—
880C23—112no—
881C23—112no—
882C23—112no—
883C23—221no—
884C23—221no—
885C23—221no—
886C23—221no—
887C23—221no—
888C23—221no—
889C23—221no—
890C23—221no—
891C23—221no—
892C23—221no—
893C23C24×D1111yescharacteristic
894D4—44no—
895D4—228no—
896D4—448no—
897D4—884no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—84no—
924C2×C4—112no—
925C2×C4—112no—
926C2×C4—112no—
927C2×C4—221no—
928C2×C4—221no—
929C2×C4—221no—
930C2×C4—221no—
931C2×C4—221no—
932C2×C4—221no—
933C2×C4—228no—
934C2×C4—221no—
935C2×C4—222no—
936C2×C4—221no—
937C2×C4—221no—
938C2×C4—222no—
939C2×C4—221no—
940C2×C4—221no—
941C2×C4—222no—
942C2×C4—221no—
943C2×C4—222no—
944C2×C4—221no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—221no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—221no—
954C2×C4—222no—
955C2×C4—444no—
956C2×C4—444no—
957C2×C4—444no—
958C2×C4—444no—
959C2×C4—448no—
960C2×C4—444no—
961C2×C4—884no—
962C2×C4#6703712yes—
963C2×C4#6704012yes—
964C2×C4#41×D1112yes—
965C2×C4#41×D1112yes—
966C2×C4#41×D1112yes—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—114no—
975C22—222no—
976C22—222no—
977C22—222no—
978C22—222no—
979C22—222no—
980C22—222no—
981C22—222no—
982C22—222no—
983C22—222no—
984C22—441no—
985C22—441no—
986C22—441no—
987C22—441no—
988C22C2×#6703711yescharacteristic
989C22C2×#6704011yescharacteristic
990C22C2×#41×D1111yescharacteristic
991C22C2×#41×D1111yescharacteristic
992C22C2×#41×D1111yescharacteristic
993C22D11×H(5,𝔽2)11yescharacteristic
994C22#1062345511yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—42no—
1000C4—42no—
1001C4—41no—
1002C4—42no—
1003C4—41no—
1004C4—222no—
1005C4—222no—
1006C4—222no—
1007C4—442no—
1008C4—442no—
1009C4—441no—
1010C4—441no—
1011C4—442no—
1012C4—442no—
1013C4—441no—
1014C4#1062316914yes—
1015C2—82no—
1016C2—224no—
1017C2—442no—
1018C2D11×#52911yescharacteristic
1019C2C2×#1062316911yescharacteristic
1020C2#1308203111yescharacteristic
1021C2#1308244311yescharacteristic
1022C2#1308252411yescharacteristic
1023C2#1308259711yescharacteristic
1024C2#1308264711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2454C2
prime radical#13072059C2
hypercenter#2454D11
hypocenterC11#35029
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2454

Complements

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

NH ≅ G/Ntype
1. #13077002C2semidirect
2. #13076980C2semidirect
3. #13076946C2semidirect
4. #13076921C2semidirect
5. #13074689C2semidirect
6. #13074624C2semidirect
7. #13073879C2semidirect
8. #13073660C2semidirect
9. #13073154C2semidirect
10. #13073107C2semidirect
11. #13073028C2semidirect
12. #13072931C2semidirect
13. #13072878C2semidirect
14. #13072354C2semidirect
15. #13072336C2semidirect
16. #13072102C2semidirect
18. #13071313C2semidirect
19. #13071251C2semidirect
20. C4×#66991C2semidirect
21. D11×#389C2semidirect
22. C4×#66946C2semidirect
23. C11×#2454C2semidirect
373. #2454D11semidirect
871. C11#35029semidirect

Maximal subgroups

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

subgroupindex
#130770022
#130769802
#130769462
#130769212
#130746892
#130746242
#130738792
#130736602
#130731542
#130731072
#130730282
#130729312
#130728782
#130723542
#130723362
#130721022
#130720592
#130713132
#130712512
C4×#669912
D11×#3892
C4×#669462
C11×#24542
#3502911