Finite Group Databasebeta

← C2×#13082859 #15661017

Subgroups — C2×#13082859 #15661017

Order 2816.

7162 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082859C2132yesmaximal, direct product factor
2C2×#10623182C212yesmaximal, complemented
3C2×#10623203C212yesmaximal, complemented
4C2×#10623060C212yesmaximal, complemented
5C2×#10623170C212yesmaximal, complemented
6C2×#10623210C212yesmaximal, complemented
7C2×#10623190C212yesmaximal, complemented
8C2×Q8×C22⋊D11C212yesmaximal, complemented
9C2×#10623163C212yesmaximal, complemented
10C2×#10623260C214yesmaximal, complemented
11C2×#10623156C212yesmaximal, complemented
12C2×#10623191C214yesmaximal, complemented
13C2×#10623356C211yesmaximal, characteristic, complemented
14C2×#10623359C211yesmaximal, characteristic
15C2×D11×C22⋊Q8C212yesmaximal, complemented
16C2×C11×#536C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C22×Q8×D11C2212yes—
20C23×C4×D11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic, complemented
22C11×#536C22116yescomplemented
23C2×C11×C4⋊Q8C2212yescomplemented
24C2×C11×#124C2212yes—
25C2×C11×#123C2212yes—
26C2×C11×#123C2212yescomplemented
27C2×C11×C22⋊Q8C2212yes—
28C2×C11×C22⋊Q8C2212yescomplemented
29C2×C11×#117C2211yescharacteristic, complemented
30#10623359C22116yes—
31#10623356C22116yescomplemented
32Q8×C22⋊D11C22132yescomplemented
33C2×#66999C2214yes—
34C2×#66999C2212yes—
35C2×#66999C2212yes—
36C2×Q8×Dic11C2212yescomplemented
37C2×#66997C2212yescomplemented
38C2×#66997C2214yescomplemented
39C2×#66997C2212yescomplemented
40C2×#66991C2212yes—
41C2×#66990C2211yescharacteristic
42C2×#66990C2211yescharacteristic
43C2×#66989C2212yes—
44C2×#66988C2212yes—
45C2×#66988C2211yescharacteristic
46C2×#66988C2211yescharacteristic
47C2×#66988C2212yescomplemented
48C2×C4×C22⋊D11C2214yes—
49C2×C4×C22⋊D11C2212yes—
50C2×C4×C22⋊D11C2212yes—
51C2×#66979C2211yescharacteristic
52C2×#66979C2211yescharacteristic, complemented
53C2×#66977C2212yes—
54C2×#66977C2212yescomplemented
55C2×#66977C2214yescomplemented
56#10623260C22164yescomplemented
57#10623210C22132yescomplemented
58#10623203C22132yescomplemented
59#10623191C22164yescomplemented
60#10623190C22132yescomplemented
61#10623182C22132yescomplemented
62#10623170C22132yescomplemented
63#10623163C22132yescomplemented
64D11×C22⋊Q8C22132yescomplemented
65#10623156C22132yescomplemented
66#10623060C22132yescomplemented
67C2×#66950C2212yes—
68C2×#66949C2214yes—
69C2×#66949C2214yes—
70C2×#66945C2214yes—
71C2×C4⋊C4×D11C2212yes—
72C2×C4⋊C4×D11C2214yes—
73C2×#66943C2212yescomplemented
74C2×#66943C2214yescomplemented
75C2×#66942C2214yescomplemented
76C2×#66942C2214yescomplemented
77C2×#66941C2214yescomplemented
78C2×#66940C2212yescomplemented
79C2×#66936C2214yes—
80C2×#66936C2214yes—
81C2×(C22⋊D11)⋊C4C2214yes—
82C2×C22⋊C4×D11C2214yes—
83C2×#66932C2214yes—
84C2×#66932C2214yes—
85C2×#66932C2214yescomplemented
86C2×#66932C2214yescomplemented
87C2×#66931C2214yes—
88C2×#66931C2214yescomplemented
89C2×#66925C2214yes—
90C2×#66923C2214yescomplemented
91C24×D11C2311yescharacteristic
92C2×C11×#41—44no—
93C2×C11×#41C2318yes—
94C22×Q8×C11—44no—
95C22×Q8×C11C2312yes—
96C22×Q8×C11C2312yes—
97C22×Q8×C11C2311yescharacteristic
98C22×Q8×C11C2318yescomplemented
99C22×D4×C11C2311yescharacteristic
100C22×D4×C11C2311yescharacteristic
101C22×D4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2311yescharacteristic
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2312yes—
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2312yes—
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2312yes—
110C2×Q8×D11—48no—
111C2×Q8×D11C23116yes—
112C22×C4×D11—44no—
113C22×C4×D11C2314yes—
114C22×C4×D11C2312yes—
115C22×C4×D11C2314yes—
116C22×C4×D11C2312yes—
117C22×C4×D11C2318yes—
118C22×Dic22—44no—
119C22×Dic22C2312yes—
120C22×Dic22C2314yes—
121C22×Dic22C2312yes—
122C22×Dic22C2318yescomplemented
123C11×C4⋊Q8C23116yescomplemented
124C11×#124C23116yes—
125C11×#123C23116yes—
126C11×#123C23116yescomplemented
127C11×C22⋊Q8C23116yes—
128C11×C22⋊Q8C23116yescomplemented
129C11×#117C2318yescomplemented
130C2×C11×C4⋊C4C2312yes—
131C2×C11×C4⋊C4C2314yes—
132C2×C11×C4⋊C4C2314yes—
133C2×C11×C22⋊C4C2314yes—
134C2×C11×C22⋊C4C2314yes—
135C2×C11×C22⋊C4C2312yes—
136C2×C42×C11C2312yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2311yescharacteristic
140C2×C22⋊Dic11C2311yescharacteristic
141C2×C22⋊Dic11C2312yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2314yes—
144#66999C23116yes—
145#66999C23132yes—
146#66999C23116yes—
147Q8×Dic11C23116yescomplemented
148#66997C23116yescomplemented
149#66997C23132yescomplemented
150#66997C23116yescomplemented
151#66991C23116yes—
152#66990C2318yes—
153#66990C2318yes—
154#66989C23116yes—
155#66988C23116yes—
156#66988C2318yes—
157#66988C2318yes—
158#66988C23116yescomplemented
159C4×C22⋊D11C23116yes—
160C4×C22⋊D11C23132yes—
161C4×C22⋊D11C23116yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2312yes—
166#66979C2318yes—
167#66979C2318yescomplemented
168C2×C4⋊Dic11C2314yes—
169C2×C4⋊Dic11C2314yes—
170C2×C4⋊Dic11C2314yes—
171C2×C4⋊Dic11C2312yes—
172C2×C4⋊Dic11C2312yes—
173#66977C23116yes—
174#66977C23116yescomplemented
175#66977C23132yescomplemented
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2314yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2314yes—
180C2×Dic11⋊C4C2314yes—
181C2×Dic11⋊C4C2314yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2314yes—
186C2×C4×Dic11C2314yes—
187C2×C4×Dic11C2314yes—
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190#66950C23116yes—
191#66949C23132yes—
192#66949C23132yes—
193#66945C23132yes—
194C4⋊C4×D11C23132yes—
195C4⋊C4×D11C23116yes—
196#66943C23132yescomplemented
197#66943C23116yescomplemented
198#66942C23132yescomplemented
199#66942C23132yescomplemented
200#66941C23132yescomplemented
201#66940C23116yescomplemented
202#66936C23132yes—
203#66936C23132yes—
204(C22⋊D11)⋊C4C23132yes—
205C22⋊C4×D11C23132yes—
206#66932C23132yes—
207#66932C23132yes—
208#66932C23132yescomplemented
209#66932C23132yescomplemented
210#66931C23132yes—
211#66931C23132yescomplemented
212#66925C23132yes—
213#66923C23132yescomplemented
214C2×#3538—111nomaximal, Sylow
215C24×C11C2411yescharacteristic
216C24×C11C2411yescharacteristic
217C24×C11C2411yescharacteristic
218C23×D11—28no—
219C23×D11—42no—
220C23×D11C2414yes—
221C23×D11C2412yes—
222C11×#41—416no—
223C2×Q8×C11—28no—
224C2×Q8×C11—44no—
225C2×Q8×C11—42no—
226C2×Q8×C11—416no—
227C2×Q8×C11C2418yes—
228C2×Q8×C11C2418yes—
229C2×Q8×C11C2414yes—
230C2×D4×C11—42no—
231C2×D4×C11—42no—
232C2×D4×C11—42no—
233C2×D4×C11C2414yes—
234C2×D4×C11C2414yes—
235C2×D4×C11C2414yes—
236C22×C4×C11—24no—
237C22×C4×C11—24no—
238C22×C4×C11—24no—
239C22×C4×C11—44no—
240C22×C4×C11C2411yescharacteristic
241C22×C4×C11C2414yes—
242C22×C4×C11C2414yes—
243C22×C4×C11C2411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C22×C4×C11C2414yes—
246C22×C4×C11C2414yes—
247C22×C4×C11C2414yes—
248C22×C4×C11C2418yes—
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11C2418yes—
253C2×C22⋊D11C2418yes—
254C22×Dic11—44no—
255C22×Dic11—42no—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2414yes—
259C22×Dic11C2414yes—
260C22×Dic11C2412yes—
261C22×Dic11C2414yes—
262C22×Dic11C2418yes—
263Q8×D11—432no—
264C2×C4×D11—216no—
265C2×C4×D11—28no—
266C2×C4×D11—44no—
267C2×C4×D11—48no—
268C2×C4×D11—416no—
269C2×C4×D11C24116yes—
270C2×C4×D11C2418yes—
271C2×C4×D11C24116yes—
272C2×C4×D11C2418yes—
273C2×Dic22—28no—
274C2×Dic22—416no—
275C2×Dic22—44no—
276C2×Dic22—48no—
277C2×Dic22C2418yes—
278C2×Dic22C24116yes—
279C2×Dic22C2418yes—
280C11×C4⋊C4C2418yes—
281C11×C4⋊C4C24116yes—
282C11×C4⋊C4C24116yes—
283C11×C22⋊C4C24116yes—
284C11×C22⋊C4C24116yes—
285C11×C22⋊C4C2418yes—
286C42×C11C2418yes—
287C22⋊Dic11C24116yes—
288C22⋊Dic11C2418yes—
289C22⋊Dic11C2414yes—
290C22⋊Dic11C2414yes—
291C22⋊Dic11C2418yes—
292C22⋊Dic11C2418yes—
293C22⋊Dic11C24116yes—
294(C2×D11)⋊C4C2418yes—
295(C2×D11)⋊C4C24116yes—
296(C2×D11)⋊C4C24116yes—
297(C2×D11)⋊C4C2418yes—
298C4⋊Dic11C24116yes—
299C4⋊Dic11C24116yes—
300C4⋊Dic11C24116yes—
301C4⋊Dic11C2418yes—
302C4⋊Dic11C2418yes—
303Dic11⋊C4C2418yes—
304Dic11⋊C4C24116yes—
305Dic11⋊C4C24116yes—
306Dic11⋊C4C24116yes—
307Dic11⋊C4C24116yes—
308Dic11⋊C4C24116yes—
309Dic11⋊C4C24116yes—
310Dic11⋊C4C24116yes—
311Dic11⋊C4C2418yes—
312Dic11⋊C4C24116yes—
313C4×Dic11C24116yes—
314C4×Dic11C24116yes—
315C4×Dic11C2418yes—
316C4×Dic11C2418yes—
317#3538—1132no—
318C2×#563—112no—
319C2×#563—112no—
320C2×#552—112no—
321C2×#552—112no—
322C2×#551—112no—
323C2×#551—112no—
324C2×D4×Q8—112no—
325C2×D4×Q8—112no—
326C2×#544—114no—
327C2×#541—112no—
328C2×#539—114no—
329C2×#536—111no—
330C2×#536D1111yescharacteristic, complemented
331C2×#525—111no—
332C22×C22⋊Q8—112no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—24no—
337C23×C11—24no—
338C23×C11—24no—
339C23×C11C2512yes—
340C23×C11C2512yes—
341C23×C11C2512yes—
342C23×C11C2511yescharacteristic
343C22×D11—24no—
344C22×D11—24no—
345C22×D11—216no—
346C22×D11—44no—
347C22×D11—416no—
348C22×D112−1+418yes—
349C22×D11C2514yes—
350Q8×C11—216no—
351Q8×C11—48no—
352Q8×C11—44no—
353D4×C11—44no—
354D4×C11—44no—
355D4×C11—44no—
356C2×C4×C11—22no—
357C2×C4×C11—28no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—28no—
361C2×C4×C11—28no—
362C2×C4×C11—28no—
363C2×C4×C11—28no—
364C2×C4×C11—48no—
365C2×C4×C11H(5,𝔽2)14yes—
366C2×C4×C11C2512yes—
367C2×C4×C11C2518yes—
368C2×C4×C11C2518yes—
369C2×C4×C11C2512yes—
370C2×C4×C11C2512yes—
371C2×C4×C11C2512yes—
372C22⋊D11—216no—
373C22⋊D11—216no—
374C2×Dic11—28no—
375C2×Dic11—24no—
376C2×Dic11—28no—
377C2×Dic11—24no—
378C2×Dic11—24no—
379C2×Dic11—48no—
380C2×Dic11—44no—
381C2×Dic11C2514yes—
382C2×Dic11C2514yes—
383C2×Dic11C2518yes—
384C2×Dic11C2518yes—
385C2×Dic11C2514yes—
386C4×D11—232no—
387C4×D11—216no—
388C4×D11—48no—
389C4×D11—416no—
390Dic22—216no—
391Dic22—48no—
392Dic22—416no—
393C22×#41C2×D1111yescharacteristic
394C23×Q8—112no—
395C23×Q8—111no—
396C23×Q8C2×D1111yescharacteristic, complemented
397C24×C4—111no—
398#563—1132no—
399#563—1132no—
400#552—1132no—
401#552—1132no—
402#551—1132no—
403#551—1132no—
404D4×Q8—1132no—
405D4×Q8—1132no—
406#544—1164no—
407#541—1132no—
408#539—1164no—
409#536—1116no—
410#536C2×D11116yescomplemented
411C2×C4⋊Q8—112no—
412C2×C4⋊Q8—112no—
413C2×C4⋊Q8—114no—
414C2×C4⋊Q8—114no—
415C2×C4⋊Q8C2×D1112yescomplemented
416C2×#126—114no—
417C2×#126—114no—
418C2×#126—114no—
419C2×#126—114no—
420C2×#125—114no—
421C2×#125—114no—
422C2×#125—114no—
423C2×#125—112no—
424C2×#125—114no—
425C2×#124—112no—
426C2×#124C2×D1112yes—
427#525—1116no—
428C2×#123—111no—
429C2×#123—111no—
430C2×#123—112no—
431C2×#123—112no—
432C2×#123—114no—
433C2×#123—114no—
434C2×#123C2×D1112yes—
435C2×#123C2×D1112yescomplemented
436C2×C22⋊Q8—112no—
437C2×C22⋊Q8—112no—
438C2×C22⋊Q8—114no—
439C2×C22⋊Q8—112no—
440C2×C22⋊Q8—112no—
441C2×C22⋊Q8—114no—
442C2×C22⋊Q8—1132no—
443C2×C22⋊Q8—114no—
444C2×C22⋊Q8—114no—
445C2×C22⋊Q8—112no—
446C2×C22⋊Q8—114no—
447C2×C22⋊Q8—114no—
448C2×C22⋊Q8C2×D1112yes—
449C2×C22⋊Q8C2×D1112yescomplemented
450C2×#121—112no—
451C2×#120—111no—
452C2×#120—111no—
453C2×C4×Q8—112no—
454C2×C4×Q8—112no—
455C2×C4×D4—112no—
456C2×C4×D4—112no—
457C2×C4×D4—114no—
458C2×C4×D4—114no—
459C2×#117—111no—
460C2×#117—111no—
461C2×#117—114no—
462C2×#117—114no—
463C2×#117C2×D1111yescharacteristic, complemented
464C22×C4⋊C4—114no—
465C22×C4⋊C4—112no—
466C22×C22⋊C4—114no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—24no—
473C22×C11—44no—
474C22×C11—44no—
475C22×C11—44no—
476C22×C11C2×H(5,𝔽2)12yes—
477C22×C11C2×2−1+414yes—
478C22×C11C2611yescharacteristic
479C2×D11—24no—
480C2×D11—24no—
481C2×D11—216no—
482C2×D11—416no—
483C2×D11C2×2−1+418yes—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11—28no—
488C4×C11—28no—
489C4×C11C2×H(5,𝔽2)14yes—
490Dic11—28no—
491Dic11—24no—
492Dic11—28no—
493Dic11—24no—
494Dic11—24no—
495C25—111no—
496C2×#41—44no—
497C2×#41C22×D1118yes—
498C22×Q8—44no—
499C22×Q8—1116no—
500C22×Q8—112no—
501C22×Q8—114no—
502C22×Q8—112no—
503C22×Q8—118no—
504C22×Q8—444no—
505C22×Q8—448no—
506C22×Q8C22×D1112yes—
507C22×Q8C22×D1112yes—
508C22×Q8C22×D1111yescharacteristic
509C22×Q8C22×D1118yescomplemented
510C22×D4—112no—
511C22×D4—112no—
512C22×D4C22×D1111yescharacteristic
513C22×D4C22×D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—112no—
516C23×C4—111no—
517C23×C4—114no—
518C23×C4—112no—
519C23×C4—114no—
520C23×C4—112no—
521C23×C4—118no—
522C23×C4—444no—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1112yes—
527C4⋊Q8—1116no—
528C4⋊Q8—1116no—
529C4⋊Q8—1132no—
530C4⋊Q8—1132no—
531C4⋊Q8C22×D11116yescomplemented
532#126—1132no—
533#126—1132no—
534#126—1132no—
535#126—1132no—
536#125—1132no—
537#125—1132no—
538#125—1116no—
539#125—1132no—
540#125—1132no—
541#124—1116no—
542#124C22×D11116yes—
543#123—118no—
544#123—118no—
545#123—1116no—
546#123—1116no—
547#123—1132no—
548#123—1132no—
549#123C22×D11116yes—
550#123C22×D11116yescomplemented
551C22⋊Q8—1116no—
552C22⋊Q8—1116no—
553C22⋊Q8—1132no—
554C22⋊Q8—1116no—
555C22⋊Q8—1116no—
556C22⋊Q8—1132no—
557C22⋊Q8—1132no—
558C22⋊Q8—1116no—
559C22⋊Q8—1132no—
560C22⋊Q8—1132no—
561C22⋊Q8—1132no—
562C22⋊Q8C22×D11116yes—
563C22⋊Q8C22×D11116yescomplemented
564#121—1116no—
565#120—118no—
566#120—118no—
567C4×Q8—1116no—
568C4×Q8—1116no—
569C4×D4—1116no—
570C4×D4—1116no—
571C4×D4—1132no—
572C4×D4—1132no—
573#117—118no—
574#117—118no—
575#117—1132no—
576#117—1132no—
577#117C22×D1118yescomplemented
578C2×C4⋊C4—112no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—114no—
582C2×C4⋊C4—114no—
583C2×C4⋊C4—112no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—114no—
587C2×C4⋊C4—114no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—112no—
590C2×C4⋊C4—112no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—114no—
593C2×C4⋊C4—1132no—
594C2×C4⋊C4—1116no—
595C2×C4⋊C4C22×D1112yes—
596C2×C4⋊C4C22×D1114yes—
597C2×C4⋊C4C22×D1114yes—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—111no—
600C2×C22⋊C4—111no—
601C2×C22⋊C4—112no—
602C2×C22⋊C4—112no—
603C2×C22⋊C4—112no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—114no—
607C2×C22⋊C4—112no—
608C2×C22⋊C4—112no—
609C2×C22⋊C4—1132no—
610C2×C22⋊C4C22×D1114yes—
611C2×C22⋊C4C22×D1112yes—
612C2×C22⋊C4C22×D1114yes—
613C2×C42—112no—
614C2×C42—112no—
615C2×C42—114no—
616C2×C42—114no—
617C2×C42C22×D1112yes—
618C2×C11—42no—
619C2×C11—42no—
620C2×C11—42no—
621C2×C11#353814yescomplemented
622C2×C11C22×H(5,𝔽2)11yescharacteristic
623C2×C11C22×2−1+412yes—
624D11—28no—
625C24—112no—
626C24—114no—
627C24—228no—
628C24—442no—
629C24C23×D1111yescharacteristic
630C24C23×D1111yescharacteristic
631C24C23×D1111yescharacteristic
632#41—416no—
633C2×Q8—28no—
634C2×Q8—44no—
635C2×Q8—42no—
636C2×Q8—416no—
637C2×Q8—118no—
638C2×Q8—1116no—
639C2×Q8—118no—
640C2×Q8—228no—
641C2×Q8—444no—
642C2×Q8—448no—
643C2×Q8—4416no—
644C2×Q8—4432no—
645C2×Q8C23×D1118yes—
646C2×Q8C23×D1118yes—
647C2×Q8C23×D1114yes—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—118no—
652C2×D4—118no—
653C2×D4—228no—
654C2×D4—228no—
655C2×D4C23×D1114yes—
656C2×D4C23×D1114yes—
657C2×D4C23×D1114yes—
658C22×C4—24no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—44no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—114no—
665C22×C4—114no—
666C22×C4—112no—
667C22×C4—118no—
668C22×C4—114no—
669C22×C4—1116no—
670C22×C4—118no—
671C22×C4—1116no—
672C22×C4—118no—
673C22×C4—2216no—
674C22×C4—228no—
675C22×C4—4416no—
676C22×C4—444no—
677C22×C4—448no—
678C22×C4—442no—
679C22×C4—444no—
680C22×C4C23×D1114yes—
681C22×C4C23×D1114yes—
682C22×C4C23×D1114yes—
683C22×C4C23×D1111yescharacteristic
684C22×C4C23×D1114yes—
685C22×C4C23×D1114yes—
686C22×C4C23×D1111yescharacteristic
687C22×C4C23×D1111yescharacteristic
688C22×C4C23×D1118yes—
689C22×C4C23×D1111yescharacteristic
690C4⋊C4—118no—
691C4⋊C4—1116no—
692C4⋊C4—1116no—
693C4⋊C4—1116no—
694C4⋊C4—1116no—
695C4⋊C4—118no—
696C4⋊C4—1116no—
697C4⋊C4—1116no—
698C4⋊C4—1116no—
699C4⋊C4—1116no—
700C4⋊C4—1116no—
701C4⋊C4—118no—
702C4⋊C4—118no—
703C4⋊C4—1116no—
704C4⋊C4—1116no—
705C4⋊C4C23×D1118yes—
706C4⋊C4C23×D11116yes—
707C4⋊C4C23×D11116yes—
708C22⋊C4—1116no—
709C22⋊C4—114no—
710C22⋊C4—114no—
711C22⋊C4—118no—
712C22⋊C4—118no—
713C22⋊C4—118no—
714C22⋊C4—1116no—
715C22⋊C4—1116no—
716C22⋊C4—1116no—
717C22⋊C4—118no—
718C22⋊C4—118no—
719C22⋊C4C23×D11116yes—
720C22⋊C4C23×D1118yes—
721C22⋊C4C23×D11116yes—
722C42—118no—
723C42—118no—
724C42—1116no—
725C42—1116no—
726C42C23×D1118yes—
727C11C2×#353811yescharacteristic, complemented, Sylow
728C23—22no—
729C23—22no—
730C23—22no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—118no—
735C23—114no—
736C23—2216no—
737C23—224no—
738C23—224no—
739C23—444no—
740C23—4416no—
741C23C24×D1112yes—
742C23C24×D1112yes—
743C23C24×D1112yes—
744C23C24×D1111yescharacteristic
745Q8—216no—
746Q8—48no—
747Q8—44no—
748Q8—2216no—
749Q8—448no—
750Q8—4416no—
751D4—44no—
752D4—44no—
753D4—44no—
754D4—2216no—
755D4—2216no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—48no—
765C2×C4—114no—
766C2×C4—114no—
767C2×C4—118no—
768C2×C4—118no—
769C2×C4—114no—
770C2×C4—2232no—
771C2×C4—224no—
772C2×C4—228no—
773C2×C4—228no—
774C2×C4—224no—
775C2×C4—224no—
776C2×C4—2216no—
777C2×C4—448no—
778C2×C4—4416no—
779C2×C4—444no—
780C2×C4—448no—
781C2×C4#6703714yes—
782C2×C4C24×D1112yes—
783C2×C4C24×D1118yes—
784C2×C4C24×D1118yes—
785C2×C4C24×D1112yes—
786C2×C4C24×D1112yes—
787C2×C4C24×D1112yes—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—118no—
798C22—224no—
799C22—224no—
800C22—2216no—
801C22—4416no—
802C22C2×#6703712yes—
803C22D11×2−1+414yes—
804C22C25×D1111yescharacteristic
805C4—22no—
806C4—22no—
807C4—22no—
808C4—28no—
809C4—28no—
810C4—224no—
811C4—228no—
812C4—228no—
813C4—224no—
814C4—224no—
815C4C2×#6703714yes—
816C2—42no—
817C2—42no—
818C2—42no—
819C2—228no—
820C2#1308285914yesdirect product factor
821C2C22×#6703711yescharacteristic
822C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#536C2
socleC23×C11C25
prime radicalC2×#10623359C2
hypercenterC2×#536D11
hypocenterC11C2×#3538
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #13082859C2direct (N × H)
2. C2×#10623182C2semidirect
3. C2×#10623203C2semidirect
4. C2×#10623060C2semidirect
5. C2×#10623170C2semidirect
6. C2×#10623210C2semidirect
7. C2×#10623190C2semidirect
8. C2×Q8×C22⋊D11C2semidirect
9. C2×#10623163C2semidirect
10. C2×#10623260C2semidirect
11. C2×#10623156C2semidirect
12. C2×#10623191C2semidirect
13. C2×#10623356C2semidirect
15. C2×D11×C22⋊Q8C2semidirect
16. C2×C11×#536C2semidirect
18. C23×Q8×C11C22semidirect
21. C23×Dic22C22semidirect
22. C11×#536C22semidirect
23. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×#123C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
29. C2×C11×#117C22semidirect
31. #10623356C22semidirect
32. Q8×C22⋊D11C22semidirect
36. C2×Q8×Dic11C22semidirect
37. C2×#66997C22semidirect
38. C2×#66997C22semidirect
39. C2×#66997C22semidirect
47. C2×#66988C22semidirect
52. C2×#66979C22semidirect
54. C2×#66977C22semidirect
55. C2×#66977C22semidirect
56. #10623260C22semidirect
57. #10623210C22semidirect
58. #10623203C22semidirect
59. #10623191C22semidirect
60. #10623190C22semidirect
61. #10623182C22semidirect
62. #10623170C22semidirect
63. #10623163C22semidirect
64. D11×C22⋊Q8C22semidirect
65. #10623156C22semidirect
66. #10623060C22semidirect
73. C2×#66943C22semidirect
74. C2×#66943C22semidirect
75. C2×#66942C22semidirect
76. C2×#66942C22semidirect
77. C2×#66941C22semidirect
78. C2×#66940C22semidirect
85. C2×#66932C22semidirect
86. C2×#66932C22semidirect
88. C2×#66931C22semidirect
90. C2×#66923C22semidirect
98. C22×Q8×C11C23semidirect
122. C22×Dic22C23semidirect
123. C11×C4⋊Q8C23semidirect
126. C11×#123C23semidirect
128. C11×C22⋊Q8C23semidirect
129. C11×#117C23semidirect
147. Q8×Dic11C23semidirect
148. #66997C23semidirect
149. #66997C23semidirect
150. #66997C23semidirect
158. #66988C23semidirect
167. #66979C23semidirect
174. #66977C23semidirect
175. #66977C23semidirect
196. #66943C23semidirect
197. #66943C23semidirect
198. #66942C23semidirect
199. #66942C23semidirect
200. #66941C23semidirect
201. #66940C23semidirect
208. #66932C23semidirect
209. #66932C23semidirect
211. #66931C23semidirect
213. #66923C23semidirect
330. C2×#536D11semidirect
396. C23×Q8C2×D11semidirect
410. #536C2×D11semidirect
415. C2×C4⋊Q8C2×D11semidirect
435. C2×#123C2×D11semidirect
449. C2×C22⋊Q8C2×D11semidirect
463. C2×#117C2×D11semidirect
509. C22×Q8C22×D11semidirect
531. C4⋊Q8C22×D11semidirect
550. #123C22×D11semidirect
563. C22⋊Q8C22×D11semidirect
577. #117C22×D11semidirect
621. C2×C11#3538semidirect
727. C11C2×#3538semidirect
820. C2#13082859direct (N × H)

Maximal subgroups

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

subgroupindex
#130828592
C2×#106231822
C2×#106232032
C2×#106230602
C2×#106231702
C2×#106232102
C2×#106231902
C2×Q8×C22⋊D112
C2×#106231632
C2×#106232602
C2×#106231562
C2×#106231912
C2×#106233562
C2×#106233592
C2×D11×C22⋊Q82
C2×C11×#5362
C2×#353811