Finite Group Databasebeta

← C2×#13072038 #14922180

Subgroups — C2×#13072038 #14922180

Order 2816.

3526 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3C22×D4×Dic11C211yesmaximal, characteristic
4C22×#66930C211yesmaximal, characteristic, complemented
5#13072038C2116yesmaximal, direct product factor
6C2×#10622565C211yesmaximal, characteristic, complemented
7C2×#10622566C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622598C211yesmaximal, characteristic, complemented
11C2×#10622260C211yesmaximal, characteristic, complemented
12C2×#10622585C211yesmaximal, characteristic, complemented
13C2×#10622564C211yesmaximal, characteristic, complemented
14C2×#10622557C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×D4×Dic11—28no—
33C2×D4×Dic11C2218yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66931—28no—
47C2×#66931—28no—
48C2×#66931C2218yescomplemented
49C2×#66931C2218yescomplemented
50C2×#66930—28no—
51C2×#66930C2218yescomplemented
52C11×#394C2218yes—
53C2×C11×#95C2211yescharacteristic
54#10622835C2218yes—
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622598C2218yescomplemented
63#10622585C2218yescomplemented
64#10622566C2218yescomplemented
65#10622565C2218yescomplemented
66#10622564C2218yescomplemented
67#10622557C2218yescomplemented
68#10622555C2218yescomplemented
69#10622260C2218yescomplemented
70#10622259C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11C2314yes—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×Dic11—24no—
83C23×Dic11—24no—
84C23×Dic11—24no—
85C23×Dic11—24no—
86C23×Dic11—24no—
87C23×Dic11D418yes—
88C23×Dic11C2314yes—
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2314yes—
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×Dic22—24no—
99C22×Dic22—24no—
100C22×Dic22—24no—
101C22×Dic22C2314yes—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C22⋊C4—24no—
105C2×C11×C22⋊C4—24no—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124D4×Dic11—232no—
125C2×C4⋊Dic11—24no—
126C2×C4⋊Dic11—24no—
127C2×C4⋊Dic11—24no—
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2314yes—
130C2×C4⋊Dic11C2314yes—
131C2×Dic11⋊C4—24no—
132C2×Dic11⋊C4—24no—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4D418yescomplemented
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11—24no—
144C2×C4×Dic11—24no—
145C2×C4×Dic11—24no—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149#66931—232no—
150#66931—232no—
151#66930—232no—
152C11×#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C2×#2415—111nomaximal, Sylow
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11C2×D414yes—
174C24×C11#4114yes—
175C24×C11C2412yes—
176C24×C11C2412yes—
177C24×C11C2411yescharacteristic
178C2×D4×C11—232no—
179C2×D4×C11—28no—
180C2×D4×C11—28no—
181C2×D4×C11—28no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11C2×D414yes—
196C22×C4×C11#4114yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C22×Dic11—232no—
203C22×Dic11—28no—
204C22×Dic11—28no—
205C22×Dic11—28no—
206C22×Dic11—28no—
207C22×Dic11—28no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—416no—
228C22×Dic11C2×D4116yes—
229C22×Dic11C2×D414yes—
230C22×Dic11C2×D414yes—
231C22×Dic11C2×D414yes—
232C22×Dic11C2×D414yes—
233C22×Dic11#4114yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C2×Dic22—28no—
243C2×Dic22—28no—
244C2×Dic22—28no—
245C2×Dic22—416no—
246C11×C4⋊C4—28no—
247C11×C22⋊C4—28no—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—28no—
251C22⋊Dic11—28no—
252C22⋊Dic11—28no—
253C22⋊Dic11—28no—
254C22⋊Dic11—28no—
255C22⋊Dic11—28no—
256C22⋊Dic11—28no—
257C4⋊Dic11—28no—
258C4⋊Dic11—28no—
259C4⋊Dic11—28no—
260Dic11⋊C4—28no—
261Dic11⋊C4—28no—
262Dic11⋊C4—28no—
263Dic11⋊C4—28no—
264Dic11⋊C4—28no—
265Dic11⋊C4C2×D4116yescomplemented
266C4×Dic11—28no—
267C4×Dic11—28no—
268C4×Dic11—28no—
269C22×C22⋊Q8—111no—
270C22×C22⋊Q8—111no—
271C22×C4×D4—111no—
272C22×#117—111no—
273#2415—1116no—
274C2×#397—111no—
275C2×#397—111no—
276C2×#394—111no—
277C2×#394D1111yescharacteristic
278C2×#391—111no—
279C2×#389—111no—
280C2×#389—111no—
281C2×#389—111no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#380—111no—
285C23×C11—28no—
286C23×C11—28no—
287C23×C11—28no—
288C23×C11—28no—
289C23×C11—28no—
290C23×C11—28no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—44no—
306C23×C11—44no—
307C23×C11—44no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11C22×D414yes—
312C23×C11C22×D412yes—
313C23×C11C22×D412yes—
314C23×C11C2×#4114yes—
315C23×C11C2×#4112yes—
316C23×C11C2×#4112yes—
317C23×C11C2×#4112yes—
318C23×C112−1+412yes—
319C23×C112−1+412yes—
320C23×C11C2511yescharacteristic
321D4×C11—232no—
322C2×C4×C11—28no—
323C2×C4×C11—28no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—44no—
338C2×C4×C11—44no—
339C2×C4×C11—44no—
340C2×C4×C11C22×D414yes—
341C2×C4×C11C2×#4114yes—
342C2×Dic11—28no—
343C2×Dic11—28no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—232no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—44no—
365C2×Dic11—44no—
366C2×Dic11—44no—
367C2×Dic11—44no—
368C2×Dic11—44no—
369C2×Dic11—416no—
370C2×Dic11#121116yes—
371C2×Dic11C22×D414yes—
372C2×Dic11C22×D414yes—
373C2×Dic11C22×D414yes—
374C2×Dic11C22×D414yes—
375C2×Dic11C2×#4114yes—
376Dic22—416no—
377C23×Q8—111no—
378C23×D4C2×D1111yescharacteristic
379C24×C4—111no—
380C24×C4—111no—
381C2×C22⋊Q8—118no—
382C2×C22⋊Q8—118no—
383C2×C22⋊Q8—228no—
384C2×C22⋊Q8—228no—
385C2×C4×D4—118no—
386C2×C4×D4—228no—
387C2×#117—118no—
388C2×#117—228no—
389C22×C4⋊C4—111no—
390C22×C4⋊C4—111no—
391C22×C4⋊C4—111no—
392C22×C4⋊C4—111no—
393C22×C4⋊C4—111no—
394C22×C4⋊C4—111no—
395C22×C4⋊C4—111no—
396C22×C4⋊C4—111no—
397C22×C4⋊C4—111no—
398C22×C4⋊C4C2×D1111yescharacteristic
399C22×C22⋊C4—111no—
400C22×C22⋊C4—111no—
401C22×C22⋊C4—111no—
402C22×C22⋊C4—111no—
403C22×C22⋊C4—111no—
404C22×C22⋊C4—111no—
405C22×C22⋊C4C2×D1111yescharacteristic
406C22×C22⋊C4C2×D1111yescharacteristic
407C22×C22⋊C4C2×D1111yescharacteristic
408C22×C22⋊C4C2×D1111yescharacteristic
409C22×C42—111no—
410C22×C42—111no—
411C22×C42—111no—
412#397—118no—
413#397—118no—
414#394—118no—
415#394C2×D1118yes—
416#391—118no—
417#389—118no—
418#389—118no—
419#389—118no—
420#388—118no—
421#388—118no—
422#380—118no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95—111no—
427C2×#95—111no—
428C2×#95—111no—
429C2×#95—111no—
430C2×#95C2×D1111yescharacteristic
431C22×C11—24no—
432C22×C11—24no—
433C22×C11—24no—
434C22×C11—24no—
435C22×C11—24no—
436C22×C11—24no—
437C22×C11—42no—
438C22×C11—416no—
439C22×C11—416no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11C2×#12114yes—
448C22×C11#52514yes—
449C22×C11#53614yes—
450C22×C11#54714yes—
451C22×C11#54814yes—
452C22×C11#55214yes—
453C22×C11#55614yes—
454C22×C11C23×D411yescharacteristic
455C22×C11C23×D411yescharacteristic
456C22×C11C22×#4111yescharacteristic
457C22×C11C22×#4111yescharacteristic
458C22×C11C22×#4111yescharacteristic
459C22×C11C2×2−1+411yescharacteristic
460C22×C11C2×2−1+411yescharacteristic
461C4×C11—24no—
462C4×C11—24no—
463C4×C11—42no—
464C4×C11—42no—
465C4×C11—42no—
466Dic11—24no—
467Dic11—24no—
468Dic11—42no—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472Dic11—42no—
473Dic11C2×#12118yes—
474C25C22×D1111yescharacteristic
475C25C22×D1111yescharacteristic
476C22×Q8—114no—
477C22×Q8—224no—
478C22×Q8—224no—
479C22×Q8—224no—
480C22×D4—24no—
481C22×D4—24no—
482C22×D4—24no—
483C22×D4C22×D1114yes—
484C23×C4—111no—
485C23×C4—118no—
486C23×C4—114no—
487C23×C4—111no—
488C23×C4—111no—
489C23×C4—114no—
490C23×C4—111no—
491C23×C4—111no—
492C23×C4—111no—
493C23×C4—111no—
494C23×C4—111no—
495C23×C4—224no—
496C23×C4—224no—
497C23×C4—224no—
498C23×C4—224no—
499C23×C4—224no—
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1111yescharacteristic
502C23×C4C22×D1111yescharacteristic
503C23×C4C22×D1111yescharacteristic
504C23×C4C22×D1111yescharacteristic
505C22⋊Q8—2232no—
506C22⋊Q8—2232no—
507C4×D4—2232no—
508#117—2232no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—118no—
511C2×C4⋊C4—114no—
512C2×C4⋊C4—114no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—114no—
520C2×C4⋊C4—224no—
521C2×C4⋊C4—224no—
522C2×C4⋊C4—224no—
523C2×C4⋊C4—224no—
524C2×C4⋊C4—224no—
525C2×C4⋊C4—224no—
526C2×C4⋊C4—224no—
527C2×C4⋊C4—224no—
528C2×C4⋊C4C22×D1114yes—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—224no—
540C2×C22⋊C4—224no—
541C2×C22⋊C4—224no—
542C2×C22⋊C4—224no—
543C2×C22⋊C4—224no—
544C2×C22⋊C4—224no—
545C2×C22⋊C4C22×D1114yes—
546C2×C22⋊C4C22×D1114yes—
547C2×C22⋊C4C22×D1114yes—
548C2×C22⋊C4C22×D1114yes—
549C2×C42—114no—
550C2×C42—114no—
551C2×C42—114no—
552C2×C42—224no—
553C2×C42—224no—
554C2×C42—224no—
555#95—114no—
556#95—114no—
557#95—114no—
558#95—114no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95C22×D1114yes—
563C2×C11—44no—
564C2×C11—44no—
565C2×C11#241518yescomplemented
566C2×C11C22×#12111yescharacteristic
567C2×C11C2×#52511yescharacteristic
568C2×C11C2×#53611yescharacteristic
569C2×C11C2×#54711yescharacteristic
570C2×C11C2×#54811yescharacteristic
571C2×C11C2×#55211yescharacteristic
572C2×C11C2×#55611yescharacteristic
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24D4×D1114yes—
586C24#434114yes—
587C24C23×D1112yes—
588C24C23×D1112yes—
589C24C23×D1111yescharacteristic
590C2×Q8—228no—
591C2×Q8—228no—
592C2×Q8—228no—
593C2×Q8—4416no—
594C2×D4—232no—
595C2×D4—28no—
596C2×D4—28no—
597C2×D4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—114no—
612C22×C4—114no—
613C22×C4—114no—
614C22×C4—112no—
615C22×C4—114no—
616C22×C4—114no—
617C22×C4—1116no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—228no—
626C22×C4—2232no—
627C22×C4—228no—
628C22×C4—228no—
629C22×C4—228no—
630C22×C4—228no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—4416no—
651C22×C4D4×D1114yes—
652C22×C4#434114yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C4⋊C4—28no—
659C4⋊C4—1116no—
660C4⋊C4—228no—
661C4⋊C4—228no—
662C4⋊C4—228no—
663C4⋊C4—228no—
664C4⋊C4—228no—
665C4⋊C4—228no—
666C4⋊C4—228no—
667C4⋊C4—228no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—228no—
673C22⋊C4—228no—
674C22⋊C4—228no—
675C22⋊C4—228no—
676C22⋊C4—228no—
677C22⋊C4—228no—
678C42—228no—
679C42—228no—
680C42—228no—
681C11C2×#241511yescharacteristic, complemented, Sylow
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—28no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23C2×D4×D1114yes—
709C23C2×D4×D1112yes—
710C23C2×D4×D1112yes—
711C23C2×#434114yes—
712C23C2×#434112yes—
713C23C2×#434112yes—
714C23#41×D1112yes—
715C23#6704312yes—
716C23#6704312yes—
717C23C24×D1111yescharacteristic
718Q8—4416no—
719D4—232no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—1116no—
739C2×C4—114no—
740C2×C4—114no—
741C2×C4—114no—
742C2×C4—114no—
743C2×C4—114no—
744C2×C4—2232no—
745C2×C4—228no—
746C2×C4—228no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—4416no—
767C2×C4—444no—
768C2×C4—444no—
769C2×C4—444no—
770C2×C4—444no—
771C2×C4—444no—
772C2×C4C2×D4×D1114yes—
773C2×C4C2×#434114yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—416no—
785C22—416no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22#1062311714yes—
791C22#1062312914yes—
792C22D11×#12114yes—
793C22#1062314214yes—
794C22#1062317914yes—
795C22#1062318114yes—
796C22#1062320214yes—
797C22C22×D4×D1111yescharacteristic
798C22C22×D4×D1111yescharacteristic
799C22C22×#434111yescharacteristic
800C22C22×#434111yescharacteristic
801C22C2×#41×D1111yescharacteristic
802C22C2×#6704311yescharacteristic
803C22C2×#6704311yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—118no—
810C4—224no—
811C4—224no—
812C4—442no—
813C4—442no—
814C4—442no—
815C4—442no—
816C4—442no—
817C2—44no—
818C2—44no—
819C2#1307203818yesdirect product factor
820C2C2×D11×#12111yescharacteristic
821C2C2×#1062311711yescharacteristic
822C2C2×#1062317911yescharacteristic
823C2C2×#1062314211yescharacteristic
824C2C2×#1062312911yescharacteristic
825C2C2×#1062318111yescharacteristic
826C2C2×#1062320211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11C2×#2415
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
2. C22×#66931C2semidirect
4. C22×#66930C2semidirect
5. #13072038C2direct (N × H)
6. C2×#10622565C2semidirect
7. C2×#10622566C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622598C2semidirect
11. C2×#10622260C2semidirect
12. C2×#10622585C2semidirect
13. C2×#10622564C2semidirect
14. C2×#10622557C2semidirect
15. C2×#10622555C2semidirect
48. C2×#66931C22semidirect
49. C2×#66931C22semidirect
51. C2×#66930C22semidirect
62. #10622598C22semidirect
63. #10622585C22semidirect
64. #10622566C22semidirect
65. #10622565C22semidirect
66. #10622564C22semidirect
67. #10622557C22semidirect
68. #10622555C22semidirect
69. #10622260C22semidirect
70. #10622259C22semidirect
136. C2×Dic11⋊C4D4semidirect
265. Dic11⋊C4C2×D4semidirect
565. C2×C11#2415semidirect
681. C11C2×#2415semidirect
819. C2#13072038direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C22×D4×Dic112
C22×#669302
#130720382
C2×#106225652
C2×#106225662
C2×#106228352
C2×#106222592
C2×#106225982
C2×#106222602
C2×#106225852
C2×#106225642
C2×#106225572
C2×#106225552
C2×C11×#3942
C2×#241511