Finite Group Databasebeta

← C2×#13071337 #14912572

Subgroups — C2×#13071337 #14912572

Order 2816.

4430 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13071337C2116yesmaximal, direct product factor
5C2×#10622570C211yesmaximal, characteristic, complemented
6C2×#10622570C211yesmaximal, characteristic, complemented
7C2×#10622833C211yesmaximal, characteristic, complemented
8C2×#10622826C211yesmaximal, characteristic, complemented
9C2×#10622278C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622571C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622263C211yesmaximal, characteristic, complemented
15C2×#10622261C211yesmaximal, 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
23C24×Dic11C2211yescharacteristic
24C23×D44C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66993C4116yescomplemented
34C2×#66993C2218yes—
35C2×C4×C22⋊D11—28no—
36C2×C4×C22⋊D11C2218yescomplemented
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×(C22⋊D11)⋊C4—28no—
49C2×(C22⋊D11)⋊C4C2218yescomplemented
50C11×#386C2218yescomplemented
51C2×C11×#95C2211yescharacteristic
52C2×C11×#95C2211yescharacteristic
53#10622833C2218yescomplemented
54#10622826C2218yescomplemented
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622571C2218yescomplemented
62#10622570C2218yescomplemented
63#10622570C2218yescomplemented
64#10622569C2218yescomplemented
65#10622569C2218yescomplemented
66#10622278C2218yescomplemented
67#10622278C2218yescomplemented
68#10622263C2218yescomplemented
69#10622261C2218yescomplemented
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C22×D4×C11—42no—
75C22×D4×C11—42no—
76C22×D4×C11C2×C418yescomplemented
77C22×D4×C11C2314yes—
78C23×C4×C11—24no—
79C23×C4×C11—42no—
80C23×C4×C11—42no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2314yes—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11C2×C418yescomplemented
96C22×C22⋊D11C2×C418yescomplemented
97C22×C22⋊D11C2×C418yescomplemented
98C22×C22⋊D11C2×C418yescomplemented
99C22×C22⋊D11C2314yes—
100C22×C22⋊D11C2314yes—
101C22×C22⋊D11C2314yes—
102C22×C22⋊D11C2314yes—
103C23×Dic11—24no—
104C23×Dic11—42no—
105C23×Dic11—42no—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2314yes—
112C23×Dic11C2311yescharacteristic
113C22×D44—42no—
114C22×D44—42no—
115C22×D44C2×C418yescomplemented
116C22×D44C2314yes—
117C22×C4×D11—24no—
118C22×C4×D11—24no—
119C22×C4×D11—42no—
120C22×C4×D11—42no—
121C22×C4×D11—42no—
122C22×C4×D11—42no—
123C22×C4×D11C2314yes—
124C22×C4×D11C2314yes—
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4—42no—
127C2×C11×C22⋊C4—42no—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C22⋊Dic11—24no—
132C2×C22⋊Dic11—42no—
133C2×C22⋊Dic11—42no—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137#66993C2×C4164yescomplemented
138C4×C22⋊D11—232no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4—42no—
143C2×(C2×D11)⋊C4—42no—
144C2×(C2×D11)⋊C4—42no—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×Dic11⋊C4—24no—
152C2×Dic11⋊C4—24no—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×C4×Dic11—24no—
156C2×C4×Dic11C2×C418yescomplemented
157C2×C4×Dic11D418yescomplemented
158C2×C4×Dic11C2314yes—
159C2×C4×Dic11C2314yes—
160C2×C4×Dic11C2314yes—
161(C22⋊D11)⋊C4—232no—
162C11×#95C2314yes—
163C11×#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C2×#2328—111nomaximal, Sylow
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11C22×C414yes—
184C24×C11C22×C414yes—
185C24×C11C2412yes—
186C24×C11C2412yes—
187C24×C11C2411yescharacteristic
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—22no—
199C23×D11—22no—
200C23×D11C22×C414yes—
201C23×D11C22×C414yes—
202C23×D11C2412yes—
203C23×D11C2412yes—
204C2×D4×C11—416no—
205C2×D4×C11—44no—
206C2×D4×C11—44no—
207C2×D4×C11C22×C4116yescomplemented
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—28no—
222C22×C4×C11—44no—
223C22×C4×C11—44no—
224C22×C4×C11—416no—
225C22×C4×C11C22×C414yes—
226C22×C4×C11C2×D414yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C2×C22⋊D11—232no—
233C2×C22⋊D11—232no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—416no—
239C2×C22⋊D11—416no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11C22×C4116yescomplemented
245C2×C22⋊D11C22×C4116yescomplemented
246C2×C22⋊D11C22×C4116yescomplemented
247C2×C22⋊D11C22×C4116yescomplemented
248C22×Dic11—28no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—22no—
261C22×Dic11—22no—
262C22×Dic11—44no—
263C22×Dic11—44no—
264C22×Dic11—416no—
265C22×Dic11C22×C414yes—
266C22×Dic11C22×C414yes—
267C22×Dic11C2×D414yes—
268C22×Dic11C2×D414yes—
269C22×Dic11#4114yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276C2×D44—416no—
277C2×D44—44no—
278C2×D44—44no—
279C2×D44C22×C4116yescomplemented
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—44no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11—44no—
286C2×C4×D11—416no—
287C2×C4×D11—416no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—44no—
290C11×C22⋊C4—44no—
291C22⋊Dic11—28no—
292C22⋊Dic11—44no—
293C22⋊Dic11—44no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—44no—
297(C2×D11)⋊C4—44no—
298(C2×D11)⋊C4—44no—
299(C2×D11)⋊C4—44no—
300Dic11⋊C4—28no—
301Dic11⋊C4—28no—
302C4×Dic11—28no—
303C4×Dic11C22×C4116yescomplemented
304C4×Dic11C2×D4116yescomplemented
305C22×#127—111no—
306C22×C4×D4—111no—
307C22×C4×D4—111no—
308#2328—1116no—
309C2×#390—111no—
310C2×#390—111no—
311C2×#386—111no—
312C2×#386—111no—
313C2×#386—111no—
314C2×#386—111no—
315C2×#386—111no—
316C2×#386—111no—
317C2×#386—111no—
318C2×#386D1111yescharacteristic, complemented
319C2×#382—111no—
320C2×#376—111no—
321C23×C11—28no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—28no—
326C23×C11—28no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11C23×C414yes—
348C23×C11C23×C414yes—
349C23×C11C23×C412yes—
350C23×C11C22×D412yes—
351C23×C11C2×#4112yes—
352C23×C11H(5,𝔽2)12yes—
353C23×C11H(5,𝔽2)12yes—
354C23×C11H(5,𝔽2)12yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11C2511yescharacteristic
357C22×D11—28no—
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—28no—
362C22×D11—28no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—44no—
376C22×D11—44no—
377C22×D11—44no—
378C22×D11—44no—
379C22×D11—44no—
380C22×D11—44no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11C23×C414yes—
384C22×D11C23×C414yes—
385D4×C11—416no—
386C2×C4×C11—28no—
387C2×C4×C11—28no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—416no—
402C2×C4×C11—44no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11C23×C414yes—
406C2×C4×C11C22×D414yes—
407C22⋊D11—232no—
408C22⋊D11—232no—
409C22⋊D11—416no—
410C22⋊D11—416no—
411C2×Dic11—28no—
412C2×Dic11—28no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—416no—
427C2×Dic11—44no—
428C2×Dic11—44no—
429C2×Dic11—44no—
430C2×Dic11C4×D4116yes—
431C2×Dic11C23×C414yes—
432C2×Dic11C23×C414yes—
433C2×Dic11C22×D414yes—
434C2×Dic11C22×D414yes—
435C2×Dic11C2×#4114yes—
436D44—416no—
437C4×D11—416no—
438C4×D11—416no—
439C23×D4—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4C2×D1111yescharacteristic
445C24×C4—111no—
446C24×C4—111no—
447C24×C4—111no—
448C24×C4C2×D1111yescharacteristic
449C2×#127—118no—
450C2×#127—1116no—
451C2×C4×D4—118no—
452C2×C4×D4—118no—
453C2×C4×D4—228no—
454C2×C4×D4—228no—
455C22×C4⋊C4—111no—
456C22×C4⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4C2×D1111yescharacteristic
467C22×C22⋊C4C2×D1111yescharacteristic
468C22×C22⋊C4C2×D1111yescharacteristic
469C22×C42—111no—
470C22×C42—111no—
471C22×C42—111no—
472#390—118no—
473#390—118no—
474#386—118no—
475#386—118no—
476#386—118no—
477#386—118no—
478#386—118no—
479#386—118no—
480#386—118no—
481#386C2×D1118yescomplemented
482#382—118no—
483#376—118no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95C2×D1111yescharacteristic
491C2×#95C2×D1111yescharacteristic
492C22×C11—24no—
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—24no—
497C22×C11—24no—
498C22×C11—416no—
499C22×C11—416no—
500C22×C11—42no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11C2×C4×D414yes—
509C22×C11#51814yes—
510C22×C11#51814yes—
511C22×C11#53514yes—
512C22×C11#53514yes—
513C22×C11#54014yes—
514C22×C11#54014yes—
515C22×C11C24×C411yescharacteristic
516C22×C11C23×D411yescharacteristic
517C22×C11C22×#4111yescharacteristic
518C22×C11C2×H(5,𝔽2)11yescharacteristic
519C22×C11C2×H(5,𝔽2)11yescharacteristic
520C22×C11C2×H(5,𝔽2)11yescharacteristic
521C22×C11C2×H(5,𝔽2)11yescharacteristic
522C2×D11—24no—
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—24no—
527C2×D11—24no—
528C2×D11—416no—
529C2×D11—416no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C4×C11—24no—
539C4×C11—24no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543Dic11—24no—
544Dic11—24no—
545Dic11—42no—
546Dic11—42no—
547Dic11—42no—
548Dic11C2×C4×D418yes—
549C25—111no—
550C25—111no—
551C25C22×D1111yescharacteristic
552C25C22×D1111yescharacteristic
553C22×D4—42no—
554C22×D4—42no—
555C22×D4—118no—
556C22×D4—118no—
557C22×D4—114no—
558C22×D4—114no—
559C22×D4—118no—
560C22×D4—118no—
561C22×D4—114no—
562C22×D4—114no—
563C22×D4—118no—
564C22×D4—114no—
565C22×D4—224no—
566C22×D4—224no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—442no—
570C22×D4—442no—
571C22×D4—442no—
572C22×D4—442no—
573C22×D4—442no—
574C22×D4—442no—
575C22×D4C4×D1118yescomplemented
576C22×D4C22×D1114yes—
577C23×C4—24no—
578C23×C4—42no—
579C23×C4—42no—
580C23×C4—111no—
581C23×C4—111no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—114no—
587C23×C4—114no—
588C23×C4—114no—
589C23×C4—224no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—442no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4—442no—
597C23×C4—442no—
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1114yes—
604#127—1164no—
605C4×D4—2232no—
606C4×D4—2232no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—224no—
610C2×C4⋊C4—224no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4—42no—
614C2×C22⋊C4—114no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—114no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4—114no—
623C2×C22⋊C4—224no—
624C2×C22⋊C4—224no—
625C2×C22⋊C4—224no—
626C2×C22⋊C4—442no—
627C2×C22⋊C4—442no—
628C2×C22⋊C4—442no—
629C2×C22⋊C4—442no—
630C2×C22⋊C4—442no—
631C2×C22⋊C4—442no—
632C2×C22⋊C4C22×D1114yes—
633C2×C22⋊C4C22×D1114yes—
634C2×C22⋊C4C22×D1114yes—
635C2×C42—118no—
636C2×C42—118no—
637C2×C42—114no—
638C2×C42—114no—
639C2×C42—114no—
640C2×C42—224no—
641#95—114no—
642#95—114no—
643#95—114no—
644#95—114no—
645#95—114no—
646#95—114no—
647#95C22×D1114yes—
648#95C22×D1114yes—
649C2×C11—44no—
650C2×C11—44no—
651C2×C11#232818yescomplemented
652C2×C11C22×C4×D411yescharacteristic
653C2×C11C2×#51811yescharacteristic
654C2×C11C2×#51811yescharacteristic
655C2×C11C2×#53511yescharacteristic
656C2×C11C2×#53511yescharacteristic
657C2×C11C2×#54011yescharacteristic
658C2×C11C2×#54011yescharacteristic
659D11—44no—
660D11—44no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—114no—
674C24—114no—
675C24—112no—
676C24—112no—
677C24—222no—
678C24—222no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24C2×C4×D1114yes—
690C24C2×C4×D1114yes—
691C24C23×D1112yes—
692C24C23×D1112yes—
693C24C23×D1111yescharacteristic
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—416no—
697C2×D4—1116no—
698C2×D4—1116no—
699C2×D4—1116no—
700C2×D4—1116no—
701C2×D4—1116no—
702C2×D4—228no—
703C2×D4—228no—
704C2×D4—2232no—
705C2×D4—2232no—
706C2×D4—228no—
707C2×D4—228no—
708C2×D4—4416no—
709C2×D4—444no—
710C2×D4—444no—
711C2×D4—4416no—
712C2×D4—4416no—
713C2×D4—444no—
714C2×D4—444no—
715C2×D4—444no—
716C2×D4—444no—
717C2×D4C2×C4×D11116yescomplemented
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—28no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—416no—
735C22×C4—114no—
736C22×C4—114no—
737C22×C4—114no—
738C22×C4—112no—
739C22×C4—114no—
740C22×C4—114no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—228no—
747C22×C4—228no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—222no—
751C22×C4—222no—
752C22×C4—222no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—228no—
762C22×C4—444no—
763C22×C4—444no—
764C22×C4—444no—
765C22×C4—444no—
766C22×C4—4416no—
767C22×C4—4416no—
768C22×C4—444no—
769C22×C4—444no—
770C22×C4—4416no—
771C22×C4C2×C4×D1114yes—
772C22×C4D4×D1114yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C22×C4C23×D1112yes—
777C22×C4C23×D1112yes—
778C4⋊C4—228no—
779C4⋊C4—228no—
780C22⋊C4—28no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—444no—
787C22⋊C4—444no—
788C22⋊C4—444no—
789C22⋊C4—444no—
790C22⋊C4—444no—
791C22⋊C4—444no—
792C42—1116no—
793C42—1116no—
794C42—228no—
795C11C2×#232811yescharacteristic, complemented, Sylow
796C23—28no—
797C23—28no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—114no—
823C23—114no—
824C23—228no—
825C23—228no—
826C23—228no—
827C23—228no—
828C23—228no—
829C23—228no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23C22×C4×D1114yes—
851C23C22×C4×D1114yes—
852C23C22×C4×D1112yes—
853C23C2×D4×D1112yes—
854C23#6703712yes—
855C23#6703712yes—
856C23#6703712yes—
857C23#41×D1112yes—
858C23#6704212yes—
859C23C24×D1111yescharacteristic
860D4—416no—
861D4—2232no—
862D4—2232no—
863D4—4416no—
864D4—4416no—
865D4—4416no—
866C2×C4—28no—
867C2×C4—28no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—416no—
882C2×C4—44no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—1116no—
886C2×C4—114no—
887C2×C4—114no—
888C2×C4—114no—
889C2×C4—114no—
890C2×C4—114no—
891C2×C4—228no—
892C2×C4—228no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—4416no—
907C2×C4—4416no—
908C2×C4—4416no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4—444no—
912C2×C4C22×C4×D1114yes—
913C2×C4C2×D4×D1114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—416no—
929C22—416no—
930C22—224no—
931C22—224no—
932C22—224no—
933C22—224no—
934C22—224no—
935C22—224no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—4416no—
945C22—4416no—
946C22#1062301714yes—
947C22C4×D4×D1114yes—
948C22#1062307614yes—
949C22#1062312314yes—
950C22#1062313814yes—
951C22#1062314614yes—
952C22#1062319414yes—
953C22C23×C4×D1111yescharacteristic
954C22C22×D4×D1111yescharacteristic
955C22C2×#6703711yescharacteristic
956C22C2×#6703711yescharacteristic
957C22C2×#6703711yescharacteristic
958C22C2×#41×D1111yescharacteristic
959C22C2×#6704211yescharacteristic
960C4—24no—
961C4—24no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—118no—
966C4—224no—
967C4—224no—
968C4—442no—
969C4—442no—
970C4—442no—
971C2—44no—
972C2—44no—
973C2—444no—
974C2—444no—
975C2#1307133718yesdirect product factor
976C2C2×C4×D4×D1111yescharacteristic
977C2C2×#1062307611yescharacteristic
978C2C2×#1062301711yescharacteristic
979C2C2×#1062312311yescharacteristic
980C2C2×#1062313811yescharacteristic
981C2C2×#1062314611yescharacteristic
982C2C2×#1062319411yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66993C2
cosocleC23×C11C25
hypercenterC2×#386D11
hypocenterC11C2×#2328
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13071337C2direct (N × H)
5. C2×#10622570C2semidirect
6. C2×#10622570C2semidirect
7. C2×#10622833C2semidirect
8. C2×#10622826C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622571C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622263C2semidirect
15. C2×#10622261C2semidirect
16. C2×C11×#386C2semidirect
33. C2×#66993C4semidirect
36. C2×C4×C22⋊D11C22semidirect
49. C2×(C22⋊D11)⋊C4C22semidirect
50. C11×#386C22semidirect
53. #10622833C22semidirect
54. #10622826C22semidirect
61. #10622571C22semidirect
62. #10622570C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
65. #10622569C22semidirect
66. #10622278C22semidirect
67. #10622278C22semidirect
68. #10622263C22semidirect
69. #10622261C22semidirect
76. C22×D4×C11C2×C4semidirect
95. C22×C22⋊D11C2×C4semidirect
96. C22×C22⋊D11C2×C4semidirect
97. C22×C22⋊D11C2×C4semidirect
98. C22×C22⋊D11C2×C4semidirect
115. C22×D44C2×C4semidirect
137. #66993C2×C4semidirect
156. C2×C4×Dic11C2×C4semidirect
157. C2×C4×Dic11D4semidirect
207. C2×D4×C11C22×C4semidirect
244. C2×C22⋊D11C22×C4semidirect
245. C2×C22⋊D11C22×C4semidirect
246. C2×C22⋊D11C22×C4semidirect
247. C2×C22⋊D11C22×C4semidirect
279. C2×D44C22×C4semidirect
303. C4×Dic11C22×C4semidirect
304. C4×Dic11C2×D4semidirect
318. C2×#386D11semidirect
481. #386C2×D11semidirect
575. C22×D4C4×D11semidirect
651. C2×C11#2328semidirect
717. C2×D4C2×C4×D11semidirect
795. C11C2×#2328semidirect
975. C2#13071337direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669932
C22×C4×C22⋊D112
C22×(C22⋊D11)⋊C42
#130713372
C2×#106225702
C2×#106228332
C2×#106228262
C2×#106222782
C2×#106225712
C2×#106225692
C2×#106222632
C2×#106222612
C2×C11×#3862
C2×#232811