Finite Group Databasebeta

← C2×#13072741 #14921349

Subgroups — C2×#13072741 #14921349

Order 2816.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66989C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3C23×C22⋊Dic11C211yesmaximal, characteristic, complemented
4#13072741C2116yesmaximal, direct product factor
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622835C211yesmaximal, characteristic, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622560C211yesmaximal, characteristic, complemented
9C2×#10622834C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622558C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622860C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C22×C11×#120C211yesmaximal, characteristic
17C26×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic, complemented
24C2×C11×#120—28no—
25C2×C11×#120C2218yes—
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11—28no—
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic
40C22×C22⋊Dic11C2218yescomplemented
41C22×C22⋊Dic11C2211yescharacteristic, complemented
42C22×C22⋊Dic11C2211yescharacteristic, complemented
43C22×C22⋊Dic11C2211yescharacteristic, complemented
44C22×C22⋊Dic11C2211yescharacteristic, complemented
45C2×#66989—28no—
46C2×#66989C2218yescomplemented
47C22×C4⋊Dic11C2211yescharacteristic, complemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50C22×C4×Dic11C2211yescharacteristic, complemented
51C22×C4×Dic11C2211yescharacteristic, complemented
52C2×#66931—28no—
53C2×#66931C2218yescomplemented
54#10622860C2218yescomplemented
55#10622835C2218yescomplemented
56#10622835C2218yescomplemented
57#10622834C2218yescomplemented
58#10622833C2218yescomplemented
59#10622833C2218yescomplemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62C2×C11⋊#95C2211yescharacteristic, complemented
63C2×C11⋊#95C2211yescharacteristic, complemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65C2×C11⋊#95C2211yescharacteristic, complemented
66#10622566C2218yescomplemented
67#10622560C2218yescomplemented
68#10622558C2218yescomplemented
69#10622558C2218yescomplemented
70C22⋊C4×Dic11C2218yescomplemented
71C25×C11—24no—
72C25×C11—24no—
73C25×C11—24no—
74C25×C11—24no—
75C25×C11—24no—
76C25×C11—42no—
77C25×C11—42no—
78C25×C11C2311yescharacteristic
79C25×C11C2311yescharacteristic
80C25×C11C2311yescharacteristic
81C25×C11C2314yes—
82C25×C11C2311yescharacteristic
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11—24no—
86C22×D4×C11—24no—
87C22×D4×C11—24no—
88C22×D4×C11—24no—
89C22×D4×C11—24no—
90C22×D4×C11—42no—
91C22×D4×C11—42no—
92C22×D4×C11C2314yes—
93C22×D4×C11C2314yes—
94C22×D4×C11C2314yes—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×Dic11—24no—
99C23×Dic11—24no—
100C23×Dic11—24no—
101C23×Dic11—24no—
102C23×Dic11—42no—
103C23×Dic11—42no—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2314yes—
111C23×Dic11C2314yes—
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×Dic22—24no—
115C22×Dic22—24no—
116C22×Dic22—42no—
117C22×Dic22C2314yescomplemented
118C11×#120—232no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4D418yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—24no—
130C2×C22⋊Dic11—24no—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11—232no—
135C2×C22⋊Dic11—42no—
136C2×C22⋊Dic11—42no—
137C2×C22⋊Dic11—42no—
138C2×C22⋊Dic11—42no—
139C2×C22⋊Dic11D418yescomplemented
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144C2×C22⋊Dic11C2314yes—
145C2×C22⋊Dic11C2314yes—
146C2×C22⋊Dic11C2314yes—
147C2×C22⋊Dic11C2314yes—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2314yes—
150C2×C22⋊Dic11C2314yescomplemented
151C2×C22⋊Dic11C2314yescomplemented
152C2×C22⋊Dic11C2314yescomplemented
153C2×C22⋊Dic11C2314yescomplemented
154#66989—232no—
155C2×C4⋊Dic11—24no—
156C2×C4⋊Dic11C2314yescomplemented
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4—24no—
159C2×Dic11⋊C4C2314yescomplemented
160C2×Dic11⋊C4C2314yescomplemented
161C2×C4×Dic11—24no—
162C2×C4×Dic11—42no—
163C2×C4×Dic11C2314yescomplemented
164C2×C4×Dic11C2314yescomplemented
165#66931—232no—
166C11⋊#95C2314yescomplemented
167C11⋊#95C2314yescomplemented
168C11⋊#95C2314yescomplemented
169C11⋊#95C2314yescomplemented
170C11⋊#95C2314yescomplemented
171C11⋊#95C2314yescomplemented
172C2×#2472—111nomaximal, Sylow
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—232no—
178C24×C11—28no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—28no—
183C24×C11—28no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11—22no—
193C24×C11—22no—
194C24×C11—28no—
195C24×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—22no—
199C24×C11—28no—
200C24×C11—22no—
201C24×C11—22no—
202C24×C11—44no—
203C24×C11—44no—
204C24×C11—416no—
205C24×C11—416no—
206C24×C11—416no—
207C24×C11—416no—
208C24×C11—416no—
209C24×C11—416no—
210C24×C11C2×D414yes—
211C24×C11C2×D414yes—
212C24×C11#4114yes—
213C24×C11#4114yes—
214C24×C11#4114yes—
215C24×C11C2412yes—
216C24×C11C2412yes—
217C24×C11C2412yes—
218C24×C11C2412yes—
219C24×C11C2411yescharacteristic
220C2×D4×C11—28no—
221C2×D4×C11—28no—
222C2×D4×C11—28no—
223C2×D4×C11—28no—
224C2×D4×C11—28no—
225C2×D4×C11—28no—
226C2×D4×C11—28no—
227C2×D4×C11—44no—
228C2×D4×C11—44no—
229C2×D4×C11—416no—
230C2×D4×C11—416no—
231C2×D4×C11—416no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11C2×D414yes—
240C22×C4×C11C2×D414yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×Dic11—28no—
245C22×Dic11—28no—
246C22×Dic11—22no—
247C22×Dic11—28no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—28no—
261C22×Dic11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—44no—
271C22×Dic11—44no—
272C22×Dic11—416no—
273C22×Dic11—416no—
274C22×Dic11C2×D414yes—
275C22×Dic11C2×D414yes—
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283C22×Dic11C2412yes—
284C2×Dic22—28no—
285C2×Dic22—28no—
286C2×Dic22—44no—
287C2×Dic22—416no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4C2×D4116yes—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—28no—
296C22⋊Dic11—28no—
297C22⋊Dic11—28no—
298C22⋊Dic11—28no—
299C22⋊Dic11—28no—
300C22⋊Dic11—44no—
301C22⋊Dic11—44no—
302C22⋊Dic11—44no—
303C22⋊Dic11—44no—
304C22⋊Dic11C2×D4116yescomplemented
305C4⋊Dic11—28no—
306Dic11⋊C4—28no—
307Dic11⋊C4—28no—
308C4×Dic11—28no—
309C4×Dic11—44no—
310C22×#124—111no—
311C22×C22⋊Q8—111no—
312C22×#120D1111yescharacteristic
313C23×C22⋊C4—111no—
314#2472—1116no—
315C2×#397—111no—
316C2×#394—111no—
317C2×#394—111no—
318C2×#393—111no—
319C2×#390—111no—
320C2×#388—111no—
321C2×#388—111no—
322C2×#386—111no—
323C2×#386—111no—
324C2×#379—111no—
325C2×C4×C22⋊C4—111no—
326C23×C11—28no—
327C23×C11—28no—
328C23×C11—28no—
329C23×C11—28no—
330C23×C11—28no—
331C23×C11—28no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—232no—
337C23×C11—28no—
338C23×C11—28no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—28no—
342C23×C11—28no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—416no—
363C23×C11—416no—
364C23×C11—416no—
365C23×C11—416no—
366C23×C11—416no—
367C23×C11—4128no—
368C23×C11—44no—
369C23×C11—44no—
370C23×C11—416no—
371C23×C11—44no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—44no—
375C23×C11—44no—
376C23×C11—44no—
377C23×C11—44no—
378C23×C11—44no—
379C23×C11—44no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11—44no—
383C23×C11—44no—
384C23×C11#124116yescomplemented
385C23×C11C22×D414yes—
386C23×C11C22×D412yes—
387C23×C11C22×D414yes—
388C23×C11C22×D412yes—
389C23×C11C2×#4114yes—
390C23×C11C2×#4114yes—
391C23×C11C2×#4114yes—
392C23×C11C2×#4112yes—
393C23×C11C2×#4112yes—
394C23×C11C2×#4112yes—
395C23×C11H(5,𝔽2)12yes—
396C23×C11H(5,𝔽2)12yes—
397C23×C11C2511yescharacteristic
398D4×C11—416no—
399D4×C11—416no—
400D4×C11—416no—
401C2×C4×C11—28no—
402C2×C4×C11—28no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—44no—
411C2×C4×C11C22×D414yes—
412C2×C4×C11C22×D414yes—
413C2×Dic11—28no—
414C2×Dic11—28no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—416no—
438C2×Dic11—416no—
439C2×Dic11—44no—
440C2×Dic11—44no—
441C2×Dic11—44no—
442C2×Dic11—44no—
443C2×Dic11—44no—
444C2×Dic11—44no—
445C2×Dic11C22×D414yes—
446C2×Dic11C22×D414yes—
447Dic22—416no—
448C26C2×D1111yescharacteristic
449C23×Q8—111no—
450C23×D4C2×D1111yescharacteristic
451C23×D4C2×D1111yescharacteristic
452C23×D4C2×D1111yescharacteristic
453C24×C4—111no—
454C24×C4—111no—
455C2×#124—118no—
456C2×#124—228no—
457C2×C22⋊Q8—118no—
458C2×C22⋊Q8—228no—
459C2×#120—28no—
460C2×#120C2×D1118yes—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4—111no—
470C22×C22⋊C4—111no—
471C22×C22⋊C4—118no—
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C22⋊C4—111no—
477C22×C22⋊C4—111no—
478C22×C22⋊C4—111no—
479C22×C22⋊C4—228no—
480C22×C22⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1111yescharacteristic
483C22×C42—111no—
484C22×C42—111no—
485#397—118no—
486#394—118no—
487#394—118no—
488#393—118no—
489#390—118no—
490#388—118no—
491#388—118no—
492#386—118no—
493#386—118no—
494#379—118no—
495C4×C22⋊C4—118no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C22×C11—24no—
503C22×C11—24no—
504C22×C11—24no—
505C22×C11—24no—
506C22×C11—24no—
507C22×C11—24no—
508C22×C11—232no—
509C22×C11—24no—
510C22×C11—24no—
511C22×C11—24no—
512C22×C11—24no—
513C22×C11—24no—
514C22×C11—24no—
515C22×C11—464no—
516C22×C11—42no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—416no—
525C22×C11—416no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—42no—
532C22×C11—42no—
533C22×C11—88no—
534C22×C11#52514yes—
535C22×C11C2×#12414yes—
536C22×C11C2×#12418yescomplemented
537C22×C11#53814yes—
538C22×C11D4214yes—
539C22×C11#54614yes—
540C22×C11#54614yes—
541C22×C11#55114yes—
542C22×C11C23×D411yescharacteristic
543C22×C11C23×D411yescharacteristic
544C22×C11C22×#4111yescharacteristic
545C22×C11C22×#4111yescharacteristic
546C22×C11C22×#4111yescharacteristic
547C22×C11C2×H(5,𝔽2)11yescharacteristic
548C22×C11C2×H(5,𝔽2)11yescharacteristic
549C4×C11—24no—
550C4×C11—24no—
551C4×C11—42no—
552Dic11—24no—
553Dic11—24no—
554Dic11—42no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—24no—
561C25—24no—
562C25—24no—
563C25—24no—
564C25—24no—
565C25—42no—
566C25—42no—
567C25C22×D1111yescharacteristic
568C25C22×D1111yescharacteristic
569C25C22×D1111yescharacteristic
570C25C22×D1114yes—
571C25C22×D1111yescharacteristic
572C22×Q8—114no—
573C22×Q8—224no—
574C22×Q8—224no—
575C22×Q8—442no—
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—24no—
579C22×D4—24no—
580C22×D4—24no—
581C22×D4—24no—
582C22×D4—24no—
583C22×D4—42no—
584C22×D4—42no—
585C22×D4C22×D1114yes—
586C22×D4C22×D1114yes—
587C22×D4C22×D1114yes—
588C23×C4—111no—
589C23×C4—111no—
590C23×C4—111no—
591C23×C4—111no—
592C23×C4—111no—
593C23×C4—111no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—114no—
597C23×C4—114no—
598C23×C4—224no—
599C23×C4—224no—
600C23×C4—224no—
601C23×C4—224no—
602C23×C4—442no—
603C23×C4—442no—
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#124—2232no—
608C22⋊Q8—2232no—
609#120—232no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—224no—
614C2×C4⋊C4—224no—
615C2×C4⋊C4—224no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—118no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—114no—
626C2×C22⋊C4—114no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—114no—
633C2×C22⋊C4—2232no—
634C2×C22⋊C4—224no—
635C2×C22⋊C4—224no—
636C2×C22⋊C4—224no—
637C2×C22⋊C4—224no—
638C2×C22⋊C4—224no—
639C2×C22⋊C4—224no—
640C2×C22⋊C4—224no—
641C2×C22⋊C4—224no—
642C2×C22⋊C4—224no—
643C2×C22⋊C4—442no—
644C2×C22⋊C4—442no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4—442no—
647C2×C22⋊C4C22⋊D1118yes—
648C2×C22⋊C4C22×D1114yes—
649C2×C22⋊C4C22×D1114yes—
650C2×C22⋊C4C22×D1114yes—
651C2×C42—114no—
652C2×C42—114no—
653C2×C42—224no—
654C2×C42—442no—
655#95—114no—
656#95—114no—
657#95—114no—
658#95—114no—
659#95—114no—
660#95—114no—
661C2×C11—28no—
662C2×C11—44no—
663C2×C11—44no—
664C2×C11—82no—
665C2×C11#247218yescomplemented
666C2×C11C2×#52511yescharacteristic
667C2×C11C22×#12411yescharacteristic
668C2×C11C2×#53811yescharacteristic
669C2×C11C2×D4211yescharacteristic
670C2×C11C2×#54611yescharacteristic
671C2×C11C2×#54611yescharacteristic
672C2×C11C2×#55111yescharacteristic
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—232no—
678C24—28no—
679C24—22no—
680C24—28no—
681C24—28no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—28no—
698C24—22no—
699C24—22no—
700C24—28no—
701C24—22no—
702C24—44no—
703C24—44no—
704C24—416no—
705C24—416no—
706C24—416no—
707C24—416no—
708C24—416no—
709C24—416no—
710C24D4×D1114yes—
711C24#434114yes—
712C24#434114yes—
713C24#434114yes—
714C24C2×C22⋊D1114yes—
715C24C23×D1112yes—
716C24C23×D1112yes—
717C24C23×D1112yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×Q8—228no—
721C2×Q8—228no—
722C2×Q8—444no—
723C2×Q8—4416no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—416no—
734C2×D4—416no—
735C2×D4—416no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—114no—
744C22×C4—114no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—112no—
748C22×C4—112no—
749C22×C4—112no—
750C22×C4—112no—
751C22×C4—112no—
752C22×C4—112no—
753C22×C4—228no—
754C22×C4—228no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—228no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—222no—
771C22×C4—222no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—222no—
775C22×C4—222no—
776C22×C4—222no—
777C22×C4—222no—
778C22×C4—228no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4—4416no—
782C22×C4—4416no—
783C22×C4C2×C22⋊D1114yes—
784C22×C4C2×C22⋊D1114yes—
785C22×C4C23×D1112yes—
786C22×C4C23×D1112yes—
787C22×C4C23×D1112yes—
788C4⋊C4—228no—
789C4⋊C4—228no—
790C4⋊C4—228no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—1116no—
794C22⋊C4—228no—
795C22⋊C4—228no—
796C22⋊C4—228no—
797C22⋊C4—228no—
798C22⋊C4—228no—
799C22⋊C4—228no—
800C22⋊C4—228no—
801C22⋊C4—228no—
802C22⋊C4—228no—
803C22⋊C4—444no—
804C22⋊C4—444no—
805C22⋊C4—444no—
806C22⋊C4—444no—
807C22⋊C4C2×C22⋊D11116yes—
808C42—228no—
809C42—444no—
810C11C2×#247211yescharacteristic, complemented, Sylow
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—232no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—416no—
848C23—416no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—4128no—
853C23—44no—
854C23—44no—
855C23—416no—
856C23—44no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23—44no—
869C23#66989116yescomplemented
870C23C2×D4×D1114yes—
871C23C2×D4×D1112yes—
872C23C2×#434114yes—
873C23C2×#434114yes—
874C23C2×#434114yes—
875C23C2×#434112yes—
876C23C2×#434112yes—
877C23C2×#434112yes—
878C23#6703712yes—
879C23#6703712yes—
880C23C22×C22⋊D1114yes—
881C23C22×C22⋊D1112yes—
882C23C24×D1111yescharacteristic
883Q8—4416no—
884D4—416no—
885D4—416no—
886D4—416no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—44no—
897C2×C4—114no—
898C2×C4—114no—
899C2×C4—228no—
900C2×C4—228no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—222no—
923C2×C4—4416no—
924C2×C4—4416no—
925C2×C4—444no—
926C2×C4—444no—
927C2×C4—444no—
928C2×C4—444no—
929C2×C4—444no—
930C2×C4—444no—
931C2×C4C22×C22⋊D1114yes—
932C2×C4C22×C22⋊D1114yes—
933C22—24no—
934C22—24no—
935C22—232no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—464no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—416no—
953C22—416no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—88no—
965C22#1062311714yes—
966C22#1062311814yes—
967C22#1062312214yes—
968C22#1062312414yes—
969C22C2×#6698914yes—
970C22C2×#6698918yescomplemented
971C22D4×C22⋊D1114yes—
972C22#1062333714yes—
973C22C22×D4×D1111yescharacteristic
974C22C22×#434111yescharacteristic
975C22C22×#434111yescharacteristic
976C22C22×#434111yescharacteristic
977C22C2×#6703711yescharacteristic
978C22C2×#6703711yescharacteristic
979C22C23×C22⋊D1111yescharacteristic
980C4—24no—
981C4—24no—
982C4—42no—
983C4—224no—
984C4—224no—
985C4—442no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—82no—
995C2#1307274118yesdirect product factor
996C2C2×#1062311711yescharacteristic
997C2C22×#6698911yescharacteristic
998C2C2×#1062312411yescharacteristic
999C2C2×D4×C22⋊D1111yescharacteristic
1000C2C2×#1062312211yescharacteristic
1001C2C2×#1062333711yescharacteristic
1002C2C2×#1062311811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC22×C11×#120C2
socleC24×C11C24
hypercenterC22×#120D11
hypocenterC11C2×#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C22×#66989C2semidirect
2. C22×#66931C2semidirect
3. C23×C22⋊Dic11C2semidirect
4. #13072741C2direct (N × H)
5. C2×#10622566C2semidirect
6. C2×#10622835C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622558C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622860C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
23. C23×Dic22C22semidirect
40. C22×C22⋊Dic11C22semidirect
41. C22×C22⋊Dic11C22semidirect
42. C22×C22⋊Dic11C22semidirect
43. C22×C22⋊Dic11C22semidirect
44. C22×C22⋊Dic11C22semidirect
46. C2×#66989C22semidirect
47. C22×C4⋊Dic11C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×Dic11⋊C4C22semidirect
50. C22×C4×Dic11C22semidirect
51. C22×C4×Dic11C22semidirect
53. C2×#66931C22semidirect
54. #10622860C22semidirect
55. #10622835C22semidirect
56. #10622835C22semidirect
57. #10622834C22semidirect
58. #10622833C22semidirect
59. #10622833C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. C2×C11⋊#95C22semidirect
63. C2×C11⋊#95C22semidirect
64. C2×C11⋊#95C22semidirect
65. C2×C11⋊#95C22semidirect
66. #10622566C22semidirect
67. #10622560C22semidirect
68. #10622558C22semidirect
69. #10622558C22semidirect
70. C22⋊C4×Dic11C22semidirect
117. C22×Dic22C23semidirect
139. C2×C22⋊Dic11D4semidirect
150. C2×C22⋊Dic11C23semidirect
151. C2×C22⋊Dic11C23semidirect
152. C2×C22⋊Dic11C23semidirect
153. C2×C22⋊Dic11C23semidirect
156. C2×C4⋊Dic11C23semidirect
159. C2×Dic11⋊C4C23semidirect
160. C2×Dic11⋊C4C23semidirect
163. C2×C4×Dic11C23semidirect
164. C2×C4×Dic11C23semidirect
166. C11⋊#95C23semidirect
167. C11⋊#95C23semidirect
168. C11⋊#95C23semidirect
169. C11⋊#95C23semidirect
170. C11⋊#95C23semidirect
171. C11⋊#95C23semidirect
304. C22⋊Dic11C2×D4semidirect
384. C23×C11#124semidirect
536. C22×C11C2×#124semidirect
665. C2×C11#2472semidirect
810. C11C2×#2472semidirect
869. C23#66989semidirect
970. C22C2×#66989semidirect
995. C2#13072741direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669892
C22×#669312
C23×C22⋊Dic112
#130727412
C2×#106225662
C2×#106228352
C2×#106225602
C2×#106228342
C2×#106225582
C2×#106228332
C2×#106228602
C2×C22⋊C4×Dic112
C22×C11×#1202
C2×#247211