Finite Group Databasebeta

← #14914640

Subgroups — #14914640

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2#13071708C212yesmaximal, complemented
3#13071692C212yesmaximal, complemented
4#13071615C214yesmaximal, complemented
5#13071567C211yesmaximal, characteristic, complemented
6#13071542C212yesmaximal, complemented
7Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
8C4⋊C4×D44C211yesmaximal, characteristic, complemented
9C4⋊C4×D44C212yesmaximal, complemented
10#13071394C214yesmaximal, complemented
11#13071226C212yesmaximal, complemented
12#13071154C212yesmaximal, complemented
13C4×#66948C212yesmaximal
14#13071021C211yesmaximal, characteristic, complemented
15#13070970C212yesmaximal, complemented
16C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
17C11×#2355C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×Q8×Dic11C2212yes—
22#10623111C4116yescomplemented
23C2×#66951C2212yes—
24C2×#66948C2211yescharacteristic
25C2×#66947C2212yes—
26C2×#66945C2212yes—
27C2×#66945C2212yes—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2212yes—
31C2×#66943C2211yescharacteristic
32C2×C4×D44C2212yes—
33C2×C4×D44C2214yes—
34C2×C4×D44C2212yes—
35C2×C4×D44C2211yescharacteristic
36C2×#66925C2212yes—
37C2×C42×D11C2212yes—
38C2×C42×D11C2211yescharacteristic
39C11×#391C2212yes—
40C11×#387C2214yes—
41C11×#384C2211yescharacteristic
42C11×#382C2212yes—
43C4×C11×C4⋊C4C2212yes—
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2212yes—
46#10622603C2214yes—
47#10622601C2212yes—
48#10622600C2212yes—
49#10622600C2212yes—
50#10622600C2212yes—
51#10622600C2212yes—
52#10622598C2212yes—
53#10622598C2214yes—
54#10622590C2212yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57C4⋊C4×Dic11C2211yescharacteristic
58C4⋊C4×Dic11C2211yescharacteristic
59C4⋊C4×Dic11C2212yes—
60C4×(C2×D11)⋊C4C2214yes—
61#10622548C2212yes—
62#10622548C2211yescharacteristic
63C4×C4⋊Dic11C2211yescharacteristic
64C4×C4⋊Dic11C2212yes—
65C4×Dic11⋊C4C2212yes—
66C4×Dic11⋊C4C2214yes—
67#10622541C2214yes—
68#10622541C2212yes—
69#10622283C2214yes—
70#10622283C2214yes—
71#10622282C2214yes—
72#10622281C2214yes—
73#10622281C2214yes—
74#10622281C2214yes—
75#10622279C2214yes—
76#10622279C2214yes—
77#10622278C2214yes—
78D11×#95C2212yes—
79#10622268C2214yes—
80#10622268C2214yes—
81#10622267C2214yes—
82#10622262C2212yes—
83#10622262C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D44C2312yes—
86C22×D44C2311yescharacteristic
87C22×C4×D11C2312yes—
88C22×C4×D11C2312yes—
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2312yes—
93C22×C4×D11C2314yes—
94C4×Q8×C11C2×C418yescomplemented
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C42×C11C2312yes—
103C2×C42×C11C2314yes—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2312yes—
106#67000C2×C418yescomplemented
107#66999C2×C418yescomplemented
108Q8×Dic11—44no—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×(C2×D11)⋊C4C2312yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2314yes—
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2314yes—
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×Dic11⋊C4C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2312yes—
131C2×Dic11⋊C4C2312yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2311yescharacteristic
141#66951C2×C4116yescomplemented
142#66948C2×C418yes—
143#66947C2×C4116yescomplemented
144#66945—28no—
145#66945—44no—
146C4⋊C4×D11—24no—
147C4⋊C4×D11—28no—
148C4⋊C4×D11—24no—
149#66943C2×C418yescomplemented
150C4×D44—44no—
151C4×D44—48no—
152C4×D44C2×C4116yescomplemented
153C4×D44C2×C418yescomplemented
154#66925C2×C4116yescomplemented
155C42×D11—44no—
156C42×D11C2×C418yescomplemented
157C11×#95C2312yes—
158C11×#95C2314yes—
159C11×#95C2314yes—
160C11×#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2312yes—
167C11⋊#95C2314yes—
168C11⋊#95C2312yes—
169#34243—111nomaximal, Sylow
170C23×D11C2412yes—
171C23×D11C2411yescharacteristic
172C2×Q8×C11—22no—
173C2×Q8×C11—22no—
174C2×Q8×C11C22×C414yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2414yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×Dic11C2412yes—
184C22×Dic11C2414yes—
185C22×Dic11C2411yescharacteristic
186C22×Dic11C2411yescharacteristic
187C22×Dic11C2412yes—
188C22×Dic11C2411yescharacteristic
189C22×Dic11C2412yes—
190C2×D44—24no—
191C2×D44—24no—
192C2×D44—22no—
193C2×D44—22no—
194C2×D44C22×C418yes—
195C2×D44C22×C414yes—
196C2×C4×D11—24no—
197C2×C4×D11—22no—
198C2×C4×D11—24no—
199C2×C4×D11—22no—
200C2×C4×D11—24no—
201C2×C4×D11—22no—
202C2×C4×D11—24no—
203C2×C4×D11—22no—
204C2×C4×D11—24no—
205C2×C4×D11—24no—
206C2×C4×D11—28no—
207C2×C4×D11—22no—
208C2×C4×D11—22no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×C4×D11—44no—
212C2×C4×D11—44no—
213C2×C4×D11C22×C414yes—
214C2×C4×D11C22×C414yes—
215C2×C4×D11C22×C414yes—
216C2×C4×D11C22×C418yes—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—42no—
221C11×C4⋊C4C22×C414yes—
222C11×C4⋊C4C22×C418yes—
223C11×C4⋊C4#4114yes—
224C42×C11—24no—
225C42×C11—44no—
226C42×C11C22×C414yes—
227C42×C11C22×C418yes—
228(C2×D11)⋊C4—28no—
229(C2×D11)⋊C4—28no—
230(C2×D11)⋊C4—44no—
231(C2×D11)⋊C4—44no—
232(C2×D11)⋊C4C22×C418yes—
233(C2×D11)⋊C4C22×C418yes—
234(C2×D11)⋊C4C22×C418yes—
235(C2×D11)⋊C4C22×C418yes—
236(C2×D11)⋊C4C22×C418yes—
237C4⋊Dic11—22no—
238C4⋊Dic11—24no—
239C4⋊Dic11—24no—
240C4⋊Dic11—44no—
241C4⋊Dic11—42no—
242C4⋊Dic11—44no—
243C4⋊Dic11C22×C418yes—
244C4⋊Dic11C22×C414yes—
245C4⋊Dic11#4114yes—
246Dic11⋊C4—24no—
247Dic11⋊C4—24no—
248Dic11⋊C4—28no—
249Dic11⋊C4C22×C418yes—
250Dic11⋊C4C22×C418yes—
251C4×Dic11—28no—
252C4×Dic11—24no—
253C4×Dic11—42no—
254C4×Dic11—42no—
255C4×Dic11—44no—
256C4×Dic11—44no—
257C4×Dic11C22×C414yes—
258C4×Dic11C22×C414yes—
259C4×Dic11C22×C414yes—
260C2×#529—111no—
261#2370—112no—
262#2367—112no—
263#2359—114no—
264#2355D1111yescharacteristic, complemented
265#2354—111no—
266#2352—112no—
267Q8×C4⋊C4—111no—
268D4×C4⋊C4—112no—
269D4×C4⋊C4—111no—
270#2334—114no—
271#2314—112no—
272C4×C22⋊Q8—112no—
273C4×#121—112no—
274#2285—111no—
275#2274—112no—
276C2×C4×C4⋊C4—111no—
277C23×C11C2511yescharacteristic
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11C23×C414yes—
289C22×D11C23×C412yes—
290C22×D11H(5,𝔽2)12yes—
291C22×D112−1+412yes—
292Q8×C11—28no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—24no—
302C2×C4×C11—22no—
303C2×C4×C11—24no—
304C2×C4×C11—22no—
305C2×C4×C11—24no—
306C2×C4×C11—22no—
307C2×C4×C11C23×C412yes—
308C2×C4×C11C23×C414yes—
309C2×C4×C11C23×C414yes—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C23×C412yes—
312C2×C4×C11C2×#4114yes—
313C2×C4×C11C2×#4112yes—
314C2×C4×C11C2×#4112yes—
315C2×C4×C11H(5,𝔽2)12yes—
316C2×C4×C112−1+412yes—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—22no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—24no—
329C2×Dic11—22no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11C23×C412yes—
334C2×Dic11C23×C412yes—
335C2×Dic11C23×C412yes—
336C2×Dic11C23×C414yes—
337C2×Dic11C2×#4114yes—
338D44—216no—
339D44—28no—
340C4×D11—28no—
341C4×D11—28no—
342C4×D11—216no—
343C4×D11—28no—
344C4×D11—48no—
345C4×D11—48no—
346C4×D11—88no—
347#529—1116no—
348C2×#126—112no—
349C2×#125—111no—
350C2×#124—111no—
351C2×#123—112no—
352C2×C22⋊Q8—111no—
353C2×#121—111no—
354C2×C4×Q8—112no—
355C2×C4×Q8C2×D1111yescharacteristic
356C2×C4×D4—112no—
357C2×C4×D4—111no—
358C2×C4×D4—114no—
359C2×C4×D4—112no—
360C2×#117—112no—
361C2×#117—112no—
362C2×#117—112no—
363C22×C4⋊C4—111no—
364C22×C4⋊C4—112no—
365C22×C4⋊C4—111no—
366C22×C42—111no—
367C22×C42—112no—
368#391C2×D1112yes—
369#390—112no—
370#389—114no—
371#389—112no—
372#389—114no—
373#389—112no—
374#388—114no—
375#388—114no—
376#388—114no—
377#388—114no—
378#387—114no—
379#387—114no—
380#387—114no—
381#387C2×D1114yes—
382#386—114no—
383#385—114no—
384#385—114no—
385#385—114no—
386#384—112no—
387#384—111no—
388#384C2×D1111yescharacteristic
389#382—112no—
390#382C2×D1112yes—
391#380—112no—
392#380—112no—
393#380—112no—
394#380—112no—
395C4×C4⋊C4—111no—
396C4×C4⋊C4—112no—
397C4×C4⋊C4—112no—
398C4×C4⋊C4—112no—
399C4×C4⋊C4—111no—
400C4×C4⋊C4—112no—
401C4×C4⋊C4—111no—
402C4×C4⋊C4—114no—
403C4×C4⋊C4—112no—
404C4×C4⋊C4—112no—
405C4×C4⋊C4—114no—
406C4×C4⋊C4C2×D1111yescharacteristic
407C4×C4⋊C4C2×D1112yes—
408C4×C4⋊C4C2×D1112yes—
409C4×C22⋊C4—114no—
410C4×C22⋊C4—114no—
411C4×C22⋊C4—114no—
412C2×#95—112no—
413C22×C11C24×C411yescharacteristic
414C22×C11C22×#4111yescharacteristic
415C22×C11C22×#4111yescharacteristic
416C22×C11C2×H(5,𝔽2)11yescharacteristic
417C22×C11C2×H(5,𝔽2)11yescharacteristic
418C22×C11C2×2−1+411yescharacteristic
419C22×C11C2×2−1+411yescharacteristic
420C2×D11—22no—
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—22no—
426C2×D11—24no—
427C2×D11—24no—
428C2×D11—24no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11#52014yes—
434C4×C11—24no—
435C4×C11—22no—
436C4×C11—24no—
437C4×C11—24no—
438C4×C11—42no—
439C4×C11—44no—
440C4×C11C4×#4114yes—
441C4×C11#52014yes—
442Dic11—24no—
443Dic11—22no—
444Dic11—22no—
445Dic11—22no—
446Dic11—24no—
447Dic11—42no—
448Dic11—44no—
449C22×Q8C22×D1111yescharacteristic
450C22×D4—112no—
451C22×D4—111no—
452C23×C4—111no—
453C23×C4—112no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—112no—
457C23×C4—112no—
458C23×C4—114no—
459#126—1116no—
460#125—118no—
461#124—118no—
462#123—1116no—
463C22⋊Q8—118no—
464#121—118no—
465C4×Q8—444no—
466C4×Q8C4×D1118yescomplemented
467C4×D4—118no—
468C4×D4—1116no—
469C4×D4—444no—
470C4×D4—448no—
471#117—1116no—
472#117—228no—
473#117—444no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—112no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—112no—
484C2×C4⋊C4—112no—
485C2×C4⋊C4—112no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—224no—
489C2×C4⋊C4—224no—
490C2×C4⋊C4—228no—
491C2×C4⋊C4C22×D1111yescharacteristic
492C2×C4⋊C4C22×D1112yes—
493C2×C4⋊C4C22×D1112yes—
494C2×C4⋊C4C22×D1112yes—
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C4⋊C4C22×D1112yes—
497C2×C4⋊C4C22×D1111yescharacteristic
498C2×C22⋊C4—112no—
499C2×C22⋊C4—112no—
500C2×C22⋊C4—112no—
501C2×C22⋊C4—112no—
502C2×C22⋊C4—112no—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C42—111no—
508C2×C42—111no—
509C2×C42—111no—
510C2×C42—118no—
511C2×C42—114no—
512C2×C42—112no—
513C2×C42—114no—
514C2×C42—114no—
515C2×C42—112no—
516C2×C42—112no—
517C2×C42—444no—
518C2×C42C22×D1112yes—
519C2×C42C22×D1114yes—
520C2×C42C22×D1112yes—
521C2×C42C22×D1111yescharacteristic
522#95—112no—
523#95—112no—
524#95—112no—
525#95—114no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95C22×D1112yes—
531#95C22×D1114yes—
532#95C22×D1114yes—
533#95C22×D1114yes—
534C2×C11C2×C4×#4111yescharacteristic
535C2×C11C2×#52011yescharacteristic
536C2×C11C2×#52011yescharacteristic
537C2×C11#351911yescharacteristic
538C2×C11#352011yescharacteristic
539C2×C11#352211yescharacteristic
540C2×C11#352311yescharacteristic
541D11—24no—
542D11—44no—
543C24—111no—
544C24—112no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8C2×C4×D1114yes—
548C2×D4—118no—
549C2×D4—114no—
550C2×D4—224no—
551C2×D4—224no—
552C2×D4—222no—
553C2×D4—222no—
554C22×C4—111no—
555C22×C4—111no—
556C22×C4—112no—
557C22×C4—111no—
558C22×C4—112no—
559C22×C4—114no—
560C22×C4—114no—
561C22×C4—114no—
562C22×C4—118no—
563C22×C4—112no—
564C22×C4—114no—
565C22×C4—224no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—224no—
569C22×C4—224no—
570C22×C4—222no—
571C22×C4—224no—
572C22×C4—222no—
573C22×C4—224no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—224no—
577C22×C4—228no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—444no—
581C22×C4—444no—
582C22×C4C23×D1112yes—
583C22×C4C23×D1114yes—
584C22×C4C23×D1111yescharacteristic
585C22×C4C23×D1112yes—
586C22×C4C23×D1112yes—
587C22×C4C23×D1112yes—
588C22×C4C23×D1111yescharacteristic
589C22×C4C23×D1111yescharacteristic
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—42no—
594C4⋊C4—118no—
595C4⋊C4—118no—
596C4⋊C4—114no—
597C4⋊C4—118no—
598C4⋊C4—114no—
599C4⋊C4—224no—
600C4⋊C4—224no—
601C4⋊C4—228no—
602C4⋊C4—222no—
603C4⋊C4—224no—
604C4⋊C4—224no—
605C4⋊C4—442no—
606C4⋊C4—444no—
607C4⋊C4—444no—
608C4⋊C4C2×C4×D1114yes—
609C4⋊C4C2×C4×D1118yes—
610C4⋊C4#434314yes—
611C22⋊C4—118no—
612C22⋊C4—118no—
613C22⋊C4—118no—
614C22⋊C4—118no—
615C22⋊C4—118no—
616C22⋊C4—228no—
617C22⋊C4—228no—
618C22⋊C4—444no—
619C22⋊C4—444no—
620C42—24no—
621C42—44no—
622C42—114no—
623C42—114no—
624C42—114no—
625C42—228no—
626C42—224no—
627C42—442no—
628C42—442no—
629C42—444no—
630C42—444no—
631C42C2×C4×D1114yes—
632C42C2×C4×D1118yes—
633C11#3424311yescharacteristic, complemented, Sylow
634C23—112no—
635C23—112no—
636C23—112no—
637C23—114no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—222no—
647C23—222no—
648C23C24×D1111yescharacteristic
649Q8—28no—
650D4—2216no—
651D4—228no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—112no—
667C2×C4—112no—
668C2×C4—112no—
669C2×C4—114no—
670C2×C4—114no—
671C2×C4—228no—
672C2×C4—221no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—221no—
676C2×C4—222no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—222no—
681C2×C4—221no—
682C2×C4—228no—
683C2×C4—228no—
684C2×C4—2216no—
685C2×C4—222no—
686C2×C4—224no—
687C2×C4—222no—
688C2×C4—224no—
689C2×C4—224no—
690C2×C4—222no—
691C2×C4—448no—
692C2×C4—448no—
693C2×C4—888no—
694C2×C4C22×C4×D1112yes—
695C2×C4C22×C4×D1114yes—
696C2×C4C22×C4×D1114yes—
697C2×C4C22×C4×D1112yes—
698C2×C4C22×C4×D1112yes—
699C2×C4C2×#434314yes—
700C2×C4C2×#434312yes—
701C2×C4#41×D1112yes—
702C2×C4#6704212yes—
703C2×C4#6704312yes—
704C22—114no—
705C22—222no—
706C22—222no—
707C22—222no—
708C22—222no—
709C22—222no—
710C22—222no—
711C22—224no—
712C22—224no—
713C22—224no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—442no—
718C22C23×C4×D1111yescharacteristic
719C22C22×#434311yescharacteristic
720C22C2×#41×D1111yescharacteristic
721C22C2×#6704211yescharacteristic
722C22C2×#6704311yescharacteristic
723C22D11×H(5,𝔽2)11yescharacteristic
724C22D11×2−1+411yescharacteristic
725C4—24no—
726C4—22no—
727C4—24no—
728C4—24no—
729C4—42no—
730C4—44no—
731C4—224no—
732C4—222no—
733C4—224no—
734C4—222no—
735C4—222no—
736C4—442no—
737C4—444no—
738C4#1062305414yes—
739C4C4×#434314yes—
740C2—224no—
741C2—444no—
742C2C2×C4×#434311yescharacteristic
743C2D11×#52011yescharacteristic
744C2C2×#1062305411yescharacteristic
745C2#1308264911yescharacteristic
746C2#1308266411yescharacteristic
747C2#1308269811yescharacteristic
748C2#1308271311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2355C2
socle, cosocleC23×C11C25
prime radicalC2×#66948C22
hypercenter#2355D11
hypocenterC11#34243
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. #13071708C2semidirect
3. #13071692C2semidirect
4. #13071615C2semidirect
5. #13071567C2semidirect
6. #13071542C2semidirect
7. Q8×C4⋊Dic11C2semidirect
8. C4⋊C4×D44C2semidirect
9. C4⋊C4×D44C2semidirect
10. #13071394C2semidirect
11. #13071226C2semidirect
12. #13071154C2semidirect
14. #13071021C2semidirect
15. #13070970C2semidirect
16. C4×C4⋊C4×D11C2semidirect
17. C11×#2355C2semidirect
22. #10623111C4semidirect
94. C4×Q8×C11C2×C4semidirect
106. #67000C2×C4semidirect
107. #66999C2×C4semidirect
141. #66951C2×C4semidirect
143. #66947C2×C4semidirect
149. #66943C2×C4semidirect
152. C4×D44C2×C4semidirect
153. C4×D44C2×C4semidirect
154. #66925C2×C4semidirect
156. C42×D11C2×C4semidirect
264. #2355D11semidirect
466. C4×Q8C4×D11semidirect
633. C11#34243semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
#130717082
#130716922
#130716152
#130715672
#130715422
Q8×C4⋊Dic112
C4⋊C4×D442
#130713942
#130712262
#130711542
C4×#669482
#130710212
#130709702
C4×C4⋊C4×D112
C11×#23552
#3424311