Finite Group Databasebeta

← #14920197

Subgroups — #14920197

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1184 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#13074540C212yesmaximal, complemented
4#13074507C212yesmaximal, complemented
5#13074465C212yesmaximal, complemented
6#13074463C212yesmaximal, complemented
7#13074433C211yesmaximal, characteristic, complemented
8#13074427C211yesmaximal, characteristic, complemented
9#13074394C211yesmaximal, characteristic, complemented
10#13074393C211yesmaximal, characteristic, complemented
11#13074362C211yesmaximal, characteristic, complemented
12#13074356C211yesmaximal, characteristic, complemented
13#13074333C211yesmaximal, characteristic, complemented
14#13074332C211yesmaximal, characteristic, complemented
15#13071879C212yesmaximal, complemented
16#13071860C212yesmaximal, complemented
17#13071856C212yesmaximal, complemented
18#13071832C212yesmaximal, complemented
19C4×#66982C211yesmaximal, characteristic, complemented
20C4×#66935C211yesmaximal, characteristic, complemented
21C4×#66990C211yesmaximal, characteristic, complemented
22#13070997C211yesmaximal, 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×#66947C2211yescharacteristic, complemented
44C2×#66937C2211yescharacteristic, complemented
45C2×#66936C2211yescharacteristic, complemented
46C2×#66935C2211yescharacteristic
47C2×#66935C2211yescharacteristic
48C2×#66931C2211yescharacteristic
49C2×C4×D44—28no—
50C2×C4×D44C2212yes—
51C2×C4×D44C2212yes—
52C2×C4×D44C2212yes—
53C2×C4×D44C2212yes—
54C2×C4×D44C2211yescharacteristic, complemented
55C2×C4×D44C2212yescomplemented
56C2×#66925C2211yescharacteristic, complemented
57C2×#66925C2212yescomplemented
58C11×#388C2212yescomplemented
59C11×#387C2212yescomplemented
60C11×#386C2211yescharacteristic
61C11×#385C2211yescharacteristic
62C11×#381C2211yescharacteristic
63C4×C11×C4⋊C4C2212yescomplemented
64C4×C11×C22⋊C4C2211yescharacteristic
65C4×C11×C22⋊C4C2212yescomplemented
66#10622833C2211yescharacteristic
67#10622826C2211yescharacteristic
68#10622824C2211yescharacteristic
69#10622823C2211yescharacteristic
70C4×C22⋊Dic11C2211yescharacteristic
71#10622607C2212yescomplemented
72#10622607C2212yescomplemented
73#10622606C2212yescomplemented
74#10622605C2212yescomplemented
75#10622604C2212yes—
76#10622604C2212yes—
77#10622604C2212yescomplemented
78#10622602C2212yescomplemented
79#10622597C2212yescomplemented
80#10622574C2212yescomplemented
81#10622574C2212yescomplemented
82#10622573C2212yes—
83#10622573C2212yes—
84#10622573C2212yescomplemented
85#10622572C2212yescomplemented
86#10622572C2212yescomplemented
87#10622571C2211yescharacteristic
88#10622569C2212yescomplemented
89#10622568C2211yescharacteristic
90#10622568C2211yescharacteristic
91#10622568C2211yescharacteristic
92#10622568C2211yescharacteristic
93#10622563C2211yescharacteristic
94#10622561C2212yescomplemented
95#10622559C2211yescharacteristic
96#10622555C2211yescharacteristic
97#10622555C2211yescharacteristic
98#10622553C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×(C2×D11)⋊C4C2212yescomplemented
101C4×(C2×D11)⋊C4C2212yescomplemented
102C4×(C2×D11)⋊C4C2212yescomplemented
103#10622546C2212yescomplemented
104C4×Dic11⋊C4C2212yescomplemented
105#10622289C2212yescomplemented
106#10622288C2212yescomplemented
107#10622288C2212yescomplemented
108#10622288C2212yescomplemented
109#10622287C2212yescomplemented
110#10622286C2212yescomplemented
111#10622285C2212yes—
112#10622285C2212yes—
113#10622285C2212yescomplemented
114#10622285C2212yescomplemented
115#10622284C2212yes—
116#10622284C2212yes—
117#10622281C2212yescomplemented
118#10622280C2212yescomplemented
119#10622278C2212yescomplemented
120#10622277C2212yescomplemented
121#10622274C2212yescomplemented
122#10622273C2212yescomplemented
123#10622270C2212yescomplemented
124#10622269C2212yescomplemented
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⋊D11C2311yescharacteristic
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2312yes—
137C23×Dic11C2311yescharacteristic
138C23×Dic11C2311yescharacteristic
139C2×#4339—24no—
140C2×#4339—44no—
141C22×D44—24no—
142C22×D44—24no—
143C22×D44—24no—
144C22×D44C2312yes—
145C22×D44C2312yes—
146C22×D44C2311yescharacteristic
147C22×D44C2312yes—
148C22×D44C2311yescharacteristic
149C22×C4×D11—24no—
150C22×C4×D11—44no—
151C22×C4×D11—44no—
152C22×C4×D11D418yescomplemented
153C22×C4×D11C2312yes—
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2312yes—
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×Dic22C2311yescharacteristic
161C11×#123—24no—
162C4×D4×C11—24no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C42×C11—24no—
173C2×C42×C11C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2312yes—
176C2×C42×C11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2312yes—
182#66992—24no—
183#66990—24no—
184#66990—24no—
185#66982—24no—
186C4×C22⋊D11—24no—
187C4×C22⋊D11—24no—
188C4×C22⋊D11—44no—
189C2×(C2×D11)⋊C4—24no—
190C2×(C2×D11)⋊C4—24no—
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×(C2×D11)⋊C4C2311yescharacteristic
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×C4⋊Dic11—24no—
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2312yes—
217C2×C4⋊Dic11C2311yescharacteristic
218C2×C4⋊Dic11C2312yes—
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2312yes—
230#66949—24no—
231#66947—24no—
232#66937—24no—
233#66936—24no—
234#66935—24no—
235#66935—24no—
236#66931—24no—
237C4×D44—28no—
238C4×D44—28no—
239C4×D44—28no—
240C4×D44—28no—
241C4×D44—24no—
242C4×D44—44no—
243#66925—24no—
244#66925—44no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
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—
261#34562—111nomaximal, Sylow
262C24×C11C2411yescharacteristic
263C24×C11C2411yescharacteristic
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—22no—
267C23×D11—22no—
268C23×D11—42no—
269C23×D11—42no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11C2×D414yes—
273C23×D11#4114yescomplemented
274C23×D11C2411yescharacteristic
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C23×D11C2412yes—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11—24no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—42no—
288C22×C4×C11C2×D414yes—
289C22×C4×C11#4114yescomplemented
290C22×C4×C11C2412yes—
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C2×C22⋊D11—22no—
300C2×C22⋊D11—22no—
301C2×C22⋊D11—22no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—22no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11—42no—
310C2×C22⋊D11—42no—
311C22×Dic11—22no—
312C22×Dic11—42no—
313C22×Dic11—42no—
314C22×Dic11C2×D414yes—
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323#4339—416no—
324C2×D44—232no—
325C2×D44—24no—
326C2×D44—24no—
327C2×D44—22no—
328C2×D44—22no—
329C2×D44—24no—
330C2×D44—24no—
331C2×D44—24no—
332C2×D44—24no—
333C2×D44—24no—
334C2×D44—42no—
335C2×D44—42no—
336C2×D44—42no—
337C2×D44—42no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—22no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—416no—
351C2×C4×D11—416no—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11C2×D414yes—
356C2×Dic22—22no—
357C2×Dic22—42no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—24no—
360C11×C4⋊C4—42no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—22no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—42no—
367C42×C11—22no—
368C42×C11—24no—
369C42×C11—24no—
370C42×C11—24no—
371C22⋊Dic11—22no—
372C22⋊Dic11—22no—
373C22⋊Dic11—22no—
374C22⋊Dic11—22no—
375C22⋊Dic11—42no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—22no—
379(C2×D11)⋊C4—22no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4—42no—
398(C2×D11)⋊C4—42no—
399C4⋊Dic11—24no—
400C4⋊Dic11—24no—
401C4⋊Dic11—22no—
402C4⋊Dic11—42no—
403Dic11⋊C4—22no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—24no—
408Dic11⋊C4—42no—
409Dic11⋊C4—42no—
410Dic11⋊C4—42no—
411Dic11⋊C4—42no—
412C4×Dic11—22no—
413C4×Dic11—24no—
414C2×#525—111no—
415C22×C4×D4—111no—
416#2638—112no—
417#2635—112no—
418#2630—112no—
419#2630—112no—
420#2627—111no—
421#2626—111no—
422#2622—111no—
423#2622—111no—
424#2618—111no—
425#2617—111no—
426#2613—111no—
427#2613—111no—
428#2395—112no—
429#2392—112no—
430#2392—112no—
431#2388—112no—
432C4×#123—111no—
433C4×#123D1111yescharacteristic, complemented
434C4×#120—111no—
435C4×#120—111no—
436#2280—111no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—21no—
440C23×C11—21no—
441C23×C11—21no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11C22×D412yes—
445C23×C11C2×#4112yes—
446C23×C11C2×#4112yes—
447C23×C11C2511yescharacteristic
448C22×D11—28no—
449C22×D11—28no—
450C22×D11—22no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—22no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—44no—
470C22×D11—44no—
471C22×D11—48no—
472C22×D11—44no—
473C22×D11—44no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11C22×D412yes—
478C22×D11C22×D412yes—
479C22×D11C2×#4114yes—
480D4×C11—44no—
481C2×C4×C11—28no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—28no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
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—44no—
503C2×C4×C11—44no—
504C2×C4×C11C22×D412yes—
505C2×C4×C11C22×D412yes—
506C2×C4×C11C2×#4114yes—
507C2×C4×C11H(5,𝔽2)14yes—
508C22⋊D11—44no—
509C22⋊D11—44no—
510C22⋊D11—44no—
511C22⋊D11—48no—
512C22⋊D11—44no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—21no—
516C2×Dic11—21no—
517C2×Dic11—21no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—22no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—44no—
532C2×Dic11—44no—
533C2×Dic11C22×D412yes—
534C2×Dic11C22×D412yes—
535D44—216no—
536D44—216no—
537D44—44no—
538D44—48no—
539D44—44no—
540C4×D11—28no—
541C4×D11—28no—
542C4×D11—44no—
543C4×D11—44no—
544C4×D11—48no—
545C4×D11—48no—
546C4×D11—44no—
547Dic22—44no—
548C22×#41—111no—
549C23×D4—111no—
550C24×C4—111no—
551C24×C4—111no—
552#525—228no—
553C2×#123—111no—
554C2×#123—111no—
555C2×#123—111no—
556C2×#123C2×D1111yescharacteristic
557C2×C22⋊Q8—111no—
558C2×C22⋊Q8—111no—
559C2×#121—111no—
560C2×#121—111no—
561C2×#120—111no—
562C2×#120—111no—
563C2×#120—111no—
564C2×#120—111no—
565C2×C4×D4—111no—
566C2×C4×D4—111no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—112no—
570C2×C4×D4—112no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—112no—
574C2×C4×D4—228no—
575C2×C4×D4C2×D1111yescharacteristic
576C2×#117—111no—
577C2×#117—112no—
578C22×C4⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—111no—
581C22×C42C2×D1111yescharacteristic
582#400—112no—
583#399—112no—
584#398—112no—
585#398—112no—
586#398—112no—
587#397—112no—
588#397—112no—
589#397—112no—
590#397—112no—
591#397—112no—
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#395—112no—
597#394—112no—
598#394—112no—
599#394—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#394—112no—
608#393—112no—
609#392—112no—
610#392—112no—
611#392—112no—
612#392—112no—
613#392—112no—
614#388—112no—
615#388C2×D1112yescomplemented
616#387—112no—
617#387C2×D1112yescomplemented
618#386—111no—
619#386—111no—
620#386—111no—
621#386—112no—
622#386—112no—
623#386C2×D1111yescharacteristic
624#385—111no—
625#385—112no—
626#385—111no—
627#385—111no—
628#385—112no—
629#385C2×D1111yescharacteristic
630#381—111no—
631#381—112no—
632#381C2×D1111yescharacteristic
633#380—111no—
634#380—111no—
635#380—112no—
636#379—111no—
637#379—111no—
638#379—111no—
639#379—111no—
640C4×C4⋊C4—112no—
641C4×C4⋊C4C2×D1112yescomplemented
642C4×C22⋊C4—111no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4C2×D1111yescharacteristic
648C4×C22⋊C4C2×D1112yescomplemented
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—41no—
654C22×C11—41no—
655C22×C11—41no—
656C22×C11—42no—
657C22×C11—42no—
658C22×C11#52514yes—
659C22×C11C23×D411yescharacteristic
660C22×C11C22×#4111yescharacteristic
661C22×C11C22×#4111yescharacteristic
662C22×C11C2×H(5,𝔽2)12yes—
663C22×C11#58512yes—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—24no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—24no—
672C2×D11—24no—
673C2×D11—416no—
674C2×D11—416no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—42no—
687C2×D11—42no—
688C4×C11—24no—
689C4×C11—22no—
690C4×C11—41no—
691C4×C11—41no—
692C4×C11—42no—
693C4×C11—41no—
694C4×C11—42no—
695C4×C11—42no—
696C4×C11#53414yes—
697Dic11—22no—
698Dic11—22no—
699Dic11—41no—
700Dic11—41no—
701Dic11—42no—
702Dic11—41no—
703Dic11—42no—
704Dic11—42no—
705C25—111no—
706C25—111no—
707C2×#41—224no—
708C2×#41—444no—
709C22×Q8—111no—
710C22×D4—111no—
711C22×D4—111no—
712C22×D4—112no—
713C22×D4—111no—
714C22×D4—111no—
715C22×D4—112no—
716C22×D4—112no—
717C22×D4—111no—
718C22×D4—112no—
719C22×D4—111no—
720C22×D4—224no—
721C22×D4—224no—
722C22×D4—224no—
723C22×D4C22×D1111yescharacteristic
724C23×C4—111no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—118no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—111no—
731C23×C4—112no—
732C23×C4—111no—
733C23×C4—112no—
734C23×C4—224no—
735C23×C4—444no—
736C23×C4—444no—
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1111yescharacteristic
741#123—24no—
742#123—224no—
743#123—224no—
744#123—224no—
745C22⋊Q8—224no—
746C22⋊Q8—224no—
747#121—224no—
748#121—224no—
749#120—224no—
750#120—224no—
751#120—224no—
752#120—224no—
753C4×D4—24no—
754C4×D4—228no—
755C4×D4—228no—
756C4×D4—228no—
757C4×D4—228no—
758C4×D4—224no—
759C4×D4—224no—
760C4×D4—224no—
761C4×D4—444no—
762C4×D4—444no—
763#117—224no—
764#117—444no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—224no—
779C2×C4⋊C4C22×D1111yescharacteristic
780C2×C4⋊C4C22×D1112yes—
781C2×C4⋊C4C22×D1112yes—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—111no—
791C2×C22⋊C4—111no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
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—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—224no—
811C2×C22⋊C4—224no—
812C2×C22⋊C4C22×D1111yescharacteristic
813C2×C22⋊C4C22×D1111yescharacteristic
814C2×C22⋊C4C22×D1111yescharacteristic
815C2×C22⋊C4C22×D1111yescharacteristic
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C42—24no—
819C2×C42—111no—
820C2×C42—112no—
821C2×C42C22×D1112yes—
822C2×C42C22×D1111yescharacteristic
823C2×C42C22×D1112yes—
824C2×C42C22×D1112yes—
825#95—112no—
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#95C22×D1112yes—
837#95C22×D1112yes—
838#95C22×D1112yes—
839#95C22×D1112yes—
840#95C22×D1112yes—
841C2×C11—24no—
842C2×C11—81no—
843C2×C11C2×#52511yescharacteristic
844C2×C11C2×#53411yescharacteristic
845C2×C11#344911yescharacteristic
846C2×C11#345912yes—
847C2×C11#346012yes—
848D11—42no—
849D11—42no—
850D11—44no—
851D11—81no—
852C24—111no—
853C24—111no—
854C24—112no—
855C24—114no—
856C24—114no—
857C24—111no—
858C24—222no—
859C24—222no—
860C24—222no—
861C24—222no—
862C24—442no—
863C24—442no—
864C24—442no—
865C24—442no—
866C24C23×D1111yescharacteristic
867C24C23×D1111yescharacteristic
868#41—4416no—
869C2×Q8—222no—
870C2×Q8—442no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—224no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—224no—
878C2×D4—2232no—
879C2×D4—222no—
880C2×D4—222no—
881C2×D4—224no—
882C2×D4—222no—
883C2×D4—222no—
884C2×D4—222no—
885C2×D4—224no—
886C2×D4—222no—
887C2×D4—222no—
888C2×D4—222no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—442no—
892C2×D4—442no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4—442no—
899C2×D4—442no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—24no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—24no—
906C22×C4—42no—
907C22×C4—111no—
908C22×C4—111no—
909C22×C4—114no—
910C22×C4—114no—
911C22×C4—114no—
912C22×C4—114no—
913C22×C4—114no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—111no—
917C22×C4—111no—
918C22×C4—112no—
919C22×C4—111no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—222no—
923C22×C4—224no—
924C22×C4—224no—
925C22×C4—222no—
926C22×C4—224no—
927C22×C4—224no—
928C22×C4—224no—
929C22×C4—4416no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—442no—
934C22×C4—4416no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4#433914yescomplemented
938C22×C4D4×D1114yes—
939C22×C4C23×D1112yes—
940C22×C4C23×D1112yes—
941C22×C4C23×D1112yes—
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1112yes—
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C4⋊C4—24no—
949C4⋊C4—22no—
950C4⋊C4—42no—
951C4⋊C4—224no—
952C4⋊C4—224no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—222no—
957C4⋊C4—224no—
958C4⋊C4—222no—
959C4⋊C4—442no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C4⋊C4—442no—
964C22⋊C4—22no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—24no—
968C22⋊C4—22no—
969C22⋊C4—42no—
970C22⋊C4—224no—
971C22⋊C4—224no—
972C22⋊C4—222no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—222no—
976C22⋊C4—222no—
977C22⋊C4—222no—
978C22⋊C4—222no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—222no—
982C22⋊C4—222no—
983C22⋊C4—222no—
984C22⋊C4—222no—
985C22⋊C4—224no—
986C22⋊C4—222no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C42—24no—
999C42—24no—
1000C42—22no—
1001C42—24no—
1002C42—222no—
1003C42—224no—
1004C11#3456211yescharacteristic, complemented, Sylow
1005C23—22no—
1006C23—22no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—22no—
1011C23—22no—
1012C23—112no—
1013C23—112no—
1014C23—114no—
1015C23—228no—
1016C23—228no—
1017C23—221no—
1018C23—221no—
1019C23—222no—
1020C23—222no—
1021C23—221no—
1022C23—221no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—222no—
1031C23—221no—
1032C23—221no—
1033C23—221no—
1034C23—222no—
1035C23—222no—
1036C23—444no—
1037C23—444no—
1038C23—448no—
1039C23—444no—
1040C23—444no—
1041C23—448no—
1042C23—448no—
1043C23—448no—
1044C23C2×#433912yes—
1045C23C2×D4×D1112yes—
1046C23#41×D1112yes—
1047C23C24×D1111yescharacteristic
1048Q8—444no—
1049D4—44no—
1050D4—2216no—
1051D4—2216no—
1052D4—444no—
1053D4—444no—
1054D4—448no—
1055D4—444no—
1056D4—444no—
1057D4—444no—
1058D4—448no—
1059D4—444no—
1060C2×C4—28no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—28no—
1065C2×C4—22no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
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—44no—
1082C2×C4—44no—
1083C2×C4—112no—
1084C2×C4—112no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—222no—
1090C2×C4—221no—
1091C2×C4—221no—
1092C2×C4—221no—
1093C2×C4—222no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—444no—
1106C2×C4—444no—
1107C2×C4—448no—
1108C2×C4—444no—
1109C2×C4—444no—
1110C2×C4—448no—
1111C2×C4—444no—
1112C2×C4C2×#433914yes—
1113C2×C4C2×D4×D1112yes—
1114C2×C4C2×D4×D1112yes—
1115C2×C4#6704214yes—
1116C22—22no—
1117C22—22no—
1118C22—24no—
1119C22—24no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—42no—
1124C22—42no—
1125C22—222no—
1126C22—222no—
1127C22—224no—
1128C22—222no—
1129C22—222no—
1130C22—222no—
1131C22—222no—
1132C22—224no—
1133C22—224no—
1134C22—4416no—
1135C22—4416no—
1136C22—442no—
1137C22—442no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—441no—
1145C22—441no—
1146C22—441no—
1147C22—442no—
1148C22—442no—
1149C22#1062307814yes—
1150C22C22×#433911yescharacteristic
1151C22C22×D4×D1111yescharacteristic
1152C22C2×#41×D1111yescharacteristic
1153C22C2×#6704212yes—
1154C22#1062345312yes—
1155C4—24no—
1156C4—22no—
1157C4—41no—
1158C4—41no—
1159C4—42no—
1160C4—41no—
1161C4—42no—
1162C4—42no—
1163C4—222no—
1164C4—222no—
1165C4—441no—
1166C4—442no—
1167C4—441no—
1168C4—441no—
1169C4—442no—
1170C4—442no—
1171C4#1062318414yes—
1172C2—24no—
1173C2—81no—
1174C2—442no—
1175C2—442no—
1176C2—444no—
1177C2—881no—
1178C2C2×#1062307811yescharacteristic
1179C2C2×#1062318411yescharacteristic
1180C2#1308194611yescharacteristic
1181C2#1308202612yes—
1182C2#1308203212yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#123C2
hypercenterC4×#123D11
hypocenterC11#34562
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. #13074540C2semidirect
4. #13074507C2semidirect
5. #13074465C2semidirect
6. #13074463C2semidirect
7. #13074433C2semidirect
8. #13074427C2semidirect
9. #13074394C2semidirect
10. #13074393C2semidirect
11. #13074362C2semidirect
12. #13074356C2semidirect
13. #13074333C2semidirect
14. #13074332C2semidirect
15. #13071879C2semidirect
16. #13071860C2semidirect
17. #13071856C2semidirect
18. #13071832C2semidirect
19. C4×#66982C2semidirect
20. C4×#66935C2semidirect
21. C4×#66990C2semidirect
22. #13070997C2semidirect
23. C4×C11×#123C2semidirect
24. C22×#4339C22semidirect
36. C2×C4×C22⋊D11C22semidirect
37. C2×C4×C22⋊D11C22semidirect
42. C2×#66949C22semidirect
43. C2×#66947C22semidirect
44. C2×#66937C22semidirect
45. C2×#66936C22semidirect
54. C2×C4×D44C22semidirect
55. C2×C4×D44C22semidirect
56. C2×#66925C22semidirect
57. C2×#66925C22semidirect
58. C11×#388C22semidirect
59. C11×#387C22semidirect
63. C4×C11×C4⋊C4C22semidirect
65. C4×C11×C22⋊C4C22semidirect
71. #10622607C22semidirect
72. #10622607C22semidirect
73. #10622606C22semidirect
74. #10622605C22semidirect
77. #10622604C22semidirect
78. #10622602C22semidirect
79. #10622597C22semidirect
80. #10622574C22semidirect
81. #10622574C22semidirect
84. #10622573C22semidirect
85. #10622572C22semidirect
86. #10622572C22semidirect
88. #10622569C22semidirect
94. #10622561C22semidirect
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. #10622289C22semidirect
106. #10622288C22semidirect
107. #10622288C22semidirect
108. #10622288C22semidirect
109. #10622287C22semidirect
110. #10622286C22semidirect
113. #10622285C22semidirect
114. #10622285C22semidirect
117. #10622281C22semidirect
118. #10622280C22semidirect
119. #10622278C22semidirect
120. #10622277C22semidirect
121. #10622274C22semidirect
122. #10622273C22semidirect
123. #10622270C22semidirect
124. #10622269C22semidirect
152. C22×C4×D11D4semidirect
273. C23×D11#41semidirect
289. C22×C4×C11#41semidirect
433. C4×#123D11semidirect
615. #388C2×D11semidirect
617. #387C2×D11semidirect
641. C4×C4⋊C4C2×D11semidirect
648. C4×C22⋊C4C2×D11semidirect
937. C22×C4#4339semidirect
1004. C11#34562semidirect

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
#130745402
#130745072
#130744652
#130744632
#130744332
#130744272
#130743942
#130743932
#130743622
#130743562
#130743332
#130743322
#130718792
#130718602
#130718562
#130718322
C4×#669822
C4×#669352
C4×#669902
#130709972
C4×C11×#1232
#3456211