Finite Group Databasebeta

← C2×#13072707 #14922285

Subgroups — C2×#13072707 #14922285

Order 2816.

3006 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic
2C22×#66930C211yesmaximal, characteristic, complemented
3#13072707C2116yesmaximal, direct product factor
4C2×#10622271C211yesmaximal, characteristic, complemented
5C2×#10622289C211yesmaximal, characteristic, complemented
6C2×#10622572C211yesmaximal, characteristic
7C2×#10622260C211yesmaximal, characteristic, complemented
8C2×#10622585C211yesmaximal, characteristic, complemented
9C2×#10622282C211yesmaximal, characteristic, complemented
10C2×#10622557C211yesmaximal, characteristic, complemented
11C2×#10622268C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic
13C2×#10622559C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#397C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66936—28no—
43C2×#66936C2218yes—
44C2×#66930—28no—
45C2×#66930C2218yescomplemented
46C11×#397C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
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#10622602C2218yescomplemented
58#10622585C2218yescomplemented
59#10622572C2218yes—
60#10622571C2218yes—
61#10622559C2218yescomplemented
62#10622557C2218yescomplemented
63#10622289C2218yescomplemented
64#10622282C2218yescomplemented
65#10622279C2218yescomplemented
66#10622271C2218yescomplemented
67#10622268C2218yescomplemented
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×Dic11—24no—
82C23×Dic11—24no—
83C23×Dic11—24no—
84C23×Dic11C2314yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×C4×D11—24no—
93C22×C4×D11—24no—
94C22×C4×D11—42no—
95C22×C4×D11C2314yes—
96C2×C11×C4⋊C4—42no—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C22⋊C4—24no—
99C2×C11×C22⋊C4—24no—
100C2×C11×C22⋊C4—42no—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11D418yes—
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⋊Dic11C2314yes—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4—24no—
123C2×Dic11⋊C4—24no—
124C2×Dic11⋊C4—24no—
125C2×Dic11⋊C4—24no—
126C2×Dic11⋊C4—42no—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×C4×Dic11—24no—
135C2×C4×Dic11—24no—
136C2×C4×Dic11—42no—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140#66936—232no—
141#66930—232no—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C11×#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C2×#2470—111nomaximal, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11C2×D414yes—
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×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
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—232no—
199C22×Dic11—28no—
200C22×Dic11—28no—
201C22×Dic11—28no—
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×Dic11C2×D414yes—
219C22×Dic11C2×D414yes—
220C22×Dic11#4114yes—
221C22×Dic11#4114yes—
222C22×Dic11#4114yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C2×C4×D11—28no—
231C2×C4×D11—28no—
232C2×C4×D11—44no—
233C2×C4×D11—416no—
234C11×C4⋊C4—44no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—28no—
237C11×C22⋊C4—44no—
238C22⋊Dic11—28no—
239C22⋊Dic11C2×D4116yes—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4—28no—
245C4⋊Dic11—28no—
246Dic11⋊C4—28no—
247Dic11⋊C4—28no—
248Dic11⋊C4—28no—
249Dic11⋊C4—28no—
250Dic11⋊C4—28no—
251Dic11⋊C4—28no—
252Dic11⋊C4—44no—
253C4×Dic11—28no—
254C4×Dic11—28no—
255C4×Dic11—44no—
256C22×#123—111no—
257C22×#117—111no—
258#2470—1116no—
259C2×#400—111no—
260C2×#397D1111yescharacteristic, complemented
261C2×#396—111no—
262C2×#394—111no—
263C2×#389—111no—
264C2×#389—111no—
265C2×#388—111no—
266C2×#388—111no—
267C2×#387—111no—
268C2×#386—111no—
269C2×#385—111no—
270C2×#385—111no—
271C2×C4×C22⋊C4—111no—
272C23×C11—28no—
273C23×C11—28no—
274C23×C11—28no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11—44no—
284C23×C11—44no—
285C23×C11C22×D414yes—
286C23×C11C22×D412yes—
287C23×C11C2×#4112yes—
288C23×C11C2×#4112yes—
289C23×C11C2×#4112yes—
290C23×C11C2×#4112yes—
291C23×C11H(5,𝔽2)12yes—
292C23×C112−1+412yes—
293C23×C11C2511yescharacteristic
294C22×D11—28no—
295C22×D11—28no—
296C22×D11—28no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11—44no—
307C22×D11C2×#4114yes—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
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—22no—
326C2×C4×C11—44no—
327C2×C4×C11—44no—
328C2×C4×C11—44no—
329C2×C4×C11—44no—
330C2×C4×C11—44no—
331C2×C4×C11—44no—
332C22⋊D11—416no—
333C2×Dic11—232no—
334C2×Dic11—28no—
335C2×Dic11—28no—
336C2×Dic11—28no—
337C2×Dic11—28no—
338C2×Dic11—28no—
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—22no—
354C2×Dic11—22no—
355C2×Dic11—44no—
356C2×Dic11—44no—
357C2×Dic11C22×D414yes—
358C2×Dic11C22×D414yes—
359C2×Dic11C2×#4114yes—
360C2×Dic11C2×#4114yes—
361C2×Dic11C2×#4114yes—
362C4×D11—416no—
363C23×D4—111no—
364C24×C4—111no—
365C24×C4—111no—
366C2×#123—118no—
367C2×#123—228no—
368C2×#117—118no—
369C2×#117—228no—
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×C4⋊C4—111no—
378C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
386C22×C22⋊C4C2×D1111yescharacteristic
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4C2×D1111yescharacteristic
389C22×C42—111no—
390C22×C42—111no—
391C22×C42—111no—
392#400—118no—
393#397C2×D1118yescomplemented
394#396—118no—
395#394—118no—
396#389—118no—
397#389—118no—
398#388—118no—
399#388—118no—
400#387—118no—
401#386—118no—
402#385—118no—
403#385—118no—
404C4×C22⋊C4—118no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95—111no—
412C2×#95C2×D1111yescharacteristic
413C2×#95C2×D1111yescharacteristic
414C2×#95C2×D1111yescharacteristic
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—24no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—416no—
423C22×C11#52514yes—
424C22×C11#52914yes—
425C22×C11#54214yes—
426C22×C11#54614yes—
427C22×C11#54714yes—
428C22×C11#55214yes—
429C22×C11#55314yes—
430C22×C11C23×D411yescharacteristic
431C22×C11C22×#4111yescharacteristic
432C22×C11C22×#4111yescharacteristic
433C22×C11C22×#4111yescharacteristic
434C22×C11C22×#4111yescharacteristic
435C22×C11C2×H(5,𝔽2)11yescharacteristic
436C22×C11C2×2−1+411yescharacteristic
437C2×D11—24no—
438C2×D11—24no—
439C2×D11—24no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—416no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11—42no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—42no—
451Dic11—24no—
452Dic11—24no—
453Dic11—24no—
454Dic11—24no—
455Dic11—24no—
456Dic11—42no—
457Dic11—42no—
458C25—111no—
459C25C22×D1111yescharacteristic
460C22×D4—114no—
461C22×D4—224no—
462C22×D4—224no—
463C22×D4—442no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—114no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—114no—
473C23×C4—224no—
474C23×C4—224no—
475C23×C4—224no—
476C23×C4—224no—
477C23×C4—224no—
478C23×C4—442no—
479C23×C4C22×D1111yescharacteristic
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1111yescharacteristic
482C23×C4C22×D1111yescharacteristic
483C23×C4C22×D1111yescharacteristic
484C23×C4C22×D1111yescharacteristic
485#123—2232no—
486#117—2232no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4—114no—
496C2×C4⋊C4—224no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—224no—
501C2×C4⋊C4—224no—
502C2×C4⋊C4—224no—
503C2×C4⋊C4—442no—
504C2×C4⋊C4C22×D1114yes—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—118no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4C22×D1114yes—
523C2×C22⋊C4C22×D1114yes—
524C2×C22⋊C4C22×D1114yes—
525C2×C42—114no—
526C2×C42—114no—
527C2×C42—114no—
528C2×C42—224no—
529C2×C42—224no—
530C2×C42—442no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95—114no—
538#95C22×D1114yes—
539#95C22×D1114yes—
540#95C22×D1114yes—
541C2×C11—44no—
542C2×C11#247018yescomplemented
543C2×C11C2×#52511yescharacteristic
544C2×C11C2×#52911yescharacteristic
545C2×C11C2×#54211yescharacteristic
546C2×C11C2×#54611yescharacteristic
547C2×C11C2×#54711yescharacteristic
548C2×C11C2×#55211yescharacteristic
549C2×C11C2×#55311yescharacteristic
550D11—44no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—114no—
558C24—112no—
559C24—222no—
560C24—222no—
561C24—222no—
562C24—222no—
563C24—222no—
564C24—222no—
565C24D4×D1114yes—
566C24C23×D1112yes—
567C24C23×D1111yescharacteristic
568C2×D4—228no—
569C2×D4—228no—
570C2×D4—444no—
571C2×D4—4416no—
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—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—114no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—114no—
594C22×C4—114no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—228no—
603C22×C4—228no—
604C22×C4—228no—
605C22×C4—228no—
606C22×C4—2232no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—228no—
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—222no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—222no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—444no—
625C22×C4—4416no—
626C22×C4C23×D1112yes—
627C22×C4C23×D1112yes—
628C22×C4C23×D1112yes—
629C22×C4C23×D1112yes—
630C22×C4C23×D1112yes—
631C22×C4C23×D1112yes—
632C4⋊C4—44no—
633C4⋊C4—228no—
634C4⋊C4—228no—
635C4⋊C4—228no—
636C4⋊C4—228no—
637C4⋊C4—228no—
638C4⋊C4—228no—
639C4⋊C4—228no—
640C4⋊C4—444no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—44no—
644C22⋊C4—1116no—
645C22⋊C4—228no—
646C22⋊C4—228no—
647C22⋊C4—228no—
648C22⋊C4—228no—
649C22⋊C4—228no—
650C22⋊C4—228no—
651C42—228no—
652C42—228no—
653C42—444no—
654C11C2×#247011yescharacteristic, complemented, Sylow
655C23—28no—
656C23—28no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—114no—
669C23—228no—
670C23—228no—
671C23—228no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23—222no—
677C23—222no—
678C23—444no—
679C23—444no—
680C23—444no—
681C23—444no—
682C23C2×D4×D1114yes—
683C23C2×D4×D1112yes—
684C23#6703712yes—
685C23#41×D1112yes—
686C23#41×D1112yes—
687C23#41×D1112yes—
688C23#41×D1112yes—
689C23#6704312yes—
690C23C24×D1111yescharacteristic
691D4—4416no—
692C2×C4—22no—
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—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—114no—
717C2×C4—114no—
718C2×C4—114no—
719C2×C4—114no—
720C2×C4—114no—
721C2×C4—2232no—
722C2×C4—228no—
723C2×C4—228no—
724C2×C4—228no—
725C2×C4—228no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—228no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—4416no—
744C2×C4—444no—
745C2×C4—444no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—416no—
753C22—42no—
754C22—224no—
755C22—224no—
756C22—224no—
757C22—442no—
758C22—4416no—
759C22—442no—
760C22—442no—
761C22—442no—
762C22#1062314114yes—
763C22#1062318614yes—
764C22#1062318714yes—
765C22#1062319214yes—
766C22#1062320014yes—
767C22#1062323714yes—
768C22#1062323914yes—
769C22C22×D4×D1111yescharacteristic
770C22C2×#6703711yescharacteristic
771C22C2×#41×D1111yescharacteristic
772C22C2×#41×D1111yescharacteristic
773C22C2×#41×D1111yescharacteristic
774C22C2×#41×D1111yescharacteristic
775C22C2×#6704311yescharacteristic
776C4—42no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—224no—
783C4—224no—
784C4—224no—
785C4—224no—
786C4—224no—
787C4—442no—
788C4—442no—
789C2—44no—
790C2—444no—
791C2#1307270718yesdirect product factor
792C2C2×#1062318711yescharacteristic
793C2C2×#1062323711yescharacteristic
794C2C2×#1062320011yescharacteristic
795C2C2×#1062314111yescharacteristic
796C2C2×#1062318611yescharacteristic
797C2C2×#1062323911yescharacteristic
798C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#397D11
hypocenterC11C2×#2470
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C22×#66930C2semidirect
3. #13072707C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622289C2semidirect
7. C2×#10622260C2semidirect
8. C2×#10622585C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622557C2semidirect
11. C2×#10622268C2semidirect
13. C2×#10622559C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#397C2semidirect
45. C2×#66930C22semidirect
46. C11×#397C22semidirect
57. #10622602C22semidirect
58. #10622585C22semidirect
61. #10622559C22semidirect
62. #10622557C22semidirect
63. #10622289C22semidirect
64. #10622282C22semidirect
65. #10622279C22semidirect
66. #10622271C22semidirect
67. #10622268C22semidirect
68. #10622260C22semidirect
260. C2×#397D11semidirect
393. #397C2×D11semidirect
542. C2×C11#2470semidirect
654. C11C2×#2470semidirect
791. C2#13072707direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669302
#130727072
C2×#106222712
C2×#106222892
C2×#106225722
C2×#106222602
C2×#106225852
C2×#106222822
C2×#106225572
C2×#106222682
C2×#106225712
C2×#106225592
C2×#106226022
C2×#106222792
C2×C11×#3972
C2×#247011