Finite Group Databasebeta

← #14680629

Subgroups — #14680629

Order 2816.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622574C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622823C211yesmaximal, characteristic, complemented
5#13066876C211yesmaximal, characteristic, complemented
6#13066868C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic, complemented
9#13066861C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic
12#13066854C211yesmaximal, characteristic, complemented
13#13066849C211yesmaximal, characteristic, complemented
14#13066846C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C4×C11×C22⋊C4—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622826—24no—
39#10622823—24no—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622574C418yescomplemented
55#10622553—24no—
56C25×C11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—41no—
61C23×C4×C11—41no—
62C23×C4×C11—41no—
63C23×C4×C11—41no—
64C23×C4×C11D414yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11C2×C414yes—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4C2×C414yes—
91C2×C42×C11—22no—
92C2×C42×C11—41no—
93C2×C42×C11—41no—
94C2×C42×C11—41no—
95C2×C42×C11—41no—
96C2×C42×C11D414yescomplemented
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—22no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—41no—
102C2×C22⋊Dic11—41no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11C2×C414yes—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—41no—
115C2×(C2×D11)⋊C4—41no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4C2×C414yescomplemented
123C2×(C2×D11)⋊C4C2×C414yescomplemented
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11—41no—
126C2×C4⋊Dic11—41no—
127C2×C4⋊Dic11—41no—
128C2×C4⋊Dic11—41no—
129C2×C4⋊Dic11C2×C414yescomplemented
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—41no—
135C2×Dic11⋊C4—41no—
136C11×#95—22no—
137C11×#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yescomplemented
152#14309—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11C22×C412yes—
166C24×C11C2×D412yes—
167C24×C11#4112yes—
168C24×C11C2411yescharacteristic
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11C22×C412yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—28no—
217C22×C4×C11—44no—
218C22×C4×C11—44no—
219C22×C4×C11—44no—
220C22×C4×C11—44no—
221C22×C4×C11—44no—
222C22×C4×C11—44no—
223C22×C4×C11C22×C412yes—
224C22×C4×C11C22×C412yes—
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2×D412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D412yes—
230C22×C4×C11#4112yes—
231C22×C4×C11#4112yes—
232C22×C4×C11#4112yes—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11C22×C412yes—
287C22×Dic11C22×C412yes—
288C22×Dic11C22×C412yes—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—28no—
291C42×C11—44no—
292C42×C11—44no—
293C22⋊Dic11—28no—
294C22⋊Dic11—44no—
295C22⋊Dic11—44no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301(C2×D11)⋊C4—44no—
302C4⋊Dic11—44no—
303C4⋊Dic11—44no—
304Dic11⋊C4—44no—
305Dic11⋊C4—44no—
306C2×#394—111no—
307C2×#388—111no—
308C2×#386—111no—
309C2×#385—111no—
310C2×C4×C22⋊C4D1111yescharacteristic, complemented
311#1443—111no—
312#1441—111no—
313#1440—111no—
314#1439—111no—
315#1439—111no—
316#1439—111no—
317#1438—111no—
318#1437—111no—
319#1436—111no—
320C4⋊#95—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—41no—
340C23×C11—41no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
349C23×C11—41no—
350C23×C11—41no—
351C23×C11—41no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11C4×D414yes—
356C23×C11C23×C411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C22×D411yescharacteristic
359C23×C11C2×#4111yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11H(5,𝔽2)11yescharacteristic
364C23×C11H(5,𝔽2)11yescharacteristic
365C23×C11H(5,𝔽2)11yescharacteristic
366C23×C11H(5,𝔽2)11yescharacteristic
367C23×C11H(5,𝔽2)11yescharacteristic
368C23×C11H(5,𝔽2)11yescharacteristic
369C23×C112−1+411yescharacteristic
370C23×C112−1+411yescharacteristic
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11—41no—
383C22×D11—41no—
384C22×D11—41no—
385C22×D11—41no—
386C22×D11—41no—
387C22×D11—41no—
388C22×D11—41no—
389C22×D11—41no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—41no—
393C22×D11—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
401C22×D11—41no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—416no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11C4×D414yes—
448C2×C4×C11#12114yes—
449C22⋊D11—416no—
450C2×Dic11—22no—
451C2×Dic11—22no—
452C2×Dic11—22no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—41no—
460C2×Dic11—41no—
461C2×Dic11—41no—
462C2×Dic11—41no—
463C2×Dic11—41no—
464C2×Dic11—41no—
465C2×Dic11—41no—
466C2×Dic11—41no—
467C2×Dic11—41no—
468C2×Dic11—41no—
469C2×Dic11—41no—
470C2×Dic11—41no—
471C2×Dic11—41no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C23×D4—111no—
500C24×C4C2×D1111yescharacteristic
501C22×C4⋊C4—111no—
502C22×C4⋊C4—111no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4C2×D1111yescharacteristic
515C22×C22⋊C4C2×D1111yescharacteristic
516C22×C42C2×D1111yescharacteristic
517C22×C42C2×D1111yescharacteristic
518#394—118no—
519#388—224no—
520#386—224no—
521#385—224no—
522C4×C22⋊C4—24no—
523C2×#95—111no—
524C2×#95—111no—
525C2×#95—111no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95C2×D1111yescharacteristic
538C2×#95C2×D1111yescharacteristic
539C22×C11—24no—
540C22×C11—24no—
541C22×C11—24no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11C2×C4×D411yescharacteristic
555C22×C11C2×C4×D411yescharacteristic
556C22×C11C4×#4111yescharacteristic
557C22×C11#51811yescharacteristic
558C22×C11#51811yescharacteristic
559C22×C11#52011yescharacteristic
560C22×C11#52011yescharacteristic
561C22×C11C2×#12111yescharacteristic
562C22×C11#52511yescharacteristic
563C22×C11#52911yescharacteristic
564C22×C11#53211yescharacteristic
565C22×C11#53411yescharacteristic
566C22×C11#53411yescharacteristic
567C22×C11#53411yescharacteristic
568C22×C11#53511yescharacteristic
569C22×C11#53511yescharacteristic
570C22×C11#53611yescharacteristic
571C22×C11#53711yescharacteristic
572C22×C11#53711yescharacteristic
573C22×C11#53811yescharacteristic
574C22×C11#53811yescharacteristic
575C22×C11#53811yescharacteristic
576C22×C11#53811yescharacteristic
577C22×C11#53811yescharacteristic
578C22×C11#53811yescharacteristic
579C22×C11#53911yescharacteristic
580C22×C11#53911yescharacteristic
581C22×C11#53911yescharacteristic
582C22×C11#53911yescharacteristic
583C22×C11#54011yescharacteristic
584C22×C11#54011yescharacteristic
585C22×C11#54211yescharacteristic
586C22×C11#54211yescharacteristic
587C22×C11#54211yescharacteristic
588C22×C11#54211yescharacteristic
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—81no—
597C2×D11—81no—
598C2×D11—81no—
599C2×D11—81no—
600C2×D11—81no—
601C2×D11—81no—
602C2×D11—81no—
603C2×D11—81no—
604C4×C11—24no—
605C4×C11—24no—
606C4×C11—42no—
607C4×C11—42no—
608C4×C11—42no—
609C4×C11—42no—
610Dic11—42no—
611Dic11—42no—
612Dic11—42no—
613Dic11—81no—
614Dic11—81no—
615Dic11—81no—
616Dic11—81no—
617C25—111no—
618C25C22×D1111yescharacteristic
619C22×D4—114no—
620C22×D4—222no—
621C22×D4—222no—
622C22×D4—441no—
623C22×D4—441no—
624C22×D4—441no—
625C22×D4—441no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—41no—
629C23×C4—41no—
630C23×C4—41no—
631C23×C4—41no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—111no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—111no—
638C23×C4—111no—
639C23×C4D4414yes—
640C23×C4C22×D1111yescharacteristic
641C23×C4C22×D1111yescharacteristic
642C23×C4C22×D1111yescharacteristic
643C23×C4C22×D1111yescharacteristic
644C23×C4C22×D1111yescharacteristic
645C23×C4C22×D1111yescharacteristic
646C2×C4⋊C4—114no—
647C2×C4⋊C4—222no—
648C2×C4⋊C4—222no—
649C2×C4⋊C4—222no—
650C2×C4⋊C4—222no—
651C2×C4⋊C4—222no—
652C2×C4⋊C4—441no—
653C2×C4⋊C4—441no—
654C2×C4⋊C4—441no—
655C2×C4⋊C4—441no—
656C2×C4⋊C4—441no—
657C2×C4⋊C4—441no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—114no—
664C2×C22⋊C4—114no—
665C2×C22⋊C4—114no—
666C2×C22⋊C4—222no—
667C2×C22⋊C4—222no—
668C2×C22⋊C4—222no—
669C2×C22⋊C4—222no—
670C2×C22⋊C4—222no—
671C2×C22⋊C4—222no—
672C2×C22⋊C4—222no—
673C2×C22⋊C4—222no—
674C2×C22⋊C4—222no—
675C2×C22⋊C4—222no—
676C2×C22⋊C4—222no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—441no—
679C2×C22⋊C4—441no—
680C2×C22⋊C4—441no—
681C2×C22⋊C4—441no—
682C2×C22⋊C4—441no—
683C2×C22⋊C4—441no—
684C2×C22⋊C4—441no—
685C2×C22⋊C4—441no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4—441no—
690C2×C22⋊C4C4×D1114yes—
691C2×C42—22no—
692C2×C42—41no—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42—41no—
696C2×C42C22⋊D1114yescomplemented
697#95—22no—
698#95—22no—
699#95—114no—
700#95—222no—
701#95—222no—
702#95—222no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—441no—
708#95—441no—
709#95—441no—
710#95—441no—
711#95—441no—
712#95—441no—
713C2×C11—44no—
714C2×C11C4×#12111yescharacteristic
715C2×C11#232111yescharacteristic
716C2×C11#232211yescharacteristic
717C2×C11#232411yescharacteristic
718C2×C11#232511yescharacteristic
719C2×C11#233511yescharacteristic
720C2×C11#233711yescharacteristic
721C2×C11#261711yescharacteristic
722C2×C11#262011yescharacteristic
723C2×C11#263011yescharacteristic
724C2×C11#263611yescharacteristic
725C2×C11#264911yescharacteristic
726C2×C11#265311yescharacteristic
727C2×C11#266111yescharacteristic
728C2×C11#266311yescharacteristic
729D11—82no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—112no—
743C24—221no—
744C24—221no—
745C24—221no—
746C24—221no—
747C24—221no—
748C24—221no—
749C24—221no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24C2×C4×D1112yes—
758C24C2×D4412yes—
759C24#433912yes—
760C24C23×D1111yescharacteristic
761C2×D4—228no—
762C2×D4—444no—
763C2×D4—444no—
764C2×D4—444no—
765C2×D4—444no—
766C2×D4—444no—
767C2×D4—444no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—28no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—221no—
811C22×C4—221no—
812C22×C4—221no—
813C22×C4—221no—
814C22×C4—221no—
815C22×C4—221no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—221no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4C2×C4×D1112yes—
857C22×C4C2×C4×D1112yes—
858C22×C4C2×D4412yes—
859C22×C4C2×D4412yes—
860C22×C4#433912yes—
861C22×C4#433912yes—
862C22×C4#433912yes—
863C22×C4C2×C22⋊D1112yes—
864C22×C4C2×C22⋊D1112yes—
865C22×C4C2×C22⋊D1112yes—
866C4⋊C4—444no—
867C4⋊C4—444no—
868C4⋊C4—444no—
869C4⋊C4—444no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—228no—
873C22⋊C4—228no—
874C22⋊C4—444no—
875C22⋊C4—444no—
876C22⋊C4—444no—
877C22⋊C4—444no—
878C22⋊C4—444no—
879C22⋊C4—444no—
880C22⋊C4—444no—
881C42—44no—
882C42—44no—
883C11#1430911yescharacteristic, complemented, Sylow
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—222no—
922C23—222no—
923C23—222no—
924C23—222no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23—441no—
930C23—441no—
931C23—441no—
932C23—441no—
933C23—441no—
934C23—441no—
935C23—441no—
936C23—441no—
937C23—441no—
938C23—441no—
939C23—441no—
940C23—441no—
941C23—441no—
942C23—441no—
943C23—441no—
944C23—441no—
945C23—441no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23C4×D4414yes—
954C23C22×C4×D1111yescharacteristic
955C23C22×D4411yescharacteristic
956C23C2×#433911yescharacteristic
957C23C2×#433911yescharacteristic
958C23C2×#433911yescharacteristic
959C23C2×#433911yescharacteristic
960C23#6703711yescharacteristic
961C23#6703711yescharacteristic
962C23#6703711yescharacteristic
963C23#6703711yescharacteristic
964C23#6704211yescharacteristic
965C23#6704211yescharacteristic
966C23#6704311yescharacteristic
967C23#6704311yescharacteristic
968C23C22×C22⋊D1111yescharacteristic
969D4—4416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—416no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—441no—
1021C2×C4—441no—
1022C2×C4—441no—
1023C2×C4—441no—
1024C2×C4—441no—
1025C2×C4—441no—
1026C2×C4—441no—
1027C2×C4—441no—
1028C2×C4—441no—
1029C2×C4—441no—
1030C2×C4—441no—
1031C2×C4—441no—
1032C2×C4—441no—
1033C2×C4—441no—
1034C2×C4—441no—
1035C2×C4—441no—
1036C2×C4—441no—
1037C2×C4—441no—
1038C2×C4—441no—
1039C2×C4—441no—
1040C2×C4—441no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4C4×C22⋊D1114yes—
1061C2×C4#6698314yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—442no—
1078C22—442no—
1079C22—442no—
1080C22—442no—
1081C22—442no—
1082C22—442no—
1083C22—442no—
1084C22—881no—
1085C22—881no—
1086C22—881no—
1087C22—881no—
1088C22—881no—
1089C22—881no—
1090C22—881no—
1091C22—881no—
1092C22C2×C4×D4411yescharacteristic
1093C22C4×#433911yescharacteristic
1094C22#1062300811yescharacteristic
1095C22#1062301011yescharacteristic
1096C22#1062302411yescharacteristic
1097C22#1062302411yescharacteristic
1098C22#1062302511yescharacteristic
1099C22#1062302511yescharacteristic
1100C22#1062305611yescharacteristic
1101C22#1062305711yescharacteristic
1102C22#1062306511yescharacteristic
1103C22#1062306511yescharacteristic
1104C22#1062307611yescharacteristic
1105C22#1062307611yescharacteristic
1106C22#1062307711yescharacteristic
1107C22#1062307711yescharacteristic
1108C22#1062309111yescharacteristic
1109C22#1062309111yescharacteristic
1110C22#1062309111yescharacteristic
1111C22#1062309111yescharacteristic
1112C22#1062309211yescharacteristic
1113C22#1062309211yescharacteristic
1114C22#1062309311yescharacteristic
1115C22#1062309311yescharacteristic
1116C22#1062309511yescharacteristic
1117C22#1062309511yescharacteristic
1118C22#1062309511yescharacteristic
1119C22#1062309511yescharacteristic
1120C22C2×C4×C22⋊D1111yescharacteristic
1121C22C2×#6698311yescharacteristic
1122C22#1062332211yescharacteristic
1123C22#1062333511yescharacteristic
1124C22#1062333611yescharacteristic
1125C22#1062336411yescharacteristic
1126C22#1062336411yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—442no—
1134C4—442no—
1135C4—442no—
1136C4—881no—
1137C4—881no—
1138C4—881no—
1139C4—881no—
1140C2—44no—
1141C2—882no—
1142C2C4×#6698311yescharacteristic
1143C2#1307127611yescharacteristic
1144C2#1307128711yescharacteristic
1145C2#1307130311yescharacteristic
1146C2#1307131411yescharacteristic
1147C2#1307140811yescharacteristic
1148C2#1307142411yescharacteristic
1149C2#1307435011yescharacteristic
1150C2#1307437311yescharacteristic
1151C2#1307445311yescharacteristic
1152C2#1307451111yescharacteristic
1153C2#1307461311yescharacteristic
1154C2#1307467311yescharacteristic
1155C2#1307474211yescharacteristic
1156C2#1307476411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14309
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
4. C2×#10622823C2semidirect
5. #13066876C2semidirect
6. #13066868C2semidirect
7. #13066863C2semidirect
8. #13066862C2semidirect
9. #13066861C2semidirect
10. #13066860C2semidirect
12. #13066854C2semidirect
13. #13066849C2semidirect
14. #13066846C2semidirect
15. C2×C4×C11×C22⋊C4C2semidirect
54. #10622574C4semidirect
96. C2×C42×C11D4semidirect
122. C2×(C2×D11)⋊C4C2×C4semidirect
123. C2×(C2×D11)⋊C4C2×C4semidirect
129. C2×C4⋊Dic11C2×C4semidirect
151. C11⋊#95C2×C4semidirect
310. C2×C4×C22⋊C4D11semidirect
696. C2×C42C22⋊D11semidirect
883. C11#14309semidirect

Maximal subgroups

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

subgroupindex
C2×#106225742
C2×#106225532
C2×#106228262
C2×#106228232
#130668762
#130668682
#130668632
#130668622
#130668612
#130668602
#130668552
#130668542
#130668492
#130668462
C2×C4×C11×C22⋊C42
#1430911