Finite Group Databasebeta

← #14769892

Subgroups — #14769892

Order 2816.

1168 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×#10623069C211yesmaximal, characteristic
2C2×#10622740C211yesmaximal, characteristic, complemented
3C2×#10622343C211yesmaximal, characteristic, complemented
4#13069554C211yesmaximal, characteristic, complemented
5#13069554C211yesmaximal, characteristic, complemented
6#13068910C211yesmaximal, characteristic, complemented
7#13068909C211yesmaximal, characteristic, complemented
8#13068905C211yesmaximal, characteristic, complemented
9#13068686C211yesmaximal, characteristic, complemented
10#13068685C211yesmaximal, characteristic, complemented
11#13068594C211yesmaximal, characteristic, complemented
12#13068380C211yesmaximal, characteristic, complemented
13#13068314C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66992C411yescharacteristic
19C2×#66988C411yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623069—24no—
28#10623069—24no—
29C2×#66951C411yescharacteristic
30C2×#66942C411yescharacteristic
31C2×#66939C411yescharacteristic
32C2×#66938C411yescharacteristic
33C2×#66932C411yescharacteristic
34C2×#66931C411yescharacteristic
35C2×#66925C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622740—24no—
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×#66879C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50#10622343—24no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2×C411yescharacteristic
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—41no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11C2×C411yescharacteristic
86C2×C22⋊Dic11C2×C411yescharacteristic
87C2×C22⋊Dic11C2×C411yescharacteristic
88C2×C22⋊Dic11C2×C411yescharacteristic
89#66992—24no—
90#66988—24no—
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C4×C22⋊D11D414yes—
94C4×C22⋊D11D414yes—
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99#66979—22no—
100#66979—22no—
101C2×C4⋊Dic11C2×C411yescharacteristic
102C2×C4⋊Dic11C2×C411yescharacteristic
103C2×C4⋊Dic11C2×C411yescharacteristic
104C2×Dic11⋊C4C2×C411yescharacteristic
105C2×Dic11⋊C4C2×C411yescharacteristic
106C2×Dic11⋊C4C2×C411yescharacteristic
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×Dic11⋊C4C2×C411yescharacteristic
109C2×Dic11⋊C4C2×C411yescharacteristic
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11C2×C411yescharacteristic
113C2×C4×Dic11C2×C411yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C22×C11⋊C8—22no—
118C22×C11⋊C8—22no—
119C22×C11⋊C8—41no—
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C2×#4313—22no—
125C2×#4313—22no—
126C2×#4313—41no—
127C2×C8×D11—22no—
128C2×C8×D11—22no—
129C2×C8×D11—41no—
130#66951—24no—
131#66942—24no—
132#66939—24no—
133#66938—24no—
134#66932—24no—
135#66931—24no—
136#66925—22no—
137#66925—22no—
138C4×Dic22—22no—
139C4×Dic22—22no—
140C11×C22⋊C8—22no—
141C11×C22⋊C8—22no—
142C11×C22⋊C8—41no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)—41no—
146(C2×D11)⋊C8—22no—
147(C2×D11)⋊C8—22no—
148#66879—22no—
149#66879—22no—
150Dic11⋊C8—22no—
151Dic11⋊C8—22no—
152#22475—111nomaximal, Sylow
153C24×C11C22×C411yescharacteristic
154C24×C11C22×C411yescharacteristic
155C23×D11C22×C411yescharacteristic
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—41no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11C22×C411yescharacteristic
170C22×C4×C11C22×C411yescharacteristic
171C22×C4×C11C22×C411yescharacteristic
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D412yes—
175C22×C4×C11C2411yescharacteristic
176C2×C22⋊D11—22no—
177C2×C22⋊D11—22no—
178C2×C22⋊D11—41no—
179C2×C22⋊D11—41no—
180C2×C22⋊D11—41no—
181C2×C22⋊D11C22⋊C414yes—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—41no—
186C22×Dic11—41no—
187C22×Dic11—41no—
188C22×Dic11C22×C411yescharacteristic
189C22×Dic11C22×C411yescharacteristic
190C22×Dic11C22×C411yescharacteristic
191C22×Dic11C22×C411yescharacteristic
192C22×Dic11C22×C411yescharacteristic
193C22×Dic11C22×C411yescharacteristic
194C22×Dic11C22×C411yescharacteristic
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—41no—
203C2×Dic22—41no—
204C11×M16—44no—
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—21no—
215C2×C8×C11—21no—
216C2×C8×C11#4112yes—
217C11×C4⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C42×C11—21no—
221C42×C11—21no—
222C22⋊Dic11—22no—
223C22⋊Dic11—22no—
224C22⋊Dic11—22no—
225C22⋊Dic11C22⋊C414yes—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4C22⋊C414yes—
230C4⋊Dic11—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—22no—
233Dic11⋊C4—22no—
234Dic11⋊C4—22no—
235Dic11⋊C4—22no—
236Dic11⋊C4—22no—
237Dic11⋊C4—22no—
238Dic11⋊C4C22⋊C414yes—
239C4×Dic11—22no—
240C4×Dic11—22no—
241C4×Dic11—21no—
242C4×Dic11—21no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C4×Dic11C2×D412yes—
246C4×Dic11C2×D412yes—
247C2×C11⋊C8—21no—
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—44no—
259C2×C11⋊C8#4112yes—
260#4313—44no—
261C8×D11—44no—
262C2×#529—111no—
263C2×#435—111no—
264C2×#435—111no—
265#1985—111no—
266#1985—111no—
267#1870—111no—
268#1870D1111yescharacteristic, complemented
269#1869—111no—
270#1869—111no—
271#1818—111no—
272#1818—111no—
273#1797—111no—
274#1749—111no—
275#1729—111no—
276#1729—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11C2×C22⋊C412yes—
290C23×C11#13112yes—
291C23×C11C23×C411yescharacteristic
292C22×D11—21no—
293C22×D11—21no—
294C22×D11—21no—
295C22×D11—21no—
296C22×D11—21no—
297C22×D11—21no—
298C22×D11C2×C22⋊C412yes—
299D4×C11—44no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
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—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11C2×C22⋊C412yes—
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—44no—
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×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—44no—
347C2×Dic11—44no—
348C2×Dic11C2×C22⋊C412yes—
349C2×Dic11C2×C22⋊C412yes—
350C2×Dic11C2×C22⋊C412yes—
351C4×D11—22no—
352C4×D11—22no—
353C4×D11—22no—
354C4×D11—22no—
355Dic22—44no—
356C8×C11—22no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C11⋊C8—22no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C22×M16—111no—
365C22×M16C2×D1111yescharacteristic
366C23×C8—111no—
367C23×C8—111no—
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×D4C2×D1111yescharacteristic
382C2×#117—111no—
383C2×#117—111no—
384C22×C42—111no—
385#435—224no—
386#435—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⋊C8C2×D1111yescharacteristic
395C2×C22⋊C8C2×D1111yescharacteristic
396C2×C22⋊C8C2×D1111yescharacteristic
397C2×#97—111no—
398C2×#97—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#336—111no—
408#336—111no—
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—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11C22×C22⋊C411yescharacteristic
426C22×C11C4×#4111yescharacteristic
427C22×C11#52011yescharacteristic
428C22×C11C2×#13111yescharacteristic
429C22×C11#56811yescharacteristic
430C22×C11#56811yescharacteristic
431C22×C11#56811yescharacteristic
432C2×D11—22no—
433C2×D11—22no—
434C2×D11—22no—
435C2×D11—41no—
436C2×D11—41no—
437C2×D11—41no—
438C2×D11—41no—
439C4×C11—22no—
440C4×C11—41no—
441C4×C11—41no—
442C4×C11—41no—
443C4×C11#54611yescharacteristic
444C4×C11#54611yescharacteristic
445C4×C11#54711yescharacteristic
446C4×C11#54711yescharacteristic
447Dic11—22no—
448Dic11—22no—
449Dic11—22no—
450Dic11—41no—
451Dic11—41no—
452Dic11—41no—
453Dic11—41no—
454C22×Q8—111no—
455C22×D4—111no—
456C22×D4—111no—
457C22×D4C4×D1111yescharacteristic
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—222no—
467C2×M16—222no—
468C2×M16—441no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—111no—
473C22×C8—222no—
474C22×C8—222no—
475C22×C8—222no—
476C22×C8—222no—
477C22×C8—441no—
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—22no—
494C4×D4—22no—
495C4×D4—114no—
496C4×D4—114no—
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⋊C4C4×D1111yescharacteristic
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⋊C4C4×D1111yescharacteristic
522C2×C22⋊C4C4×D1111yescharacteristic
523C2×C42—111no—
524C2×C42—111no—
525C2×C42—111no—
526C2×C42—111no—
527C2×C42—111no—
528C2×C42—222no—
529C2×C42—222no—
530C2×C42C22×D1111yescharacteristic
531C4⋊C8—222no—
532C4⋊C8—222no—
533C22⋊C8—22no—
534C22⋊C8—22no—
535C22⋊C8—41no—
536C22⋊C8—222no—
537C22⋊C8—222no—
538C22⋊C8—222no—
539C22⋊C8—222no—
540C22⋊C8—441no—
541#97—222no—
542#97—222no—
543C2×C11—42no—
544C2×C11—42no—
545C2×C11#233911yescharacteristic
546C2×C11#287911yescharacteristic
547C2×C11#288011yescharacteristic
548C2×C11#296711yescharacteristic
549C2×C11#296811yescharacteristic
550C2×C11#299211yescharacteristic
551C2×C11#299511yescharacteristic
552D11—42no—
553C24—111no—
554C24C2×C4×D1111yescharacteristic
555C24C2×C4×D1111yescharacteristic
556C2×Q8—222no—
557C2×Q8—441no—
558C2×Q8—441no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—41no—
562C2×D4—114no—
563C2×D4—222no—
564C2×D4—222no—
565C2×D4—441no—
566C2×D4—441no—
567C2×D4—441no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
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—111no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—222no—
594C22×C4—441no—
595C22×C4—441no—
596C22×C4—441no—
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—44no—
605M16—444no—
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—21no—
616C2×C8—21no—
617C2×C8—112no—
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—444no—
631C2×C8#434112yes—
632C4⋊C4—22no—
633C4⋊C4—114no—
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—22no—
643C22⋊C4—22no—
644C22⋊C4—114no—
645C22⋊C4—114no—
646C22⋊C4—222no—
647C22⋊C4—222no—
648C22⋊C4—222no—
649C22⋊C4—222no—
650C22⋊C4—222no—
651C22⋊C4—222no—
652C42—21no—
653C42—21no—
654C42—112no—
655C42—112no—
656C42—222no—
657C42—222no—
658C42—221no—
659C42—221no—
660C42—221no—
661C42—221no—
662C11#2247511yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—112no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23—221no—
682C23C22⋊C4×D1112yes—
683C23#6696012yes—
684C23C22×C4×D1111yescharacteristic
685Q8—444no—
686D4—44no—
687D4—444no—
688D4—444no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
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—221no—
731C2×C4—221no—
732C2×C4—221no—
733C2×C4—444no—
734C2×C4—444no—
735C2×C4C22⋊C4×D1112yes—
736C2×C4C2×D4×D1111yescharacteristic
737C2×C4C2×D4×D1111yescharacteristic
738C2×C4C2×#434111yescharacteristic
739C2×C4#6703711yescharacteristic
740C2×C4#41×D1111yescharacteristic
741C2×C4#6704311yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—222no—
747C8—441no—
748C8—441no—
749C8—441no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—222no—
765C22—222no—
766C22—222no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22—441no—
771C22C2×C22⋊C4×D1111yescharacteristic
772C22C4×#434111yescharacteristic
773C22#1062307711yescharacteristic
774C22C2×#6696011yescharacteristic
775C22#1062327611yescharacteristic
776C22#1062328111yescharacteristic
777C22#1062328111yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—222no—
783C4—222no—
784C4—222no—
785C4—441no—
786C4—441no—
787C4—441no—
788C4—441no—
789C4#1062312211yescharacteristic
790C4#1062314111yescharacteristic
791C4#1062314211yescharacteristic
792C4#1062318611yescharacteristic
793C2—42no—
794C2—42no—
795C2—442no—
796C2#1307144211yescharacteristic
797C2#1307705811yescharacteristic
798C2#1307706611yescharacteristic
799C2#1307760211yescharacteristic
800C2#1307761111yescharacteristic
801C2#1307775611yescharacteristic
802C2#1307778011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#66992C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#22475
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#10622740C2semidirect
3. C2×#10622343C2semidirect
4. #13069554C2semidirect
5. #13069554C2semidirect
6. #13068910C2semidirect
7. #13068909C2semidirect
8. #13068905C2semidirect
9. #13068686C2semidirect
10. #13068685C2semidirect
11. #13068594C2semidirect
12. #13068380C2semidirect
13. #13068314C2semidirect
14. #13068311C2semidirect
15. C11×#1870C2semidirect
268. #1870D11semidirect
662. C11#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#106230692
C2×#106227402
C2×#106223432
#130695542
#130689102
#130689092
#130689052
#130686862
#130686852
#130685942
#130683802
#130683142
#130683112
C11×#18702
#2247511