Finite Group Databasebeta

← #14925912

Subgroups — #14925912

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic, complemented
2C22×C4×D44C211yesmaximal, characteristic, complemented
3#13074234C212yesmaximal, complemented
4#13074226C212yesmaximal, complemented
5#13074093C211yesmaximal, characteristic, complemented
6#13073993C211yesmaximal, characteristic, complemented
7#13073795C212yesmaximal, complemented
8#13073773C211yesmaximal, characteristic, complemented
9#13073581C212yesmaximal, complemented
10#13073546C211yesmaximal, characteristic, complemented
11#13072014C211yesmaximal, characteristic, complemented
12#13072008C211yesmaximal, characteristic, complemented
13#13071993C211yesmaximal, characteristic, complemented
14#13071988C211yesmaximal, characteristic, complemented
15#13071879C212yesmaximal, complemented
16#13071832C212yesmaximal, complemented
17C4×#66982C211yesmaximal, characteristic, complemented
18C4×#66948C212yesmaximal, complemented
19C4×#66937C212yesmaximal, complemented
20C4×#66935C211yesmaximal, characteristic, complemented
21C4×#66990C211yesmaximal, characteristic, complemented
22C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
23C4×C11×#123C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic, complemented
25C23×D44C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C11×#123C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C2×#66992C2211yescharacteristic
32C2×#66990C2211yescharacteristic
33C2×#66990C2211yescharacteristic
34C2×#66982C2211yescharacteristic
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×C4×C22⋊D11C2211yescharacteristic, complemented
37C2×C4×C22⋊D11C2212yescomplemented
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41#10623078—28no—
42C2×#66949C2211yescharacteristic, complemented
43C2×#66948C2212yes—
44C2×#66947C2211yescharacteristic, complemented
45C2×#66937C2212yes—
46C2×#66937C2211yescharacteristic, complemented
47C2×#66936C2211yescharacteristic, complemented
48C2×#66935C2211yescharacteristic
49C2×#66935C2211yescharacteristic
50C2×C22⋊C4×D11C2211yescharacteristic
51C2×C22⋊C4×D11C2211yescharacteristic
52C2×#66931C2211yescharacteristic
53C2×C4×D44—28no—
54C2×C4×D44C2212yes—
55C2×C4×D44C2212yes—
56C2×C4×D44C2212yes—
57C2×C4×D44C2212yes—
58C2×C4×D44C2211yescharacteristic, complemented
59C2×C4×D44C2212yescomplemented
60C2×#66925C2211yescharacteristic, complemented
61C2×C42×D11C2212yescomplemented
62C11×#388C2212yescomplemented
63C11×#387C2212yescomplemented
64C11×#386C2211yescharacteristic
65C11×#385C2211yescharacteristic
66C11×#381C2211yescharacteristic
67C4×C11×C4⋊C4C2212yescomplemented
68C4×C11×C22⋊C4C2211yescharacteristic
69C4×C11×C22⋊C4C2212yescomplemented
70#10622833C2211yescharacteristic
71#10622826C2211yescharacteristic
72#10622824C2211yescharacteristic
73#10622823C2211yescharacteristic
74C4×C22⋊Dic11C2211yescharacteristic
75#10622606C2212yescomplemented
76#10622605C2212yescomplemented
77#10622604C2212yes—
78#10622602C2212yescomplemented
79#10622601C2212yescomplemented
80#10622600C2212yescomplemented
81#10622598C2212yescomplemented
82#10622597C2212yescomplemented
83#10622574C2212yescomplemented
84#10622574C2212yescomplemented
85#10622573C2212yes—
86#10622573C2212yescomplemented
87#10622571C2211yescharacteristic
88#10622570C2212yescomplemented
89#10622569C2212yescomplemented
90#10622569C2212yescomplemented
91#10622568C2211yescharacteristic
92#10622568C2211yescharacteristic
93#10622564C2212yescomplemented
94#10622563C2211yescharacteristic
95#10622559C2211yescharacteristic
96C22⋊C4×Dic11C2211yescharacteristic
97C22⋊C4×Dic11C2211yescharacteristic
98#10622553C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×(C2×D11)⋊C4C2212yescomplemented
101C4×(C2×D11)⋊C4C2212yescomplemented
102C4×(C2×D11)⋊C4C2212yescomplemented
103#10622546C2212yescomplemented
104C4×Dic11⋊C4C2212yescomplemented
105#10622288C2212yescomplemented
106#10622288C2212yescomplemented
107#10622286C2212yescomplemented
108#10622285C2212yes—
109#10622285C2212yescomplemented
110#10622284C2212yes—
111#10622283C2212yescomplemented
112#10622283C2212yescomplemented
113#10622282C2212yescomplemented
114#10622281C2212yescomplemented
115#10622280C2212yescomplemented
116#10622279C2212yescomplemented
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121D11×#95C2212yescomplemented
122#10622273C2212yescomplemented
123#10622269C2212yescomplemented
124#10622260C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2311yescharacteristic
132C22×C22⋊D11C2311yescharacteristic
133C22×C22⋊D11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C2×#4339—24no—
140C2×#4339—44no—
141C22×D44—24no—
142C22×D44—28no—
143C22×D44C2312yes—
144C22×D44C2311yescharacteristic
145C22×D44C2312yes—
146C22×D44C2312yes—
147C22×D44C2311yescharacteristic
148C22×C4×D11—24no—
149C22×C4×D11—44no—
150C22×C4×D11—44no—
151C22×C4×D11D418yescomplemented
152C22×C4×D11C2312yes—
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2312yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2312yes—
159C22×C4×D11C2311yescharacteristic
160C22×C4×D11C2311yescharacteristic
161C22×Dic22C2311yescharacteristic
162C11×#123—24no—
163C4×D4×C11—24no—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C4⋊C4C2312yes—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C42×C11—24no—
174C2×C42×C11C2312yes—
175C2×C42×C11C2311yescharacteristic
176C2×C42×C11C2312yes—
177C2×C42×C11C2312yes—
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2311yescharacteristic
183#66992—24no—
184#66990—24no—
185#66990—24no—
186#66982—24no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—24no—
189C4×C22⋊D11—44no—
190C2×(C2×D11)⋊C4—24no—
191C2×(C2×D11)⋊C4—24no—
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×C4⋊Dic11—24no—
214C2×C4⋊Dic11C2312yes—
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2311yescharacteristic
217C2×C4⋊Dic11C2312yes—
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2312yes—
228C2×C4×Dic11C2312yes—
229#66949—24no—
230#66948—28no—
231#66947—24no—
232#66937—28no—
233#66937—24no—
234#66936—24no—
235#66935—24no—
236#66935—24no—
237C22⋊C4×D11—24no—
238C22⋊C4×D11—24no—
239#66931—24no—
240C4×D44—28no—
241C4×D44—28no—
242C4×D44—28no—
243C4×D44—28no—
244C4×D44—24no—
245C4×D44—44no—
246#66925—24no—
247C42×D11—44no—
248C11×#95C2312yes—
249C11×#95C2312yes—
250C11×#95C2312yes—
251C11×#95C2312yes—
252C11×#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34957—111nomaximal, Sylow
265C24×C11C2411yescharacteristic
266C24×C11C2411yescharacteristic
267C23×D11—22no—
268C23×D11—22no—
269C23×D11—22no—
270C23×D11—24no—
271C23×D11—24no—
272C23×D11—22no—
273C23×D11—22no—
274C23×D11—42no—
275C23×D11—42no—
276C23×D11C2×D414yes—
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C23×D11C2412yes—
280C23×D11C2411yescharacteristic
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—24no—
286C22×C4×C11—24no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—24no—
292C22×C4×C11C2×D414yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2412yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C2×C22⋊D11—22no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—22no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—22no—
308C2×C22⋊D11—22no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C22×Dic11—22no—
315C22×Dic11—42no—
316C22×Dic11—42no—
317C22×Dic11C2×D414yes—
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2412yes—
326#4339—416no—
327C2×D44—232no—
328C2×D44—24no—
329C2×D44—24no—
330C2×D44—22no—
331C2×D44—22no—
332C2×D44—24no—
333C2×D44—24no—
334C2×D44—24no—
335C2×D44—24no—
336C2×D44—24no—
337C2×D44—24no—
338C2×D44—42no—
339C2×D44—42no—
340C2×D44#4118yescomplemented
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—22no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—24no—
350C2×C4×D11—24no—
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—42no—
358C2×C4×D11—42no—
359C2×C4×D11—416no—
360C2×C4×D11—416no—
361C2×C4×D11C2×D414yes—
362C2×C4×D11C2×D414yes—
363C2×C4×D11C2×D414yes—
364C2×C4×D11C2×D414yes—
365C2×Dic22—22no—
366C2×Dic22—42no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—24no—
369C11×C4⋊C4—24no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—22no—
372C11×C22⋊C4—22no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4#4114yescomplemented
376C42×C11—22no—
377C42×C11—24no—
378C42×C11—24no—
379C42×C11—24no—
380C22⋊Dic11—22no—
381C22⋊Dic11—22no—
382C22⋊Dic11—22no—
383C22⋊Dic11—42no—
384C22⋊Dic11#4114yescomplemented
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—22no—
392(C2×D11)⋊C4—22no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—22no—
396(C2×D11)⋊C4—22no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—22no—
400(C2×D11)⋊C4—24no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—24no—
403(C2×D11)⋊C4—42no—
404(C2×D11)⋊C4—42no—
405(C2×D11)⋊C4—42no—
406C4⋊Dic11—24no—
407C4⋊Dic11—24no—
408C4⋊Dic11—22no—
409C4⋊Dic11—42no—
410Dic11⋊C4—22no—
411Dic11⋊C4—22no—
412Dic11⋊C4—22no—
413Dic11⋊C4—24no—
414Dic11⋊C4—22no—
415Dic11⋊C4—24no—
416Dic11⋊C4—42no—
417C4×Dic11—22no—
418C4×Dic11—24no—
419C4×Dic11—42no—
420C4×Dic11—42no—
421C2×#525—111no—
422C22×C4×D4—111no—
423#2602—112no—
424#2602—112no—
425#2591—111no—
426#2583—111no—
427#2564—112no—
428#2561—111no—
429#2543—112no—
430#2539—111no—
431#2412—111no—
432#2412—111no—
433#2410—111no—
434#2410—111no—
435#2395—112no—
436#2388—112no—
437C4×#123—111no—
438C4×#123D1111yescharacteristic, complemented
439C4×#121—112no—
440C4×#121—112no—
441C4×#120—111no—
442C4×#120—111no—
443C2×C4×C22⋊C4—111no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11C22×D412yes—
452C23×C11C2×#4112yes—
453C23×C11C2×#4112yes—
454C23×C11C2511yescharacteristic
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—22no—
458C22×D11—28no—
459C22×D11—28no—
460C22×D11—22no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—28no—
471C22×D11—21no—
472C22×D11—21no—
473C22×D11—22no—
474C22×D11—21no—
475C22×D11—22no—
476C22×D11—44no—
477C22×D11—48no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—48no—
481C22×D11—44no—
482C22×D11—44no—
483C22×D11C22×D412yes—
484C22×D11C22×D412yes—
485C22×D11C2×#4114yes—
486C22×D11C2×#4114yes—
487D4×C11—44no—
488C2×C4×C11—28no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—28no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—44no—
509C2×C4×C11—44no—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C2×#4114yes—
513C2×C4×C11C2×#4114yes—
514C2×C4×C11H(5,𝔽2)14yes—
515C22⋊D11—48no—
516C22⋊D11—44no—
517C22⋊D11—44no—
518C22⋊D11—44no—
519C22⋊D11—44no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—22no—
528C2×Dic11—21no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—44no—
538C2×Dic11—44no—
539C2×Dic11C22×D412yes—
540C2×Dic11C22×D412yes—
541C2×Dic11C2×#4114yes—
542D44—216no—
543D44—216no—
544D44—48no—
545D44—44no—
546D44—44no—
547C4×D11—28no—
548C4×D11—28no—
549C4×D11—44no—
550C4×D11—44no—
551C4×D11—48no—
552C4×D11—48no—
553C4×D11—48no—
554C4×D11—48no—
555C4×D11—44no—
556Dic22—44no—
557C22×#41—111no—
558C23×D4—111no—
559C24×C4—111no—
560C24×C4—111no—
561#525—228no—
562C2×#123—111no—
563C2×#123—111no—
564C2×#123—111no—
565C2×#123C2×D1111yescharacteristic
566C2×C22⋊Q8—111no—
567C2×C22⋊Q8—111no—
568C2×#121—111no—
569C2×#121—112no—
570C2×#121—112no—
571C2×#121—111no—
572C2×#120—111no—
573C2×#120—111no—
574C2×#120—111no—
575C2×#120—111no—
576C2×C4×D4—111no—
577C2×C4×D4—111no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—112no—
581C2×C4×D4—112no—
582C2×C4×D4—112no—
583C2×C4×D4—111no—
584C2×C4×D4—112no—
585C2×C4×D4—228no—
586C2×C4×D4C2×D1111yescharacteristic
587C2×#117—111no—
588C22×C4⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C42—112no—
594C22×C42C2×D1111yescharacteristic
595#400—112no—
596#399—112no—
597#398—112no—
598#397—112no—
599#397—112no—
600#397—112no—
601#395—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#393—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—112no—
612#390—112no—
613#389—112no—
614#389—112no—
615#388—112no—
616#388—112no—
617#388—112no—
618#388—112no—
619#388—112no—
620#388C2×D1112yescomplemented
621#387—112no—
622#387C2×D1112yescomplemented
623#386—111no—
624#386—111no—
625#386—111no—
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386C2×D1111yescharacteristic
633#385—111no—
634#385—112no—
635#385—111no—
636#385—111no—
637#385—112no—
638#385C2×D1111yescharacteristic
639#381—111no—
640#381C2×D1111yescharacteristic
641#380—112no—
642#380—112no—
643#379—111no—
644#379—111no—
645C4×C4⋊C4—112no—
646C4×C4⋊C4C2×D1112yescomplemented
647C4×C22⋊C4—111no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—111no—
650C4×C22⋊C4—112no—
651C4×C22⋊C4—112no—
652C4×C22⋊C4—112no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4C2×D1111yescharacteristic
656C4×C22⋊C4C2×D1112yescomplemented
657C2×#95—112no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—24no—
661C22×C11—24no—
662C22×C11—41no—
663C22×C11—41no—
664C22×C11—41no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11#53214yes—
668C22×C11C23×D411yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C22×#4112yes—
671C22×C11C22×#4111yescharacteristic
672C22×C11C2×H(5,𝔽2)12yes—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—24no—
676C2×D11—24no—
677C2×D11—22no—
678C2×D11—24no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—24no—
682C2×D11—24no—
683C2×D11—416no—
684C2×D11—416no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—41no—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11#52514yes—
697C4×C11—24no—
698C4×C11—22no—
699C4×C11—24no—
700C4×C11—41no—
701C4×C11—42no—
702C4×C11—41no—
703C4×C11—41no—
704C4×C11—42no—
705C4×C11#53414yes—
706Dic11—22no—
707Dic11—22no—
708Dic11—24no—
709Dic11—41no—
710Dic11—41no—
711Dic11—41no—
712Dic11—42no—
713Dic11—42no—
714C25—111no—
715C25—111no—
716C2×#41—224no—
717C2×#41—444no—
718C22×Q8—111no—
719C22×D4—111no—
720C22×D4—111no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4—111no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—111no—
727C22×D4—112no—
728C22×D4—111no—
729C22×D4—228no—
730C22×D4—224no—
731C22×D4C22×D1111yescharacteristic
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—118no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—112no—
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—112no—
743C23×C4—112no—
744C23×C4—224no—
745C23×C4—444no—
746C23×C4—444no—
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1111yescharacteristic
750C23×C4C22×D1111yescharacteristic
751#123—24no—
752#123—224no—
753#123—224no—
754#123—224no—
755C22⋊Q8—224no—
756C22⋊Q8—224no—
757#121—224no—
758#121—228no—
759#121—228no—
760#121—224no—
761#120—224no—
762#120—224no—
763#120—224no—
764#120—224no—
765C4×D4—24no—
766C4×D4—228no—
767C4×D4—228no—
768C4×D4—228no—
769C4×D4—228no—
770C4×D4—224no—
771C4×D4—224no—
772C4×D4—224no—
773C4×D4—444no—
774C4×D4—444no—
775#117—224no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—224no—
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1112yes—
790C2×C4⋊C4C22×D1112yes—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
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—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—224no—
818C2×C22⋊C4—224no—
819C2×C22⋊C4—224no—
820C2×C22⋊C4—224no—
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C22⋊C4C22×D1111yescharacteristic
823C2×C22⋊C4C22×D1111yescharacteristic
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1111yescharacteristic
827C2×C42—24no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42—444no—
833C2×C42C22×D1112yes—
834C2×C42C22×D1111yescharacteristic
835C2×C42C22×D1112yes—
836C2×C42C22×D1112yes—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95C22×D1112yes—
849#95C22×D1112yes—
850#95C22×D1112yes—
851#95C22×D1112yes—
852#95C22×D1112yes—
853C2×C11—24no—
854C2×C11—81no—
855C2×C11C2×#52511yescharacteristic
856C2×C11C2×#53211yescharacteristic
857C2×C11C2×#53411yescharacteristic
858C2×C11#348112yes—
859C2×C11#348112yes—
860D11—24no—
861D11—42no—
862D11—44no—
863D11—81no—
864C24—111no—
865C24—111no—
866C24—112no—
867C24—114no—
868C24—111no—
869C24—224no—
870C24—224no—
871C24—222no—
872C24—222no—
873C24—222no—
874C24—222no—
875C24—222no—
876C24—442no—
877C24—442no—
878C24C23×D1111yescharacteristic
879C24C23×D1111yescharacteristic
880#41—4416no—
881C2×Q8—222no—
882C2×Q8—442no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—118no—
887C2×D4—224no—
888C2×D4—224no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—2232no—
892C2×D4—222no—
893C2×D4—222no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—224no—
897C2×D4—222no—
898C2×D4—222no—
899C2×D4—222no—
900C2×D4—224no—
901C2×D4—224no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—224no—
906C2×D4—224no—
907C2×D4—442no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—24no—
920C22×C4—112no—
921C22×C4—111no—
922C22×C4—111no—
923C22×C4—114no—
924C22×C4—114no—
925C22×C4—114no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—112no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—112no—
932C22×C4—111no—
933C22×C4—224no—
934C22×C4—224no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—4416no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—4416no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4D4×D1114yes—
957C22×C4C23×D1112yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1112yes—
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1112yes—
965C22×C4C23×D1111yescharacteristic
966C4⋊C4—24no—
967C4⋊C4—22no—
968C4⋊C4—24no—
969C4⋊C4—224no—
970C4⋊C4—224no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—222no—
975C4⋊C4—224no—
976C4⋊C4—222no—
977C4⋊C4—224no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—24no—
983C22⋊C4—22no—
984C22⋊C4—24no—
985C22⋊C4—114no—
986C22⋊C4—224no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—222no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—222no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—222no—
1001C22⋊C4—222no—
1002C22⋊C4—222no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—222no—
1006C22⋊C4—224no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4#433914yescomplemented
1012C42—24no—
1013C42—24no—
1014C42—22no—
1015C42—24no—
1016C42—222no—
1017C42—224no—
1018C42—442no—
1019C42—442no—
1020C11#3495711yescharacteristic, complemented, Sylow
1021C23—22no—
1022C23—22no—
1023C23—21no—
1024C23—21no—
1025C23—22no—
1026C23—21no—
1027C23—22no—
1028C23—112no—
1029C23—114no—
1030C23—112no—
1031C23—114no—
1032C23—228no—
1033C23—228no—
1034C23—221no—
1035C23—221no—
1036C23—222no—
1037C23—228no—
1038C23—221no—
1039C23—222no—
1040C23—222no—
1041C23—221no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—221no—
1049C23—221no—
1050C23—221no—
1051C23—222no—
1052C23—222no—
1053C23—444no—
1054C23—448no—
1055C23—448no—
1056C23—448no—
1057C23—448no—
1058C23—444no—
1059C23—444no—
1060C23C2×#433912yes—
1061C23C2×D4×D1112yes—
1062C23#41×D1112yes—
1063C23C24×D1111yescharacteristic
1064Q8—444no—
1065D4—44no—
1066D4—2216no—
1067D4—2216no—
1068D4—448no—
1069D4—444no—
1070D4—444no—
1071D4—448no—
1072D4—444no—
1073D4—444no—
1074D4—444no—
1075D4—444no—
1076C2×C4—28no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—28no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—44no—
1097C2×C4—44no—
1098C2×C4—112no—
1099C2×C4—112no—
1100C2×C4—114no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—228no—
1106C2×C4—228no—
1107C2×C4—222no—
1108C2×C4—221no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—221no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—221no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—444no—
1121C2×C4—444no—
1122C2×C4—448no—
1123C2×C4—448no—
1124C2×C4—448no—
1125C2×C4—444no—
1126C2×C4—444no—
1127C2×C4—448no—
1128C2×C4—444no—
1129C2×C4C2×#433914yes—
1130C2×C4C2×D4×D1112yes—
1131C2×C4C2×D4×D1112yes—
1132C2×C4#41×D1114yes—
1133C2×C4#6704214yes—
1134C22—22no—
1135C22—24no—
1136C22—24no—
1137C22—22no—
1138C22—41no—
1139C22—41no—
1140C22—42no—
1141C22—42no—
1142C22—41no—
1143C22—114no—
1144C22—222no—
1145C22—222no—
1146C22—224no—
1147C22—224no—
1148C22—222no—
1149C22—222no—
1150C22—224no—
1151C22—224no—
1152C22—224no—
1153C22—222no—
1154C22—4416no—
1155C22—4416no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22—441no—
1163C22—441no—
1164C22—442no—
1165C22—442no—
1166C22—441no—
1167C22#1062307914yes—
1168C22C22×#433911yescharacteristic
1169C22C22×D4×D1111yescharacteristic
1170C22C2×#41×D1111yescharacteristic
1171C22C2×#41×D1112yes—
1172C22C2×#6704212yes—
1173C4—22no—
1174C4—24no—
1175C4—24no—
1176C4—42no—
1177C4—41no—
1178C4—41no—
1179C4—42no—
1180C4—41no—
1181C4—222no—
1182C4—222no—
1183C4—224no—
1184C4—441no—
1185C4—442no—
1186C4—441no—
1187C4—442no—
1188C4—441no—
1189C4#1062318414yes—
1190C2—24no—
1191C2—81no—
1192C2—224no—
1193C2—442no—
1194C2—444no—
1195C2—881no—
1196C2D11×#52511yescharacteristic
1197C2C2×#1062307911yescharacteristic
1198C2C2×#1062318411yescharacteristic
1199C2#1308222212yes—
1200C2#1308222612yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#123C2
hypercenterC4×#123D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10623078C2semidirect
2. C22×C4×D44C2semidirect
3. #13074234C2semidirect
4. #13074226C2semidirect
5. #13074093C2semidirect
6. #13073993C2semidirect
7. #13073795C2semidirect
8. #13073773C2semidirect
9. #13073581C2semidirect
10. #13073546C2semidirect
11. #13072014C2semidirect
12. #13072008C2semidirect
13. #13071993C2semidirect
14. #13071988C2semidirect
15. #13071879C2semidirect
16. #13071832C2semidirect
17. C4×#66982C2semidirect
18. C4×#66948C2semidirect
19. C4×#66937C2semidirect
20. C4×#66935C2semidirect
21. C4×#66990C2semidirect
22. C4×C22⋊C4×D11C2semidirect
23. C4×C11×#123C2semidirect
24. C22×#4339C22semidirect
36. C2×C4×C22⋊D11C22semidirect
37. C2×C4×C22⋊D11C22semidirect
42. C2×#66949C22semidirect
44. C2×#66947C22semidirect
46. C2×#66937C22semidirect
47. C2×#66936C22semidirect
58. C2×C4×D44C22semidirect
59. C2×C4×D44C22semidirect
60. C2×#66925C22semidirect
61. C2×C42×D11C22semidirect
62. C11×#388C22semidirect
63. C11×#387C22semidirect
67. C4×C11×C4⋊C4C22semidirect
69. C4×C11×C22⋊C4C22semidirect
75. #10622606C22semidirect
76. #10622605C22semidirect
78. #10622602C22semidirect
79. #10622601C22semidirect
80. #10622600C22semidirect
81. #10622598C22semidirect
82. #10622597C22semidirect
83. #10622574C22semidirect
84. #10622574C22semidirect
86. #10622573C22semidirect
88. #10622570C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
93. #10622564C22semidirect
98. #10622553C22semidirect
99. C4×(C2×D11)⋊C4C22semidirect
100. C4×(C2×D11)⋊C4C22semidirect
101. C4×(C2×D11)⋊C4C22semidirect
102. C4×(C2×D11)⋊C4C22semidirect
103. #10622546C22semidirect
104. C4×Dic11⋊C4C22semidirect
105. #10622288C22semidirect
106. #10622288C22semidirect
107. #10622286C22semidirect
109. #10622285C22semidirect
111. #10622283C22semidirect
112. #10622283C22semidirect
113. #10622282C22semidirect
114. #10622281C22semidirect
115. #10622280C22semidirect
116. #10622279C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. D11×#95C22semidirect
122. #10622273C22semidirect
123. #10622269C22semidirect
124. #10622260C22semidirect
151. C22×C4×D11D4semidirect
340. C2×D44#41semidirect
375. C11×C22⋊C4#41semidirect
384. C22⋊Dic11#41semidirect
438. C4×#123D11semidirect
620. #388C2×D11semidirect
622. #387C2×D11semidirect
646. C4×C4⋊C4C2×D11semidirect
656. C4×C22⋊C4C2×D11semidirect
1011. C22⋊C4#4339semidirect
1020. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C22×C4×D442
#130742342
#130742262
#130740932
#130739932
#130737952
#130737732
#130735812
#130735462
#130720142
#130720082
#130719932
#130719882
#130718792
#130718322
C4×#669822
C4×#669482
C4×#669372
C4×#669352
C4×#669902
C4×C22⋊C4×D112
C4×C11×#1232
#3495711