Finite Group Databasebeta

← C2×#13074209 #14924423

Subgroups — C2×#13074209 #14924423

Order 2816.

2898 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C211yesmaximal, characteristic, complemented
2C22×#66979C211yesmaximal, characteristic, complemented
3#13074209C2116yesmaximal, direct product factor
4C2×#10622274C211yesmaximal, characteristic, complemented
5C2×#10622561C211yesmaximal, characteristic, complemented
6C2×#10622561C211yesmaximal, characteristic, complemented
7C2×#10622835C211yesmaximal, characteristic
8C2×#10622834C211yesmaximal, characteristic
9C2×#10622260C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic, complemented
11C2×#10622557C211yesmaximal, characteristic, complemented
12C2×#10622557C211yesmaximal, characteristic, complemented
13C2×#10622266C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×#10622262C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C2×#66979—28no—
31C2×#66979C2218yescomplemented
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66932—28no—
47C2×#66932C2218yescomplemented
48C11×#386C2218yes—
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51#10622835C2218yes—
52#10622834C2218yes—
53#10622823C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622564C2218yescomplemented
61#10622561C2218yescomplemented
62#10622561C2218yescomplemented
63#10622557C2218yescomplemented
64#10622557C2218yescomplemented
65#10622274C2218yescomplemented
66#10622266C2218yescomplemented
67#10622262C2218yescomplemented
68#10622260C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C22×D4×C11—24no—
72C22×D4×C11—24no—
73C22×D4×C11—42no—
74C22×D4×C11C2314yes—
75C23×C4×C11—24no—
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—42no—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—24no—
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⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2314yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114#66979—232no—
115C2×C4⋊Dic11—24no—
116C2×C4⋊Dic11—24no—
117C2×C4⋊Dic11—24no—
118C2×C4⋊Dic11—24no—
119C2×C4⋊Dic11C2314yes—
120C2×C4⋊Dic11C2314yes—
121C2×C4⋊Dic11C2314yes—
122C2×C4⋊Dic11C2314yes—
123C2×Dic11⋊C4—24no—
124C2×Dic11⋊C4—24no—
125C2×Dic11⋊C4—24no—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4—24no—
128C2×Dic11⋊C4—42no—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×C4×Dic11—24no—
136C2×C4×Dic11—42no—
137C2×C4×Dic11—42no—
138C2×C4×Dic11D418yescomplemented
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2314yes—
143#66932—232no—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C2×#2601—111nomaximal, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11#4114yes—
167C24×C11C2412yes—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C2×D4×C11—28no—
171C2×D4×C11—28no—
172C2×D4×C11—44no—
173C2×D4×C11—416no—
174C22×C4×C11—232no—
175C22×C4×C11—22no—
176C22×C4×C11—28no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—28no—
183C22×C4×C11—28no—
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×C11C2×D414yes—
191C22×C4×C11#4114yes—
192C22×C4×C11#4114yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
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—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×Dic11C2×D414yes—
220C22×Dic11C2×D414yes—
221C22×Dic11#4114yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C11×C22⋊C4—28no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—44no—
233C22⋊Dic11—28no—
234C22⋊Dic11—28no—
235C22⋊Dic11—28no—
236C22⋊Dic11—28no—
237C22⋊Dic11—28no—
238C22⋊Dic11—28no—
239C22⋊Dic11—28no—
240C22⋊Dic11—44no—
241C4⋊Dic11—28no—
242C4⋊Dic11—28no—
243C4⋊Dic11—28no—
244C4⋊Dic11—28no—
245Dic11⋊C4—28no—
246Dic11⋊C4—28no—
247Dic11⋊C4—28no—
248Dic11⋊C4—28no—
249Dic11⋊C4—28no—
250Dic11⋊C4—44no—
251C4×Dic11—28no—
252C4×Dic11—44no—
253C4×Dic11—44no—
254C4×Dic11C2×D4116yescomplemented
255C22×#126—111no—
256C22×#117—111no—
257#2601—1116no—
258C2×#398—111no—
259C2×#396—111no—
260C2×#396—111no—
261C2×#394—111no—
262C2×#390—111no—
263C2×#389—111no—
264C2×#388—111no—
265C2×#388—111no—
266C2×#388—111no—
267C2×#387—111no—
268C2×#386D1111yescharacteristic
269C2×#385—111no—
270C2×C4×C4⋊C4—111no—
271C23×C11—28no—
272C23×C11—28no—
273C23×C11—28no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11—44no—
290C23×C11—44no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11—44no—
294C23×C11—44no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11C22×D412yes—
299C23×C11C2×#4112yes—
300C23×C11C2×#4114yes—
301C23×C11C2×#4112yes—
302C23×C11C2×#4112yes—
303C23×C11C2×#4112yes—
304C23×C11H(5,𝔽2)12yes—
305C23×C112−1+412yes—
306C23×C11C2511yescharacteristic
307D4×C11—416no—
308C2×C4×C11—232no—
309C2×C4×C11—28no—
310C2×C4×C11—28no—
311C2×C4×C11—28no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11C22×D414yes—
327C2×C4×C11C2×#4114yes—
328C2×C4×C11C2×#4114yes—
329C2×Dic11—28no—
330C2×Dic11—28no—
331C2×Dic11—28no—
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—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—44no—
354C2×Dic11—44no—
355C2×Dic11—44no—
356C2×Dic11—44no—
357C2×Dic11—44no—
358C2×Dic11C22×D414yes—
359C2×Dic11C22×D414yes—
360C2×Dic11C2×#4114yes—
361C23×D4C2×D1111yescharacteristic
362C24×C4C2×D1111yescharacteristic
363C2×#126—118no—
364C2×#126—228no—
365C2×#117—118no—
366C2×#117—228no—
367C22×C4⋊C4—111no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4—111no—
376C22×C4⋊C4—111no—
377C22×C22⋊C4—111no—
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4—111no—
381C22×C22⋊C4—111no—
382C22×C22⋊C4—111no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4—111no—
385C22×C22⋊C4C2×D1111yescharacteristic
386C22×C22⋊C4C2×D1111yescharacteristic
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C42—111no—
389C22×C42—111no—
390C22×C42—111no—
391C22×C42—111no—
392#398—118no—
393#396—118no—
394#396—118no—
395#394—118no—
396#390—118no—
397#389—118no—
398#388—118no—
399#388—118no—
400#388—118no—
401#387—118no—
402#386C2×D1118yes—
403#385—118no—
404C4×C4⋊C4—118no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95C2×D1111yescharacteristic
412C2×#95C2×D1111yescharacteristic
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—416no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—42no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—88no—
429C22×C11#52514yes—
430C22×C11#53214yes—
431C22×C11#53714yes—
432C22×C11#55114yes—
433C22×C11#55214yes—
434C22×C11#55314yes—
435C22×C11#55614yes—
436C22×C11C23×D411yescharacteristic
437C22×C11C22×#4111yescharacteristic
438C22×C11C22×#4111yescharacteristic
439C22×C11C22×#4111yescharacteristic
440C22×C11C22×#4111yescharacteristic
441C22×C11C2×H(5,𝔽2)11yescharacteristic
442C22×C11C2×2−1+411yescharacteristic
443C4×C11—24no—
444C4×C11—24no—
445C4×C11—24no—
446C4×C11—42no—
447C4×C11—42no—
448Dic11—24no—
449Dic11—24no—
450Dic11—24no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455Dic11—42no—
456C25C22×D1111yescharacteristic
457C25C22×D1111yescharacteristic
458C22×D4—24no—
459C22×D4—24no—
460C22×D4—42no—
461C22×D4C22×D1114yes—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4C22×D1114yes—
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479#126—2232no—
480#117—2232no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—224no—
492C2×C4⋊C4—224no—
493C2×C4⋊C4—224no—
494C2×C4⋊C4—224no—
495C2×C4⋊C4—224no—
496C2×C4⋊C4—224no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—442no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—224no—
513C2×C22⋊C4—224no—
514C2×C22⋊C4—224no—
515C2×C22⋊C4—224no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—442no—
520C2×C22⋊C4C22×D1114yes—
521C2×C22⋊C4C22×D1114yes—
522C2×C22⋊C4C22×D1114yes—
523C2×C42—118no—
524C2×C42—114no—
525C2×C42—114no—
526C2×C42—114no—
527C2×C42—114no—
528C2×C42—224no—
529C2×C42—442no—
530C2×C42—442no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95C22×D1114yes—
538#95C22×D1114yes—
539C2×C11—44no—
540C2×C11—82no—
541C2×C11#260118yescomplemented
542C2×C11C2×#52511yescharacteristic
543C2×C11C2×#53211yescharacteristic
544C2×C11C2×#53711yescharacteristic
545C2×C11C2×#55111yescharacteristic
546C2×C11C2×#55211yescharacteristic
547C2×C11C2×#55311yescharacteristic
548C2×C11C2×#55611yescharacteristic
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24#434114yes—
563C24C23×D1112yes—
564C24C23×D1112yes—
565C24C23×D1111yescharacteristic
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—44no—
569C2×D4—416no—
570C22×C4—232no—
571C22×C4—22no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—114no—
587C22×C4—114no—
588C22×C4—114no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4#433914yes—
619C22×C4D4×D1114yes—
620C22×C4#434114yes—
621C22×C4C23×D1112yes—
622C22×C4C23×D1112yes—
623C22×C4C23×D1112yes—
624C22×C4C23×D1112yes—
625C22×C4C23×D1112yes—
626C4⋊C4—228no—
627C4⋊C4—228no—
628C4⋊C4—228no—
629C4⋊C4—228no—
630C4⋊C4—228no—
631C4⋊C4—228no—
632C4⋊C4—228no—
633C4⋊C4—228no—
634C4⋊C4—228no—
635C4⋊C4—444no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—228no—
640C22⋊C4—228no—
641C22⋊C4—228no—
642C22⋊C4—228no—
643C22⋊C4—228no—
644C22⋊C4—228no—
645C22⋊C4—228no—
646C22⋊C4—444no—
647C42—1116no—
648C42—228no—
649C42—444no—
650C42—444no—
651C11C2×#260111yescharacteristic, complemented, Sylow
652C23—28no—
653C23—28no—
654C23—28no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23C2×#433912yes—
680C23C2×D4×D1112yes—
681C23C2×#434114yes—
682C23C2×#434112yes—
683C23C2×#434112yes—
684C23#6703712yes—
685C23#41×D1112yes—
686C23#6704312yes—
687C23C24×D1111yescharacteristic
688D4—416no—
689C2×C4—232no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—114no—
708C2×C4—114no—
709C2×C4—114no—
710C2×C4—228no—
711C2×C4—228no—
712C2×C4—228no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—444no—
735C2×C4—444no—
736C2×C4—444no—
737C2×C4—444no—
738C2×C4—444no—
739C2×C4C2×#433914yes—
740C2×C4C2×D4×D1114yes—
741C2×C4C2×#434114yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—416no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—88no—
758C22#1062302614yes—
759C22#1062307314yes—
760C22#1062307914yes—
761C22#1062311714yes—
762C22#1062313914yes—
763C22#1062314514yes—
764C22#1062318114yes—
765C22C22×#433911yescharacteristic
766C22C22×D4×D1111yescharacteristic
767C22C22×#434111yescharacteristic
768C22C22×#434111yescharacteristic
769C22C2×#6703711yescharacteristic
770C22C2×#41×D1111yescharacteristic
771C22C2×#6704311yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—224no—
778C4—224no—
779C4—224no—
780C4—442no—
781C4—442no—
782C4—442no—
783C4—442no—
784C4—442no—
785C2—44no—
786C2—82no—
787C2#1307420918yesdirect product factor
788C2C2×#1062311711yescharacteristic
789C2C2×#1062307911yescharacteristic
790C2C2×#1062313911yescharacteristic
791C2C2×#1062302611yescharacteristic
792C2C2×#1062318111yescharacteristic
793C2C2×#1062314511yescharacteristic
794C2C2×#1062307311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11C2×#2601
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
2. C22×#66979C2semidirect
3. #13074209C2direct (N × H)
4. C2×#10622274C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622561C2semidirect
9. C2×#10622260C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622557C2semidirect
12. C2×#10622557C2semidirect
13. C2×#10622266C2semidirect
14. C2×#10622823C2semidirect
15. C2×#10622262C2semidirect
31. C2×#66979C22semidirect
47. C2×#66932C22semidirect
53. #10622823C22semidirect
60. #10622564C22semidirect
61. #10622561C22semidirect
62. #10622561C22semidirect
63. #10622557C22semidirect
64. #10622557C22semidirect
65. #10622274C22semidirect
66. #10622266C22semidirect
67. #10622262C22semidirect
68. #10622260C22semidirect
138. C2×C4×Dic11D4semidirect
254. C4×Dic11C2×D4semidirect
541. C2×C11#2601semidirect
651. C11C2×#2601semidirect
787. C2#13074209direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C22×#669792
#130742092
C2×#106222742
C2×#106225612
C2×#106228352
C2×#106228342
C2×#106222602
C2×#106225642
C2×#106225572
C2×#106222662
C2×#106228232
C2×#106222622
C2×C11×#3862
C2×#260111