Finite Group Databasebeta

← C2×#13073729 #14923925

Subgroups — C2×#13073729 #14923925

Order 2816.

2834 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×#66943C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic
3#13073729C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622561C211yesmaximal, characteristic, complemented
6C2×#10622607C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic
8C2×#10622570C211yesmaximal, characteristic
9C2×#10622260C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622553C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66943—28no—
45C2×#66943C2218yescomplemented
46C2×#66936—28no—
47C2×#66936C2218yes—
48C11×#388C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622607C2218yescomplemented
58#10622574C2218yes—
59#10622570C2218yes—
60#10622564C2218yescomplemented
61#10622561C2218yescomplemented
62#10622558C2218yescomplemented
63#10622553C2218yescomplemented
64C4×C4⋊Dic11C2218yescomplemented
65#10622281C2218yescomplemented
66#10622279C2218yescomplemented
67#10622271C2218yescomplemented
68#10622260C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—24no—
78C22×C22⋊D11—24no—
79C22×C22⋊D11—42no—
80C22×C22⋊D11C2314yes—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C22×C4×D11—24no—
89C22×C4×D11—24no—
90C22×C4×D11—42no—
91C22×C4×D11C2314yes—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C22⋊C4—24no—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C42×C11—24no—
101C2×C42×C11C2314yes—
102C2×C22⋊Dic11—24no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—42no—
105C2×C22⋊Dic11C2314yes—
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×(C2×D11)⋊C4—24no—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4—24no—
112C2×(C2×D11)⋊C4—24no—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×C4⋊Dic11—24no—
119C2×C4⋊Dic11—24no—
120C2×C4⋊Dic11—24no—
121C2×C4⋊Dic11D418yes—
122C2×C4⋊Dic11C2314yes—
123C2×C4⋊Dic11C2314yes—
124C2×C4⋊Dic11C2314yes—
125C2×C4⋊Dic11C2314yes—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4—24no—
128C2×Dic11⋊C4—24no—
129C2×Dic11⋊C4—24no—
130C2×Dic11⋊C4—42no—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×C4×Dic11—24no—
137C2×C4×Dic11—42no—
138C2×C4×Dic11—42no—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142#66943—232no—
143#66936—232no—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C2×#2558—111nomaximal, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11C2412yes—
161C24×C11C2411yescharacteristic
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11#4114yes—
169C23×D11C2412yes—
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—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11C2×D414yes—
186C22×C4×C11#4114yes—
187C22×C4×C11#4114yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C2×C22⋊D11—28no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—44no—
197C2×C22⋊D11—416no—
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×Dic11C2×D414yes—
217C22×Dic11C2×D414yes—
218C22×Dic11#4114yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C2×C4×D11—28no—
227C2×C4×D11—28no—
228C2×C4×D11—44no—
229C2×C4×D11—416no—
230C11×C4⋊C4—28no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C11×C22⋊C4—28no—
234C42×C11—28no—
235C22⋊Dic11—28no—
236C22⋊Dic11—28no—
237C22⋊Dic11—44no—
238(C2×D11)⋊C4—28no—
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—28no—
243C4⋊Dic11—28no—
244C4⋊Dic11—28no—
245C4⋊Dic11—28no—
246C4⋊Dic11C2×D4116yes—
247Dic11⋊C4—28no—
248Dic11⋊C4—28no—
249Dic11⋊C4—28no—
250Dic11⋊C4—28no—
251Dic11⋊C4—44no—
252C4×Dic11—28no—
253C4×Dic11—44no—
254C4×Dic11—44no—
255C22×#125—111no—
256C22×#123—111no—
257#2558—1116no—
258C2×#400—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×#388D1111yescharacteristic, complemented
268C2×#385—111no—
269C2×C4×C4⋊C4—111no—
270C2×C4×C22⋊C4—111no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—44no—
279C23×C11—44no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11—44no—
284C23×C11—44no—
285C23×C11C22×D412yes—
286C23×C11C2×#4112yes—
287C23×C11C2×#4112yes—
288C23×C11C2×#4112yes—
289C23×C11C2×#4112yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C112−1+412yes—
292C23×C11C2511yescharacteristic
293C22×D11—28no—
294C22×D11—28no—
295C22×D11—28no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11C2×#4114yes—
307C2×C4×C11—28no—
308C2×C4×C11—28no—
309C2×C4×C11—28no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
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—22no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11—44no—
328C2×C4×C11C22×D414yes—
329C2×C4×C11C2×#4114yes—
330C2×C4×C11C2×#4114yes—
331C22⋊D11—416no—
332C2×Dic11—28no—
333C2×Dic11—28no—
334C2×Dic11—28no—
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×Dic11C22×D414yes—
358C2×Dic11C22×D414yes—
359C2×Dic11C2×#4114yes—
360C4×D11—416no—
361C23×D4—111no—
362C24×C4—111no—
363C2×#125—118no—
364C2×#125—228no—
365C2×#123—118no—
366C2×#123—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⋊C4C2×D1111yescharacteristic
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×C42C2×D1111yescharacteristic
392#400—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#388C2×D1118yescomplemented
402#385—118no—
403C4×C4⋊C4—118no—
404C4×C22⋊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—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—88no—
421C22×C11#52914yes—
422C22×C11#53214yes—
423C22×C11#53914yes—
424C22×C11#54614yes—
425C22×C11#54814yes—
426C22×C11#55214yes—
427C22×C11#55314yes—
428C22×C11C23×D411yescharacteristic
429C22×C11C22×#4111yescharacteristic
430C22×C11C22×#4111yescharacteristic
431C22×C11C22×#4111yescharacteristic
432C22×C11C22×#4111yescharacteristic
433C22×C11C2×H(5,𝔽2)11yescharacteristic
434C22×C11C2×2−1+411yescharacteristic
435C2×D11—24no—
436C2×D11—24no—
437C2×D11—24no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—416no—
443C4×C11—24no—
444C4×C11—24no—
445C4×C11—24no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11—42no—
449Dic11—24no—
450Dic11—24no—
451Dic11—24no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455Dic11—42no—
456C25—111no—
457C25C22×D1111yescharacteristic
458C22×D4—114no—
459C22×D4—224no—
460C22×D4—224no—
461C22×D4—442no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—114no—
470C23×C4—224no—
471C23×C4—224no—
472C23×C4—442no—
473C23×C4C22×D1111yescharacteristic
474C23×C4C22×D1111yescharacteristic
475C23×C4C22×D1111yescharacteristic
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1111yescharacteristic
478C23×C4C22×D1111yescharacteristic
479#125—2232no—
480#123—2232no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—118no—
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—114no—
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—442no—
500C2×C4⋊C4C22×D1114yes—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
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—24no—
524C2×C42—114no—
525C2×C42—114no—
526C2×C42—114no—
527C2×C42—224no—
528C2×C42—442no—
529C2×C42—442no—
530C2×C42C22×D1114yes—
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—82no—
540C2×C11#255818yescomplemented
541C2×C11C2×#52911yescharacteristic
542C2×C11C2×#53211yescharacteristic
543C2×C11C2×#53911yescharacteristic
544C2×C11C2×#54611yescharacteristic
545C2×C11C2×#54811yescharacteristic
546C2×C11C2×#55211yescharacteristic
547C2×C11C2×#55311yescharacteristic
548D11—44no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—114no—
557C24—112no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24—222no—
562C24—222no—
563C24—222no—
564C24C23×D1112yes—
565C24C23×D1111yescharacteristic
566C2×D4—228no—
567C2×D4—228no—
568C2×D4—444no—
569C2×D4—4416no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—114no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—228no—
596C22×C4—228no—
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—444no—
616C22×C4—4416no—
617C22×C4#433914yes—
618C22×C4D4×D1114yes—
619C22×C4#434114yes—
620C22×C4C23×D1112yes—
621C22×C4C23×D1112yes—
622C22×C4C23×D1112yes—
623C22×C4C23×D1112yes—
624C22×C4C23×D1112yes—
625C22×C4C23×D1112yes—
626C4⋊C4—28no—
627C4⋊C4—1116no—
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—28no—
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—28no—
648C42—228no—
649C42—444no—
650C42—444no—
651C11C2×#255811yescharacteristic, complemented, Sylow
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—114no—
667C23—228no—
668C23—228no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—228no—
676C23—444no—
677C23—444no—
678C23—444no—
679C23—444no—
680C23C2×#433912yes—
681C23C2×D4×D1112yes—
682C23C2×#434112yes—
683C23#41×D1112yes—
684C23#41×D1112yes—
685C23#6704212yes—
686C23#6704312yes—
687C23C24×D1111yescharacteristic
688D4—4416no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—28no—
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—22no—
706C2×C4—22no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—114no—
711C2×C4—114no—
712C2×C4—114no—
713C2×C4—228no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—228no—
721C2×C4—228no—
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—4416no—
735C2×C4—444no—
736C2×C4—444no—
737C2×C4—444no—
738C2×C4—444no—
739C2×C4C2×#433914yes—
740C2×C4C2×D4×D1114yes—
741C2×C4C2×#434114yes—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—88no—
750C22—224no—
751C22—224no—
752C22—224no—
753C22—442no—
754C22—442no—
755C22—4416no—
756C22—442no—
757C22—442no—
758C22#1062306114yes—
759C22#1062308314yes—
760C22#1062308814yes—
761C22#1062312714yes—
762C22#1062319614yes—
763C22#1062320714yes—
764C22#1062323914yes—
765C22C22×#433911yescharacteristic
766C22C22×D4×D1111yescharacteristic
767C22C22×#434111yescharacteristic
768C22C2×#41×D1111yescharacteristic
769C22C2×#41×D1111yescharacteristic
770C22C2×#6704211yescharacteristic
771C22C2×#6704311yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—224no—
779C4—224no—
780C4—224no—
781C4—442no—
782C4—442no—
783C4—442no—
784C4—442no—
785C2—82no—
786C2—444no—
787C2#1307372918yesdirect product factor
788C2C2×#1062308811yescharacteristic
789C2C2×#1062312711yescharacteristic
790C2C2×#1062319611yescharacteristic
791C2C2×#1062320711yescharacteristic
792C2C2×#1062308311yescharacteristic
793C2C2×#1062323911yescharacteristic
794C2C2×#1062306111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#388D11
hypocenterC11C2×#2558
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
3. #13073729C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622607C2semidirect
9. C2×#10622260C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622553C2semidirect
13. C2×#10622281C2semidirect
14. C2×C4×C4⋊Dic11C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#388C2semidirect
45. C2×#66943C22semidirect
48. C11×#388C22semidirect
57. #10622607C22semidirect
60. #10622564C22semidirect
61. #10622561C22semidirect
62. #10622558C22semidirect
63. #10622553C22semidirect
64. C4×C4⋊Dic11C22semidirect
65. #10622281C22semidirect
66. #10622279C22semidirect
67. #10622271C22semidirect
68. #10622260C22semidirect
267. C2×#388D11semidirect
401. #388C2×D11semidirect
540. C2×C11#2558semidirect
651. C11C2×#2558semidirect
787. C2#13073729direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669432
C22×#669362
#130737292
C2×#106222712
C2×#106225612
C2×#106226072
C2×#106225742
C2×#106225702
C2×#106222602
C2×#106225582
C2×#106225642
C2×#106225532
C2×#106222812
C2×C4×C4⋊Dic112
C2×#106222792
C2×C11×#3882
C2×#255811