Finite Group Databasebeta

← C2×#13073554 #14924944

Subgroups — C2×#13073554 #14924944

Order 2816.

4566 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
1C22×#67000C211yesmaximal, characteristic, complemented
2C22×#66999C211yesmaximal, characteristic, complemented
3C22×#66948C211yesmaximal, characteristic, complemented
4C22×#66983C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
6#13073554C2116yesmaximal, direct product factor
7C2×#10622605C212yesmaximal, complemented
8C2×#10622573C212yesmaximal, complemented
9C2×#10622601C212yesmaximal, complemented
10C2×#10622570C212yesmaximal, complemented
11C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×D44C2211yescharacteristic
18C23×D44C2212yes—
19C23×C4×D11C2211yescharacteristic
20C2×C11×C22⋊Q8—28no—
21C2×C11×C22⋊Q8C2218yescomplemented
22C22×C11×C4⋊C4C2212yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C2×#67000—28no—
27C2×#67000C2218yescomplemented
28C2×#66999—28no—
29C2×#66999C2218yescomplemented
30C2×#66983—28no—
31C2×#66983C2218yescomplemented
32C2×C4×C22⋊D11—28no—
33C2×C4×C22⋊D11C2218yescomplemented
34C22×(C2×D11)⋊C4C2212yes—
35C22×(C2×D11)⋊C4C2212yes—
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2212yes—
38C22×(C2×D11)⋊C4C2212yes—
39C22×(C2×D11)⋊C4C2212yes—
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2212yes—
43C22×C4×Dic11C2212yes—
44C22×C4×Dic11C2211yescharacteristic
45C2×#66948—28no—
46C2×#66948C2218yescomplemented
47C2×C11⋊#95C2212yes—
48#10622605C22116yescomplemented
49#10622601C22116yescomplemented
50C4⋊C4×Dic11C2218yescomplemented
51#10622573C22116yescomplemented
52#10622570C22116yescomplemented
53C25×C11C2311yescharacteristic
54C24×D11C2312yes—
55C24×D11C2311yescharacteristic
56C22×Q8×C11—24no—
57C22×Q8×C11—24no—
58C22×Q8×C11—24no—
59C22×Q8×C11C2314yes—
60C23×C4×C11—24no—
61C23×C4×C11—24no—
62C23×C4×C11—24no—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2314yes—
66C23×C4×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—24no—
69C22×C22⋊D11—24no—
70C22×C22⋊D11—28no—
71C22×C22⋊D11—24no—
72C22×C22⋊D11—28no—
73C22×C22⋊D11—44no—
74C22×C22⋊D11C2314yes—
75C22×C22⋊D11C2318yes—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2312yes—
79C23×Dic11C2311yescharacteristic
80C22×D44—28no—
81C22×D44—28no—
82C22×D44—24no—
83C22×D44—24no—
84C22×D44—24no—
85C22×D44—44no—
86C22×D44C2314yes—
87C22×D44C2318yes—
88C22×C4×D11—24no—
89C22×C4×D11—24no—
90C22×C4×D11—24no—
91C22×C4×D11C2314yes—
92C11×C22⋊Q8—232no—
93C2×C11×C4⋊C4—28no—
94C2×C11×C4⋊C4D418yescomplemented
95C2×C11×C4⋊C4C2318yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C22⋊C4—28no—
98C2×C11×C22⋊C4C2318yes—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11C2314yes—
101#67000—232no—
102#66999—232no—
103#66983—232no—
104C4×C22⋊D11—232no—
105C2×(C2×D11)⋊C4—28no—
106C2×(C2×D11)⋊C4—24no—
107C2×(C2×D11)⋊C4—28no—
108C2×(C2×D11)⋊C4—28no—
109C2×(C2×D11)⋊C4—28no—
110C2×(C2×D11)⋊C4—28no—
111C2×(C2×D11)⋊C4C2318yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2318yes—
114C2×(C2×D11)⋊C4C2318yes—
115C2×(C2×D11)⋊C4C2318yes—
116C2×(C2×D11)⋊C4C2318yes—
117C2×C4⋊Dic11D418yescomplemented
118C2×C4⋊Dic11C2314yes—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—28no—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2318yes—
123C2×C4×Dic11—44no—
124C2×C4×Dic11D418yescomplemented
125C2×C4×Dic11C2318yes—
126C2×C4×Dic11C2314yes—
127#66948—232no—
128C11⋊#95C2318yes—
129C2×#2540—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—22no—
136C24×C11#4114yes—
137C24×C11C2412yes—
138C24×C11C2411yescharacteristic
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—24no—
146C23×D11—24no—
147C23×D11—24no—
148C23×D11—24no—
149C23×D11—24no—
150C23×D11—24no—
151C23×D11—24no—
152C23×D11#4114yes—
153C23×D11C2414yes—
154C23×D11C2412yes—
155C2×Q8×C11—28no—
156C2×Q8×C11—28no—
157C2×Q8×C11—28no—
158C2×Q8×C11—416no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—22no—
162C22×C4×C11—24no—
163C22×C4×C11—22no—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—28no—
168C22×C4×C11—28no—
169C22×C4×C11—28no—
170C22×C4×C11—416no—
171C22×C4×C11C2×D418yes—
172C22×C4×C11C2×D414yes—
173C22×C4×C11C2×D414yes—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2414yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2414yes—
178C22×C4×C11C2412yes—
179C2×C22⋊D11—232no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—216no—
182C2×C22⋊D11—28no—
183C2×C22⋊D11—216no—
184C2×C22⋊D11—28no—
185C2×C22⋊D11—48no—
186C2×C22⋊D11—432no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—24no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—24no—
195C22×Dic11—22no—
196C22×Dic11C2×D414yes—
197C22×Dic11C2×D414yes—
198C22×Dic11C2×D418yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2414yes—
202C22×Dic11C2412yes—
203C2×D44—216no—
204C2×D44—216no—
205C2×D44—28no—
206C2×D44—28no—
207C2×D44—28no—
208C2×D44—48no—
209C2×D44—432no—
210C2×D44—416no—
211C2×C4×D11—28no—
212C2×C4×D11—28no—
213C2×C4×D11—28no—
214C2×C4×D11—416no—
215C11×C4⋊C4—216no—
216C11×C4⋊C4C2×D4116yescomplemented
217C11×C22⋊C4—216no—
218C22⋊Dic11—28no—
219(C2×D11)⋊C4—28no—
220(C2×D11)⋊C4—216no—
221(C2×D11)⋊C4—216no—
222(C2×D11)⋊C4—216no—
223(C2×D11)⋊C4—216no—
224(C2×D11)⋊C4—216no—
225C4⋊Dic11C2×D4116yescomplemented
226Dic11⋊C4—28no—
227Dic11⋊C4—216no—
228C4×Dic11—48no—
229C4×Dic11C2×D4116yescomplemented
230C22×#124—111no—
231C22×C22⋊Q8—111no—
232C22×C22⋊Q8D1111yescharacteristic, complemented
233C22×#121—111no—
234C22×#121—111no—
235C22×C4×D4—111no—
236#2540—1116no—
237C2×#399—112no—
238C2×#392—112no—
239C2×#390—112no—
240C2×#390—112no—
241C2×C4×C4⋊C4—111no—
242C23×C11—28no—
243C23×C11—28no—
244C23×C11—28no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—44no—
252C23×C11—44no—
253C23×C11—44no—
254C23×C11—44no—
255C23×C11C22×D412yes—
256C23×C11C22×D412yes—
257C23×C11C22×D412yes—
258C23×C11C2×#4114yes—
259C23×C11C2×#4112yes—
260C23×C11C2×#4112yes—
261C23×C11H(5,𝔽2)12yes—
262C23×C112−1+412yes—
263C23×C11C2511yescharacteristic
264C22×D11—28no—
265C22×D11—28no—
266C22×D11—28no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—24no—
274C22×D11—24no—
275C22×D11—24no—
276C22×D11—24no—
277C22×D11—24no—
278C22×D11—24no—
279C22×D11—24no—
280C22×D11—44no—
281C22×D11—44no—
282C22×D11—44no—
283C22×D11—44no—
284C22×D11—48no—
285C22×D11—48no—
286C22×D11—48no—
287C22×D11—48no—
288C22×D11—48no—
289C22×D11—48no—
290C22×D11—48no—
291C22×D11C2×#4114yes—
292Q8×C11—416no—
293C2×C4×C11—216no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—22no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—44no—
303C2×C4×C11—48no—
304C2×C4×C11—416no—
305C2×C4×C11#127116yes—
306C2×C4×C11C22×D414yes—
307C2×C4×C11C22×D414yes—
308C2×C4×C11C22×D418yes—
309C2×C4×C11C22×D414yes—
310C22⋊D11—232no—
311C22⋊D11—432no—
312C2×Dic11—28no—
313C2×Dic11—28no—
314C2×Dic11—216no—
315C2×Dic11—22no—
316C2×Dic11—24no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—24no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—44no—
325C2×Dic11C22×D414yes—
326C2×Dic11C22×D414yes—
327C2×Dic11C22×D418yes—
328D44—432no—
329D44—416no—
330C4×D11—416no—
331C23×Q8C2×D1111yescharacteristic
332C23×D4—111no—
333C23×D4—112no—
334C23×D4—111no—
335C23×D4—112no—
336C24×C4—111no—
337C24×C4C2×D1111yescharacteristic
338C2×#124—118no—
339C2×#124—228no—
340C2×C22⋊Q8—28no—
341C2×C22⋊Q8—118no—
342C2×C22⋊Q8—228no—
343C2×C22⋊Q8C2×D1118yescomplemented
344C2×#121—118no—
345C2×#121—118no—
346C2×#121—228no—
347C2×#121—228no—
348C2×C4×D4—118no—
349C2×C4×D4—228no—
350C22×C4⋊C4—111no—
351C22×C4⋊C4—111no—
352C22×C4⋊C4—112no—
353C22×C4⋊C4C2×D1112yes—
354C22×C4⋊C4C2×D1111yescharacteristic
355C22×C22⋊C4—111no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4—112no—
358C22×C22⋊C4—112no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4C2×D1112yes—
363C22×C42—111no—
364C22×C42—112no—
365#399—1116no—
366#392—1116no—
367#390—1116no—
368#390—1116no—
369C4×C4⋊C4—118no—
370C2×#95—112no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—24no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—416no—
379C22×C11#52514yes—
380C22×C11C2×#12714yes—
381C22×C11#53714yes—
382C22×C11#54614yes—
383C22×C11#54614yes—
384C22×C11#54814yes—
385C22×C11#54814yes—
386C22×C11C23×D411yescharacteristic
387C22×C11C23×D411yescharacteristic
388C22×C11C23×D411yescharacteristic
389C22×C11C22×#4111yescharacteristic
390C22×C11C22×#4111yescharacteristic
391C22×C11C2×H(5,𝔽2)11yescharacteristic
392C22×C11C2×2−1+411yescharacteristic
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—42no—
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—42no—
400C2×D11—416no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—44no—
407C2×D11—44no—
408C2×D11—816no—
409C4×C11—28no—
410C4×C11—42no—
411C4×C11—44no—
412C4×C11C2×#12718yes—
413Dic11—24no—
414Dic11—24no—
415Dic11—28no—
416Dic11—42no—
417C25—111no—
418C25—112no—
419C25C22×D1111yescharacteristic
420C22×Q8—24no—
421C22×Q8—24no—
422C22×Q8—24no—
423C22×Q8C22×D1114yes—
424C22×D4—114no—
425C22×D4—118no—
426C22×D4—114no—
427C22×D4—118no—
428C22×D4—228no—
429C22×D4—224no—
430C22×D4—228no—
431C22×D4—224no—
432C22×D4—224no—
433C22×D4—228no—
434C22×D4—224no—
435C22×D4—224no—
436C22×D4—228no—
437C22×D4—224no—
438C22×D4—444no—
439C22×D4—444no—
440C23×C4—24no—
441C23×C4—24no—
442C23×C4—24no—
443C23×C4—111no—
444C23×C4—112no—
445C23×C4—111no—
446C23×C4—111no—
447C23×C4—114no—
448C23×C4—224no—
449C23×C4—224no—
450C23×C4—224no—
451C23×C4C22×D1114yes—
452C23×C4C22×D1112yes—
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1112yes—
455C23×C4C22×D1111yescharacteristic
456#124—2232no—
457C22⋊Q8—232no—
458C22⋊Q8—2232no—
459#121—2232no—
460#121—2232no—
461C4×D4—2232no—
462C2×C4⋊C4—28no—
463C2×C4⋊C4—118no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—118no—
467C2×C4⋊C4—224no—
468C2×C4⋊C4—228no—
469C2×C4⋊C4C22⋊D1118yescomplemented
470C2×C4⋊C4C22×D1118yes—
471C2×C4⋊C4C22×D1114yes—
472C2×C22⋊C4—28no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—114no—
475C2×C22⋊C4—118no—
476C2×C22⋊C4—118no—
477C2×C22⋊C4—118no—
478C2×C22⋊C4—118no—
479C2×C22⋊C4—118no—
480C2×C22⋊C4—224no—
481C2×C22⋊C4—228no—
482C2×C22⋊C4—228no—
483C2×C22⋊C4—228no—
484C2×C22⋊C4—228no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4—228no—
487C2×C22⋊C4C22×D1118yes—
488C2×C42—118no—
489C2×C42—114no—
490C2×C42—118no—
491C2×C42—444no—
492#95—118no—
493C2×C11—44no—
494C2×C11#254018yescomplemented
495C2×C11C2×#52511yescharacteristic
496C2×C11C22×#12711yescharacteristic
497C2×C11C2×#53711yescharacteristic
498C2×C11C2×#54611yescharacteristic
499C2×C11C2×#54611yescharacteristic
500C2×C11C2×#54811yescharacteristic
501C2×C11C2×#54811yescharacteristic
502D11—44no—
503D11—84no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—114no—
511C24—112no—
512C24—114no—
513C24—222no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24—222no—
518C24—222no—
519C24—224no—
520C24—224no—
521C24—224no—
522C24—224no—
523C24—224no—
524C24—224no—
525C24—224no—
526C24#434314yes—
527C24C23×D1112yes—
528C24C23×D1111yescharacteristic
529C2×Q8—28no—
530C2×Q8—28no—
531C2×Q8—28no—
532C2×Q8—416no—
533C2×D4—2216no—
534C2×D4—228no—
535C2×D4—2216no—
536C2×D4—228no—
537C2×D4—2232no—
538C2×D4—228no—
539C2×D4—2216no—
540C2×D4—228no—
541C2×D4—228no—
542C2×D4—2216no—
543C2×D4—228no—
544C2×D4—448no—
545C2×D4—4432no—
546C2×D4—448no—
547C2×D4—4432no—
548C2×D4—4416no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—416no—
561C22×C4—114no—
562C22×C4—114no—
563C22×C4—118no—
564C22×C4—112no—
565C22×C4—114no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—222no—
569C22×C4—224no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—224no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—228no—
578C22×C4—228no—
579C22×C4—228no—
580C22×C4—4416no—
581C22×C4D4×D1114yes—
582C22×C4D4×D1114yes—
583C22×C4C2×C22⋊D1118yes—
584C22×C4C2×C22⋊D1114yes—
585C22×C4C23×D1114yes—
586C22×C4C23×D1112yes—
587C22×C4C23×D1114yes—
588C22×C4C23×D1112yes—
589C4⋊C4—216no—
590C4⋊C4—1116no—
591C4⋊C4—228no—
592C4⋊C4—2216no—
593C4⋊C4C2×C22⋊D11116yescomplemented
594C22⋊C4—216no—
595C22⋊C4—228no—
596C22⋊C4—2216no—
597C22⋊C4—2216no—
598C22⋊C4—2216no—
599C22⋊C4—2216no—
600C22⋊C4—228no—
601C22⋊C4—2216no—
602C42—1116no—
603C42—448no—
604C11C2×#254011yescharacteristic, complemented, Sylow
605C23—28no—
606C23—28no—
607C23—28no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—114no—
619C23—228no—
620C23—228no—
621C23—228no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—224no—
629C23—224no—
630C23—224no—
631C23—224no—
632C23—224no—
633C23—224no—
634C23—224no—
635C23—444no—
636C23—444no—
637C23—444no—
638C23—444no—
639C23—448no—
640C23—448no—
641C23—448no—
642C23—448no—
643C23—448no—
644C23—448no—
645C23—448no—
646C23C2×D4×D1112yes—
647C23C2×D4×D1112yes—
648C23C2×#434314yes—
649C23C2×#434312yes—
650C23#6704012yes—
651C23#41×D1112yes—
652C23#6704212yes—
653C23C22×C22⋊D1112yes—
654C23C24×D1111yescharacteristic
655Q8—416no—
656D4—2232no—
657D4—4432no—
658D4—4432no—
659D4—4416no—
660C2×C4—216no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—44no—
670C2×C4—48no—
671C2×C4—416no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—118no—
675C2×C4—228no—
676C2×C4—228no—
677C2×C4—2216no—
678C2×C4—222no—
679C2×C4—224no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—224no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—444no—
688C2×C4—4416no—
689C2×C4#66993116yes—
690C2×C4C2×D4×D1114yes—
691C2×C4C2×D4×D1114yes—
692C2×C4C22×C22⋊D1118yes—
693C2×C4C22×C22⋊D1114yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—42no—
698C22—42no—
699C22—416no—
700C22—42no—
701C22—42no—
702C22—224no—
703C22—224no—
704C22—224no—
705C22—442no—
706C22—442no—
707C22—4416no—
708C22—442no—
709C22—442no—
710C22—444no—
711C22—444no—
712C22—444no—
713C22—444no—
714C22—444no—
715C22—444no—
716C22—444no—
717C22—8816no—
718C22#1062315814yes—
719C22#1062316014yes—
720C22#1062316114yes—
721C22#1062316414yes—
722C22C2×#6699314yes—
723C22#1062334814yes—
724C22#1062336014yes—
725C22C22×D4×D1111yescharacteristic
726C22C22×D4×D1111yescharacteristic
727C22C22×#434311yescharacteristic
728C22C2×#6704011yescharacteristic
729C22C2×#41×D1111yescharacteristic
730C22C2×#6704211yescharacteristic
731C22C23×C22⋊D1111yescharacteristic
732C4—28no—
733C4—42no—
734C4—44no—
735C4—224no—
736C4—224no—
737C4—228no—
738C4—442no—
739C4C2×#6699318yes—
740C2—44no—
741C2—444no—
742C2—884no—
743C2#1307355418yesdirect product factor
744C2C2×#1062315811yescharacteristic
745C2C22×#6699311yescharacteristic
746C2C2×#1062316011yescharacteristic
747C2C2×#1062336011yescharacteristic
748C2C2×#1062316111yescharacteristic
749C2C2×#1062316411yescharacteristic
750C2C2×#1062334811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2540
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#67000C2semidirect
2. C22×#66999C2semidirect
3. C22×#66948C2semidirect
4. C22×#66983C2semidirect
5. C22×C4×C22⋊D11C2semidirect
6. #13073554C2direct (N × H)
7. C2×#10622605C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622570C2semidirect
11. C2×C4⋊C4×Dic11C2semidirect
12. C22×C11×C22⋊Q8C2semidirect
21. C2×C11×C22⋊Q8C22semidirect
27. C2×#67000C22semidirect
29. C2×#66999C22semidirect
31. C2×#66983C22semidirect
33. C2×C4×C22⋊D11C22semidirect
46. C2×#66948C22semidirect
48. #10622605C22semidirect
49. #10622601C22semidirect
50. C4⋊C4×Dic11C22semidirect
51. #10622573C22semidirect
52. #10622570C22semidirect
94. C2×C11×C4⋊C4D4semidirect
117. C2×C4⋊Dic11D4semidirect
124. C2×C4×Dic11D4semidirect
216. C11×C4⋊C4C2×D4semidirect
225. C4⋊Dic11C2×D4semidirect
229. C4×Dic11C2×D4semidirect
232. C22×C22⋊Q8D11semidirect
343. C2×C22⋊Q8C2×D11semidirect
469. C2×C4⋊C4C22⋊D11semidirect
494. C2×C11#2540semidirect
593. C4⋊C4C2×C22⋊D11semidirect
604. C11C2×#2540semidirect
743. C2#13073554direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670002
C22×#669992
C22×#669482
C22×#669832
C22×C4×C22⋊D112
#130735542
C2×#106226052
C2×#106225732
C2×#106226012
C2×#106225702
C2×C4⋊C4×Dic112
C22×C11×C22⋊Q82
C2×#254011