Finite Group Databasebeta

← #14920200

Subgroups — #14920200

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074541C211yesmaximal, characteristic, complemented
4#13074538C211yesmaximal, characteristic, complemented
5#13074509C211yesmaximal, characteristic, complemented
6#13074506C211yesmaximal, characteristic, complemented
7#13074458C212yesmaximal, complemented
8#13074454C212yesmaximal, complemented
9#13074430C211yesmaximal, characteristic, complemented
10#13074422C211yesmaximal, characteristic, complemented
11#13074390C212yesmaximal, complemented
12#13074359C211yesmaximal, characteristic, complemented
13#13074351C211yesmaximal, characteristic, complemented
14#13074329C212yesmaximal, complemented
15#13071873C211yesmaximal, characteristic, complemented
16#13071860C212yesmaximal, complemented
17#13071856C212yesmaximal, complemented
18#13071832C211yesmaximal, characteristic, complemented
19#13071831C211yesmaximal, characteristic, complemented
20C4×#66947C212yesmaximal, complemented
21C4×#66935C212yesmaximal, complemented
22#13070997C211yesmaximal, characteristic, complemented
23C11×#2395C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C22×#4339C2211yescharacteristic, complemented
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic, complemented
30C2×D4×Dic11C2211yescharacteristic
31C2×C4×C22⋊D11C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2212yescomplemented
34C4×D4×D11—28no—
35#10623055—28no—
36C2×#66950C2211yescharacteristic
37C2×#66950C2211yescharacteristic, complemented
38C2×#66948C2211yescharacteristic
39C2×#66948C2211yescharacteristic, complemented
40C2×#66947C2212yes—
41C2×#66946C2211yescharacteristic
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×#66939C2212yescomplemented
44C2×#66935C2212yes—
45C2×#66935C2212yes—
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×(C22⋊D11)⋊C4C2211yescharacteristic
48C2×C22⋊C4×D11C2211yescharacteristic
49C2×C22⋊C4×D11C2211yescharacteristic
50C2×C4×D44C2212yes—
51C2×C4×D44C2211yescharacteristic
52C2×C4×D44C2212yescomplemented
53C2×C4×D44C2212yescomplemented
54C2×#66925C2212yescomplemented
55C2×C42×D11C2211yescharacteristic
56C11×#400C2211yescharacteristic, complemented
57C11×#399C2211yescharacteristic, complemented
58C11×#398C2211yescharacteristic, complemented
59C11×#397C2212yescomplemented
60C11×#397C2211yescharacteristic, complemented
61C11×#394C2212yes—
62C4×C11×C4⋊C4C2212yescomplemented
63C4×C11×C22⋊C4C2212yescomplemented
64C4×C11×C22⋊C4C2211yescharacteristic, complemented
65#10622836C2212yes—
66C4×C22⋊Dic11C2211yescharacteristic, complemented
67#10622607C2212yescomplemented
68#10622607C2212yescomplemented
69#10622606C2211yescharacteristic, complemented
70#10622605C2211yescharacteristic, complemented
71#10622604C2212yes—
72#10622604C2212yescomplemented
73#10622604C2211yescharacteristic, complemented
74#10622603C2212yescomplemented
75#10622602C2212yes—
76#10622595C2211yescharacteristic, complemented
77#10622594C2212yescomplemented
78#10622593C2211yescharacteristic, complemented
79#10622592C2211yescharacteristic, complemented
80#10622574C2212yescomplemented
81#10622573C2212yes—
82#10622573C2212yes—
83#10622573C2211yescharacteristic, complemented
84#10622572C2212yes—
85#10622572C2212yes—
86#10622572C2212yescomplemented
87#10622572C2212yescomplemented
88#10622571C2212yescomplemented
89#10622568C2212yes—
90#10622568C2212yes—
91#10622565C2212yescomplemented
92#10622563C2212yescomplemented
93#10622561C2212yescomplemented
94#10622560C2211yescharacteristic, complemented
95#10622555C2212yescomplemented
96C4×(C2×D11)⋊C4C2212yes—
97C4×(C2×D11)⋊C4C2212yescomplemented
98C4×(C2×D11)⋊C4C2212yescomplemented
99C4×(C2×D11)⋊C4C2212yescomplemented
100C4×Dic11⋊C4C2212yescomplemented
101#10622289C2212yescomplemented
102#10622288C2212yescomplemented
103#10622287C2212yescomplemented
104#10622286C2211yescharacteristic, complemented
105#10622285C2212yescomplemented
106#10622285C2211yescharacteristic, complemented
107#10622285C2212yescomplemented
108#10622284C2212yes—
109#10622284C2211yescharacteristic, complemented
110#10622282C2212yescomplemented
111#10622281C2212yes—
112#10622281C2212yescomplemented
113#10622280C2211yescharacteristic
114#10622280C2211yescharacteristic
115#10622278C2212yes—
116#10622278C2212yes—
117#10622278C2212yescomplemented
118#10622277C2212yes—
119#10622277C2211yescharacteristic, complemented
120#10622277C2211yescharacteristic, complemented
121#10622274C2212yescomplemented
122#10622270C2212yescomplemented
123#10622269C2211yescharacteristic, complemented
124#10622268C2212yescomplemented
125C24×D11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C2×D4×D11—24no—
137C2×D4×D11—24no—
138C2×D4×D11—24no—
139C2×#4339—24no—
140C2×#4339—44no—
141C22×D44C2312yes—
142C22×D44C2311yescharacteristic
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×D44C2311yescharacteristic
146C22×C4×D11—24no—
147C22×C4×D11—44no—
148C22×C4×D11—44no—
149C22×C4×D11D418yescomplemented
150C22×C4×D11C2311yescharacteristic
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2311yescharacteristic
154C22×C4×D11C2311yescharacteristic
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×Dic22C2311yescharacteristic
161C4×D4×C11—24no—
162C11×#117—24no—
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2312yes—
165C2×C11×C4⋊C4C2311yescharacteristic
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊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×C42×C11C2311yescharacteristic
175C2×C42×C11C2312yes—
176C2×C42×C11C2312yes—
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181D4×Dic11—24no—
182C4×C22⋊D11—24no—
183C4×C22⋊D11—24no—
184C4×C22⋊D11—44no—
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2311yescharacteristic
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2312yes—
221#66950—24no—
222#66950—24no—
223#66948—24no—
224#66948—24no—
225#66947—28no—
226#66946—24no—
227C4⋊C4×D11—24no—
228#66939—28no—
229#66935—28no—
230#66935—28no—
231(C22⋊D11)⋊C4—24no—
232(C22⋊D11)⋊C4—24no—
233C22⋊C4×D11—24no—
234C22⋊C4×D11—24no—
235C4×D44—28no—
236C4×D44—24no—
237C4×D44—28no—
238C4×D44—44no—
239#66925—44no—
240C42×D11—24no—
241C11×#95C2312yes—
242C11×#95C2311yescharacteristic
243C11×#95C2312yes—
244C11×#95C2312yes—
245C11×#95C2311yescharacteristic
246C11×#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259#34562—111nomaximal, Sylow
260C24×C11C2411yescharacteristic
261C24×C11C2411yescharacteristic
262C23×D11—22no—
263C23×D11—22no—
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11—42no—
270C23×D11C2×D414yes—
271C23×D11#4114yescomplemented
272C23×D11C2412yes—
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C23×D11C2411yescharacteristic
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C22×C4×C11—24no—
280C22×C4×C11—22no—
281C22×C4×C11—24no—
282C22×C4×C11C2×D414yes—
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C2×C22⋊D11—22no—
293C2×C22⋊D11—22no—
294C2×C22⋊D11—22no—
295C2×C22⋊D11—24no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C22×Dic11—22no—
305C22×Dic11—42no—
306C22×Dic11—42no—
307C22×Dic11C2×D414yes—
308C22×Dic11C2412yes—
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2411yescharacteristic
316D4×D11—232no—
317#4339—416no—
318C2×D44—22no—
319C2×D44—24no—
320C2×D44—24no—
321C2×D44—22no—
322C2×D44—24no—
323C2×D44—24no—
324C2×D44—24no—
325C2×D44—22no—
326C2×D44—22no—
327C2×D44—42no—
328C2×D44—42no—
329C2×D44—42no—
330C2×D44—42no—
331C2×D44—42no—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—24no—
338C2×C4×D11—22no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—24no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—42no—
345C2×C4×D11—42no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—416no—
350C2×C4×D11—416no—
351C2×C4×D11C2×D414yes—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11#4114yescomplemented
356C2×Dic22—22no—
357C2×Dic22—42no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—24no—
362C11×C4⋊C4—42no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—22no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—42no—
369C42×C11—22no—
370C42×C11—24no—
371C42×C11—24no—
372C22⋊Dic11—22no—
373C22⋊Dic11—22no—
374C22⋊Dic11—42no—
375C22⋊Dic11—42no—
376(C2×D11)⋊C4—22no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—22no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—24no—
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—
397C4⋊Dic11—24no—
398C4⋊Dic11—24no—
399C4⋊Dic11—22no—
400C4⋊Dic11—42no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—22no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11—24no—
412C2×#525—111no—
413C22×C4×D4—111no—
414#2638—111no—
415#2638—111no—
416#2635—111no—
417#2635—111no—
418#2630—112no—
419#2630—112no—
420#2627—111no—
421#2626—111no—
422#2622—112no—
423#2618—111no—
424#2617—111no—
425#2613—112no—
426#2395—111no—
427#2395D1111yescharacteristic, complemented
428#2392—112no—
429#2392—112no—
430#2388—111no—
431#2388—111no—
432C4×#123—112no—
433C4×#120—112no—
434#2280—111no—
435C23×C11—21no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11C22×D412yes—
444C23×C11C2×#4112yes—
445C23×C11C2511yescharacteristic
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—28no—
457C22×D11—28no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—48no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11—48no—
473C22×D11C22×D412yes—
474C22×D11C22×D412yes—
475C22×D11C2×#4112yes—
476C22×D11C2×#4112yes—
477C22×D11C2×#4112yes—
478D4×C11—28no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—28no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
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—44no—
500C2×C4×C11C22×D412yes—
501C2×C4×C11C22×D412yes—
502C2×C4×C11C2×#4112yes—
503C2×C4×C11H(5,𝔽2)14yes—
504C22⋊D11—28no—
505C22⋊D11—28no—
506C22⋊D11—48no—
507C22⋊D11—48no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—44no—
526C2×Dic11—44no—
527C2×Dic11C22×D412yes—
528C2×Dic11C22×D412yes—
529C2×Dic11C2×#4112yes—
530D44—28no—
531D44—44no—
532D44—48no—
533D44—48no—
534D44—48no—
535C4×D11—28no—
536C4×D11—28no—
537C4×D11—28no—
538C4×D11—44no—
539C4×D11—44no—
540C4×D11—44no—
541C4×D11—44no—
542C4×D11—44no—
543C4×D11—44no—
544C4×D11—48no—
545Dic22—44no—
546C22×#41—111no—
547C23×D4—111no—
548C24×C4—111no—
549C24×C4—111no—
550#525—228no—
551C2×#123—112no—
552C2×#123—112no—
553C2×C22⋊Q8—111no—
554C2×C22⋊Q8—111no—
555C2×#121—111no—
556C2×#121—111no—
557C2×#120—112no—
558C2×#120—112no—
559C2×C4×D4—111no—
560C2×C4×D4—111no—
561C2×C4×D4—111no—
562C2×C4×D4—112no—
563C2×C4×D4—111no—
564C2×C4×D4—111no—
565C2×C4×D4—111no—
566C2×C4×D4—111no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—112no—
570C2×C4×D4—228no—
571C2×C4×D4C2×D1111yescharacteristic
572C2×#117—112no—
573C2×#117C2×D1111yescharacteristic, complemented
574C22×C4⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C42—111no—
578#400—111no—
579#400C2×D1111yescharacteristic, complemented
580#399—111no—
581#399C2×D1111yescharacteristic, complemented
582#398—111no—
583#398—112no—
584#398—112no—
585#398C2×D1111yescharacteristic, complemented
586#397—111no—
587#397—112no—
588#397—112no—
589#397—112no—
590#397C2×D1111yescharacteristic, complemented
591#397C2×D1112yescomplemented
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#395—111no—
597#395—111no—
598#394—112no—
599#394—111no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#394—111no—
608#394—112no—
609#394C2×D1112yes—
610#393—111no—
611#393—111no—
612#392—112no—
613#392—112no—
614#392—112no—
615#392—111no—
616#392—112no—
617#392—111no—
618#388—112no—
619#388—112no—
620#387—112no—
621#387—112no—
622#386—112no—
623#386—112no—
624#386—112no—
625#386—112no—
626#385—112no—
627#385—112no—
628#385—112no—
629#385—112no—
630#381—112no—
631#381—111no—
632#381—111no—
633#380—112no—
634#380—111no—
635#380—111no—
636#379—112no—
637#379—112no—
638C4×C4⋊C4—112no—
639C4×C4⋊C4C2×D1112yescomplemented
640C4×C22⋊C4—111no—
641C4×C22⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4C2×D1111yescharacteristic, complemented
646C4×C22⋊C4C2×D1112yescomplemented
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—41no—
653C22×C11—41no—
654C22×C11—42no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11C23×D411yescharacteristic
658C22×C11C22×#4111yescharacteristic
659C22×C11C22×#4111yescharacteristic
660C22×C11C2×H(5,𝔽2)12yes—
661C22×C11#58512yes—
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—24no—
665C2×D11—24no—
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—24no—
671C2×D11—416no—
672C2×D11—416no—
673C2×D11—41no—
674C2×D11—41no—
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—42no—
684C2×D11—42no—
685C2×D11#52514yes—
686C4×C11—22no—
687C4×C11—22no—
688C4×C11—42no—
689C4×C11—41no—
690C4×C11—41no—
691C4×C11—42no—
692C4×C11—42no—
693C4×C11—42no—
694C4×C11#53414yes—
695Dic11—22no—
696Dic11—22no—
697Dic11—22no—
698Dic11—42no—
699Dic11—41no—
700Dic11—41no—
701Dic11—42no—
702Dic11—42no—
703C25—111no—
704C25—111no—
705C2×#41—224no—
706C2×#41—444no—
707C22×Q8—111no—
708C22×D4—111no—
709C22×D4—111no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—111no—
713C22×D4—112no—
714C22×D4—112no—
715C22×D4—112no—
716C22×D4—111no—
717C22×D4—224no—
718C22×D4—224no—
719C22×D4—224no—
720C22×D4C22×D1111yescharacteristic
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—118no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—112no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—224no—
735C23×C4—444no—
736C23×C4—444no—
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739#123—228no—
740#123—228no—
741C22⋊Q8—224no—
742C22⋊Q8—224no—
743#121—224no—
744#121—224no—
745#120—228no—
746#120—228no—
747C4×D4—24no—
748C4×D4—224no—
749C4×D4—228no—
750C4×D4—228no—
751C4×D4—224no—
752C4×D4—224no—
753C4×D4—224no—
754C4×D4—224no—
755C4×D4—224no—
756C4×D4—224no—
757C4×D4—444no—
758C4×D4—444no—
759#117—24no—
760#117—444no—
761C2×C4⋊C4—111no—
762C2×C4⋊C4—111no—
763C2×C4⋊C4—111no—
764C2×C4⋊C4—112no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—112no—
768C2×C4⋊C4—112no—
769C2×C4⋊C4—112no—
770C2×C4⋊C4—112no—
771C2×C4⋊C4—112no—
772C2×C4⋊C4—224no—
773C2×C4⋊C4C22×D1111yescharacteristic
774C2×C4⋊C4C22×D1111yescharacteristic
775C2×C4⋊C4C22×D1111yescharacteristic
776C2×C4⋊C4C22×D1112yes—
777C2×C4⋊C4C22×D1112yes—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—111no—
780C2×C22⋊C4—111no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—111no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
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—224no—
804C2×C22⋊C4—224no—
805C2×C22⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4C22×D1111yescharacteristic
807C2×C22⋊C4C22×D1112yes—
808C2×C22⋊C4C22×D1112yes—
809C2×C22⋊C4C22×D1112yes—
810C2×C22⋊C4C22×D1112yes—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—112no—
814C2×C42—111no—
815C2×C42—224no—
816C2×C42C22×D1112yes—
817C2×C42C22×D1112yes—
818C2×C42C22×D1111yescharacteristic
819#95—112no—
820#95—112no—
821#95—111no—
822#95—111no—
823#95—112no—
824#95—112no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95C22×D1111yescharacteristic
832#95C22×D1111yescharacteristic
833#95C22×D1112yes—
834#95C22×D1112yes—
835#95C22×D1112yes—
836#95C22×D1112yes—
837C2×C11—42no—
838C2×C11—42no—
839C2×C11C2×#52511yescharacteristic
840C2×C11C2×#53411yescharacteristic
841C2×C11#344911yescharacteristic
842C2×C11#345912yes—
843C2×C11#346012yes—
844D11—24no—
845D11—42no—
846D11—42no—
847D11—82no—
848C24—111no—
849C24—111no—
850C24—111no—
851C24—114no—
852C24—114no—
853C24—112no—
854C24—222no—
855C24—222no—
856C24—222no—
857C24—222no—
858C24—442no—
859C24—442no—
860C24—442no—
861C24—442no—
862C24C23×D1111yescharacteristic
863C24C23×D1111yescharacteristic
864#41—4416no—
865C2×Q8—222no—
866C2×Q8—442no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—22no—
870C2×D4—222no—
871C2×D4—222no—
872C2×D4—224no—
873C2×D4—224no—
874C2×D4—224no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—222no—
878C2×D4—222no—
879C2×D4—2232no—
880C2×D4—222no—
881C2×D4—222no—
882C2×D4—222no—
883C2×D4—222no—
884C2×D4—224no—
885C2×D4—224no—
886C2×D4—222no—
887C2×D4—222no—
888C2×D4—442no—
889C2×D4—442no—
890C2×D4—442no—
891C2×D4—442no—
892C2×D4—442no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C22×C4—24no—
898C22×C4—22no—
899C22×C4—24no—
900C22×C4—111no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—114no—
904C22×C4—114no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—114no—
908C22×C4—114no—
909C22×C4—112no—
910C22×C4—111no—
911C22×C4—112no—
912C22×C4—111no—
913C22×C4—112no—
914C22×C4—222no—
915C22×C4—222no—
916C22×C4—222no—
917C22×C4—222no—
918C22×C4—222no—
919C22×C4—222no—
920C22×C4—224no—
921C22×C4—224no—
922C22×C4—222no—
923C22×C4—224no—
924C22×C4—224no—
925C22×C4—224no—
926C22×C4—224no—
927C22×C4—4416no—
928C22×C4—442no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4—442no—
933C22×C4—4416no—
934C22×C4—442no—
935C22×C4—442no—
936C22×C4D4×D1114yes—
937C22×C4C23×D1112yes—
938C22×C4C23×D1111yescharacteristic
939C22×C4C23×D1112yes—
940C22×C4C23×D1112yes—
941C22×C4C23×D1112yes—
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—24no—
950C4⋊C4—42no—
951C4⋊C4—222no—
952C4⋊C4—222no—
953C4⋊C4—224no—
954C4⋊C4—224no—
955C4⋊C4—224no—
956C4⋊C4—222no—
957C4⋊C4—442no—
958C4⋊C4—442no—
959C4⋊C4—442no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C22⋊C4—22no—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—22no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—222no—
969C22⋊C4—224no—
970C22⋊C4—224no—
971C22⋊C4—224no—
972C22⋊C4—222no—
973C22⋊C4—222no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—224no—
979C22⋊C4—222no—
980C22⋊C4—222no—
981C22⋊C4—222no—
982C22⋊C4—224no—
983C22⋊C4—442no—
984C22⋊C4—442no—
985C22⋊C4—442no—
986C22⋊C4—442no—
987C22⋊C4—442no—
988C22⋊C4—442no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C42—22no—
994C42—24no—
995C42—24no—
996C42—222no—
997C42—222no—
998C42—222no—
999C42—224no—
1000C11#3456211yescharacteristic, complemented, Sylow
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—112no—
1010C23—112no—
1011C23—112no—
1012C23—112no—
1013C23—112no—
1014C23—228no—
1015C23—228no—
1016C23—222no—
1017C23—222no—
1018C23—221no—
1019C23—221no—
1020C23—221no—
1021C23—221no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—444no—
1034C23—444no—
1035C23—448no—
1036C23—444no—
1037C23—444no—
1038C23—448no—
1039C23—448no—
1040C23—448no—
1041C23C2×D4×D1112yes—
1042C23#41×D1112yes—
1043C23C24×D1111yescharacteristic
1044Q8—444no—
1045D4—28no—
1046D4—228no—
1047D4—228no—
1048D4—228no—
1049D4—444no—
1050D4—448no—
1051D4—448no—
1052D4—448no—
1053D4—448no—
1054D4—448no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—28no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—44no—
1076C2×C4—112no—
1077C2×C4—112no—
1078C2×C4—112no—
1079C2×C4—228no—
1080C2×C4—221no—
1081C2×C4—221no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—228no—
1085C2×C4—228no—
1086C2×C4—221no—
1087C2×C4—221no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—444no—
1100C2×C4—444no—
1101C2×C4—444no—
1102C2×C4—444no—
1103C2×C4—444no—
1104C2×C4—444no—
1105C2×C4—444no—
1106C2×C4—444no—
1107C2×C4—448no—
1108C2×C4C2×D4×D1112yes—
1109C2×C4C2×D4×D1112yes—
1110C2×C4#41×D1112yes—
1111C2×C4#6704214yes—
1112C22—22no—
1113C22—22no—
1114C22—24no—
1115C22—22no—
1116C22—22no—
1117C22—41no—
1118C22—41no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—114no—
1123C22—222no—
1124C22—222no—
1125C22—224no—
1126C22—224no—
1127C22—222no—
1128C22—222no—
1129C22—224no—
1130C22—222no—
1131C22—222no—
1132C22—4416no—
1133C22—4416no—
1134C22—441no—
1135C22—441no—
1136C22—442no—
1137C22—442no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22C22×D4×D1111yescharacteristic
1147C22C2×#41×D1111yescharacteristic
1148C22C2×#41×D1111yescharacteristic
1149C22C2×#6704212yes—
1150C22#1062345312yes—
1151C4—22no—
1152C4—22no—
1153C4—41no—
1154C4—41no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—222no—
1160C4—222no—
1161C4—222no—
1162C4—441no—
1163C4—442no—
1164C4—441no—
1165C4—442no—
1166C4—442no—
1167C4#1062318414yes—
1168C2—42no—
1169C2—42no—
1170C2—224no—
1171C2—442no—
1172C2—442no—
1173C2—882no—
1174C2D11×#52511yescharacteristic
1175C2C2×#1062318411yescharacteristic
1176C2#1308194311yescharacteristic
1177C2#1308202612yes—
1178C2#1308203712yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2395C2
hypercenter#2395D11
hypocenterC11#34562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
1. C2×#10623055C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074541C2semidirect
4. #13074538C2semidirect
5. #13074509C2semidirect
6. #13074506C2semidirect
7. #13074458C2semidirect
8. #13074454C2semidirect
9. #13074430C2semidirect
10. #13074422C2semidirect
11. #13074390C2semidirect
12. #13074359C2semidirect
13. #13074351C2semidirect
14. #13074329C2semidirect
15. #13071873C2semidirect
16. #13071860C2semidirect
17. #13071856C2semidirect
18. #13071832C2semidirect
19. #13071831C2semidirect
20. C4×#66947C2semidirect
21. C4×#66935C2semidirect
22. #13070997C2semidirect
23. C11×#2395C2semidirect
25. C22×#4339C22semidirect
29. C2×C11×#117C22semidirect
33. C2×C4×C22⋊D11C22semidirect
37. C2×#66950C22semidirect
39. C2×#66948C22semidirect
43. C2×#66939C22semidirect
52. C2×C4×D44C22semidirect
53. C2×C4×D44C22semidirect
54. C2×#66925C22semidirect
56. C11×#400C22semidirect
57. C11×#399C22semidirect
58. C11×#398C22semidirect
59. C11×#397C22semidirect
60. C11×#397C22semidirect
62. C4×C11×C4⋊C4C22semidirect
63. C4×C11×C22⋊C4C22semidirect
64. C4×C11×C22⋊C4C22semidirect
66. C4×C22⋊Dic11C22semidirect
67. #10622607C22semidirect
68. #10622607C22semidirect
69. #10622606C22semidirect
70. #10622605C22semidirect
72. #10622604C22semidirect
73. #10622604C22semidirect
74. #10622603C22semidirect
76. #10622595C22semidirect
77. #10622594C22semidirect
78. #10622593C22semidirect
79. #10622592C22semidirect
80. #10622574C22semidirect
83. #10622573C22semidirect
86. #10622572C22semidirect
87. #10622572C22semidirect
88. #10622571C22semidirect
91. #10622565C22semidirect
92. #10622563C22semidirect
93. #10622561C22semidirect
94. #10622560C22semidirect
95. #10622555C22semidirect
97. C4×(C2×D11)⋊C4C22semidirect
98. C4×(C2×D11)⋊C4C22semidirect
99. C4×(C2×D11)⋊C4C22semidirect
100. C4×Dic11⋊C4C22semidirect
101. #10622289C22semidirect
102. #10622288C22semidirect
103. #10622287C22semidirect
104. #10622286C22semidirect
105. #10622285C22semidirect
106. #10622285C22semidirect
107. #10622285C22semidirect
109. #10622284C22semidirect
110. #10622282C22semidirect
112. #10622281C22semidirect
117. #10622278C22semidirect
119. #10622277C22semidirect
120. #10622277C22semidirect
121. #10622274C22semidirect
122. #10622270C22semidirect
123. #10622269C22semidirect
124. #10622268C22semidirect
149. C22×C4×D11D4semidirect
271. C23×D11#41semidirect
355. C2×C4×D11#41semidirect
427. #2395D11semidirect
573. C2×#117C2×D11semidirect
579. #400C2×D11semidirect
581. #399C2×D11semidirect
585. #398C2×D11semidirect
590. #397C2×D11semidirect
591. #397C2×D11semidirect
639. C4×C4⋊C4C2×D11semidirect
645. C4×C22⋊C4C2×D11semidirect
646. C4×C22⋊C4C2×D11semidirect
1000. C11#34562semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×C4×D4×D112
#130745412
#130745382
#130745092
#130745062
#130744582
#130744542
#130744302
#130744222
#130743902
#130743592
#130743512
#130743292
#130718732
#130718602
#130718562
#130718322
#130718312
C4×#669472
C4×#669352
#130709972
C11×#23952
#3456211