Finite Group Databasebeta

← #14916809

Subgroups — #14916809

Order 2816.

2318 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2#13071805C214yesmaximal, complemented
3#13071630C212yesmaximal
4#13071619C212yesmaximal, complemented
5#13071571C211yesmaximal, characteristic, complemented
6#13071563C211yesmaximal, characteristic, complemented
7#13071547C212yesmaximal, complemented
8C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
9C4⋊C4×D44C211yesmaximal, characteristic, complemented
10#13071512C212yesmaximal, complemented
11#13071357C212yesmaximal, complemented
12#13071327C212yesmaximal, complemented
13#13071282C214yesmaximal, complemented
14#13071241C212yesmaximal, complemented
15#13071226C212yesmaximal, complemented
16C2×#10622548C211yesmaximal, characteristic, complemented
17C11×#2283C211yesmaximal, characteristic, complemented
18C22×C42×C11C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66982C2212yes—
21C2×C4×C22⋊D11C2212yes—
22C22×C4⋊Dic11C2212yes—
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2212yes—
25C2×#66977C2211yescharacteristic
26C2×#66945C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×(C22⋊D11)⋊C4C2214yes—
29#10623010C4116yescomplemented
30C2×#66929C2212yes—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2212yes—
33C2×C4×D44C2211yescharacteristic
34C2×#66925C2212yes—
35C2×#66923C2211yescharacteristic
36C2×C4×Dic22C2212yes—
37C2×C4×Dic22C2211yescharacteristic
38C11×#383C2212yes—
39C11×#382C2211yescharacteristic
40C11×#382C2211yescharacteristic
41C11×#381C2212yes—
42C11×#380C2211yescharacteristic
43C11×#380C2211yescharacteristic
44C4×C11×C4⋊C4C2211yescharacteristic
45C4×C11×C4⋊C4C2211yescharacteristic
46C4×C11×C22⋊C4C2212yes—
47C11×#376C2212yes—
48#10622600C2212yes—
49#10622600C2212yes—
50#10622590C2212yes—
51#10622589C2212yes—
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2212yes—
54#10622571C2214yes—
55#10622559C2214yes—
56C22⋊C4×Dic11C2214yes—
57#10622552C2212yes—
58#10622548C2212yes—
59#10622548C2211yescharacteristic
60#10622548C2211yescharacteristic
61#10622548C2212yes—
62#10622548C2212yes—
63C4×C4⋊Dic11C2212yes—
64C4×C4⋊Dic11C2212yes—
65#10622542C2212yes—
66#10622541C2212yes—
67#10622541C2212yes—
68#10622283C2214yes—
69#10622283C2214yes—
70#10622283C2214yes—
71#10622283C2214yes—
72#10622281C2214yes—
73#10622281C2214yes—
74#10622281C2214yes—
75#10622281C2214yes—
76#10622268C2214yes—
77#10622268C2214yes—
78#10622268C2214yes—
79#10622268C2214yes—
80#10622260C2214yes—
81#10622260C2214yes—
82#10622260C2214yes—
83#10622260C2214yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11C2312yes—
88C23×Dic11C2314yes—
89C22×D44C2311yescharacteristic
90C22×C4×D11C2312yes—
91C22×C4×D11C2314yes—
92C22×Dic22C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4C2312yes—
98C2×C11×C22⋊C4C2312yes—
99C2×C42×C11C2×C418yescomplemented
100C2×C42×C11C2312yes—
101C2×C42×C11C2312yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11C2312yes—
107#66983C2×C418yes—
108#66982C2×C4116yescomplemented
109C4×C22⋊D11C2×C4116yescomplemented
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×C4⋊Dic11—44no—
118C2×C4⋊Dic11—44no—
119C2×C4⋊Dic11—44no—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2312yes—
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2314yes—
126C2×C4⋊Dic11C2314yes—
127C2×C4⋊Dic11C2314yes—
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131#66977C2×C418yescomplemented
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2312yes—
143#66945—44no—
144C4⋊C4×D11—44no—
145(C22⋊D11)⋊C4—48no—
146#66929C2×C4116yescomplemented
147#66928C2×C418yescomplemented
148C4×D44—44no—
149C4×D44C2×C418yescomplemented
150#66925C2×C4116yescomplemented
151#66923C2×C418yescomplemented
152C4×Dic22—44no—
153C4×Dic22C2×C418yescomplemented
154C11×#95C2312yes—
155C11×#95C2312yes—
156C11×#95C2312yes—
157C11×#95C2312yes—
158C11×#95C2312yes—
159C11×#95C2312yes—
160C11×#95C2312yes—
161C11×#95C2312yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168#34384—111nomaximal, Sylow
169C24×C11C2411yescharacteristic
170C23×D11C2412yes—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11C22×C414yes—
178C22×C4×C11C22×C414yes—
179C22×C4×C11C22×C414yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—24no—
191C2×C22⋊D11—24no—
192C2×C22⋊D11C22×C418yes—
193C22×Dic11—28no—
194C22×Dic11—44no—
195C22×Dic11—44no—
196C22×Dic11C2414yes—
197C22×Dic11C2414yes—
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C2×D44—22no—
202C2×D44—22no—
203C2×D44C22×C414yes—
204C2×C4×D11—24no—
205C2×C4×D11—24no—
206C2×C4×D11—44no—
207C2×C4×D11—44no—
208C2×C4×D11—44no—
209C2×C4×D11C22×C418yes—
210C2×Dic22—22no—
211C2×Dic22—22no—
212C2×Dic22C22×C414yes—
213C11×C4⋊C4—22no—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—24no—
219C42×C11—24no—
220C42×C11—24no—
221C42×C11C22×C414yes—
222C42×C11C22×C414yes—
223C42×C11C22×C414yes—
224C42×C11C22×C414yes—
225C22⋊Dic11C22×C418yes—
226(C2×D11)⋊C4—44no—
227(C2×D11)⋊C4—44no—
228(C2×D11)⋊C4—44no—
229(C2×D11)⋊C4C22×C418yes—
230(C2×D11)⋊C4C22×C418yes—
231(C2×D11)⋊C4C22×C418yes—
232(C2×D11)⋊C4C22×C418yes—
233C4⋊Dic11—24no—
234C4⋊Dic11—24no—
235C4⋊Dic11—24no—
236C4⋊Dic11—24no—
237C4⋊Dic11—44no—
238C4⋊Dic11—44no—
239C4⋊Dic11—42no—
240C4⋊Dic11—44no—
241C4⋊Dic11—42no—
242C4⋊Dic11C22×C414yes—
243C4⋊Dic11C22×C414yes—
244Dic11⋊C4—44no—
245Dic11⋊C4—44no—
246Dic11⋊C4—44no—
247Dic11⋊C4C22×C418yes—
248Dic11⋊C4C22×C418yes—
249Dic11⋊C4C22×C418yes—
250Dic11⋊C4C22×C418yes—
251C4×Dic11—44no—
252C4×Dic11—44no—
253C4×Dic11—44no—
254C4×Dic11C22×C418yes—
255C2×#529—111no—
256#2383—114no—
257#2361—112no—
258#2360—112no—
259#2355—111no—
260#2354—111no—
261#2352—112no—
262Q8×C4⋊C4—111no—
263D4×C4⋊C4—112no—
264D4×C4⋊C4—111no—
265#2330—112no—
266#2326—112no—
267#2322—114no—
268#2317—112no—
269#2314—112no—
270C2×#384—111no—
271#2283D1111yescharacteristic, complemented
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11C23×C412yes—
277C23×C11H(5,𝔽2)12yes—
278C23×C112−1+412yes—
279C23×C11C2511yescharacteristic
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11C23×C414yes—
287C2×C4×C11—28no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—28no—
297C2×C4×C11—28no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C23×C412yes—
312C2×C4×C11C23×C412yes—
313C2×C4×C11C23×C412yes—
314C2×C4×C11C23×C412yes—
315C2×C4×C11C23×C412yes—
316C2×C4×C11H(5,𝔽2)12yes—
317C2×C4×C11H(5,𝔽2)12yes—
318C2×C4×C112−1+412yes—
319C2×C4×C112−1+412yes—
320C22⋊D11—216no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—88no—
334C2×Dic11C23×C414yes—
335C2×Dic11C23×C414yes—
336C2×Dic11C23×C414yes—
337D44—28no—
338C4×D11—216no—
339C4×D11—88no—
340Dic22—28no—
341#529—1116no—
342C2×#126—112no—
343C2×#125—111no—
344C2×#124—111no—
345C2×#123—112no—
346C2×C22⋊Q8—111no—
347C2×#121—111no—
348C2×C4×Q8—111no—
349C2×C4×Q8—112no—
350C2×C4×D4—112no—
351C2×C4×D4—114no—
352C2×C4×D4—111no—
353C2×C4×D4—112no—
354C2×#117—112no—
355C2×#117—112no—
356C22×C4⋊C4—112no—
357C22×C4⋊C4—112no—
358C22×C4⋊C4—112no—
359C22×C4⋊C4—112no—
360C22×C42C2×D1111yescharacteristic
361#391—112no—
362#390—112no—
363#389—112no—
364#389—112no—
365#389—114no—
366#389—114no—
367#389—114no—
368#389—114no—
369#388—114no—
370#388—114no—
371#388—114no—
372#388—114no—
373#387—114no—
374#387—114no—
375#387—114no—
376#387—114no—
377#386—114no—
378#385—114no—
379#385—114no—
380#385—114no—
381#385—114no—
382#385—114no—
383#384—112no—
384#384—112no—
385#384—112no—
386#384—111no—
387#384—111no—
388#384—112no—
389#383C2×D1112yes—
390#382—112no—
391#382C2×D1111yescharacteristic
392#382C2×D1111yescharacteristic
393#381C2×D1112yes—
394#380—112no—
395#380—112no—
396#380C2×D1111yescharacteristic
397#380C2×D1111yescharacteristic
398C4×C4⋊C4—112no—
399C4×C4⋊C4—112no—
400C4×C4⋊C4—112no—
401C4×C4⋊C4—112no—
402C4×C4⋊C4C2×D1111yescharacteristic
403C4×C4⋊C4C2×D1111yescharacteristic
404C4×C22⋊C4—114no—
405C4×C22⋊C4C2×D1112yes—
406#376C2×D1112yes—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11#52014yes—
414C22×C11C24×C411yescharacteristic
415C22×C11C2×H(5,𝔽2)11yescharacteristic
416C22×C11C2×H(5,𝔽2)11yescharacteristic
417C22×C11C2×H(5,𝔽2)11yescharacteristic
418C22×C11C2×2−1+411yescharacteristic
419C22×C11C2×2−1+411yescharacteristic
420C22×C11C2×2−1+411yescharacteristic
421C2×D11—24no—
422C2×D11—24no—
423C2×D11—24no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11#52014yes—
437C4×C11#52014yes—
438Dic11—24no—
439Dic11—24no—
440Dic11—24no—
441Dic11—44no—
442Dic11—44no—
443C22×Q8—111no—
444C22×D4—112no—
445C22×D4—111no—
446C23×C4—112no—
447C23×C4—114no—
448C23×C4—114no—
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1111yescharacteristic
452#126—1116no—
453#125—118no—
454#124—118no—
455#123—1116no—
456C22⋊Q8—118no—
457#121—118no—
458C4×Q8—118no—
459C4×Q8—444no—
460C4×D4—1116no—
461C4×D4—118no—
462C4×D4—444no—
463C4×D4—448no—
464#117—1116no—
465#117—444no—
466C2×C4⋊C4—112no—
467C2×C4⋊C4—112no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—112no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—112no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—112no—
474C2×C4⋊C4—112no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—114no—
479C2×C4⋊C4—114no—
480C2×C4⋊C4—112no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—444no—
485C2×C4⋊C4—444no—
486C2×C4⋊C4—444no—
487C2×C4⋊C4—444no—
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C4⋊C4C22×D1111yescharacteristic
492C2×C22⋊C4—112no—
493C2×C22⋊C4—112no—
494C2×C22⋊C4—112no—
495C2×C22⋊C4—112no—
496C2×C22⋊C4—112no—
497C2×C22⋊C4—114no—
498C2×C22⋊C4—114no—
499C2×C22⋊C4—114no—
500C2×C22⋊C4C22×D1112yes—
501C2×C22⋊C4C22×D1112yes—
502C2×C42—112no—
503C2×C42—114no—
504C2×C42—114no—
505C2×C42—114no—
506C2×C42C4×D1118yescomplemented
507C2×C42C22×D1112yes—
508C2×C42C22×D1112yes—
509C2×C42C22×D1111yescharacteristic
510C2×C42C22×D1111yescharacteristic
511C2×C42C22×D1111yescharacteristic
512C2×C42C22×D1111yescharacteristic
513#95—114no—
514#95—114no—
515#95—114no—
516#95—114no—
517#95—114no—
518#95—114no—
519#95C22×D1112yes—
520#95C22×D1112yes—
521#95C22×D1112yes—
522#95C22×D1112yes—
523#95C22×D1112yes—
524#95C22×D1112yes—
525#95C22×D1112yes—
526#95C22×D1112yes—
527C2×C11—24no—
528C2×C11C2×#52011yescharacteristic
529C2×C11C2×#52011yescharacteristic
530C2×C11C2×#52011yescharacteristic
531C2×C11#354311yescharacteristic
532C2×C11#354411yescharacteristic
533C2×C11#355211yescharacteristic
534C2×C11#355211yescharacteristic
535D11—44no—
536C24—112no—
537C24C23×D1111yescharacteristic
538C2×Q8—114no—
539C2×Q8—222no—
540C2×Q8—222no—
541C2×D4—118no—
542C2×D4—114no—
543C2×D4—224no—
544C2×D4—224no—
545C2×D4—222no—
546C2×D4—222no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—118no—
557C22×C4—114no—
558C22×C4—114no—
559C22×C4—224no—
560C22×C4—224no—
561C22×C4—228no—
562C22×C4—444no—
563C22×C4—444no—
564C22×C4—444no—
565C22×C4—444no—
566C22×C4—444no—
567C22×C4C2×C4×D1114yes—
568C22×C4C2×C4×D1114yes—
569C22×C4C2×C4×D1114yes—
570C22×C4C23×D1112yes—
571C22×C4C23×D1112yes—
572C22×C4C23×D1112yes—
573C22×C4C23×D1112yes—
574C22×C4C23×D1111yescharacteristic
575C22×C4C23×D1111yescharacteristic
576C22×C4C23×D1111yescharacteristic
577C22×C4C23×D1111yescharacteristic
578C22×C4C23×D1111yescharacteristic
579C22×C4C23×D1111yescharacteristic
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—118no—
585C4⋊C4—118no—
586C4⋊C4—114no—
587C4⋊C4—118no—
588C4⋊C4—114no—
589C4⋊C4—118no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—224no—
593C4⋊C4—224no—
594C4⋊C4—444no—
595C4⋊C4—444no—
596C4⋊C4—444no—
597C4⋊C4—442no—
598C4⋊C4—444no—
599C4⋊C4—442no—
600C4⋊C4—444no—
601C4⋊C4—444no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—118no—
605C22⋊C4—118no—
606C22⋊C4—118no—
607C22⋊C4—118no—
608C22⋊C4—118no—
609C22⋊C4—444no—
610C22⋊C4—444no—
611C22⋊C4—444no—
612C42—24no—
613C42—24no—
614C42—118no—
615C42—444no—
616C42—444no—
617C42—444no—
618C42C2×C4×D1114yes—
619C42C2×C4×D1114yes—
620C42C2×C4×D1114yes—
621C42C2×C4×D1114yes—
622C11#3438411yescharacteristic, complemented, Sylow
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—114no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23C22×C4×D1112yes—
635C23#6704212yes—
636C23#6704312yes—
637C23C24×D1111yescharacteristic
638Q8—228no—
639D4—2216no—
640D4—228no—
641C2×C4—28no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—28no—
651C2×C4—28no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—114no—
665C2×C4—114no—
666C2×C4—114no—
667C2×C4—222no—
668C2×C4—222no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—2216no—
674C2×C4—224no—
675C2×C4—224no—
676C2×C4—224no—
677C2×C4—224no—
678C2×C4—224no—
679C2×C4—224no—
680C2×C4—888no—
681C2×C4—888no—
682C2×C4C22×C4×D1112yes—
683C2×C4C22×C4×D1112yes—
684C2×C4C22×C4×D1112yes—
685C2×C4C22×C4×D1112yes—
686C2×C4C22×C4×D1112yes—
687C2×C4C22×C4×D1112yes—
688C2×C4#6704212yes—
689C2×C4#6704212yes—
690C2×C4#6704312yes—
691C2×C4#6704312yes—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—224no—
699C22—224no—
700C22—224no—
701C22—442no—
702C22—442no—
703C22—442no—
704C22—442no—
705C22#1062305414yes—
706C22C23×C4×D1111yescharacteristic
707C22C2×#6704211yescharacteristic
708C22C2×#6704211yescharacteristic
709C22C2×#6704211yescharacteristic
710C22C2×#6704311yescharacteristic
711C22C2×#6704311yescharacteristic
712C22C2×#6704311yescharacteristic
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—224no—
722C4—224no—
723C4—224no—
724C4—444no—
725C4—444no—
726C4#1062305414yes—
727C4#1062305414yes—
728C2—24no—
729C2—444no—
730C2C2×#1062305411yescharacteristic
731C2C2×#1062305411yescharacteristic
732C2C2×#1062305411yescharacteristic
733C2#1308294611yescharacteristic
734C2#1308295611yescharacteristic
735C2#1308305311yescharacteristic
736C2#1308306111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2283C2
socle, cosocleC23×C11C25
prime radicalC2×#66983C22
hypercenter#2283D11
hypocenterC11#34384
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2283

Complements

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

NH ≅ G/Ntype
2. #13071805C2semidirect
4. #13071619C2semidirect
5. #13071571C2semidirect
6. #13071563C2semidirect
7. #13071547C2semidirect
8. C4⋊C4×Dic22C2semidirect
9. C4⋊C4×D44C2semidirect
10. #13071512C2semidirect
11. #13071357C2semidirect
12. #13071327C2semidirect
13. #13071282C2semidirect
14. #13071241C2semidirect
15. #13071226C2semidirect
16. C2×#10622548C2semidirect
17. C11×#2283C2semidirect
29. #10623010C4semidirect
99. C2×C42×C11C2×C4semidirect
108. #66982C2×C4semidirect
109. C4×C22⋊D11C2×C4semidirect
131. #66977C2×C4semidirect
146. #66929C2×C4semidirect
147. #66928C2×C4semidirect
149. C4×D44C2×C4semidirect
150. #66925C2×C4semidirect
151. #66923C2×C4semidirect
153. C4×Dic22C2×C4semidirect
271. #2283D11semidirect
506. C2×C42C4×D11semidirect
622. C11#34384semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
#130718052
#130716302
#130716192
#130715712
#130715632
#130715472
C4⋊C4×Dic222
C4⋊C4×D442
#130715122
#130713572
#130713272
#130712822
#130712412
#130712262
C2×#106225482
C11×#22832
#3438411