Finite Group Databasebeta

← #14914633

Subgroups — #14914633

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×#10623010C211yesmaximal, characteristic
2#13071712C212yesmaximal, complemented
3#13071687C212yesmaximal, complemented
4#13071608C214yesmaximal, complemented
5#13071575C211yesmaximal, characteristic, complemented
6#13071567C211yesmaximal, characteristic, complemented
7#13071547C212yesmaximal, complemented
8#13071528C211yesmaximal, characteristic, complemented
9#13071516C211yesmaximal, characteristic, complemented
10#13071512C212yesmaximal, complemented
11#13071387C214yesmaximal, complemented
12#13071221C212yesmaximal, complemented
13#13071144C212yesmaximal, complemented
14#13071122C212yesmaximal
15#13070970C212yesmaximal, complemented
16C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
17C11×#2285C211yesmaximal, characteristic, complemented
18C2×C11×#117C2212yes—
19C22×C42×C11C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66982C2212yes—
22C2×C4×C22⋊D11C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×C4×Dic11C2212yes—
27C2×#66946C2212yes—
28C2×#66945C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×#66940C2212yes—
31C2×(C22⋊D11)⋊C4C2214yes—
32#10623010C4116yescomplemented
33C2×#66929C2212yes—
34C2×#66928C2211yescharacteristic
35C2×C4×D44C2211yescharacteristic
36C2×#66925C2212yes—
37C2×#66923C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C11×#384C2211yescharacteristic
40C11×#384C2211yescharacteristic
41C11×#382C2212yes—
42C11×#380C2212yes—
43C11×#380C2212yes—
44C4×C11×C4⋊C4C2212yes—
45C4×C11×C4⋊C4C2212yes—
46C2×C11⋊#95C2212yes—
47#10622603C2214yes—
48#10622602C2214yes—
49#10622601C2212yes—
50#10622600C2212yes—
51#10622600C2212yes—
52#10622591C2214yes—
53#10622590C2212yes—
54#10622589C2212yes—
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2212yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2212yes—
59#10622587C2212yes—
60#10622586C2212yes—
61#10622586C2212yes—
62#10622585C2214yes—
63#10622571C2214yes—
64#10622559C2214yes—
65C22⋊C4×Dic11C2214yes—
66#10622553C2214yes—
67C4×(C2×D11)⋊C4C2214yes—
68C4×C4⋊Dic11C2212yes—
69C4×C4⋊Dic11C2212yes—
70C4×C4⋊Dic11C2211yescharacteristic
71C4×C4⋊Dic11C2211yescharacteristic
72C4×C4⋊Dic11C2211yescharacteristic
73C4×C4⋊Dic11C2211yescharacteristic
74#10622546C2214yes—
75C4×Dic11⋊C4C2214yes—
76#10622283C2214yes—
77#10622282C2214yes—
78#10622281C2214yes—
79#10622279C2214yes—
80#10622268C2214yes—
81#10622265C2214yes—
82#10622262C2214yes—
83#10622260C2214yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11C2312yes—
88C23×Dic11C2312yes—
89C23×Dic11C2312yes—
90C22×D44C2311yescharacteristic
91C22×C4×D11C2312yes—
92C22×C4×D11C2314yes—
93C22×Dic22C2311yescharacteristic
94C11×#117—44no—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C42×C11C2×C418yescomplemented
103C2×C42×C11C2314yes—
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11C2312yes—
109#66983C2×C418yes—
110#66982C2×C4116yescomplemented
111C4×C22⋊D11C2×C4116yescomplemented
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2312yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×C4⋊Dic11—24no—
120C2×C4⋊Dic11—24no—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129#66977C2×C418yescomplemented
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×C4×Dic11—44no—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2312yes—
146#66946—44no—
147#66945—28no—
148C4⋊C4×D11—28no—
149#66940—44no—
150(C22⋊D11)⋊C4—48no—
151#66929C2×C4116yescomplemented
152#66928C2×C418yescomplemented
153C4×D44C2×C418yescomplemented
154#66925C2×C4116yescomplemented
155#66923C2×C418yescomplemented
156C4×Dic22C2×C418yescomplemented
157C11×#95C2314yes—
158C11×#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2312yes—
166C11⋊#95C2312yes—
167C11⋊#95C2312yes—
168C11⋊#95C2312yes—
169#34243—111nomaximal, Sylow
170C24×C11C2411yescharacteristic
171C23×D11C2412yes—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11C22×C414yes—
179C22×C4×C11C22×C414yes—
180C22×C4×C11C22×C414yes—
181C22×C4×C11C2414yes—
182C22×C4×C11C2414yes—
183C22×C4×C11C2411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—24no—
190C2×C22⋊D11—24no—
191C2×C22⋊D11C22×C418yes—
192C22×Dic11—24no—
193C22×Dic11—24no—
194C22×Dic11—24no—
195C22×Dic11—24no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2412yes—
202C22×Dic11C2412yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44C22×C414yes—
208C2×C4×D11—28no—
209C2×C4×D11—24no—
210C2×C4×D11—24no—
211C2×C4×D11—44no—
212C2×C4×D11—44no—
213C2×C4×D11C22×C418yes—
214C2×Dic22—22no—
215C2×Dic22—22no—
216C2×Dic22C22×C414yes—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—42no—
222C11×C4⋊C4—42no—
223C11×C22⋊C4—28no—
224C42×C11—44no—
225C42×C11C22×C414yes—
226C42×C11C22×C414yes—
227C42×C11C22×C414yes—
228C42×C11C22×C414yes—
229C22⋊Dic11C22×C418yes—
230(C2×D11)⋊C4—28no—
231(C2×D11)⋊C4—44no—
232(C2×D11)⋊C4—44no—
233(C2×D11)⋊C4C22×C418yes—
234(C2×D11)⋊C4C22×C418yes—
235(C2×D11)⋊C4C22×C418yes—
236(C2×D11)⋊C4C22×C418yes—
237C4⋊Dic11—24no—
238C4⋊Dic11—24no—
239C4⋊Dic11—22no—
240C4⋊Dic11—22no—
241C4⋊Dic11C22×C414yes—
242C4⋊Dic11C22×C414yes—
243C4⋊Dic11#4114yes—
244C4⋊Dic11#4114yes—
245Dic11⋊C4—28no—
246Dic11⋊C4—44no—
247Dic11⋊C4—44no—
248Dic11⋊C4C22×C418yes—
249Dic11⋊C4C22×C418yes—
250Dic11⋊C4C22×C418yes—
251Dic11⋊C4C22×C418yes—
252C4×Dic11—28no—
253C4×Dic11—24no—
254C4×Dic11—24no—
255C4×Dic11—44no—
256C4×Dic11—44no—
257C4×Dic11—42no—
258C4×Dic11—42no—
259C4×Dic11C22×C418yes—
260C2×#529—111no—
261#2370—112no—
262#2367—112no—
263#2359—114no—
264#2355—111no—
265#2354—111no—
266#2352—112no—
267Q8×C4⋊C4—111no—
268D4×C4⋊C4—111no—
269D4×C4⋊C4—112no—
270#2334—114no—
271#2314—112no—
272C4×C22⋊Q8—112no—
273C4×#121—112no—
274#2285D1111yescharacteristic, complemented
275#2274—112no—
276C2×C4×C4⋊C4—111no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11C23×C412yes—
282C23×C11H(5,𝔽2)12yes—
283C23×C112−1+412yes—
284C23×C11C2511yescharacteristic
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—22no—
291C22×D11C23×C414yes—
292C2×C4×C11—28no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—28no—
302C2×C4×C11—28no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11C23×C412yes—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C23×C412yes—
312C2×C4×C11C23×C412yes—
313C2×C4×C11C23×C412yes—
314C2×C4×C11C23×C412yes—
315C2×C4×C11C2×#4112yes—
316C2×C4×C11C2×#4112yes—
317C2×C4×C11H(5,𝔽2)12yes—
318C2×C4×C112−1+412yes—
319C22⋊D11—216no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—48no—
337C2×Dic11—48no—
338C2×Dic11C23×C414yes—
339C2×Dic11C23×C414yes—
340C2×Dic11C23×C414yes—
341C2×Dic11C2×#4114yes—
342C2×Dic11C2×#4114yes—
343D44—28no—
344C4×D11—216no—
345C4×D11—88no—
346Dic22—28no—
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×Q8—111no—
356C2×C4×D4—112no—
357C2×C4×D4—112no—
358C2×C4×D4—114no—
359C2×C4×D4—111no—
360C2×#117—112no—
361C2×#117—112no—
362C2×#117C2×D1112yes—
363C22×C4⋊C4—111no—
364C22×C4⋊C4—111no—
365C22×C4⋊C4—112no—
366C22×C42—112no—
367C22×C42C2×D1111yescharacteristic
368#391—112no—
369#390—112no—
370#389—114no—
371#389—112no—
372#389—112no—
373#389—114no—
374#388—114no—
375#388—114no—
376#388—114no—
377#388—114no—
378#387—114no—
379#387—114no—
380#387—114no—
381#387—114no—
382#386—114no—
383#385—114no—
384#385—114no—
385#385—114no—
386#384—112no—
387#384C2×D1111yescharacteristic
388#384C2×D1111yescharacteristic
389#382—112no—
390#382C2×D1112yes—
391#380—112no—
392#380—112no—
393#380C2×D1112yes—
394#380C2×D1112yes—
395C4×C4⋊C4—112no—
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—111no—
403C4×C4⋊C4—114no—
404C4×C4⋊C4—112no—
405C4×C4⋊C4—111no—
406C4×C4⋊C4—114no—
407C4×C4⋊C4C2×D1112yes—
408C4×C4⋊C4C2×D1112yes—
409C4×C22⋊C4—114no—
410C4×C22⋊C4—114no—
411C4×C22⋊C4—114no—
412C2×#95—112no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11#52014yes—
420C22×C11C24×C411yescharacteristic
421C22×C11C22×#4111yescharacteristic
422C22×C11C22×#4111yescharacteristic
423C22×C11C2×H(5,𝔽2)11yescharacteristic
424C22×C11C2×H(5,𝔽2)11yescharacteristic
425C22×C11C2×2−1+411yescharacteristic
426C22×C11C2×2−1+411yescharacteristic
427C2×D11—24no—
428C2×D11—24no—
429C2×D11—24no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—42no—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11—22no—
437C4×C11—22no—
438C4×C11—44no—
439C4×C11—44no—
440C4×C11C4×#4114yes—
441C4×C11#52014yes—
442Dic11—24no—
443Dic11—24no—
444Dic11—24no—
445Dic11—24no—
446Dic11—24no—
447Dic11—42no—
448Dic11—42no—
449C22×Q8—111no—
450C22×D4—112no—
451C22×D4—111no—
452C23×C4—112no—
453C23×C4—112no—
454C23×C4—112no—
455C23×C4—114no—
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459#126—1116no—
460#125—118no—
461#124—118no—
462#123—1116no—
463C22⋊Q8—118no—
464#121—118no—
465C4×Q8—118no—
466C4×Q8—444no—
467C4×D4—1116no—
468C4×D4—118no—
469C4×D4—444no—
470C4×D4—448no—
471#117—44no—
472#117—1116no—
473#117—228no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—111no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—112no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—112no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—112no—
486C2×C4⋊C4—112no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—228no—
490C2×C4⋊C4—224no—
491C2×C4⋊C4—224no—
492C2×C4⋊C4C22×D1112yes—
493C2×C4⋊C4C22×D1112yes—
494C2×C4⋊C4C22×D1112yes—
495C2×C4⋊C4C22×D1112yes—
496C2×C4⋊C4C22×D1112yes—
497C2×C4⋊C4C22×D1112yes—
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⋊C4C22×D1114yes—
507C2×C42—112no—
508C2×C42—114no—
509C2×C42—112no—
510C2×C42—112no—
511C2×C42—114no—
512C2×C42—114no—
513C2×C42—112no—
514C2×C42—112no—
515C2×C42—444no—
516C2×C42C4×D1118yescomplemented
517C2×C42C22×D1114yes—
518C2×C42C22×D1111yescharacteristic
519C2×C42C22×D1111yescharacteristic
520C2×C42C22×D1111yescharacteristic
521C2×C42C22×D1111yescharacteristic
522#95—112no—
523#95—112no—
524#95—112no—
525#95—112no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95C22×D1114yes—
533#95C22×D1114yes—
534C2×C11—24no—
535C2×C11C2×C4×#4111yescharacteristic
536C2×C11C2×#52011yescharacteristic
537C2×C11C2×#52011yescharacteristic
538C2×C11#351911yescharacteristic
539C2×C11#352011yescharacteristic
540C2×C11#352211yescharacteristic
541C2×C11#352311yescharacteristic
542D11—44no—
543C24—112no—
544C24C23×D1111yescharacteristic
545C2×Q8—114no—
546C2×Q8—222no—
547C2×Q8—222no—
548C2×D4—118no—
549C2×D4—114no—
550C2×D4—224no—
551C2×D4—224no—
552C2×D4—222no—
553C2×D4—222no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—118no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—228no—
569C22×C4—224no—
570C22×C4—224no—
571C22×C4—224no—
572C22×C4—224no—
573C22×C4—224no—
574C22×C4—224no—
575C22×C4—444no—
576C22×C4—444no—
577C22×C4—442no—
578C22×C4—442no—
579C22×C4C2×C4×D1114yes—
580C22×C4C2×C4×D1114yes—
581C22×C4C2×C4×D1114yes—
582C22×C4C23×D1114yes—
583C22×C4C23×D1114yes—
584C22×C4C23×D1111yescharacteristic
585C22×C4C23×D1111yescharacteristic
586C22×C4C23×D1111yescharacteristic
587C22×C4C23×D1111yescharacteristic
588C22×C4C23×D1111yescharacteristic
589C22×C4C23×D1111yescharacteristic
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—118no—
597C4⋊C4—118no—
598C4⋊C4—114no—
599C4⋊C4—118no—
600C4⋊C4—114no—
601C4⋊C4—118no—
602C4⋊C4—114no—
603C4⋊C4—114no—
604C4⋊C4—228no—
605C4⋊C4—224no—
606C4⋊C4—224no—
607C4⋊C4—222no—
608C4⋊C4—222no—
609C4⋊C4—444no—
610C4⋊C4—444no—
611C22⋊C4—28no—
612C22⋊C4—118no—
613C22⋊C4—118no—
614C22⋊C4—118no—
615C22⋊C4—118no—
616C22⋊C4—118no—
617C22⋊C4—228no—
618C22⋊C4—444no—
619C22⋊C4—444no—
620C42—44no—
621C42—118no—
622C42—228no—
623C42—224no—
624C42—224no—
625C42—442no—
626C42—442no—
627C42—444no—
628C42—444no—
629C42C2×C4×D1114yes—
630C42C2×C4×D1114yes—
631C42C2×C4×D1114yes—
632C42C2×C4×D1114yes—
633C11#3424311yescharacteristic, complemented, Sylow
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—114no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23C22×C4×D1112yes—
646C23#6703712yes—
647C23#6704012yes—
648C23C24×D1111yescharacteristic
649Q8—228no—
650D4—2216no—
651D4—228no—
652C2×C4—28no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—28no—
662C2×C4—28no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—114no—
670C2×C4—114no—
671C2×C4—114no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—2216no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—448no—
692C2×C4—448no—
693C2×C4—888no—
694C2×C4C22×C4×D1112yes—
695C2×C4C22×C4×D1112yes—
696C2×C4C22×C4×D1112yes—
697C2×C4C22×C4×D1112yes—
698C2×C4C22×C4×D1112yes—
699C2×C4C22×C4×D1112yes—
700C2×C4#41×D1112yes—
701C2×C4#41×D1112yes—
702C2×C4#6704212yes—
703C2×C4#6704312yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—224no—
711C22—224no—
712C22—224no—
713C22—442no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22#1062303514yes—
718C22C23×C4×D1111yescharacteristic
719C22C2×#6703711yescharacteristic
720C22C2×#6704011yescharacteristic
721C22C2×#41×D1111yescharacteristic
722C22C2×#41×D1111yescharacteristic
723C22C2×#6704211yescharacteristic
724C22C2×#6704311yescharacteristic
725C4—22no—
726C4—22no—
727C4—22no—
728C4—22no—
729C4—44no—
730C4—44no—
731C4—224no—
732C4—224no—
733C4—224no—
734C4—224no—
735C4—224no—
736C4—442no—
737C4—442no—
738C4#1062305314yes—
739C4#1062305414yes—
740C2—24no—
741C2—444no—
742C2C2×#1062305311yescharacteristic
743C2C2×#1062305411yescharacteristic
744C2C2×#1062303511yescharacteristic
745C2#1308264311yescharacteristic
746C2#1308266011yescharacteristic
747C2#1308269311yescharacteristic
748C2#1308270411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2285C2
socle, cosocleC23×C11C25
prime radicalC2×#66983C22
hypercenter#2285D11
hypocenterC11#34243
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13071712C2semidirect
3. #13071687C2semidirect
4. #13071608C2semidirect
5. #13071575C2semidirect
6. #13071567C2semidirect
7. #13071547C2semidirect
8. #13071528C2semidirect
9. #13071516C2semidirect
10. #13071512C2semidirect
11. #13071387C2semidirect
12. #13071221C2semidirect
13. #13071144C2semidirect
15. #13070970C2semidirect
16. C2×C4×C4⋊Dic11C2semidirect
17. C11×#2285C2semidirect
32. #10623010C4semidirect
102. C2×C42×C11C2×C4semidirect
110. #66982C2×C4semidirect
111. C4×C22⋊D11C2×C4semidirect
129. #66977C2×C4semidirect
151. #66929C2×C4semidirect
152. #66928C2×C4semidirect
153. C4×D44C2×C4semidirect
154. #66925C2×C4semidirect
155. #66923C2×C4semidirect
156. C4×Dic22C2×C4semidirect
274. #2285D11semidirect
516. C2×C42C4×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×#106230102
#130717122
#130716872
#130716082
#130715752
#130715672
#130715472
#130715282
#130715162
#130715122
#130713872
#130712212
#130711442
#130711222
#130709702
C2×C4×C4⋊Dic112
C11×#22852
#3424311