Finite Group Databasebeta

← C2×#13073275 #14922774

Subgroups — C2×#13073275 #14922774

Order 2816.

2442 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073275C2116yesmaximal, direct product factor
2C2×#10622565C211yesmaximal, characteristic, complemented
3C2×#10622561C211yesmaximal, characteristic, complemented
4C2×#10622835C211yesmaximal, characteristic
5C2×#10622586C211yesmaximal, characteristic, complemented
6C2×#10622558C211yesmaximal, characteristic, complemented
7C2×#10622558C211yesmaximal, characteristic, complemented
8C2×#10622558C211yesmaximal, characteristic, complemented
9C2×#10622564C211yesmaximal, characteristic, complemented
10C2×#10622591C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic
12C2×#10622264C211yesmaximal, characteristic, complemented
13C2×#10622263C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C11×#394C2218yes—
41C2×C11×#95C2211yescharacteristic
42#10622835C2218yes—
43#10622833C2218yes—
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622591C2218yescomplemented
56#10622586C2218yescomplemented
57#10622565C2218yescomplemented
58#10622564C2218yescomplemented
59#10622561C2218yescomplemented
60#10622558C2218yescomplemented
61#10622558C2218yescomplemented
62#10622558C2218yescomplemented
63C22⋊C4×Dic11C2218yescomplemented
64C22⋊C4×Dic11C2218yescomplemented
65#10622264C2218yescomplemented
66#10622263C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C22×D4×C11—24no—
70C22×D4×C11—42no—
71C22×D4×C11—42no—
72C22×D4×C11C2314yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×Dic11—24no—
79C23×Dic11—24no—
80C23×Dic11—42no—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2314yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C2×C11×C4⋊C4—42no—
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—42no—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—24no—
102C2×C22⋊Dic11—24no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11—42no—
106C2×C22⋊Dic11—42no—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2314yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×C4⋊Dic11—24no—
115C2×C4⋊Dic11C2314yes—
116C2×Dic11⋊C4—24no—
117C2×Dic11⋊C4—42no—
118C2×Dic11⋊C4—42no—
119C2×Dic11⋊C4—42no—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×C4×Dic11—24no—
125C2×C4×Dic11—24no—
126C2×C4×Dic11—42no—
127C2×C4×Dic11—42no—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132C11×#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C2×#2518—111nomaximal, Sylow
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—22no—
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11#4114yes—
159C24×C11C2412yes—
160C24×C11C2412yes—
161C24×C11C2411yescharacteristic
162C2×D4×C11—28no—
163C2×D4×C11—44no—
164C2×D4×C11—44no—
165C2×D4×C11—416no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
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×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11#4114yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×Dic11—28no—
187C22×Dic11—28no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—44no—
210C22×Dic11—416no—
211C22×Dic11#4114yes—
212C22×Dic11#4114yes—
213C22×Dic11#4114yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C11×C4⋊C4—44no—
223C11×C22⋊C4—28no—
224C11×C22⋊C4—28no—
225C11×C22⋊C4—28no—
226C11×C22⋊C4—44no—
227C22⋊Dic11—28no—
228C22⋊Dic11—28no—
229C22⋊Dic11—28no—
230C22⋊Dic11—28no—
231C22⋊Dic11—28no—
232C22⋊Dic11—44no—
233C22⋊Dic11—44no—
234C4⋊Dic11—28no—
235Dic11⋊C4—28no—
236Dic11⋊C4—44no—
237Dic11⋊C4—44no—
238Dic11⋊C4—44no—
239C4×Dic11—28no—
240C4×Dic11—28no—
241C4×Dic11—44no—
242C4×Dic11—44no—
243#2518—1116no—
244C2×#397—111no—
245C2×#396—111no—
246C2×#394—111no—
247C2×#394D1111yescharacteristic
248C2×#389—111no—
249C2×#388—111no—
250C2×#388—111no—
251C2×#388—111no—
252C2×#388—111no—
253C2×#387—111no—
254C2×#386—111no—
255C2×#383—111no—
256C2×#382—111no—
257C2×C4×C22⋊C4—111no—
258C2×C4×C22⋊C4—111no—
259C23×C11—28no—
260C23×C11—28no—
261C23×C11—28no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11—44no—
284C23×C11—44no—
285C23×C11—44no—
286C23×C11C2×#4114yes—
287C23×C11C2×#4112yes—
288C23×C11C2×#4112yes—
289C23×C11C2×#4112yes—
290C23×C11C2×#4112yes—
291C23×C11C2×#4112yes—
292C23×C11H(5,𝔽2)12yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C11C2511yescharacteristic
295D4×C11—416no—
296C2×C4×C11—28no—
297C2×C4×C11—22no—
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×C11—22no—
311C2×C4×C11—44no—
312C2×C4×C11—44no—
313C2×C4×C11—44no—
314C2×C4×C11—44no—
315C2×C4×C11C2×#4114yes—
316C2×Dic11—28no—
317C2×Dic11—28no—
318C2×Dic11—28no—
319C2×Dic11—22no—
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—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—416no—
341C2×Dic11—44no—
342C2×Dic11—44no—
343C2×Dic11—44no—
344C2×Dic11—44no—
345C2×Dic11—44no—
346C2×Dic11C2×#4114yes—
347C2×Dic11C2×#4114yes—
348C2×Dic11C2×#4114yes—
349C23×D4C2×D1111yescharacteristic
350C24×C4—111no—
351C22×C4⋊C4—111no—
352C22×C4⋊C4—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4C2×D1111yescharacteristic
357C22×C22⋊C4—111no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4C2×D1111yescharacteristic
365C22×C22⋊C4C2×D1111yescharacteristic
366C22×C22⋊C4C2×D1111yescharacteristic
367C22×C22⋊C4C2×D1111yescharacteristic
368C22×C42—111no—
369C22×C42—111no—
370C22×C42—111no—
371C22×C42—111no—
372#397—118no—
373#396—118no—
374#394—118no—
375#394C2×D1118yes—
376#389—118no—
377#388—118no—
378#388—118no—
379#388—118no—
380#388—118no—
381#387—118no—
382#386—118no—
383#383—118no—
384#382—118no—
385C4×C22⋊C4—118no—
386C4×C22⋊C4—118no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95—111no—
396C2×#95—111no—
397C2×#95—111no—
398C2×#95C2×D1111yescharacteristic
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—24no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—416no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—88no—
415C22×C11#52914yes—
416C22×C11#52914yes—
417C22×C11#53814yes—
418C22×C11#55114yes—
419C22×C11#55314yes—
420C22×C11#55314yes—
421C22×C11#55514yes—
422C22×C11C22×#4111yescharacteristic
423C22×C11C22×#4111yescharacteristic
424C22×C11C22×#4111yescharacteristic
425C22×C11C22×#4111yescharacteristic
426C22×C11C22×#4111yescharacteristic
427C22×C11C2×H(5,𝔽2)11yescharacteristic
428C22×C11C2×H(5,𝔽2)11yescharacteristic
429C4×C11—24no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—42no—
434Dic11—24no—
435Dic11—24no—
436Dic11—24no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442C25C22×D1111yescharacteristic
443C25C22×D1111yescharacteristic
444C22×D4—24no—
445C22×D4—42no—
446C22×D4—42no—
447C22×D4C22×D1114yes—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—111no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—114no—
457C23×C4—224no—
458C23×C4—224no—
459C23×C4—442no—
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1111yescharacteristic
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1111yescharacteristic
465C2×C4⋊C4—42no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—224no—
473C2×C4⋊C4—442no—
474C2×C4⋊C4—442no—
475C2×C4⋊C4—442no—
476C2×C4⋊C4C22×D1114yes—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—114no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—114no—
484C2×C22⋊C4—114no—
485C2×C22⋊C4—114no—
486C2×C22⋊C4—114no—
487C2×C22⋊C4—114no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—442no—
494C2×C22⋊C4—442no—
495C2×C22⋊C4C22×D1114yes—
496C2×C22⋊C4C22×D1114yes—
497C2×C22⋊C4C22×D1114yes—
498C2×C22⋊C4C22×D1114yes—
499C2×C42—114no—
500C2×C42—114no—
501C2×C42—114no—
502C2×C42—114no—
503C2×C42—224no—
504C2×C42—224no—
505C2×C42—442no—
506C2×C42—442no—
507#95—114no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95—114no—
514#95—114no—
515#95—114no—
516#95—114no—
517#95—114no—
518#95C22×D1114yes—
519C2×C11—44no—
520C2×C11—82no—
521C2×C11#251818yescomplemented
522C2×C11C2×#52911yescharacteristic
523C2×C11C2×#52911yescharacteristic
524C2×C11C2×#53811yescharacteristic
525C2×C11C2×#55111yescharacteristic
526C2×C11C2×#55311yescharacteristic
527C2×C11C2×#55311yescharacteristic
528C2×C11C2×#55511yescharacteristic
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24#434114yes—
543C24C23×D1112yes—
544C24C23×D1112yes—
545C24C23×D1111yescharacteristic
546C2×D4—28no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—416no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—114no—
565C22×C4—114no—
566C22×C4—114no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—112no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—112no—
575C22×C4—228no—
576C22×C4—228no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—444no—
599C22×C4—4416no—
600C22×C4#434114yes—
601C22×C4C23×D1112yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1112yes—
604C22×C4C23×D1112yes—
605C22×C4C23×D1112yes—
606C4⋊C4—44no—
607C4⋊C4—228no—
608C4⋊C4—228no—
609C4⋊C4—444no—
610C4⋊C4—444no—
611C4⋊C4—444no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—44no—
616C22⋊C4—228no—
617C22⋊C4—228no—
618C22⋊C4—228no—
619C22⋊C4—228no—
620C22⋊C4—228no—
621C22⋊C4—444no—
622C22⋊C4—444no—
623C42—228no—
624C42—228no—
625C42—444no—
626C42—444no—
627C11C2×#251811yescharacteristic, complemented, Sylow
628C23—28no—
629C23—28no—
630C23—28no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23C2×#434114yes—
656C23C2×#434112yes—
657C23C2×#434112yes—
658C23#6703712yes—
659C23#6703712yes—
660C23#41×D1112yes—
661C23#41×D1112yes—
662C23#41×D1112yes—
663C23C24×D1111yescharacteristic
664D4—416no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—114no—
685C2×C4—114no—
686C2×C4—114no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—228no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—228no—
695C2×C4—228no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—4416no—
712C2×C4—444no—
713C2×C4—444no—
714C2×C4—444no—
715C2×C4—444no—
716C2×C4—444no—
717C2×C4C2×#434114yes—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—416no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22#1062312414yes—
735C22#1062313114yes—
736C22#1062313214yes—
737C22#1062314714yes—
738C22#1062318014yes—
739C22#1062319214yes—
740C22#1062321014yes—
741C22C22×#434111yescharacteristic
742C22C22×#434111yescharacteristic
743C22C2×#6703711yescharacteristic
744C22C2×#6703711yescharacteristic
745C22C2×#41×D1111yescharacteristic
746C22C2×#41×D1111yescharacteristic
747C22C2×#41×D1111yescharacteristic
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—224no—
754C4—224no—
755C4—224no—
756C4—442no—
757C4—442no—
758C4—442no—
759C4—442no—
760C4—442no—
761C2—44no—
762C2—82no—
763C2#1307327518yesdirect product factor
764C2C2×#1062318011yescharacteristic
765C2C2×#1062313111yescharacteristic
766C2C2×#1062312411yescharacteristic
767C2C2×#1062321011yescharacteristic
768C2C2×#1062313211yescharacteristic
769C2C2×#1062319211yescharacteristic
770C2C2×#1062314711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11C2×#2518
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13073275C2direct (N × H)
2. C2×#10622565C2semidirect
3. C2×#10622561C2semidirect
5. C2×#10622586C2semidirect
6. C2×#10622558C2semidirect
7. C2×#10622558C2semidirect
8. C2×#10622558C2semidirect
9. C2×#10622564C2semidirect
10. C2×#10622591C2semidirect
12. C2×#10622264C2semidirect
13. C2×#10622263C2semidirect
14. C2×C22⋊C4×Dic11C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
55. #10622591C22semidirect
56. #10622586C22semidirect
57. #10622565C22semidirect
58. #10622564C22semidirect
59. #10622561C22semidirect
60. #10622558C22semidirect
61. #10622558C22semidirect
62. #10622558C22semidirect
63. C22⋊C4×Dic11C22semidirect
64. C22⋊C4×Dic11C22semidirect
65. #10622264C22semidirect
66. #10622263C22semidirect
521. C2×C11#2518semidirect
627. C11C2×#2518semidirect
763. C2#13073275direct (N × H)

Maximal subgroups

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

subgroupindex
#130732752
C2×#106225652
C2×#106225612
C2×#106228352
C2×#106225862
C2×#106225582
C2×#106225642
C2×#106225912
C2×#106228332
C2×#106222642
C2×#106222632
C2×C22⋊C4×Dic112
C2×C11×#3942
C2×#251811