Finite Group Databasebeta

← #14769833

Subgroups — #14769833

Order 2816.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2C2×#10622724C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
4#13069554C211yesmaximal, characteristic, complemented
5#13069550C211yesmaximal, characteristic, complemented
6#13068912C211yesmaximal, characteristic, complemented
7#13068908C211yesmaximal, characteristic, complemented
8#13068908C211yesmaximal, characteristic, complemented
9#13068907C211yesmaximal, characteristic, complemented
10#13068686C211yesmaximal, characteristic, complemented
11#13068684C211yesmaximal, characteristic, complemented
12#13068599C211yesmaximal, characteristic, complemented
13#13068381C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C2×C11×#336C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C2×#66983C411yescharacteristic
20C2×#66982C411yescharacteristic
21C2×#66982C411yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C2×C4×C22⋊D11C2211yescharacteristic
24C2×#66977C411yescharacteristic
25C22×#4313C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623010—24no—
28#10623010—24no—
29C2×#66929C411yescharacteristic
30C2×#66929C411yescharacteristic
31C2×#66928C411yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66925C2211yescharacteristic
34C2×#66925C2211yescharacteristic
35C2×#66923C411yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39#10622724—24no—
40C8×C22⋊D11—24no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50C2×C8×Dic11C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C23×C4×C11C2×C411yescharacteristic
64C23×C4×C11C2×C411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C22×D44C2×C411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2×C411yescharacteristic
72C22×C8×C11—22no—
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11—41no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×C42×C11C2×C411yescharacteristic
85C2×C42×C11C2×C411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89C2×C22⋊Dic11C2×C411yescharacteristic
90#66983—24no—
91#66982—24no—
92#66982—24no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11—22no—
95C4×C22⋊D11D414yes—
96C4×C22⋊D11D414yes—
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×(C2×D11)⋊C4C2×C411yescharacteristic
100C2×(C2×D11)⋊C4C2×C411yescharacteristic
101C2×(C2×D11)⋊C4C2×C411yescharacteristic
102C2×(C2×D11)⋊C4C2×C411yescharacteristic
103C2×(C2×D11)⋊C4C2×C411yescharacteristic
104C2×(C2×D11)⋊C4C2×C411yescharacteristic
105C2×C4⋊Dic11C2×C411yescharacteristic
106C2×C4⋊Dic11C2×C411yescharacteristic
107#66977—24no—
108C2×Dic11⋊C4C2×C411yescharacteristic
109C2×Dic11⋊C4C2×C411yescharacteristic
110C2×Dic11⋊C4C2×C411yescharacteristic
111C2×Dic11⋊C4C2×C411yescharacteristic
112C2×Dic11⋊C4C2×C411yescharacteristic
113C2×Dic11⋊C4C2×C411yescharacteristic
114C2×Dic11⋊C4C2×C411yescharacteristic
115C2×Dic11⋊C4C2×C411yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C2×#4313—22no—
123C2×#4313—22no—
124C2×#4313—41no—
125C2×C8×D11—22no—
126C2×C8×D11—22no—
127C2×C8×D11—41no—
128#66929—24no—
129#66929—24no—
130#66928—24no—
131C4×D44—22no—
132C4×D44—22no—
133#66925—22no—
134#66925—22no—
135#66925—22no—
136#66925—22no—
137#66923—24no—
138C4×Dic22—22no—
139C4×Dic22—22no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142(C2×D11)⋊C8—22no—
143(C2×D11)⋊C8—22no—
144(C2×D11)⋊C8—22no—
145(C2×D11)⋊C8—22no—
146(C2×D11)⋊C8—41no—
147(C2×D11)⋊C8—41no—
148#66879—22no—
149Dic11⋊C8—22no—
150Dic11⋊C8—22no—
151C8×Dic11—22no—
152#22470—111nomaximal, Sylow
153C24×C11C22×C411yescharacteristic
154C23×D11C22×C411yescharacteristic
155C23×D11C22×C411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—41no—
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C22×C411yescharacteristic
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2411yescharacteristic
174C2×C22⋊D11—22no—
175C2×C22⋊D11—22no—
176C2×C22⋊D11—22no—
177C2×C22⋊D11—22no—
178C2×C22⋊D11—22no—
179C2×C22⋊D11C22⋊C414yes—
180C22×Dic11C22×C411yescharacteristic
181C22×Dic11C22×C411yescharacteristic
182C22×Dic11C22×C411yescharacteristic
183C22×Dic11C22×C411yescharacteristic
184C22×Dic11C22×C411yescharacteristic
185C22×Dic11C22×C411yescharacteristic
186C2×D44—22no—
187C2×D44—22no—
188C2×D44—41no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11C2×D412yes—
200C2×C4×D11C2×D412yes—
201C2×Dic22—22no—
202C2×Dic22—22no—
203C2×Dic22—41no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—44no—
215C2×C8×C11—44no—
216C2×C8×C11#4112yes—
217C2×C8×C11#4112yes—
218C42×C11—22no—
219C42×C11—22no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C22⋊Dic11—22no—
225C22⋊Dic11C22⋊C414yes—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—22no—
231(C2×D11)⋊C4—22no—
232(C2×D11)⋊C4—22no—
233(C2×D11)⋊C4C22⋊C414yes—
234C4⋊Dic11—22no—
235C4⋊Dic11—22no—
236Dic11⋊C4—22no—
237Dic11⋊C4—22no—
238Dic11⋊C4—22no—
239Dic11⋊C4—22no—
240Dic11⋊C4—22no—
241Dic11⋊C4—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4C22⋊C414yes—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11C2×D412yes—
247C4×Dic11C2×D412yes—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260#4313—44no—
261C8×D11—44no—
262C2×#529—111no—
263C2×#435—111no—
264C2×C8×D4—111no—
265#1985—111no—
266#1984—111no—
267#1870—111no—
268#1869—111no—
269#1869—111no—
270#1869—111no—
271#1818—111no—
272#1817—111no—
273#1798—111no—
274#1750—111no—
275#1729—111no—
276C2×#336D1111yescharacteristic, complemented
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11C2×C22⋊C412yes—
282C23×C11#13112yes—
283C23×C11#13112yes—
284C23×C11C23×C411yescharacteristic
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—21no—
290C22×D11—21no—
291C22×D11—21no—
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11C2×C22⋊C412yes—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—44no—
317C2×C4×C11—44no—
318C2×C4×C11C2×C22⋊C412yes—
319C2×C4×C11#13112yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C2×#4111yescharacteristic
323C2×C4×C11C2×#4111yescharacteristic
324C2×C4×C11H(5,𝔽2)11yescharacteristic
325C2×C4×C112−1+411yescharacteristic
326C22⋊D11—28no—
327C22⋊D11—44no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—21no—
342C2×Dic11—21no—
343C2×Dic11C2×C22⋊C412yes—
344C2×Dic11C2×C22⋊C412yes—
345C2×Dic11C2×C22⋊C412yes—
346D44—44no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—41no—
352C4×D11—41no—
353C4×D11—41no—
354C4×D11—41no—
355Dic22—44no—
356C8×C11—22no—
357C8×C11—22no—
358C8×C11—41no—
359C8×C11—41no—
360C11⋊C8—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C22×M16—111no—
365C23×C8—111no—
366C23×C8C2×D1111yescharacteristic
367C23×C8C2×D1111yescharacteristic
368#529—224no—
369#529—224no—
370C2×#126—111no—
371C2×#126—111no—
372C2×#125—111no—
373C2×#124—111no—
374C2×#123—111no—
375C2×#123—111no—
376C2×C22⋊Q8—111no—
377C2×#121—111no—
378C2×C4×Q8—111no—
379C2×C4×D4—111no—
380C2×C4×D4—111no—
381C2×C4×D4—111no—
382C2×#117—111no—
383C2×#117—111no—
384C22×C42C2×D1111yescharacteristic
385#435—224no—
386C8×D4—224no—
387C2×C4⋊C8—111no—
388C2×C4⋊C8—111no—
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×C22⋊C8—111no—
392C2×C22⋊C8—111no—
393C2×C22⋊C8—111no—
394C2×C22⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
397C2×#97—111no—
398C2×C4×C8—111no—
399#336—111no—
400#336—111no—
401#336—111no—
402#336—111no—
403#336—111no—
404#336—111no—
405#336—111no—
406#336—111no—
407#336C2×D1111yescharacteristic
408#336C2×D1111yescharacteristic
409#336C2×D1111yescharacteristic
410#336C2×D1111yescharacteristic
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11#40814yes—
418C22×C11C22×C22⋊C411yescharacteristic
419C22×C11C4×#4111yescharacteristic
420C22×C11#52011yescharacteristic
421C22×C11C2×#13111yescharacteristic
422C22×C11C2×#13111yescharacteristic
423C22×C11C2×#13111yescharacteristic
424C22×C11#56811yescharacteristic
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—41no—
429C2×D11—41no—
430C2×D11—41no—
431C2×D11—41no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11—41no—
435C2×D11—41no—
436C2×D11—41no—
437C2×D11—41no—
438C2×D11—41no—
439C4×C11—22no—
440C4×C11—22no—
441C4×C11—41no—
442C4×C11—41no—
443C4×C11—41no—
444C4×C11#54611yescharacteristic
445C4×C11#54611yescharacteristic
446C4×C11#54711yescharacteristic
447C4×C11#54711yescharacteristic
448Dic11—22no—
449Dic11—22no—
450Dic11—22no—
451Dic11—41no—
452Dic11—41no—
453Dic11—41no—
454C22×Q8—111no—
455C22×D4—111no—
456C22×D4—111no—
457C22×D4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4C4×D1111yescharacteristic
461C23×C4C4×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C2×M16—222no—
464C2×M16—222no—
465C2×M16—441no—
466C22×C8—22no—
467C22×C8—22no—
468C22×C8—22no—
469C22×C8—22no—
470C22×C8—41no—
471C22×C8—41no—
472C22×C8—111no—
473C22×C8—111no—
474C22×C8—111no—
475C22×C8—111no—
476C22×C8—222no—
477C22×C8—222no—
478C22×C8—441no—
479C22×C8C22×D1111yescharacteristic
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C22×C8C22×D1111yescharacteristic
483#126—224no—
484#126—224no—
485#125—224no—
486#124—224no—
487#123—224no—
488#123—224no—
489C22⋊Q8—224no—
490#121—224no—
491C4×Q8—222no—
492C4×Q8—222no—
493C4×D4—114no—
494C4×D4—114no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4—222no—
498C4×D4—222no—
499#117—222no—
500#117—222no—
501#117—222no—
502#117—222no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C22⋊C4—111no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—111no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—111no—
522C2×C22⋊C4—111no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—111no—
526C2×C42—111no—
527C2×C42C4×D1111yescharacteristic
528C2×C42C4×D1111yescharacteristic
529C2×C42C22×D1111yescharacteristic
530C2×C42C22×D1111yescharacteristic
531C4⋊C8—222no—
532C4⋊C8—222no—
533C22⋊C8—222no—
534C22⋊C8—222no—
535C22⋊C8—222no—
536C22⋊C8—222no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C22⋊C8—441no—
540C22⋊C8—441no—
541#97—222no—
542C4×C8—222no—
543C2×C11—24no—
544C2×C11#233911yescharacteristic
545C2×C11C2×#40811yescharacteristic
546C2×C11#288011yescharacteristic
547C2×C11#296611yescharacteristic
548C2×C11#296811yescharacteristic
549C2×C11#299211yescharacteristic
550C2×C11#299411yescharacteristic
551D11—42no—
552D11—81no—
553C24—111no—
554C24—111no—
555C24C2×C4×D1111yescharacteristic
556C2×Q8—222no—
557C2×Q8—222no—
558C2×Q8—441no—
559C2×D4—114no—
560C2×D4—222no—
561C2×D4—222no—
562C2×D4—222no—
563C2×D4—222no—
564C2×D4—222no—
565C2×D4—222no—
566C2×D4—222no—
567C2×D4—441no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—41no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—111no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4C2×C4×D1111yescharacteristic
597C22×C4C2×C4×D1111yescharacteristic
598C22×C4C2×C4×D1111yescharacteristic
599C22×C4C2×C4×D1111yescharacteristic
600C22×C4C2×C4×D1111yescharacteristic
601C22×C4D4×D1112yes—
602C22×C4D4×D1112yes—
603C22×C4C23×D1111yescharacteristic
604M16—444no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—44no—
616C2×C8—44no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8—221no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8—221no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—444no—
630C2×C8#433912yes—
631C2×C8#433912yes—
632C4⋊C4—114no—
633C4⋊C4—222no—
634C4⋊C4—222no—
635C4⋊C4—222no—
636C4⋊C4—222no—
637C4⋊C4—222no—
638C4⋊C4—222no—
639C4⋊C4—222no—
640C4⋊C4—222no—
641C4⋊C4—222no—
642C22⋊C4—114no—
643C22⋊C4—114no—
644C22⋊C4—222no—
645C22⋊C4—222no—
646C22⋊C4—222no—
647C22⋊C4—222no—
648C22⋊C4—222no—
649C22⋊C4—222no—
650C22⋊C4—222no—
651C22⋊C4—222no—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—112no—
659C42—112no—
660C42—221no—
661C42—221no—
662C11#2247011yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—112no—
668C23—221no—
669C23—221no—
670C23—221no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—221no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23C22⋊C4×D1112yes—
682C23#6695412yes—
683C23#6696012yes—
684C23C22×C4×D1111yescharacteristic
685Q8—444no—
686D4—228no—
687D4—444no—
688D4—444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—112no—
709C2×C4—112no—
710C2×C4—112no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—221no—
716C2×C4—221no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4C22⋊C4×D1112yes—
735C2×C4#6695412yes—
736C2×C4C2×#433911yescharacteristic
737C2×C4C2×#433911yescharacteristic
738C2×C4C2×D4×D1111yescharacteristic
739C2×C4C2×D4×D1111yescharacteristic
740C2×C4#6703711yescharacteristic
741C2×C4#6704011yescharacteristic
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C8—441no—
747C8—441no—
748C8—441no—
749C8—441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—222no—
757C22—222no—
758C22—222no—
759C22—441no—
760C22—441no—
761C22—441no—
762C22—441no—
763C22—441no—
764C22—441no—
765C22—441no—
766C22—441no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22#1062234014yes—
771C22C4×#433911yescharacteristic
772C22C2×C22⋊C4×D1111yescharacteristic
773C22#1062303511yescharacteristic
774C22C2×#6695411yescharacteristic
775C22C2×#6695411yescharacteristic
776C22C2×#6696011yescharacteristic
777C22#1062327611yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—222no—
784C4—222no—
785C4—222no—
786C4—441no—
787C4—441no—
788C4—441no—
789C4#1062302111yescharacteristic
790C4#1062302111yescharacteristic
791C4#1062303811yescharacteristic
792C4#1062303811yescharacteristic
793C2—24no—
794C2—442no—
795C2—881no—
796C2#1307144311yescharacteristic
797C2C2×#1062234011yescharacteristic
798C2#1307706211yescharacteristic
799C2#1307759111yescharacteristic
800C2#1307761011yescharacteristic
801C2#1307775211yescharacteristic
802C2#1307777211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#336C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenterC2×#336D11
hypocenterC11#22470
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
2. C2×#10622724C2semidirect
3. C2×C8×C22⋊D11C2semidirect
4. #13069554C2semidirect
5. #13069550C2semidirect
6. #13068912C2semidirect
7. #13068908C2semidirect
8. #13068908C2semidirect
9. #13068907C2semidirect
10. #13068686C2semidirect
11. #13068684C2semidirect
12. #13068599C2semidirect
13. #13068381C2semidirect
14. #13068311C2semidirect
15. C2×C11×#336C2semidirect
276. C2×#336D11semidirect
662. C11#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C2×#106227242
C2×C8×C22⋊D112
#130695542
#130695502
#130689122
#130689082
#130689072
#130686862
#130686842
#130685992
#130683812
#130683112
C2×C11×#3362
#2247011