Finite Group Databasebeta

← #14769867

Subgroups — #14769867

Order 2816.

1162 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×#10622342C211yesmaximal, characteristic, complemented
3C2×#10622341C211yesmaximal, characteristic, complemented
4#13069554C211yesmaximal, characteristic, complemented
5#13069550C211yesmaximal, characteristic, complemented
6#13068912C211yesmaximal, characteristic, complemented
7#13068911C211yesmaximal, characteristic, complemented
8#13068911C211yesmaximal, characteristic, complemented
9#13068907C211yesmaximal, characteristic, complemented
10#13068686C211yesmaximal, characteristic, complemented
11#13068599C211yesmaximal, characteristic, complemented
12#13068381C211yesmaximal, characteristic, complemented
13#13068311C211yesmaximal, characteristic, complemented
14#13068310C211yesmaximal, characteristic, complemented
15C11×#1817C211yesmaximal, characteristic, complemented
16C22×C42×C11C2211yescharacteristic
17C2×#66983C411yescharacteristic
18C2×#66982C411yescharacteristic
19C2×#66982C411yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C2×#66977C411yescharacteristic
23C22×#4318C2211yescharacteristic
24C22×#4318C2211yescharacteristic
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×C11×C22⋊C8C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×(C2×D11)⋊C8C2211yescharacteristic
45C2×#66879C2211yescharacteristic
46C2×Dic11⋊C8C2211yescharacteristic
47C2×Dic11⋊C8C2211yescharacteristic
48C2×C8×Dic11C2211yescharacteristic
49#10622342—24no—
50#10622341—24no—
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×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C42×C11—22no—
77C2×C42×C11—22no—
78C2×C42×C11C2×C411yescharacteristic
79C2×C42×C11C2×C411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83C2×C22⋊Dic11C2×C411yescharacteristic
84#66983—24no—
85#66982—24no—
86#66982—24no—
87C4×C22⋊D11—22no—
88C4×C22⋊D11—22no—
89C4×C22⋊D11D414yes—
90C4×C22⋊D11D414yes—
91C2×(C2×D11)⋊C4C2×C411yescharacteristic
92C2×(C2×D11)⋊C4C2×C411yescharacteristic
93C2×(C2×D11)⋊C4C2×C411yescharacteristic
94C2×(C2×D11)⋊C4C2×C411yescharacteristic
95C2×(C2×D11)⋊C4C2×C411yescharacteristic
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×(C2×D11)⋊C4C2×C411yescharacteristic
98C2×(C2×D11)⋊C4C2×C411yescharacteristic
99C2×C4⋊Dic11C2×C411yescharacteristic
100C2×C4⋊Dic11C2×C411yescharacteristic
101#66977—24no—
102C2×Dic11⋊C4C2×C411yescharacteristic
103C2×Dic11⋊C4C2×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×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C2×#4318—22no—
113C2×#4318—22no—
114C2×#4318—22no—
115C2×#4318—22no—
116C2×#4318—41no—
117C2×#4318—41no—
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—
140C11×C22⋊C8—22no—
141C11×C22⋊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#22472—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—41no—
164C22×C4×C11—41no—
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—41no—
176C2×C22⋊D11—41no—
177C2×C22⋊D11—41no—
178C2×C22⋊D11—41no—
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—21no—
215C2×C8×C11—21no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C22⋊Dic11—22no—
223C22⋊Dic11C22⋊C414yes—
224(C2×D11)⋊C4—22no—
225(C2×D11)⋊C4—22no—
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)⋊C4C22⋊C414yes—
232C4⋊Dic11—22no—
233C4⋊Dic11—22no—
234Dic11⋊C4—22no—
235Dic11⋊C4—22no—
236Dic11⋊C4—22no—
237Dic11⋊C4—22no—
238Dic11⋊C4—22no—
239Dic11⋊C4—22no—
240Dic11⋊C4—22no—
241Dic11⋊C4C22⋊C414yes—
242C4×Dic11—21no—
243C4×Dic11—21no—
244C4×Dic11C2×D412yes—
245C4×Dic11C2×D412yes—
246#4318—44no—
247#4318—44no—
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#4112yes—
259C2×C11⋊C8#4112yes—
260#4313—44no—
261C8×D11—44no—
262C2×#529—111no—
263C2×#436—111no—
264C2×#435—111no—
265#1985—111no—
266#1984—111no—
267#1870—111no—
268#1870—111no—
269#1870—111no—
270#1869—111no—
271#1818—111no—
272#1817D1111yescharacteristic, complemented
273#1798—111no—
274#1750—111no—
275#1729—111no—
276#1728—111no—
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×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—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×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—41no—
357C8×C11—41no—
358C8×C11—41no—
359C8×C11—41no—
360C11⋊C8—22no—
361C11⋊C8—22no—
362C11⋊C8—41no—
363C11⋊C8—41no—
364C22×M16—111no—
365C22×M16—111no—
366C22×M16—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×D4—111no—
382C2×#117—111no—
383C2×#117—111no—
384C22×C42C2×D1111yescharacteristic
385#436—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⋊C8C2×D1111yescharacteristic
396C2×C22⋊C8C2×D1111yescharacteristic
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—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—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—222no—
466C2×M16—222no—
467C2×M16—222no—
468C2×M16—222no—
469C2×M16—441no—
470C2×M16—441no—
471C2×M16—441no—
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—22no—
534C22⋊C8—22no—
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—42no—
544C2×C11#233911yescharacteristic
545C2×C11#287911yescharacteristic
546C2×C11#288011yescharacteristic
547C2×C11#296711yescharacteristic
548C2×C11#296911yescharacteristic
549C2×C11#299311yescharacteristic
550C2×C11#299511yescharacteristic
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—441no—
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—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—41no—
576C22×C4—41no—
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—
605M16—444no—
606M16—444no—
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—21no—
618C2×C8—21no—
619C2×C8—112no—
620C2×C8—112no—
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—221no—
630C2×C8—221no—
631C2×C8—444no—
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#2247211yescharacteristic, complemented, Sylow
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—112no—
670C23—221no—
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—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×D4×D1111yescharacteristic
737C2×C4C2×D4×D1111yescharacteristic
738C2×C4#41×D1111yescharacteristic
739C2×C4#41×D1111yescharacteristic
740C2×C4#6704211yescharacteristic
741C2×C4#6704311yescharacteristic
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—222no—
747C8—222no—
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—441no—
761C22—441no—
762C22—441no—
763C22—441no—
764C22—441no—
765C22—441no—
766C22—441no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22—441no—
771C22C2×C22⋊C4×D1111yescharacteristic
772C22#1062305311yescharacteristic
773C22#1062305411yescharacteristic
774C22C2×#6695411yescharacteristic
775C22#1062327611yescharacteristic
776C22#1062327611yescharacteristic
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#1062318511yescharacteristic
790C4#1062318511yescharacteristic
791C4#1062318611yescharacteristic
792C4#1062318611yescharacteristic
793C2—42no—
794C2—442no—
795C2—881no—
796C2#1307144011yescharacteristic
797C2#1307705911yescharacteristic
798C2#1307706211yescharacteristic
799C2#1307759611yescharacteristic
800C2#1307761411yescharacteristic
801C2#1307776711yescharacteristic
802C2#1307778811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1817C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1817D11
hypocenterC11#22472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#10622342C2semidirect
3. C2×#10622341C2semidirect
4. #13069554C2semidirect
5. #13069550C2semidirect
6. #13068912C2semidirect
7. #13068911C2semidirect
8. #13068911C2semidirect
9. #13068907C2semidirect
10. #13068686C2semidirect
11. #13068599C2semidirect
12. #13068381C2semidirect
13. #13068311C2semidirect
14. #13068310C2semidirect
15. C11×#1817C2semidirect
272. #1817D11semidirect
662. C11#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C2×#106223422
C2×#106223412
#130695542
#130695502
#130689122
#130689112
#130689072
#130686862
#130685992
#130683812
#130683112
#130683102
C11×#18172
#2247211