Finite Group Databasebeta

← C2×#13072222 #14922402

Subgroups — C2×#13072222 #14922402

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×#4341C211yesmaximal, characteristic, complemented
2C22×#66988C211yesmaximal, characteristic, complemented
3C22×#66992C211yesmaximal, characteristic, complemented
4#13072222C2116yesmaximal, direct product factor
5C2×#10622592C211yesmaximal, characteristic, complemented
6C2×#10622572C211yesmaximal, characteristic, complemented
7C2×#10622560C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622833C211yesmaximal, characteristic, complemented
10C2×#10622833C211yesmaximal, characteristic, complemented
11C2×#10622826C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622559C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C22×C11⋊#95C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic
27C22×#4341—28no—
28C22×#4341—28no—
29C22×#4341—28no—
30C22×#4341C2218yescomplemented
31C23×C4×D11C2211yescharacteristic
32C23×Dic22C2211yescharacteristic
33C2×C11×#121—28no—
34C2×C11×#121C2218yescomplemented
35C22×C11×C4⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic
40C22×C22⋊Dic11C2211yescharacteristic
41C22×C22⋊Dic11C2211yescharacteristic
42C22×C22⋊Dic11C2211yescharacteristic
43C22×C22⋊Dic11C2211yescharacteristic
44C2×#66992—28no—
45C2×#66992C2218yescomplemented
46C2×#66988—28no—
47C2×#66988C2218yescomplemented
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C2211yescharacteristic
51C22×Dic11⋊C4C2211yescharacteristic
52C22×Dic11⋊C4C2211yescharacteristic
53C22×Dic11⋊C4C2211yescharacteristic
54#10622836C2218yescomplemented
55#10622833C2218yescomplemented
56#10622833C2218yescomplemented
57#10622826C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66C2×C11⋊#95C2218yescomplemented
67#10622602C2218yescomplemented
68#10622592C2218yescomplemented
69#10622572C2218yescomplemented
70#10622569C2218yescomplemented
71#10622560C2218yescomplemented
72#10622559C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C25×C11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11—24no—
83C22×D4×C11—24no—
84C22×D4×C11—42no—
85C22×D4×C11D418yescomplemented
86C22×D4×C11C2314yes—
87C22×D4×C11C2314yes—
88C22×D4×C11C2314yes—
89C23×C4×C11—24no—
90C23×C4×C11—24no—
91C23×C4×C11—42no—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2314yes—
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—42no—
105C22×C22⋊D11D418yescomplemented
106C22×C22⋊D11C2314yes—
107C22×C22⋊D11C2314yes—
108C22×C22⋊D11C2314yes—
109C23×Dic11—24no—
110C23×Dic11—24no—
111C23×Dic11—24no—
112C23×Dic11—24no—
113C23×Dic11—24no—
114C23×Dic11—24no—
115C23×Dic11—24no—
116C23×Dic11—42no—
117C23×Dic11D418yescomplemented
118C23×Dic11C2311yescharacteristic
119C23×Dic11C2311yescharacteristic
120C23×Dic11C2311yescharacteristic
121C23×Dic11C2314yes—
122C23×Dic11C2314yes—
123C23×Dic11C2311yescharacteristic
124C23×Dic11C2311yescharacteristic
125C23×Dic11C2311yescharacteristic
126C23×Dic11C2314yes—
127C23×Dic11C2311yescharacteristic
128C2×#4341—2128no—
129C2×#4341—232no—
130C2×#4341—232no—
131C2×#4341—232no—
132C22×C4×D11—24no—
133C22×C4×D11—24no—
134C22×C4×D11—24no—
135C22×C4×D11C2314yes—
136C22×Dic22—24no—
137C22×Dic22—24no—
138C22×Dic22—24no—
139C22×Dic22C2314yes—
140C11×#121—232no—
141C2×C11×C4⋊C4—24no—
142C2×C11×C4⋊C4C2314yes—
143C2×C11×C22⋊C4—24no—
144C2×C11×C22⋊C4—24no—
145C2×C11×C22⋊C4C2314yes—
146C2×C11×C22⋊C4C2314yes—
147C2×C22⋊Dic11—24no—
148C2×C22⋊Dic11—24no—
149C2×C22⋊Dic11—24no—
150C2×C22⋊Dic11—24no—
151C2×C22⋊Dic11—24no—
152C2×C22⋊Dic11—42no—
153C2×C22⋊Dic11C2314yes—
154C2×C22⋊Dic11C2314yes—
155C2×C22⋊Dic11C2314yes—
156C2×C22⋊Dic11C2314yes—
157C2×C22⋊Dic11C2314yes—
158C2×C22⋊Dic11C2314yes—
159#66992—232no—
160#66988—232no—
161C2×(C2×D11)⋊C4—24no—
162C2×(C2×D11)⋊C4—24no—
163C2×(C2×D11)⋊C4—42no—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×(C2×D11)⋊C4C2314yes—
167C2×Dic11⋊C4—24no—
168C2×Dic11⋊C4—24no—
169C2×Dic11⋊C4—24no—
170C2×Dic11⋊C4C2314yes—
171C2×Dic11⋊C4C2314yes—
172C2×Dic11⋊C4C2314yes—
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×C11—22no—
196C24×C11—22no—
197C24×C11—22no—
198C24×C11—22no—
199C24×C11C2×D414yes—
200C24×C11C2×D414yes—
201C24×C11C2×D414yes—
202C24×C11C2×D414yes—
203C24×C11C2412yes—
204C24×C11C2412yes—
205C24×C11C2412yes—
206C24×C11C2411yescharacteristic
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—22no—
210C23×D11—22no—
211C23×D11—22no—
212C23×D11—22no—
213C23×D11C2×D414yes—
214C23×D11C2412yes—
215C2×D4×C11—232no—
216C2×D4×C11—28no—
217C2×D4×C11—28no—
218C2×D4×C11—28no—
219C2×D4×C11—28no—
220C2×D4×C11—28no—
221C2×D4×C11—28no—
222C2×D4×C11—28no—
223C2×D4×C11—44no—
224C2×D4×C11—416no—
225C2×D4×C11—416no—
226C2×D4×C11C2×D4116yescomplemented
227C22×C4×C11—22no—
228C22×C4×C11—22no—
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×C11—28no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—28no—
239C22×C4×C11—44no—
240C22×C4×C11—416no—
241C22×C4×C11C2×D414yes—
242C22×C4×C11#4114yescomplemented
243C22×C4×C11C2412yes—
244C22×C4×C11C2412yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2412yes—
247C2×C22⋊D11—232no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—232no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—416no—
258C2×C22⋊D11C2×D4116yescomplemented
259C22×Dic11—232no—
260C22×Dic11—28no—
261C22×Dic11—28no—
262C22×Dic11—28no—
263C22×Dic11—232no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—28no—
272C22×Dic11—28no—
273C22×Dic11—28no—
274C22×Dic11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—28no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11—22no—
282C22×Dic11—22no—
283C22×Dic11—22no—
284C22×Dic11—22no—
285C22×Dic11—44no—
286C22×Dic11—416no—
287C22×Dic11C2×D414yes—
288C22×Dic11C2×D414yes—
289C22×Dic11C2×D414yes—
290C22×Dic11C2×D4116yescomplemented
291C22×Dic11#4114yescomplemented
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299#4341—2256no—
300C2×C4×D11—232no—
301C2×C4×D11—28no—
302C2×C4×D11—28no—
303C2×C4×D11—28no—
304C2×Dic22—232no—
305C2×Dic22—28no—
306C2×Dic22—28no—
307C2×Dic22—28no—
308C11×C4⋊C4—28no—
309C11×C22⋊C4—28no—
310C11×C22⋊C4—28no—
311C22⋊Dic11—28no—
312C22⋊Dic11—28no—
313C22⋊Dic11—28no—
314C22⋊Dic11—28no—
315C22⋊Dic11—28no—
316C22⋊Dic11—44no—
317(C2×D11)⋊C4—28no—
318(C2×D11)⋊C4—28no—
319(C2×D11)⋊C4—44no—
320Dic11⋊C4—28no—
321Dic11⋊C4—28no—
322Dic11⋊C4—28no—
323C23×#41—111no—
324C22×#123—111no—
325C22×#121—111no—
326C22×#121D1111yescharacteristic, complemented
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×#386—111no—
336C2×#385—111no—
337C2×#385—111no—
338C22×#95—111no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—28no—
342C23×C11—28no—
343C23×C11—28no—
344C23×C11—28no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—28no—
350C23×C11—28no—
351C23×C11—28no—
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—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—44no—
366C23×C11—44no—
367C23×C11—44no—
368C23×C11—44no—
369C23×C11—44no—
370C23×C11—44no—
371C23×C11—44no—
372C23×C11—44no—
373C23×C11—44no—
374C23×C11—44no—
375C23×C11—44no—
376C23×C11#120116yes—
377C23×C11C22×D414yes—
378C23×C11C22×D414yes—
379C23×C11C22×D412yes—
380C23×C11C22×D412yes—
381C23×C11C22×D414yes—
382C23×C11C22×D414yes—
383C23×C11C22×D412yes—
384C23×C11C2×#4112yes—
385C23×C11C2×#4112yes—
386C23×C11H(5,𝔽2)12yes—
387C23×C112−1+412yes—
388C23×C11C2511yescharacteristic
389C22×D11—28no—
390C22×D11—28no—
391C22×D11—28no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—44no—
399C22×D11—44no—
400C22×D11—44no—
401C22×D11—44no—
402C22×D11C22×D414yes—
403D4×C11—232no—
404D4×C11—416no—
405D4×C11—416no—
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—416no—
419C2×C4×C11—44no—
420C2×C4×C11—44no—
421C2×C4×C11C22×D414yes—
422C2×C4×C11C2×#4114yescomplemented
423C22⋊D11—232no—
424C22⋊D11—232no—
425C22⋊D11—416no—
426C2×Dic11—232no—
427C2×Dic11—28no—
428C2×Dic11—28no—
429C2×Dic11—28no—
430C2×Dic11—232no—
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—22no—
448C2×Dic11—22no—
449C2×Dic11—416no—
450C2×Dic11—44no—
451C2×Dic11—44no—
452C2×Dic11—44no—
453C2×Dic11C22×D414yes—
454C2×Dic11C22×D414yes—
455C2×Dic11C22×D414yes—
456C2×Dic11C2×#4114yescomplemented
457C4×D11—232no—
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×D4C2×D1111yescharacteristic
468C23×D4C2×D1111yescharacteristic
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—28no—
478C2×#121—118no—
479C2×#121—228no—
480C2×#121C2×D1118yescomplemented
481C22×C4⋊C4—111no—
482C22×C4⋊C4—111no—
483C22×C4⋊C4—111no—
484C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
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#386—118no—
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—111no—
513C2×#95—111no—
514C2×#95—118no—
515C22×C11—24no—
516C22×C11—24no—
517C22×C11—232no—
518C22×C11—24no—
519C22×C11—24no—
520C22×C11—24no—
521C22×C11—24no—
522C22×C11—24no—
523C22×C11—24no—
524C22×C11—24no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—416no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11—42no—
531C22×C11—42no—
532C22×C11—42no—
533C22×C11—42no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—42no—
537C22×C11—88no—
538C22×C11C2×#12018yes—
539C22×C11C2×#12014yes—
540C22×C11#53214yes—
541C22×C11#53714yes—
542C22×C11#54614yes—
543C22×C11#54614yes—
544C22×C11#54714yes—
545C22×C11#54714yes—
546C22×C11C23×D411yescharacteristic
547C22×C11C23×D411yescharacteristic
548C22×C11C23×D411yescharacteristic
549C22×C11C22×#4111yescharacteristic
550C22×C11C22×#4111yescharacteristic
551C22×C11C2×H(5,𝔽2)11yescharacteristic
552C22×C11C2×2−1+411yescharacteristic
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—416no—
559C2×D11—42no—
560C2×D11—42no—
561C4×C11—24no—
562C4×C11—24no—
563C4×C11—42no—
564C4×C11—42no—
565Dic11—24no—
566Dic11—24no—
567Dic11—24no—
568Dic11—24no—
569Dic11—42no—
570Dic11—42no—
571Dic11—42no—
572C25—111no—
573C25C22×D1111yescharacteristic
574C25C22×D1111yescharacteristic
575C25C22×D1111yescharacteristic
576C2×#41—2232no—
577C2×#41—2232no—
578C2×#41—22128no—
579C2×#41—2232no—
580C22×Q8—114no—
581C22×Q8—224no—
582C22×Q8—224no—
583C22×Q8—224no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—118no—
593C22×D4—114no—
594C22×D4—114no—
595C22×D4—114no—
596C22×D4—224no—
597C22×D4—224no—
598C22×D4—224no—
599C22×D4—224no—
600C22×D4—224no—
601C22×D4—224no—
602C22×D4—224no—
603C22×D4—442no—
604C22×D4C22⋊D1118yescomplemented
605C22×D4C22×D1114yes—
606C22×D4C22×D1114yes—
607C22×D4C22×D1114yes—
608C23×C4—24no—
609C23×C4—24no—
610C23×C4—42no—
611C23×C4—118no—
612C23×C4—114no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—111no—
616C23×C4—111no—
617C23×C4—114no—
618C23×C4—111no—
619C23×C4—111no—
620C23×C4—111no—
621C23×C4—114no—
622C23×C4—114no—
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—224no—
632C23×C4—224no—
633C23×C4—442no—
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1114yes—
637C23×C4C22×D1111yescharacteristic
638C23×C4C22×D1111yescharacteristic
639#123—2232no—
640#121—232no—
641#121—2232no—
642C2×C4⋊C4—24no—
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⋊C4C22×D1114yes—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—114no—
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⋊C4—442no—
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#95—114no—
679#95—114no—
680C2×C11—28no—
681C2×C11—44no—
682C2×C11—82no—
683C2×C11#243018yescomplemented
684C2×C11C22×#12011yescharacteristic
685C2×C11C2×#53211yescharacteristic
686C2×C11C2×#53711yescharacteristic
687C2×C11C2×#54611yescharacteristic
688C2×C11C2×#54611yescharacteristic
689C2×C11C2×#54711yescharacteristic
690C2×C11C2×#54711yescharacteristic
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—22no—
706C24—22no—
707C24—22no—
708C24—22no—
709C24—114no—
710C24—112no—
711C24—222no—
712C24—222no—
713C24—222no—
714C24—222no—
715C24—222no—
716C24—222no—
717C24D4×D1114yes—
718C24D4×D1114yes—
719C24C2×C22⋊D1114yes—
720C24C2×C22⋊D1114yes—
721C24C23×D1112yes—
722C24C23×D1112yes—
723C24C23×D1112yes—
724C24C23×D1111yescharacteristic
725#41—22256no—
726C2×Q8—228no—
727C2×Q8—228no—
728C2×Q8—2232no—
729C2×Q8—228no—
730C2×D4—232no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—44no—
739C2×D4—416no—
740C2×D4—416no—
741C2×D4—1116no—
742C2×D4—228no—
743C2×D4—228no—
744C2×D4—228no—
745C2×D4—2232no—
746C2×D4—2232no—
747C2×D4—228no—
748C2×D4—228no—
749C2×D4—228no—
750C2×D4—228no—
751C2×D4—444no—
752C2×D4—4416no—
753C2×D4C2×C22⋊D11116yescomplemented
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—44no—
767C22×C4—416no—
768C22×C4—114no—
769C22×C4—114no—
770C22×C4—114no—
771C22×C4—1116no—
772C22×C4—114no—
773C22×C4—112no—
774C22×C4—112no—
775C22×C4—112no—
776C22×C4—112no—
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—2232no—
788C22×C4—222no—
789C22×C4—222no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—228no—
793C22×C4—222no—
794C22×C4—222no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—228no—
798C22×C4—228no—
799C22×C4—228no—
800C22×C4—222no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—228no—
804C22×C4—222no—
805C22×C4—222no—
806C22×C4—222no—
807C22×C4—222no—
808C22×C4—222no—
809C22×C4—222no—
810C22×C4—444no—
811C22×C4—4416no—
812C22×C4#434114yescomplemented
813C22×C4C2×C22⋊D1114yes—
814C22×C4C23×D1112yes—
815C22×C4C23×D1112yes—
816C22×C4C23×D1112yes—
817C22×C4C23×D1112yes—
818C4⋊C4—28no—
819C4⋊C4—228no—
820C4⋊C4—228no—
821C4⋊C4—228no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—228no—
825C22⋊C4—228no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—228no—
830C22⋊C4—228no—
831C22⋊C4—444no—
832C22⋊C4—444no—
833C11C2×#243011yescharacteristic, complemented, Sylow
834C23—28no—
835C23—28no—
836C23—28no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—28no—
845C23—28no—
846C23—28no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23—44no—
869C23—44no—
870C23—44no—
871C23—114no—
872C23—228no—
873C23—228no—
874C23—228no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—444no—
882C23—444no—
883C23—444no—
884C23—444no—
885C23#66990116yes—
886C23C2×D4×D1114yes—
887C23C2×D4×D1114yes—
888C23C2×D4×D1112yes—
889C23C2×D4×D1112yes—
890C23C2×#434112yes—
891C23#6703712yes—
892C23#41×D1112yes—
893C23#6704312yes—
894C23C22×C22⋊D1114yes—
895C23C22×C22⋊D1114yes—
896C23C22×C22⋊D1112yes—
897C23C24×D1111yescharacteristic
898Q8—2232no—
899D4—232no—
900D4—416no—
901D4—416no—
902D4—2232no—
903D4—2232no—
904D4—4416no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—22no—
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—416no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—114no—
921C2×C4—114no—
922C2×C4—114no—
923C2×C4—114no—
924C2×C4—2232no—
925C2×C4—2232no—
926C2×C4—228no—
927C2×C4—228no—
928C2×C4—228no—
929C2×C4—2232no—
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—222no—
947C2×C4—222no—
948C2×C4—4416no—
949C2×C4—444no—
950C2×C4—444no—
951C2×C4—444no—
952C2×C4C2×#434114yescomplemented
953C2×C4C22×C22⋊D1114yes—
954C22—24no—
955C22—24no—
956C22—232no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—42no—
965C22—42no—
966C22—416no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—88no—
977C22—224no—
978C22—224no—
979C22—224no—
980C22—442no—
981C22—442no—
982C22—4416no—
983C22—442no—
984C22—442no—
985C22#1062312714yes—
986C22#1062312814yes—
987C22#1062314114yes—
988C22#1062314214yes—
989C22C2×#6699018yes—
990C22C2×#6699014yes—
991C22#1062333714yes—
992C22#1062335514yes—
993C22C22×D4×D1111yescharacteristic
994C22C22×D4×D1111yescharacteristic
995C22C22×#434111yescharacteristic
996C22C2×#6703711yescharacteristic
997C22C2×#41×D1111yescharacteristic
998C22C2×#6704311yescharacteristic
999C22C23×C22⋊D1111yescharacteristic
1000C4—24no—
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—224no—
1005C4—224no—
1006C4—224no—
1007C4—224no—
1008C4—442no—
1009C4—442no—
1010C4—442no—
1011C2—28no—
1012C2—44no—
1013C2—82no—
1014C2—444no—
1015C2#1307222218yesdirect product factor
1016C2C22×#6699011yescharacteristic
1017C2C2×#1062312711yescharacteristic
1018C2C2×#1062312811yescharacteristic
1019C2C2×#1062314111yescharacteristic
1020C2C2×#1062333711yescharacteristic
1021C2C2×#1062335511yescharacteristic
1022C2C2×#1062314211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C23×#4341C2semidirect
2. C22×#66988C2semidirect
3. C22×#66992C2semidirect
4. #13072222C2direct (N × H)
5. C2×#10622592C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622560C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622833C2semidirect
11. C2×#10622826C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622559C2semidirect
14. C2×#10622602C2semidirect
15. C22×C11⋊#95C2semidirect
16. C22×C11×#121C2semidirect
30. C22×#4341C22semidirect
34. C2×C11×#121C22semidirect
45. C2×#66992C22semidirect
47. C2×#66988C22semidirect
54. #10622836C22semidirect
55. #10622833C22semidirect
56. #10622833C22semidirect
57. #10622826C22semidirect
66. C2×C11⋊#95C22semidirect
67. #10622602C22semidirect
68. #10622592C22semidirect
69. #10622572C22semidirect
70. #10622569C22semidirect
71. #10622560C22semidirect
72. #10622559C22semidirect
85. C22×D4×C11D4semidirect
105. C22×C22⋊D11D4semidirect
117. C23×Dic11D4semidirect
226. C2×D4×C11C2×D4semidirect
242. C22×C4×C11#41semidirect
258. C2×C22⋊D11C2×D4semidirect
290. C22×Dic11C2×D4semidirect
291. C22×Dic11#41semidirect
326. C22×#121D11semidirect
422. C2×C4×C11C2×#41semidirect
456. C2×Dic11C2×#41semidirect
480. C2×#121C2×D11semidirect
604. C22×D4C22⋊D11semidirect
683. C2×C11#2430semidirect
753. C2×D4C2×C22⋊D11semidirect
812. C22×C4#4341semidirect
833. C11C2×#2430semidirect
952. C2×C4C2×#4341semidirect
1015. C2#13072222direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43412
C22×#669882
C22×#669922
#130722222
C2×#106225922
C2×#106225722
C2×#106225602
C2×#106228362
C2×#106228332
C2×#106228262
C2×#106225692
C2×#106225592
C2×#106226022
C22×C11⋊#952
C22×C11×#1212
C2×#243011