Finite Group Databasebeta

← #14769859

Subgroups — #14769859

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×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622740C211yesmaximal, characteristic, complemented
4#13069554C211yesmaximal, characteristic, complemented
5#13069550C211yesmaximal, characteristic, complemented
6#13068913C211yesmaximal, characteristic, complemented
7#13068913C211yesmaximal, characteristic, complemented
8#13068912C211yesmaximal, 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
15C11×#1728C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
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#10622741—24no—
40#10622740—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
72C2×C11×M16—22no—
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C2×C11×M16—41no—
77C2×C11×M16—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#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—
204C11×M16—44no—
205C11×M16—44no—
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—
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×#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#1817—111no—
273#1798—111no—
274#1750—111no—
275#1729—111no—
276#1728D1111yescharacteristic, 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×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—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
366C22×M16C2×D1111yescharacteristic
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⋊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—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—22no—
464C2×M16—22no—
465C2×M16—22no—
466C2×M16—22no—
467C2×M16—41no—
468C2×M16—41no—
469C2×M16—222no—
470C2×M16—222no—
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—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—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—44no—
605M16—44no—
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—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#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#6696012yes—
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—441no—
761C22—441no—
762C22—441no—
763C22—441no—
764C22—441no—
765C22—441no—
766C22—441no—
767C22—441no—
768C22—441no—
769C22—441no—
770C22—441no—
771C22C4×#433911yescharacteristic
772C22C2×C22⋊C4×D1111yescharacteristic
773C22#1062303511yescharacteristic
774C22C2×#6696011yescharacteristic
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#1062302111yescharacteristic
790C4#1062302111yescharacteristic
791C4#1062303811yescharacteristic
792C4#1062303811yescharacteristic
793C2—42no—
794C2—442no—
795C2—881no—
796C2#1307144311yescharacteristic
797C2#1307705911yescharacteristic
798C2#1307706611yescharacteristic
799C2#1307760111yescharacteristic
800C2#1307762011yescharacteristic
801C2#1307776111yescharacteristic
802C2#1307778311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1728C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1728D11
hypocenterC11#22472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1728

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×#10622740C2semidirect
4. #13069554C2semidirect
5. #13069550C2semidirect
6. #13068913C2semidirect
7. #13068913C2semidirect
8. #13068912C2semidirect
9. #13068907C2semidirect
10. #13068686C2semidirect
11. #13068684C2semidirect
12. #13068599C2semidirect
13. #13068381C2semidirect
14. #13068311C2semidirect
15. C11×#1728C2semidirect
276. #1728D11semidirect
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×#106227412
C2×#106227402
#130695542
#130695502
#130689132
#130689122
#130689072
#130686862
#130686842
#130685992
#130683812
#130683112
C11×#17282
#2247211