Finite Group Databasebeta

← #14914906

Subgroups — #14914906

Order 2816.

3658 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
1C2×#10623120C211yesmaximal, characteristic
2C2×#10623076C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13071667C212yesmaximal, complemented
5#13071665C212yesmaximal, complemented
6#13071635C212yesmaximal, complemented
7#13071628C212yesmaximal, complemented
8#13071611C212yesmaximal, complemented
9#13071609C212yesmaximal, complemented
10#13071599C212yesmaximal, complemented
11#13071593C212yesmaximal, complemented
12#13071287C211yesmaximal, characteristic, complemented
13#13071281C211yesmaximal, characteristic, complemented
14#13071277C211yesmaximal, characteristic, complemented
15#13071271C211yesmaximal, characteristic, complemented
16#13071192C211yesmaximal, characteristic, complemented
17#13071141C211yesmaximal, characteristic, complemented
18#13071135C211yesmaximal, characteristic, complemented
19C4×#67006C211yesmaximal, characteristic, complemented
20D11×#386C211yesmaximal, characteristic, complemented
21D11×#385C211yesmaximal, characteristic, complemented
22#13070968C211yesmaximal, characteristic, complemented
23C4×C11×#120C211yesmaximal, characteristic, complemented
24C24×C4×C11C2211yescharacteristic, complemented
25C23×C22⋊D11C2211yescharacteristic
26C22×D4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2212yescomplemented
31C2×#67006C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic, complemented
33C2×#66991C2212yes—
34C2×#66990C2212yes—
35C2×#66988C2211yescharacteristic
36C2×D4×Dic11C2211yescharacteristic
37C2×C4×C22⋊D11—28no—
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2211yescharacteristic, complemented
42C2×C4×C22⋊D11C2212yescomplemented
43C2×C4×C22⋊D11C2212yescomplemented
44C2×C4×C22⋊D11C2212yescomplemented
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
47C22×Dic11⋊C4C2211yescharacteristic, complemented
48C22×C4×Dic11C2211yescharacteristic, complemented
49#10623120C4116yescomplemented
50#10623076—28no—
51C2×#66946C2211yescharacteristic, complemented
52C2×#66945C2211yescharacteristic, complemented
53C2×C4⋊C4×D11C2212yescomplemented
54C2×#66939C2211yescharacteristic
55C2×#66937C2212yes—
56C2×#66936C2212yes—
57C2×(C22⋊D11)⋊C4C2211yescharacteristic
58C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
59C2×C22⋊C4×D11C2211yescharacteristic
60C2×C22⋊C4×D11C2211yescharacteristic
61C2×C22⋊C4×D11C2211yescharacteristic
62C2×C22⋊C4×D11C2211yescharacteristic, complemented
63C2×C22⋊C4×D11C2212yescomplemented
64C2×C4×D44C2211yescharacteristic, complemented
65C2×#66925C2211yescharacteristic, complemented
66C11×#386C2211yescharacteristic
67C11×#386C2212yescomplemented
68C11×#385C2212yescomplemented
69C11×#385C2211yescharacteristic, complemented
70C11×#379C2211yescharacteristic, complemented
71C4×C11×C22⋊C4C2212yescomplemented
72C4×C11×C22⋊C4C2211yescharacteristic, complemented
73#10622860C2211yescharacteristic, complemented
74#10622834C2212yescomplemented
75#10622833C2211yescharacteristic
76#10622833C2212yescomplemented
77#10622826C2211yescharacteristic
78#10622826C2212yescomplemented
79#10622823C2212yescomplemented
80#10622823C2212yescomplemented
81#10622823C2211yescharacteristic, complemented
82C4×C22⋊Dic11C2212yescomplemented
83C4×C22⋊Dic11C2211yescharacteristic, complemented
84#10622603C2212yescomplemented
85#10622602C2212yescomplemented
86C4⋊C4×Dic11C2212yescomplemented
87#10622585C2212yescomplemented
88#10622571C2211yescharacteristic
89#10622570C2212yescomplemented
90#10622569C2212yes—
91#10622569C2212yes—
92#10622569C2212yescomplemented
93#10622569C2212yescomplemented
94#10622569C2212yescomplemented
95#10622569C2212yescomplemented
96#10622564C2212yescomplemented
97#10622564C2212yescomplemented
98#10622563C2211yescharacteristic, complemented
99#10622559C2211yescharacteristic, complemented
100#10622558C2212yescomplemented
101#10622558C2212yescomplemented
102#10622558C2212yescomplemented
103#10622557C2212yescomplemented
104#10622556C2211yescharacteristic, complemented
105#10622556C2211yescharacteristic, complemented
106C22⋊C4×Dic11C2211yescharacteristic, complemented
107C22⋊C4×Dic11C2212yescomplemented
108C22⋊C4×Dic11C2211yescharacteristic, complemented
109#10622553C2212yescomplemented
110C4×(C2×D11)⋊C4C2212yescomplemented
111C4×(C2×D11)⋊C4C2212yescomplemented
112#10622546C2212yescomplemented
113#10622541C2212yescomplemented
114#10622281C2212yescomplemented
115#10622281C2212yescomplemented
116#10622279C2212yescomplemented
117#10622279C2212yescomplemented
118#10622279C2212yescomplemented
119#10622278C2212yescomplemented
120D11×#95C2212yescomplemented
121D11×#95C2212yescomplemented
122#10622268C2212yescomplemented
123#10622267C2212yescomplemented
124#10622266C2212yescomplemented
125#10622262C2212yescomplemented
126C25×C11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2312yes—
131C23×C4×C11—24no—
132C23×C4×C11—44no—
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2312yes—
135C23×C4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11—24no—
139C22×C22⋊D11—24no—
140C22×C22⋊D11C2×C418yescomplemented
141C22×C22⋊D11C2311yescharacteristic
142C22×C22⋊D11C2312yes—
143C22×C22⋊D11C2312yes—
144C22×C22⋊D11C2311yescharacteristic
145C22×C22⋊D11C2312yes—
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C23×Dic11C2311yescharacteristic
150C2×D4×D11—24no—
151C2×D4×D11—24no—
152C2×D4×D11C2×C418yescomplemented
153C22×D44C2311yescharacteristic
154C22×C4×D11—24no—
155C22×C4×D11—44no—
156C22×C4×D11C2312yes—
157C22×C4×D11C2312yes—
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×C4×D11C2312yes—
162C22×C4×D11C2311yescharacteristic
163C22×C4×D11C2311yescharacteristic
164C22×C4×D11C2312yes—
165C11×#120C2×C418yescomplemented
166C4×D4×C11—24no—
167C4×D4×C11—44no—
168C2×C11×C4⋊C4C2312yes—
169C2×C11×C4⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4C2312yes—
178C2×C42×C11C2311yescharacteristic
179C2×C42×C11C2312yes—
180#67006C2×C418yescomplemented
181C2×C22⋊Dic11—24no—
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2311yescharacteristic
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2312yes—
193#66991C2×C4116yescomplemented
194#66990C2×C4116yescomplemented
195#66988C2×C418yescomplemented
196D4×Dic11—24no—
197C4×C22⋊D11—24no—
198C4×C22⋊D11—28no—
199C4×C22⋊D11—28no—
200C4×C22⋊D11—28no—
201C4×C22⋊D11—28no—
202C4×C22⋊D11—24no—
203C4×C22⋊D11—44no—
204C2×(C2×D11)⋊C4—24no—
205C2×(C2×D11)⋊C4D418yescomplemented
206C2×(C2×D11)⋊C4C2311yescharacteristic
207C2×(C2×D11)⋊C4C2311yescharacteristic
208C2×(C2×D11)⋊C4C2311yescharacteristic
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2311yescharacteristic
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×(C2×D11)⋊C4C2311yescharacteristic
216C2×(C2×D11)⋊C4C2311yescharacteristic
217C2×(C2×D11)⋊C4C2311yescharacteristic
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×C4⋊Dic11C2311yescharacteristic
220C2×C4⋊Dic11C2312yes—
221C2×C4⋊Dic11C2312yes—
222C2×Dic11⋊C4—24no—
223C2×Dic11⋊C4C2311yescharacteristic
224C2×Dic11⋊C4C2311yescharacteristic
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2312yes—
230C2×C4×Dic11—24no—
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234C2×C4×Dic11C2312yes—
235C2×C4×Dic11C2312yes—
236C2×C4×Dic11C2312yes—
237C2×C4×Dic11C2312yes—
238C2×C4×Dic11C2312yes—
239#66946—24no—
240#66945—24no—
241C4⋊C4×D11—44no—
242#66939C2×C418yescomplemented
243#66937C2×C4116yescomplemented
244#66936C2×C4116yescomplemented
245(C22⋊D11)⋊C4—24no—
246(C22⋊D11)⋊C4—24no—
247C22⋊C4×D11—24no—
248C22⋊C4×D11—24no—
249C22⋊C4×D11—24no—
250C22⋊C4×D11—44no—
251C22⋊C4×D11C2×C418yescomplemented
252C4×D44—24no—
253#66925—24no—
254C11×#95C2312yes—
255C11×#95C2312yes—
256C11×#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267C11⋊#95C2312yes—
268C11⋊#95C2312yes—
269C11⋊#95C2312yes—
270#34264—111nomaximal, Sylow
271C24×C11—22no—
272C24×C11—22no—
273C24×C11—42no—
274C24×C11—42no—
275C24×C11C22×C414yes—
276C24×C11C2411yescharacteristic
277C24×C11C2412yes—
278C24×C11C2411yescharacteristic
279C23×D11—22no—
280C23×D11—22no—
281C23×D11—42no—
282C23×D11—42no—
283C23×D11—42no—
284C23×D11—42no—
285C23×D11C22×C414yes—
286C23×D11C22×C414yescomplemented
287C23×D11C2×D414yes—
288C23×D11#4114yes—
289C23×D11C2411yescharacteristic
290C23×D11C2411yescharacteristic
291C23×D11C2411yescharacteristic
292C2×D4×C11—22no—
293C2×D4×C11—22no—
294C2×D4×C11—42no—
295C2×D4×C11—42no—
296C2×D4×C11C22×C414yes—
297C2×D4×C11C22×C418yescomplemented
298C22×C4×C11—22no—
299C22×C4×C11—24no—
300C22×C4×C11—24no—
301C22×C4×C11—24no—
302C22×C4×C11—24no—
303C22×C4×C11—24no—
304C22×C4×C11—22no—
305C22×C4×C11—42no—
306C22×C4×C11—42no—
307C22×C4×C11—42no—
308C22×C4×C11—42no—
309C22×C4×C11—416no—
310C22×C4×C11C2×D414yes—
311C22×C4×C11C2412yes—
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2411yescharacteristic
315C22×C4×C11C2412yes—
316C22×C4×C11C2411yescharacteristic
317C22×C4×C11C2411yescharacteristic
318C22×C4×C11C2412yes—
319C2×C22⋊D11—22no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—232no—
322C2×C22⋊D11—22no—
323C2×C22⋊D11—24no—
324C2×C22⋊D11—24no—
325C2×C22⋊D11—22no—
326C2×C22⋊D11—24no—
327C2×C22⋊D11—24no—
328C2×C22⋊D11—42no—
329C2×C22⋊D11—42no—
330C2×C22⋊D11C22×C418yes—
331C2×C22⋊D11C22×C418yes—
332C2×C22⋊D11C22×C414yes—
333C2×C22⋊D11C22×C414yescomplemented
334C2×C22⋊D11C22×C418yescomplemented
335C22×Dic11—22no—
336C22×Dic11—22no—
337C22×Dic11—22no—
338C22×Dic11—22no—
339C22×Dic11—42no—
340C22×Dic11—42no—
341C22×Dic11—42no—
342C22×Dic11C22×C414yes—
343C22×Dic11C2×D414yes—
344C22×Dic11C2412yes—
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2412yes—
347C22×Dic11C2411yescharacteristic
348C22×Dic11C2412yes—
349C22×Dic11C2412yes—
350C22×Dic11C2411yescharacteristic
351C22×Dic11C2411yescharacteristic
352C22×Dic11C2411yescharacteristic
353D4×D11—232no—
354C2×D44—22no—
355C2×D44—22no—
356C2×D44C22×C414yescomplemented
357C2×C4×D11—22no—
358C2×C4×D11—22no—
359C2×C4×D11—24no—
360C2×C4×D11—24no—
361C2×C4×D11—22no—
362C2×C4×D11—22no—
363C2×C4×D11—22no—
364C2×C4×D11—24no—
365C2×C4×D11—22no—
366C2×C4×D11—24no—
367C2×C4×D11—24no—
368C2×C4×D11—42no—
369C2×C4×D11—42no—
370C2×C4×D11—42no—
371C2×C4×D11—42no—
372C2×C4×D11—42no—
373C2×C4×D11—42no—
374C2×C4×D11—42no—
375C2×C4×D11—42no—
376C2×C4×D11—42no—
377C2×C4×D11—42no—
378C2×C4×D11—416no—
379C2×C4×D11C22×C414yescomplemented
380C2×C4×D11C22×C418yescomplemented
381C11×C4⋊C4—22no—
382C11×C4⋊C4—24no—
383C11×C22⋊C4—22no—
384C11×C22⋊C4—22no—
385C11×C22⋊C4—22no—
386C11×C22⋊C4—24no—
387C11×C22⋊C4—42no—
388C11×C22⋊C4—42no—
389C11×C22⋊C4C22×C414yes—
390C11×C22⋊C4C22×C418yescomplemented
391C42×C11—22no—
392C42×C11—42no—
393C22⋊Dic11—22no—
394C22⋊Dic11—24no—
395C22⋊Dic11—24no—
396C22⋊Dic11—22no—
397C22⋊Dic11—22no—
398C22⋊Dic11—42no—
399C22⋊Dic11—42no—
400C22⋊Dic11—42no—
401C22⋊Dic11C22×C414yes—
402C22⋊Dic11C22×C418yescomplemented
403C22⋊Dic11C22×C418yescomplemented
404(C2×D11)⋊C4—22no—
405(C2×D11)⋊C4—22no—
406(C2×D11)⋊C4—22no—
407(C2×D11)⋊C4—24no—
408(C2×D11)⋊C4—22no—
409(C2×D11)⋊C4—24no—
410(C2×D11)⋊C4—42no—
411(C2×D11)⋊C4C22×C418yescomplemented
412(C2×D11)⋊C4C22×C418yescomplemented
413(C2×D11)⋊C4C2×D414yes—
414(C2×D11)⋊C4C2×D414yes—
415(C2×D11)⋊C4C2×D414yes—
416(C2×D11)⋊C4C2×D414yes—
417C4⋊Dic11—22no—
418C4⋊Dic11—42no—
419C4⋊Dic11C22×C418yescomplemented
420Dic11⋊C4—22no—
421Dic11⋊C4—22no—
422Dic11⋊C4—24no—
423Dic11⋊C4—24no—
424Dic11⋊C4—24no—
425Dic11⋊C4—42no—
426Dic11⋊C4C22×C418yescomplemented
427C4×Dic11—22no—
428C4×Dic11—22no—
429C4×Dic11—24no—
430C4×Dic11—24no—
431C4×Dic11—22no—
432C4×Dic11—42no—
433C4×Dic11—42no—
434C4×Dic11—42no—
435C2×#534—111no—
436C2×#518—111no—
437C22×C4×D4—111no—
438#2364—112no—
439#2364—112no—
440#2361—112no—
441#2361—112no—
442#2359—112no—
443#2359—112no—
444#2358—112no—
445#2358—112no—
446#2322—111no—
447#2322—111no—
448#2321—111no—
449#2321—111no—
450#2308—111no—
451C4×#123—111no—
452C4×#123—111no—
453C4×#120—111no—
454C4×#120D1111yescharacteristic, complemented
455C2×#386—111no—
456C2×#385—111no—
457#2273—111no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—28no—
461C23×C11—22no—
462C23×C11—21no—
463C23×C11—22no—
464C23×C11—21no—
465C23×C11—22no—
466C23×C11—22no—
467C23×C11—22no—
468C23×C11—22no—
469C23×C11—22no—
470C23×C11—22no—
471C23×C11—48no—
472C23×C11—44no—
473C23×C11—44no—
474C23×C11—48no—
475C23×C11C23×C412yes—
476C23×C11C23×C414yes—
477C23×C11C23×C412yes—
478C23×C11C22×D412yes—
479C23×C11C2×#4112yes—
480C23×C11C2511yescharacteristic
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—21no—
486C22×D11—21no—
487C22×D11—22no—
488C22×D11—22no—
489C22×D11—28no—
490C22×D11—44no—
491C22×D11—48no—
492C22×D11—44no—
493C22×D11—48no—
494C22×D11—48no—
495C22×D11—82no—
496C22×D11—82no—
497C22×D11—84no—
498C22×D11C4×D4116yescomplemented
499C22×D11C23×C412yes—
500C22×D11C23×C412yes—
501C22×D11C23×C412yes—
502C22×D11C22×D412yes—
503C22×D11C22×D412yes—
504C22×D11C2×#4112yes—
505C22×D11C2×#4112yes—
506D4×C11—28no—
507D4×C11—48no—
508C2×C4×C11—28no—
509C2×C4×C11—22no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—22no—
513C2×C4×C11—22no—
514C2×C4×C11—22no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—21no—
518C2×C4×C11—21no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—44no—
525C2×C4×C11—48no—
526C2×C4×C11—48no—
527C2×C4×C11—82no—
528C2×C4×C11C23×C412yes—
529C2×C4×C11C23×C414yes—
530C2×C4×C11C22×D412yes—
531C2×C4×C11C22×D412yes—
532C2×C4×C11H(5,𝔽2)14yes—
533C22⋊D11—28no—
534C22⋊D11—28no—
535C22⋊D11—216no—
536C22⋊D11—216no—
537C22⋊D11—48no—
538C2×Dic11—28no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—21no—
548C2×Dic11—21no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—44no—
558C2×Dic11—44no—
559C2×Dic11—82no—
560C2×Dic11C23×C414yes—
561C2×Dic11C23×C414yes—
562C2×Dic11C23×C412yes—
563C2×Dic11C22×D412yes—
564C2×Dic11C22×D412yes—
565D44—28no—
566C4×D11—28no—
567C4×D11—48no—
568C4×D11—48no—
569C4×D11—48no—
570C4×D11—82no—
571C4×D11—82no—
572C4×D11—82no—
573C4×D11—82no—
574C4×D11—84no—
575C23×D4—111no—
576C23×D4—111no—
577C24×C4—111no—
578C24×C4C2×D1111yescharacteristic, complemented
579#534—1116no—
580C2×#123—111no—
581C2×#123—111no—
582C2×#123—112no—
583C2×#121—112no—
584C2×#121—112no—
585C2×#120—111no—
586C2×#120—112no—
587C2×#120C2×D1111yescharacteristic
588#518—228no—
589C2×C4×D4—111no—
590C2×C4×D4—111no—
591C2×C4×D4—112no—
592C2×C4×D4—112no—
593C2×C4×D4—111no—
594C2×C4×D4—112no—
595C2×C4×D4—112no—
596C2×C4×D4—112no—
597C2×C4×D4—111no—
598C2×C4×D4—111no—
599C2×C4×D4—111no—
600C2×C4×D4—111no—
601C2×C4×D4—228no—
602C2×C4×D4C2×D1111yescharacteristic
603C2×C4×D4C2×D1112yescomplemented
604C2×#117—111no—
605C2×#117—111no—
606C22×C4⋊C4—111no—
607C22×C4⋊C4—112no—
608C22×C22⋊C4—111no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4—111no—
611C22×C22⋊C4—111no—
612C22×C22⋊C4—111no—
613C22×C22⋊C4—111no—
614C22×C22⋊C4—111no—
615C22×C22⋊C4—112no—
616C22×C42—111no—
617#390—112no—
618#390—112no—
619#389—112no—
620#389—112no—
621#388—112no—
622#388—112no—
623#388—112no—
624#388—112no—
625#388—112no—
626#388—112no—
627#388—112no—
628#388—112no—
629#387—112no—
630#387—112no—
631#387—112no—
632#387—112no—
633#386—111no—
634#386—112no—
635#386—112no—
636#386—111no—
637#386—112no—
638#386—112no—
639#386—112no—
640#386—112no—
641#386—111no—
642#386—112no—
643#386—112no—
644#386—112no—
645#386C2×D1111yescharacteristic
646#386C2×D1112yescomplemented
647#385—112no—
648#385—112no—
649#385—111no—
650#385—112no—
651#385—111no—
652#385—111no—
653#385—112no—
654#385—112no—
655#385C2×D1112yescomplemented
656#385C2×D1111yescharacteristic, complemented
657#381—111no—
658#381—111no—
659#379—111no—
660#379C2×D1111yescharacteristic, complemented
661C4×C4⋊C4—112no—
662C4×C4⋊C4—112no—
663C4×C22⋊C4—111no—
664C4×C22⋊C4—112no—
665C4×C22⋊C4—111no—
666C4×C22⋊C4—111no—
667C4×C22⋊C4—112no—
668C4×C22⋊C4—112no—
669C4×C22⋊C4—112no—
670C4×C22⋊C4—112no—
671C4×C22⋊C4—112no—
672C4×C22⋊C4—112no—
673C4×C22⋊C4C2×D1111yescharacteristic, complemented
674C4×C22⋊C4C2×D1112yescomplemented
675C2×#95—112no—
676C2×#95—112no—
677C22×C11—24no—
678C22×C11—22no—
679C22×C11—22no—
680C22×C11—24no—
681C22×C11—22no—
682C22×C11—24no—
683C22×C11—24no—
684C22×C11—24no—
685C22×C11—24no—
686C22×C11—416no—
687C22×C11—42no—
688C22×C11—41no—
689C22×C11—41no—
690C22×C11—42no—
691C22×C11—42no—
692C22×C11—42no—
693C22×C11—42no—
694C22×C11C2×C4×D414yes—
695C22×C11C24×C411yescharacteristic
696C22×C11C23×D411yescharacteristic
697C22×C11C22×#4111yescharacteristic
698C22×C11C2×H(5,𝔽2)12yes—
699C22×C11#58512yes—
700C2×D11—24no—
701C2×D11—24no—
702C2×D11—22no—
703C2×D11—22no—
704C2×D11—22no—
705C2×D11—22no—
706C2×D11—24no—
707C2×D11—24no—
708C2×D11—22no—
709C2×D11—24no—
710C2×D11—416no—
711C2×D11—41no—
712C2×D11—41no—
713C2×D11—42no—
714C2×D11—88no—
715C2×D11C2×C4×D414yes—
716C2×D11C2×C4×D414yes—
717C4×C11—22no—
718C4×C11—24no—
719C4×C11—24no—
720C4×C11—22no—
721C4×C11—22no—
722C4×C11—41no—
723C4×C11—41no—
724C4×C11—42no—
725Dic11—22no—
726Dic11—24no—
727Dic11—24no—
728Dic11—22no—
729Dic11—22no—
730Dic11—42no—
731Dic11—41no—
732Dic11—41no—
733Dic11—42no—
734C25—111no—
735C25—111no—
736C25C22×D1111yescharacteristic
737C22×D4—118no—
738C22×D4—112no—
739C22×D4—111no—
740C22×D4—112no—
741C22×D4—111no—
742C22×D4—112no—
743C22×D4—118no—
744C22×D4—111no—
745C22×D4—224no—
746C22×D4—224no—
747C22×D4—224no—
748C22×D4—224no—
749C22×D4C22×D1111yescharacteristic
750C22×D4C22×D1112yes—
751C23×C4—24no—
752C23×C4—44no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—111no—
756C23×C4—112no—
757C23×C4—111no—
758C23×C4—111no—
759C23×C4—112no—
760C23×C4—112no—
761C23×C4—112no—
762C23×C4—111no—
763C23×C4—111no—
764C23×C4—111no—
765C23×C4—111no—
766C23×C4—224no—
767C23×C4—444no—
768C23×C4C22×D1111yescharacteristic
769C23×C4C22×D1112yes—
770C23×C4C22×D1112yes—
771C23×C4C22×D1111yescharacteristic
772C23×C4C22×D1111yescharacteristic
773#123—118no—
774#123—118no—
775#123—1116no—
776#121—1116no—
777#121—1116no—
778#120—118no—
779#120—1116no—
780#120C4×D1118yescomplemented
781C4×D4—24no—
782C4×D4—44no—
783C4×D4—224no—
784C4×D4—224no—
785C4×D4—224no—
786C4×D4—224no—
787C4×D4—228no—
788C4×D4—228no—
789C4×D4—228no—
790C4×D4—228no—
791C4×D4—224no—
792C4×D4—224no—
793C4×D4—224no—
794C4×D4—444no—
795#117—224no—
796#117—224no—
797C2×C4⋊C4—112no—
798C2×C4⋊C4—112no—
799C2×C4⋊C4—112no—
800C2×C4⋊C4—112no—
801C2×C4⋊C4—112no—
802C2×C4⋊C4—111no—
803C2×C4⋊C4—111no—
804C2×C4⋊C4—111no—
805C2×C4⋊C4—112no—
806C2×C4⋊C4—112no—
807C2×C4⋊C4—224no—
808C2×C4⋊C4—444no—
809C2×C4⋊C4C22×D1112yes—
810C2×C4⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4—111no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—118no—
815C2×C22⋊C4—111no—
816C2×C22⋊C4—111no—
817C2×C22⋊C4—111no—
818C2×C22⋊C4—111no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—118no—
822C2×C22⋊C4—111no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—111no—
826C2×C22⋊C4—111no—
827C2×C22⋊C4—111no—
828C2×C22⋊C4—111no—
829C2×C22⋊C4—111no—
830C2×C22⋊C4—111no—
831C2×C22⋊C4—112no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—224no—
838C2×C22⋊C4—224no—
839C2×C22⋊C4—224no—
840C2×C22⋊C4—224no—
841C2×C22⋊C4—224no—
842C2×C22⋊C4—444no—
843C2×C22⋊C4C22×D1111yescharacteristic
844C2×C22⋊C4C22×D1111yescharacteristic
845C2×C22⋊C4C22×D1112yes—
846C2×C22⋊C4C22×D1111yescharacteristic
847C2×C22⋊C4C22×D1112yes—
848C2×C22⋊C4C22×D1112yes—
849C2×C22⋊C4C22×D1111yescharacteristic
850C2×C22⋊C4C22×D1112yes—
851C2×C42—111no—
852C2×C42—111no—
853C2×C42—111no—
854C2×C42—112no—
855C2×C42—112no—
856C2×C42—112no—
857C2×C42—112no—
858C2×C42—112no—
859C2×C42—224no—
860C2×C42C22×D1111yescharacteristic
861C2×C42C22×D1112yes—
862#95—112no—
863#95—112no—
864#95—112no—
865#95—112no—
866#95—112no—
867#95—112no—
868#95—112no—
869#95—112no—
870#95—112no—
871#95—112no—
872#95—112no—
873#95—112no—
874#95—112no—
875#95C22×D1112yes—
876#95C22×D1112yes—
877#95C22×D1112yes—
878C2×C11—24no—
879C2×C11—42no—
880C2×C11—44no—
881C2×C11C22×C4×D411yescharacteristic
882C2×C11C4×H(5,𝔽2)12yes—
883C2×C11#348411yescharacteristic
884C2×C11#348511yescharacteristic
885C2×C11#350512yes—
886D11—24no—
887D11—24no—
888D11—42no—
889C24—22no—
890C24—22no—
891C24—42no—
892C24—42no—
893C24—111no—
894C24—111no—
895C24—114no—
896C24—114no—
897C24—114no—
898C24—111no—
899C24—114no—
900C24—222no—
901C24—222no—
902C24—442no—
903C24—442no—
904C24—442no—
905C24—442no—
906C24C2×C4×D1114yes—
907C24C23×D1111yescharacteristic
908C24C23×D1112yes—
909C24C23×D1111yescharacteristic
910C2×D4—22no—
911C2×D4—22no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—118no—
915C2×D4—114no—
916C2×D4—118no—
917C2×D4—114no—
918C2×D4—118no—
919C2×D4—114no—
920C2×D4—222no—
921C2×D4—222no—
922C2×D4—2232no—
923C2×D4—222no—
924C2×D4—224no—
925C2×D4—224no—
926C2×D4—2232no—
927C2×D4—222no—
928C2×D4—224no—
929C2×D4—224no—
930C2×D4—222no—
931C2×D4—222no—
932C2×D4—442no—
933C2×D4—442no—
934C2×D4C2×C4×D1114yes—
935C2×D4C2×C4×D1118yescomplemented
936C22×C4—22no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—24no—
942C22×C4—22no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—416no—
948C22×C4—114no—
949C22×C4—112no—
950C22×C4—111no—
951C22×C4—112no—
952C22×C4—111no—
953C22×C4—111no—
954C22×C4—114no—
955C22×C4—114no—
956C22×C4—118no—
957C22×C4—112no—
958C22×C4—111no—
959C22×C4—112no—
960C22×C4—111no—
961C22×C4—222no—
962C22×C4—222no—
963C22×C4—222no—
964C22×C4—224no—
965C22×C4—224no—
966C22×C4—222no—
967C22×C4—222no—
968C22×C4—224no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—222no—
973C22×C4—224no—
974C22×C4—224no—
975C22×C4—222no—
976C22×C4—442no—
977C22×C4—442no—
978C22×C4—442no—
979C22×C4—442no—
980C22×C4—442no—
981C22×C4—442no—
982C22×C4—442no—
983C22×C4—442no—
984C22×C4—442no—
985C22×C4—442no—
986C22×C4—4416no—
987C22×C4—442no—
988C22×C4—442no—
989C22×C4—442no—
990C22×C4D4×D1114yes—
991C22×C4C23×D1112yes—
992C22×C4C23×D1111yescharacteristic
993C22×C4C23×D1111yescharacteristic
994C22×C4C23×D1112yes—
995C22×C4C23×D1111yescharacteristic
996C22×C4C23×D1111yescharacteristic
997C22×C4C23×D1111yescharacteristic
998C22×C4C23×D1112yes—
999C4⋊C4—22no—
1000C4⋊C4—24no—
1001C4⋊C4—118no—
1002C4⋊C4—118no—
1003C4⋊C4—222no—
1004C4⋊C4—222no—
1005C4⋊C4—224no—
1006C4⋊C4—224no—
1007C4⋊C4—222no—
1008C4⋊C4—224no—
1009C4⋊C4—442no—
1010C4⋊C4—442no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—24no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—114no—
1018C22⋊C4—118no—
1019C22⋊C4—118no—
1020C22⋊C4—118no—
1021C22⋊C4—118no—
1022C22⋊C4—114no—
1023C22⋊C4—114no—
1024C22⋊C4—114no—
1025C22⋊C4—114no—
1026C22⋊C4—222no—
1027C22⋊C4—222no—
1028C22⋊C4—222no—
1029C22⋊C4—224no—
1030C22⋊C4—222no—
1031C22⋊C4—224no—
1032C22⋊C4—224no—
1033C22⋊C4—222no—
1034C22⋊C4—222no—
1035C22⋊C4—222no—
1036C22⋊C4—224no—
1037C22⋊C4—442no—
1038C22⋊C4—442no—
1039C22⋊C4—442no—
1040C22⋊C4—442no—
1041C22⋊C4C2×C4×D1114yes—
1042C22⋊C4C2×C4×D1118yescomplemented
1043C42—22no—
1044C42—42no—
1045C42—224no—
1046C42—224no—
1047C42—222no—
1048C42—222no—
1049C42—222no—
1050C42—442no—
1051C42—442no—
1052C42—442no—
1053C11#3426411yescharacteristic, complemented, Sylow
1054C23—22no—
1055C23—22no—
1056C23—28no—
1057C23—21no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—21no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—48no—
1068C23—44no—
1069C23—48no—
1070C23—44no—
1071C23—112no—
1072C23—112no—
1073C23—112no—
1074C23—112no—
1075C23—112no—
1076C23—112no—
1077C23—1116no—
1078C23—112no—
1079C23—228no—
1080C23—222no—
1081C23—222no—
1082C23—222no—
1083C23—222no—
1084C23—221no—
1085C23—222no—
1086C23—221no—
1087C23—222no—
1088C23—444no—
1089C23—448no—
1090C23—444no—
1091C23—448no—
1092C23—448no—
1093C23—884no—
1094C23—882no—
1095C23—882no—
1096C23C22×C4×D1112yes—
1097C23C22×C4×D1114yes—
1098C23C22×C4×D1112yes—
1099C23C2×D4×D1112yes—
1100C23#41×D1112yes—
1101C23C24×D1111yescharacteristic
1102D4—28no—
1103D4—48no—
1104D4—228no—
1105D4—228no—
1106D4—2216no—
1107D4—2216no—
1108D4—228no—
1109D4—448no—
1110C2×C4—28no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—44no—
1127C2×C4—48no—
1128C2×C4—48no—
1129C2×C4—82no—
1130C2×C4—114no—
1131C2×C4—112no—
1132C2×C4—114no—
1133C2×C4—112no—
1134C2×C4—112no—
1135C2×C4—228no—
1136C2×C4—228no—
1137C2×C4—222no—
1138C2×C4—221no—
1139C2×C4—222no—
1140C2×C4—221no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—222no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—448no—
1156C2×C4—448no—
1157C2×C4—448no—
1158C2×C4—444no—
1159C2×C4—444no—
1160C2×C4—882no—
1161C2×C4—882no—
1162C2×C4—884no—
1163C2×C4—882no—
1164C2×C4—882no—
1165C2×C4—882no—
1166C2×C4C22×C4×D1114yes—
1167C2×C4C22×C4×D1112yes—
1168C2×C4C2×D4×D1112yes—
1169C2×C4C2×D4×D1112yes—
1170C2×C4#6703714yes—
1171C22—24no—
1172C22—22no—
1173C22—22no—
1174C22—24no—
1175C22—22no—
1176C22—24no—
1177C22—24no—
1178C22—24no—
1179C22—24no—
1180C22—416no—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—41no—
1186C22—41no—
1187C22—42no—
1188C22—114no—
1189C22—114no—
1190C22—224no—
1191C22—224no—
1192C22—222no—
1193C22—222no—
1194C22—222no—
1195C22—222no—
1196C22—224no—
1197C22—224no—
1198C22—222no—
1199C22—224no—
1200C22—4416no—
1201C22—442no—
1202C22—441no—
1203C22—441no—
1204C22—888no—
1205C22C4×D4×D1114yes—
1206C22C23×C4×D1111yescharacteristic
1207C22C22×D4×D1111yescharacteristic
1208C22C2×#6703712yes—
1209C22C2×#41×D1111yescharacteristic
1210C22#1062345312yes—
1211C4—24no—
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—24no—
1216C4—42no—
1217C4—41no—
1218C4—41no—
1219C4—222no—
1220C4—222no—
1221C4—222no—
1222C4—224no—
1223C4—224no—
1224C4—442no—
1225C4—442no—
1226C4—441no—
1227C4—441no—
1228C2—24no—
1229C2—44no—
1230C2—42no—
1231C2—224no—
1232C2—224no—
1233C2—442no—
1234C2C2×C4×D4×D1111yescharacteristic
1235C2C4×#6703712yes—
1236C2#1308224511yescharacteristic
1237C2#1308225811yescharacteristic
1238C2#1308244412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#120C2
socle, cosocleC23×C11C25
prime radicalC2×#10623120C2
hypercenterC4×#120D11
hypocenterC11#34264
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
2. C2×#10623076C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. #13071667C2semidirect
5. #13071665C2semidirect
6. #13071635C2semidirect
7. #13071628C2semidirect
8. #13071611C2semidirect
9. #13071609C2semidirect
10. #13071599C2semidirect
11. #13071593C2semidirect
12. #13071287C2semidirect
13. #13071281C2semidirect
14. #13071277C2semidirect
15. #13071271C2semidirect
16. #13071192C2semidirect
17. #13071141C2semidirect
18. #13071135C2semidirect
19. C4×#67006C2semidirect
20. D11×#386C2semidirect
21. D11×#385C2semidirect
22. #13070968C2semidirect
23. C4×C11×#120C2semidirect
24. C24×C4×C11C22semidirect
30. C2×C4×D4×C11C22semidirect
32. C22×C22⋊Dic11C22semidirect
41. C2×C4×C22⋊D11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
43. C2×C4×C22⋊D11C22semidirect
44. C2×C4×C22⋊D11C22semidirect
46. C22×(C2×D11)⋊C4C22semidirect
47. C22×Dic11⋊C4C22semidirect
48. C22×C4×Dic11C22semidirect
49. #10623120C4semidirect
51. C2×#66946C22semidirect
52. C2×#66945C22semidirect
53. C2×C4⋊C4×D11C22semidirect
58. C2×(C22⋊D11)⋊C4C22semidirect
62. C2×C22⋊C4×D11C22semidirect
63. C2×C22⋊C4×D11C22semidirect
64. C2×C4×D44C22semidirect
65. C2×#66925C22semidirect
67. C11×#386C22semidirect
68. C11×#385C22semidirect
69. C11×#385C22semidirect
70. C11×#379C22semidirect
71. C4×C11×C22⋊C4C22semidirect
72. C4×C11×C22⋊C4C22semidirect
73. #10622860C22semidirect
74. #10622834C22semidirect
76. #10622833C22semidirect
78. #10622826C22semidirect
79. #10622823C22semidirect
80. #10622823C22semidirect
81. #10622823C22semidirect
82. C4×C22⋊Dic11C22semidirect
83. C4×C22⋊Dic11C22semidirect
84. #10622603C22semidirect
85. #10622602C22semidirect
86. C4⋊C4×Dic11C22semidirect
87. #10622585C22semidirect
89. #10622570C22semidirect
92. #10622569C22semidirect
93. #10622569C22semidirect
94. #10622569C22semidirect
95. #10622569C22semidirect
96. #10622564C22semidirect
97. #10622564C22semidirect
98. #10622563C22semidirect
99. #10622559C22semidirect
100. #10622558C22semidirect
101. #10622558C22semidirect
102. #10622558C22semidirect
103. #10622557C22semidirect
104. #10622556C22semidirect
105. #10622556C22semidirect
106. C22⋊C4×Dic11C22semidirect
107. C22⋊C4×Dic11C22semidirect
108. C22⋊C4×Dic11C22semidirect
109. #10622553C22semidirect
110. C4×(C2×D11)⋊C4C22semidirect
111. C4×(C2×D11)⋊C4C22semidirect
112. #10622546C22semidirect
113. #10622541C22semidirect
114. #10622281C22semidirect
115. #10622281C22semidirect
116. #10622279C22semidirect
117. #10622279C22semidirect
118. #10622279C22semidirect
119. #10622278C22semidirect
120. D11×#95C22semidirect
121. D11×#95C22semidirect
122. #10622268C22semidirect
123. #10622267C22semidirect
124. #10622266C22semidirect
125. #10622262C22semidirect
140. C22×C22⋊D11C2×C4semidirect
152. C2×D4×D11C2×C4semidirect
165. C11×#120C2×C4semidirect
180. #67006C2×C4semidirect
193. #66991C2×C4semidirect
194. #66990C2×C4semidirect
195. #66988C2×C4semidirect
205. C2×(C2×D11)⋊C4D4semidirect
242. #66939C2×C4semidirect
243. #66937C2×C4semidirect
244. #66936C2×C4semidirect
251. C22⋊C4×D11C2×C4semidirect
286. C23×D11C22×C4semidirect
297. C2×D4×C11C22×C4semidirect
333. C2×C22⋊D11C22×C4semidirect
334. C2×C22⋊D11C22×C4semidirect
356. C2×D44C22×C4semidirect
379. C2×C4×D11C22×C4semidirect
380. C2×C4×D11C22×C4semidirect
390. C11×C22⋊C4C22×C4semidirect
402. C22⋊Dic11C22×C4semidirect
403. C22⋊Dic11C22×C4semidirect
411. (C2×D11)⋊C4C22×C4semidirect
412. (C2×D11)⋊C4C22×C4semidirect
419. C4⋊Dic11C22×C4semidirect
426. Dic11⋊C4C22×C4semidirect
454. C4×#120D11semidirect
498. C22×D11C4×D4semidirect
578. C24×C4C2×D11semidirect
603. C2×C4×D4C2×D11semidirect
646. #386C2×D11semidirect
655. #385C2×D11semidirect
656. #385C2×D11semidirect
660. #379C2×D11semidirect
673. C4×C22⋊C4C2×D11semidirect
674. C4×C22⋊C4C2×D11semidirect
780. #120C4×D11semidirect
935. C2×D4C2×C4×D11semidirect
1042. C22⋊C4C2×C4×D11semidirect
1053. C11#34264semidirect

Maximal subgroups

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

subgroupindex
C2×#106231202
C2×#106230762
C22×C4×C22⋊D112
#130716672
#130716652
#130716352
#130716282
#130716112
#130716092
#130715992
#130715932
#130712872
#130712812
#130712772
#130712712
#130711922
#130711412
#130711352
C4×#670062
D11×#3862
D11×#3852
#130709682
C4×C11×#1202
#3426411