Finite Group Databasebeta

← #14923280

Subgroups — #14923280

Order 2816.

2028 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#13073379C212yesmaximal, complemented
2#13073256C212yesmaximal, complemented
3#13073216C211yesmaximal, characteristic, complemented
4#13073173C212yesmaximal, complemented
5#13073168C211yesmaximal, characteristic, complemented
6#13073105C211yesmaximal, characteristic, complemented
7#13073019C211yesmaximal, characteristic, complemented
8#13072971C211yesmaximal, characteristic, complemented
9#13072931C211yesmaximal, characteristic, complemented
10#13072371C212yesmaximal, complemented
11#13072336C211yesmaximal, characteristic, complemented
12#13072054C211yesmaximal, characteristic
13#13071917C212yesmaximal, complemented
14#13071879C212yesmaximal, complemented
15C4×#66948C211yesmaximal, characteristic, complemented
16C4×#66948C211yesmaximal, characteristic, complemented
17C4×#66948C212yesmaximal, complemented
18#13071080C211yesmaximal, characteristic, complemented
19#13071057C212yesmaximal, complemented
20#13071012C211yesmaximal, characteristic, complemented
21C42×D44C211yesmaximal, characteristic, complemented
22C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
23C4×C11×#125C211yesmaximal, characteristic, complemented
24C2×C11×#125C2211yescharacteristic
25C2×#66948C2211yescharacteristic
26C2×#66948C2211yescharacteristic
27C2×#66948C2212yes—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2212yes—
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C2×C4×D44C2212yes—
36C2×#66925C2212yes—
37C2×C42×D11C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C2×C42×D11C2212yes—
40C11×#389C2211yescharacteristic
41C11×#389C2211yescharacteristic
42C11×#387C2212yes—
43C11×#387C2212yes—
44C11×#382C2211yescharacteristic
45C4×C11×C4⋊C4C2212yes—
46C4×C11×C4⋊C4C2212yes—
47C4×C11×C4⋊C4C2211yescharacteristic
48C4×C11×C4⋊C4C2211yescharacteristic
49C43×C11C2211yescharacteristic
50#10622607C2212yes—
51#10622606C2212yes—
52#10622606C2212yes—
53#10622605C2212yes—
54#10622604C2212yes—
55#10622603C2212yes—
56#10622603C2212yes—
57#10622602C2212yes—
58#10622602C2212yes—
59#10622601C2211yescharacteristic
60#10622601C2211yescharacteristic
61#10622601C2212yes—
62#10622600C2212yes—
63#10622600C2211yescharacteristic
64#10622600C2211yescharacteristic
65#10622600C2211yescharacteristic
66#10622600C2211yescharacteristic
67#10622599C2212yes—
68#10622598C2211yescharacteristic
69#10622598C2211yescharacteristic
70#10622598C2212yes—
71#10622597C2212yes—
72#10622595C2212yes—
73#10622590C2211yescharacteristic
74#10622590C2211yescharacteristic
75C4⋊C4×Dic11C2211yescharacteristic
76C4⋊C4×Dic11C2211yescharacteristic
77#10622553C2212yes—
78#10622553C2212yes—
79#10622552C2211yescharacteristic
80#10622552C2211yescharacteristic
81C4×(C2×D11)⋊C4C2211yescharacteristic
82C4×(C2×D11)⋊C4C2212yes—
83C4×(C2×D11)⋊C4C2212yes—
84C4×(C2×D11)⋊C4C2211yescharacteristic
85C4×(C2×D11)⋊C4C2212yes—
86C4×(C2×D11)⋊C4C2212yes—
87C4×(C2×D11)⋊C4C2211yescharacteristic
88C4×(C2×D11)⋊C4C2211yescharacteristic
89C4×(C2×D11)⋊C4C2211yescharacteristic
90C4×(C2×D11)⋊C4C2211yescharacteristic
91C4×C4⋊Dic11C2211yescharacteristic
92C4×C4⋊Dic11C2211yescharacteristic
93C4×C4⋊Dic11C2211yescharacteristic
94C4×C4⋊Dic11C2211yescharacteristic
95#10622545C2212yes—
96C4×Dic11⋊C4C2212yes—
97#10622541C2211yescharacteristic
98#10622541C2211yescharacteristic
99#10622288C2212yes—
100#10622288C2212yes—
101#10622288C2212yes—
102#10622287C2212yes—
103#10622285C2212yes—
104#10622283C2212yes—
105#10622283C2212yes—
106#10622283C2212yes—
107#10622283C2212yes—
108#10622278C2212yes—
109#10622278C2212yes—
110#10622278C2212yes—
111#10622278C2212yes—
112#10622278C2212yes—
113#10622278C2212yes—
114#10622277C2212yes—
115D11×#95C2212yes—
116C11⋊#401C2212yes—
117#10622273C2212yes—
118#10622273C2212yes—
119#10622267C2212yes—
120#10622267C2212yes—
121#10622264C2212yes—
122#10622262C2212yes—
123C22×D44C2312yes—
124C22×D44C2311yescharacteristic
125C22×D44C2312yes—
126C22×D44C2311yescharacteristic
127C22×C4×D11C2311yescharacteristic
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2312yes—
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2312yes—
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2312yes—
136C11×#125—24no—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C42×C11C2312yes—
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2312yes—
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2311yescharacteristic
156C2×(C2×D11)⋊C4C2311yescharacteristic
157C2×(C2×D11)⋊C4C2311yescharacteristic
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2311yescharacteristic
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2311yescharacteristic
162C2×(C2×D11)⋊C4C2311yescharacteristic
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×C4⋊Dic11C2312yes—
176C2×C4⋊Dic11C2311yescharacteristic
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196#66948—28no—
197#66948—24no—
198#66948—24no—
199C4⋊C4×D11—24no—
200C4⋊C4×D11—24no—
201C4×D44—24no—
202C4×D44—24no—
203C4×D44—28no—
204C4×D44—24no—
205C4×D44—24no—
206C4×D44—44no—
207#66925—44no—
208C42×D11—24no—
209C42×D11—24no—
210C42×D11—44no—
211C11×#95C2312yes—
212C11×#95C2312yes—
213C11×#95C2312yes—
214C11×#95C2312yes—
215C11×#95C2312yes—
216C11×#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2311yescharacteristic
223C11⋊#95C2311yescharacteristic
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2311yescharacteristic
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2312yes—
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238#34788—111nomaximal, Sylow
239C23×D11C2412yes—
240C23×D11C2411yescharacteristic
241C23×D11C2411yescharacteristic
242C22×C4×C11C2412yes—
243C22×C4×C11C2411yescharacteristic
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C22×Dic11C2411yescharacteristic
254C22×Dic11C2411yescharacteristic
255C22×Dic11C2411yescharacteristic
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2411yescharacteristic
259C22×Dic11C2412yes—
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2411yescharacteristic
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—24no—
265C2×D44—24no—
266C2×D44—24no—
267C2×D44—24no—
268C2×D44—22no—
269C2×D44—24no—
270C2×D44—22no—
271C2×D44—22no—
272C2×D44—42no—
273C2×D44#4114yes—
274C2×C4×D11—22no—
275C2×C4×D11—22no—
276C2×C4×D11—24no—
277C2×C4×D11—24no—
278C2×C4×D11—22no—
279C2×C4×D11—22no—
280C2×C4×D11—22no—
281C2×C4×D11—22no—
282C2×C4×D11—22no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—24no—
286C2×C4×D11—22no—
287C2×C4×D11—22no—
288C2×C4×D11—24no—
289C2×C4×D11—24no—
290C2×C4×D11—22no—
291C2×C4×D11—22no—
292C2×C4×D11—24no—
293C2×C4×D11—22no—
294C2×C4×D11—42no—
295C2×C4×D11—42no—
296C2×C4×D11—41no—
297C2×C4×D11—41no—
298C2×C4×D11—42no—
299C2×C4×D11#4114yes—
300C2×C4×D11#4114yes—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—24no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—24no—
305C11×C4⋊C4—24no—
306C11×C4⋊C4—22no—
307C11×C4⋊C4—42no—
308C11×C4⋊C4#4114yes—
309C42×C11—22no—
310C42×C11—22no—
311C42×C11—22no—
312C42×C11—24no—
313C42×C11—22no—
314C42×C11—24no—
315C42×C11—22no—
316C42×C11—41no—
317C42×C11#4114yes—
318(C2×D11)⋊C4—22no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—24no—
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—42no—
332(C2×D11)⋊C4—42no—
333(C2×D11)⋊C4—42no—
334(C2×D11)⋊C4—42no—
335(C2×D11)⋊C4—42no—
336(C2×D11)⋊C4—42no—
337(C2×D11)⋊C4—42no—
338(C2×D11)⋊C4—42no—
339C4⋊Dic11—22no—
340C4⋊Dic11—22no—
341C4⋊Dic11—24no—
342C4⋊Dic11—22no—
343C4⋊Dic11—22no—
344C4⋊Dic11—22no—
345C4⋊Dic11—22no—
346C4⋊Dic11—42no—
347Dic11⋊C4—24no—
348Dic11⋊C4—24no—
349Dic11⋊C4—42no—
350Dic11⋊C4—42no—
351C4×Dic11—22no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354C4×Dic11—22no—
355C4×Dic11—22no—
356C4×Dic11—22no—
357C4×Dic11—24no—
358C4×Dic11—42no—
359C4×Dic11—42no—
360#2525—112no—
361#2516—112no—
362#2513—111no—
363#2510—112no—
364#2509—111no—
365#2504—111no—
366#2494—111no—
367#2490—111no—
368#2487—111no—
369#2444—112no—
370#2442—111no—
371#2416—111no—
372#2401—112no—
373#2395—112no—
374C4×#125D1111yescharacteristic, complemented
375C4×#121—112no—
376C4×#121—111no—
377C4×#121—111no—
378#2293—111no—
379#2290—112no—
380#2283—111no—
381C42×D4—111no—
382C2×C4×C4⋊C4—111no—
383C23×C11C2511yescharacteristic
384C22×D11—21no—
385C22×D11—21no—
386C22×D11—21no—
387C22×D11—21no—
388C22×D11—21no—
389C22×D11—21no—
390C22×D11—21no—
391C22×D11—21no—
392C22×D11—21no—
393C22×D11—21no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11C2×#4112yes—
402C22×D11C2×#4112yes—
403C22×D11C2×#4112yes—
404C22×D11C2×#4112yes—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—21no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—21no—
414C2×C4×C11—21no—
415C2×C4×C11—22no—
416C2×C4×C11—21no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—21no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—21no—
429C2×C4×C11C2×#4114yes—
430C2×C4×C11C2×#4112yes—
431C2×C4×C11C2×#4112yes—
432C2×C4×C11C2×#4112yes—
433C2×C4×C11C2×#4112yes—
434C2×C4×C11C2×#4112yes—
435C2×C4×C11C2×#4112yes—
436C2×C4×C11C2×#4112yes—
437C2×C4×C11H(5,𝔽2)12yes—
438C2×Dic11—21no—
439C2×Dic11—21no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—21no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—21no—
453C2×Dic11—21no—
454C2×Dic11—21no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—21no—
460C2×Dic11—22no—
461C2×Dic11—21no—
462C2×Dic11—21no—
463C2×Dic11C2×#4112yes—
464C2×Dic11C2×#4112yes—
465D44—28no—
466D44—48no—
467D44—48no—
468D44—44no—
469C4×D11—28no—
470C4×D11—28no—
471C4×D11—44no—
472C4×D11—44no—
473C4×D11—48no—
474C4×D11—48no—
475C4×D11—44no—
476C4×D11—44no—
477C4×D11—48no—
478C2×#125C2×D1111yescharacteristic
479C2×#121—112no—
480C2×#121—111no—
481C2×#121—111no—
482C2×C4×D4—111no—
483C2×C4×D4—111no—
484C2×C4×D4—111no—
485C2×C4×D4—112no—
486C2×C4×D4—111no—
487C2×C4×D4—112no—
488C2×#117—112no—
489C22×C4⋊C4—111no—
490C22×C4⋊C4—111no—
491C22×C42—111no—
492C22×C42—111no—
493C22×C42—112no—
494#401—112no—
495#400—112no—
496#400—112no—
497#400—112no—
498#400—112no—
499#399—112no—
500#398—112no—
501#397—112no—
502#397—112no—
503#397—112no—
504#397—112no—
505#397—112no—
506#397—112no—
507#396—112no—
508#394—112no—
509#394—112no—
510#390—111no—
511#390—112no—
512#390—111no—
513#390—111no—
514#390—111no—
515#389—111no—
516#389—111no—
517#389—112no—
518#389—111no—
519#389—111no—
520#389C2×D1111yescharacteristic
521#389C2×D1111yescharacteristic
522#388—112no—
523#388—112no—
524#388—112no—
525#388—112no—
526#388—112no—
527#388—112no—
528#388—112no—
529#388—112no—
530#387—112no—
531#387—112no—
532#387C2×D1112yes—
533#387C2×D1112yes—
534#386—112no—
535#386—112no—
536#386—112no—
537#386—112no—
538#386—112no—
539#386—112no—
540#385—112no—
541#385—112no—
542#383—112no—
543#382—111no—
544#382—111no—
545#382C2×D1111yescharacteristic
546#381—112no—
547#380—111no—
548#380—111no—
549#380—112no—
550#380—111no—
551#380—111no—
552C4×C4⋊C4—111no—
553C4×C4⋊C4—111no—
554C4×C4⋊C4—112no—
555C4×C4⋊C4—111no—
556C4×C4⋊C4—111no—
557C4×C4⋊C4—111no—
558C4×C4⋊C4—111no—
559C4×C4⋊C4—112no—
560C4×C4⋊C4C2×D1112yes—
561C4×C4⋊C4C2×D1112yes—
562C4×C4⋊C4C2×D1111yescharacteristic
563C4×C4⋊C4C2×D1111yescharacteristic
564C4×C22⋊C4—111no—
565C4×C22⋊C4—112no—
566C4×C22⋊C4—112no—
567C4×C22⋊C4—112no—
568C4×C22⋊C4—112no—
569C4×C22⋊C4—111no—
570C4×C22⋊C4—111no—
571C4×C22⋊C4—111no—
572C4×C22⋊C4—111no—
573C4×C22⋊C4—111no—
574#376—112no—
575C2×#95—112no—
576C43C2×D1111yescharacteristic
577C22×C11C22×#4111yescharacteristic
578C22×C11C22×#4111yescharacteristic
579C22×C11C22×#4111yescharacteristic
580C22×C11C22×#4111yescharacteristic
581C22×C11C22×#4111yescharacteristic
582C22×C11C2×H(5,𝔽2)11yescharacteristic
583C22×C11#58511yescharacteristic
584C2×D11—22no—
585C2×D11—22no—
586C2×D11—22no—
587C2×D11—22no—
588C2×D11—22no—
589C2×D11—22no—
590C2×D11—22no—
591C2×D11—22no—
592C2×D11—22no—
593C2×D11—41no—
594C2×D11—41no—
595C2×D11—41no—
596C2×D11—41no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11#52914yes—
605C4×C11—22no—
606C4×C11—22no—
607C4×C11—24no—
608C4×C11—42no—
609C4×C11—41no—
610C4×C11—42no—
611C4×C11—41no—
612C4×C11—42no—
613C4×C11—41no—
614C4×C11#52914yes—
615C4×C11#55314yes—
616Dic11—22no—
617Dic11—22no—
618Dic11—41no—
619Dic11—42no—
620Dic11—41no—
621Dic11—42no—
622Dic11—41no—
623Dic11—41no—
624Dic11—42no—
625C22×D4—111no—
626C22×D4—112no—
627C22×D4—111no—
628C22×D4—112no—
629C23×C4—111no—
630C23×C4—111no—
631C23×C4—111no—
632C23×C4—112no—
633C23×C4—111no—
634C23×C4—112no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—112no—
638#125—24no—
639#121—224no—
640#121—228no—
641#121—224no—
642C4×D4—224no—
643C4×D4—224no—
644C4×D4—228no—
645C4×D4—224no—
646C4×D4—224no—
647C4×D4—444no—
648#117—444no—
649C2×C4⋊C4—111no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—112no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—111no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—224no—
662C2×C4⋊C4—224no—
663C2×C4⋊C4C22×D1111yescharacteristic
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1112yes—
666C2×C4⋊C4C22×D1111yescharacteristic
667C2×C4⋊C4C22×D1112yes—
668C2×C4⋊C4C22×D1112yes—
669C2×C4⋊C4C22×D1112yes—
670C2×C4⋊C4C22×D1111yescharacteristic
671C2×C22⋊C4—111no—
672C2×C22⋊C4—111no—
673C2×C22⋊C4—111no—
674C2×C22⋊C4—111no—
675C2×C22⋊C4—111no—
676C2×C22⋊C4—111no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—112no—
679C2×C22⋊C4—112no—
680C2×C22⋊C4—112no—
681C2×C22⋊C4—112no—
682C2×C22⋊C4—112no—
683C2×C22⋊C4—112no—
684C2×C22⋊C4—112no—
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×C42—111no—
693C2×C42—111no—
694C2×C42—111no—
695C2×C42—111no—
696C2×C42—112no—
697C2×C42—111no—
698C2×C42—111no—
699C2×C42—112no—
700C2×C42—112no—
701C2×C42—224no—
702C2×C42—224no—
703C2×C42—444no—
704C2×C42C22×D1111yescharacteristic
705C2×C42C22×D1111yescharacteristic
706C2×C42C22×D1111yescharacteristic
707C2×C42C22×D1111yescharacteristic
708C2×C42C22×D1111yescharacteristic
709C2×C42C22×D1112yes—
710C2×C42C22×D1112yes—
711C2×C42C22×D1111yescharacteristic
712C2×C42C22×D1111yescharacteristic
713#95—112no—
714#95—112no—
715#95—112no—
716#95—112no—
717#95—112no—
718#95—112no—
719#95—112no—
720#95—111no—
721#95—111no—
722#95—111no—
723#95—111no—
724#95—111no—
725#95—111no—
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#95C22×D1112yes—
735#95C22×D1112yes—
736#95C22×D1112yes—
737#95C22×D1112yes—
738#95C22×D1112yes—
739#95C22×D1112yes—
740C2×C11C2×#52911yescharacteristic
741C2×C11C2×#52911yescharacteristic
742C2×C11#346011yescharacteristic
743C2×C11C2×#55311yescharacteristic
744C2×C11#347511yescharacteristic
745C2×C11#348011yescharacteristic
746C2×C11#348111yescharacteristic
747D11—24no—
748D11—42no—
749D11—82no—
750C24—111no—
751C24—111no—
752C24—112no—
753C2×D4—114no—
754C2×D4—222no—
755C2×D4—222no—
756C2×D4—224no—
757C2×D4—224no—
758C2×D4—224no—
759C2×D4—224no—
760C2×D4—224no—
761C2×D4—222no—
762C2×D4—222no—
763C2×D4—222no—
764C2×D4—442no—
765C22×C4—111no—
766C22×C4—111no—
767C22×C4—114no—
768C22×C4—114no—
769C22×C4—111no—
770C22×C4—111no—
771C22×C4—111no—
772C22×C4—112no—
773C22×C4—111no—
774C22×C4—112no—
775C22×C4—112no—
776C22×C4—224no—
777C22×C4—222no—
778C22×C4—222no—
779C22×C4—224no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—222no—
783C22×C4—222no—
784C22×C4—224no—
785C22×C4—222no—
786C22×C4—222no—
787C22×C4—222no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—224no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—224no—
794C22×C4—224no—
795C22×C4—222no—
796C22×C4—442no—
797C22×C4—442no—
798C22×C4—441no—
799C22×C4—441no—
800C22×C4—442no—
801C22×C4C23×D1112yes—
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—24no—
813C4⋊C4—24no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—24no—
817C4⋊C4—22no—
818C4⋊C4—42no—
819C4⋊C4—224no—
820C4⋊C4—222no—
821C4⋊C4—222no—
822C4⋊C4—224no—
823C4⋊C4—224no—
824C4⋊C4—222no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4—222no—
828C4⋊C4—442no—
829C4⋊C4—442no—
830C4⋊C4—442no—
831C4⋊C4#433914yes—
832C22⋊C4—222no—
833C22⋊C4—222no—
834C22⋊C4—224no—
835C22⋊C4—224no—
836C22⋊C4—222no—
837C22⋊C4—224no—
838C22⋊C4—222no—
839C22⋊C4—222no—
840C22⋊C4—222no—
841C22⋊C4—224no—
842C22⋊C4—224no—
843C22⋊C4—224no—
844C22⋊C4—224no—
845C22⋊C4—442no—
846C22⋊C4—442no—
847C22⋊C4—442no—
848C22⋊C4—442no—
849C22⋊C4—442no—
850C22⋊C4—442no—
851C22⋊C4—442no—
852C22⋊C4—442no—
853C42—22no—
854C42—22no—
855C42—22no—
856C42—22no—
857C42—24no—
858C42—24no—
859C42—22no—
860C42—41no—
861C42—222no—
862C42—222no—
863C42—222no—
864C42—222no—
865C42—222no—
866C42—222no—
867C42—224no—
868C42—442no—
869C42—442no—
870C42#434314yes—
871C11#3478811yescharacteristic, complemented, Sylow
872C23—112no—
873C23—112no—
874C23—112no—
875C23—112no—
876C23—221no—
877C23—221no—
878C23—221no—
879C23—221no—
880C23—221no—
881C23—221no—
882C23—221no—
883C23—221no—
884C23—221no—
885C23—221no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—222no—
890C23—222no—
891C23—222no—
892C23—222no—
893C23C24×D1111yescharacteristic
894D4—228no—
895D4—448no—
896D4—448no—
897D4—444no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—112no—
923C2×C4—112no—
924C2×C4—221no—
925C2×C4—221no—
926C2×C4—221no—
927C2×C4—221no—
928C2×C4—228no—
929C2×C4—228no—
930C2×C4—221no—
931C2×C4—222no—
932C2×C4—221no—
933C2×C4—221no—
934C2×C4—221no—
935C2×C4—221no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—221no—
939C2×C4—221no—
940C2×C4—222no—
941C2×C4—221no—
942C2×C4—221no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—221no—
947C2×C4—222no—
948C2×C4—221no—
949C2×C4—221no—
950C2×C4—222no—
951C2×C4—444no—
952C2×C4—444no—
953C2×C4—448no—
954C2×C4—448no—
955C2×C4—444no—
956C2×C4—444no—
957C2×C4—448no—
958C2×C4C2×#433914yes—
959C2×C4C2×#433912yes—
960C2×C4C2×#434312yes—
961C2×C4C2×#434312yes—
962C2×C4C2×#434312yes—
963C2×C4#41×D1112yes—
964C2×C4#41×D1112yes—
965C2×C4#41×D1112yes—
966C2×C4#6704212yes—
967C22—114no—
968C22—222no—
969C22—222no—
970C22—222no—
971C22—222no—
972C22—222no—
973C22—222no—
974C22—222no—
975C22—222no—
976C22—222no—
977C22—441no—
978C22—441no—
979C22—441no—
980C22—441no—
981C22—442no—
982C22—442no—
983C22—442no—
984C22—442no—
985C22—442no—
986C22—442no—
987C22—442no—
988C22C22×#433911yescharacteristic
989C22C22×#434311yescharacteristic
990C22C2×#41×D1111yescharacteristic
991C22C2×#41×D1111yescharacteristic
992C22C2×#41×D1111yescharacteristic
993C22C2×#6704211yescharacteristic
994C22#1062345311yescharacteristic
995C4—22no—
996C4—22no—
997C4—24no—
998C4—42no—
999C4—41no—
1000C4—42no—
1001C4—41no—
1002C4—42no—
1003C4—41no—
1004C4—222no—
1005C4—222no—
1006C4—441no—
1007C4—441no—
1008C4—442no—
1009C4—441no—
1010C4—441no—
1011C4—442no—
1012C4—442no—
1013C4#1062311114yes—
1014C4#1062322614yes—
1015C2—224no—
1016C2—442no—
1017C2—882no—
1018C2D11×#52911yescharacteristic
1019C2C2×#1062311111yescharacteristic
1020C2#1308203711yescharacteristic
1021C2C2×#1062322611yescharacteristic
1022C2#1308218311yescharacteristic
1023C2#1308221411yescharacteristic
1024C2#1308222611yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#125C2
prime radical#13072054C2
hypercenterC4×#125D11
hypocenterC11#34788
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
1. #13073379C2semidirect
2. #13073256C2semidirect
3. #13073216C2semidirect
4. #13073173C2semidirect
5. #13073168C2semidirect
6. #13073105C2semidirect
7. #13073019C2semidirect
8. #13072971C2semidirect
9. #13072931C2semidirect
10. #13072371C2semidirect
11. #13072336C2semidirect
13. #13071917C2semidirect
14. #13071879C2semidirect
15. C4×#66948C2semidirect
16. C4×#66948C2semidirect
17. C4×#66948C2semidirect
18. #13071080C2semidirect
19. #13071057C2semidirect
20. #13071012C2semidirect
21. C42×D44C2semidirect
22. C4×C4⋊C4×D11C2semidirect
23. C4×C11×#125C2semidirect
374. C4×#125D11semidirect
871. C11#34788semidirect

Maximal subgroups

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

subgroupindex
#130733792
#130732562
#130732162
#130731732
#130731682
#130731052
#130730192
#130729712
#130729312
#130723712
#130723362
#130720542
#130719172
#130718792
C4×#669482
#130710802
#130710572
#130710122
C42×D442
C4×C4⋊C4×D112
C4×C11×#1252
#3478811