Finite Group Databasebeta

← C2×#13082427 #15662097

Subgroups — C2×#13082427 #15662097

Order 2816.

7478 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082427C2132yesmaximal, direct product factor
2C2×#10623253C212yesmaximal, complemented
3C2×#10623098C211yesmaximal, characteristic, complemented
4C2×#10623252C211yesmaximal, characteristic, complemented
5C2×#10623070C212yesmaximal, complemented
6C2×#10623167C214yesmaximal, complemented
7C2×D4×Dic22C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D11C212yesmaximal, complemented
9C2×#10623163C212yesmaximal, complemented
10C2×#10623154C214yesmaximal, complemented
11C2×#10623260C212yesmaximal, complemented
12C2×#10623109C211yesmaximal, characteristic, complemented
13C2×#10623153C212yesmaximal, complemented
14C22×#66997C212yesmaximal, complemented
15C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#10623077C212yesmaximal
17C2×C4×#4341C211yesmaximal, characteristic
18C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
19C23×Q8×C11C2212yes—
20C22×Q8×D11C2212yes—
21C22×#4341C2211yescharacteristic
22C23×Dic22C2212yes—
23D4×Q8×C11C22116yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×C4⋊Q8C2212yes—
26C2×C11×C22⋊Q8C2214yes—
27C2×C11×C22⋊Q8C2212yes—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31Q8×C22⋊D11C22132yescomplemented
32C2×#66999C2214yes—
33C2×#66999C2211yescharacteristic
34C2×Q8×Dic11C2212yes—
35C2×#66997C2214yes—
36C2×#66997C2212yes—
37C2×#66997C2211yescharacteristic
38C2×#66997C2212yes—
39C2×#66997C2212yes—
40C2×#66997C2214yes—
41C2×#66997C2214yes—
42C2×#66997C22132yescomplemented
43C2×D4×Dic11C2211yescharacteristic
44C2×D4×Dic11C2212yes—
45C2×C4×C22⋊D11C2214yes—
46C2×C4×C22⋊D11C2212yes—
47C2×#66977C2214yes—
48C2×#66977C2212yes—
49C22×Dic11⋊C4C2214yes—
50C22×Dic11⋊C4C2214yes—
51C22×C4×Dic11C2212yes—
52#10623260C22132yescomplemented
53D11×C4⋊Q8C22116yescomplemented
54#10623253C22132yescomplemented
55#10623252C22116yescomplemented
56#10623167C22164yescomplemented
57#10623163C22132yescomplemented
58#10623154C22164yescomplemented
59#10623153C22132yescomplemented
60#10623109C22116yescomplemented
61#10623098C22116yescomplemented
62#10623077C22132yes—
63#10623070C22132yescomplemented
64D4×Dic22C22116yescomplemented
65C4×#4341C22116yes—
66C2×#66950C2211yescharacteristic
67C2×#66949C2212yes—
68C2×#66949C2214yes—
69C2×#66945C2211yescharacteristic
70C2×C4⋊C4×D11C2212yes—
71C2×C4⋊C4×D11C2212yes—
72C2×#66943C2212yes—
73C2×#66942C2214yes—
74C2×#66942C2214yes—
75C2×#66942C2214yes—
76C2×#66942C2212yes—
77C2×#66941C2212yes—
78C2×#66941C2212yes—
79C2×#66941C2211yescharacteristic
80C2×#66941C2212yes—
81C2×#66941C2214yes—
82C2×#66940C2214yes—
83C2×#66940C2212yes—
84C2×#66940C2212yes—
85C2×#66940C2211yescharacteristic
86C2×(C22⋊D11)⋊C4C2212yes—
87C2×(C22⋊D11)⋊C4C2214yes—
88C2×#66931C2214yes—
89C2×#66931C2214yes—
90C2×#66931C2214yes—
91C2×#66930C2214yes—
92C2×#66930C2212yes—
93C2×#66925C2212yes—
94C2×C42×D11C2211yescharacteristic
95C2×#66923C2212yes—
96C2×#66922C2211yescharacteristic
97C2×C4×Dic22C2212yes—
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C2212yes—
101C22×Q8×C11—48no—
102C22×Q8×C11C2311yescharacteristic
103C22×Q8×C11C2312yes—
104C22×Q8×C11C2314yes—
105C22×Q8×C11C23116yes—
106C22×D4×C11C2311yescharacteristic
107C23×C4×C11C2312yes—
108C23×C4×C11C2314yes—
109C22×C22⋊D11C2312yes—
110C23×Dic11C2312yes—
111C23×Dic11C2314yes—
112C23×Dic11C2312yes—
113C2×Q8×D11—48no—
114C2×Q8×D11C23116yes—
115C2×#4341Q8116yescomplemented
116C2×#4341C2318yes—
117C22×C4×D11C2311yescharacteristic
118C22×C4×D11C2311yescharacteristic
119C22×C4×D11C2314yes—
120C22×C4×D11C2311yescharacteristic
121C22×Dic22—48no—
122C22×Dic22C2312yes—
123C22×Dic22C2311yescharacteristic
124C22×Dic22C2312yes—
125C22×Dic22C2314yes—
126C22×Dic22C2314yes—
127C22×Dic22C23116yes—
128C22×Dic22C2311yescharacteristic
129C11×C4⋊Q8C2318yes—
130C11×C4⋊Q8C23116yes—
131C11×C22⋊Q8C23116yes—
132C11×C22⋊Q8C23132yes—
133C4×Q8×C11C2318yes—
134C4×D4×C11C2318yes—
135C4×D4×C11C23116yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2314yes—
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C22⋊C4C2314yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C42×C11C2311yescharacteristic
145C2×C42×C11C2312yes—
146C2×C22⋊Dic11C2314yes—
147C2×C22⋊Dic11C2312yes—
148#66999C23132yes—
149#66999C2318yes—
150Q8×Dic11C23116yes—
151#66997C23116yes—
152#66997C23132yes—
153#66997C23132yes—
154#66997C23116yes—
155#66997C23132yes—
156#66997C2318yes—
157#66997C23116yes—
158D4×Dic11C2318yes—
159D4×Dic11C23116yes—
160C4×C22⋊D11C23116yes—
161C4×C22⋊D11C23132yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×C4⋊Dic11C2312yes—
166C2×C4⋊Dic11C2311yescharacteristic
167C2×C4⋊Dic11C2312yes—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2314yes—
171#66977C23116yes—
172#66977C23132yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2312yes—
175C2×Dic11⋊C4C2314yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2314yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2314yes—
186C2×Dic11⋊C4C2314yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C23132yes—
189C2×Dic11⋊C4C23132yes—
190C2×C4×Dic11C2311yescharacteristic
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2314yes—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2314yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C23116yes—
200#66950C2318yes—
201#66949C23132yes—
202#66949C23116yes—
203#66945C2318yes—
204C4⋊C4×D11C23116yes—
205C4⋊C4×D11C23116yes—
206#66943C23116yes—
207#66942C23132yes—
208#66942C23132yes—
209#66942C23132yes—
210#66942C23116yes—
211#66941C23116yes—
212#66941C23116yes—
213#66941C23132yes—
214#66941C23116yes—
215#66941C2318yes—
216#66940C23116yes—
217#66940C2318yes—
218#66940C23132yes—
219#66940C23116yes—
220(C22⋊D11)⋊C4C23116yes—
221(C22⋊D11)⋊C4C23132yes—
222#66931C23132yes—
223#66931C23132yes—
224#66931C23132yes—
225#66930C23116yes—
226#66930C23132yes—
227#66925C23116yes—
228C42×D11C2318yes—
229#66923C23116yes—
230#66922C2318yes—
231C4×Dic22C2318yes—
232C4×Dic22C2318yes—
233C4×Dic22C23116yes—
234C4×Dic22C23116yes—
235C2×#3503—111nomaximal, Sylow
236C24×C11C2412yes—
237C23×D11C2411yescharacteristic
238C2×Q8×C11—28no—
239C2×Q8×C11—24no—
240C2×Q8×C11—48no—
241C2×Q8×C11—432no—
242C2×Q8×C11C2414yes—
243C2×Q8×C11C2418yes—
244C2×Q8×C11C24116yes—
245C2×D4×C11C2×Q818yescomplemented
246C2×D4×C11C2414yes—
247C22×C4×C11—28no—
248C22×C4×C11—48no—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2418yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2414yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C24116yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11C2×Q8116yescomplemented
259C2×C22⋊D11C2418yes—
260C22×Dic11—28no—
261C22×Dic11—48no—
262C22×Dic11C2×Q8116yescomplemented
263C22×Dic11C2418yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2411yescharacteristic
267C22×Dic11C2412yes—
268C22×Dic11C2414yes—
269C22×Dic11C24116yes—
270C22×Dic11C2412yes—
271C22×Dic11C2411yescharacteristic
272C22×Dic11C2418yes—
273C22×Dic11C2411yescharacteristic
274Q8×D11—432no—
275#4341C2×Q8164yescomplemented
276C2×C4×D11—24no—
277C2×C4×D11—24no—
278C2×C4×D11—48no—
279C2×C4×D11C2×Q818yescomplemented
280C2×C4×D11C2414yes—
281C2×C4×D11C2414yes—
282C2×C4×D11C24116yes—
283C2×C4×D11C2414yes—
284C2×Dic22—28no—
285C2×Dic22—24no—
286C2×Dic22—28no—
287C2×Dic22—432no—
288C2×Dic22—48no—
289C2×Dic22—48no—
290C2×Dic22C2×Q818yescomplemented
291C2×Dic22C2418yes—
292C2×Dic22C2414yes—
293C2×Dic22C2418yes—
294C2×Dic22C24116yes—
295C2×Dic22C24116yes—
296C2×Dic22C2414yes—
297C11×C4⋊C4C2414yes—
298C11×C4⋊C4C2414yes—
299C11×C4⋊C4C24116yes—
300C11×C4⋊C4C2418yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C2418yes—
303C11×C22⋊C4C24116yes—
304C11×C22⋊C4C2418yes—
305C42×C11C2414yes—
306C42×C11C2418yes—
307C22⋊Dic11C24116yes—
308C22⋊Dic11C2418yes—
309(C2×D11)⋊C4C2418yes—
310(C2×D11)⋊C4C2418yes—
311(C2×D11)⋊C4C2418yes—
312C4⋊Dic11C2418yes—
313C4⋊Dic11C2414yes—
314C4⋊Dic11C2418yes—
315C4⋊Dic11C2414yes—
316C4⋊Dic11C2418yes—
317C4⋊Dic11C24116yes—
318Dic11⋊C4C2418yes—
319Dic11⋊C4C2418yes—
320Dic11⋊C4C24116yes—
321Dic11⋊C4C2418yes—
322Dic11⋊C4C2418yes—
323Dic11⋊C4C24116yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C2418yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C2418yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333C4×Dic11C2414yes—
334C4×Dic11C2418yes—
335C4×Dic11C24116yes—
336C4×Dic11C2418yes—
337C4×Dic11C2414yes—
338C4×Dic11C2414yes—
339C4×Dic11C24116yes—
340C4×Dic11C2418yes—
341C4×Dic11C2418yes—
342#3503—1132no—
343C2×Q82—112no—
344C2×#557—111no—
345C2×#557—111no—
346C2×#554—114no—
347C2×#554—112no—
348C2×D4×Q8—112no—
349C2×D4×Q8—112no—
350C2×D4×Q8—111no—
351C2×D4×Q8D1111yescharacteristic, complemented
352C2×#544—112no—
353C2×#544—114no—
354C2×#533—112no—
355C2×#533—111no—
356C22×C4⋊Q8—112no—
357C22×C4⋊Q8—111no—
358C2×#520—112no—
359C2×C4×#41—111no—
360C23×C11—24no—
361C23×C11—24no—
362C23×C11C22×Q818yes—
363C23×C11C2514yes—
364C23×C11C2511yescharacteristic
365C22×D11—22no—
366C22×D11—22no—
367C22×D11C22×Q814yes—
368C22×D11C2512yes—
369Q8×C11—216no—
370Q8×C11—28no—
371Q8×C11—416no—
372D4×C11C22×Q8116yescomplemented
373C2×C4×C11—24no—
374C2×C4×C11—28no—
375C2×C4×C11—24no—
376C2×C4×C11—24no—
377C2×C4×C11—22no—
378C2×C4×C11—216no—
379C2×C4×C11—416no—
380C2×C4×C11C22×Q814yes—
381C2×C4×C11H(5,𝔽2)14yes—
382C2×C4×C11C2514yes—
383C2×C4×C11C2514yes—
384C2×C4×C11C2512yes—
385C2×C4×C11C2518yes—
386C2×C4×C11C2514yes—
387C2×C4×C11C2512yes—
388C2×C4×C11C2512yes—
389C22⋊D11C22×Q8132yescomplemented
390C2×Dic11—28no—
391C2×Dic11—24no—
392C2×Dic11—22no—
393C2×Dic11—24no—
394C2×Dic11—24no—
395C2×Dic11—216no—
396C2×Dic11—416no—
397C2×Dic11C22×Q818yes—
398C2×Dic11C22×Q814yes—
399C2×Dic11C22×Q8132yescomplemented
400C2×Dic112−1+414yes—
401C2×Dic11C2514yes—
402C2×Dic11C2514yes—
403C2×Dic11C2512yes—
404C2×Dic11C2514yes—
405C2×Dic11C2518yes—
406C2×Dic11C2514yes—
407C2×Dic11C2512yes—
408C2×Dic11C2512yes—
409C4×D11—28no—
410C4×D11—28no—
411C4×D11—416no—
412C4×D11C22×Q8116yescomplemented
413Dic22—28no—
414Dic22—216no—
415Dic22—216no—
416Dic22—416no—
417Dic22—416no—
418Dic22C22×Q8116yescomplemented
419C22×#41—111no—
420C23×Q8—112no—
421C23×Q8—112no—
422C23×Q8C2×D1112yes—
423Q82—1132no—
424#557—1116no—
425#557—1116no—
426#554—1164no—
427#554—1132no—
428D4×Q8—1132no—
429D4×Q8—1132no—
430D4×Q8—1116no—
431D4×Q8C2×D11116yescomplemented
432#544—1132no—
433#544—1164no—
434#533—1132no—
435#533—1116no—
436C2×C4⋊Q8—112no—
437C2×C4⋊Q8—111no—
438C2×C4⋊Q8—114no—
439C2×C4⋊Q8—112no—
440C2×C4⋊Q8—112no—
441C2×C4⋊Q8—114no—
442C2×C4⋊Q8—114no—
443C2×C4⋊Q8—1132no—
444C2×C4⋊Q8—1116no—
445C2×C4⋊Q8—112no—
446C2×C4⋊Q8—112no—
447C2×C4⋊Q8—111no—
448C2×C4⋊Q8—114no—
449C2×C4⋊Q8—112no—
450C2×C4⋊Q8—111no—
451C2×C4⋊Q8C2×D1111yescharacteristic
452C2×C4⋊Q8C2×D1112yes—
453C2×#125—114no—
454C2×#125—112no—
455C2×#125—114no—
456C2×#125—114no—
457C2×#125—112no—
458C2×#125—112no—
459C2×C22⋊Q8—111no—
460C2×C22⋊Q8—114no—
461C2×C22⋊Q8—112no—
462C2×C22⋊Q8—114no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—114no—
465C2×C22⋊Q8—111no—
466C2×C22⋊Q8—114no—
467C2×C22⋊Q8—114no—
468C2×C22⋊Q8—114no—
469C2×C22⋊Q8C2×D1112yes—
470C2×C22⋊Q8C2×D1114yes—
471#520—1132no—
472C4×#41—1116no—
473C2×C4×Q8—112no—
474C2×C4×Q8—111no—
475C2×C4×Q8—112no—
476C2×C4×Q8—112no—
477C2×C4×Q8—114no—
478C2×C4×Q8—111no—
479C2×C4×Q8—112no—
480C2×C4×Q8—111no—
481C2×C4×Q8—112no—
482C2×C4×Q8C2×D1111yescharacteristic
483C2×C4×D4—111no—
484C2×C4×D4—112no—
485C2×C4×D4—112no—
486C2×C4×D4—114no—
487C2×C4×D4—112no—
488C2×C4×D4—114no—
489C2×C4×D4C2×D1111yescharacteristic
490C2×C4×D4C2×D1112yes—
491C2×#117—111no—
492C2×#117—112no—
493C2×#117—114no—
494C2×#117—112no—
495C22×C4⋊C4—114no—
496C22×C4⋊C4—114no—
497C22×C4⋊C4—112no—
498C22×C4⋊C4—112no—
499C22×C42—112no—
500C22×C42—111no—
501C22×C11—24no—
502C22×C11—24no—
503C22×C11—216no—
504C22×C11C23×Q818yes—
505C22×C11C23×Q812yes—
506C22×C11C2×H(5,𝔽2)12yes—
507C22×C11C2×2−1+412yes—
508C22×C11C2611yescharacteristic
509C2×D11—22no—
510C2×D11—22no—
511C2×D11—28no—
512C2×D11C23×Q814yes—
513C4×C11—24no—
514C4×C11—24no—
515C4×C11—28no—
516C4×C11—24no—
517C4×C11—22no—
518C4×C11C23×Q814yes—
519C4×C11C2×H(5,𝔽2)14yes—
520Dic11—28no—
521Dic11—24no—
522Dic11—22no—
523Dic11—24no—
524Dic11—24no—
525Dic11C23×Q818yes—
526Dic11C23×Q814yes—
527Dic11C2×2−1+414yes—
528C2×#41—1116no—
529C2×#41—118no—
530C22×Q8—48no—
531C22×Q8—1116no—
532C22×Q8—111no—
533C22×Q8—112no—
534C22×Q8—112no—
535C22×Q8—111no—
536C22×Q8—114no—
537C22×Q8—114no—
538C22×Q8—1116no—
539C22×Q8—448no—
540C22×Q8—448no—
541C22×Q8C22×D1112yes—
542C22×Q8C22×D1111yescharacteristic
543C22×Q8C22×D1114yes—
544C22×Q8C22×D11116yes—
545C22×D4—112no—
546C22×D4C22×D1111yescharacteristic
547C23×C4—112no—
548C23×C4—111no—
549C23×C4—112no—
550C23×C4—114no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—114no—
554C23×C4C22×D1112yes—
555C23×C4C22×D1114yes—
556C4⋊Q8—1116no—
557C4⋊Q8—118no—
558C4⋊Q8—1132no—
559C4⋊Q8—1116no—
560C4⋊Q8—1116no—
561C4⋊Q8—1132no—
562C4⋊Q8—1132no—
563C4⋊Q8—1116no—
564C4⋊Q8—1116no—
565C4⋊Q8—118no—
566C4⋊Q8—1132no—
567C4⋊Q8—1116no—
568C4⋊Q8—118no—
569C4⋊Q8C22×D1118yes—
570C4⋊Q8C22×D11116yes—
571#125—1132no—
572#125—1116no—
573#125—1132no—
574#125—1132no—
575#125—1116no—
576#125—1116no—
577C22⋊Q8—118no—
578C22⋊Q8—1132no—
579C22⋊Q8—1116no—
580C22⋊Q8—1132no—
581C22⋊Q8—118no—
582C22⋊Q8—1116no—
583C22⋊Q8—1132no—
584C22⋊Q8—1132no—
585C22⋊Q8—1132no—
586C22⋊Q8—1132no—
587C22⋊Q8C22×D11116yes—
588C22⋊Q8C22×D11132yes—
589C4×Q8—1116no—
590C4×Q8—118no—
591C4×Q8—1116no—
592C4×Q8—1116no—
593C4×Q8—1132no—
594C4×Q8—118no—
595C4×Q8—1116no—
596C4×Q8—118no—
597C4×Q8—1116no—
598C4×Q8C22×D1118yes—
599C4×D4—118no—
600C4×D4—1116no—
601C4×D4—1116no—
602C4×D4—1132no—
603C4×D4—1116no—
604C4×D4—1132no—
605C4×D4C22×D1118yes—
606C4×D4C22×D11116yes—
607#117—118no—
608#117—1116no—
609#117—1132no—
610#117—1116no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—112no—
613C2×C4⋊C4—114no—
614C2×C4⋊C4—112no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—1132no—
619C2×C4⋊C4—114no—
620C2×C4⋊C4—114no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—1132no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—112no—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—114no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—1116no—
635C2×C4⋊C4—1116no—
636C2×C4⋊C4C22×D1112yes—
637C2×C4⋊C4C22×D1112yes—
638C2×C4⋊C4C22×D1111yescharacteristic
639C2×C4⋊C4C22×D1111yescharacteristic
640C2×C4⋊C4C22×D1114yes—
641C2×C4⋊C4C22×D1112yes—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4—112no—
645C2×C22⋊C4—112no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4C22×D1114yes—
648C2×C22⋊C4C22×D1112yes—
649C2×C42—112no—
650C2×C42—111no—
651C2×C42—114no—
652C2×C42—114no—
653C2×C42—112no—
654C2×C42—112no—
655C2×C42—112no—
656C2×C42—111no—
657C2×C42—1116no—
658C2×C42—111no—
659C2×C42—118no—
660C2×C42C22×D1112yes—
661C2×C42C22×D1111yescharacteristic
662C2×C11—28no—
663C2×C11#350314yescomplemented
664C2×C11C24×Q811yescharacteristic
665C2×C11C22×H(5,𝔽2)11yescharacteristic
666C2×C11C22×2−1+411yescharacteristic
667D11—24no—
668C24—111no—
669C24C23×D1112yes—
670#41—1164no—
671C2×Q8—24no—
672C2×Q8—28no—
673C2×Q8—48no—
674C2×Q8—432no—
675C2×Q8—118no—
676C2×Q8—114no—
677C2×Q8—118no—
678C2×Q8—118no—
679C2×Q8—114no—
680C2×Q8—1116no—
681C2×Q8—1116no—
682C2×Q8—228no—
683C2×Q8—224no—
684C2×Q8—228no—
685C2×Q8—448no—
686C2×Q8—448no—
687C2×Q8—4432no—
688C2×Q8—4432no—
689C2×Q8C23×D1118yes—
690C2×Q8C23×D1114yes—
691C2×Q8C23×D11116yes—
692C2×D4—1116no—
693C2×D4—118no—
694C2×D4Q8×D1118yescomplemented
695C2×D4C23×D1114yes—
696C22×C4—28no—
697C22×C4—48no—
698C22×C4—1116no—
699C22×C4—118no—
700C22×C4—112no—
701C22×C4—111no—
702C22×C4—111no—
703C22×C4—118no—
704C22×C4—114no—
705C22×C4—118no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—111no—
709C22×C4—114no—
710C22×C4—112no—
711C22×C4—1116no—
712C22×C4—114no—
713C22×C4—114no—
714C22×C4—1116no—
715C22×C4—224no—
716C22×C4—228no—
717C22×C4—224no—
718C22×C4—448no—
719C22×C4—448no—
720C22×C4C23×D1118yes—
721C22×C4C23×D1112yes—
722C22×C4C23×D1112yes—
723C22×C4C23×D1111yescharacteristic
724C22×C4C23×D1114yes—
725C22×C4C23×D1112yes—
726C22×C4C23×D11116yes—
727C22×C4C23×D1111yescharacteristic
728C22×C4C23×D1111yescharacteristic
729C4⋊C4—1116no—
730C4⋊C4—118no—
731C4⋊C4—1116no—
732C4⋊C4—118no—
733C4⋊C4—1116no—
734C4⋊C4—1116no—
735C4⋊C4—118no—
736C4⋊C4—1116no—
737C4⋊C4—1116no—
738C4⋊C4—118no—
739C4⋊C4—118no—
740C4⋊C4—118no—
741C4⋊C4—114no—
742C4⋊C4—118no—
743C4⋊C4—114no—
744C4⋊C4—118no—
745C4⋊C4—1116no—
746C4⋊C4—1116no—
747C4⋊C4—118no—
748C4⋊C4—1116no—
749C4⋊C4—118no—
750C4⋊C4C23×D1118yes—
751C4⋊C4C23×D1118yes—
752C4⋊C4C23×D1114yes—
753C4⋊C4C23×D1114yes—
754C4⋊C4C23×D11116yes—
755C4⋊C4C23×D1118yes—
756C22⋊C4—1116no—
757C22⋊C4—118no—
758C22⋊C4—118no—
759C22⋊C4—118no—
760C22⋊C4—118no—
761C22⋊C4C23×D11116yes—
762C22⋊C4C23×D1118yes—
763C42—114no—
764C42—118no—
765C42—114no—
766C42—118no—
767C42—118no—
768C42—114no—
769C42—1116no—
770C42—1116no—
771C42—118no—
772C42C23×D1114yes—
773C42C23×D1118yes—
774C11C2×#350311yescharacteristic, complemented, Sylow
775C23—24no—
776C23—24no—
777C23—114no—
778C23—112no—
779C23—222no—
780C23—222no—
781C23C2×Q8×D1118yes—
782C23C24×D1114yes—
783C23C24×D1111yescharacteristic
784Q8—28no—
785Q8—216no—
786Q8—416no—
787Q8—1116no—
788Q8—2216no—
789Q8—228no—
790Q8—2216no—
791Q8—4416no—
792Q8—4416no—
793D4—1132no—
794D4C2×Q8×D11116yescomplemented
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—216no—
801C2×C4—416no—
802C2×C4—114no—
803C2×C4—118no—
804C2×C4—1132no—
805C2×C4—114no—
806C2×C4—114no—
807C2×C4—112no—
808C2×C4—112no—
809C2×C4—1116no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—112no—
813C2×C4—118no—
814C2×C4—114no—
815C2×C4—228no—
816C2×C4—2216no—
817C2×C4—222no—
818C2×C4—228no—
819C2×C4—224no—
820C2×C4—224no—
821C2×C4—224no—
822C2×C4—228no—
823C2×C4—4416no—
824C2×C4—4416no—
825C2×C4#6703714yes—
826C2×C4C2×Q8×D1114yes—
827C2×C4C24×D1114yes—
828C2×C4C24×D1114yes—
829C2×C4C24×D1112yes—
830C2×C4C24×D1118yes—
831C2×C4C24×D1114yes—
832C2×C4C24×D1112yes—
833C2×C4C24×D1112yes—
834C22—24no—
835C22—24no—
836C22—216no—
837C22—114no—
838C22—222no—
839C22—222no—
840C22—228no—
841C22C2×#6703712yes—
842C22C22×Q8×D1118yes—
843C22C22×Q8×D1112yes—
844C22D11×2−1+412yes—
845C22C25×D1111yescharacteristic
846C4—24no—
847C4—24no—
848C4—28no—
849C4—22no—
850C4—24no—
851C4—114no—
852C4—118no—
853C4—114no—
854C4—222no—
855C4—228no—
856C4—224no—
857C4—224no—
858C4—224no—
859C4C2×#6703714yes—
860C4C22×Q8×D1114yes—
861C2—28no—
862C2—224no—
863C2#1308242714yesdirect product factor
864C2C23×Q8×D1111yescharacteristic
865C2C22×#6703711yescharacteristic
866C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C25
prime radicalC22×#4341C22
hypercenterC2×D4×Q8D11
hypocenterC11C2×#3503
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13082427C2direct (N × H)
2. C2×#10623253C2semidirect
3. C2×#10623098C2semidirect
4. C2×#10623252C2semidirect
5. C2×#10623070C2semidirect
6. C2×#10623167C2semidirect
7. C2×D4×Dic22C2semidirect
8. C2×Q8×C22⋊D11C2semidirect
9. C2×#10623163C2semidirect
10. C2×#10623154C2semidirect
11. C2×#10623260C2semidirect
12. C2×#10623109C2semidirect
13. C2×#10623153C2semidirect
14. C22×#66997C2semidirect
15. C2×D11×C4⋊Q8C2semidirect
18. C2×D4×Q8×C11C2semidirect
23. D4×Q8×C11C22semidirect
31. Q8×C22⋊D11C22semidirect
42. C2×#66997C22semidirect
52. #10623260C22semidirect
53. D11×C4⋊Q8C22semidirect
54. #10623253C22semidirect
55. #10623252C22semidirect
56. #10623167C22semidirect
57. #10623163C22semidirect
58. #10623154C22semidirect
59. #10623153C22semidirect
60. #10623109C22semidirect
61. #10623098C22semidirect
63. #10623070C22semidirect
64. D4×Dic22C22semidirect
115. C2×#4341Q8semidirect
245. C2×D4×C11C2×Q8semidirect
258. C2×C22⋊D11C2×Q8semidirect
262. C22×Dic11C2×Q8semidirect
275. #4341C2×Q8semidirect
279. C2×C4×D11C2×Q8semidirect
290. C2×Dic22C2×Q8semidirect
351. C2×D4×Q8D11semidirect
372. D4×C11C22×Q8semidirect
389. C22⋊D11C22×Q8semidirect
399. C2×Dic11C22×Q8semidirect
412. C4×D11C22×Q8semidirect
418. Dic22C22×Q8semidirect
431. D4×Q8C2×D11semidirect
663. C2×C11#3503semidirect
694. C2×D4Q8×D11semidirect
774. C11C2×#3503semidirect
794. D4C2×Q8×D11semidirect
863. C2#13082427direct (N × H)

Maximal subgroups

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

subgroupindex
#130824272
C2×#106232532
C2×#106230982
C2×#106232522
C2×#106230702
C2×#106231672
C2×D4×Dic222
C2×Q8×C22⋊D112
C2×#106231632
C2×#106231542
C2×#106232602
C2×#106231092
C2×#106231532
C22×#669972
C2×D11×C4⋊Q82
C2×#106230772
C2×C4×#43412
C2×D4×Q8×C112
C2×#350311