Finite Group Databasebeta

← C2×#13072223 #14922401

Subgroups — C2×#13072223 #14922401

Order 2816.

6042 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic, complemented
2C22×#66936C211yesmaximal, characteristic, complemented
3C22×#66937C211yesmaximal, characteristic, complemented
4C22×#66991C211yesmaximal, characteristic, complemented
5#13072223C2116yesmaximal, direct product factor
6C2×#10622269C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622560C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622281C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×D11×#95C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C22×#4339—28no—
24C22×#4339—28no—
25C22×#4339—28no—
26C22×#4339C2218yescomplemented
27C23×D44C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C23×C4×D11C2211yescharacteristic
30C23×C4×D11C2211yescharacteristic
31C23×C4×D11C2211yescharacteristic
32C23×Dic22C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic
40C2×#66991—28no—
41C2×#66991C2218yescomplemented
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×C4⋊Dic11C2211yescharacteristic
47C22×C4⋊Dic11C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C2×#66937—28no—
51C2×#66937C2218yescomplemented
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54C11×#386C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57#10622836C2218yescomplemented
58#10622823C2218yescomplemented
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65#10622574C2218yescomplemented
66#10622569C2218yescomplemented
67#10622569C2218yescomplemented
68#10622560C2218yescomplemented
69#10622281C2218yescomplemented
70#10622278C2218yescomplemented
71D11×#95C2218yescomplemented
72#10622269C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—42no—
80C22×D4×C11C2314yes—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—24no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2314yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11D418yescomplemented
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C22×C22⋊D11C2314yes—
105C22×C22⋊D11C2314yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C2×#4339—2128no—
113C2×#4339—232no—
114C2×#4339—232no—
115C2×#4339—232no—
116C22×D44—24no—
117C22×D44—24no—
118C22×D44D418yescomplemented
119C22×D44C2314yes—
120C22×C4×D11—24no—
121C22×C4×D11—24no—
122C22×C4×D11—24no—
123C22×C4×D11—24no—
124C22×C4×D11—24no—
125C22×C4×D11—24no—
126C22×C4×D11—24no—
127C22×C4×D11—24no—
128C22×C4×D11—24no—
129C22×C4×D11—42no—
130C22×C4×D11—42no—
131C22×C4×D11D418yescomplemented
132C22×C4×D11C2314yes—
133C22×C4×D11C2314yes—
134C22×C4×D11C2314yes—
135C22×C4×D11C2314yes—
136C22×Dic22—24no—
137C22×Dic22—24no—
138C22×Dic22—24no—
139C22×Dic22C2314yes—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4—42no—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C22⋊Dic11—24no—
147C2×C22⋊Dic11—24no—
148C2×C22⋊Dic11—24no—
149C2×C22⋊Dic11—24no—
150C2×C22⋊Dic11C2314yes—
151C2×C22⋊Dic11C2314yes—
152C2×C22⋊Dic11C2314yes—
153C2×C22⋊Dic11C2314yes—
154#66991—232no—
155C2×(C2×D11)⋊C4—24no—
156C2×(C2×D11)⋊C4—24no—
157C2×(C2×D11)⋊C4—24no—
158C2×(C2×D11)⋊C4—42no—
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×C4⋊Dic11—24no—
164C2×C4⋊Dic11—24no—
165C2×C4⋊Dic11C2314yes—
166C2×C4⋊Dic11C2314yes—
167C2×Dic11⋊C4—24no—
168C2×Dic11⋊C4—24no—
169C2×Dic11⋊C4C2314yes—
170C2×Dic11⋊C4C2314yes—
171#66937—232no—
172#66936—232no—
173C11×#95C2314yes—
174C11×#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C2×#2430—111nomaximal, Sylow
182C24×C11—22no—
183C24×C11—22no—
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—22no—
195C24×C11C2×D414yes—
196C24×C11C2412yes—
197C24×C11C2412yes—
198C24×C11C2411yescharacteristic
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—22no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—22no—
209C23×D11C2×D414yes—
210C23×D11C2×D414yes—
211C23×D11C2×D414yes—
212C23×D11C2×D414yes—
213C23×D11C2412yes—
214C23×D11C2412yes—
215C2×D4×C11—28no—
216C2×D4×C11—28no—
217C2×D4×C11—44no—
218C2×D4×C11—416no—
219C22×C4×C11—232no—
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—28no—
228C22×C4×C11—28no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11—22no—
235C22×C4×C11C2×D414yes—
236C22×C4×C11C2×D414yes—
237C22×C4×C11#4114yescomplemented
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C2×C22⋊D11—232no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—232no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—416no—
257C2×C22⋊D11—416no—
258C2×C22⋊D11C2×D4116yescomplemented
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×Dic11C2×D414yes—
275C22×Dic11C2×D414yes—
276C22×Dic11#4114yescomplemented
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2412yes—
281C22×Dic11C2412yes—
282C22×Dic11C2412yes—
283#4339—2256no—
284C2×D44—232no—
285C2×D44—28no—
286C2×D44—28no—
287C2×D44C2×D4116yescomplemented
288C2×C4×D11—232no—
289C2×C4×D11—28no—
290C2×C4×D11—28no—
291C2×C4×D11—232no—
292C2×C4×D11—28no—
293C2×C4×D11—28no—
294C2×C4×D11—28no—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—28no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—416no—
302C2×C4×D11—416no—
303C2×C4×D11C2×D4116yescomplemented
304C2×Dic22—232no—
305C2×Dic22—28no—
306C2×Dic22—28no—
307C2×Dic22—28no—
308C11×C22⋊C4—28no—
309C11×C22⋊C4—28no—
310C11×C22⋊C4—44no—
311C22⋊Dic11—28no—
312C22⋊Dic11—28no—
313C22⋊Dic11—28no—
314C22⋊Dic11—28no—
315(C2×D11)⋊C4—28no—
316(C2×D11)⋊C4—28no—
317(C2×D11)⋊C4—28no—
318(C2×D11)⋊C4—44no—
319C4⋊Dic11—28no—
320C4⋊Dic11—28no—
321Dic11⋊C4—28no—
322Dic11⋊C4—28no—
323C23×#41—111no—
324C22×#123—111no—
325C22×#121—111no—
326C22×#121—111no—
327#2430—1116no—
328C2×#395—111no—
329C2×#394—111no—
330C2×#393—111no—
331C2×#392—111no—
332C2×#386—111no—
333C2×#386—111no—
334C2×#386—111no—
335C2×#386D1111yescharacteristic, complemented
336C2×#385—111no—
337C2×#385—111no—
338C22×#95—111no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—28no—
342C23×C11—22no—
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—44no—
356C23×C11—44no—
357C23×C11—44no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11—44no—
364C23×C11—44no—
365C23×C11—44no—
366C23×C11C22×D414yes—
367C23×C11C22×D412yes—
368C23×C11C22×D412yes—
369C23×C11C22×D412yes—
370C23×C11C2×#4112yes—
371C23×C11C2×#4112yes—
372C23×C11H(5,𝔽2)12yes—
373C23×C112−1+412yes—
374C23×C11C2511yescharacteristic
375C22×D11—28no—
376C22×D11—28no—
377C22×D11—28no—
378C22×D11—28no—
379C22×D11—28no—
380C22×D11—28no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—28no—
386C22×D11—28no—
387C22×D11—28no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11—44no—
397C22×D11—44no—
398C22×D11#120116yes—
399C22×D11C22×D414yes—
400C22×D11C22×D414yes—
401C22×D11C22×D414yes—
402C22×D11C22×D414yes—
403D4×C11—416no—
404C2×C4×C11—232no—
405C2×C4×C11—28no—
406C2×C4×C11—28no—
407C2×C4×C11—28no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—44no—
421C2×C4×C11—44no—
422C2×C4×C11C22×D414yes—
423C2×C4×C11C22×D414yes—
424C2×C4×C11C2×#4114yescomplemented
425C22⋊D11—232no—
426C22⋊D11—232no—
427C22⋊D11—416no—
428C22⋊D11—416no—
429C2×Dic11—28no—
430C2×Dic11—28no—
431C2×Dic11—28no—
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—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—44no—
448C2×Dic11—44no—
449C2×Dic11—44no—
450C2×Dic11C22×D414yes—
451C2×Dic11C22×D414yes—
452C2×Dic11C2×#4114yescomplemented
453D44—232no—
454C4×D11—232no—
455C4×D11—232no—
456C4×D11—416no—
457C4×D11—416no—
458Dic22—232no—
459C22×#41—118no—
460C22×#41—228no—
461C22×#41—228no—
462C22×#41—228no—
463C23×Q8—111no—
464C23×D4—111no—
465C23×D4—111no—
466C23×D4—111no—
467C23×D4—111no—
468C23×D4—111no—
469C23×D4C2×D1111yescharacteristic
470C24×C4—111no—
471C24×C4—111no—
472C24×C4—111no—
473C24×C4—111no—
474C24×C4C2×D1111yescharacteristic
475C2×#123—118no—
476C2×#123—228no—
477C2×#121—118no—
478C2×#121—118no—
479C2×#121—228no—
480C2×#121—228no—
481C22×C4⋊C4—111no—
482C22×C4⋊C4—111no—
483C22×C4⋊C4—111no—
484C22×C4⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4—111no—
493C22×C22⋊C4C2×D1111yescharacteristic
494C22×C22⋊C4C2×D1111yescharacteristic
495C22×C22⋊C4C2×D1111yescharacteristic
496#395—118no—
497#394—118no—
498#393—118no—
499#392—118no—
500#386—118no—
501#386—118no—
502#386—118no—
503#386C2×D1118yescomplemented
504#385—118no—
505#385—118no—
506C2×#95—111no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—118no—
513C2×#95C2×D1111yescharacteristic
514C2×#95C2×D1111yescharacteristic
515C22×C11—24no—
516C22×C11—24no—
517C22×C11—24no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—416no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—88no—
531C22×C11C2×#12014yes—
532C22×C11#53214yes—
533C22×C11#53714yes—
534C22×C11#54614yes—
535C22×C11#54614yes—
536C22×C11#54714yes—
537C22×C11#54714yes—
538C22×C11C23×D411yescharacteristic
539C22×C11C23×D411yescharacteristic
540C22×C11C23×D411yescharacteristic
541C22×C11C22×#4111yescharacteristic
542C22×C11C22×#4111yescharacteristic
543C22×C11C2×H(5,𝔽2)11yescharacteristic
544C22×C11C2×2−1+411yescharacteristic
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—232no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—416no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11C2×#12018yes—
561C4×C11—24no—
562C4×C11—24no—
563C4×C11—24no—
564C4×C11—42no—
565C4×C11—42no—
566Dic11—24no—
567Dic11—24no—
568Dic11—24no—
569Dic11—42no—
570Dic11—42no—
571Dic11—42no—
572C25—111no—
573C25—111no—
574C25C22×D1111yescharacteristic
575C25C22×D1111yescharacteristic
576C2×#41—2232no—
577C2×#41—2232no—
578C2×#41—2232no—
579C2×#41—22128no—
580C22×Q8—114no—
581C22×Q8—224no—
582C22×Q8—224no—
583C22×Q8—224no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—42no—
587C22×D4—118no—
588C22×D4—114no—
589C22×D4—114no—
590C22×D4—114no—
591C22×D4—114no—
592C22×D4—118no—
593C22×D4—114no—
594C22×D4—224no—
595C22×D4—224no—
596C22×D4—224no—
597C22×D4—224no—
598C22×D4—224no—
599C22×D4—224no—
600C22×D4—224no—
601C22×D4—224no—
602C22×D4—224no—
603C22×D4—224no—
604C22×D4—224no—
605C22×D4—224no—
606C22×D4—442no—
607C22×D4C22×D1114yes—
608C23×C4—24no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—111no—
612C23×C4—111no—
613C23×C4—111no—
614C23×C4—118no—
615C23×C4—114no—
616C23×C4—111no—
617C23×C4—111no—
618C23×C4—111no—
619C23×C4—114no—
620C23×C4—114no—
621C23×C4—114no—
622C23×C4—224no—
623C23×C4—224no—
624C23×C4—224no—
625C23×C4—224no—
626C23×C4—224no—
627C23×C4—224no—
628C23×C4—224no—
629C23×C4—224no—
630C23×C4—224no—
631C23×C4—442no—
632C23×C4—442no—
633C23×C4C22×D1114yes—
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1111yescharacteristic
637C23×C4C22×D1111yescharacteristic
638C23×C4C22×D1111yescharacteristic
639#123—2232no—
640#121—2232no—
641#121—2232no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—114no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—114no—
646C2×C4⋊C4—224no—
647C2×C4⋊C4—224no—
648C2×C4⋊C4—224no—
649C2×C4⋊C4—224no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—42no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—114no—
659C2×C22⋊C4—114no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—224no—
665C2×C22⋊C4—224no—
666C2×C22⋊C4—224no—
667C2×C22⋊C4—224no—
668C2×C22⋊C4—442no—
669C2×C22⋊C4C22×D1114yes—
670C2×C22⋊C4C22×D1114yes—
671C2×C22⋊C4C22×D1114yes—
672#95—114no—
673#95—114no—
674#95—114no—
675#95—114no—
676#95—114no—
677#95—114no—
678#95C22×D1114yes—
679#95C22×D1114yes—
680C2×C11—44no—
681C2×C11—82no—
682C2×C11#243018yescomplemented
683C2×C11C22×#12011yescharacteristic
684C2×C11C2×#53211yescharacteristic
685C2×C11C2×#53711yescharacteristic
686C2×C11C2×#54611yescharacteristic
687C2×C11C2×#54611yescharacteristic
688C2×C11C2×#54711yescharacteristic
689C2×C11C2×#54711yescharacteristic
690D11—28no—
691D11—44no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—22no—
703C24—22no—
704C24—22no—
705C24—114no—
706C24—114no—
707C24—114no—
708C24—112no—
709C24—114no—
710C24—112no—
711C24—222no—
712C24—222no—
713C24—222no—
714C24—222no—
715C24—222no—
716C24—222no—
717C24—222no—
718C24—222no—
719C24—222no—
720C24—222no—
721C24D4×D1114yes—
722C24C23×D1112yes—
723C24C23×D1112yes—
724C24C23×D1111yescharacteristic
725#41—22256no—
726C2×Q8—228no—
727C2×Q8—228no—
728C2×Q8—2232no—
729C2×Q8—228no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—44no—
733C2×D4—416no—
734C2×D4—1116no—
735C2×D4—1116no—
736C2×D4—2232no—
737C2×D4—228no—
738C2×D4—228no—
739C2×D4—228no—
740C2×D4—228no—
741C2×D4—2232no—
742C2×D4—228no—
743C2×D4—228no—
744C2×D4—228no—
745C2×D4—2232no—
746C2×D4—228no—
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—228no—
750C2×D4—228no—
751C2×D4—444no—
752C2×D4—4416no—
753C2×D4—4416no—
754C22×C4—232no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—28no—
761C22×C4—22no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—114no—
771C22×C4—114no—
772C22×C4—114no—
773C22×C4—112no—
774C22×C4—112no—
775C22×C4—112no—
776C22×C4—1116no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—112no—
780C22×C4—228no—
781C22×C4—228no—
782C22×C4—2232no—
783C22×C4—228no—
784C22×C4—228no—
785C22×C4—228no—
786C22×C4—2232no—
787C22×C4—228no—
788C22×C4—228no—
789C22×C4—222no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—228no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—222no—
799C22×C4—222no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—228no—
806C22×C4—444no—
807C22×C4—444no—
808C22×C4—4416no—
809C22×C4—4416no—
810C22×C4#433914yescomplemented
811C22×C4D4×D1114yes—
812C22×C4D4×D1114yes—
813C22×C4C23×D1112yes—
814C22×C4C23×D1112yes—
815C22×C4C23×D1112yes—
816C22×C4C23×D1112yes—
817C22×C4C23×D1112yes—
818C4⋊C4—228no—
819C4⋊C4—228no—
820C4⋊C4—228no—
821C4⋊C4—228no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—44no—
825C22⋊C4—228no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—228no—
830C22⋊C4—228no—
831C22⋊C4—228no—
832C22⋊C4—444no—
833C11C2×#243011yescharacteristic, complemented, Sylow
834C23—28no—
835C23—28no—
836C23—28no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—44no—
855C23—44no—
856C23—44no—
857C23—44no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—1116no—
862C23—114no—
863C23—114no—
864C23—114no—
865C23—114no—
866C23—228no—
867C23—228no—
868C23—228no—
869C23—228no—
870C23—228no—
871C23—228no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—228no—
877C23—228no—
878C23—228no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—444no—
886C23—444no—
887C23—444no—
888C23—444no—
889C23C2×#433912yes—
890C23C2×D4×D1114yes—
891C23C2×D4×D1112yes—
892C23C2×D4×D1112yes—
893C23C2×D4×D1112yes—
894C23#6703712yes—
895C23#41×D1112yes—
896C23#6704312yes—
897C23C24×D1111yescharacteristic
898Q8—2232no—
899D4—416no—
900D4—2232no—
901D4—2232no—
902D4—2232no—
903D4—4416no—
904D4—4416no—
905C2×C4—232no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—114no—
924C2×C4—114no—
925C2×C4—114no—
926C2×C4—2232no—
927C2×C4—2232no—
928C2×C4—228no—
929C2×C4—228no—
930C2×C4—228no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—4416no—
947C2×C4—4416no—
948C2×C4—444no—
949C2×C4—444no—
950C2×C4—444no—
951C2×C4C2×#433914yescomplemented
952C2×C4C2×D4×D1114yes—
953C2×C4C2×D4×D1114yes—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—42no—
958C22—42no—
959C22—416no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—88no—
970C22—118no—
971C22—224no—
972C22—224no—
973C22—2232no—
974C22—224no—
975C22—224no—
976C22—224no—
977C22—224no—
978C22—224no—
979C22—224no—
980C22—224no—
981C22—442no—
982C22—442no—
983C22—4416no—
984C22—442no—
985C22—442no—
986C22#1062302114yes—
987C22#1062307914yes—
988C22#1062308214yes—
989C22D11×#12014yes—
990C22#1062313914yes—
991C22#1062314314yes—
992C22#1062318614yes—
993C22C22×#433911yescharacteristic
994C22C22×D4×D1111yescharacteristic
995C22C22×D4×D1111yescharacteristic
996C22C22×D4×D1111yescharacteristic
997C22C2×#6703711yescharacteristic
998C22C2×#41×D1111yescharacteristic
999C22C2×#6704311yescharacteristic
1000C4—24no—
1001C4—24no—
1002C4—24no—
1003C4—42no—
1004C4—42no—
1005C4—224no—
1006C4—224no—
1007C4—224no—
1008C4—442no—
1009C4—442no—
1010C4—442no—
1011C2—44no—
1012C2—82no—
1013C2—228no—
1014C2—444no—
1015C2#1307222318yesdirect product factor
1016C2C2×D11×#12011yescharacteristic
1017C2C2×#1062307911yescharacteristic
1018C2C2×#1062313911yescharacteristic
1019C2C2×#1062302111yescharacteristic
1020C2C2×#1062314311yescharacteristic
1021C2C2×#1062318611yescharacteristic
1022C2C2×#1062308211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×#4339C2semidirect
2. C22×#66936C2semidirect
3. C22×#66937C2semidirect
4. C22×#66991C2semidirect
5. #13072223C2direct (N × H)
6. C2×#10622269C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622281C2semidirect
14. C2×#10622823C2semidirect
15. C2×D11×#95C2semidirect
16. C2×C11×#386C2semidirect
26. C22×#4339C22semidirect
41. C2×#66991C22semidirect
51. C2×#66937C22semidirect
53. C2×#66936C22semidirect
54. C11×#386C22semidirect
57. #10622836C22semidirect
58. #10622823C22semidirect
65. #10622574C22semidirect
66. #10622569C22semidirect
67. #10622569C22semidirect
68. #10622560C22semidirect
69. #10622281C22semidirect
70. #10622278C22semidirect
71. D11×#95C22semidirect
72. #10622269C22semidirect
101. C22×C22⋊D11D4semidirect
118. C22×D44D4semidirect
131. C22×C4×D11D4semidirect
237. C22×C4×C11#41semidirect
258. C2×C22⋊D11C2×D4semidirect
276. C22×Dic11#41semidirect
287. C2×D44C2×D4semidirect
303. C2×C4×D11C2×D4semidirect
335. C2×#386D11semidirect
424. C2×C4×C11C2×#41semidirect
452. C2×Dic11C2×#41semidirect
503. #386C2×D11semidirect
682. C2×C11#2430semidirect
810. C22×C4#4339semidirect
833. C11C2×#2430semidirect
951. C2×C4C2×#4339semidirect
1015. C2#13072223direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#669362
C22×#669372
C22×#669912
#130722232
C2×#106222692
C2×#106225742
C2×#106225602
C2×#106228362
C2×#106222782
C2×#106225692
C2×#106222812
C2×#106228232
C2×D11×#952
C2×C11×#3862
C2×#243011