Finite Group Databasebeta

← C2×#13073582 #14924930

Subgroups — C2×#13073582 #14924930

Order 2816.

4174 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×#66938C211yesmaximal, characteristic, complemented
3C22×#66938C211yesmaximal, characteristic, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
5#13073582C2116yesmaximal, direct product factor
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, 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×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C23×D44C2211yescharacteristic
24C23×C4×D11C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C2×#66993—28no—
35C2×#66993C2218yes—
36C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66938—28no—
49C2×#66938—28no—
50C2×#66938C2218yescomplemented
51C2×#66938C2218yescomplemented
52C2×(C22⋊D11)⋊C4—28no—
53C2×(C22⋊D11)⋊C4C2218yescomplemented
54C11×#394C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56#10622833C2218yescomplemented
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622604C2218yescomplemented
63C4⋊C4×Dic11C2218yescomplemented
64#10622574C2218yescomplemented
65#10622574C2218yescomplemented
66#10622571C2218yescomplemented
67#10622570C2218yescomplemented
68#10622569C2218yescomplemented
69#10622278C2218yescomplemented
70#10622259C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11C2314yes—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11D418yes—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C23×Dic11—24no—
101C23×Dic11—42no—
102C23×Dic11—42no—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2314yes—
109C23×Dic11C2311yescharacteristic
110C22×D44—24no—
111C22×D44—24no—
112C22×D44—42no—
113C22×D44C2314yes—
114C22×C4×D11—24no—
115C22×C4×D11—42no—
116C22×C4×D11—42no—
117C22×C4×D11C2314yes—
118C22×Dic22—24no—
119C22×Dic22—24no—
120C22×Dic22—24no—
121C22×Dic22C2314yes—
122C2×C11×C4⋊C4—24no—
123C2×C11×C4⋊C4C2314yes—
124C2×C11×C22⋊C4—24no—
125C2×C11×C22⋊C4—24no—
126C2×C11×C22⋊C4—24no—
127C2×C11×C22⋊C4—42no—
128C2×C11×C22⋊C4C2314yes—
129C2×C11×C22⋊C4C2314yes—
130C2×C11×C22⋊C4C2314yes—
131C2×C11×C22⋊C4C2314yes—
132C2×C22⋊Dic11—24no—
133C2×C22⋊Dic11—24no—
134C2×C22⋊Dic11—42no—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138#66993—232no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—42no—
145C2×(C2×D11)⋊C4—42no—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×C4⋊Dic11—24no—
154C2×C4⋊Dic11C2314yes—
155C2×Dic11⋊C4—24no—
156C2×Dic11⋊C4C2314yes—
157C2×C4×Dic11—24no—
158C2×C4×Dic11—24no—
159C2×C4×Dic11D418yescomplemented
160C2×C4×Dic11C2314yes—
161C2×C4×Dic11C2314yes—
162C2×C4×Dic11C2314yes—
163#66938—232no—
164#66938—232no—
165(C22⋊D11)⋊C4—232no—
166C11×#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C2×#2544—111nomaximal, Sylow
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×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11C2×D414yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
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×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11C2×D414yes—
204C23×D11C2412yes—
205C23×D11C2412yes—
206C2×D4×C11—28no—
207C2×D4×C11—28no—
208C2×D4×C11—44no—
209C2×D4×C11—416no—
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—22no—
222C22×C4×C11—22no—
223C22×C4×C11C2×D414yes—
224C22×C4×C11#4114yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C2×C22⋊D11—232no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—44no—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—416no—
243C2×C22⋊D11—416no—
244C2×C22⋊D11—416no—
245C2×C22⋊D11C2×D4116yes—
246C22×Dic11—28no—
247C22×Dic11—22no—
248C22×Dic11—22no—
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—44no—
261C22×Dic11—44no—
262C22×Dic11—416no—
263C22×Dic11C2×D414yes—
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11#4114yes—
267C22×Dic11#4114yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C2×D44—28no—
275C2×D44—28no—
276C2×D44—44no—
277C2×D44—416no—
278C2×C4×D11—28no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—416no—
282C2×Dic22—28no—
283C2×Dic22—28no—
284C2×Dic22—28no—
285C2×Dic22—416no—
286C11×C4⋊C4—28no—
287C11×C22⋊C4—28no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C11×C22⋊C4—44no—
291C22⋊Dic11—28no—
292C22⋊Dic11—28no—
293C22⋊Dic11—44no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298(C2×D11)⋊C4—28no—
299(C2×D11)⋊C4—44no—
300(C2×D11)⋊C4—44no—
301C4⋊Dic11—28no—
302Dic11⋊C4—28no—
303C4×Dic11—28no—
304C4×Dic11—28no—
305C4×Dic11C2×D4116yescomplemented
306C22×#127—111no—
307C22×#124—111no—
308C22×#124—111no—
309C22×C4×D4—111no—
310#2544—1116no—
311C2×#394—111no—
312C2×#394—111no—
313C2×#394—111no—
314C2×#394D1111yescharacteristic, complemented
315C2×#391—111no—
316C2×#390—111no—
317C2×#386—111no—
318C2×#386—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×C4×C4⋊C4—111no—
322C23×C11—28no—
323C23×C11—28no—
324C23×C11—28no—
325C23×C11—22no—
326C23×C11—22no—
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—44no—
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×C11—44no—
348C23×C11—44no—
349C23×C11C22×D414yes—
350C23×C11C22×D412yes—
351C23×C11C22×D412yes—
352C23×C11C2×#4112yes—
353C23×C11C2×#4112yes—
354C23×C11C2×#4112yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11H(5,𝔽2)12yes—
357C23×C11C2511yescharacteristic
358C22×D11—28no—
359C22×D11—28no—
360C22×D11—28no—
361C22×D11—22no—
362C22×D11—22no—
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—44no—
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×D11—44no—
384C22×D11—44no—
385C22×D11C22×D414yes—
386D4×C11—416no—
387C2×C4×C11—28no—
388C2×C4×C11—28no—
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—22no—
402C2×C4×C11—44no—
403C2×C4×C11—44no—
404C2×C4×C11—44no—
405C2×C4×C11C22×D414yes—
406C2×C4×C11C2×#4114yes—
407C22⋊D11—232no—
408C22⋊D11—416no—
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×Dic11#121116yes—
431C2×Dic11C22×D414yes—
432C2×Dic11C22×D414yes—
433C2×Dic11C22×D414yes—
434C2×Dic11C2×#4114yes—
435C2×Dic11C2×#4114yes—
436D44—416no—
437C4×D11—416no—
438Dic22—416no—
439C23×Q8—111no—
440C23×D4—111no—
441C23×D4—111no—
442C23×D4—111no—
443C23×D4—111no—
444C23×D4—111no—
445C23×D4C2×D1111yescharacteristic
446C24×C4—111no—
447C24×C4—111no—
448C2×#127—118no—
449C2×#127—228no—
450C2×#124—118no—
451C2×#124—118no—
452C2×#124—228no—
453C2×#124—228no—
454C2×C4×D4—118no—
455C2×C4×D4—228no—
456C22×C4⋊C4—111no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C22⋊C4—111no—
469C22×C22⋊C4C2×D1111yescharacteristic
470C22×C22⋊C4C2×D1111yescharacteristic
471C22×C22⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4C2×D1111yescharacteristic
473C22×C42—111no—
474C22×C42—111no—
475C22×C42—111no—
476#394—118no—
477#394—118no—
478#394—118no—
479#394C2×D1118yescomplemented
480#391—118no—
481#390—118no—
482#386—118no—
483#386—118no—
484#386—118no—
485#386—118no—
486C4×C4⋊C4—118no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95C2×D1111yescharacteristic
493C22×C11—24no—
494C22×C11—24no—
495C22×C11—24no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—416no—
501C22×C11—42no—
502C22×C11—42no—
503C22×C11—42no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—88no—
509C22×C11C2×#12114yes—
510C22×C11#53214yes—
511C22×C11#53514yes—
512C22×C11#54614yes—
513C22×C11#54614yes—
514C22×C11#55914yes—
515C22×C11#55914yes—
516C22×C11C23×D411yescharacteristic
517C22×C11C23×D411yescharacteristic
518C22×C11C22×#4111yescharacteristic
519C22×C11C22×#4111yescharacteristic
520C22×C11C22×#4111yescharacteristic
521C22×C11C2×H(5,𝔽2)11yescharacteristic
522C22×C11C2×H(5,𝔽2)11yescharacteristic
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—416no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—88no—
539C4×C11—24no—
540C4×C11—24no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544Dic11—24no—
545Dic11—24no—
546Dic11—42no—
547Dic11—42no—
548Dic11—42no—
549Dic11C2×#12118yes—
550C25—111no—
551C25—111no—
552C25C22×D1111yescharacteristic
553C25C22×D1111yescharacteristic
554C22×Q8—114no—
555C22×Q8—224no—
556C22×Q8—224no—
557C22×Q8—224no—
558C22×D4—24no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—118no—
562C22×D4—114no—
563C22×D4—114no—
564C22×D4—114no—
565C22×D4—114no—
566C22×D4—114no—
567C22×D4—224no—
568C22×D4—224no—
569C22×D4—224no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—224no—
574C22×D4—224no—
575C22×D4—224no—
576C22×D4—224no—
577C22×D4—224no—
578C22×D4—442no—
579C22×D4—442no—
580C22×D4—442no—
581C22×D4C22×D1114yes—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—111no—
586C23×C4—111no—
587C23×C4—111no—
588C23×C4—114no—
589C23×C4—114no—
590C23×C4—224no—
591C23×C4—224no—
592C23×C4—442no—
593C23×C4—442no—
594C23×C4—442no—
595C23×C4—442no—
596C23×C4C22×D1111yescharacteristic
597C23×C4C22×D1111yescharacteristic
598C23×C4C22×D1111yescharacteristic
599C23×C4C22×D1111yescharacteristic
600C23×C4C22×D1111yescharacteristic
601#127—2232no—
602#124—2232no—
603#124—2232no—
604C4×D4—2232no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—224no—
609C2×C4⋊C4—224no—
610C2×C4⋊C4C22×D1114yes—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—24no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—42no—
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—114no—
624C2×C22⋊C4—114no—
625C2×C22⋊C4—224no—
626C2×C22⋊C4—224no—
627C2×C22⋊C4—224no—
628C2×C22⋊C4—224no—
629C2×C22⋊C4—224no—
630C2×C22⋊C4—224no—
631C2×C22⋊C4—224no—
632C2×C22⋊C4—442no—
633C2×C22⋊C4—442no—
634C2×C22⋊C4—442no—
635C2×C22⋊C4C22×D1114yes—
636C2×C22⋊C4C22×D1114yes—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C42—118no—
640C2×C42—114no—
641C2×C42—114no—
642C2×C42—114no—
643C2×C42—224no—
644C2×C42—224no—
645#95—114no—
646#95—114no—
647#95—114no—
648#95—114no—
649#95—114no—
650#95C22×D1114yes—
651C2×C11—44no—
652C2×C11—82no—
653C2×C11#254418yescomplemented
654C2×C11C22×#12111yescharacteristic
655C2×C11C2×#53211yescharacteristic
656C2×C11C2×#53511yescharacteristic
657C2×C11C2×#54611yescharacteristic
658C2×C11C2×#54611yescharacteristic
659C2×C11C2×#55911yescharacteristic
660C2×C11C2×#55911yescharacteristic
661D11—44no—
662D11—82no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—114no—
677C24—112no—
678C24—112no—
679C24—222no—
680C24—222no—
681C24—222no—
682C24—222no—
683C24—222no—
684C24—222no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—222no—
689C24—222no—
690C24—222no—
691C24—222no—
692C24D4×D1114yes—
693C24C23×D1112yes—
694C24C23×D1112yes—
695C24C23×D1111yescharacteristic
696C2×Q8—228no—
697C2×Q8—228no—
698C2×Q8—228no—
699C2×Q8—4416no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—44no—
703C2×D4—416no—
704C2×D4—1116no—
705C2×D4—228no—
706C2×D4—228no—
707C2×D4—2232no—
708C2×D4—228no—
709C2×D4—228no—
710C2×D4—228no—
711C2×D4—228no—
712C2×D4—228no—
713C2×D4—228no—
714C2×D4—228no—
715C2×D4—228no—
716C2×D4—228no—
717C2×D4—444no—
718C2×D4—4416no—
719C2×D4—4416no—
720C2×D4—444no—
721C2×D4—444no—
722C2×D4—4416no—
723C2×D4—4416no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—114no—
738C22×C4—114no—
739C22×C4—114no—
740C22×C4—112no—
741C22×C4—114no—
742C22×C4—114no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—112no—
747C22×C4—112no—
748C22×C4—228no—
749C22×C4—228no—
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—222no—
762C22×C4—222no—
763C22×C4—444no—
764C22×C4—444no—
765C22×C4—4416no—
766C22×C4—444no—
767C22×C4—444no—
768C22×C4—4416no—
769C22×C4D4×D1114yes—
770C22×C4#434114yes—
771C22×C4C23×D1112yes—
772C22×C4C23×D1112yes—
773C22×C4C23×D1112yes—
774C22×C4C23×D1112yes—
775C22×C4C23×D1112yes—
776C4⋊C4—28no—
777C4⋊C4—228no—
778C4⋊C4—228no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—44no—
783C22⋊C4—228no—
784C22⋊C4—228no—
785C22⋊C4—228no—
786C22⋊C4—228no—
787C22⋊C4—228no—
788C22⋊C4—228no—
789C22⋊C4—228no—
790C22⋊C4—444no—
791C22⋊C4—444no—
792C22⋊C4—444no—
793C42—1116no—
794C42—228no—
795C42—228no—
796C11C2×#254411yescharacteristic, complemented, Sylow
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—44no—
814C23—44no—
815C23—44no—
816C23—44no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—44no—
822C23—44no—
823C23—44no—
824C23—114no—
825C23—228no—
826C23—228no—
827C23—228no—
828C23—222no—
829C23—222no—
830C23—222no—
831C23—222no—
832C23—222no—
833C23—222no—
834C23—222no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—444no—
842C23—444no—
843C23—444no—
844C23—444no—
845C23—444no—
846C23—444no—
847C23—444no—
848C23—444no—
849C23—444no—
850C23—444no—
851C23—444no—
852C23C2×D4×D1114yes—
853C23C2×D4×D1112yes—
854C23C2×D4×D1112yes—
855C23C2×#434112yes—
856C23#6703712yes—
857C23#41×D1112yes—
858C23#41×D1112yes—
859C23#6704212yes—
860C23C24×D1111yescharacteristic
861Q8—4416no—
862D4—416no—
863D4—2232no—
864D4—4416no—
865D4—4416no—
866D4—4416no—
867D4—4416no—
868C2×C4—28no—
869C2×C4—28no—
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—22no—
882C2×C4—22no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—1116no—
887C2×C4—114no—
888C2×C4—114no—
889C2×C4—114no—
890C2×C4—114no—
891C2×C4—114no—
892C2×C4—228no—
893C2×C4—228no—
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—222no—
907C2×C4—4416no—
908C2×C4—4416no—
909C2×C4—444no—
910C2×C4—444no—
911C2×C4—444no—
912C2×C4C2×D4×D1114yes—
913C2×C4C2×#434114yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—416no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—88no—
930C22—224no—
931C22—224no—
932C22—224no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—4416no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—888no—
946C22#1062312214yes—
947C22#1062312714yes—
948C22D11×#12114yes—
949C22#1062313814yes—
950C22#1062318514yes—
951C22#1062319514yes—
952C22#1062321214yes—
953C22C22×D4×D1111yescharacteristic
954C22C22×D4×D1111yescharacteristic
955C22C22×#434111yescharacteristic
956C22C2×#6703711yescharacteristic
957C22C2×#41×D1111yescharacteristic
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—82no—
973C2—444no—
974C2—882no—
975C2#1307358218yesdirect product factor
976C2C2×D11×#12111yescharacteristic
977C2C2×#1062312711yescharacteristic
978C2C2×#1062313811yescharacteristic
979C2C2×#1062312211yescharacteristic
980C2C2×#1062318511yescharacteristic
981C2C2×#1062321211yescharacteristic
982C2C2×#1062319511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC22×#66993C2
hypercenterC2×#394D11
hypocenterC11C2×#2544
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#66938C2semidirect
3. C22×#66938C2semidirect
4. C22×(C22⋊D11)⋊C4C2semidirect
5. #13073582C2direct (N × H)
6. C2×#10622604C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622259C2semidirect
10. C2×#10622570C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622569C2semidirect
15. C2×C4⋊C4×Dic11C2semidirect
16. C2×C11×#394C2semidirect
50. C2×#66938C22semidirect
51. C2×#66938C22semidirect
53. C2×(C22⋊D11)⋊C4C22semidirect
54. C11×#394C22semidirect
56. #10622833C22semidirect
62. #10622604C22semidirect
63. C4⋊C4×Dic11C22semidirect
64. #10622574C22semidirect
65. #10622574C22semidirect
66. #10622571C22semidirect
67. #10622570C22semidirect
68. #10622569C22semidirect
69. #10622278C22semidirect
70. #10622259C22semidirect
159. C2×C4×Dic11D4semidirect
305. C4×Dic11C2×D4semidirect
314. C2×#394D11semidirect
479. #394C2×D11semidirect
653. C2×C11#2544semidirect
796. C11C2×#2544semidirect
975. C2#13073582direct (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×#669382
C22×(C22⋊D11)⋊C42
#130735822
C2×#106226042
C2×#106225742
C2×#106222592
C2×#106225702
C2×#106228332
C2×#106222782
C2×#106225712
C2×#106225692
C2×C4⋊C4×Dic112
C2×C11×#3942
C2×#254411