Finite Group Databasebeta

← #14719764

Subgroups — #14719764

Order 2816.

1446 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic, complemented
2C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3#13066980C212yesmaximal, complemented
4#13066976C212yesmaximal, complemented
5#13066964C214yesmaximal, complemented
6#13066934C214yesmaximal, complemented
7C2×C11×#525C211yesmaximal, characteristic
8C22×C11×#41C411yescharacteristic
9C24×C4×C11C2211yescharacteristic
10C11×#525—21no—
11C11×#525—21no—
12C11×#525—21no—
13C11×#525—21no—
14C11×#525—21no—
15C11×#525—21no—
16C11×#525—21no—
17C11×#525—21no—
18C2×C11×#123C2212yes—
19C2×C11×C22⋊Q8C411yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C411yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120C412yes—
24C2×C4×D4×C11C412yes—
25C2×C4×D4×C11C2212yes—
26C2×C11×#117C411yescharacteristic
27C22×#4318—21no—
28C23×C11⋊C8—21no—
29#10622820—21no—
30#10622820—21no—
31#10622820C2212yes—
32#10622820C2212yes—
33C2×C22⋊(C11⋊C8)—21no—
34C2×C22⋊(C11⋊C8)—21no—
35C2×C22⋊(C11⋊C8)—21no—
36C2×C22⋊(C11⋊C8)—21no—
37C2×C22⋊(C11⋊C8)C2212yes—
38C2×C22⋊(C11⋊C8)C2212yes—
39C2×C22⋊(C11⋊C8)C2212yes—
40C2×C22⋊(C11⋊C8)C2212yes—
41#10622166C2218yescomplemented
42#10622163C2218yescomplemented
43C25×C11C2×C411yescharacteristic
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—44no—
49C22×Q8×C11C2×C411yescharacteristic
50C22×D4×C11C2×C412yes—
51C22×D4×C11C2×C412yes—
52C22×D4×C11C2×C412yes—
53C22×D4×C11C2×C411yescharacteristic
54C23×C4×C11—44no—
55C23×C4×C11C2×C411yescharacteristic
56C23×C4×C11C2×C412yes—
57C23×C4×C11C2×C411yescharacteristic
58C23×C4×C11C2×C411yescharacteristic
59C23×C4×C11D411yescharacteristic
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#120—22no—
91C11×#120—22no—
92C11×#120—22no—
93C11×#120—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C11×#117—21no—
103C11×#117—21no—
104C11×#117—21no—
105C11×#117—21no—
106C2×C11×C4⋊C4C2×C411yescharacteristic
107C2×C11×C4⋊C4C2×C411yescharacteristic
108C2×C11×C4⋊C4C2×C412yes—
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C22⋊C4C2×C412yes—
111C2×C11×C22⋊C4C2×C412yes—
112C2×C11×C22⋊C4C2×C412yes—
113C2×C11×C22⋊C4C2×C412yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C42×C11C2×C412yes—
116C2×#4318—22no—
117C2×#4318—22no—
118C2×#4318—44no—
119C22×C11⋊C8—22no—
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—22no—
123C22×C11⋊C8—44no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126C22⋊(C11⋊C8)—22no—
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)C2314yes—
131C22⋊(C11⋊C8)C2314yes—
132#17381—111nomaximal, Sylow
133C24×C11—24no—
134C24×C11—42no—
135C24×C11—42no—
136C24×C11C22⋊C411yescharacteristic
137C24×C11C22⋊C411yescharacteristic
138C24×C11C22⋊C411yescharacteristic
139C24×C11C22⋊C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C24×C11C22×C412yes—
143C24×C11C22×C411yescharacteristic
144C11×#41—44no—
145C11×#41—44no—
146C11×#41—44no—
147C11×#41—44no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—42no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—28no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—42no—
161C2×D4×C11—44no—
162C2×D4×C11—44no—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—44no—
180C22×C4×C11C22⋊C411yescharacteristic
181C22×C4×C11C22⋊C411yescharacteristic
182C22×C4×C11C22⋊C411yescharacteristic
183C22×C4×C11C22⋊C411yescharacteristic
184C22×C4×C11C22⋊C411yescharacteristic
185C22×C4×C11C22⋊C411yescharacteristic
186C22×C4×C11C22⋊C411yescharacteristic
187C22×C4×C11C22⋊C411yescharacteristic
188C22×C4×C11C22⋊C411yescharacteristic
189C22×C4×C11C22⋊C411yescharacteristic
190C22×C4×C11C22⋊C411yescharacteristic
191C22×C4×C11C22⋊C411yescharacteristic
192C22×C4×C11C22×C412yes—
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C22×C411yescharacteristic
195C22×C4×C11C22×C412yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C22×C411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—22no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—22no—
229C42×C11—22no—
230C42×C11—22no—
231#4318—44no—
232#4318—44no—
233C2×C11⋊C8—24no—
234C2×C11⋊C8—24no—
235C2×C11⋊C8—44no—
236C2×C11⋊C8—44no—
237C2×C11⋊C8—44no—
238C2×C11⋊C8—44no—
239C2×#525D1111yescharacteristic
240C2×#407—111no—
241C22×C22⋊C8—111no—
242#1472—112no—
243#1471—112no—
244#1468—114no—
245#1459—114no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—416no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11C2×C22⋊C411yescharacteristic
272C23×C11C2×C22⋊C411yescharacteristic
273C23×C11C2×C22⋊C411yescharacteristic
274C23×C11C2×C22⋊C411yescharacteristic
275C23×C11C2×C22⋊C411yescharacteristic
276C23×C11C2×C22⋊C411yescharacteristic
277C23×C11#13114yes—
278C23×C11C23×C411yescharacteristic
279Q8×C11—42no—
280Q8×C11—42no—
281D4×C11—42no—
282D4×C11—44no—
283D4×C11—44no—
284D4×C11—44no—
285D4×C11—44no—
286D4×C11—44no—
287D4×C11—44no—
288D4×C11—42no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11#9914yes—
325C2×C4×C11C2×C22⋊C411yescharacteristic
326C2×C4×C11C2×C22⋊C411yescharacteristic
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C2×C4×C11C2×C22⋊C411yescharacteristic
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C11⋊C8—44no—
334C11⋊C8—44no—
335C22×#41Dic1111yescharacteristic
336C24×C4C2×D1111yescharacteristic
337C22×M16—221no—
338C23×C8—221no—
339#525—21no—
340#525—21no—
341#525—21no—
342#525—21no—
343#525—21no—
344#525—21no—
345#525—21no—
346#525—21no—
347C2×#123C2×D1112yes—
348C2×C22⋊Q8Dic1111yescharacteristic
349C2×C22⋊Q8C2×D1111yescharacteristic
350C2×#121Dic1111yescharacteristic
351C2×#121C2×D1111yescharacteristic
352C2×#120Dic1112yes—
353C2×C4×D4Dic1112yes—
354C2×C4×D4C2×D1112yes—
355C2×#117Dic1111yescharacteristic
356#407—112no—
357#407—112no—
358#407—221no—
359#407—221no—
360C2×C22⋊C8—112no—
361C2×C22⋊C8—112no—
362C2×C22⋊C8—112no—
363C2×C22⋊C8—112no—
364C2×C22⋊C8—221no—
365C2×C22⋊C8—221no—
366C2×C22⋊C8—221no—
367C2×C22⋊C8—221no—
368#324—118no—
369#323—118no—
370C22×C11—28no—
371C22×C11—21no—
372C22×C11—21no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—44no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—84no—
397C22×C11#40812yes—
398C22×C11#40812yes—
399C22×C11C2×#9912yes—
400C22×C11#41312yes—
401C22×C11C22×C22⋊C411yescharacteristic
402C22×C11C2×#13112yes—
403C4×C11—21no—
404C4×C11—21no—
405C4×C11—21no—
406C4×C11—21no—
407C4×C11—21no—
408C4×C11—21no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11C2×#9912yes—
413C4×C11C2×#9912yes—
414C25C2×Dic1111yescharacteristic
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—44no—
420C22×Q8C2×Dic1111yescharacteristic
421C22×D4C2×Dic1112yes—
422C22×D4C2×Dic1112yes—
423C22×D4C2×Dic1112yes—
424C22×D4C2×Dic1111yescharacteristic
425C23×C4—44no—
426C23×C4C2×Dic1111yescharacteristic
427C23×C4C2×Dic1112yes—
428C23×C4C2×Dic1111yescharacteristic
429C23×C4C2×Dic1111yescharacteristic
430C23×C4C22⋊D1111yescharacteristic
431C23×C4C22⋊D1111yescharacteristic
432C23×C4C22⋊D1111yescharacteristic
433C23×C4C22⋊D1111yescharacteristic
434C23×C4C22⋊D1111yescharacteristic
435C23×C4C22⋊D1111yescharacteristic
436C23×C4C22⋊D1111yescharacteristic
437C23×C4C22⋊D1111yescharacteristic
438C23×C4C22×D1111yescharacteristic
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C2×M16—222no—
442C2×M16—222no—
443C2×M16—444no—
444C22×C8—222no—
445C22×C8—222no—
446C22×C8—222no—
447C22×C8—222no—
448C22×C8—444no—
449#123—22no—
450#123—22no—
451#123—22no—
452#123—22no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—21no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#120—22no—
470#120—22no—
471#120—22no—
472#120—22no—
473C4×D4—22no—
474C4×D4—22no—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481#117—21no—
482#117—21no—
483#117—21no—
484#117—21no—
485C2×C4⋊C4C2×Dic1111yescharacteristic
486C2×C4⋊C4C2×Dic1111yescharacteristic
487C2×C4⋊C4C2×Dic1112yes—
488C2×C4⋊C4C22×D1112yes—
489C2×C22⋊C4C2×Dic1112yes—
490C2×C22⋊C4C2×Dic1112yes—
491C2×C22⋊C4C2×Dic1112yes—
492C2×C22⋊C4C2×Dic1112yes—
493C2×C22⋊C4C22×D1112yes—
494C2×C42C2×Dic1112yes—
495C22⋊C8—114no—
496C22⋊C8—114no—
497C22⋊C8—222no—
498C22⋊C8—222no—
499C22⋊C8—222no—
500C22⋊C8—222no—
501C22⋊C8—222no—
502C22⋊C8—222no—
503C2×C11—22no—
504C2×C11—22no—
505C2×C11—22no—
506C2×C11—22no—
507C2×C11—22no—
508C2×C11—41no—
509C2×C11—41no—
510C2×C11—82no—
511C2×C11C2×#40811yescharacteristic
512C2×C11C22×#9911yescharacteristic
513C2×C11C2×#41311yescharacteristic
514C24—24no—
515C24—42no—
516C24—42no—
517C24C22⋊Dic1111yescharacteristic
518C24C22⋊Dic1111yescharacteristic
519C24C22⋊Dic1111yescharacteristic
520C24C22⋊Dic1111yescharacteristic
521C24C22×Dic1111yescharacteristic
522C24C22×Dic1111yescharacteristic
523C24C22×Dic1112yes—
524C24C22×Dic1111yescharacteristic
525#41—44no—
526#41—44no—
527#41—44no—
528#41—44no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—42no—
532C2×D4—28no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—44no—
543C2×D4—44no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—44no—
561C22×C4C22⋊Dic1111yescharacteristic
562C22×C4C22⋊Dic1111yescharacteristic
563C22×C4C22⋊Dic1111yescharacteristic
564C22×C4C22⋊Dic1111yescharacteristic
565C22×C4C22⋊Dic1111yescharacteristic
566C22×C4C22⋊Dic1111yescharacteristic
567C22×C4C22⋊Dic1111yescharacteristic
568C22×C4C22⋊Dic1111yescharacteristic
569C22×C4C22⋊Dic1111yescharacteristic
570C22×C4C22⋊Dic1111yescharacteristic
571C22×C4C22⋊Dic1111yescharacteristic
572C22×C4C22⋊Dic1111yescharacteristic
573C22×C4C22×Dic1112yes—
574C22×C4C22×Dic1111yescharacteristic
575C22×C4C22×Dic1111yescharacteristic
576C22×C4C22×Dic1112yes—
577C22×C4C22×Dic1112yes—
578C22×C4C22×Dic1111yescharacteristic
579C22×C4C2×C22⋊D1111yescharacteristic
580C22×C4C2×C22⋊D1111yescharacteristic
581C22×C4C2×C22⋊D1111yescharacteristic
582C22×C4C2×C22⋊D1111yescharacteristic
583C22×C4C2×C22⋊D1111yescharacteristic
584C22×C4C2×C22⋊D1111yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C23×D1111yescharacteristic
592M16—444no—
593M16—444no—
594C2×C8—224no—
595C2×C8—224no—
596C2×C8—444no—
597C2×C8—444no—
598C2×C8—444no—
599C2×C8—444no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C42—22no—
619C42—22no—
620C11#1738111yescharacteristic, complemented, Sylow
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—416no—
644C23—42no—
645C23—42no—
646C23#6700114yes—
647C23C2×C22⋊Dic1111yescharacteristic
648C23C2×C22⋊Dic1111yescharacteristic
649C23C2×C22⋊Dic1111yescharacteristic
650C23C2×C22⋊Dic1111yescharacteristic
651C23C2×C22⋊Dic1111yescharacteristic
652C23C2×C22⋊Dic1111yescharacteristic
653C23C23×Dic1111yescharacteristic
654Q8—42no—
655Q8—42no—
656D4—42no—
657D4—44no—
658D4—44no—
659D4—44no—
660D4—44no—
661D4—44no—
662D4—44no—
663D4—42no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4#6689814yes—
700C2×C4C2×C22⋊Dic1111yescharacteristic
701C2×C4C2×C22⋊Dic1111yescharacteristic
702C2×C4C2×C22⋊Dic1111yescharacteristic
703C2×C4C2×C22⋊Dic1111yescharacteristic
704C2×C4C2×C22⋊Dic1111yescharacteristic
705C2×C4C2×C22⋊Dic1111yescharacteristic
706C2×C4C22×C22⋊D1111yescharacteristic
707C2×C4C22×C22⋊D1111yescharacteristic
708C8—444no—
709C8—444no—
710C22—28no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22C2×#6689812yes—
738C22#1062284712yes—
739C22#1062284712yes—
740C22#1062285012yes—
741C22C2×#6700112yes—
742C22C22×C22⋊Dic1111yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4C2×#6689812yes—
753C4C2×#6689812yes—
754C2—22no—
755C2—22no—
756C2—22no—
757C2—22no—
758C2—22no—
759C2—41no—
760C2—41no—
761C2—82no—
762C2C2×#1062284711yescharacteristic
763C2C22×#6689811yescharacteristic
764C2C2×#1062285011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#525C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC2×#525D11
hypocenterC11#17381
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10622820C2semidirect
2. C22×C22⋊(C11⋊C8)C2semidirect
3. #13066980C2semidirect
4. #13066976C2semidirect
5. #13066964C2semidirect
6. #13066934C2semidirect
41. #10622166C22semidirect
42. #10622163C22semidirect
620. C11#17381semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
C22×C22⋊(C11⋊C8)2
#130669802
#130669762
#130669642
#130669342
C2×C11×#5252
#1738111