Finite Group Databasebeta

← #14769893

Subgroups — #14769893

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×#10623059C211yesmaximal, characteristic
2C2×#10622724C211yesmaximal, characteristic, complemented
3C2×#10622740C211yesmaximal, characteristic, complemented
4#13069554C211yesmaximal, characteristic, complemented
5#13069554C211yesmaximal, characteristic, complemented
6#13068913C211yesmaximal, characteristic, complemented
7#13068912C211yesmaximal, characteristic, complemented
8#13068908C211yesmaximal, characteristic, complemented
9#13068907C211yesmaximal, characteristic, complemented
10#13068687C211yesmaximal, characteristic, complemented
11#13068686C211yesmaximal, characteristic, complemented
12#13068595C211yesmaximal, characteristic, complemented
13#13068377C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#1729C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23#10623059—24no—
24#10623059—24no—
25C2×#66951C411yescharacteristic
26C2×#66949C411yescharacteristic
27C2×#66947C411yescharacteristic
28C2×#66942C411yescharacteristic
29C2×#66938C411yescharacteristic
30C2×#66937C411yescharacteristic
31C2×#66936C411yescharacteristic
32C2×#66932C411yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×#66925C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39#10622740—24no—
40#10622724—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×#66879C2211yescharacteristic
49C2×Dic11⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic
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×C11C2311yescharacteristic
64C22×C22⋊D11C2×C411yescharacteristic
65C22×C22⋊D11C2×C411yescharacteristic
66C22×D44C2×C411yescharacteristic
67C22×C4×D11C2×C411yescharacteristic
68C22×C4×D11C2×C411yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2×C411yescharacteristic
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—41no—
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×#117—22no—
83C11×#117—22no—
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C4⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11C2×C411yescharacteristic
91C2×C22⋊Dic11C2×C411yescharacteristic
92C4×C22⋊D11—22no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11D414yes—
95C4×C22⋊D11D414yes—
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×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×Dic11C2×C411yescharacteristic
111C2×C4×Dic11C2×C411yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C2×#4313—22no—
119C2×#4313—22no—
120C2×#4313—41no—
121C2×C8×D11—22no—
122C2×C8×D11—22no—
123C2×C8×D11—41no—
124#66951—24no—
125#66949—24no—
126#66947—24no—
127#66942—24no—
128#66938—24no—
129#66937—24no—
130#66936—24no—
131#66932—24no—
132C4×D44—22no—
133C4×D44—22no—
134#66925—22no—
135#66925—22no—
136C42×D11—22no—
137C42×D11—22no—
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—
149#66879—22no—
150Dic11⋊C8—22no—
151Dic11⋊C8—22no—
152#22475—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×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—22no—
169C2×C22⋊D11—22no—
170C2×C22⋊D11—41no—
171C2×C22⋊D11—41no—
172C2×C22⋊D11—41no—
173C2×C22⋊D11C22⋊C414yes—
174C22×Dic11C22×C411yescharacteristic
175C22×Dic11C22×C411yescharacteristic
176C22×Dic11C22×C411yescharacteristic
177C22×Dic11C22×C411yescharacteristic
178C22×Dic11C22×C411yescharacteristic
179C22×Dic11C22×C411yescharacteristic
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—41no—
183C2×C4×D11—22no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
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—41no—
197C2×C4×D11—41no—
198C2×C4×D11—41no—
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—44no—
216C2×C8×C11#4112yes—
217C2×C8×C11#4112yes—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C22⋊Dic11—22no—
227C22⋊Dic11C22⋊C414yes—
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⋊C4C22⋊C414yes—
242C4×Dic11—22no—
243C4×Dic11—22no—
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×#435—111no—
265#1985—111no—
266#1985—111no—
267#1870—111no—
268#1870—111no—
269#1869—111no—
270#1869—111no—
271#1818—111no—
272#1818—111no—
273#1797—111no—
274#1749—111no—
275#1729—111no—
276#1729D1111yescharacteristic, complemented
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11C2×C22⋊C412yes—
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×D11C2×C22⋊C412yes—
298C22×D11#13112yes—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—21no—
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—21no—
316C2×C4×C11—21no—
317C2×C4×C11C2×C22⋊C412yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C112−1+411yescharacteristic
324C22⋊D11—44no—
325C22⋊D11—44no—
326C2×Dic11—21no—
327C2×Dic11—21no—
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×Dic11C2×C22⋊C412yes—
342C2×Dic11C2×C22⋊C412yes—
343C2×Dic11C2×C22⋊C412yes—
344D44—44no—
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—44no—
350C4×D11—44no—
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—
365C22×M16C2×D1111yescharacteristic
366C23×C8—111no—
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×#117C2×D1111yescharacteristic
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⋊C8—111no—
395C2×C22⋊C8—111no—
396C2×C22⋊C8—111no—
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#336C2×D1111yescharacteristic
408#336C2×D1111yescharacteristic
409#336C2×D1111yescharacteristic
410#336C2×D1111yescharacteristic
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11C22×C22⋊C411yescharacteristic
419C22×C11C4×#4111yescharacteristic
420C22×C11#52011yescharacteristic
421C22×C11C2×#13111yescharacteristic
422C22×C11#56811yescharacteristic
423C22×C11#56811yescharacteristic
424C22×C11#56811yescharacteristic
425C2×D11—22no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
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—41no—
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×C4—111no—
461C23×C4—111no—
462C23×C4C22×D1111yescharacteristic
463C2×M16—22no—
464C2×M16—22no—
465C2×M16—41no—
466C2×M16—222no—
467C2×M16—222no—
468C2×M16—441no—
469C22×C8—22no—
470C22×C8—22no—
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—22no—
500#117—22no—
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⋊C4C4×D1111yescharacteristic
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—222no—
528C2×C42—222no—
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—
542#97—222no—
543C2×C11—42no—
544C2×C11#233911yescharacteristic
545C2×C11#287911yescharacteristic
546C2×C11#288011yescharacteristic
547C2×C11#296711yescharacteristic
548C2×C11#296811yescharacteristic
549C2×C11#299211yescharacteristic
550C2×C11#299511yescharacteristic
551D11—42no—
552D11—42no—
553C24—111no—
554C24—111no—
555C24C2×C4×D1111yescharacteristic
556C2×Q8—222no—
557C2×Q8—441no—
558C2×Q8—441no—
559C2×D4—114no—
560C2×D4—222no—
561C2×D4—222no—
562C2×D4—222no—
563C2×D4—222no—
564C2×D4—441no—
565C2×D4—441no—
566C2×D4—441no—
567C2×D4—441no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—111no—
573C22×C4—111no—
574C22×C4—111no—
575C22×C4—112no—
576C22×C4—112no—
577C22×C4—111no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—441no—
594C22×C4—441no—
595C22×C4—441no—
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—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—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—22no—
633C4⋊C4—22no—
634C4⋊C4—114no—
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—21no—
655C42—21no—
656C42—112no—
657C42—112no—
658C42—222no—
659C42—222no—
660C42—221no—
661C42—221no—
662C11#2247511yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—112no—
670C23—112no—
671C23—221no—
672C23—221no—
673C23—221no—
674C23—221no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—221no—
681C23—221no—
682C23—221no—
683C23C22⋊C4×D1112yes—
684C23C22×C4×D1111yescharacteristic
685Q8—444no—
686D4—444no—
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—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—112no—
708C2×C4—112no—
709C2×C4—112no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—221no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—221no—
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—444no—
730C2×C4—444no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4C22⋊C4×D1112yes—
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—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—222no—
758C22—222no—
759C22—222no—
760C22—222no—
761C22—222no—
762C22—222no—
763C22—441no—
764C22—441no—
765C22—441no—
766C22—441no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22—441no—
771C22C4×#433911yescharacteristic
772C22C2×C22⋊C4×D1111yescharacteristic
773C22#1062303511yescharacteristic
774C22D11×#13111yescharacteristic
775C22#1062328111yescharacteristic
776C22#1062328111yescharacteristic
777C22#1062328111yescharacteristic
778C4—22no—
779C4—41no—
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—42no—
794C2—442no—
795C2—442no—
796C2#1307144311yescharacteristic
797C2#1307705811yescharacteristic
798C2#1307706411yescharacteristic
799C2#1307759711yescharacteristic
800C2#1307760611yescharacteristic
801C2#1307775311yescharacteristic
802C2#1307778411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1729C2
prime radicalC2×#66937C4
cosocleC22×C4×C11C24
hypercenter#1729D11
hypocenterC11#22475
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1729

Complements

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

NH ≅ G/Ntype
2. C2×#10622724C2semidirect
3. C2×#10622740C2semidirect
4. #13069554C2semidirect
5. #13069554C2semidirect
6. #13068913C2semidirect
7. #13068912C2semidirect
8. #13068908C2semidirect
9. #13068907C2semidirect
10. #13068687C2semidirect
11. #13068686C2semidirect
12. #13068595C2semidirect
13. #13068377C2semidirect
14. #13068311C2semidirect
15. C11×#1729C2semidirect
276. #1729D11semidirect
662. C11#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#106230592
C2×#106227242
C2×#106227402
#130695542
#130689132
#130689122
#130689082
#130689072
#130686872
#130686862
#130685952
#130683772
#130683112
C11×#17292
#2247511