Finite Group Databasebeta

← #14914105

Subgroups — #14914105

Order 2816.

3614 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C2×#10623017C211yesmaximal, characteristic, complemented
3C22×#66930C211yesmaximal, characteristic, complemented
4#13071657C212yesmaximal, complemented
5#13071651C212yesmaximal, complemented
6#13071633C212yesmaximal, complemented
7#13071627C212yesmaximal, complemented
8#13071468C211yesmaximal, characteristic, complemented
9#13071467C211yesmaximal, characteristic, complemented
10#13071462C211yesmaximal, characteristic, complemented
11#13071461C211yesmaximal, characteristic, complemented
12D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
13C22⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
14#13071432C211yesmaximal, characteristic, complemented
15#13071306C212yesmaximal, complemented
16#13071302C212yesmaximal, complemented
17#13071233C211yesmaximal, characteristic, complemented
18#13071197C211yesmaximal, characteristic, complemented
19#13071126C212yesmaximal, complemented
20C4×#66992C212yesmaximal, complemented
21#13070994C211yesmaximal, characteristic, complemented
22#13070971C211yesmaximal, characteristic, complemented
23D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×C22⋊D11C2211yescharacteristic
27C24×Dic11C2211yescharacteristic
28C2×C4×D4×C11C2212yescomplemented
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C2×#66992C4116yescomplemented
35C2×#66992C2211yescharacteristic
36C2×#66992C2211yescharacteristic
37C2×#66992C2211yescharacteristic
38C2×#66992C2211yescharacteristic
39C2×#66992C2211yescharacteristic
40C2×#66992C2211yescharacteristic
41C2×#66992C2211yescharacteristic
42C2×#66992C2211yescharacteristic
43C2×D4×Dic11C2212yescomplemented
44C2×C4×C22⋊D11C2212yescomplemented
45C2×C4×C22⋊D11C2212yescomplemented
46C2×C4×C22⋊D11C2212yescomplemented
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2212yescomplemented
50C22×C4×Dic11C2212yescomplemented
51#10623017—28no—
52C2×(C22⋊D11)⋊C4C2212yescomplemented
53C2×(C22⋊D11)⋊C4C2212yescomplemented
54C2×(C22⋊D11)⋊C4C2212yescomplemented
55C2×C22⋊C4×D11C2211yescharacteristic
56C2×C22⋊C4×D11C2211yescharacteristic
57C2×#66930—28no—
58C2×#66930C2211yescharacteristic
59C2×#66930C2211yescharacteristic
60C2×#66930C2211yescharacteristic
61C2×#66930C2211yescharacteristic
62C2×#66930C2211yescharacteristic
63C2×#66930C2211yescharacteristic
64C2×#66930C2212yescomplemented
65C2×#66930C2212yescomplemented
66C11×#390C2212yescomplemented
67C11×#386C2212yescomplemented
68C11×#386C2212yescomplemented
69C11×#380C2211yescharacteristic
70C11×#379C2211yescharacteristic
71C11×#379C2211yescharacteristic
72C4×C11×C22⋊C4C2211yescharacteristic
73#10622860C2211yescharacteristic
74#10622860C2211yescharacteristic
75#10622834C2212yescomplemented
76#10622833C2212yescomplemented
77#10622833C2212yescomplemented
78#10622826C2212yescomplemented
79#10622825C2211yescharacteristic
80#10622823C2212yescomplemented
81C4×C22⋊Dic11C2211yescharacteristic
82C4×C22⋊Dic11C2212yescomplemented
83#10622603C2212yescomplemented
84#10622602C2212yescomplemented
85#10622585C2212yescomplemented
86#10622585C2212yescomplemented
87#10622571C2212yescomplemented
88#10622570C2212yescomplemented
89#10622570C2212yescomplemented
90#10622570C2212yescomplemented
91#10622570C2212yescomplemented
92#10622570C2212yescomplemented
93#10622570C2212yescomplemented
94#10622569C2212yescomplemented
95#10622569C2212yescomplemented
96#10622568C2211yescharacteristic
97#10622568C2211yescharacteristic
98#10622559C2212yescomplemented
99#10622558C2212yescomplemented
100#10622558C2212yescomplemented
101#10622557C2212yescomplemented
102#10622557C2212yescomplemented
103#10622556C2211yescharacteristic
104#10622556C2211yescharacteristic
105#10622555C2211yescharacteristic
106#10622555C2211yescharacteristic
107#10622555C2212yescomplemented
108#10622555C2212yescomplemented
109C22⋊C4×Dic11C2211yescharacteristic
110C22⋊C4×Dic11C2211yescharacteristic
111C22⋊C4×Dic11C2212yescomplemented
112C22⋊C4×Dic11C2212yescomplemented
113C22⋊C4×Dic11C2212yescomplemented
114#10622553C2212yescomplemented
115C4×(C2×D11)⋊C4C2212yescomplemented
116C4×Dic11⋊C4C2212yescomplemented
117C4×Dic11⋊C4C2212yescomplemented
118#10622283C2212yescomplemented
119#10622282C2212yescomplemented
120#10622281C2212yescomplemented
121#10622279C2212yescomplemented
122#10622262C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125#10622260C2212yescomplemented
126C25×C11C2311yescharacteristic
127C25×C11C2311yescharacteristic
128C24×D11C2311yescharacteristic
129C22×D4×C11—44no—
130C22×D4×C11C2×C418yescomplemented
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C23×C4×C11C2312yes—
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11—24no—
139C22×C22⋊D11—24no—
140C22×C22⋊D11—44no—
141C22×C22⋊D11C2×C418yescomplemented
142C22×C22⋊D11C2×C418yescomplemented
143C22×C22⋊D11C2311yescharacteristic
144C22×C22⋊D11C2311yescharacteristic
145C22×C22⋊D11C2311yescharacteristic
146C22×C22⋊D11C2311yescharacteristic
147C22×C22⋊D11C2311yescharacteristic
148C22×C22⋊D11C2311yescharacteristic
149C22×C22⋊D11C2311yescharacteristic
150C22×C22⋊D11C2311yescharacteristic
151C23×Dic11—24no—
152C23×Dic11—24no—
153C23×Dic11C2×C418yescomplemented
154C23×Dic11C2312yes—
155C23×Dic11C2311yescharacteristic
156C23×Dic11C2311yescharacteristic
157C23×Dic11C2311yescharacteristic
158C23×Dic11C2311yescharacteristic
159C23×Dic11C2311yescharacteristic
160C23×Dic11C2312yes—
161C23×Dic11C2311yescharacteristic
162C23×Dic11C2311yescharacteristic
163C22×C4×D11C2312yes—
164C22×C4×D11C2312yes—
165C4×D4×C11—44no—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C22⋊C4—24no—
168C2×C11×C22⋊C4—24no—
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2311yescharacteristic
179C2×C42×C11C2312yes—
180C2×C22⋊Dic11—24no—
181C2×C22⋊Dic11—24no—
182C2×C22⋊Dic11C2×C418yescomplemented
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2311yescharacteristic
193C2×C22⋊Dic11C2311yescharacteristic
194C2×C22⋊Dic11C2311yescharacteristic
195C2×C22⋊Dic11C2311yescharacteristic
196C2×C22⋊Dic11C2311yescharacteristic
197#66992C2×C418yescomplemented
198#66992C2×C418yescomplemented
199#66992C2×C418yescomplemented
200#66992C2×C418yescomplemented
201#66992C2×C418yescomplemented
202#66992C2×C418yescomplemented
203#66992C2×C418yescomplemented
204#66992C2×C418yescomplemented
205D4×Dic11—44no—
206C4×C22⋊D11—28no—
207C4×C22⋊D11—28no—
208C4×C22⋊D11—44no—
209C2×(C2×D11)⋊C4C2×C418yescomplemented
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×(C2×D11)⋊C4C2312yes—
216C2×(C2×D11)⋊C4C2311yescharacteristic
217C2×(C2×D11)⋊C4C2311yescharacteristic
218C2×(C2×D11)⋊C4C2311yescharacteristic
219C2×(C2×D11)⋊C4C2311yescharacteristic
220C2×C4⋊Dic11C2312yes—
221C2×Dic11⋊C4—28no—
222C2×Dic11⋊C4C2×C418yescomplemented
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2312yes—
230C2×Dic11⋊C4C2311yescharacteristic
231C2×Dic11⋊C4C2311yescharacteristic
232C2×Dic11⋊C4C2311yescharacteristic
233C2×Dic11⋊C4C2311yescharacteristic
234C2×Dic11⋊C4C2312yes—
235C2×C4×Dic11—28no—
236C2×C4×Dic11C2312yes—
237C2×C4×Dic11C2312yes—
238C2×C4×Dic11C2312yes—
239C2×C4×Dic11C2312yes—
240C2×C4×Dic11C2312yes—
241C2×C4×Dic11C2312yes—
242C2×C4×Dic11C2312yes—
243C2×C4×Dic11C2312yes—
244C2×C4×Dic11C2312yes—
245(C22⋊D11)⋊C4—28no—
246(C22⋊D11)⋊C4—28no—
247(C22⋊D11)⋊C4—44no—
248C22⋊C4×D11—24no—
249C22⋊C4×D11—24no—
250#66930—24no—
251#66930—24no—
252#66930—24no—
253#66930—24no—
254#66930—24no—
255#66930—28no—
256#66930—28no—
257#66930D418yescomplemented
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#34204—111nomaximal, Sylow
271C24×C11—22no—
272C24×C11—22no—
273C24×C11—24no—
274C24×C11—22no—
275C24×C11—22no—
276C24×C11—42no—
277C24×C11—42no—
278C24×C11—42no—
279C24×C11C22×C414yes—
280C24×C11C22×C414yes—
281C24×C11C2411yescharacteristic
282C24×C11C2411yescharacteristic
283C24×C11C2411yescharacteristic
284C24×C11C2411yescharacteristic
285C24×C11C2411yescharacteristic
286C23×D11—22no—
287C23×D11—22no—
288C23×D11—42no—
289C23×D11—42no—
290C23×D11C22×C414yes—
291C23×D11C2411yescharacteristic
292C23×D11C2411yescharacteristic
293C2×D4×C11—24no—
294C2×D4×C11—24no—
295C2×D4×C11—42no—
296C2×D4×C11—42no—
297C2×D4×C11—416no—
298C2×D4×C11C22×C414yes—
299C2×D4×C11C22×C414yes—
300C2×D4×C11C22×C414yes—
301C2×D4×C11C22×C414yes—
302C22×C4×C11—24no—
303C22×C4×C11—24no—
304C22×C4×C11—24no—
305C22×C4×C11—42no—
306C22×C4×C11—42no—
307C22×C4×C11—42no—
308C22×C4×C11—42no—
309C22×C4×C11C22×C414yes—
310C22×C4×C11C2412yes—
311C22×C4×C11C2412yes—
312C22×C4×C11C2412yes—
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2411yescharacteristic
315C22×C4×C11C2412yes—
316C2×C22⋊D11—232no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—22no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—22no—
322C2×C22⋊D11—22no—
323C2×C22⋊D11—22no—
324C2×C22⋊D11—22no—
325C2×C22⋊D11—24no—
326C2×C22⋊D11—24no—
327C2×C22⋊D11—42no—
328C2×C22⋊D11—42no—
329C2×C22⋊D11—416no—
330C2×C22⋊D11C22×C414yes—
331C2×C22⋊D11C22×C414yes—
332C2×C22⋊D11C22×C414yes—
333C2×C22⋊D11C22×C414yes—
334C2×C22⋊D11C22×C414yes—
335C2×C22⋊D11C22×C414yes—
336C2×C22⋊D11C22×C414yes—
337C2×C22⋊D11C22×C414yes—
338C22×Dic11—232no—
339C22×Dic11—22no—
340C22×Dic11—22no—
341C22×Dic11—22no—
342C22×Dic11—22no—
343C22×Dic11—22no—
344C22×Dic11—22no—
345C22×Dic11—22no—
346C22×Dic11—22no—
347C22×Dic11—24no—
348C22×Dic11—24no—
349C22×Dic11—22no—
350C22×Dic11—22no—
351C22×Dic11—24no—
352C22×Dic11—42no—
353C22×Dic11—42no—
354C22×Dic11—42no—
355C22×Dic11—42no—
356C22×Dic11C22×C414yes—
357C22×Dic11C22×C414yes—
358C22×Dic11C22×C414yes—
359C22×Dic11C22×C414yes—
360C22×Dic11C22×C414yes—
361C22×Dic11C22×C414yes—
362C22×Dic11C22×C414yes—
363C22×Dic11C2×D414yes—
364C22×Dic11#4114yes—
365C22×Dic11C2412yes—
366C22×Dic11C2412yes—
367C22×Dic11C2412yes—
368C22×Dic11C2411yescharacteristic
369C22×Dic11C2411yescharacteristic
370C22×Dic11C2411yescharacteristic
371C22×Dic11C2411yescharacteristic
372C22×Dic11C2412yes—
373C22×Dic11C2411yescharacteristic
374C22×Dic11C2411yescharacteristic
375C2×C4×D11—24no—
376C2×C4×D11—24no—
377C2×C4×D11—42no—
378C2×C4×D11—42no—
379C2×C4×D11—42no—
380C2×C4×D11—42no—
381C11×C4⋊C4—42no—
382C11×C22⋊C4—22no—
383C11×C22⋊C4—22no—
384C11×C22⋊C4—22no—
385C11×C22⋊C4—24no—
386C11×C22⋊C4—24no—
387C11×C22⋊C4—24no—
388C11×C22⋊C4—42no—
389C11×C22⋊C4—42no—
390C11×C22⋊C4—42no—
391C11×C22⋊C4C2×D414yes—
392C42×C11—42no—
393C22⋊Dic11—24no—
394C22⋊Dic11—24no—
395C22⋊Dic11—22no—
396C22⋊Dic11—22no—
397C22⋊Dic11—22no—
398C22⋊Dic11—24no—
399C22⋊Dic11—42no—
400C22⋊Dic11—42no—
401C22⋊Dic11—42no—
402C22⋊Dic11C22×C414yes—
403C22⋊Dic11C22×C414yes—
404C22⋊Dic11C22×C414yes—
405C22⋊Dic11C22×C414yes—
406C22⋊Dic11C2×D414yes—
407(C2×D11)⋊C4—24no—
408(C2×D11)⋊C4—24no—
409(C2×D11)⋊C4—42no—
410(C2×D11)⋊C4—42no—
411(C2×D11)⋊C4—42no—
412(C2×D11)⋊C4—42no—
413(C2×D11)⋊C4C22×C414yes—
414(C2×D11)⋊C4C22×C414yes—
415(C2×D11)⋊C4C22×C414yes—
416(C2×D11)⋊C4C22×C414yes—
417C4⋊Dic11—42no—
418Dic11⋊C4—24no—
419Dic11⋊C4—24no—
420Dic11⋊C4—24no—
421Dic11⋊C4—24no—
422Dic11⋊C4—24no—
423Dic11⋊C4—42no—
424Dic11⋊C4—42no—
425Dic11⋊C4C22×C414yes—
426Dic11⋊C4C22×C414yes—
427Dic11⋊C4C22×C414yes—
428Dic11⋊C4C22×C414yes—
429Dic11⋊C4C2×D418yescomplemented
430C4×Dic11—24no—
431C4×Dic11—24no—
432C4×Dic11—24no—
433C4×Dic11—24no—
434C4×Dic11—24no—
435C4×Dic11—42no—
436C4×Dic11—42no—
437C4×Dic11—42no—
438C4×Dic11C2×D418yescomplemented
439C22×#121—111no—
440C2×#518—111no—
441C22×#117—111no—
442#2363—112no—
443#2363—112no—
444#2361—112no—
445#2361—112no—
446#2342—111no—
447#2342—111no—
448#2342—111no—
449#2342—111no—
450D4×C22⋊C4—111no—
451D4×C22⋊C4—111no—
452D4×C22⋊C4—111no—
453D4×C22⋊C4D1111yescharacteristic, complemented
454#2324—112no—
455#2324—112no—
456#2316—111no—
457#2309—111no—
458C4×#121—112no—
459C4×#121—112no—
460#2280—111no—
461#2274—111no—
462C23×C11—21no—
463C23×C11—21no—
464C23×C11—22no—
465C23×C11—22no—
466C23×C11—22no—
467C23×C11—28no—
468C23×C11—28no—
469C23×C11—21no—
470C23×C11—21no—
471C23×C11—21no—
472C23×C11—21no—
473C23×C11—21no—
474C23×C11—21no—
475C23×C11—22no—
476C23×C11—22no—
477C23×C11—22no—
478C23×C11—22no—
479C23×C11—22no—
480C23×C11—22no—
481C23×C11—28no—
482C23×C11—44no—
483C23×C11—44no—
484C23×C11—44no—
485C23×C11—48no—
486C23×C11—48no—
487C23×C11—84no—
488C23×C11—84no—
489C23×C11C23×C412yes—
490C23×C11C23×C412yes—
491C23×C11C23×C412yes—
492C23×C11C23×C412yes—
493C23×C11C23×C412yes—
494C23×C11C22×D412yes—
495C23×C11C2×#4112yes—
496C23×C11H(5,𝔽2)14yes—
497C23×C11C2511yescharacteristic
498C22×D11—21no—
499C22×D11—21no—
500C22×D11—21no—
501C22×D11—21no—
502C22×D11—22no—
503C22×D11—22no—
504C22×D11—22no—
505C22×D11—22no—
506C22×D11—28no—
507C22×D11—44no—
508C22×D11—44no—
509C22×D11—84no—
510C22×D11—84no—
511C22×D11C23×C412yes—
512C22×D11C23×C412yes—
513D4×C11—28no—
514D4×C11—28no—
515D4×C11—44no—
516D4×C11—44no—
517C2×C4×C11—22no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—22no—
521C2×C4×C11—22no—
522C2×C4×C11—22no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—44no—
531C2×C4×C11—48no—
532C2×C4×C11—84no—
533C2×C4×C11C23×C412yes—
534C2×C4×C11C23×C412yes—
535C2×C4×C11C22×D414yes—
536C22⋊D11—28no—
537C22⋊D11—28no—
538C22⋊D11—28no—
539C22⋊D11—28no—
540C22⋊D11—28no—
541C22⋊D11—28no—
542C22⋊D11—44no—
543C22⋊D11—44no—
544C2×Dic11—28no—
545C2×Dic11—21no—
546C2×Dic11—21no—
547C2×Dic11—21no—
548C2×Dic11—21no—
549C2×Dic11—22no—
550C2×Dic11—22no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—28no—
554C2×Dic11—28no—
555C2×Dic11—28no—
556C2×Dic11—28no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—44no—
567C2×Dic11—48no—
568C2×Dic11—84no—
569C2×Dic11C4×D4116yescomplemented
570C2×Dic11C23×C412yes—
571C2×Dic11C23×C412yes—
572C2×Dic11C23×C412yes—
573C2×Dic11C23×C412yes—
574C2×Dic11C23×C412yes—
575C2×Dic11C23×C412yes—
576C2×Dic11C22×D414yes—
577C2×Dic11C22×D412yes—
578C2×Dic11C22×D412yes—
579C2×Dic11C2×#4112yes—
580C2×Dic11C2×#4112yes—
581C4×D11—84no—
582C4×D11—84no—
583C23×D4—111no—
584C23×D4—111no—
585C23×D4C2×D1111yescharacteristic
586C24×C4—111no—
587C2×#121—111no—
588C2×#121—111no—
589C2×#121—111no—
590C2×#121—111no—
591C2×#121—111no—
592C2×#121—111no—
593C2×#121—111no—
594C2×#121—111no—
595C2×#121—1116no—
596#518—228no—
597C2×C4×D4—112no—
598C2×C4×D4—112no—
599C2×C4×D4—112no—
600C2×C4×D4—112no—
601C2×C4×D4—112no—
602C2×C4×D4—112no—
603C2×C4×D4—112no—
604C2×C4×D4C2×D1112yescomplemented
605C2×#117—111no—
606C2×#117—111no—
607C2×#117—111no—
608C2×#117—111no—
609C2×#117—112no—
610C2×#117—111no—
611C2×#117—111no—
612C2×#117—112no—
613C2×#117—228no—
614C22×C4⋊C4—111no—
615C22×C4⋊C4—112no—
616C22×C22⋊C4—111no—
617C22×C22⋊C4—111no—
618C22×C22⋊C4—111no—
619C22×C22⋊C4—111no—
620C22×C22⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4C2×D1111yescharacteristic
623C22×C22⋊C4C2×D1111yescharacteristic
624C22×C42—112no—
625#390—112no—
626#390—112no—
627#390—112no—
628#390—112no—
629#390—112no—
630#390—112no—
631#390—112no—
632#390C2×D1112yescomplemented
633#389—112no—
634#389—112no—
635#389—112no—
636#389—112no—
637#388—112no—
638#388—112no—
639#388—112no—
640#388—112no—
641#388—112no—
642#388—112no—
643#388—112no—
644#388—112no—
645#386—112no—
646#386—112no—
647#386—112no—
648#386—112no—
649#386—112no—
650#386—112no—
651#386C2×D1112yescomplemented
652#386C2×D1112yescomplemented
653#385—112no—
654#385—112no—
655#385—112no—
656#385—112no—
657#381—111no—
658#381—111no—
659#380—111no—
660#380—111no—
661#380—111no—
662#380—112no—
663#380—112no—
664#380C2×D1111yescharacteristic
665#379—111no—
666#379—111no—
667#379—111no—
668#379—111no—
669#379C2×D1111yescharacteristic
670#379C2×D1111yescharacteristic
671C4×C4⋊C4—112no—
672C4×C4⋊C4—112no—
673C4×C4⋊C4—112no—
674C4×C4⋊C4—112no—
675C4×C22⋊C4—111no—
676C4×C22⋊C4—112no—
677C4×C22⋊C4—111no—
678C4×C22⋊C4—111no—
679C4×C22⋊C4—112no—
680C4×C22⋊C4—112no—
681C4×C22⋊C4—112no—
682C4×C22⋊C4—112no—
683C4×C22⋊C4—112no—
684C4×C22⋊C4C2×D1111yescharacteristic
685C22×C11—22no—
686C22×C11—22no—
687C22×C11—22no—
688C22×C11—22no—
689C22×C11—24no—
690C22×C11—24no—
691C22×C11—24no—
692C22×C11—24no—
693C22×C11—22no—
694C22×C11—22no—
695C22×C11—22no—
696C22×C11—22no—
697C22×C11—22no—
698C22×C11—22no—
699C22×C11—22no—
700C22×C11—22no—
701C22×C11—22no—
702C22×C11—416no—
703C22×C11—42no—
704C22×C11—42no—
705C22×C11—42no—
706C22×C11—42no—
707C22×C11—42no—
708C22×C11—42no—
709C22×C11—88no—
710C22×C11C2×C4×D414yes—
711C22×C11#51814yescomplemented
712C22×C11C24×C411yescharacteristic
713C22×C11C23×D411yescharacteristic
714C22×C11C22×#4111yescharacteristic
715C22×C11C2×H(5,𝔽2)12yes—
716C22×C11#58512yes—
717C2×D11—22no—
718C2×D11—22no—
719C2×D11—22no—
720C2×D11—22no—
721C2×D11—22no—
722C2×D11—22no—
723C2×D11—42no—
724C2×D11—42no—
725C2×D11—42no—
726C2×D11—42no—
727C2×D11—88no—
728C4×C11—22no—
729C4×C11—22no—
730C4×C11—24no—
731C4×C11—42no—
732C4×C11—42no—
733C4×C11—42no—
734Dic11—22no—
735Dic11—22no—
736Dic11—22no—
737Dic11—22no—
738Dic11—24no—
739Dic11—42no—
740Dic11—42no—
741Dic11—42no—
742Dic11C2×C4×D414yes—
743Dic11C2×C4×D414yes—
744C25—111no—
745C25C22×D1111yescharacteristic
746C25C22×D1111yescharacteristic
747C22×D4—44no—
748C22×D4—118no—
749C22×D4—111no—
750C22×D4—111no—
751C22×D4—111no—
752C22×D4—111no—
753C22×D4—111no—
754C22×D4—111no—
755C22×D4—118no—
756C22×D4—111no—
757C22×D4—111no—
758C22×D4—224no—
759C22×D4—224no—
760C22×D4—444no—
761C22×D4C4×D1118yescomplemented
762C22×D4C22×D1111yescharacteristic
763C22×D4C22×D1111yescharacteristic
764C22×D4C22×D1111yescharacteristic
765C22×D4C22×D1111yescharacteristic
766C23×C4—111no—
767C23×C4—118no—
768C23×C4—111no—
769C23×C4—111no—
770C23×C4—111no—
771C23×C4—111no—
772C23×C4—111no—
773C23×C4—111no—
774C23×C4—112no—
775C23×C4—112no—
776C23×C4—112no—
777C23×C4—112no—
778C23×C4—224no—
779C23×C4—224no—
780C23×C4C22×D1112yes—
781C23×C4C22×D1112yes—
782C23×C4C22×D1111yescharacteristic
783#121—118no—
784#121—118no—
785#121—118no—
786#121—118no—
787#121—118no—
788#121—118no—
789#121—118no—
790#121—118no—
791C4×D4—44no—
792C4×D4—228no—
793C4×D4—228no—
794C4×D4—228no—
795C4×D4—228no—
796C4×D4—444no—
797C4×D4—444no—
798C4×D4—444no—
799#117—118no—
800#117—228no—
801#117—224no—
802#117—228no—
803#117—224no—
804#117—224no—
805#117—224no—
806#117—224no—
807C2×C4⋊C4—118no—
808C2×C4⋊C4—112no—
809C2×C4⋊C4—111no—
810C2×C4⋊C4—111no—
811C2×C4⋊C4—111no—
812C2×C4⋊C4—111no—
813C2×C4⋊C4—112no—
814C2×C4⋊C4—112no—
815C2×C4⋊C4—112no—
816C2×C4⋊C4—112no—
817C2×C4⋊C4—112no—
818C2×C4⋊C4—112no—
819C2×C4⋊C4—112no—
820C2×C4⋊C4—112no—
821C2×C4⋊C4—228no—
822C2×C4⋊C4C22×D1112yes—
823C2×C22⋊C4—24no—
824C2×C22⋊C4—24no—
825C2×C22⋊C4—118no—
826C2×C22⋊C4—111no—
827C2×C22⋊C4—111no—
828C2×C22⋊C4—111no—
829C2×C22⋊C4—111no—
830C2×C22⋊C4—111no—
831C2×C22⋊C4—118no—
832C2×C22⋊C4—111no—
833C2×C22⋊C4—111no—
834C2×C22⋊C4—111no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—111no—
837C2×C22⋊C4—111no—
838C2×C22⋊C4—112no—
839C2×C22⋊C4—112no—
840C2×C22⋊C4—111no—
841C2×C22⋊C4—112no—
842C2×C22⋊C4—112no—
843C2×C22⋊C4—112no—
844C2×C22⋊C4—112no—
845C2×C22⋊C4—112no—
846C2×C22⋊C4—112no—
847C2×C22⋊C4—112no—
848C2×C22⋊C4—112no—
849C2×C22⋊C4—112no—
850C2×C22⋊C4—112no—
851C2×C22⋊C4—224no—
852C2×C22⋊C4—224no—
853C2×C22⋊C4—224no—
854C2×C22⋊C4—224no—
855C2×C22⋊C4C22×D1111yescharacteristic
856C2×C22⋊C4C22×D1111yescharacteristic
857C2×C22⋊C4C22×D1112yes—
858C2×C22⋊C4C22×D1112yes—
859C2×C22⋊C4C22×D1111yescharacteristic
860C2×C22⋊C4C22×D1112yes—
861C2×C22⋊C4C22×D1112yes—
862C2×C22⋊C4C22×D1112yes—
863C2×C22⋊C4C22×D1112yes—
864C2×C22⋊C4C22×D1111yescharacteristic
865C2×C42—112no—
866C2×C42—112no—
867C2×C42—112no—
868C2×C42—112no—
869C2×C42—112no—
870C2×C42—112no—
871C2×C42—112no—
872C2×C42—112no—
873C2×C42—112no—
874C2×C42—228no—
875C2×C42C22×D1112yes—
876#95—112no—
877#95—112no—
878#95—112no—
879#95—112no—
880#95—112no—
881#95—112no—
882#95—112no—
883#95—112no—
884#95—112no—
885#95—112no—
886#95C22×D1112yes—
887#95C22×D1112yes—
888C2×C11—24no—
889C2×C11—24no—
890C2×C11—42no—
891C2×C11—42no—
892C2×C11—42no—
893C2×C11C22×C4×D411yescharacteristic
894C2×C11C2×#51811yescharacteristic
895C2×C11#342811yescharacteristic
896C2×C11#348812yes—
897C2×C11#349412yes—
898D11—42no—
899D11—42no—
900C24—22no—
901C24—24no—
902C24—22no—
903C24—22no—
904C24—22no—
905C24—42no—
906C24—42no—
907C24—42no—
908C24—111no—
909C24—111no—
910C24—114no—
911C24—222no—
912C24—222no—
913C24—442no—
914C24—442no—
915C24C2×C4×D1114yes—
916C24C2×C4×D1114yes—
917C24C23×D1111yescharacteristic
918C24C23×D1111yescharacteristic
919C24C23×D1111yescharacteristic
920C24C23×D1111yescharacteristic
921C24C23×D1111yescharacteristic
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—416no—
927C2×D4—114no—
928C2×D4—114no—
929C2×D4—114no—
930C2×D4—114no—
931C2×D4—114no—
932C2×D4—114no—
933C2×D4—114no—
934C2×D4—114no—
935C2×D4—222no—
936C2×D4—222no—
937C2×D4—222no—
938C2×D4—222no—
939C2×D4—2232no—
940C2×D4—222no—
941C2×D4—222no—
942C2×D4—222no—
943C2×D4—222no—
944C2×D4—224no—
945C2×D4—224no—
946C2×D4—442no—
947C2×D4—442no—
948C2×D4—4416no—
949C2×D4C2×C4×D1114yes—
950C2×D4C2×C4×D1114yes—
951C2×D4C2×C4×D1114yes—
952C2×D4C2×C4×D1114yes—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—114no—
961C22×C4—114no—
962C22×C4—114no—
963C22×C4—111no—
964C22×C4—111no—
965C22×C4—114no—
966C22×C4—114no—
967C22×C4—114no—
968C22×C4—114no—
969C22×C4—114no—
970C22×C4—111no—
971C22×C4—111no—
972C22×C4—111no—
973C22×C4—111no—
974C22×C4—112no—
975C22×C4—114no—
976C22×C4—112no—
977C22×C4—112no—
978C22×C4—112no—
979C22×C4—224no—
980C22×C4—222no—
981C22×C4—222no—
982C22×C4—222no—
983C22×C4—222no—
984C22×C4—2232no—
985C22×C4—222no—
986C22×C4—222no—
987C22×C4—222no—
988C22×C4—222no—
989C22×C4—224no—
990C22×C4—224no—
991C22×C4—222no—
992C22×C4—222no—
993C22×C4—224no—
994C22×C4—224no—
995C22×C4—442no—
996C22×C4—442no—
997C22×C4—442no—
998C22×C4—442no—
999C22×C4—442no—
1000C22×C4—442no—
1001C22×C4—442no—
1002C22×C4—442no—
1003C22×C4C2×C4×D1114yes—
1004C22×C4C23×D1112yes—
1005C22×C4C23×D1112yes—
1006C22×C4C23×D1112yes—
1007C22×C4C23×D1111yescharacteristic
1008C22×C4C23×D1111yescharacteristic
1009C22×C4C23×D1112yes—
1010C4⋊C4—42no—
1011C4⋊C4—114no—
1012C4⋊C4—114no—
1013C4⋊C4—114no—
1014C4⋊C4—114no—
1015C4⋊C4—118no—
1016C4⋊C4—224no—
1017C4⋊C4—224no—
1018C4⋊C4—224no—
1019C4⋊C4—224no—
1020C4⋊C4—224no—
1021C4⋊C4—442no—
1022C4⋊C4—442no—
1023C4⋊C4—442no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—24no—
1027C22⋊C4—22no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—114no—
1034C22⋊C4—114no—
1035C22⋊C4—114no—
1036C22⋊C4—114no—
1037C22⋊C4—114no—
1038C22⋊C4—114no—
1039C22⋊C4—114no—
1040C22⋊C4—114no—
1041C22⋊C4—114no—
1042C22⋊C4—224no—
1043C22⋊C4—224no—
1044C22⋊C4—224no—
1045C22⋊C4—222no—
1046C22⋊C4—222no—
1047C22⋊C4—224no—
1048C22⋊C4—222no—
1049C22⋊C4—224no—
1050C22⋊C4—442no—
1051C22⋊C4—442no—
1052C22⋊C4—442no—
1053C22⋊C4—442no—
1054C22⋊C4—442no—
1055C22⋊C4—442no—
1056C22⋊C4—442no—
1057C22⋊C4D4×D1114yes—
1058C42—42no—
1059C42—118no—
1060C42—224no—
1061C42—224no—
1062C42—224no—
1063C42—224no—
1064C42—224no—
1065C42—442no—
1066C42—442no—
1067C42—442no—
1068C11#3420411yescharacteristic, complemented, Sylow
1069C23—21no—
1070C23—22no—
1071C23—21no—
1072C23—22no—
1073C23—22no—
1074C23—28no—
1075C23—28no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—28no—
1089C23—44no—
1090C23—44no—
1091C23—44no—
1092C23—48no—
1093C23—48no—
1094C23—84no—
1095C23—84no—
1096C23—112no—
1097C23—112no—
1098C23—221no—
1099C23—221no—
1100C23—222no—
1101C23—222no—
1102C23—221no—
1103C23—221no—
1104C23—222no—
1105C23—222no—
1106C23—228no—
1107C23—444no—
1108C23—444no—
1109C23—884no—
1110C23—884no—
1111C23C22×C4×D1112yes—
1112C23C22×C4×D1112yes—
1113C23C22×C4×D1112yes—
1114C23C22×C4×D1112yes—
1115C23C22×C4×D1112yes—
1116C23C2×D4×D1112yes—
1117C23#6703714yes—
1118C23#41×D1112yes—
1119C23C24×D1111yescharacteristic
1120D4—28no—
1121D4—28no—
1122D4—44no—
1123D4—44no—
1124D4—228no—
1125D4—228no—
1126D4—228no—
1127D4—228no—
1128D4—228no—
1129D4—228no—
1130D4—444no—
1131D4—444no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—44no—
1146C2×C4—48no—
1147C2×C4—84no—
1148C2×C4—1116no—
1149C2×C4—112no—
1150C2×C4—112no—
1151C2×C4—112no—
1152C2×C4—112no—
1153C2×C4—112no—
1154C2×C4—112no—
1155C2×C4—112no—
1156C2×C4—112no—
1157C2×C4—112no—
1158C2×C4—112no—
1159C2×C4—114no—
1160C2×C4—228no—
1161C2×C4—228no—
1162C2×C4—228no—
1163C2×C4—228no—
1164C2×C4—228no—
1165C2×C4—221no—
1166C2×C4—221no—
1167C2×C4—222no—
1168C2×C4—222no—
1169C2×C4—222no—
1170C2×C4—221no—
1171C2×C4—221no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—222no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—222no—
1182C2×C4—444no—
1183C2×C4—448no—
1184C2×C4—884no—
1185C2×C4—884no—
1186C2×C4—884no—
1187C2×C4C22×C4×D1112yes—
1188C2×C4C22×C4×D1112yes—
1189C2×C4C2×D4×D1114yes—
1190C22—24no—
1191C22—24no—
1192C22—22no—
1193C22—22no—
1194C22—22no—
1195C22—22no—
1196C22—24no—
1197C22—24no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—416no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—88no—
1215C22—222no—
1216C22—222no—
1217C22—222no—
1218C22—222no—
1219C22—222no—
1220C22—222no—
1221C22—442no—
1222C22—442no—
1223C22—442no—
1224C22—442no—
1225C22—888no—
1226C22#1062301714yescomplemented
1227C22C4×D4×D1114yes—
1228C22C23×C4×D1111yescharacteristic
1229C22C22×D4×D1111yescharacteristic
1230C22C2×#6703712yes—
1231C22C2×#41×D1111yescharacteristic
1232C22#1062345512yes—
1233C4—24no—
1234C4—22no—
1235C4—22no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—114no—
1240C4—114no—
1241C4—224no—
1242C4—222no—
1243C4—222no—
1244C4—222no—
1245C4—222no—
1246C4—442no—
1247C4—442no—
1248C4—442no—
1249C2—24no—
1250C2—24no—
1251C2—42no—
1252C2—42no—
1253C2—42no—
1254C2—442no—
1255C2—442no—
1256C2C2×C4×D4×D1111yescharacteristic
1257C2C2×#1062301711yescharacteristic
1258C2#1308181411yescharacteristic
1259C2#1308227612yes—
1260C2#1308233812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC22×#66992C2
hypercenterD4×C22⋊C4D11
hypocenterC11#34204
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10623017C2semidirect
3. C22×#66930C2semidirect
4. #13071657C2semidirect
5. #13071651C2semidirect
6. #13071633C2semidirect
7. #13071627C2semidirect
8. #13071468C2semidirect
9. #13071467C2semidirect
10. #13071462C2semidirect
11. #13071461C2semidirect
12. D4×C22⋊Dic11C2semidirect
13. C22⋊C4×C22⋊D11C2semidirect
14. #13071432C2semidirect
15. #13071306C2semidirect
16. #13071302C2semidirect
17. #13071233C2semidirect
18. #13071197C2semidirect
19. #13071126C2semidirect
20. C4×#66992C2semidirect
21. #13070994C2semidirect
22. #13070971C2semidirect
23. D4×C11×C22⋊C4C2semidirect
28. C2×C4×D4×C11C22semidirect
34. C2×#66992C4semidirect
43. C2×D4×Dic11C22semidirect
44. C2×C4×C22⋊D11C22semidirect
45. C2×C4×C22⋊D11C22semidirect
46. C2×C4×C22⋊D11C22semidirect
49. C22×Dic11⋊C4C22semidirect
50. C22×C4×Dic11C22semidirect
52. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
54. C2×(C22⋊D11)⋊C4C22semidirect
64. C2×#66930C22semidirect
65. C2×#66930C22semidirect
66. C11×#390C22semidirect
67. C11×#386C22semidirect
68. C11×#386C22semidirect
75. #10622834C22semidirect
76. #10622833C22semidirect
77. #10622833C22semidirect
78. #10622826C22semidirect
80. #10622823C22semidirect
82. C4×C22⋊Dic11C22semidirect
83. #10622603C22semidirect
84. #10622602C22semidirect
85. #10622585C22semidirect
86. #10622585C22semidirect
87. #10622571C22semidirect
88. #10622570C22semidirect
89. #10622570C22semidirect
90. #10622570C22semidirect
91. #10622570C22semidirect
92. #10622570C22semidirect
93. #10622570C22semidirect
94. #10622569C22semidirect
95. #10622569C22semidirect
98. #10622559C22semidirect
99. #10622558C22semidirect
100. #10622558C22semidirect
101. #10622557C22semidirect
102. #10622557C22semidirect
107. #10622555C22semidirect
108. #10622555C22semidirect
111. C22⋊C4×Dic11C22semidirect
112. C22⋊C4×Dic11C22semidirect
113. C22⋊C4×Dic11C22semidirect
114. #10622553C22semidirect
115. C4×(C2×D11)⋊C4C22semidirect
116. C4×Dic11⋊C4C22semidirect
117. C4×Dic11⋊C4C22semidirect
118. #10622283C22semidirect
119. #10622282C22semidirect
120. #10622281C22semidirect
121. #10622279C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622260C22semidirect
130. C22×D4×C11C2×C4semidirect
141. C22×C22⋊D11C2×C4semidirect
142. C22×C22⋊D11C2×C4semidirect
153. C23×Dic11C2×C4semidirect
182. C2×C22⋊Dic11C2×C4semidirect
197. #66992C2×C4semidirect
198. #66992C2×C4semidirect
199. #66992C2×C4semidirect
200. #66992C2×C4semidirect
201. #66992C2×C4semidirect
202. #66992C2×C4semidirect
203. #66992C2×C4semidirect
204. #66992C2×C4semidirect
209. C2×(C2×D11)⋊C4C2×C4semidirect
222. C2×Dic11⋊C4C2×C4semidirect
257. #66930D4semidirect
429. Dic11⋊C4C2×D4semidirect
438. C4×Dic11C2×D4semidirect
453. D4×C22⋊C4D11semidirect
569. C2×Dic11C4×D4semidirect
604. C2×C4×D4C2×D11semidirect
632. #390C2×D11semidirect
651. #386C2×D11semidirect
652. #386C2×D11semidirect
711. C22×C11#518semidirect
761. C22×D4C4×D11semidirect
1068. C11#34204semidirect
1226. C22#10623017semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C2×#106230172
C22×#669302
#130716572
#130716512
#130716332
#130716272
#130714682
#130714672
#130714622
#130714612
D4×C22⋊Dic112
C22⋊C4×C22⋊D112
#130714322
#130713062
#130713022
#130712332
#130711972
#130711262
C4×#669922
#130709942
#130709712
D4×C11×C22⋊C42
#3420411