Finite Group Databasebeta

← C2×#13072736 #14921347

Subgroups — C2×#13072736 #14921347

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×#66938C211yesmaximal, characteristic, complemented
2C22×#66977C211yesmaximal, characteristic, complemented
3C22×#67006C211yesmaximal, characteristic
4#13072736C2116yesmaximal, direct product factor
5C2×#10622565C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622560C211yesmaximal, characteristic, complemented
9C2×#10622570C211yesmaximal, characteristic, complemented
10C2×#10622564C211yesmaximal, characteristic, complemented
11C2×#10622557C211yesmaximal, characteristic, complemented
12C2×#10622826C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622860C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
16C23×C11×C22⋊C4C211yesmaximal, characteristic, complemented
17C26×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic, complemented
24C22×C11×C22⋊C4—28no—
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2218yescomplemented
30C2×#67006—28no—
31C2×#67006C2218yes—
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⋊Dic11C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C22×C4⋊Dic11C2211yescharacteristic, complemented
46C2×#66977—28no—
47C2×#66977C2218yescomplemented
48C22×Dic11⋊C4C2211yescharacteristic, complemented
49C22×Dic11⋊C4C2211yescharacteristic, complemented
50C22×C4×Dic11C2211yescharacteristic, complemented
51C22×C4×Dic11C2211yescharacteristic, complemented
52C2×#66938—28no—
53C2×#66938C2218yescomplemented
54#10622860C2218yescomplemented
55#10622826C2218yescomplemented
56#10622826C2218yescomplemented
57C4×C22⋊Dic11C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic, complemented
59C2×C11⋊#95C2211yescharacteristic, complemented
60C2×C11⋊#95C2211yescharacteristic, complemented
61C2×C11⋊#95C2211yescharacteristic, complemented
62C2×C11⋊#95C2211yescharacteristic, complemented
63C2×C11⋊#95C2211yescharacteristic, complemented
64#10622574C2218yescomplemented
65#10622572C2218yescomplemented
66#10622570C2218yescomplemented
67#10622565C2218yescomplemented
68#10622564C2218yescomplemented
69#10622560C2218yescomplemented
70#10622557C2218yescomplemented
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×C11C2314yes—
81C25×C11C2311yescharacteristic
82C24×D11C2311yescharacteristic
83C23×C4×C11—24no—
84C23×C4×C11—24no—
85C23×C4×C11—24no—
86C23×C4×C11—24no—
87C23×C4×C11—42no—
88C23×C4×C11—42no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2314yes—
92C23×C4×C11C2314yes—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—42no—
103C22×C22⋊D11—42no—
104C22×C22⋊D11C2314yes—
105C22×C22⋊D11C2314yes—
106C22×C22⋊D11C2314yes—
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×Dic22—24no—
115C22×Dic22—24no—
116C22×Dic22—42no—
117C22×Dic22C2314yescomplemented
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—24no—
120C2×C11×C22⋊C4—24no—
121C2×C11×C22⋊C4—232no—
122C2×C11×C22⋊C4D418yescomplemented
123C2×C11×C22⋊C4C2314yes—
124C2×C11×C22⋊C4C2314yes—
125C2×C11×C22⋊C4C2314yes—
126C2×C11×C22⋊C4C2314yes—
127#67006—232no—
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—42no—
135C2×C22⋊Dic11—42no—
136C2×C22⋊Dic11D418yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C2314yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144C2×C22⋊Dic11C2314yes—
145C2×C22⋊Dic11C2314yes—
146C2×(C2×D11)⋊C4—24no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4—42no—
149C2×(C2×D11)⋊C4—42no—
150C2×(C2×D11)⋊C4C2314yescomplemented
151C2×(C2×D11)⋊C4C2314yescomplemented
152C2×(C2×D11)⋊C4C2314yescomplemented
153C2×(C2×D11)⋊C4C2314yescomplemented
154C2×C4⋊Dic11—24no—
155C2×C4⋊Dic11C2314yescomplemented
156#66977—232no—
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#66938—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—22no—
179C24×C11—22no—
180C24×C11—28no—
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—28no—
194C24×C11—28no—
195C24×C11—44no—
196C24×C11—44no—
197C24×C11—416no—
198C24×C11—416no—
199C24×C11—416no—
200C24×C11—416no—
201C24×C11—416no—
202C24×C11—416no—
203C24×C11C2×D414yes—
204C24×C11C2×D414yes—
205C24×C11#4114yes—
206C24×C11#4114yes—
207C24×C11#4114yes—
208C24×C11C2412yes—
209C24×C11C2412yes—
210C24×C11C2412yes—
211C24×C11C2411yescharacteristic
212C23×D11—22no—
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—22no—
217C23×D11—22no—
218C23×D11—22no—
219C23×D11C2412yes—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—28no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—28no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—28no—
233C22×C4×C11—28no—
234C22×C4×C11—44no—
235C22×C4×C11—44no—
236C22×C4×C11—416no—
237C22×C4×C11—416no—
238C22×C4×C11C2×D414yes—
239C22×C4×C11C2×D414yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—44no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—416no—
254C2×C22⋊D11—416no—
255C2×C22⋊D11—416no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
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—22no—
271C22×Dic11—22no—
272C22×Dic11—22no—
273C22×Dic11—22no—
274C22×Dic11—22no—
275C22×Dic11C2×D414yes—
276C22×Dic11C2×D414yes—
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⋊C4—28no—
291C11×C22⋊C4C2×D4116yescomplemented
292C22⋊Dic11—28no—
293C22⋊Dic11—28no—
294C22⋊Dic11—28no—
295C22⋊Dic11—28no—
296C22⋊Dic11—28no—
297C22⋊Dic11—28no—
298C22⋊Dic11—44no—
299C22⋊Dic11—44no—
300C22⋊Dic11C2×D4116yes—
301(C2×D11)⋊C4—28no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—44no—
304(C2×D11)⋊C4—44no—
305C4⋊Dic11—28no—
306Dic11⋊C4—28no—
307Dic11⋊C4—28no—
308C4×Dic11—28no—
309C4×Dic11—44no—
310C22×#124—111no—
311C22×C22⋊Q8—111no—
312C22×#120—111no—
313C23×C22⋊C4D1111yescharacteristic, complemented
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—416no—
356C23×C11—416no—
357C23×C11—416no—
358C23×C11—416no—
359C23×C11—416no—
360C23×C11—4128no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11—416no—
364C23×C11—44no—
365C23×C11—44no—
366C23×C11—44no—
367C23×C11—44no—
368C23×C11—44no—
369C23×C11—44no—
370C23×C11#124116yescomplemented
371C23×C11C22×D414yes—
372C23×C11C22×D412yes—
373C23×C11C22×D414yes—
374C23×C11C22×D412yes—
375C23×C11C2×#4114yes—
376C23×C11C2×#4114yes—
377C23×C11C2×#4112yes—
378C23×C11C2×#4112yes—
379C23×C11C2×#4114yes—
380C23×C11C2×#4112yes—
381C23×C11H(5,𝔽2)12yes—
382C23×C11H(5,𝔽2)12yes—
383C23×C11C2511yescharacteristic
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—44no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11—44no—
397C22×D11—44no—
398C2×C4×C11—28no—
399C2×C4×C11—28no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
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—416no—
411C2×C4×C11—416no—
412C2×C4×C11—44no—
413C2×C4×C11—44no—
414C2×C4×C11C22×D414yes—
415C2×C4×C11C22×D414yes—
416C22⋊D11—416no—
417C22⋊D11—416no—
418C22⋊D11—416no—
419C2×Dic11—28no—
420C2×Dic11—28no—
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—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
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×D4—111no—
451C23×D4—111no—
452C23×D4—111no—
453C24×C4C2×D1111yescharacteristic
454C24×C4C2×D1111yescharacteristic
455C2×#124—118no—
456C2×#124—228no—
457C2×C22⋊Q8—118no—
458C2×C22⋊Q8—228no—
459C2×#120—118no—
460C2×#120—228no—
461C22×C4⋊C4—111no—
462C22×C4⋊C4—111no—
463C22×C4⋊C4—111no—
464C22×C22⋊C4—28no—
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—111no—
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⋊C4C2×D1111yescharacteristic
479C22×C22⋊C4C2×D1111yescharacteristic
480C22×C22⋊C4C2×D1111yescharacteristic
481C22×C22⋊C4C2×D1111yescharacteristic
482C22×C22⋊C4C2×D1118yescomplemented
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#52514yes—
527C22×C11C2×#12414yes—
528C22×C11C2×#12418yescomplemented
529C22×C11#53814yes—
530C22×C11D4214yes—
531C22×C11#54614yes—
532C22×C11#54614yes—
533C22×C11#55114yes—
534C22×C11C23×D411yescharacteristic
535C22×C11C23×D411yescharacteristic
536C22×C11C22×#4111yescharacteristic
537C22×C11C22×#4111yescharacteristic
538C22×C11C22×#4111yescharacteristic
539C22×C11C2×H(5,𝔽2)11yescharacteristic
540C22×C11C2×H(5,𝔽2)11yescharacteristic
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—88no—
549C4×C11—24no—
550C4×C11—24no—
551C4×C11—42no—
552C4×C11—42no—
553Dic11—24no—
554Dic11—24no—
555Dic11—42no—
556Dic11—42no—
557Dic11—42no—
558Dic11—42no—
559Dic11—42no—
560C25—24no—
561C25—24no—
562C25—24no—
563C25—24no—
564C25—24no—
565C25—42no—
566C25—42no—
567C25—111no—
568C25C22×D1111yescharacteristic
569C25C22×D1111yescharacteristic
570C25C22×D1114yes—
571C25C22×D1111yescharacteristic
572C22×Q8—114no—
573C22×Q8—224no—
574C22×Q8—224no—
575C22×Q8—442no—
576C22×D4—114no—
577C22×D4—114no—
578C22×D4—114no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—224no—
582C22×D4—224no—
583C22×D4—224no—
584C22×D4—224no—
585C22×D4—224no—
586C22×D4—442no—
587C22×D4—442no—
588C23×C4—24no—
589C23×C4—24no—
590C23×C4—24no—
591C23×C4—24no—
592C23×C4—42no—
593C23×C4—42no—
594C23×C4—111no—
595C23×C4—111no—
596C23×C4—111no—
597C23×C4—111no—
598C23×C4—111no—
599C23×C4—111no—
600C23×C4—111no—
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1114yes—
604C23×C4C22×D1114yes—
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607#124—2232no—
608C22⋊Q8—2232no—
609#120—2232no—
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—24no—
619C2×C22⋊C4—232no—
620C2×C22⋊C4—118no—
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—114no—
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—442no—
643C2×C22⋊C4—442no—
644C2×C22⋊C4—442no—
645C2×C22⋊C4—442no—
646C2×C22⋊C4C22⋊D1118yescomplemented
647C2×C22⋊C4C22×D1114yes—
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#247218yescomplemented
665C2×C11C2×#52511yescharacteristic
666C2×C11C22×#12411yescharacteristic
667C2×C11C2×#53811yescharacteristic
668C2×C11C2×D4211yescharacteristic
669C2×C11C2×#54611yescharacteristic
670C2×C11C2×#54611yescharacteristic
671C2×C11C2×#55111yescharacteristic
672D11—82no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—232no—
678C24—28no—
679C24—28no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—28no—
692C24—22no—
693C24—28no—
694C24—28no—
695C24—44no—
696C24—44no—
697C24—416no—
698C24—416no—
699C24—416no—
700C24—416no—
701C24—416no—
702C24—416no—
703C24—112no—
704C24—222no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—222no—
710C24—222no—
711C24#433914yes—
712C24#433914yes—
713C24D4×D1114yes—
714C24#434114yes—
715C24C2×C22⋊D1114yes—
716C24C23×D1112yes—
717C24C23×D1112yes—
718C24C23×D1112yes—
719C24C23×D1111yescharacteristic
720C2×Q8—228no—
721C2×Q8—228no—
722C2×Q8—444no—
723C2×Q8—4416no—
724C2×D4—228no—
725C2×D4—228no—
726C2×D4—228no—
727C2×D4—228no—
728C2×D4—228no—
729C2×D4—228no—
730C2×D4—228no—
731C2×D4—444no—
732C2×D4—444no—
733C2×D4—4416no—
734C2×D4—4416no—
735C2×D4—4416no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—416no—
753C22×C4—416no—
754C22×C4—114no—
755C22×C4—114no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—112no—
760C22×C4—112no—
761C22×C4—112no—
762C22×C4—112no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
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—222no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4C2×C22⋊D1114yes—
783C22×C4C2×C22⋊D1114yes—
784C22×C4C23×D1112yes—
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—28no—
794C22⋊C4—1116no—
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⋊D11116yescomplemented
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—416no—
841C23—416no—
842C23—416no—
843C23—416no—
844C23—4128no—
845C23—416no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—416no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—44no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—444no—
863C23—444no—
864C23—444no—
865C23—444no—
866C23—444no—
867C23—444no—
868C23—444no—
869C23#66938116yescomplemented
870C23C2×#433914yes—
871C23C2×#433914yes—
872C23C2×#433912yes—
873C23C2×#433912yes—
874C23C2×D4×D1114yes—
875C23C2×D4×D1112yes—
876C23C2×#434114yes—
877C23C2×#434112yes—
878C23#6703712yes—
879C23#6703712yes—
880C23C22×C22⋊D1114yes—
881C23C22×C22⋊D1112yes—
882C23C24×D1111yescharacteristic
883Q8—4416no—
884D4—4416no—
885D4—4416no—
886D4—4416no—
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—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—416no—
900C2×C4—416no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—114no—
904C2×C4—114no—
905C2×C4—228no—
906C2×C4—228no—
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—222no—
924C2×C4—222no—
925C2×C4—222no—
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—416no—
951C22—416no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—888no—
965C22#1062302114yes—
966C22C2×#6693814yes—
967C22C2×#6693818yescomplemented
968C22#1062302514yes—
969C22#1062302614yes—
970C22#1062332214yes—
971C22D4×C22⋊D1114yes—
972C22#1062333714yes—
973C22C22×#433911yescharacteristic
974C22C22×#433911yescharacteristic
975C22C22×D4×D1111yescharacteristic
976C22C22×#434111yescharacteristic
977C22C2×#6703711yescharacteristic
978C22C2×#6703711yescharacteristic
979C22C23×C22⋊D1111yescharacteristic
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—224no—
985C4—224no—
986C4—442no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—882no—
995C2#1307273618yesdirect product factor
996C2C2×#1062332211yescharacteristic
997C2C22×#6693811yescharacteristic
998C2C2×#1062302511yescharacteristic
999C2C2×D4×C22⋊D1111yescharacteristic
1000C2C2×#1062302111yescharacteristic
1001C2C2×#1062333711yescharacteristic
1002C2C2×#1062302611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC23×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC22×#67006C2
hypercenterC23×C22⋊C4D11
hypocenterC11C2×#2472
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×#66977C2semidirect
4. #13072736C2direct (N × H)
5. C2×#10622565C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622564C2semidirect
11. C2×#10622557C2semidirect
12. C2×#10622826C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622860C2semidirect
15. C2×C4×C22⋊Dic11C2semidirect
16. C23×C11×C22⋊C4C2semidirect
23. C23×Dic22C22semidirect
29. C22×C11×C22⋊C4C22semidirect
41. C22×(C2×D11)⋊C4C22semidirect
42. C22×(C2×D11)⋊C4C22semidirect
43. C22×(C2×D11)⋊C4C22semidirect
44. C22×(C2×D11)⋊C4C22semidirect
45. C22×C4⋊Dic11C22semidirect
47. C2×#66977C22semidirect
48. C22×Dic11⋊C4C22semidirect
49. C22×Dic11⋊C4C22semidirect
50. C22×C4×Dic11C22semidirect
51. C22×C4×Dic11C22semidirect
53. C2×#66938C22semidirect
54. #10622860C22semidirect
55. #10622826C22semidirect
56. #10622826C22semidirect
57. C4×C22⋊Dic11C22semidirect
58. C2×C11⋊#95C22semidirect
59. C2×C11⋊#95C22semidirect
60. C2×C11⋊#95C22semidirect
61. C2×C11⋊#95C22semidirect
62. C2×C11⋊#95C22semidirect
63. C2×C11⋊#95C22semidirect
64. #10622574C22semidirect
65. #10622572C22semidirect
66. #10622570C22semidirect
67. #10622565C22semidirect
68. #10622564C22semidirect
69. #10622560C22semidirect
70. #10622557C22semidirect
117. C22×Dic22C23semidirect
122. C2×C11×C22⋊C4D4semidirect
150. C2×(C2×D11)⋊C4C23semidirect
151. C2×(C2×D11)⋊C4C23semidirect
152. C2×(C2×D11)⋊C4C23semidirect
153. C2×(C2×D11)⋊C4C23semidirect
155. 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
291. C11×C22⋊C4C2×D4semidirect
313. C23×C22⋊C4D11semidirect
370. C23×C11#124semidirect
482. C22×C22⋊C4C2×D11semidirect
528. C22×C11C2×#124semidirect
646. C2×C22⋊C4C22⋊D11semidirect
664. C2×C11#2472semidirect
807. C22⋊C4C2×C22⋊D11semidirect
810. C11C2×#2472semidirect
869. C23#66938semidirect
967. C22C2×#66938semidirect
995. C2#13072736direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×#669772
C22×#670062
#130727362
C2×#106225652
C2×#106225742
C2×#106225722
C2×#106225602
C2×#106225702
C2×#106225642
C2×#106225572
C2×#106228262
C2×#106228602
C2×C4×C22⋊Dic112
C23×C11×C22⋊C42
C2×#247211