Finite Group Databasebeta

← #14925406

Subgroups — #14925406

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#13073946C212yesmaximal, complemented
2#13073918C212yesmaximal, complemented
3#13073846C211yesmaximal, characteristic, complemented
4#13073813C211yesmaximal, characteristic, complemented
5#13073781C211yesmaximal, characteristic, complemented
6#13073519C211yesmaximal, characteristic
7#13073234C212yesmaximal, complemented
8#13073052C211yesmaximal, characteristic, complemented
9#13073018C211yesmaximal, characteristic, complemented
10#13072530C212yesmaximal, complemented
11#13072133C211yesmaximal, characteristic, complemented
12#13072110C211yesmaximal, characteristic, complemented
13#13071917C212yesmaximal, complemented
14#13071852C212yesmaximal, complemented
15C4×#66943C211yesmaximal, characteristic, complemented
16C4×#66947C212yesmaximal, complemented
17C4×#66948C211yesmaximal, characteristic, complemented
18C4×#66983C211yesmaximal, characteristic, complemented
19#13071053C212yesmaximal, complemented
20#13071012C211yesmaximal, characteristic, complemented
21C42×C22⋊D11C211yesmaximal, characteristic, complemented
22C4×#66946C211yesmaximal, characteristic, complemented
23C11×#2285C211yesmaximal, characteristic, complemented
24C2×C11×#117C2212yes—
25C22×C42×C11C2211yescharacteristic
26C2×#66983C2211yescharacteristic
27C2×C4×C22⋊D11C2212yes—
28C2×C4×C22⋊D11C2211yescharacteristic
29C2×C4×C22⋊D11C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×#66948C2211yescharacteristic
32C2×#66947C2212yes—
33C2×#66946C2211yescharacteristic
34C2×#66946C2211yescharacteristic
35C2×#66943C2211yescharacteristic
36C2×C4×D44C2211yescharacteristic
37C2×C4×D44C2212yes—
38C2×C42×D11C2211yescharacteristic
39C2×C42×D11C2212yes—
40C11×#384C2211yescharacteristic
41C11×#384C2211yescharacteristic
42C11×#382C2212yes—
43C11×#380C2212yes—
44C11×#380C2211yescharacteristic
45C11×#380C2211yescharacteristic
46C4×C11×C4⋊C4C2211yescharacteristic
47C4×C11×C4⋊C4C2212yes—
48C4×C11×C4⋊C4C2211yescharacteristic
49#10622826C2212yes—
50#10622825C2211yescharacteristic
51C4×C22⋊Dic11C2211yescharacteristic
52C4×C22⋊Dic11C2211yescharacteristic
53C4×C22⋊Dic11C2211yescharacteristic
54#10622607C2212yes—
55#10622607C2212yes—
56#10622607C2212yes—
57#10622606C2212yes—
58#10622604C2212yes—
59#10622603C2212yes—
60#10622602C2212yes—
61#10622602C2212yes—
62#10622602C2212yes—
63#10622601C2211yescharacteristic
64#10622600C2211yescharacteristic
65#10622600C2211yescharacteristic
66#10622600C2211yescharacteristic
67#10622599C2212yes—
68#10622598C2211yescharacteristic
69#10622598C2211yescharacteristic
70#10622596C2212yes—
71#10622595C2212yes—
72#10622594C2212yes—
73#10622591C2212yes—
74#10622591C2212yes—
75#10622590C2211yescharacteristic
76#10622590C2211yescharacteristic
77#10622590C2211yescharacteristic
78C4⋊C4×Dic11C2211yescharacteristic
79C4⋊C4×Dic11C2211yescharacteristic
80#10622586C2211yescharacteristic
81#10622574C2212yes—
82#10622574C2212yes—
83#10622573C2212yes—
84#10622569C2212yes—
85#10622569C2212yes—
86#10622566C2212yes—
87#10622557C2212yes—
88#10622557C2212yes—
89#10622553C2212yes—
90#10622552C2211yescharacteristic
91C4×(C2×D11)⋊C4C2211yescharacteristic
92C4×(C2×D11)⋊C4C2212yes—
93C4×(C2×D11)⋊C4C2212yes—
94C4×(C2×D11)⋊C4C2211yescharacteristic
95C4×(C2×D11)⋊C4C2212yes—
96C4×(C2×D11)⋊C4C2212yes—
97C4×(C2×D11)⋊C4C2211yescharacteristic
98C4×C4⋊Dic11C2211yescharacteristic
99C4×C4⋊Dic11C2212yes—
100#10622545C2212yes—
101C4×Dic11⋊C4C2212yes—
102C4×Dic11⋊C4C2211yescharacteristic
103C4×Dic11⋊C4C2211yescharacteristic
104C4×Dic11⋊C4C2211yescharacteristic
105C42×Dic11C2211yescharacteristic
106#10622541C2211yescharacteristic
107#10622288C2212yes—
108#10622287C2212yes—
109#10622283C2212yes—
110#10622282C2212yes—
111#10622279C2212yes—
112#10622279C2212yes—
113#10622278C2212yes—
114#10622278C2212yes—
115#10622277C2212yes—
116#10622277C2212yes—
117C11⋊#401C2212yes—
118#10622273C2212yes—
119#10622268C2212yes—
120#10622268C2212yes—
121#10622267C2212yes—
122#10622264C2212yes—
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C22×C22⋊D11C2311yescharacteristic
127C22×C22⋊D11C2312yes—
128C22×D44C2312yes—
129C22×D44C2311yescharacteristic
130C22×C4×D11C2311yescharacteristic
131C22×C4×D11C2312yes—
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2312yes—
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2312yes—
136C11×#117—44no—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C42×C11—24no—
148C2×C42×C11C2312yes—
149C2×C42×C11C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2311yescharacteristic
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2311yescharacteristic
156C2×C22⋊Dic11C2311yescharacteristic
157C2×C22⋊Dic11C2311yescharacteristic
158#66983—24no—
159C4×C22⋊D11—24no—
160C4×C22⋊D11—28no—
161C4×C22⋊D11—24no—
162C4×C22⋊D11—24no—
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)⋊C4C2311yescharacteristic
171C2×(C2×D11)⋊C4C2311yescharacteristic
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2311yescharacteristic
182C2×C4⋊Dic11C2312yes—
183C2×C4⋊Dic11C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2311yescharacteristic
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2311yescharacteristic
189C2×Dic11⋊C4C2311yescharacteristic
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202#66948—24no—
203#66947—28no—
204#66946—24no—
205#66946—24no—
206#66943—24no—
207C4×D44—24no—
208C4×D44—44no—
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⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2311yescharacteristic
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233C11⋊#95C2312yes—
234C11⋊#95C2311yescharacteristic
235C11⋊#95C2311yescharacteristic
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238#34917—111nomaximal, Sylow
239C24×C11C2411yescharacteristic
240C23×D11C2412yes—
241C23×D11C2411yescharacteristic
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—41no—
250C22×C4×C11#4114yes—
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C2×C22⋊D11—22no—
262C2×C22⋊D11—22no—
263C2×C22⋊D11—24no—
264C2×C22⋊D11—22no—
265C2×C22⋊D11—24no—
266C2×C22⋊D11—42no—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2411yescharacteristic
269C22×Dic11C2412yes—
270C22×Dic11C2411yescharacteristic
271C22×Dic11C2411yescharacteristic
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2411yescharacteristic
277C2×D44—24no—
278C2×D44—24no—
279C2×D44—22no—
280C2×D44—22no—
281C2×D44—42no—
282C2×D44#4114yes—
283C2×C4×D11—24no—
284C2×C4×D11—24no—
285C2×C4×D11—24no—
286C2×C4×D11—22no—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—24no—
291C2×C4×D11—22no—
292C2×C4×D11—22no—
293C2×C4×D11—24no—
294C2×C4×D11—22no—
295C2×C4×D11—24no—
296C2×C4×D11—22no—
297C2×C4×D11—42no—
298C2×C4×D11—42no—
299C2×C4×D11—41no—
300C2×C4×D11—42no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—22no—
303C11×C4⋊C4—22no—
304C11×C4⋊C4—24no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—42no—
307C11×C4⋊C4—42no—
308C11×C4⋊C4—42no—
309C11×C22⋊C4—42no—
310C11×C22⋊C4—42no—
311C42×C11—22no—
312C42×C11—22no—
313C42×C11—22no—
314C42×C11—24no—
315C42×C11—24no—
316C42×C11#4114yes—
317C22⋊Dic11—22no—
318C22⋊Dic11—22no—
319C22⋊Dic11—24no—
320C22⋊Dic11—22no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—24no—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—24no—
327(C2×D11)⋊C4—24no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—22no—
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#4114yes—
336C4⋊Dic11—24no—
337C4⋊Dic11—22no—
338C4⋊Dic11—22no—
339C4⋊Dic11—22no—
340C4⋊Dic11—42no—
341C4⋊Dic11—42no—
342Dic11⋊C4—24no—
343Dic11⋊C4—24no—
344Dic11⋊C4—22no—
345Dic11⋊C4—22no—
346Dic11⋊C4—24no—
347Dic11⋊C4—22no—
348C4×Dic11—22no—
349C4×Dic11—22no—
350C4×Dic11—22no—
351C4×Dic11—22no—
352C4×Dic11—22no—
353C4×Dic11—22no—
354C4×Dic11—24no—
355C4×Dic11—22no—
356C4×Dic11—42no—
357C4×Dic11—42no—
358C4×Dic11—41no—
359C4×Dic11#4114yes—
360#2578—112no—
361#2576—112no—
362#2570—111no—
363#2566—111no—
364#2562—111no—
365#2535—111no—
366#2515—112no—
367#2497—111no—
368#2494—111no—
369#2457—112no—
370#2422—111no—
371#2420—111no—
372#2401—112no—
373#2392—112no—
374C4×#125—111no—
375C4×#123—112no—
376C4×#121—111no—
377C4×#121—111no—
378#2290—112no—
379#2285D1111yescharacteristic, complemented
380#2283—111no—
381C42×D4—111no—
382C42×D4—111no—
383C23×C11—21no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—21no—
387C23×C11—21no—
388C23×C11—21no—
389C23×C11C2×#4112yes—
390C23×C11C2511yescharacteristic
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—21no—
395C22×D11—22no—
396C22×D11—21no—
397C22×D11—21no—
398C22×D11—21no—
399C22×D11—21no—
400C22×D11—22no—
401C22×D11—21no—
402C22×D11—22no—
403C22×D11C2×#4114yes—
404C22×D11C2×#4112yes—
405C2×C4×C11—21no—
406C2×C4×C11—21no—
407C2×C4×C11—21no—
408C2×C4×C11—21no—
409C2×C4×C11—21no—
410C2×C4×C11—21no—
411C2×C4×C11—28no—
412C2×C4×C11—22no—
413C2×C4×C11—21no—
414C2×C4×C11—22no—
415C2×C4×C11—21no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—21no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—44no—
428C2×C4×C11—44no—
429C2×C4×C11C2×#4112yes—
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—
438C22⋊D11—28no—
439C22⋊D11—48no—
440C2×Dic11—21no—
441C2×Dic11—21no—
442C2×Dic11—21no—
443C2×Dic11—21no—
444C2×Dic11—21no—
445C2×Dic11—21no—
446C2×Dic11—21no—
447C2×Dic11—21no—
448C2×Dic11—21no—
449C2×Dic11—22no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—21no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—21no—
456C2×Dic11—22no—
457C2×Dic11—21no—
458C2×Dic11—21no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—21no—
462C2×Dic11—22no—
463C2×Dic11—21no—
464C2×Dic11—21no—
465C2×Dic11—22no—
466C2×Dic11—21no—
467C2×Dic11C2×#4112yes—
468C2×Dic11C2×#4112yes—
469C2×Dic11C2×#4112yes—
470D44—28no—
471D44—48no—
472C4×D11—48no—
473C4×D11—48no—
474C4×D11—44no—
475C4×D11—44no—
476C4×D11—44no—
477C4×D11—48no—
478C2×#125—111no—
479C2×#123—112no—
480C2×#121—111no—
481C2×#121—111no—
482C2×C4×D4—111no—
483C2×C4×D4—111no—
484C2×C4×D4—112no—
485C2×C4×D4—111no—
486C2×C4×D4—111no—
487C2×C4×D4—111no—
488C2×C4×D4—111no—
489C2×C4×D4—112no—
490C2×#117C2×D1112yes—
491C22×C42—111no—
492C22×C42—112no—
493C22×C42C2×D1111yescharacteristic
494#401—112no—
495#400—112no—
496#400—112no—
497#400—112no—
498#398—112no—
499#397—112no—
500#397—112no—
501#397—112no—
502#397—112no—
503#396—112no—
504#396—112no—
505#396—112no—
506#394—112no—
507#394—112no—
508#394—112no—
509#392—112no—
510#390—111no—
511#390—111no—
512#389—111no—
513#389—111no—
514#389—111no—
515#389—111no—
516#388—112no—
517#388—112no—
518#388—112no—
519#388—112no—
520#388—112no—
521#388—112no—
522#387—112no—
523#387—112no—
524#387—112no—
525#387—112no—
526#387—112no—
527#387—112no—
528#386—112no—
529#386—112no—
530#386—112no—
531#386—112no—
532#386—112no—
533#385—112no—
534#385—112no—
535#385—112no—
536#384C2×D1111yescharacteristic
537#384C2×D1111yescharacteristic
538#383—112no—
539#382—111no—
540#382—111no—
541#382—111no—
542#382C2×D1112yes—
543#381—112no—
544#381—112no—
545#380—111no—
546#380—111no—
547#380—111no—
548#380—111no—
549#380C2×D1111yescharacteristic
550#380C2×D1112yes—
551#380C2×D1111yescharacteristic
552C4×C4⋊C4—111no—
553C4×C4⋊C4—111no—
554C4×C4⋊C4—112no—
555C4×C4⋊C4—112no—
556C4×C4⋊C4—111no—
557C4×C4⋊C4—111no—
558C4×C4⋊C4—111no—
559C4×C4⋊C4—111no—
560C4×C4⋊C4C2×D1111yescharacteristic
561C4×C4⋊C4C2×D1112yes—
562C4×C4⋊C4C2×D1111yescharacteristic
563C4×C22⋊C4—111no—
564C4×C22⋊C4—111no—
565C4×C22⋊C4—111no—
566C4×C22⋊C4—111no—
567C4×C22⋊C4—112no—
568C4×C22⋊C4—112no—
569C4×C22⋊C4—112no—
570C4×C22⋊C4—112no—
571C4×C22⋊C4—111no—
572C4×C22⋊C4—111no—
573C4×C22⋊C4—112no—
574C4×C22⋊C4—112no—
575#376—112no—
576C43—111no—
577C22×C11—22no—
578C22×C11—22no—
579C22×C11—22no—
580C22×C11—41no—
581C22×C11—41no—
582C22×C11—41no—
583C22×C11—41no—
584C22×C11C22×#4111yescharacteristic
585C22×C11C22×#4111yescharacteristic
586C22×C11C22×#4111yescharacteristic
587C22×C11C22×#4111yescharacteristic
588C22×C11C22×#4111yescharacteristic
589C22×C11C2×H(5,𝔽2)11yescharacteristic
590C22×C11#58511yescharacteristic
591C2×D11—24no—
592C2×D11—22no—
593C2×D11—22no—
594C2×D11—24no—
595C2×D11—24no—
596C2×D11—22no—
597C2×D11—41no—
598C2×D11—42no—
599C2×D11—41no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—41no—
603C2×D11—42no—
604C2×D11—41no—
605C4×C11—22no—
606C4×C11—22no—
607C4×C11—22no—
608C4×C11—41no—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11—42no—
613C4×C11#52914yes—
614C4×C11#55314yes—
615Dic11—22no—
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—112no—
632C23×C4—112no—
633C23×C4—111no—
634C23×C4—112no—
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1111yescharacteristic
637C23×C4C22×D1111yescharacteristic
638#125—224no—
639#123—228no—
640#121—224no—
641#121—224no—
642C4×D4—224no—
643C4×D4—224no—
644C4×D4—224no—
645C4×D4—224no—
646C4×D4—224no—
647C4×D4—228no—
648C4×D4—224no—
649C4×D4—444no—
650#117—44no—
651C2×C4⋊C4—111no—
652C2×C4⋊C4—111no—
653C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
664C2×C4⋊C4C22×D1111yescharacteristic
665C2×C4⋊C4C22×D1111yescharacteristic
666C2×C4⋊C4C22×D1112yes—
667C2×C4⋊C4C22×D1111yescharacteristic
668C2×C4⋊C4C22×D1112yes—
669C2×C4⋊C4C22×D1112yes—
670C2×C4⋊C4C22×D1112yes—
671C2×C22⋊C4—111no—
672C2×C22⋊C4—111no—
673C2×C22⋊C4—111no—
674C2×C22⋊C4—111no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—111no—
677C2×C22⋊C4—112no—
678C2×C22⋊C4—112no—
679C2×C22⋊C4—111no—
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⋊C4C22×D1112yes—
691C2×C22⋊C4C22×D1112yes—
692C2×C42—24no—
693C2×C42—111no—
694C2×C42—111no—
695C2×C42—111no—
696C2×C42—111no—
697C2×C42—111no—
698C2×C42—111no—
699C2×C42—112no—
700C2×C42—111no—
701C2×C42—111no—
702C2×C42—111no—
703C2×C42—112no—
704C2×C42—112no—
705C2×C42—224no—
706C2×C42—444no—
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—111no—
718#95—111no—
719#95—111no—
720#95—111no—
721#95—112no—
722#95—112no—
723#95—111no—
724#95—111no—
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×D1112yes—
738#95C22×D1112yes—
739#95C22×D1112yes—
740C2×C11—42no—
741C2×C11C2×#52911yescharacteristic
742C2×C11#344411yescharacteristic
743C2×C11#346011yescharacteristic
744C2×C11C2×#55311yescharacteristic
745C2×C11#347511yescharacteristic
746C2×C11#347511yescharacteristic
747C2×C11#348111yescharacteristic
748D11—44no—
749D11—42no—
750C24—111no—
751C24—112no—
752C24C23×D1111yescharacteristic
753C2×D4—114no—
754C2×D4—224no—
755C2×D4—224no—
756C2×D4—222no—
757C2×D4—222no—
758C2×D4—222no—
759C2×D4—224no—
760C2×D4—224no—
761C2×D4—222no—
762C2×D4—222no—
763C2×D4—442no—
764C2×D4—442no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—41no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—111no—
776C22×C4—111no—
777C22×C4—111no—
778C22×C4—112no—
779C22×C4—111no—
780C22×C4—111no—
781C22×C4—112no—
782C22×C4—112no—
783C22×C4—224no—
784C22×C4—224no—
785C22×C4—222no—
786C22×C4—224no—
787C22×C4—222no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—224no—
791C22×C4—224no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—224no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—442no—
798C22×C4—442no—
799C22×C4—441no—
800C22×C4—442no—
801C22×C4#434314yes—
802C22×C4C23×D1111yescharacteristic
803C22×C4C23×D1112yes—
804C22×C4C23×D1112yes—
805C22×C4C23×D1112yes—
806C22×C4C23×D1112yes—
807C22×C4C23×D1111yescharacteristic
808C22×C4C23×D1111yescharacteristic
809C22×C4C23×D1111yescharacteristic
810C22×C4C23×D1111yescharacteristic
811C22×C4C23×D1111yescharacteristic
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—24no—
816C4⋊C4—22no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4—42no—
820C4⋊C4—222no—
821C4⋊C4—224no—
822C4⋊C4—224no—
823C4⋊C4—224no—
824C4⋊C4—222no—
825C4⋊C4—222no—
826C4⋊C4—224no—
827C4⋊C4—222no—
828C4⋊C4—222no—
829C4⋊C4—222no—
830C4⋊C4—442no—
831C4⋊C4—442no—
832C22⋊C4—42no—
833C22⋊C4—42no—
834C22⋊C4—114no—
835C22⋊C4—224no—
836C22⋊C4—222no—
837C22⋊C4—224no—
838C22⋊C4—224no—
839C22⋊C4—224no—
840C22⋊C4—224no—
841C22⋊C4—222no—
842C22⋊C4—222no—
843C22⋊C4—222no—
844C22⋊C4—224no—
845C22⋊C4—224no—
846C22⋊C4—222no—
847C22⋊C4—224no—
848C22⋊C4—224no—
849C22⋊C4—442no—
850C22⋊C4—442no—
851C22⋊C4—442no—
852C22⋊C4—442no—
853C42—22no—
854C42—22no—
855C42—22no—
856C42—24no—
857C42—24no—
858C42—114no—
859C42—222no—
860C42—222no—
861C42—222no—
862C42—222no—
863C42—222no—
864C42—222no—
865C42—224no—
866C42—222no—
867C42—442no—
868C42—442no—
869C42—441no—
870C42#433914yes—
871C11#3491711yescharacteristic, complemented, Sylow
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—112no—
879C23—114no—
880C23—222no—
881C23—221no—
882C23—221no—
883C23—222no—
884C23—221no—
885C23—222no—
886C23—222no—
887C23—221no—
888C23—222no—
889C23—221no—
890C23—221no—
891C23—222no—
892C23C2×#434312yes—
893C23C24×D1111yescharacteristic
894D4—228no—
895D4—228no—
896D4—448no—
897D4—448no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—28no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—112no—
923C2×C4—112no—
924C2×C4—112no—
925C2×C4—221no—
926C2×C4—221no—
927C2×C4—221no—
928C2×C4—221no—
929C2×C4—221no—
930C2×C4—221no—
931C2×C4—221no—
932C2×C4—221no—
933C2×C4—221no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—221no—
937C2×C4—222no—
938C2×C4—221no—
939C2×C4—222no—
940C2×C4—221no—
941C2×C4—222no—
942C2×C4—221no—
943C2×C4—222no—
944C2×C4—221no—
945C2×C4—221no—
946C2×C4—221no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—221no—
950C2×C4—221no—
951C2×C4—222no—
952C2×C4—444no—
953C2×C4—448no—
954C2×C4—448no—
955C2×C4—444no—
956C2×C4—448no—
957C2×C4—444no—
958C2×C4C2×#433912yes—
959C2×C4C2×#433912yes—
960C2×C4C2×#433912yes—
961C2×C4#6703712yes—
962C2×C4C2×#434312yes—
963C2×C4C2×#434312yes—
964C2×C4#41×D1112yes—
965C2×C4#41×D1112yes—
966C2×C4#41×D1112yes—
967C22—22no—
968C22—22no—
969C22—22no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—224no—
975C22—222no—
976C22—222no—
977C22—224no—
978C22—224no—
979C22—222no—
980C22—441no—
981C22—442no—
982C22—441no—
983C22—442no—
984C22—442no—
985C22—441no—
986C22—442no—
987C22—441no—
988C22C22×#433911yescharacteristic
989C22C2×#6703711yescharacteristic
990C22C22×#434311yescharacteristic
991C22C2×#41×D1111yescharacteristic
992C22C2×#41×D1111yescharacteristic
993C22C2×#41×D1111yescharacteristic
994C22#1062345311yescharacteristic
995C4—22no—
996C4—22no—
997C4—22no—
998C4—41no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—222no—
1004C4—222no—
1005C4—222no—
1006C4—441no—
1007C4—441no—
1008C4—442no—
1009C4—442no—
1010C4—441no—
1011C4—442no—
1012C4—441no—
1013C4#1062304514yes—
1014C4#1062305914yes—
1015C2—42no—
1016C2—444no—
1017C2—442no—
1018C2C2×#1062305911yescharacteristic
1019C2#1308191311yescharacteristic
1020C2#1308203011yescharacteristic
1021C2C2×#1062304511yescharacteristic
1022C2#1308217011yescharacteristic
1023C2#1308218311yescharacteristic
1024C2#1308222411yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2285C2
prime radical#13073519C2
hypercenter#2285D11
hypocenterC11#34917
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2285

Complements

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

NH ≅ G/Ntype
1. #13073946C2semidirect
2. #13073918C2semidirect
3. #13073846C2semidirect
4. #13073813C2semidirect
5. #13073781C2semidirect
7. #13073234C2semidirect
8. #13073052C2semidirect
9. #13073018C2semidirect
10. #13072530C2semidirect
11. #13072133C2semidirect
12. #13072110C2semidirect
13. #13071917C2semidirect
14. #13071852C2semidirect
15. C4×#66943C2semidirect
16. C4×#66947C2semidirect
17. C4×#66948C2semidirect
18. C4×#66983C2semidirect
19. #13071053C2semidirect
20. #13071012C2semidirect
21. C42×C22⋊D11C2semidirect
22. C4×#66946C2semidirect
23. C11×#2285C2semidirect
379. #2285D11semidirect
871. C11#34917semidirect

Maximal subgroups

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

subgroupindex
#130739462
#130739182
#130738462
#130738132
#130737812
#130735192
#130732342
#130730522
#130730182
#130725302
#130721332
#130721102
#130719172
#130718522
C4×#669432
C4×#669472
C4×#669482
C4×#669832
#130710532
#130710122
C42×C22⋊D112
C4×#669462
C11×#22852
#3491711