Finite Group Databasebeta

← #14681778

Subgroups — #14681778

Order 2816.

2018 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×#10622834C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622823C211yesmaximal, characteristic, complemented
4C2×#10622555C211yesmaximal, characteristic, complemented
5#13066880C211yesmaximal, characteristic, complemented
6#13066872C211yesmaximal, characteristic, complemented
7#13066859C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066859C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13#13066839C211yesmaximal, characteristic, complemented
14#13066838C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C11×#386—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
38#10622834—24no—
39#10622833C418yescomplemented
40#10622823—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55#10622555—24no—
56C25×C11C2311yescharacteristic
57C25×C11C2311yescharacteristic
58C22×D4×C11—41no—
59C22×D4×C11—41no—
60C22×D4×C11—41no—
61C22×D4×C11—41no—
62C22×D4×C11C2×C414yes—
63C22×D4×C11D414yes—
64C22×D4×C11Q814yes—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—41no—
69C23×C4×C11—41no—
70C23×C4×C11—41no—
71C23×C4×C11—41no—
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—41no—
80C23×Dic11—41no—
81C23×Dic11—41no—
82C23×Dic11—41no—
83C23×Dic11C2×C414yescomplemented
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4—41no—
99C2×C11×C22⋊C4—41no—
100C2×C11×C22⋊C4—41no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—22no—
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⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11—41no—
118C2×C22⋊Dic11—41no—
119C2×C22⋊Dic11C2×C414yes—
120C2×C22⋊Dic11C2×C414yes—
121C2×C22⋊Dic11C2×C414yescomplemented
122C2×C4⋊Dic11—22no—
123C2×C4⋊Dic11—41no—
124C2×C4⋊Dic11—41no—
125C2×Dic11⋊C4—22no—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—41no—
129C2×Dic11⋊C4—41no—
130C2×Dic11⋊C4—41no—
131C2×Dic11⋊C4—41no—
132C2×Dic11⋊C4—41no—
133C2×Dic11⋊C4—41no—
134C2×Dic11⋊C4—41no—
135C2×Dic11⋊C4—41no—
136C2×Dic11⋊C4D414yescomplemented
137C2×C4×Dic11—22no—
138C2×C4×Dic11—41no—
139C2×C4×Dic11—41no—
140C11×#95—22no—
141C11×#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95—41no—
152C11⋊#95—41no—
153C11⋊#95—41no—
154C11⋊#95C2×C414yescomplemented
155C11⋊#95C2×C414yescomplemented
156#14407—111nomaximal, Sylow
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×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×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11C22×C412yes—
182C24×C11C22×C412yes—
183C24×C11C2×D412yes—
184C24×C11C2×D412yes—
185C24×C11C2×Q812yes—
186C24×C11C2×Q812yes—
187C24×C11C2411yescharacteristic
188C2×D4×C11—44no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11C4⋊C4116yescomplemented
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—44no—
226C22×C4×C11—44no—
227C22×C4×C11—44no—
228C22×C4×C11—44no—
229C22×C4×C11—44no—
230C22×C4×C11—44no—
231C22×C4×C11—44no—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×Q812yes—
236C22×C4×C11#4112yes—
237C22×Dic11—28no—
238C22×Dic11—21no—
239C22×Dic11—21no—
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×Dic11—44no—
287C22×Dic11—44no—
288C22×Dic11—44no—
289C22×Dic11—44no—
290C22×Dic11—44no—
291C22×Dic11—44no—
292C22×Dic11C22×C412yes—
293C22×Dic11C22×C412yes—
294C22×Dic11C22×C412yes—
295C22×Dic11C22×C412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11#4112yes—
299C22×Dic11#4112yes—
300C11×C22⋊C4—44no—
301C11×C22⋊C4—44no—
302C11×C22⋊C4—44no—
303C22⋊Dic11—28no—
304C22⋊Dic11—44no—
305C22⋊Dic11—44no—
306C22⋊Dic11—44no—
307C22⋊Dic11—44no—
308C22⋊Dic11—44no—
309C22⋊Dic11—44no—
310C4⋊Dic11—44no—
311Dic11⋊C4—44no—
312Dic11⋊C4—44no—
313Dic11⋊C4—44no—
314Dic11⋊C4—44no—
315C4×Dic11—44no—
316C2×#390—111no—
317C2×#386—111no—
318C2×#386D1111yescharacteristic
319C2×#385—111no—
320C2×#380—111no—
321#1444—111no—
322#1442—111no—
323#1439—111no—
324#1439—111no—
325#1439—111no—
326#1439—111no—
327#1436—111no—
328#1436—111no—
329C22⋊#95—111no—
330C22⋊#95—111no—
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—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—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11C2×C4⋊C414yes—
400C23×C11C2×C4⋊C414yes—
401C23×C11C23×C411yescharacteristic
402C23×C11C22×D411yescharacteristic
403C23×C11C22×D411yescharacteristic
404C23×C11C22×Q811yescharacteristic
405C23×C11C2×#4111yescharacteristic
406C23×C11C2×#4111yescharacteristic
407C23×C11C2×#4111yescharacteristic
408C23×C11H(5,𝔽2)11yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
410C23×C11H(5,𝔽2)11yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C11H(5,𝔽2)11yescharacteristic
413C23×C11H(5,𝔽2)11yescharacteristic
414C23×C11H(5,𝔽2)11yescharacteristic
415C23×C112−1+411yescharacteristic
416D4×C11—416no—
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—416no—
430C2×C4×C11—41no—
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×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11C2×C4⋊C414yes—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—416no—
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—
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×Dic11C4×D414yes—
510C23×D4C2×D1111yescharacteristic
511C24×C4—111no—
512C24×C4C2×D1111yescharacteristic
513C22×C4⋊C4—111no—
514C22×C4⋊C4—111no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C22⋊C4C2×D1111yescharacteristic
527C22×C22⋊C4C2×D1111yescharacteristic
528C22×C42—111no—
529#390—224no—
530#386—24no—
531#386—118no—
532#385—224no—
533#380—224no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95C2×D1111yescharacteristic
549C2×#95C2×D1111yescharacteristic
550C22×C11—24no—
551C22×C11—24no—
552C22×C11—24no—
553C22×C11—24no—
554C22×C11—24no—
555C22×C11—24no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
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×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11C22×C4⋊C411yescharacteristic
581C22×C11C2×C4×D411yescharacteristic
582C22×C11C4×#4111yescharacteristic
583C22×C11#51811yescharacteristic
584C22×C11#51811yescharacteristic
585C22×C11#51811yescharacteristic
586C22×C11#52011yescharacteristic
587C22×C11#53411yescharacteristic
588C22×C11#53411yescharacteristic
589C22×C11#53411yescharacteristic
590C22×C11#53511yescharacteristic
591C22×C11#53811yescharacteristic
592C22×C11#53811yescharacteristic
593C22×C11#53811yescharacteristic
594C22×C11#53911yescharacteristic
595C22×C11#54011yescharacteristic
596C22×C11#54211yescharacteristic
597C22×C11#54311yescharacteristic
598C22×C11#54311yescharacteristic
599C22×C11D4211yescharacteristic
600C22×C11#54611yescharacteristic
601C22×C11#54611yescharacteristic
602C22×C11#54611yescharacteristic
603C22×C11#54711yescharacteristic
604C22×C11D4×Q811yescharacteristic
605C22×C11#55011yescharacteristic
606C22×C11#55311yescharacteristic
607C22×C11#55411yescharacteristic
608C22×C11#55411yescharacteristic
609C22×C11#55411yescharacteristic
610C22×C11#55511yescharacteristic
611C22×C11#56011yescharacteristic
612C22×C11#56011yescharacteristic
613C22×C11#56211yescharacteristic
614C22×C11#56211yescharacteristic
615C4×C11—24no—
616C4×C11—42no—
617C4×C11—42no—
618C4×C11—81no—
619C4×C11—81no—
620Dic11—24no—
621Dic11—42no—
622Dic11—42no—
623Dic11—42no—
624Dic11—42no—
625Dic11—42no—
626Dic11—81no—
627Dic11—81no—
628C25C22×D1111yescharacteristic
629C25C22×D1111yescharacteristic
630C22×D4—41no—
631C22×D4—41no—
632C22×D4—41no—
633C22×D4—41no—
634C22×D4Dic2214yes—
635C22×D4C4×D1114yes—
636C22×D4C22⋊D1114yes—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—22no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4—41no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—111no—
648C23×C4—111no—
649C23×C4—111no—
650C23×C4—114no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—222no—
654C23×C4—222no—
655C23×C4—441no—
656C23×C4—441no—
657C23×C4—441no—
658C23×C4—441no—
659C23×C4C22×D1111yescharacteristic
660C23×C4C22×D1111yescharacteristic
661C23×C4C22×D1111yescharacteristic
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C2×C4⋊C4—114no—
665C2×C4⋊C4—222no—
666C2×C4⋊C4—222no—
667C2×C4⋊C4—222no—
668C2×C4⋊C4—222no—
669C2×C4⋊C4—441no—
670C2×C4⋊C4—441no—
671C2×C4⋊C4—441no—
672C2×C4⋊C4—441no—
673C2×C4⋊C4—441no—
674C2×C4⋊C4—441no—
675C2×C4⋊C4—441no—
676C2×C4⋊C4—441no—
677C2×C4⋊C4—441no—
678C2×C4⋊C4—441no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—114no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—114no—
691C2×C22⋊C4—222no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—441no—
702C2×C22⋊C4—441no—
703C2×C22⋊C4—441no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4—441no—
709C2×C42—222no—
710C2×C42—441no—
711C2×C42—441no—
712#95—22no—
713#95—22no—
714#95—114no—
715#95—114no—
716#95—222no—
717#95—222no—
718#95—222no—
719#95—222no—
720#95—222no—
721#95—222no—
722#95—441no—
723#95—441no—
724#95—441no—
725#95—441no—
726#95—441no—
727#95—441no—
728C2×C11—44no—
729C2×C11—44no—
730C2×C11#231511yescharacteristic
731C2×C11#232111yescharacteristic
732C2×C11#233511yescharacteristic
733C2×C11D4×C4⋊C411yescharacteristic
734C2×C11#234911yescharacteristic
735C2×C11#236311yescharacteristic
736C2×C11#237711yescharacteristic
737C2×C11#266811yescharacteristic
738C2×C11#267311yescharacteristic
739C2×C11#268611yescharacteristic
740C2×C11#269211yescharacteristic
741C2×C11#270811yescharacteristic
742C2×C11#273211yescharacteristic
743C2×C11#278011yescharacteristic
744C2×C11#278411yescharacteristic
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24C2×Dic2212yes—
770C24C2×Dic2212yes—
771C24C2×C4×D1112yes—
772C24C2×C4×D1112yes—
773C24C2×C22⋊D1112yes—
774C24C2×C22⋊D1112yes—
775C24C23×D1111yescharacteristic
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4Dic11⋊C4116yescomplemented
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—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—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—112no—
821C22×C4—112no—
822C22×C4—112no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—228no—
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×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—444no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4C2×Dic2212yes—
884C22×C4C2×C4×D1112yes—
885C22×C4D4×D1112yes—
886C22×C4#434112yes—
887C22×C4C2×C22⋊D1112yes—
888C4⋊C4—444no—
889C4⋊C4—444no—
890C4⋊C4—444no—
891C4⋊C4—444no—
892C4⋊C4—444no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—228no—
897C22⋊C4—444no—
898C22⋊C4—444no—
899C22⋊C4—444no—
900C22⋊C4—444no—
901C22⋊C4—444no—
902C22⋊C4—444no—
903C42—444no—
904C11#1440711yescharacteristic, complemented, Sylow
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
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—22no—
940C23—22no—
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—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23C2×Dic11⋊C414yes—
974C23C2×Dic11⋊C414yes—
975C23C22×Dic2211yescharacteristic
976C23C22×C4×D1111yescharacteristic
977C23C2×D4×D1111yescharacteristic
978C23C2×#434111yescharacteristic
979C23#6703711yescharacteristic
980C23#6703711yescharacteristic
981C23#6703711yescharacteristic
982C23#6703711yescharacteristic
983C23#6703711yescharacteristic
984C23#6703711yescharacteristic
985C23#41×D1111yescharacteristic
986C23#41×D1111yescharacteristic
987C23#6704211yescharacteristic
988C23#6704311yescharacteristic
989C23C22×C22⋊D1111yescharacteristic
990D4—416no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—416no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—114no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—4416no—
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×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
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×C4C2×Dic11⋊C414yes—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22#1062301411yescharacteristic
1115C22#1062301411yescharacteristic
1116C22#1062301711yescharacteristic
1117C22#1062301711yescharacteristic
1118C22C4×#434111yescharacteristic
1119C22D4×Dic2211yescharacteristic
1120C22#1062307011yescharacteristic
1121C22#1062307011yescharacteristic
1122C22#1062307411yescharacteristic
1123C22C4×D4×D1111yescharacteristic
1124C22#1062307611yescharacteristic
1125C22#1062307711yescharacteristic
1126C22#1062312011yescharacteristic
1127C22#1062312211yescharacteristic
1128C22#1062312411yescharacteristic
1129C22#1062312611yescharacteristic
1130C22#1062313011yescharacteristic
1131C22#1062313411yescharacteristic
1132C22#1062313811yescharacteristic
1133C22#1062314411yescharacteristic
1134C22#1062314611yescharacteristic
1135C22#1062314711yescharacteristic
1136C22#1062315111yescharacteristic
1137C22#1062315211yescharacteristic
1138C22#1062318811yescharacteristic
1139C22#1062319111yescharacteristic
1140C22#1062319211yescharacteristic
1141C22#1062319811yescharacteristic
1142C22C22×Dic11⋊C411yescharacteristic
1143C22D4×C22⋊D1111yescharacteristic
1144C22#1062333511yescharacteristic
1145C22#1062333511yescharacteristic
1146C22#1062333711yescharacteristic
1147C22#1062335511yescharacteristic
1148C22#1062336011yescharacteristic
1149C4—24no—
1150C4—42no—
1151C4—42no—
1152C4—81no—
1153C4—81no—
1154C4—224no—
1155C4—442no—
1156C4—442no—
1157C4—442no—
1158C4—442no—
1159C4—442no—
1160C4—881no—
1161C4—881no—
1162C2—44no—
1163C2—44no—
1164C2#1307122811yescharacteristic
1165C2#1307127211yescharacteristic
1166C2#1307140711yescharacteristic
1167C2D4×Dic11⋊C411yescharacteristic
1168C2#1307152111yescharacteristic
1169C2#1307165711yescharacteristic
1170C2#1307177411yescharacteristic
1171C2#1307482011yescharacteristic
1172C2#1307487811yescharacteristic
1173C2#1307501811yescharacteristic
1174C2#1307511611yescharacteristic
1175C2#1307533011yescharacteristic
1176C2#1307563611yescharacteristic
1177C2#1307626111yescharacteristic
1178C2#1307631411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14407
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#10622823C2semidirect
4. C2×#10622555C2semidirect
5. #13066880C2semidirect
6. #13066872C2semidirect
7. #13066859C2semidirect
8. #13066859C2semidirect
9. #13066859C2semidirect
10. #13066859C2semidirect
11. #13066847C2semidirect
12. #13066847C2semidirect
13. #13066839C2semidirect
14. #13066838C2semidirect
39. #10622833C4semidirect
83. C23×Dic11C2×C4semidirect
121. C2×C22⋊Dic11C2×C4semidirect
136. C2×Dic11⋊C4D4semidirect
154. C11⋊#95C2×C4semidirect
155. C11⋊#95C2×C4semidirect
194. C2×D4×C11C4⋊C4semidirect
782. C2×D4Dic11⋊C4semidirect
904. C11#14407semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106228332
C2×#106228232
C2×#106225552
#130668802
#130668722
#130668592
#130668472
#130668392
#130668382
C2×C11×#3862
#1440711