Finite Group Databasebeta

← C2×#13071205 #14912337

Subgroups — C2×#13071205 #14912337

Order 2816.

5822 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic, complemented
3C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13071205C2116yesmaximal, direct product factor
5C2×#10622259C212yesmaximal, complemented
6C2×#10622570C212yesmaximal, complemented
7C2×#10622278C212yesmaximal, complemented
8C2×#10622569C212yesmaximal, complemented
9C2×#10622825C211yesmaximal, characteristic, complemented
10C2×#10622600C211yesmaximal, characteristic, complemented
11C2×#10622600C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C22×#4339—28no—
17C22×#4339—28no—
18C22×#4339C4116yescomplemented
19C22×#4339C2218yes—
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2212yes—
23C23×C4×D11C2211yescharacteristic
24C23×Dic22C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2212yes—
28C22×C22⋊Dic11C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2212yes—
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2212yes—
35C22×C4×Dic11C2212yes—
36C2×#66945—28no—
37C2×#66945C2218yescomplemented
38C2×C4⋊C4×D11—28no—
39C2×C4⋊C4×D11C2218yescomplemented
40C11×#380C2218yescomplemented
41C2×C11×#95C2212yes—
42#10622825C2218yescomplemented
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45C2×C11⋊#95C2212yes—
46#10622600C2218yescomplemented
47#10622600C2218yescomplemented
48#10622570C22116yescomplemented
49#10622569C22116yescomplemented
50#10622278C22116yescomplemented
51#10622259C22116yescomplemented
52C25×C11C2311yescharacteristic
53C24×D11C2311yescharacteristic
54C24×D11C2311yescharacteristic
55C23×C4×C11—24no—
56C23×C4×C11—24no—
57C23×C4×C11C2×C418yescomplemented
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2314yes—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—24no—
64C22×C22⋊D11—24no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—24no—
67C22×C22⋊D11C2×C418yes—
68C22×C22⋊D11C2×C418yescomplemented
69C22×C22⋊D11C2314yes—
70C22×C22⋊D11C2314yes—
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C2×#4339—2128no—
76C2×#4339—232no—
77C2×#4339—232no—
78C2×#4339C2×C4164yescomplemented
79C22×D44—24no—
80C22×D44—24no—
81C22×D44C2×C418yes—
82C22×D44C2314yes—
83C22×C4×D11—24no—
84C22×C4×D11—24no—
85C22×C4×D11—28no—
86C22×C4×D11—44no—
87C22×C4×D11—44no—
88C22×C4×D11C2×C418yes—
89C22×C4×D11C2×C418yescomplemented
90C22×C4×D11D418yes—
91C22×C4×D11D418yes—
92C22×C4×D11C2314yes—
93C22×C4×D11C2318yes—
94C22×C4×D11C2314yes—
95C22×Dic22—24no—
96C22×Dic22—24no—
97C22×Dic22C2×C418yescomplemented
98C22×Dic22C2314yes—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4—24no—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C22⋊C4—44no—
104C2×C11×C22⋊C4C2318yes—
105C2×C22⋊Dic11—44no—
106C2×C22⋊Dic11C2318yes—
107C2×(C2×D11)⋊C4—28no—
108C2×(C2×D11)⋊C4—44no—
109C2×(C2×D11)⋊C4—44no—
110C2×(C2×D11)⋊C4C2318yes—
111C2×(C2×D11)⋊C4C2318yes—
112C2×(C2×D11)⋊C4C2318yes—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11—24no—
115C2×C4⋊Dic11C2314yes—
116C2×C4⋊Dic11C2314yes—
117C2×Dic11⋊C4—28no—
118C2×Dic11⋊C4C2318yes—
119C2×C4×Dic11—28no—
120C2×C4×Dic11C2318yes—
121#66945—232no—
122C4⋊C4×D11—232no—
123C11×#95C2318yes—
124C11⋊#95C2318yes—
125C11⋊#95C2318yes—
126C11⋊#95C2318yes—
127C2×#2311—111nomaximal, Sylow
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11C22×C414yes—
135C24×C11C2412yes—
136C24×C11C2411yescharacteristic
137C23×D11—22no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11C22×C414yes—
148C23×D11C22×C414yes—
149C23×D11C2×D414yes—
150C23×D11C2×D414yes—
151C23×D11C2412yes—
152C23×D11C2412yes—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—232no—
156C22×C4×C11—28no—
157C22×C4×C11—28no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11C22×C414yes—
165C22×C4×C11C22×C414yes—
166C22×C4×C11C22×C4116yescomplemented
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2414yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2412yes—
173C2×C22⋊D11—232no—
174C2×C22⋊D11—28no—
175C2×C22⋊D11—28no—
176C2×C22⋊D11—232no—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—28no—
179C2×C22⋊D11C22×C4116yes—
180C2×C22⋊D11C22×C4116yescomplemented
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—24no—
184C22×Dic11—24no—
185C22×Dic11—24no—
186C22×Dic11—24no—
187C22×Dic11—24no—
188C22×Dic11—24no—
189C22×Dic11C22×C414yes—
190C22×Dic11C22×C414yes—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D414yes—
193C22×Dic11C2414yes—
194C22×Dic11C2414yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197#4339—2256no—
198C2×D44—232no—
199C2×D44—28no—
200C2×D44—28no—
201C2×D44C22×C4116yes—
202C2×C4×D11—216no—
203C2×C4×D11—232no—
204C2×C4×D11—28no—
205C2×C4×D11—28no—
206C2×C4×D11—48no—
207C2×C4×D11—48no—
208C2×C4×D11—432no—
209C2×C4×D11C22⋊C4164yescomplemented
210C2×C4×D11C22×C4116yes—
211C2×C4×D11C22×C4116yescomplemented
212C2×C4×D11C2×D4116yes—
213C2×C4×D11C2×D4116yes—
214C2×Dic22—232no—
215C2×Dic22—28no—
216C2×Dic22—28no—
217C2×Dic22C22×C4116yescomplemented
218C11×C4⋊C4—28no—
219C11×C4⋊C4—28no—
220C11×C22⋊C4—48no—
221C22⋊Dic11—48no—
222(C2×D11)⋊C4—216no—
223(C2×D11)⋊C4—48no—
224(C2×D11)⋊C4—48no—
225C4⋊Dic11—28no—
226C4⋊Dic11—28no—
227Dic11⋊C4—216no—
228C4×Dic11—216no—
229C23×#41—111no—
230C22×#117—111no—
231C23×C4⋊C4—111no—
232#2311—1116no—
233C2×#391—112no—
234C2×#390—112no—
235C2×#386—112no—
236C2×#386—112no—
237C2×#380—111no—
238C2×#380—111no—
239C2×#380—111no—
240C2×#380D1111yescharacteristic, complemented
241C23×C11—28no—
242C23×C11—28no—
243C23×C11—28no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—44no—
251C23×C11—44no—
252C23×C11—44no—
253C23×C11—44no—
254C23×C11C23×C414yes—
255C23×C11C23×C412yes—
256C23×C11C22×D412yes—
257C23×C11C22×D412yes—
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)12yes—
260C23×C112−1+412yes—
261C23×C112−1+412yes—
262C23×C11C2511yescharacteristic
263C22×D11—28no—
264C22×D11—28no—
265C22×D11—28no—
266C22×D11—28no—
267C22×D11—28no—
268C22×D11—28no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—28no—
274C22×D11—28no—
275C22×D11—28no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—44no—
283C22×D11—44no—
284C22×D11—44no—
285C22×D11—44no—
286C22×D11C2×C22⋊C4116yes—
287C22×D11C23×C414yes—
288C22×D11C23×C414yes—
289C22×D11C22×D414yes—
290C22×D11C22×D414yes—
291C2×C4×C11—28no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—232no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—48no—
302C2×C4×C11—48no—
303C2×C4×C11C2×C22⋊C4116yes—
304C2×C4×C11C23×C414yes—
305C2×C4×C11C23×C414yes—
306C2×C4×C11C22×D414yes—
307C2×C4×C11C22×D414yes—
308C22⋊D11—232no—
309C22⋊D11—232no—
310C2×Dic11—28no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—48no—
320C2×Dic11—48no—
321C2×Dic11C2×C22⋊C4116yes—
322C2×Dic11C23×C414yes—
323C2×Dic11C23×C414yes—
324C2×Dic11C22×D414yes—
325C2×Dic11C22×D414yes—
326D44—232no—
327C4×D11—232no—
328C4×D11—432no—
329C4×D11C2×C22⋊C4164yescomplemented
330Dic22—232no—
331C22×#41—118no—
332C22×#41—1116no—
333C22×#41—228no—
334C22×#41—228no—
335C23×Q8—111no—
336C23×D4—111no—
337C23×D4—111no—
338C23×D4—111no—
339C24×C4—111no—
340C24×C4—111no—
341C24×C4—112no—
342C24×C4C2×D1111yescharacteristic
343C2×#117—118no—
344C2×#117—228no—
345C22×C4⋊C4—112no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—118no—
349C22×C4⋊C4—228no—
350C22×C4⋊C4C2×D1111yescharacteristic
351C22×C4⋊C4C2×D1111yescharacteristic
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4C2×D1112yes—
357C22×C42—112no—
358#391—1116no—
359#390—1116no—
360#386—1116no—
361#386—1116no—
362#380—118no—
363#380—118no—
364#380—118no—
365#380C2×D1118yescomplemented
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95C2×D1112yes—
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—416no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11C22×C22⋊C414yes—
379C22×C11#52014yes—
380C22×C11#52014yes—
381C22×C11#53514yes—
382C22×C11#53614yes—
383C22×C11#53714yes—
384C22×C11#53714yes—
385C22×C11C24×C411yescharacteristic
386C22×C11C23×D411yescharacteristic
387C22×C11C23×D411yescharacteristic
388C22×C11C2×H(5,𝔽2)11yescharacteristic
389C22×C11C2×H(5,𝔽2)11yescharacteristic
390C22×C11C2×2−1+411yescharacteristic
391C22×C11C2×2−1+411yescharacteristic
392C2×D11—232no—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—24no—
397C2×D11—24no—
398C2×D11—24no—
399C2×D11—24no—
400C2×D11—24no—
401C2×D11—24no—
402C2×D11—416no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11C22×C22⋊C418yes—
408C4×C11—24no—
409C4×C11—44no—
410C4×C11—44no—
411C4×C11C22×C22⋊C418yes—
412Dic11—24no—
413Dic11—44no—
414Dic11—44no—
415Dic11C22×C22⋊C418yes—
416C25—111no—
417C25—111no—
418C25C22×D1111yescharacteristic
419C2×#41—1164no—
420C2×#41—22128no—
421C2×#41—2232no—
422C2×#41—2232no—
423C22×Q8—118no—
424C22×Q8—114no—
425C22×Q8—224no—
426C22×Q8—224no—
427C22×D4—118no—
428C22×D4—118no—
429C22×D4—114no—
430C22×D4—114no—
431C22×D4—118no—
432C22×D4—114no—
433C22×D4—224no—
434C22×D4—224no—
435C22×D4—224no—
436C22×D4—224no—
437C22×D4—224no—
438C22×D4—224no—
439C23×C4—24no—
440C23×C4—24no—
441C23×C4—111no—
442C23×C4—118no—
443C23×C4—118no—
444C23×C4—118no—
445C23×C4—114no—
446C23×C4—111no—
447C23×C4—118no—
448C23×C4—114no—
449C23×C4—112no—
450C23×C4—112no—
451C23×C4—118no—
452C23×C4—228no—
453C23×C4—224no—
454C23×C4—224no—
455C23×C4—444no—
456C23×C4—444no—
457C23×C4C4×D1118yescomplemented
458C23×C4C22×D1112yes—
459C23×C4C22×D1112yes—
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1114yes—
462C23×C4C22×D1111yescharacteristic
463#117—2232no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—118no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—2232no—
470C2×C4⋊C4—228no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4C22×D1114yes—
474C2×C4⋊C4C22×D1114yes—
475C2×C22⋊C4—44no—
476C2×C22⋊C4—118no—
477C2×C22⋊C4—118no—
478C2×C22⋊C4—118no—
479C2×C22⋊C4—118no—
480C2×C22⋊C4—228no—
481C2×C22⋊C4—444no—
482C2×C22⋊C4—444no—
483C2×C22⋊C4—444no—
484C2×C22⋊C4C22×D1118yes—
485C2×C42—118no—
486C2×C42—228no—
487#95—118no—
488#95—118no—
489#95—118no—
490#95C22×D1118yes—
491C2×C11—44no—
492C2×C11#231118yescomplemented
493C2×C11C23×C22⋊C411yescharacteristic
494C2×C11C2×#52011yescharacteristic
495C2×C11C2×#52011yescharacteristic
496C2×C11C2×#53511yescharacteristic
497C2×C11C2×#53611yescharacteristic
498C2×C11C2×#53711yescharacteristic
499C2×C11C2×#53711yescharacteristic
500D11—28no—
501D11—44no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—114no—
509C24—114no—
510C24—114no—
511C24—112no—
512C24—114no—
513C24—112no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24—222no—
518C24—222no—
519C24—222no—
520C24—222no—
521C24—222no—
522C24—222no—
523C24—222no—
524C24C2×C4×D1114yes—
525C24C23×D1112yes—
526C24C23×D1111yescharacteristic
527#41—22256no—
528C2×Q8—1116no—
529C2×Q8—2232no—
530C2×Q8—228no—
531C2×Q8—228no—
532C2×D4—1116no—
533C2×D4—1116no—
534C2×D4—1116no—
535C2×D4—2232no—
536C2×D4—228no—
537C2×D4—228no—
538C2×D4—2232no—
539C2×D4—228no—
540C2×D4—228no—
541C2×D4—2232no—
542C2×D4—228no—
543C2×D4—228no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—232no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—114no—
556C22×C4—114no—
557C22×C4—114no—
558C22×C4—112no—
559C22×C4—1164no—
560C22×C4—1116no—
561C22×C4—1116no—
562C22×C4—1116no—
563C22×C4—114no—
564C22×C4—112no—
565C22×C4—1116no—
566C22×C4—114no—
567C22×C4—114no—
568C22×C4—2216no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—2232no—
572C22×C4—228no—
573C22×C4—228no—
574C22×C4—224no—
575C22×C4—224no—
576C22×C4—224no—
577C22×C4—224no—
578C22×C4—224no—
579C22×C4—224no—
580C22×C4—448no—
581C22×C4—448no—
582C22×C4—4432no—
583C22×C4C2×C4×D1114yes—
584C22×C4C2×C4×D1114yes—
585C22×C4C2×C4×D11116yescomplemented
586C22×C4D4×D1114yes—
587C22×C4D4×D1114yes—
588C22×C4C23×D1114yes—
589C22×C4C23×D1114yes—
590C22×C4C23×D1112yes—
591C22×C4C23×D1112yes—
592C4⋊C4—28no—
593C4⋊C4—28no—
594C4⋊C4—2216no—
595C4⋊C4—228no—
596C4⋊C4—228no—
597C22⋊C4—48no—
598C22⋊C4—2216no—
599C22⋊C4—448no—
600C22⋊C4—448no—
601C22⋊C4—448no—
602C42—2216no—
603C11C2×#231111yescharacteristic, complemented, Sylow
604C23—28no—
605C23—28no—
606C23—28no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—1116no—
618C23—114no—
619C23—114no—
620C23—114no—
621C23—114no—
622C23—228no—
623C23—228no—
624C23—228no—
625C23—228no—
626C23—228no—
627C23—228no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—228no—
633C23—228no—
634C23—228no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—444no—
642C23—444no—
643C23—444no—
644C23—444no—
645C23C22×C4×D1114yes—
646C23C22×C4×D1112yes—
647C23C2×D4×D1112yes—
648C23C2×D4×D1112yes—
649C23#6703712yes—
650C23#6704012yes—
651C23#6704212yes—
652C23#6704312yes—
653C23C24×D1111yescharacteristic
654Q8—2232no—
655D4—2232no—
656D4—2232no—
657D4—2232no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—232no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—48no—
669C2×C4—48no—
670C2×C4—1116no—
671C2×C4—114no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—1164no—
675C2×C4—114no—
676C2×C4—228no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—2232no—
680C2×C4—224no—
681C2×C4—224no—
682C2×C4—224no—
683C2×C4—224no—
684C2×C4—224no—
685C2×C4—224no—
686C2×C4—4432no—
687C2×C4—448no—
688C2×C4—448no—
689C2×C4C22⋊C4×D11116yes—
690C2×C4C22×C4×D1114yes—
691C2×C4C22×C4×D1114yes—
692C2×C4C2×D4×D1114yes—
693C2×C4C2×D4×D1114yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—416no—
702C22—118no—
703C22—224no—
704C22—224no—
705C22—224no—
706C22—224no—
707C22—2232no—
708C22—224no—
709C22—224no—
710C22—224no—
711C22—224no—
712C22—224no—
713C22—442no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—4416no—
718C22C2×C22⋊C4×D1114yes—
719C22#1062303514yes—
720C22#1062305414yes—
721C22#1062313814yes—
722C22#1062313914yes—
723C22#1062315914yes—
724C22#1062316014yes—
725C22C23×C4×D1111yescharacteristic
726C22C22×D4×D1111yescharacteristic
727C22C22×D4×D1111yescharacteristic
728C22C2×#6703711yescharacteristic
729C22C2×#6704011yescharacteristic
730C22C2×#6704211yescharacteristic
731C22C2×#6704311yescharacteristic
732C4—24no—
733C4—44no—
734C4—44no—
735C4—118no—
736C4—224no—
737C4—444no—
738C4—444no—
739C4C2×C22⋊C4×D1118yes—
740C2—44no—
741C2—228no—
742C2—444no—
743C2#1307120518yesdirect product factor
744C2C22×C22⋊C4×D1111yescharacteristic
745C2C2×#1062305411yescharacteristic
746C2C2×#1062303511yescharacteristic
747C2C2×#1062313811yescharacteristic
748C2C2×#1062315911yescharacteristic
749C2C2×#1062313911yescharacteristic
750C2C2×#1062316011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC23×#4339C2
cosocleC23×C11C25
hypercenterC2×#380D11
hypocenterC11C2×#2311
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#66945C2semidirect
3. C22×C4⋊C4×D11C2semidirect
4. #13071205C2direct (N × H)
5. C2×#10622259C2semidirect
6. C2×#10622570C2semidirect
7. C2×#10622278C2semidirect
8. C2×#10622569C2semidirect
9. C2×#10622825C2semidirect
10. C2×#10622600C2semidirect
11. C2×#10622600C2semidirect
12. C2×C11×#380C2semidirect
18. C22×#4339C4semidirect
37. C2×#66945C22semidirect
39. C2×C4⋊C4×D11C22semidirect
40. C11×#380C22semidirect
42. #10622825C22semidirect
46. #10622600C22semidirect
47. #10622600C22semidirect
48. #10622570C22semidirect
49. #10622569C22semidirect
50. #10622278C22semidirect
51. #10622259C22semidirect
57. C23×C4×C11C2×C4semidirect
68. C22×C22⋊D11C2×C4semidirect
78. C2×#4339C2×C4semidirect
89. C22×C4×D11C2×C4semidirect
97. C22×Dic22C2×C4semidirect
166. C22×C4×C11C22×C4semidirect
180. C2×C22⋊D11C22×C4semidirect
209. C2×C4×D11C22⋊C4semidirect
211. C2×C4×D11C22×C4semidirect
217. C2×Dic22C22×C4semidirect
240. C2×#380D11semidirect
329. C4×D11C2×C22⋊C4semidirect
365. #380C2×D11semidirect
457. C23×C4C4×D11semidirect
492. C2×C11#2311semidirect
585. C22×C4C2×C4×D11semidirect
603. C11C2×#2311semidirect
743. C2#13071205direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#669452
C22×C4⋊C4×D112
#130712052
C2×#106222592
C2×#106225702
C2×#106222782
C2×#106225692
C2×#106228252
C2×#106226002
C2×C11×#3802
C2×#231111