Finite Group Databasebeta

← C2×#13072521 #14921887

Subgroups — C2×#13072521 #14921887

Order 2816.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13072521C2116yesmaximal, direct product factor
4C2×#10622272C211yesmaximal, characteristic, complemented
5C2×#10622607C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic
8C2×#10622553C211yesmaximal, characteristic, complemented
9C2×#10622266C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic, complemented
13C2×#10622556C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66936—28no—
43C2×#66936C2218yescomplemented
44C2×(C22⋊D11)⋊C4—28no—
45C2×(C22⋊D11)⋊C4C2218yescomplemented
46C11×#388C2218yescomplemented
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#10622607C2218yescomplemented
58#10622600C2218yescomplemented
59#10622574C2218yescomplemented
60#10622573C2218yes—
61#10622571C2218yescomplemented
62#10622556C2218yescomplemented
63#10622553C2218yescomplemented
64C4×(C2×D11)⋊C4C2218yescomplemented
65#10622278C2218yescomplemented
66#10622278C2218yescomplemented
67#10622272C2218yescomplemented
68#10622266C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—24no—
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11C2314yes—
85C22×C22⋊D11C2314yes—
86C23×Dic11—24no—
87C23×Dic11—24no—
88C23×Dic11—42no—
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2314yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C22×D44—24no—
97C22×D44—24no—
98C22×D44—42no—
99C22×D44C2314yes—
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—24no—
103C22×C4×D11—24no—
104C22×C4×D11—42no—
105C22×C4×D11—42no—
106C22×C4×D11C2314yes—
107C22×C4×D11C2314yes—
108C2×C11×C4⋊C4—42no—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4D418yescomplemented
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C42×C11—42no—
117C2×C42×C11C2314yes—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11C2314yes—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—24no—
122C2×(C2×D11)⋊C4—24no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4—42no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×C4⋊Dic11—24no—
137C2×C4⋊Dic11—24no—
138C2×C4⋊Dic11C2314yes—
139C2×C4⋊Dic11C2314yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—24no—
145C2×C4×Dic11C2314yes—
146#66936—232no—
147(C22⋊D11)⋊C4—232no—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2457—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11C2×D414yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11#4114yes—
181C23×D11#4114yes—
182C23×D11C2412yes—
183C23×D11C2412yes—
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×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C2×C22⋊D11—232no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—28no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—416no—
216C22×Dic11—28no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—28no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—44no—
235C22×Dic11—416no—
236C22×Dic11#4114yes—
237C22×Dic11#4114yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×D44—28no—
245C2×D44—28no—
246C2×D44—44no—
247C2×D44—416no—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—28no—
251C2×C4×D11—28no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11—416no—
255C2×C4×D11—416no—
256C11×C4⋊C4—44no—
257C11×C22⋊C4—44no—
258C11×C22⋊C4—44no—
259C11×C22⋊C4C2×D4116yescomplemented
260C42×C11—44no—
261C22⋊Dic11—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—28no—
271C4⋊Dic11—28no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274C4×Dic11—28no—
275C22×#123—111no—
276C22×C4×D4—111no—
277#2457—1116no—
278C2×#400—111no—
279C2×#396—111no—
280C2×#394—111no—
281C2×#392—111no—
282C2×#388—111no—
283C2×#388D1111yescharacteristic, complemented
284C2×#387—111no—
285C2×#386—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#381—111no—
289C2×#380—111no—
290C2×C4×C22⋊C4—111no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11C22×D414yes—
305C23×C11C22×D412yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11C2×#4112yes—
309C23×C11C2×#4112yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C11H(5,𝔽2)12yes—
312C23×C11C2511yescharacteristic
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—28no—
317C22×D11—28no—
318C22×D11—28no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11C2×#4114yes—
340C22×D11C2×#4114yes—
341C2×C4×C11—28no—
342C2×C4×C11—28no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11C22×D414yes—
364C2×C4×C11C22×D414yes—
365C22⋊D11—232no—
366C22⋊D11—416no—
367C2×Dic11—28no—
368C2×Dic11—28no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—416no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11C2×#4114yes—
391C2×Dic11C2×#4114yes—
392D44—416no—
393C4×D11—416no—
394C4×D11—416no—
395C23×D4—111no—
396C23×D4—111no—
397C23×D4—111no—
398C24×C4—111no—
399C24×C4—111no—
400C24×C4—111no—
401C2×#123—118no—
402C2×#123—228no—
403C2×C4×D4—118no—
404C2×C4×D4—228no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4C2×D1111yescharacteristic
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C42—111no—
423C22×C42C2×D1111yescharacteristic
424#400—118no—
425#396—118no—
426#394—118no—
427#392—118no—
428#388—118no—
429#388C2×D1118yescomplemented
430#387—118no—
431#386—118no—
432#386—118no—
433#386—118no—
434#381—118no—
435#380—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—416no—
455C22×C11#52514yes—
456C22×C11#52914yes—
457C22×C11#54014yes—
458C22×C11#54614yes—
459C22×C11#54614yes—
460C22×C11#55114yes—
461C22×C11#55314yes—
462C22×C11C23×D411yescharacteristic
463C22×C11C22×#4111yescharacteristic
464C22×C11C22×#4111yescharacteristic
465C22×C11C22×#4111yescharacteristic
466C22×C11C22×#4111yescharacteristic
467C22×C11C2×H(5,𝔽2)11yescharacteristic
468C22×C11C2×H(5,𝔽2)11yescharacteristic
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—24no—
473C2×D11—24no—
474C2×D11—24no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—416no—
484C2×D11—416no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491Dic11—24no—
492Dic11—24no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C25—111no—
498C25—111no—
499C25C22×D1111yescharacteristic
500C22×D4—114no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—224no—
510C22×D4—442no—
511C22×D4—442no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—114no—
519C23×C4—114no—
520C23×C4—114no—
521C23×C4—224no—
522C23×C4—224no—
523C23×C4—224no—
524C23×C4—224no—
525C23×C4—224no—
526C23×C4—224no—
527C23×C4—442no—
528C23×C4—442no—
529C23×C4—442no—
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536#123—2232no—
537C4×D4—2232no—
538C2×C4⋊C4—42no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—114no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—224no—
546C2×C4⋊C4—224no—
547C2×C4⋊C4C22×D1114yes—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4D4418yescomplemented
569C2×C22⋊C4C22×D1114yes—
570C2×C22⋊C4C22×D1114yes—
571C2×C22⋊C4C22×D1114yes—
572C2×C42—42no—
573C2×C42—114no—
574C2×C42—224no—
575C2×C42C22×D1114yes—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584#95C22×D1114yes—
585#95C22×D1114yes—
586C2×C11—44no—
587C2×C11#245718yescomplemented
588C2×C11C2×#52511yescharacteristic
589C2×C11C2×#52911yescharacteristic
590C2×C11C2×#54011yescharacteristic
591C2×C11C2×#54611yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#55111yescharacteristic
594C2×C11C2×#55311yescharacteristic
595D11—44no—
596D11—44no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—114no—
604C24—114no—
605C24—112no—
606C24—112no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24—222no—
619C24C2×D4414yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C2×D4—228no—
623C2×D4—228no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—2232no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—444no—
631C2×D4—4416no—
632C2×D4—444no—
633C2×D4—4416no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—114no—
651C22×C4—114no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—228no—
659C22×C4—228no—
660C22×C4—228no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—228no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—228no—
679C22×C4—228no—
680C22×C4—444no—
681C22×C4—444no—
682C22×C4—4416no—
683C22×C4—4416no—
684C22×C4—444no—
685C22×C4—4416no—
686C22×C4C2×D4414yes—
687C22×C4C2×D4414yes—
688C22×C4C23×D1112yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1112yes—
694C4⋊C4—44no—
695C4⋊C4—228no—
696C4⋊C4—228no—
697C4⋊C4—228no—
698C4⋊C4—228no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—228no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C22⋊C4C2×D44116yescomplemented
711C42—44no—
712C42—228no—
713C11C2×#245711yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—114no—
728C23—114no—
729C23—228no—
730C23—228no—
731C23—228no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—228no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—228no—
746C23—228no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23C22×D4414yes—
756C23C22×D4412yes—
757C23#6703712yes—
758C23#6703712yes—
759C23#41×D1112yes—
760C23#41×D1112yes—
761C23#41×D1112yes—
762C23#41×D1112yes—
763C23C24×D1111yescharacteristic
764D4—2232no—
765D4—4416no—
766D4—4416no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—114no—
790C2×C4—114no—
791C2×C4—228no—
792C2×C4—228no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—4416no—
810C2×C4—4416no—
811C2×C4—4416no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4—444no—
816C2×C4C22×D4414yes—
817C2×C4C22×D4414yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—416no—
826C22—224no—
827C22—224no—
828C22—224no—
829C22—224no—
830C22—224no—
831C22—224no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—4416no—
838C22—4416no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22#1062305514yes—
843C22#1062308514yes—
844C22#1062308514yes—
845C22#1062314614yes—
846C22#1062319214yes—
847C22#1062321014yes—
848C22#1062323714yes—
849C22C23×D4411yescharacteristic
850C22C2×#6703711yescharacteristic
851C22C2×#6703711yescharacteristic
852C22C2×#41×D1111yescharacteristic
853C22C2×#41×D1111yescharacteristic
854C22C2×#41×D1111yescharacteristic
855C22C2×#41×D1111yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—224no—
863C4—224no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—444no—
870C2—444no—
871C2#1307252118yesdirect product factor
872C2C2×#1062305511yescharacteristic
873C2C2×#1062323711yescharacteristic
874C2C2×#1062314611yescharacteristic
875C2C2×#1062308511yescharacteristic
876C2C2×#1062308511yescharacteristic
877C2C2×#1062321011yescharacteristic
878C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#388D11
hypocenterC11C2×#2457
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13072521C2direct (N × H)
4. C2×#10622272C2semidirect
5. C2×#10622607C2semidirect
6. C2×#10622574C2semidirect
8. C2×#10622553C2semidirect
9. C2×#10622266C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622571C2semidirect
13. C2×#10622556C2semidirect
14. C2×#10622600C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#388C2semidirect
43. C2×#66936C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
46. C11×#388C22semidirect
57. #10622607C22semidirect
58. #10622600C22semidirect
59. #10622574C22semidirect
61. #10622571C22semidirect
62. #10622556C22semidirect
63. #10622553C22semidirect
64. C4×(C2×D11)⋊C4C22semidirect
65. #10622278C22semidirect
66. #10622278C22semidirect
67. #10622272C22semidirect
68. #10622266C22semidirect
112. C2×C11×C22⋊C4D4semidirect
259. C11×C22⋊C4C2×D4semidirect
283. C2×#388D11semidirect
429. #388C2×D11semidirect
568. C2×C22⋊C4D44semidirect
587. C2×C11#2457semidirect
710. C22⋊C4C2×D44semidirect
713. C11C2×#2457semidirect
871. C2#13072521direct (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×(C22⋊D11)⋊C42
#130725212
C2×#106222722
C2×#106226072
C2×#106225742
C2×#106225732
C2×#106225532
C2×#106222662
C2×#106222782
C2×#106225712
C2×#106225562
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×C11×#3882
C2×#245711