Finite Group Databasebeta

← #14916732

Subgroups — #14916732

Order 2816.

3082 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2#13071774C212yesmaximal, complemented
3#13071767C212yesmaximal, complemented
4#13071633C212yesmaximal, complemented
5#13071627C212yesmaximal, complemented
6#13071494C211yesmaximal, characteristic, complemented
7#13071488C211yesmaximal, characteristic, complemented
8D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
9C22⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
10C22⋊C4×C22⋊D11C211yesmaximal, characteristic, complemented
11#13071432C211yesmaximal, characteristic, complemented
12#13071432C211yesmaximal, characteristic, complemented
13#13071317C212yesmaximal, complemented
14#13071314C212yesmaximal, complemented
15#13071306C212yesmaximal, complemented
16#13071302C212yesmaximal, complemented
17#13071229C211yesmaximal, characteristic, complemented
18#13071228C211yesmaximal, characteristic, complemented
19#13071212C211yesmaximal, characteristic, complemented
20#13071211C211yesmaximal, characteristic, complemented
21#13070994C211yesmaximal, characteristic, complemented
22C2×#10622555C211yesmaximal, 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
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2212yescomplemented
49C2×(C22⋊D11)⋊C4C2212yescomplemented
50C2×(C22⋊D11)⋊C4C2212yescomplemented
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×C22⋊C4×D11C2211yescharacteristic
53C2×#66930C2212yescomplemented
54C11×#390C2212yescomplemented
55C11×#386C2212yescomplemented
56C11×#386C2212yescomplemented
57C11×#380C2211yescharacteristic
58C11×#379C2211yescharacteristic
59C11×#379C2211yescharacteristic
60C4×C11×C22⋊C4C2211yescharacteristic
61#10622860C2211yescharacteristic
62#10622860C2211yescharacteristic
63#10622834C2212yescomplemented
64#10622833C2212yescomplemented
65#10622833C2212yescomplemented
66#10622826C2212yescomplemented
67#10622826C2212yescomplemented
68#10622825C2211yescharacteristic
69#10622823C2212yescomplemented
70#10622823C2212yescomplemented
71C4×C22⋊Dic11C2211yescharacteristic
72C2×C11⋊#95C2212yescomplemented
73#10622602C2212yescomplemented
74#10622602C2212yescomplemented
75#10622591C2212yescomplemented
76#10622585C2212yescomplemented
77#10622571C2212yescomplemented
78#10622571C2212yescomplemented
79#10622570C2212yescomplemented
80#10622570C2212yescomplemented
81#10622570C2212yescomplemented
82#10622570C2212yescomplemented
83#10622569C2212yescomplemented
84#10622569C2212yescomplemented
85#10622569C2212yescomplemented
86#10622569C2212yescomplemented
87#10622568C2211yescharacteristic
88#10622568C2211yescharacteristic
89#10622559C2212yescomplemented
90#10622559C2212yescomplemented
91#10622558C2212yescomplemented
92#10622558C2212yescomplemented
93#10622557C2212yescomplemented
94#10622557C2212yescomplemented
95#10622556C2212yescomplemented
96#10622555C2211yescharacteristic
97#10622555C2211yescharacteristic
98#10622555C2211yescharacteristic
99#10622555C2211yescharacteristic
100#10622555C2211yescharacteristic
101#10622555C2211yescharacteristic
102#10622555C2211yescharacteristic
103#10622555C2211yescharacteristic
104#10622555C2212yescomplemented
105#10622555C2212yescomplemented
106#10622555C2212yescomplemented
107C22⋊C4×Dic11C2211yescharacteristic
108C22⋊C4×Dic11C2211yescharacteristic
109C22⋊C4×Dic11C2211yescharacteristic
110C22⋊C4×Dic11C2211yescharacteristic
111C22⋊C4×Dic11C2212yescomplemented
112#10622553C2212yescomplemented
113#10622553C2212yescomplemented
114#10622546C2212yescomplemented
115C4×Dic11⋊C4C2212yescomplemented
116#10622282C2212yescomplemented
117#10622282C2212yescomplemented
118#10622281C2212yescomplemented
119#10622281C2212yescomplemented
120#10622268C2212yescomplemented
121#10622265C2212yescomplemented
122#10622262C2212yescomplemented
123#10622260C2212yescomplemented
124C25×C11C2311yescharacteristic
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11—44no—
128C22×D4×C11C2×C418yescomplemented
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C23×C4×C11C2312yes—
134C23×C4×C11C2312yes—
135C23×C4×C11C2311yescharacteristic
136C22×C22⋊D11—44no—
137C22×C22⋊D11—44no—
138C22×C22⋊D11C2×C418yescomplemented
139C22×C22⋊D11C2×C418yescomplemented
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2311yescharacteristic
144C22×C22⋊D11C2311yescharacteristic
145C22×C22⋊D11C2311yescharacteristic
146C22×C22⋊D11C2311yescharacteristic
147C22×C22⋊D11C2311yescharacteristic
148C23×Dic11—44no—
149C23×Dic11C2×C418yescomplemented
150C23×Dic11C2311yescharacteristic
151C23×Dic11C2311yescharacteristic
152C23×Dic11C2311yescharacteristic
153C23×Dic11C2312yes—
154C23×Dic11C2312yes—
155C23×Dic11C2311yescharacteristic
156C23×Dic11C2311yescharacteristic
157C23×Dic11C2311yescharacteristic
158C23×Dic11C2311yescharacteristic
159C22×C4×D11C2312yes—
160C22×C4×D11C2312yes—
161C4×D4×C11—44no—
162C2×C11×C4⋊C4C2312yes—
163C2×C11×C22⋊C4—42no—
164C2×C11×C22⋊C4—42no—
165C2×C11×C22⋊C4C2311yescharacteristic
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C42×C11C2312yes—
176C2×C22⋊Dic11—42no—
177C2×C22⋊Dic11—42no—
178C2×C22⋊Dic11C2×C418yescomplemented
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2311yescharacteristic
190C2×C22⋊Dic11C2311yescharacteristic
191C2×C22⋊Dic11C2311yescharacteristic
192C2×C22⋊Dic11C2311yescharacteristic
193#66992C2×C418yescomplemented
194#66992C2×C418yescomplemented
195#66992C2×C418yescomplemented
196#66992C2×C418yescomplemented
197#66992C2×C418yescomplemented
198#66992C2×C418yescomplemented
199#66992C2×C418yescomplemented
200#66992C2×C418yescomplemented
201D4×Dic11—44no—
202C4×C22⋊D11—44no—
203C4×C22⋊D11—44no—
204C2×(C2×D11)⋊C4C2×C418yescomplemented
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2311yescharacteristic
212C2×(C2×D11)⋊C4C2311yescharacteristic
213C2×(C2×D11)⋊C4C2311yescharacteristic
214C2×(C2×D11)⋊C4C2311yescharacteristic
215C2×C4⋊Dic11C2312yes—
216C2×Dic11⋊C4—44no—
217C2×Dic11⋊C4C2×C418yescomplemented
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2311yescharacteristic
227C2×Dic11⋊C4C2311yescharacteristic
228C2×Dic11⋊C4C2311yescharacteristic
229C2×Dic11⋊C4C2311yescharacteristic
230C2×C4×Dic11C2312yes—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2312yes—
233C2×C4×Dic11C2312yes—
234C2×C4×Dic11C2312yes—
235(C22⋊D11)⋊C4—44no—
236(C22⋊D11)⋊C4—44no—
237C22⋊C4×D11—42no—
238C22⋊C4×D11—42no—
239#66930—44no—
240C11×#95C2312yes—
241C11×#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256#34379—111nomaximal, Sylow
257C24×C11—22no—
258C24×C11—24no—
259C24×C11—22no—
260C24×C11—22no—
261C24×C11—22no—
262C24×C11—42no—
263C24×C11—42no—
264C24×C11—42no—
265C24×C11C22×C414yes—
266C24×C11C22×C414yes—
267C24×C11C2411yescharacteristic
268C24×C11C2411yescharacteristic
269C24×C11C2411yescharacteristic
270C24×C11C2411yescharacteristic
271C24×C11C2411yescharacteristic
272C23×D11—22no—
273C23×D11—22no—
274C23×D11—42no—
275C23×D11—42no—
276C23×D11C22×C414yes—
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C2×D4×C11—24no—
280C2×D4×C11—24no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C2×D4×C11—416no—
284C2×D4×C11C22×C414yes—
285C2×D4×C11C22×C414yes—
286C2×D4×C11C22×C414yes—
287C2×D4×C11C22×C414yes—
288C22×C4×C11—24no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11—42no—
292C22×C4×C11—42no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11C22×C414yes—
296C22×C4×C11C2412yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11—42no—
310C2×C22⋊D11—416no—
311C2×C22⋊D11—416no—
312C2×C22⋊D11C22×C414yes—
313C2×C22⋊D11C22×C414yes—
314C2×C22⋊D11C22×C414yes—
315C2×C22⋊D11C22×C414yes—
316C2×C22⋊D11C22×C414yes—
317C2×C22⋊D11C22×C414yes—
318C2×C22⋊D11C22×C414yes—
319C2×C22⋊D11C22×C414yes—
320C22×Dic11—24no—
321C22×Dic11—24no—
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—42no—
325C22×Dic11—42no—
326C22×Dic11—42no—
327C22×Dic11—42no—
328C22×Dic11—42no—
329C22×Dic11—42no—
330C22×Dic11—42no—
331C22×Dic11—42no—
332C22×Dic11—42no—
333C22×Dic11—416no—
334C22×Dic11C22×C414yes—
335C22×Dic11C22×C414yes—
336C22×Dic11C22×C414yes—
337C22×Dic11C22×C414yes—
338C22×Dic11C22×C414yes—
339C22×Dic11C22×C414yes—
340C22×Dic11C22×C414yes—
341C22×Dic11C2412yes—
342C22×Dic11C2412yes—
343C22×Dic11C2412yes—
344C22×Dic11C2412yes—
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C22×Dic11C2411yescharacteristic
348C22×Dic11C2411yescharacteristic
349C22×Dic11C2411yescharacteristic
350C22×Dic11C2411yescharacteristic
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C11×C4⋊C4—42no—
358C11×C22⋊C4—22no—
359C11×C22⋊C4—22no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—42no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C42×C11—42no—
369C22⋊Dic11—22no—
370C22⋊Dic11—22no—
371C22⋊Dic11—24no—
372C22⋊Dic11—22no—
373C22⋊Dic11—22no—
374C22⋊Dic11—42no—
375C22⋊Dic11—42no—
376C22⋊Dic11—42no—
377C22⋊Dic11—42no—
378C22⋊Dic11—42no—
379C22⋊Dic11C22×C414yes—
380C22⋊Dic11C22×C414yes—
381C22⋊Dic11C22×C414yes—
382C22⋊Dic11C22×C414yes—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—42no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—42no—
387(C2×D11)⋊C4—42no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4C22×C414yes—
390(C2×D11)⋊C4C22×C414yes—
391(C2×D11)⋊C4C22×C414yes—
392(C2×D11)⋊C4C22×C414yes—
393C4⋊Dic11—42no—
394Dic11⋊C4—24no—
395Dic11⋊C4—24no—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398Dic11⋊C4—42no—
399Dic11⋊C4—42no—
400Dic11⋊C4—42no—
401Dic11⋊C4—42no—
402Dic11⋊C4C22×C414yes—
403Dic11⋊C4C22×C414yes—
404Dic11⋊C4C22×C414yes—
405Dic11⋊C4C22×C414yes—
406C4×Dic11—24no—
407C4×Dic11—24no—
408C4×Dic11—42no—
409C4×Dic11—42no—
410C4×Dic11—42no—
411C22×#121—111no—
412#2377—112no—
413#2377—112no—
414#2361—112no—
415#2361—112no—
416#2345—111no—
417#2345—111no—
418D4×C22⋊C4—111no—
419D4×C22⋊C4—111no—
420D4×C22⋊C4—111no—
421D4×C22⋊C4—111no—
422D4×C22⋊C4—111no—
423D4×C22⋊C4D1111yescharacteristic, complemented
424#2325—112no—
425#2325—112no—
426#2324—112no—
427#2324—112no—
428#2315—111no—
429#2315—111no—
430#2312—111no—
431#2312—111no—
432#2280—111no—
433C2×#380—111no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—21no—
437C23×C11—22no—
438C23×C11—21no—
439C23×C11—28no—
440C23×C11—28no—
441C23×C11—21no—
442C23×C11—21no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—21no—
453C23×C11—28no—
454C23×C11—44no—
455C23×C11—44no—
456C23×C11—44no—
457C23×C11—48no—
458C23×C11—48no—
459C23×C11—84no—
460C23×C11—84no—
461C23×C11C23×C412yes—
462C23×C11C23×C412yes—
463C23×C11C23×C412yes—
464C23×C11C23×C412yes—
465C23×C11C23×C412yes—
466C23×C11H(5,𝔽2)14yes—
467C23×C11H(5,𝔽2)12yes—
468C23×C112−1+412yes—
469C23×C11C2511yescharacteristic
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—21no—
477C22×D11—21no—
478C22×D11—28no—
479C22×D11—44no—
480C22×D11—44no—
481C22×D11—84no—
482C22×D11—84no—
483C22×D11C23×C412yes—
484C22×D11C23×C412yes—
485D4×C11—28no—
486D4×C11—28no—
487D4×C11—44no—
488D4×C11—44no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—44no—
504C2×C4×C11—84no—
505C2×C4×C11—84no—
506C2×C4×C11C23×C412yes—
507C2×C4×C11C23×C412yes—
508C22⋊D11—28no—
509C22⋊D11—28no—
510C22⋊D11—28no—
511C22⋊D11—28no—
512C22⋊D11—44no—
513C22⋊D11—44no—
514C22⋊D11—44no—
515C22⋊D11—44no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—28no—
522C2×Dic11—28no—
523C2×Dic11—28no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—44no—
537C2×Dic11—44no—
538C2×Dic11—44no—
539C2×Dic11—44no—
540C2×Dic11—84no—
541C2×Dic11—84no—
542C2×Dic11C23×C412yes—
543C2×Dic11C23×C412yes—
544C2×Dic11C23×C412yes—
545C2×Dic11C23×C412yes—
546C2×Dic11C23×C412yes—
547C2×Dic11C23×C412yes—
548C2×Dic11H(5,𝔽2)14yes—
549C4×D11—84no—
550C4×D11—84no—
551C23×D4—111no—
552C23×D4—111no—
553C23×D4C2×D1111yescharacteristic
554C24×C4—111no—
555C2×#121—111no—
556C2×#121—111no—
557C2×#121—111no—
558C2×#121—111no—
559C2×#121—111no—
560C2×#121—111no—
561C2×#121—111no—
562C2×#121—111no—
563C2×#121—1116no—
564C2×C4×D4—112no—
565C2×C4×D4—112no—
566C2×C4×D4—112no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4C2×D1112yescomplemented
570C2×#117—112no—
571C22×C4⋊C4—111no—
572C22×C4⋊C4—112no—
573C22×C22⋊C4—111no—
574C22×C22⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C22⋊C4—111no—
578C22×C22⋊C4—111no—
579C22×C22⋊C4C2×D1111yescharacteristic
580C22×C22⋊C4C2×D1111yescharacteristic
581#390—112no—
582#390—112no—
583#390—112no—
584#390—112no—
585#390—112no—
586#390C2×D1112yescomplemented
587#389—112no—
588#389—112no—
589#388—112no—
590#388—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#387—112no—
598#387—112no—
599#387—112no—
600#387—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#386—112no—
606#386—112no—
607#386—112no—
608#386—112no—
609#386—112no—
610#386—112no—
611#386C2×D1112yescomplemented
612#386C2×D1112yescomplemented
613#385—112no—
614#385—112no—
615#385—112no—
616#385—112no—
617#385—112no—
618#385—112no—
619#385—112no—
620#385—112no—
621#381—112no—
622#380—111no—
623#380—111no—
624#380—111no—
625#380—111no—
626#380—111no—
627#380—111no—
628#380—111no—
629#380—112no—
630#380—112no—
631#380—111no—
632#380—111no—
633#380—112no—
634#380C2×D1111yescharacteristic
635#379—111no—
636#379—111no—
637#379—111no—
638#379—111no—
639#379C2×D1111yescharacteristic
640#379C2×D1111yescharacteristic
641C4×C4⋊C4—112no—
642C4×C4⋊C4—112no—
643C4×C22⋊C4—111no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—111no—
646C4×C22⋊C4—111no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—112no—
649C4×C22⋊C4C2×D1111yescharacteristic
650C2×#95—112no—
651C22×C11—22no—
652C22×C11—22no—
653C22×C11—22no—
654C22×C11—22no—
655C22×C11—24no—
656C22×C11—24no—
657C22×C11—24no—
658C22×C11—24no—
659C22×C11—22no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—416no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11—88no—
676C22×C11#51814yes—
677C22×C11#52014yes—
678C22×C11C24×C411yescharacteristic
679C22×C11C2×H(5,𝔽2)12yes—
680C22×C11C2×H(5,𝔽2)11yescharacteristic
681C22×C11C2×H(5,𝔽2)12yes—
682C22×C11C2×2−1+411yescharacteristic
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—88no—
694C4×C11—22no—
695C4×C11—22no—
696C4×C11—42no—
697C4×C11—42no—
698C4×C11—42no—
699C4×C11—42no—
700Dic11—22no—
701Dic11—22no—
702Dic11—22no—
703Dic11—22no—
704Dic11—22no—
705Dic11—42no—
706Dic11—42no—
707Dic11—42no—
708Dic11—42no—
709Dic11#51814yes—
710C25—111no—
711C25C22×D1111yescharacteristic
712C25C22×D1111yescharacteristic
713C22×D4—44no—
714C22×D4—111no—
715C22×D4—111no—
716C22×D4—111no—
717C22×D4—111no—
718C22×D4—118no—
719C22×D4—118no—
720C22×D4—111no—
721C22×D4—111no—
722C22×D4—111no—
723C22×D4—111no—
724C22×D4—444no—
725C22×D4—444no—
726C22×D4C4×D1118yescomplemented
727C22×D4C22×D1111yescharacteristic
728C22×D4C22×D1111yescharacteristic
729C22×D4C22×D1111yescharacteristic
730C22×D4C22×D1111yescharacteristic
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—118no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—112no—
740C23×C4—112no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—444no—
744C23×C4C22×D1112yes—
745C23×C4C22×D1112yes—
746C23×C4C22×D1111yescharacteristic
747#121—118no—
748#121—118no—
749#121—118no—
750#121—118no—
751#121—118no—
752#121—118no—
753#121—118no—
754#121—118no—
755C4×D4—44no—
756C4×D4—444no—
757C4×D4—444no—
758C4×D4—444no—
759C4×D4—444no—
760C4×D4—444no—
761#117—444no—
762C2×C4⋊C4—118no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—111no—
765C2×C4⋊C4—111no—
766C2×C4⋊C4—111no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—444no—
777C2×C4⋊C4C22×D1112yes—
778C2×C22⋊C4—42no—
779C2×C22⋊C4—42no—
780C2×C22⋊C4—118no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—118no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—111no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—111no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—442no—
807C2×C22⋊C4—442no—
808C2×C22⋊C4—442no—
809C2×C22⋊C4—442no—
810C2×C22⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4C22×D1111yescharacteristic
812C2×C22⋊C4C22×D1111yescharacteristic
813C2×C22⋊C4C22×D1112yes—
814C2×C22⋊C4C22×D1111yescharacteristic
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1112yes—
820C2×C42—112no—
821C2×C42—112no—
822C2×C42—112no—
823C2×C42—112no—
824C2×C42—112no—
825C2×C42C22×D1112yes—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95C22×D1112yes—
841#95C22×D1112yes—
842C2×C11—24no—
843C2×C11—24no—
844C2×C11—42no—
845C2×C11—42no—
846C2×C11—42no—
847C2×C11C2×#51811yescharacteristic
848C2×C11C2×#51811yescharacteristic
849C2×C11C2×#52011yescharacteristic
850C2×C11#353612yes—
851C2×C11#353712yes—
852D11—42no—
853D11—42no—
854C24—22no—
855C24—24no—
856C24—22no—
857C24—22no—
858C24—22no—
859C24—42no—
860C24—42no—
861C24—42no—
862C24—111no—
863C24—111no—
864C24—114no—
865C24—222no—
866C24—222no—
867C24—442no—
868C24—442no—
869C24C2×C4×D1114yes—
870C24C2×C4×D1114yes—
871C24C23×D1111yescharacteristic
872C24C23×D1111yescharacteristic
873C24C23×D1111yescharacteristic
874C24C23×D1111yescharacteristic
875C24C23×D1111yescharacteristic
876C2×D4—24no—
877C2×D4—24no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—416no—
881C2×D4—114no—
882C2×D4—114no—
883C2×D4—114no—
884C2×D4—114no—
885C2×D4—114no—
886C2×D4—114no—
887C2×D4—114no—
888C2×D4—114no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—4416no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4—4416no—
899C2×D4C2×C4×D1114yes—
900C2×D4C2×C4×D1114yes—
901C2×D4C2×C4×D1114yes—
902C2×D4C2×C4×D1114yes—
903C22×C4—24no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—111no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—111no—
917C22×C4—111no—
918C22×C4—111no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—114no—
922C22×C4—114no—
923C22×C4—112no—
924C22×C4—112no—
925C22×C4—112no—
926C22×C4—112no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—442no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4—4416no—
938C22×C4—442no—
939C22×C4—442no—
940C22×C4—442no—
941C22×C4—442no—
942C22×C4—442no—
943C22×C4—442no—
944C22×C4—442no—
945C22×C4—442no—
946C22×C4—442no—
947C22×C4C2×C4×D1114yes—
948C22×C4C23×D1112yes—
949C22×C4C23×D1112yes—
950C22×C4C23×D1112yes—
951C22×C4C23×D1112yes—
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954C4⋊C4—42no—
955C4⋊C4—114no—
956C4⋊C4—114no—
957C4⋊C4—114no—
958C4⋊C4—114no—
959C4⋊C4—224no—
960C4⋊C4—224no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C4⋊C4—442no—
964C4⋊C4—442no—
965C4⋊C4—442no—
966C4⋊C4—442no—
967C4⋊C4—442no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—24no—
972C22⋊C4—22no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—114no—
979C22⋊C4—114no—
980C22⋊C4—114no—
981C22⋊C4—114no—
982C22⋊C4—114no—
983C22⋊C4—114no—
984C22⋊C4—114no—
985C22⋊C4—114no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—224no—
990C22⋊C4—222no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C22⋊C4—442no—
999C22⋊C4—442no—
1000C22⋊C4—442no—
1001C22⋊C4—442no—
1002C42—42no—
1003C42—224no—
1004C42—224no—
1005C42—442no—
1006C42—442no—
1007C42—442no—
1008C11#3437911yescharacteristic, complemented, Sylow
1009C23—21no—
1010C23—22no—
1011C23—21no—
1012C23—22no—
1013C23—22no—
1014C23—28no—
1015C23—28no—
1016C23—21no—
1017C23—21no—
1018C23—22no—
1019C23—21no—
1020C23—22no—
1021C23—22no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—28no—
1029C23—44no—
1030C23—44no—
1031C23—44no—
1032C23—48no—
1033C23—48no—
1034C23—84no—
1035C23—84no—
1036C23—112no—
1037C23—112no—
1038C23—221no—
1039C23—221no—
1040C23—222no—
1041C23—222no—
1042C23—221no—
1043C23—221no—
1044C23—222no—
1045C23—222no—
1046C23—228no—
1047C23—444no—
1048C23—444no—
1049C23—884no—
1050C23—884no—
1051C23C22×C4×D1112yes—
1052C23C22×C4×D1112yes—
1053C23C22×C4×D1112yes—
1054C23C22×C4×D1112yes—
1055C23C22×C4×D1112yes—
1056C23#6703714yes—
1057C23#6703712yes—
1058C23#6704312yes—
1059C23C24×D1111yescharacteristic
1060D4—28no—
1061D4—28no—
1062D4—44no—
1063D4—44no—
1064D4—228no—
1065D4—228no—
1066D4—228no—
1067D4—228no—
1068D4—444no—
1069D4—444no—
1070D4—444no—
1071D4—444no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—84no—
1088C2×C4—84no—
1089C2×C4—112no—
1090C2×C4—114no—
1091C2×C4—112no—
1092C2×C4—112no—
1093C2×C4—112no—
1094C2×C4—112no—
1095C2×C4—112no—
1096C2×C4—228no—
1097C2×C4—228no—
1098C2×C4—228no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—444no—
1117C2×C4—444no—
1118C2×C4—444no—
1119C2×C4—444no—
1120C2×C4—884no—
1121C2×C4—884no—
1122C2×C4—884no—
1123C2×C4—884no—
1124C2×C4C22×C4×D1112yes—
1125C2×C4C22×C4×D1112yes—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—24no—
1130C22—24no—
1131C22—22no—
1132C22—24no—
1133C22—24no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—22no—
1140C22—22no—
1141C22—22no—
1142C22—22no—
1143C22—416no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—42no—
1149C22—42no—
1150C22—88no—
1151C22—222no—
1152C22—222no—
1153C22—222no—
1154C22—222no—
1155C22—222no—
1156C22—222no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—888no—
1162C22#1062301714yes—
1163C22#1062307714yes—
1164C22C23×C4×D1111yescharacteristic
1165C22C2×#6703712yes—
1166C22C2×#6703711yescharacteristic
1167C22C2×#6704311yescharacteristic
1168C22D11×H(5,𝔽2)12yes—
1169C4—22no—
1170C4—22no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—114no—
1176C4—222no—
1177C4—222no—
1178C4—222no—
1179C4—222no—
1180C4—222no—
1181C4—442no—
1182C4—442no—
1183C4—442no—
1184C4—442no—
1185C2—24no—
1186C2—24no—
1187C2—42no—
1188C2—42no—
1189C2—42no—
1190C2—442no—
1191C2—442no—
1192C2D11×#51811yescharacteristic
1193C2C2×#1062301711yescharacteristic
1194C2C2×#1062307711yescharacteristic
1195C2#1308283112yes—
1196C2#1308284612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingD4×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC22×#66992C2
hypercenterD4×C22⋊C4D11
hypocenterC11#34379
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071774C2semidirect
3. #13071767C2semidirect
4. #13071633C2semidirect
5. #13071627C2semidirect
6. #13071494C2semidirect
7. #13071488C2semidirect
8. D4×C22⋊Dic11C2semidirect
9. C22⋊C4×C22⋊D11C2semidirect
10. C22⋊C4×C22⋊D11C2semidirect
11. #13071432C2semidirect
12. #13071432C2semidirect
13. #13071317C2semidirect
14. #13071314C2semidirect
15. #13071306C2semidirect
16. #13071302C2semidirect
17. #13071229C2semidirect
18. #13071228C2semidirect
19. #13071212C2semidirect
20. #13071211C2semidirect
21. #13070994C2semidirect
22. C2×#10622555C2semidirect
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
48. C22×Dic11⋊C4C22semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
50. C2×(C22⋊D11)⋊C4C22semidirect
53. C2×#66930C22semidirect
54. C11×#390C22semidirect
55. C11×#386C22semidirect
56. C11×#386C22semidirect
63. #10622834C22semidirect
64. #10622833C22semidirect
65. #10622833C22semidirect
66. #10622826C22semidirect
67. #10622826C22semidirect
69. #10622823C22semidirect
70. #10622823C22semidirect
72. C2×C11⋊#95C22semidirect
73. #10622602C22semidirect
74. #10622602C22semidirect
75. #10622591C22semidirect
76. #10622585C22semidirect
77. #10622571C22semidirect
78. #10622571C22semidirect
79. #10622570C22semidirect
80. #10622570C22semidirect
81. #10622570C22semidirect
82. #10622570C22semidirect
83. #10622569C22semidirect
84. #10622569C22semidirect
85. #10622569C22semidirect
86. #10622569C22semidirect
89. #10622559C22semidirect
90. #10622559C22semidirect
91. #10622558C22semidirect
92. #10622558C22semidirect
93. #10622557C22semidirect
94. #10622557C22semidirect
95. #10622556C22semidirect
104. #10622555C22semidirect
105. #10622555C22semidirect
106. #10622555C22semidirect
111. C22⋊C4×Dic11C22semidirect
112. #10622553C22semidirect
113. #10622553C22semidirect
114. #10622546C22semidirect
115. C4×Dic11⋊C4C22semidirect
116. #10622282C22semidirect
117. #10622282C22semidirect
118. #10622281C22semidirect
119. #10622281C22semidirect
120. #10622268C22semidirect
121. #10622265C22semidirect
122. #10622262C22semidirect
123. #10622260C22semidirect
128. C22×D4×C11C2×C4semidirect
138. C22×C22⋊D11C2×C4semidirect
139. C22×C22⋊D11C2×C4semidirect
149. C23×Dic11C2×C4semidirect
178. C2×C22⋊Dic11C2×C4semidirect
193. #66992C2×C4semidirect
194. #66992C2×C4semidirect
195. #66992C2×C4semidirect
196. #66992C2×C4semidirect
197. #66992C2×C4semidirect
198. #66992C2×C4semidirect
199. #66992C2×C4semidirect
200. #66992C2×C4semidirect
204. C2×(C2×D11)⋊C4C2×C4semidirect
217. C2×Dic11⋊C4C2×C4semidirect
423. D4×C22⋊C4D11semidirect
569. C2×C4×D4C2×D11semidirect
586. #390C2×D11semidirect
611. #386C2×D11semidirect
612. #386C2×D11semidirect
726. C22×D4C4×D11semidirect
1008. C11#34379semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
#130717742
#130717672
#130716332
#130716272
#130714942
#130714882
D4×C22⋊Dic112
C22⋊C4×C22⋊D112
#130714322
#130713172
#130713142
#130713062
#130713022
#130712292
#130712282
#130712122
#130712112
#130709942
C2×#106225552
D4×C11×C22⋊C42
#3437911