Finite Group Databasebeta

← C2×#13072230 #14922103

Subgroups — C2×#13072230 #14922103

Order 2816.

6278 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4341C211yesmaximal, characteristic, complemented
2C22×#66993C211yesmaximal, characteristic, complemented
3C22×#66938C211yesmaximal, characteristic, complemented
4C22×#66992C211yesmaximal, characteristic, complemented
5#13072230C2116yesmaximal, direct product factor
6C2×#10622573C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622259C211yesmaximal, characteristic, complemented
10C2×#10622570C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622571C211yesmaximal, characteristic, complemented
14C2×#10622569C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic
27C24×Dic11C2211yescharacteristic
28C22×#4341—28no—
29C22×#4341—28no—
30C22×#4341—28no—
31C22×#4341C2218yescomplemented
32C23×D44C2211yescharacteristic
33C23×C4×D11C2211yescharacteristic
34C23×Dic22C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C11×C22⋊C4C2211yescharacteristic
37C22×C11×C22⋊C4C2211yescharacteristic
38C22×C22⋊Dic11C2211yescharacteristic
39C22×C22⋊Dic11C2211yescharacteristic
40C22×C22⋊Dic11C2211yescharacteristic
41C22×C22⋊Dic11C2211yescharacteristic
42C2×#66993—28no—
43C2×#66993C2218yescomplemented
44C2×#66992—28no—
45C2×#66992C2218yescomplemented
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C2211yescharacteristic
51C22×Dic11⋊C4C2211yescharacteristic
52C22×C4×Dic11C2211yescharacteristic
53C22×C4×Dic11C2211yescharacteristic
54C2×#66938—28no—
55C2×#66938C2218yescomplemented
56C11×#392C2218yescomplemented
57C2×C11×#95C2211yescharacteristic
58#10622836C2218yescomplemented
59#10622836C2218yescomplemented
60#10622833C2218yescomplemented
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65C2×C11⋊#95C2211yescharacteristic
66#10622573C2218yescomplemented
67#10622571C2218yescomplemented
68#10622570C2218yescomplemented
69#10622569C2218yescomplemented
70C22⋊C4×Dic11C2218yescomplemented
71#10622278C2218yescomplemented
72#10622259C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C25×C11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C24×D11C2311yescharacteristic
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×C11—42no—
86C22×D4×C11—42no—
87C22×D4×C11C2314yes—
88C22×D4×C11C2314yes—
89C22×D4×C11C2314yes—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
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—24no—
101C22×C22⋊D11—24no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—24no—
105C22×C22⋊D11—24no—
106C22×C22⋊D11—24no—
107C22×C22⋊D11—42no—
108C22×C22⋊D11—42no—
109C22×C22⋊D11—42no—
110C22×C22⋊D11—42no—
111C22×C22⋊D11D418yescomplemented
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2314yes—
114C22×C22⋊D11C2314yes—
115C22×C22⋊D11C2314yes—
116C22×C22⋊D11C2314yes—
117C22×C22⋊D11C2314yes—
118C23×Dic11—24no—
119C23×Dic11—24no—
120C23×Dic11—24no—
121C23×Dic11—24no—
122C23×Dic11—24no—
123C23×Dic11D418yescomplemented
124C23×Dic11C2311yescharacteristic
125C23×Dic11C2311yescharacteristic
126C23×Dic11C2314yes—
127C23×Dic11C2311yescharacteristic
128C23×Dic11C2311yescharacteristic
129C23×Dic11C2314yes—
130C23×Dic11C2311yescharacteristic
131C23×Dic11C2311yescharacteristic
132C2×#4341—2128no—
133C2×#4341—232no—
134C2×#4341—232no—
135C2×#4341—232no—
136C22×D44—24no—
137C22×D44—24no—
138C22×D44—42no—
139C22×D44C2314yes—
140C22×C4×D11—24no—
141C22×C4×D11—24no—
142C22×C4×D11—24no—
143C22×C4×D11C2314yes—
144C22×Dic22—24no—
145C22×Dic22—24no—
146C22×Dic22D418yescomplemented
147C22×Dic22C2314yes—
148C2×C11×C22⋊C4—24no—
149C2×C11×C22⋊C4—24no—
150C2×C11×C22⋊C4—42no—
151C2×C11×C22⋊C4C2314yes—
152C2×C11×C22⋊C4C2314yes—
153C2×C11×C22⋊C4C2314yes—
154C2×C22⋊Dic11—24no—
155C2×C22⋊Dic11—24no—
156C2×C22⋊Dic11—24no—
157C2×C22⋊Dic11—42no—
158C2×C22⋊Dic11C2314yes—
159C2×C22⋊Dic11C2314yes—
160C2×C22⋊Dic11C2314yes—
161C2×C22⋊Dic11C2314yes—
162#66993—232no—
163#66992—232no—
164C2×(C2×D11)⋊C4—24no—
165C2×(C2×D11)⋊C4—24no—
166C2×(C2×D11)⋊C4—24no—
167C2×(C2×D11)⋊C4—42no—
168C2×(C2×D11)⋊C4—42no—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2314yes—
171C2×(C2×D11)⋊C4C2314yes—
172C2×(C2×D11)⋊C4C2314yes—
173C2×(C2×D11)⋊C4C2314yes—
174C2×Dic11⋊C4—24no—
175C2×Dic11⋊C4C2314yes—
176C2×C4×Dic11—24no—
177C2×C4×Dic11—24no—
178C2×C4×Dic11C2314yes—
179C2×C4×Dic11C2314yes—
180#66938—232no—
181C11×#95C2314yes—
182C11⋊#95C2314yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2314yes—
186C11⋊#95C2314yes—
187C2×#2431—111nomaximal, Sylow
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×C11—22no—
200C24×C11—22no—
201C24×C11—22no—
202C24×C11—22no—
203C24×C11—22no—
204C24×C11—22no—
205C24×C11—22no—
206C24×C11—22no—
207C24×C11C2×D414yes—
208C24×C11C2×D414yes—
209C24×C11C2412yes—
210C24×C11C2412yes—
211C24×C11C2412yes—
212C24×C11C2411yescharacteristic
213C23×D11—22no—
214C23×D11—22no—
215C23×D11—22no—
216C23×D11—22no—
217C23×D11—22no—
218C23×D11—22no—
219C23×D11—22no—
220C23×D11—22no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11—22no—
226C23×D11C2×D414yes—
227C23×D11C2412yes—
228C23×D11C2412yes—
229C2×D4×C11—232no—
230C2×D4×C11—28no—
231C2×D4×C11—28no—
232C2×D4×C11—28no—
233C2×D4×C11—28no—
234C2×D4×C11—28no—
235C2×D4×C11—28no—
236C2×D4×C11—44no—
237C2×D4×C11—44no—
238C2×D4×C11—44no—
239C2×D4×C11—416no—
240C2×D4×C11—416no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—22no—
248C22×C4×C11—22no—
249C22×C4×C11—22no—
250C22×C4×C11—22no—
251C22×C4×C11C2×D414yes—
252C22×C4×C11#4114yescomplemented
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2412yes—
257C2×C22⋊D11—232no—
258C2×C22⋊D11—232no—
259C2×C22⋊D11—28no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—28no—
264C2×C22⋊D11—28no—
265C2×C22⋊D11—28no—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—28no—
271C2×C22⋊D11—28no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—416no—
277C2×C22⋊D11—416no—
278C2×C22⋊D11—416no—
279C2×C22⋊D11—416no—
280C2×C22⋊D11C2×D4116yescomplemented
281C22×Dic11—232no—
282C22×Dic11—232no—
283C22×Dic11—28no—
284C22×Dic11—28no—
285C22×Dic11—28no—
286C22×Dic11—28no—
287C22×Dic11—22no—
288C22×Dic11—22no—
289C22×Dic11—22no—
290C22×Dic11—22no—
291C22×Dic11—22no—
292C22×Dic11—28no—
293C22×Dic11—22no—
294C22×Dic11—22no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11C2×D414yes—
301C22×Dic11C2×D414yes—
302C22×Dic11C2×D414yes—
303C22×Dic11C2×D414yes—
304C22×Dic11C2×D414yes—
305C22×Dic11C2×D4116yescomplemented
306C22×Dic11#4114yescomplemented
307C22×Dic11C2412yes—
308C22×Dic11C2412yes—
309C22×Dic11C2412yes—
310C22×Dic11C2412yes—
311C22×Dic11C2412yes—
312C22×Dic11C2412yes—
313#4341—2256no—
314C2×D44—28no—
315C2×D44—28no—
316C2×D44—44no—
317C2×D44—416no—
318C2×C4×D11—232no—
319C2×C4×D11—28no—
320C2×C4×D11—28no—
321C2×C4×D11—28no—
322C2×Dic22—232no—
323C2×Dic22—28no—
324C2×Dic22—28no—
325C2×Dic22C2×D4116yescomplemented
326C11×C22⋊C4—28no—
327C11×C22⋊C4—28no—
328C11×C22⋊C4—44no—
329C22⋊Dic11—28no—
330C22⋊Dic11—28no—
331C22⋊Dic11—28no—
332C22⋊Dic11—44no—
333(C2×D11)⋊C4—28no—
334(C2×D11)⋊C4—28no—
335(C2×D11)⋊C4—28no—
336(C2×D11)⋊C4—44no—
337(C2×D11)⋊C4—44no—
338Dic11⋊C4—28no—
339C4×Dic11—28no—
340C4×Dic11—28no—
341C23×#41—111no—
342C22×#127—111no—
343C22×#124—111no—
344C22×#121—111no—
345#2431—1116no—
346C2×#392—111no—
347C2×#392—111no—
348C2×#392—111no—
349C2×#392D1111yescharacteristic, complemented
350C2×#391—111no—
351C2×#390—111no—
352C2×#386—111no—
353C2×#386—111no—
354C2×#386—111no—
355C2×#386—111no—
356C2×C4×C22⋊C4—111no—
357C23×C11—28no—
358C23×C11—28no—
359C23×C11—28no—
360C23×C11—28no—
361C23×C11—28no—
362C23×C11—28no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—44no—
383C23×C11—44no—
384C23×C11—44no—
385C23×C11—44no—
386C23×C11—44no—
387C23×C11—44no—
388C23×C11—44no—
389C23×C11—44no—
390C23×C11—44no—
391C23×C11—44no—
392C23×C11—44no—
393C23×C11—44no—
394C23×C11—44no—
395C23×C11—44no—
396C23×C11—44no—
397C23×C11C22×D414yes—
398C23×C11C22×D414yes—
399C23×C11C22×D412yes—
400C23×C11C22×D412yes—
401C23×C11C22×D412yes—
402C23×C11C2×#4112yes—
403C23×C11C2×#4112yes—
404C23×C11H(5,𝔽2)12yes—
405C23×C11H(5,𝔽2)12yes—
406C23×C11C2511yescharacteristic
407C22×D11—28no—
408C22×D11—28no—
409C22×D11—28no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—44no—
424C22×D11—44no—
425C22×D11—44no—
426C22×D11—44no—
427C22×D11—44no—
428C22×D11—44no—
429C22×D11—44no—
430C22×D11—44no—
431C22×D11—44no—
432C22×D11—44no—
433C22×D11—44no—
434C22×D11C22×D414yes—
435D4×C11—232no—
436D4×C11—416no—
437D4×C11—416no—
438C2×C4×C11—28no—
439C2×C4×C11—28no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—44no—
451C2×C4×C11—44no—
452C2×C4×C11C22×D414yes—
453C2×C4×C11C2×#4114yescomplemented
454C22⋊D11—232no—
455C22⋊D11—232no—
456C22⋊D11—416no—
457C22⋊D11—416no—
458C22⋊D11—416no—
459C22⋊D11—416no—
460C2×Dic11—232no—
461C2×Dic11—28no—
462C2×Dic11—28no—
463C2×Dic11—28no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—232no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—44no—
478C2×Dic11—44no—
479C2×Dic11#120116yes—
480C2×Dic11C22×D414yes—
481C2×Dic11C22×D414yes—
482C2×Dic11C22×D414yes—
483C2×Dic11C22×D414yes—
484C2×Dic11C22×D414yes—
485C2×Dic11C2×#4114yescomplemented
486D44—416no—
487C4×D11—232no—
488Dic22—232no—
489C22×#41—118no—
490C22×#41—228no—
491C22×#41—228no—
492C22×#41—228no—
493C23×Q8—111no—
494C23×D4—111no—
495C23×D4—111no—
496C23×D4—111no—
497C23×D4—111no—
498C23×D4—111no—
499C23×D4—111no—
500C23×D4—111no—
501C23×D4C2×D1111yescharacteristic
502C23×D4C2×D1111yescharacteristic
503C23×D4C2×D1111yescharacteristic
504C24×C4—111no—
505C24×C4—111no—
506C24×C4—111no—
507C2×#127—118no—
508C2×#127—228no—
509C2×#124—118no—
510C2×#124—228no—
511C2×#121—118no—
512C2×#121—228no—
513C22×C4⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517C22×C22⋊C4—111no—
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4C2×D1111yescharacteristic
524C22×C22⋊C4C2×D1111yescharacteristic
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C42—111no—
527C22×C42—111no—
528#392—118no—
529#392—118no—
530#392—118no—
531#392C2×D1118yescomplemented
532#391—118no—
533#390—118no—
534#386—118no—
535#386—118no—
536#386—118no—
537#386—118no—
538C4×C22⋊C4—118no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95C2×D1111yescharacteristic
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—24no—
548C22×C11—24no—
549C22×C11—24no—
550C22×C11—24no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—416no—
554C22×C11—416no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—88no—
569C22×C11C2×#12014yes—
570C22×C11#53214yes—
571C22×C11#53514yes—
572C22×C11#54614yes—
573C22×C11#54614yes—
574C22×C11#55014yes—
575C22×C11#55014yes—
576C22×C11C23×D411yescharacteristic
577C22×C11C23×D411yescharacteristic
578C22×C11C23×D411yescharacteristic
579C22×C11C22×#4111yescharacteristic
580C22×C11C22×#4111yescharacteristic
581C22×C11C2×H(5,𝔽2)11yescharacteristic
582C22×C11C2×H(5,𝔽2)11yescharacteristic
583C2×D11—24no—
584C2×D11—24no—
585C2×D11—24no—
586C2×D11—42no—
587C2×D11—42no—
588C2×D11—416no—
589C2×D11—42no—
590C2×D11—42no—
591C2×D11—42no—
592C2×D11—42no—
593C2×D11—42no—
594C2×D11—42no—
595C2×D11—42no—
596C2×D11—42no—
597C2×D11—42no—
598C2×D11—88no—
599C4×C11—24no—
600C4×C11—24no—
601C4×C11—42no—
602C4×C11—42no—
603Dic11—24no—
604Dic11—24no—
605Dic11—24no—
606Dic11—42no—
607Dic11—42no—
608Dic11C2×#12018yes—
609C25—111no—
610C25—111no—
611C25C22×D1111yescharacteristic
612C25C22×D1111yescharacteristic
613C25C22×D1111yescharacteristic
614C2×#41—2232no—
615C2×#41—2232no—
616C2×#41—2232no—
617C2×#41—22128no—
618C22×Q8—118no—
619C22×Q8—114no—
620C22×Q8—224no—
621C22×Q8—224no—
622C22×D4—24no—
623C22×D4—24no—
624C22×D4—24no—
625C22×D4—24no—
626C22×D4—24no—
627C22×D4—24no—
628C22×D4—42no—
629C22×D4—42no—
630C22×D4—42no—
631C22×D4—118no—
632C22×D4—114no—
633C22×D4—114no—
634C22×D4—114no—
635C22×D4—114no—
636C22×D4—114no—
637C22×D4—114no—
638C22×D4—114no—
639C22×D4—224no—
640C22×D4—224no—
641C22×D4—224no—
642C22×D4—224no—
643C22×D4—224no—
644C22×D4—224no—
645C22×D4—224no—
646C22×D4—224no—
647C22×D4—224no—
648C22×D4—224no—
649C22×D4—224no—
650C22×D4—224no—
651C22×D4—224no—
652C22×D4—224no—
653C22×D4—224no—
654C22×D4—442no—
655C22×D4—442no—
656C22×D4—442no—
657C22×D4—442no—
658C22×D4—442no—
659C22×D4C22×D1114yes—
660C22×D4C22×D1114yes—
661C22×D4C22×D1114yes—
662C23×C4—111no—
663C23×C4—118no—
664C23×C4—114no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4—111no—
668C23×C4—114no—
669C23×C4—111no—
670C23×C4—111no—
671C23×C4—114no—
672C23×C4—224no—
673C23×C4—224no—
674C23×C4—224no—
675C23×C4—224no—
676C23×C4—224no—
677C23×C4—224no—
678C23×C4—224no—
679C23×C4—224no—
680C23×C4C22×D1111yescharacteristic
681C23×C4C22×D1111yescharacteristic
682C23×C4C22×D1111yescharacteristic
683C23×C4C22×D1111yescharacteristic
684#127—2232no—
685#124—2232no—
686#121—2232no—
687C2×C4⋊C4—114no—
688C2×C4⋊C4—224no—
689C2×C22⋊C4—24no—
690C2×C22⋊C4—24no—
691C2×C22⋊C4—42no—
692C2×C22⋊C4—114no—
693C2×C22⋊C4—114no—
694C2×C22⋊C4—114no—
695C2×C22⋊C4—114no—
696C2×C22⋊C4—114no—
697C2×C22⋊C4—114no—
698C2×C22⋊C4—114no—
699C2×C22⋊C4—114no—
700C2×C22⋊C4—114no—
701C2×C22⋊C4—224no—
702C2×C22⋊C4—224no—
703C2×C22⋊C4—224no—
704C2×C22⋊C4—224no—
705C2×C22⋊C4—224no—
706C2×C22⋊C4—224no—
707C2×C22⋊C4—442no—
708C2×C22⋊C4—442no—
709C2×C22⋊C4—442no—
710C2×C22⋊C4C22×D1114yes—
711C2×C22⋊C4C22×D1114yes—
712C2×C22⋊C4C22×D1114yes—
713C2×C42—114no—
714C2×C42—114no—
715C2×C42—224no—
716C2×C42—224no—
717#95—114no—
718#95—114no—
719#95—114no—
720#95—114no—
721#95—114no—
722#95C22×D1114yes—
723C2×C11—44no—
724C2×C11—44no—
725C2×C11—82no—
726C2×C11#243118yescomplemented
727C2×C11C22×#12011yescharacteristic
728C2×C11C2×#53211yescharacteristic
729C2×C11C2×#53511yescharacteristic
730C2×C11C2×#54611yescharacteristic
731C2×C11C2×#54611yescharacteristic
732C2×C11C2×#55011yescharacteristic
733C2×C11C2×#55011yescharacteristic
734D11—44no—
735D11—82no—
736C24—22no—
737C24—22no—
738C24—22no—
739C24—22no—
740C24—22no—
741C24—22no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—22no—
754C24—22no—
755C24—114no—
756C24—112no—
757C24—112no—
758C24—222no—
759C24—222no—
760C24—222no—
761C24—222no—
762C24—222no—
763C24—222no—
764C24—222no—
765C24—222no—
766C24—222no—
767C24—222no—
768C24—222no—
769C24—222no—
770C24—222no—
771C24D4×D1114yes—
772C24D4×D1114yes—
773C24C23×D1112yes—
774C24C23×D1112yes—
775C24C23×D1112yes—
776C24C23×D1111yescharacteristic
777#41—22256no—
778C2×Q8—1116no—
779C2×Q8—2232no—
780C2×Q8—228no—
781C2×Q8—228no—
782C2×D4—232no—
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—28no—
786C2×D4—28no—
787C2×D4—28no—
788C2×D4—28no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—416no—
793C2×D4—416no—
794C2×D4—1116no—
795C2×D4—228no—
796C2×D4—2232no—
797C2×D4—228no—
798C2×D4—228no—
799C2×D4—228no—
800C2×D4—228no—
801C2×D4—228no—
802C2×D4—228no—
803C2×D4—228no—
804C2×D4—228no—
805C2×D4—228no—
806C2×D4—2232no—
807C2×D4—228no—
808C2×D4—228no—
809C2×D4—228no—
810C2×D4—228no—
811C2×D4—228no—
812C2×D4—444no—
813C2×D4—4416no—
814C2×D4—4416no—
815C2×D4—444no—
816C2×D4—444no—
817C2×D4—444no—
818C2×D4—444no—
819C2×D4—4416no—
820C2×D4—4416no—
821C2×D4—4416no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—114no—
833C22×C4—114no—
834C22×C4—114no—
835C22×C4—112no—
836C22×C4—114no—
837C22×C4—114no—
838C22×C4—1116no—
839C22×C4—114no—
840C22×C4—112no—
841C22×C4—112no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—228no—
846C22×C4—228no—
847C22×C4—2232no—
848C22×C4—2232no—
849C22×C4—228no—
850C22×C4—228no—
851C22×C4—228no—
852C22×C4—228no—
853C22×C4—2232no—
854C22×C4—222no—
855C22×C4—222no—
856C22×C4—222no—
857C22×C4—222no—
858C22×C4—222no—
859C22×C4—228no—
860C22×C4—222no—
861C22×C4—228no—
862C22×C4—222no—
863C22×C4—222no—
864C22×C4—222no—
865C22×C4—222no—
866C22×C4—222no—
867C22×C4—222no—
868C22×C4D4×D1114yes—
869C22×C4#434114yescomplemented
870C22×C4C23×D1112yes—
871C22×C4C23×D1112yes—
872C22×C4C23×D1112yes—
873C22×C4C23×D1112yes—
874C4⋊C4—228no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—44no—
878C22⋊C4—228no—
879C22⋊C4—228no—
880C22⋊C4—228no—
881C22⋊C4—228no—
882C22⋊C4—228no—
883C22⋊C4—228no—
884C22⋊C4—444no—
885C22⋊C4—444no—
886C22⋊C4—444no—
887C42—228no—
888C42—228no—
889C11C2×#243111yescharacteristic, complemented, Sylow
890C23—28no—
891C23—28no—
892C23—28no—
893C23—28no—
894C23—28no—
895C23—28no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—44no—
921C23—44no—
922C23—44no—
923C23—44no—
924C23—44no—
925C23—44no—
926C23—44no—
927C23—44no—
928C23—44no—
929C23—44no—
930C23—114no—
931C23—228no—
932C23—228no—
933C23—228no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—444no—
948C23—444no—
949C23—444no—
950C23—444no—
951C23—444no—
952C23—444no—
953C23—444no—
954C23—444no—
955C23—444no—
956C23—444no—
957C23—444no—
958C23C2×D4×D1114yes—
959C23C2×D4×D1114yes—
960C23C2×D4×D1112yes—
961C23C2×D4×D1112yes—
962C23C2×D4×D1112yes—
963C23C2×#434112yes—
964C23#6703712yes—
965C23#6703712yes—
966C23#41×D1112yes—
967C23C24×D1111yescharacteristic
968Q8—2232no—
969D4—232no—
970D4—416no—
971D4—416no—
972D4—2232no—
973D4—2232no—
974D4—4416no—
975D4—4416no—
976D4—4416no—
977D4—4416no—
978D4—4416no—
979C2×C4—28no—
980C2×C4—28no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—44no—
992C2×C4—44no—
993C2×C4—1116no—
994C2×C4—114no—
995C2×C4—114no—
996C2×C4—114no—
997C2×C4—114no—
998C2×C4—114no—
999C2×C4—114no—
1000C2×C4—2232no—
1001C2×C4—2232no—
1002C2×C4—2232no—
1003C2×C4—228no—
1004C2×C4—228no—
1005C2×C4—228no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—444no—
1019C2×C4—444no—
1020C2×C4C2×D4×D1114yes—
1021C2×C4C2×#434114yescomplemented
1022C22—24no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—24no—
1027C22—24no—
1028C22—42no—
1029C22—42no—
1030C22—416no—
1031C22—416no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—88no—
1046C22—224no—
1047C22—224no—
1048C22—224no—
1049C22—442no—
1050C22—442no—
1051C22—4416no—
1052C22—442no—
1053C22—442no—
1054C22—442no—
1055C22—442no—
1056C22—442no—
1057C22—442no—
1058C22—442no—
1059C22—442no—
1060C22—442no—
1061C22—888no—
1062C22D11×#12014yes—
1063C22#1062312214yes—
1064C22#1062312314yes—
1065C22#1062312714yes—
1066C22#1062313014yes—
1067C22#1062314114yes—
1068C22#1062324914yes—
1069C22C22×D4×D1111yescharacteristic
1070C22C22×D4×D1111yescharacteristic
1071C22C22×D4×D1111yescharacteristic
1072C22C22×#434111yescharacteristic
1073C22C2×#6703711yescharacteristic
1074C22C2×#6703711yescharacteristic
1075C22C2×#41×D1111yescharacteristic
1076C4—24no—
1077C4—24no—
1078C4—42no—
1079C4—42no—
1080C4—118no—
1081C4—224no—
1082C4—224no—
1083C4—224no—
1084C4—442no—
1085C4—442no—
1086C2—44no—
1087C2—44no—
1088C2—82no—
1089C2—444no—
1090C2—882no—
1091C2#1307223018yesdirect product factor
1092C2C2×D11×#12011yescharacteristic
1093C2C2×#1062312711yescharacteristic
1094C2C2×#1062312311yescharacteristic
1095C2C2×#1062312211yescharacteristic
1096C2C2×#1062314111yescharacteristic
1097C2C2×#1062313011yescharacteristic
1098C2C2×#1062324911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2431
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C23×#4341C2semidirect
2. C22×#66993C2semidirect
3. C22×#66938C2semidirect
4. C22×#66992C2semidirect
5. #13072230C2direct (N × H)
6. C2×#10622573C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622569C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#392C2semidirect
31. C22×#4341C22semidirect
43. C2×#66993C22semidirect
45. C2×#66992C22semidirect
55. C2×#66938C22semidirect
56. C11×#392C22semidirect
58. #10622836C22semidirect
59. #10622836C22semidirect
60. #10622833C22semidirect
66. #10622573C22semidirect
67. #10622571C22semidirect
68. #10622570C22semidirect
69. #10622569C22semidirect
70. C22⋊C4×Dic11C22semidirect
71. #10622278C22semidirect
72. #10622259C22semidirect
111. C22×C22⋊D11D4semidirect
123. C23×Dic11D4semidirect
146. C22×Dic22D4semidirect
252. C22×C4×C11#41semidirect
280. C2×C22⋊D11C2×D4semidirect
305. C22×Dic11C2×D4semidirect
306. C22×Dic11#41semidirect
325. C2×Dic22C2×D4semidirect
349. C2×#392D11semidirect
453. C2×C4×C11C2×#41semidirect
485. C2×Dic11C2×#41semidirect
531. #392C2×D11semidirect
726. C2×C11#2431semidirect
869. C22×C4#4341semidirect
889. C11C2×#2431semidirect
1021. C2×C4C2×#4341semidirect
1091. C2#13072230direct (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×#669932
C22×#669382
C22×#669922
#130722302
C2×#106225732
C2×#106228362
C2×#106222592
C2×#106225702
C2×#106228332
C2×#106222782
C2×#106225712
C2×#106225692
C2×C22⋊C4×Dic112
C2×C11×#3922
C2×#243111