Finite Group Databasebeta

← #14682186

Subgroups — #14682186

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622570C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4C2×#10622823C211yesmaximal, characteristic, complemented
5C2×#10622602C211yesmaximal, characteristic, complemented
6C2×#10622602C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066866C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066861C211yesmaximal, characteristic, complemented
11#13066860C211yesmaximal, characteristic, complemented
12#13066859C211yesmaximal, characteristic, complemented
13#13066845C211yesmaximal, characteristic, complemented
14Dic11⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C11×#385—24no—
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40#10622826—24no—
41#10622823—24no—
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#10622602—24no—
55#10622602—24no—
56#10622570C418yescomplemented
57#10622569—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11—22no—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—41no—
64C23×C4×C11—41no—
65C23×C4×C11—41no—
66C23×C4×C11—41no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11C2×C414yes—
78C22×C22⋊D11D414yes—
79C22×C22⋊D11Q814yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4—41no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4D414yescomplemented
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—41no—
105C2×C11×C22⋊C4C2×C414yescomplemented
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—22no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11C2×C414yescomplemented
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4C2×C414yescomplemented
129C2×(C2×D11)⋊C4C2×C414yescomplemented
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11—41no—
132C2×C4⋊Dic11—41no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—41no—
137C2×Dic11⋊C4—41no—
138C2×Dic11⋊C4—41no—
139C2×Dic11⋊C4—41no—
140C2×Dic11⋊C4—41no—
141C2×Dic11⋊C4—41no—
142C2×Dic11⋊C4—41no—
143C2×Dic11⋊C4C2×C414yescomplemented
144C2×Dic11⋊C4D414yescomplemented
145C2×C4×Dic11—41no—
146C2×C4×Dic11—41no—
147C2×C4×Dic11C2×C414yescomplemented
148C11×#95—22no—
149C11×#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—41no—
161C11⋊#95—41no—
162#14440—111nomaximal, Sylow
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11C22×C412yes—
176C24×C11C2×D412yes—
177C24×C11C2×Q812yes—
178C24×C11C2411yescharacteristic
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11C22×C412yes—
192C23×D11C2×D412yes—
193C23×D11C2×Q812yes—
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—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—44no—
230C22×C4×C11—44no—
231C22×C4×C11—44no—
232C22×C4×C11—44no—
233C22×C4×C11—44no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11C22×C412yes—
237C22×C4×C11C22×C412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2×D412yes—
241C22×C4×C11C2×D412yes—
242C22×C4×C11#4112yes—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—44no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11C4⋊C4116yescomplemented
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×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11C22×C412yes—
292C22×Dic11C22×C412yes—
293C22×Dic11C22×C412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×Q812yes—
298C22×Dic11#4112yes—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C2×C4×D11—44no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C11×C4⋊C4—44no—
307C11×C4⋊C4—44no—
308C11×C22⋊C4—28no—
309C11×C22⋊C4—44no—
310C22⋊Dic11—28no—
311C22⋊Dic11—44no—
312C22⋊Dic11—44no—
313(C2×D11)⋊C4—28no—
314(C2×D11)⋊C4—28no—
315(C2×D11)⋊C4—44no—
316(C2×D11)⋊C4—44no—
317(C2×D11)⋊C4—44no—
318C4⋊Dic11—44no—
319Dic11⋊C4—44no—
320Dic11⋊C4—44no—
321Dic11⋊C4—44no—
322Dic11⋊C4—44no—
323C4×Dic11—44no—
324C2×#390—111no—
325C2×#386—111no—
326C2×#386—111no—
327C2×#385—111no—
328C2×#385—111no—
329C2×#385—111no—
330C2×#385D1111yescharacteristic, complemented
331#1441—111no—
332#1441—111no—
333#1439—111no—
334#1439—111no—
335#1439—111no—
336#1439—111no—
337C4⋊#95—111no—
338C4⋊#95—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11C2×C4⋊C414yes—
374C23×C11C23×C411yescharacteristic
375C23×C11C22×D411yescharacteristic
376C23×C11C22×D411yescharacteristic
377C23×C11C22×D411yescharacteristic
378C23×C11C22×Q811yescharacteristic
379C23×C11C2×#4111yescharacteristic
380C23×C11C2×#4111yescharacteristic
381C23×C11H(5,𝔽2)11yescharacteristic
382C23×C11H(5,𝔽2)11yescharacteristic
383C23×C11H(5,𝔽2)11yescharacteristic
384C23×C11H(5,𝔽2)11yescharacteristic
385C23×C11H(5,𝔽2)11yescharacteristic
386C23×C11H(5,𝔽2)11yescharacteristic
387C23×C112−1+411yescharacteristic
388C23×C112−1+411yescharacteristic
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11C2×C4⋊C414yes—
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—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—416no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11C4×D414yes—
467C22⋊D11—416no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
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—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11C2×C4⋊C414yes—
516C2×Dic11C4×D414yes—
517C4×D11—416no—
518C23×D4—111no—
519C24×C4—111no—
520C24×C4C2×D1111yescharacteristic
521C22×C4⋊C4—111no—
522C22×C4⋊C4—111no—
523C22×C4⋊C4—111no—
524C22×C4⋊C4—111no—
525C22×C4⋊C4—111no—
526C22×C4⋊C4C2×D1111yescharacteristic
527C22×C4⋊C4C2×D1111yescharacteristic
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4—111no—
532C22×C22⋊C4—111no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4C2×D1111yescharacteristic
537C22×C22⋊C4C2×D1111yescharacteristic
538C22×C42—111no—
539#390—118no—
540#386—224no—
541#386—224no—
542#385—24no—
543#385—224no—
544#385—224no—
545#385—224no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95—111no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95C2×D1111yescharacteristic
559C2×#95C2×D1111yescharacteristic
560C22×C11—24no—
561C22×C11—24no—
562C22×C11—24no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11—42no—
571C22×C11—42no—
572C22×C11—42no—
573C22×C11—42no—
574C22×C11—42no—
575C22×C11C22×C4⋊C411yescharacteristic
576C22×C11C2×C4×D411yescharacteristic
577C22×C11C2×C4×D411yescharacteristic
578C22×C11#51811yescharacteristic
579C22×C11#51811yescharacteristic
580C22×C11#52011yescharacteristic
581C22×C11#52011yescharacteristic
582C22×C11#53411yescharacteristic
583C22×C11#53411yescharacteristic
584C22×C11#53411yescharacteristic
585C22×C11#53411yescharacteristic
586C22×C11#53711yescharacteristic
587C22×C11#53711yescharacteristic
588C22×C11#53811yescharacteristic
589C22×C11#53811yescharacteristic
590C22×C11#53911yescharacteristic
591C22×C11#53911yescharacteristic
592C22×C11#54311yescharacteristic
593C22×C11#54311yescharacteristic
594C22×C11D4211yescharacteristic
595C22×C11D4211yescharacteristic
596C22×C11D4211yescharacteristic
597C22×C11#54711yescharacteristic
598C22×C11#54711yescharacteristic
599C22×C11D4×Q811yescharacteristic
600C22×C11D4×Q811yescharacteristic
601C22×C11#55011yescharacteristic
602C22×C11#55011yescharacteristic
603C22×C11#55411yescharacteristic
604C22×C11#55411yescharacteristic
605C22×C11#55911yescharacteristic
606C22×C11H(3,𝔽4)11yescharacteristic
607C22×C11#56211yescharacteristic
608C22×C11#56211yescharacteristic
609C22×C11#56311yescharacteristic
610C2×D11—24no—
611C2×D11—24no—
612C2×D11—24no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—42no—
619C2×D11—42no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C4×C11—24no—
626C4×C11—42no—
627C4×C11—42no—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—81no—
631Dic11—24no—
632Dic11—24no—
633Dic11—42no—
634Dic11—42no—
635Dic11—81no—
636Dic11—81no—
637Dic11—81no—
638C25—111no—
639C25C22×D1111yescharacteristic
640C22×D4—114no—
641C22×D4—114no—
642C22×D4—114no—
643C22×D4—441no—
644C22×D4—441no—
645C22×D4—441no—
646C22×D4—441no—
647C23×C4—22no—
648C23×C4—22no—
649C23×C4—22no—
650C23×C4—41no—
651C23×C4—41no—
652C23×C4—41no—
653C23×C4—41no—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—222no—
662C23×C4—222no—
663C23×C4—222no—
664C23×C4—441no—
665C23×C4—441no—
666C23×C4—441no—
667C23×C4—441no—
668C23×C4C22×D1111yescharacteristic
669C23×C4C22×D1111yescharacteristic
670C23×C4C22×D1111yescharacteristic
671C23×C4C22×D1111yescharacteristic
672C23×C4C22×D1111yescharacteristic
673C23×C4C22×D1111yescharacteristic
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—114no—
680C2×C4⋊C4—114no—
681C2×C4⋊C4—222no—
682C2×C4⋊C4—222no—
683C2×C4⋊C4—222no—
684C2×C4⋊C4—222no—
685C2×C4⋊C4—441no—
686C2×C4⋊C4—441no—
687C2×C4⋊C4—441no—
688C2×C4⋊C4—441no—
689C2×C4⋊C4—441no—
690C2×C4⋊C4—441no—
691C2×C4⋊C4—441no—
692C2×C4⋊C4—441no—
693C2×C4⋊C4—441no—
694C2×C4⋊C4C22⋊D1114yescomplemented
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—114no—
702C2×C22⋊C4—114no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—222no—
706C2×C22⋊C4—222no—
707C2×C22⋊C4—222no—
708C2×C22⋊C4—222no—
709C2×C22⋊C4—222no—
710C2×C22⋊C4—222no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—441no—
718C2×C22⋊C4—441no—
719C2×C22⋊C4—441no—
720C2×C22⋊C4—441no—
721C2×C22⋊C4—441no—
722C2×C22⋊C4—441no—
723C2×C22⋊C4—441no—
724C2×C22⋊C4C4×D1114yescomplemented
725C2×C42—114no—
726C2×C42—441no—
727C2×C42—441no—
728#95—22no—
729#95—22no—
730#95—222no—
731#95—222no—
732#95—222no—
733#95—222no—
734#95—222no—
735#95—222no—
736#95—222no—
737#95—222no—
738#95—222no—
739#95—222no—
740#95—441no—
741#95—441no—
742C2×C11—44no—
743C2×C11#231511yescharacteristic
744C2×C11#232511yescharacteristic
745C2×C11#232511yescharacteristic
746C2×C11D4×C4⋊C411yescharacteristic
747C2×C11D4×C4⋊C411yescharacteristic
748C2×C11#236611yescharacteristic
749C2×C11#237911yescharacteristic
750C2×C11#267911yescharacteristic
751C2×C11#268211yescharacteristic
752C2×C11#268211yescharacteristic
753C2×C11#268311yescharacteristic
754C2×C11#272411yescharacteristic
755C2×C11#273211yescharacteristic
756C2×C11#273211yescharacteristic
757C2×C11#280411yescharacteristic
758D11—44no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—112no—
772C24—112no—
773C24—112no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24—221no—
779C24—221no—
780C24—221no—
781C24—221no—
782C24—221no—
783C24—221no—
784C24—221no—
785C24—221no—
786C24C2×C4×D1112yes—
787C24D4×D1112yes—
788C24Q8×D1112yes—
789C24C23×D1111yescharacteristic
790C2×D4—1116no—
791C2×D4—444no—
792C2×D4—444no—
793C2×D4—444no—
794C2×D4—444no—
795C2×D4—444no—
796C2×D4—444no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—112no—
846C22×C4—112no—
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×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—444no—
889C22×C4—444no—
890C22×C4—444no—
891C22×C4—444no—
892C22×C4—444no—
893C22×C4—444no—
894C22×C4—444no—
895C22×C4C2×C4×D1112yes—
896C22×C4C2×C4×D1112yes—
897C22×C4#433912yes—
898C22×C4D4×D1112yes—
899C22×C4C2×C22⋊D1112yes—
900C22×C4C2×C22⋊D1112yes—
901C22×C4C2×C22⋊D1112yes—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—444no—
905C4⋊C4—444no—
906C4⋊C4—444no—
907C4⋊C4—444no—
908C4⋊C4—444no—
909C22⋊C4—28no—
910C22⋊C4—44no—
911C22⋊C4—228no—
912C22⋊C4—228no—
913C22⋊C4—228no—
914C22⋊C4—444no—
915C22⋊C4—444no—
916C22⋊C4—444no—
917C22⋊C4—444no—
918C22⋊C4—444no—
919C42—444no—
920C11#1444011yescharacteristic, complemented, Sylow
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—114no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
980C23—441no—
981C23—441no—
982C23—441no—
983C23—441no—
984C23—441no—
985C23—441no—
986C23—441no—
987C23—441no—
988C23—441no—
989C23—441no—
990C23C4⋊C4×D1114yes—
991C23C22×C4×D1111yescharacteristic
992C23C2×#433911yescharacteristic
993C23C2×D4×D1111yescharacteristic
994C23C2×D4×D1111yescharacteristic
995C23#6703711yescharacteristic
996C23#6703711yescharacteristic
997C23#6703711yescharacteristic
998C23#6703711yescharacteristic
999C23C2×Q8×D1111yescharacteristic
1000C23#6704011yescharacteristic
1001C23#41×D1111yescharacteristic
1002C23#6704211yescharacteristic
1003C23#6704211yescharacteristic
1004C23#6704311yescharacteristic
1005C23C22×C22⋊D1111yescharacteristic
1006D4—4416no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—416no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—114no—
1050C2×C4—114no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—4416no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C2×C4—441no—
1091C2×C4—441no—
1092C2×C4—441no—
1093C2×C4—441no—
1094C2×C4—441no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4C4×C22⋊D1114yes—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—224no—
1116C22—224no—
1117C22—224no—
1118C22—442no—
1119C22—442no—
1120C22—442no—
1121C22—442no—
1122C22—442no—
1123C22—442no—
1124C22—442no—
1125C22—442no—
1126C22—442no—
1127C22—442no—
1128C22—442no—
1129C22—442no—
1130C22C2×C4⋊C4×D1111yescharacteristic
1131C22#1062303511yescharacteristic
1132C22#1062303811yescharacteristic
1133C22#1062304211yescharacteristic
1134C22C4×D4×D1111yescharacteristic
1135C22#1062307611yescharacteristic
1136C22#1062307611yescharacteristic
1137C22#1062307711yescharacteristic
1138C22#1062308411yescharacteristic
1139C22#1062309011yescharacteristic
1140C22#1062309111yescharacteristic
1141C22#1062309511yescharacteristic
1142C22#1062312011yescharacteristic
1143C22#1062312011yescharacteristic
1144C22#1062312111yescharacteristic
1145C22#1062312511yescharacteristic
1146C22#1062316011yescharacteristic
1147C22#1062316311yescharacteristic
1148C22#1062316511yescharacteristic
1149C22#1062316511yescharacteristic
1150C22#1062316711yescharacteristic
1151C22#1062316911yescharacteristic
1152C22#1062317711yescharacteristic
1153C22#1062317811yescharacteristic
1154C22#1062318411yescharacteristic
1155C22#1062318611yescharacteristic
1156C22#1062318811yescharacteristic
1157C22#1062319811yescharacteristic
1158C22C2×C4×C22⋊D1111yescharacteristic
1159C22D4×C22⋊D1111yescharacteristic
1160C22D4×C22⋊D1111yescharacteristic
1161C22#1062333511yescharacteristic
1162C22Q8×C22⋊D1111yescharacteristic
1163C22#1062336411yescharacteristic
1164C22#1062336511yescharacteristic
1165C4—24no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—81no—
1171C4—224no—
1172C4—224no—
1173C4—442no—
1174C4—442no—
1175C4—881no—
1176C4—881no—
1177C4—881no—
1178C2—44no—
1179C2—444no—
1180C2#1307122711yescharacteristic
1181C2#1307131311yescharacteristic
1182C2#1307131411yescharacteristic
1183C2#1307151411yescharacteristic
1184C2C4⋊C4×C22⋊D1111yescharacteristic
1185C2#1307167811yescharacteristic
1186C2#1307178911yescharacteristic
1187C2#1307495011yescharacteristic
1188C2#1307498111yescharacteristic
1189C2#1307498211yescharacteristic
1190C2#1307498611yescharacteristic
1191C2#1307554711yescharacteristic
1192C2#1307563111yescharacteristic
1193C2#1307563511yescharacteristic
1194C2#1307655811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#14440
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#10622823C2semidirect
5. C2×#10622602C2semidirect
6. C2×#10622602C2semidirect
7. #13066867C2semidirect
8. #13066866C2semidirect
9. #13066862C2semidirect
10. #13066861C2semidirect
11. #13066860C2semidirect
12. #13066859C2semidirect
13. #13066845C2semidirect
14. Dic11⋊#95C2semidirect
15. C2×C11×#385C2semidirect
56. #10622570C4semidirect
99. C2×C11×C4⋊C4D4semidirect
105. C2×C11×C22⋊C4C2×C4semidirect
114. C2×C22⋊Dic11C2×C4semidirect
128. C2×(C2×D11)⋊C4C2×C4semidirect
129. C2×(C2×D11)⋊C4C2×C4semidirect
143. C2×Dic11⋊C4C2×C4semidirect
144. C2×Dic11⋊C4D4semidirect
147. C2×C4×Dic11C2×C4semidirect
249. C2×C22⋊D11C4⋊C4semidirect
330. C2×#385D11semidirect
694. C2×C4⋊C4C22⋊D11semidirect
724. C2×C22⋊C4C4×D11semidirect
920. C11#14440semidirect

Maximal subgroups

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

subgroupindex
C2×#106225702
C2×#106228262
C2×#106225692
C2×#106228232
C2×#106226022
#130668672
#130668662
#130668622
#130668612
#130668602
#130668592
#130668452
Dic11⋊#952
C2×C11×#3852
#1444011