Finite Group Databasebeta

← C2×#13082431 #15662103

Subgroups — C2×#13082431 #15662103

Order 2816.

7478 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082431C2132yesmaximal, direct product factor
2C2×#10623253C212yesmaximal, complemented
3C2×#10623216C212yesmaximal, complemented
4C2×#10623221C212yesmaximal, complemented
5C2×#10623167C214yesmaximal, complemented
6C2×#10623258C212yesmaximal, complemented
7C2×#10623163C214yesmaximal, complemented
8C2×#10623220C212yesmaximal, complemented
9C2×#10623050C211yesmaximal, characteristic, complemented
10C2×#10623260C212yesmaximal, complemented
11C2×#10623219C212yesmaximal, complemented
12C2×#10623048C211yesmaximal, characteristic, complemented
13C22×#66941C211yesmaximal, characteristic, complemented
14C2×D11×C4⋊Q8C212yesmaximal, complemented
15C2×#10623035C211yesmaximal, characteristic
16C2×#10623054C211yesmaximal, characteristic
17C2×#10623053C211yesmaximal, characteristic
18C2×C11×#544C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2214yes—
20C22×#4339C2211yescharacteristic
21C23×Dic22C2212yes—
22C11×#544C22116yescomplemented
23C2×C11×C4⋊Q8C2212yes—
24C2×C11×C4⋊Q8C2212yes—
25C2×C11×#125C2212yes—
26C2×C11×#125C2212yes—
27C2×C11×C22⋊Q8C2214yes—
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C2×#66999C2214yes—
32C2×#66997C2214yes—
33C2×#66997C2214yes—
34C2×C4×C22⋊D11C2214yes—
35C2×#66979C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C22×Dic11⋊C4C2212yes—
38C22×C4×Dic11C2211yescharacteristic
39#10623260C22132yescomplemented
40#10623258C22132yescomplemented
41D11×C4⋊Q8C22132yescomplemented
42#10623253C22132yescomplemented
43#10623221C22132yescomplemented
44#10623220C22132yescomplemented
45#10623219C22132yescomplemented
46#10623216C22132yescomplemented
47#10623167C22164yescomplemented
48#10623163C22164yescomplemented
49#10623054C22116yes—
50#10623053C22116yes—
51#10623050C22116yescomplemented
52#10623048C22116yescomplemented
53C2×#66950C2214yes—
54C2×#66949C2214yes—
55C2×#66949C2214yes—
56C2×#66949C2214yes—
57C2×#66949C2214yes—
58#10623035C22116yes—
59C2×#66946C2211yescharacteristic
60C2×#66946C2212yes—
61C2×#66946C2211yescharacteristic
62C2×#66945C2212yes—
63C2×#66945C2212yes—
64C2×C4⋊C4×D11C2214yes—
65C2×C4⋊C4×D11C2212yes—
66C2×C4⋊C4×D11C2212yes—
67C2×#66943C2212yes—
68C2×#66943C2211yescharacteristic
69C2×#66943C2211yescharacteristic
70C2×#66942C2214yes—
71C2×#66942C2214yes—
72C2×#66941C2211yescharacteristic
73C2×#66941C2212yes—
74C2×#66941C2214yes—
75C2×#66941C2212yes—
76C2×#66941C2212yes—
77C2×#66941C2212yes—
78C2×#66941C2211yescharacteristic
79C2×#66941C2212yes—
80C2×#66941C2214yes—
81C2×#66941C22116yescomplemented
82C2×#66940C2214yes—
83C2×#66940C2214yes—
84C2×#66940C2211yescharacteristic
85C2×#66940C2212yes—
86C2×#66940C2211yescharacteristic
87C2×(C22⋊D11)⋊C4C2212yes—
88C2×(C22⋊D11)⋊C4C2214yes—
89C2×(C22⋊D11)⋊C4C2212yes—
90C2×#66931C2212yes—
91C2×#66931C2214yes—
92C2×#66931C2212yes—
93C2×C4×D44C2212yes—
94C2×#66925C2212yes—
95C2×C42×D11C2212yes—
96C2×#66923C2212yes—
97C2×#66922C2212yes—
98C2×C4×Dic22C2212yes—
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2212yes—
101C22×Q8×C11C2314yes—
102C23×C4×C11C2312yes—
103C23×C4×C11C2311yescharacteristic
104C22×C22⋊D11C2312yes—
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2312yes—
108C2×Q8×D11—416no—
109C2×Q8×D11C23132yes—
110C2×#4339Q8116yescomplemented
111C2×#4339C2318yes—
112C22×D44C2311yescharacteristic
113C22×C4×D11C2312yes—
114C22×C4×D11C2312yes—
115C22×C4×D11C2314yes—
116C22×C4×D11C2314yes—
117C22×C4×D11C2312yes—
118C22×Dic22—48no—
119C22×Dic22C2312yes—
120C22×Dic22C2312yes—
121C22×Dic22C2314yes—
122C22×Dic22C2314yes—
123C22×Dic22C2314yes—
124C22×Dic22C23116yes—
125C22×Dic22C2311yescharacteristic
126C11×C4⋊Q8C23116yes—
127C11×C4⋊Q8C23116yes—
128C11×#125C23116yes—
129C11×#125C23116yes—
130C11×C22⋊Q8C23132yes—
131C11×#117C2318yes—
132C11×#117C2318yes—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2314yes—
136C2×C11×C4⋊C4C2314yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2314yes—
140C2×C11×C4⋊C4C2311yescharacteristic
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2318yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C42×C11C2312yes—
146C2×C42×C11C2312yes—
147C2×C22⋊Dic11C2312yes—
148#66999C23132yes—
149#66997C23132yes—
150#66997C23132yes—
151C4×C22⋊D11C23132yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156#66979C2318yes—
157C2×C4⋊Dic11C2312yes—
158C2×C4⋊Dic11C2312yes—
159C2×C4⋊Dic11C2312yes—
160C2×C4⋊Dic11C2311yescharacteristic
161C2×C4⋊Dic11C2312yes—
162C2×C4⋊Dic11C2314yes—
163C2×C4⋊Dic11C2311yescharacteristic
164C2×C4⋊Dic11C2318yes—
165C2×Dic11⋊C4C2312yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2312yes—
168C2×Dic11⋊C4C2312yes—
169C2×Dic11⋊C4C2314yes—
170C2×Dic11⋊C4C2314yes—
171C2×Dic11⋊C4C2314yes—
172C2×Dic11⋊C4C2312yes—
173C2×Dic11⋊C4C2312yes—
174C2×Dic11⋊C4C2314yes—
175C2×Dic11⋊C4C2314yes—
176C2×Dic11⋊C4C2314yes—
177C2×Dic11⋊C4C23116yes—
178C2×C4×Dic11C2311yescharacteristic
179C2×C4×Dic11C2311yescharacteristic
180C2×C4×Dic11C2312yes—
181C2×C4×Dic11C2314yes—
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2312yes—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2314yes—
187C2×C4×Dic11C2318yes—
188#66950C23132yes—
189#66949C23132yes—
190#66949C23132yes—
191#66949C23132yes—
192#66949C23132yes—
193#66946C2318yes—
194#66946C23116yes—
195#66946C2318yes—
196#66945C23116yes—
197#66945C23116yes—
198C4⋊C4×D11C23116yes—
199C4⋊C4×D11C23116yes—
200C4⋊C4×D11C23132yes—
201#66943C2318yes—
202#66943C2318yes—
203#66943C23116yes—
204#66942C23132yes—
205#66942C23132yes—
206#66941C23116yes—
207#66941C23116yes—
208#66941C23132yes—
209#66941C2318yes—
210#66941C23116yes—
211#66941C23132yes—
212#66941C23116yes—
213#66941C23116yes—
214#66941C2318yes—
215#66940C2318yes—
216#66940C23116yes—
217#66940C23132yes—
218#66940C2318yes—
219#66940C23132yes—
220(C22⋊D11)⋊C4C23116yes—
221(C22⋊D11)⋊C4C23116yes—
222(C22⋊D11)⋊C4C23132yes—
223#66931C23116yes—
224#66931C23116yes—
225#66931C23132yes—
226C4×D44C23116yes—
227#66925C23116yes—
228C42×D11C23116yes—
229#66923C23116yes—
230#66922C23116yes—
231C4×Dic22C23116yes—
232C4×Dic22C23116yes—
233C4×Dic22C23116yes—
234C2×#3503—111nomaximal, Sylow
235C24×C11C2411yescharacteristic
236C23×D11C2412yes—
237C2×Q8×C11—48no—
238C2×Q8×C11C24116yes—
239C22×C4×C11—44no—
240C22×C4×C11C2×Q818yescomplemented
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2414yes—
245C22×C4×C11C2412yes—
246C22×C4×C11C2418yes—
247C22×C4×C11C2411yescharacteristic
248C22×C4×C11C2411yescharacteristic
249C22×C4×C11C2414yes—
250C2×C22⋊D11C2×Q8116yescomplemented
251C2×C22⋊D11C2418yes—
252C22×Dic11—24no—
253C22×Dic11—24no—
254C22×Dic11—44no—
255C22×Dic11C2414yes—
256C22×Dic11C2414yes—
257C22×Dic11C2412yes—
258C22×Dic11C2411yescharacteristic
259C22×Dic11C2411yescharacteristic
260C22×Dic11C2414yes—
261C22×Dic11C2412yes—
262C22×Dic11C2418yes—
263C22×Dic11C2412yes—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2411yescharacteristic
266Q8×D11—464no—
267#4339C2×Q8164yescomplemented
268C2×D44C2×Q818yescomplemented
269C2×D44C2414yes—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11—48no—
273C2×C4×D11—48no—
274C2×C4×D11C2×Q8116yescomplemented
275C2×C4×D11C2418yes—
276C2×C4×D11C2418yes—
277C2×C4×D11C24116yes—
278C2×C4×D11C24116yes—
279C2×C4×D11C2418yes—
280C2×Dic22—216no—
281C2×Dic22—28no—
282C2×Dic22—28no—
283C2×Dic22—48no—
284C2×Dic22—48no—
285C2×Dic22—432no—
286C2×Dic22C2×Q818yescomplemented
287C2×Dic22C2418yes—
288C2×Dic22C2418yes—
289C2×Dic22C24116yes—
290C2×Dic22C24116yes—
291C2×Dic22C24116yes—
292C2×Dic22C2414yes—
293C11×C4⋊C4C2418yes—
294C11×C4⋊C4C2414yes—
295C11×C4⋊C4C24116yes—
296C11×C4⋊C4C24116yes—
297C11×C4⋊C4C2414yes—
298C11×C4⋊C4C2418yes—
299C11×C4⋊C4C24116yes—
300C11×C4⋊C4C2414yes—
301C11×C4⋊C4C2414yes—
302C11×C22⋊C4C2418yes—
303C11×C22⋊C4C2418yes—
304C42×C11C2418yes—
305C42×C11C2418yes—
306C22⋊Dic11C2418yes—
307(C2×D11)⋊C4C2418yes—
308(C2×D11)⋊C4C2418yes—
309(C2×D11)⋊C4C24116yes—
310(C2×D11)⋊C4C24116yes—
311C4⋊Dic11C2418yes—
312C4⋊Dic11C2418yes—
313C4⋊Dic11C2418yes—
314C4⋊Dic11C2414yes—
315C4⋊Dic11C2418yes—
316C4⋊Dic11C24116yes—
317C4⋊Dic11C2414yes—
318Dic11⋊C4C2418yes—
319Dic11⋊C4C2418yes—
320Dic11⋊C4C2418yes—
321Dic11⋊C4C2418yes—
322Dic11⋊C4C24116yes—
323Dic11⋊C4C24116yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C2418yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C24116yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330C4×Dic11C2414yes—
331C4×Dic11C2414yes—
332C4×Dic11C2418yes—
333C4×Dic11C24116yes—
334C4×Dic11C2414yes—
335C4×Dic11C2418yes—
336C4×Dic11C2418yes—
337C4×Dic11C2414yes—
338C4×Dic11C24116yes—
339#3503—1132no—
340C2×Q82—112no—
341C2×#557—112no—
342C2×#554—112no—
343C2×#554—114no—
344C2×D4×Q8—112no—
345C2×D4×Q8—114no—
346C2×#544—112no—
347C2×#544—112no—
348C2×#544—111no—
349C2×#544D1111yescharacteristic, complemented
350C2×#533—112no—
351C2×#533—111no—
352C22×C4⋊Q8—112no—
353C22×C4⋊Q8—111no—
354C2×#520—111no—
355C2×#520—111no—
356C2×C4×#41—111no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11C22×Q814yes—
360C23×C11C2512yes—
361C23×C11C2511yescharacteristic
362C22×D11—24no—
363C22×D11—24no—
364C22×D11C22×Q818yes—
365C22×D11C2514yes—
366Q8×C11—416no—
367C2×C4×C11—28no—
368C2×C4×C11—24no—
369C2×C4×C11—24no—
370C2×C4×C11—24no—
371C2×C4×C11—24no—
372C2×C4×C11—48no—
373C2×C4×C11C22×Q814yes—
374C2×C4×C11C22×Q814yes—
375C2×C4×C11C22×Q8116yescomplemented
376C2×C4×C11C2514yes—
377C2×C4×C11C2514yes—
378C2×C4×C11C2514yes—
379C2×C4×C11C2518yes—
380C2×C4×C11C2514yes—
381C2×C4×C11C2512yes—
382C2×C4×C11C2512yes—
383C22⋊D11C22×Q8132yescomplemented
384C2×Dic11—24no—
385C2×Dic11—28no—
386C2×Dic11—22no—
387C2×Dic11—24no—
388C2×Dic11—22no—
389C2×Dic11—28no—
390C2×Dic11—28no—
391C2×Dic11—48no—
392C2×Dic11C22×Q818yes—
393C2×Dic11H(5,𝔽2)14yes—
394C2×Dic112−1+414yes—
395C2×Dic11C2514yes—
396C2×Dic11C2512yes—
397C2×Dic11C2512yes—
398C2×Dic11C2518yes—
399C2×Dic11C2514yes—
400C2×Dic11C2514yes—
401C2×Dic11C2512yes—
402C2×Dic11C2512yes—
403D44C22×Q8116yescomplemented
404C4×D11—216no—
405C4×D11—216no—
406C4×D11—416no—
407C4×D11—416no—
408C4×D11C22×Q8132yescomplemented
409Dic22—232no—
410Dic22—216no—
411Dic22—216no—
412Dic22—416no—
413Dic22—416no—
414Dic22C22×Q8116yescomplemented
415C22×#41—111no—
416C23×Q8—114no—
417C23×Q8—112no—
418Q82—1132no—
419#557—1132no—
420#554—1132no—
421#554—1164no—
422D4×Q8—1132no—
423D4×Q8—1164no—
424#544—1132no—
425#544—1132no—
426#544—1116no—
427#544C2×D11116yescomplemented
428#533—1132no—
429#533—1116no—
430C2×C4⋊Q8—114no—
431C2×C4⋊Q8—114no—
432C2×C4⋊Q8—1132no—
433C2×C4⋊Q8—111no—
434C2×C4⋊Q8—112no—
435C2×C4⋊Q8—112no—
436C2×C4⋊Q8—114no—
437C2×C4⋊Q8—112no—
438C2×C4⋊Q8—112no—
439C2×C4⋊Q8—111no—
440C2×C4⋊Q8—114no—
441C2×C4⋊Q8—112no—
442C2×C4⋊Q8—1116no—
443C2×C4⋊Q8—112no—
444C2×C4⋊Q8C2×D1112yes—
445C2×C4⋊Q8C2×D1112yes—
446C2×#125—114no—
447C2×#125—114no—
448C2×#125—111no—
449C2×#125—111no—
450C2×#125—112no—
451C2×#125—112no—
452C2×#125C2×D1112yes—
453C2×#125C2×D1112yes—
454C2×C22⋊Q8—114no—
455C2×C22⋊Q8—114no—
456C2×C22⋊Q8—114no—
457C2×C22⋊Q8—114no—
458C2×C22⋊Q8—114no—
459C2×C22⋊Q8—114no—
460C2×C22⋊Q8—112no—
461C2×C22⋊Q8—112no—
462C2×C22⋊Q8—114no—
463C2×C22⋊Q8C2×D1114yes—
464#520—1116no—
465#520—1116no—
466C4×#41—1116no—
467C2×C4×Q8—111no—
468C2×C4×Q8—111no—
469C2×C4×Q8—112no—
470C2×C4×Q8—114no—
471C2×C4×Q8—114no—
472C2×C4×Q8—112no—
473C2×C4×Q8—112no—
474C2×C4×Q8—112no—
475C2×C4×D4—114no—
476C2×C4×D4—111no—
477C2×C4×D4—111no—
478C2×C4×D4—112no—
479C2×C4×D4—112no—
480C2×C4×D4—112no—
481C2×C4×D4—114no—
482C2×C4×D4—112no—
483C2×#117—111no—
484C2×#117—112no—
485C2×#117—112no—
486C2×#117—112no—
487C2×#117C2×D1111yescharacteristic
488C2×#117C2×D1111yescharacteristic
489C22×C4⋊C4—112no—
490C22×C4⋊C4—111no—
491C22×C4⋊C4—112no—
492C22×C4⋊C4—112no—
493C22×C4⋊C4—114no—
494C22×C4⋊C4C2×D1111yescharacteristic
495C22×C42—111no—
496C22×C42—112no—
497C22×C11—22no—
498C22×C11—22no—
499C22×C11—28no—
500C22×C11C23×Q814yes—
501C22×C11C23×Q812yes—
502C22×C11C2×H(5,𝔽2)12yes—
503C22×C11C2×2−1+412yes—
504C22×C11C2611yescharacteristic
505C2×D11—24no—
506C2×D11—24no—
507C2×D11—216no—
508C2×D11C23×Q818yes—
509C4×C11—28no—
510C4×C11—24no—
511C4×C11—24no—
512C4×C11—24no—
513C4×C11—24no—
514C4×C11C23×Q814yes—
515C4×C11C23×Q814yes—
516Dic11—24no—
517Dic11—28no—
518Dic11—22no—
519Dic11—24no—
520Dic11—22no—
521Dic11C23×Q818yes—
522Dic11C2×H(5,𝔽2)14yes—
523Dic11C2×2−1+414yes—
524C2×#41—1116no—
525C2×#41—118no—
526C22×Q8—1132no—
527C22×Q8—111no—
528C22×Q8—112no—
529C22×Q8—114no—
530C22×Q8—112no—
531C22×Q8—114no—
532C22×Q8—114no—
533C22×Q8—1116no—
534C22×Q8—448no—
535C22×Q8—4416no—
536C22×Q8C22×D1114yes—
537C22×D4—112no—
538C22×D4—111no—
539C23×C4—112no—
540C23×C4—111no—
541C23×C4—111no—
542C23×C4—112no—
543C23×C4—112no—
544C23×C4—112no—
545C23×C4—114no—
546C23×C4—114no—
547C23×C4C22×D1112yes—
548C23×C4C22×D1111yescharacteristic
549C4⋊Q8—1132no—
550C4⋊Q8—1132no—
551C4⋊Q8—118no—
552C4⋊Q8—1116no—
553C4⋊Q8—1116no—
554C4⋊Q8—1132no—
555C4⋊Q8—1116no—
556C4⋊Q8—1116no—
557C4⋊Q8—118no—
558C4⋊Q8—1132no—
559C4⋊Q8—1116no—
560C4⋊Q8—1116no—
561C4⋊Q8C22×D11116yes—
562C4⋊Q8C22×D11116yes—
563#125—118no—
564#125—118no—
565#125—1132no—
566#125—1132no—
567#125—1116no—
568#125—1116no—
569#125C22×D11116yes—
570#125C22×D11116yes—
571C22⋊Q8—1132no—
572C22⋊Q8—1132no—
573C22⋊Q8—1132no—
574C22⋊Q8—1132no—
575C22⋊Q8—1132no—
576C22⋊Q8—1132no—
577C22⋊Q8—1116no—
578C22⋊Q8—1116no—
579C22⋊Q8—1132no—
580C22⋊Q8C22×D11132yes—
581C4×Q8—118no—
582C4×Q8—118no—
583C4×Q8—1116no—
584C4×Q8—1132no—
585C4×Q8—1132no—
586C4×Q8—1116no—
587C4×Q8—1116no—
588C4×Q8—1116no—
589C4×D4—1132no—
590C4×D4—118no—
591C4×D4—118no—
592C4×D4—1116no—
593C4×D4—1116no—
594C4×D4—1116no—
595C4×D4—1132no—
596C4×D4—1116no—
597#117—118no—
598#117—1116no—
599#117—1116no—
600#117—1116no—
601#117C22×D1118yes—
602#117C22×D1118yes—
603C2×C4⋊C4—112no—
604C2×C4⋊C4—111no—
605C2×C4⋊C4—114no—
606C2×C4⋊C4—112no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—114no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—118no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4—1116no—
614C2×C4⋊C4—111no—
615C2×C4⋊C4—112no—
616C2×C4⋊C4—112no—
617C2×C4⋊C4—112no—
618C2×C4⋊C4—114no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—112no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—1116no—
625C2×C4⋊C4—1116no—
626C2×C4⋊C4—1132no—
627C2×C4⋊C4C22×D1111yescharacteristic
628C2×C4⋊C4C22×D1112yes—
629C2×C4⋊C4C22×D1114yes—
630C2×C4⋊C4C22×D1112yes—
631C2×C4⋊C4C22×D1118yes—
632C2×C4⋊C4C22×D1111yescharacteristic
633C2×C4⋊C4C22×D1111yescharacteristic
634C2×C4⋊C4C22×D1111yescharacteristic
635C2×C4⋊C4C22×D1114yes—
636C2×C4⋊C4C22×D1114yes—
637C2×C22⋊C4—112no—
638C2×C22⋊C4—114no—
639C2×C22⋊C4—112no—
640C2×C22⋊C4—112no—
641C2×C22⋊C4—114no—
642C2×C22⋊C4C22×D1112yes—
643C2×C22⋊C4C22×D1112yes—
644C2×C42—111no—
645C2×C42—114no—
646C2×C42—114no—
647C2×C42—112no—
648C2×C42—112no—
649C2×C42—112no—
650C2×C42—111no—
651C2×C42—111no—
652C2×C42—118no—
653C2×C42—111no—
654C2×C42—1116no—
655C2×C42C22×D1112yes—
656C2×C42C22×D1112yes—
657C2×C11—24no—
658C2×C11#350314yescomplemented
659C2×C11C24×Q811yescharacteristic
660C2×C11C22×H(5,𝔽2)11yescharacteristic
661C2×C11C22×2−1+411yescharacteristic
662D11—28no—
663C24—112no—
664C24C23×D1111yescharacteristic
665#41—1164no—
666C2×Q8—48no—
667C2×Q8—118no—
668C2×Q8—114no—
669C2×Q8—118no—
670C2×Q8—1116no—
671C2×Q8—118no—
672C2×Q8—1116no—
673C2×Q8—1116no—
674C2×Q8—2216no—
675C2×Q8—228no—
676C2×Q8—228no—
677C2×Q8—448no—
678C2×Q8—448no—
679C2×Q8—4432no—
680C2×Q8—4464no—
681C2×Q8C23×D11116yes—
682C2×D4—1116no—
683C2×D4—118no—
684C2×D4—118no—
685C2×D4—114no—
686C22×C4—44no—
687C22×C4—112no—
688C22×C4—111no—
689C22×C4—111no—
690C22×C4—1116no—
691C22×C4—118no—
692C22×C4—114no—
693C22×C4—114no—
694C22×C4—112no—
695C22×C4—111no—
696C22×C4—111no—
697C22×C4—112no—
698C22×C4—114no—
699C22×C4—118no—
700C22×C4—118no—
701C22×C4—118no—
702C22×C4—1116no—
703C22×C4—1116no—
704C22×C4—228no—
705C22×C4—228no—
706C22×C4—224no—
707C22×C4—224no—
708C22×C4—448no—
709C22×C4—448no—
710C22×C4—444no—
711C22×C4Q8×D1118yescomplemented
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1114yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1118yes—
718C22×C4C23×D1111yescharacteristic
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1114yes—
721C4⋊C4—118no—
722C4⋊C4—114no—
723C4⋊C4—1116no—
724C4⋊C4—118no—
725C4⋊C4—1116no—
726C4⋊C4—1116no—
727C4⋊C4—118no—
728C4⋊C4—1116no—
729C4⋊C4—1116no—
730C4⋊C4—114no—
731C4⋊C4—118no—
732C4⋊C4—118no—
733C4⋊C4—118no—
734C4⋊C4—1116no—
735C4⋊C4—118no—
736C4⋊C4—118no—
737C4⋊C4—118no—
738C4⋊C4—1116no—
739C4⋊C4—118no—
740C4⋊C4C23×D1114yes—
741C4⋊C4C23×D1118yes—
742C4⋊C4C23×D11116yes—
743C4⋊C4C23×D1118yes—
744C4⋊C4C23×D1114yes—
745C4⋊C4C23×D1114yes—
746C4⋊C4C23×D1114yes—
747C4⋊C4C23×D11116yes—
748C4⋊C4C23×D11116yes—
749C22⋊C4—118no—
750C22⋊C4—1116no—
751C22⋊C4—118no—
752C22⋊C4—118no—
753C22⋊C4—1116no—
754C22⋊C4C23×D1118yes—
755C22⋊C4C23×D1118yes—
756C42—114no—
757C42—114no—
758C42—118no—
759C42—118no—
760C42—114no—
761C42—114no—
762C42—1116no—
763C42—1116no—
764C42—118no—
765C42C23×D1118yes—
766C42C23×D1118yes—
767C11C2×#350311yescharacteristic, complemented, Sylow
768C23—22no—
769C23—22no—
770C23—118no—
771C23—114no—
772C23—224no—
773C23—224no—
774C23C2×Q8×D1114yes—
775C23C24×D1112yes—
776C23C24×D1111yescharacteristic
777Q8—416no—
778Q8—1116no—
779Q8—2232no—
780Q8—2216no—
781Q8—2216no—
782Q8—4416no—
783Q8—4416no—
784D4—1132no—
785D4—1116no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—48no—
792C2×C4—118no—
793C2×C4—114no—
794C2×C4—114no—
795C2×C4—114no—
796C2×C4—112no—
797C2×C4—112no—
798C2×C4—1132no—
799C2×C4—114no—
800C2×C4—112no—
801C2×C4—112no—
802C2×C4—114no—
803C2×C4—118no—
804C2×C4—2216no—
805C2×C4—2216no—
806C2×C4—228no—
807C2×C4—228no—
808C2×C4—222no—
809C2×C4—224no—
810C2×C4—228no—
811C2×C4—222no—
812C2×C4—224no—
813C2×C4—4416no—
814C2×C4—4416no—
815C2×C4—448no—
816C2×C4C2×Q8×D1114yes—
817C2×C4C2×Q8×D1114yes—
818C2×C4C2×Q8×D11116yescomplemented
819C2×C4C24×D1114yes—
820C2×C4C24×D1114yes—
821C2×C4C24×D1114yes—
822C2×C4C24×D1118yes—
823C2×C4C24×D1114yes—
824C2×C4C24×D1112yes—
825C2×C4C24×D1112yes—
826C22—22no—
827C22—22no—
828C22—28no—
829C22—118no—
830C22—224no—
831C22—224no—
832C22—2216no—
833C22C22×Q8×D1114yes—
834C22C22×Q8×D1112yes—
835C22D11×H(5,𝔽2)12yes—
836C22D11×2−1+412yes—
837C22C25×D1111yescharacteristic
838C4—28no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—118no—
844C4—114no—
845C4—114no—
846C4—222no—
847C4—224no—
848C4—228no—
849C4—222no—
850C4—224no—
851C4C22×Q8×D1114yes—
852C4C22×Q8×D1114yes—
853C2—24no—
854C2—228no—
855C2#1308243114yesdirect product factor
856C2C23×Q8×D1111yescharacteristic
857C2C2×D11×H(5,𝔽2)11yescharacteristic
858C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#544C2
socleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×#544D11
hypocenterC11C2×#3503
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13082431C2direct (N × H)
2. C2×#10623253C2semidirect
3. C2×#10623216C2semidirect
4. C2×#10623221C2semidirect
5. C2×#10623167C2semidirect
6. C2×#10623258C2semidirect
7. C2×#10623163C2semidirect
8. C2×#10623220C2semidirect
9. C2×#10623050C2semidirect
10. C2×#10623260C2semidirect
11. C2×#10623219C2semidirect
12. C2×#10623048C2semidirect
13. C22×#66941C2semidirect
14. C2×D11×C4⋊Q8C2semidirect
18. C2×C11×#544C2semidirect
22. C11×#544C22semidirect
39. #10623260C22semidirect
40. #10623258C22semidirect
41. D11×C4⋊Q8C22semidirect
42. #10623253C22semidirect
43. #10623221C22semidirect
44. #10623220C22semidirect
45. #10623219C22semidirect
46. #10623216C22semidirect
47. #10623167C22semidirect
48. #10623163C22semidirect
51. #10623050C22semidirect
52. #10623048C22semidirect
81. C2×#66941C22semidirect
110. C2×#4339Q8semidirect
240. C22×C4×C11C2×Q8semidirect
250. C2×C22⋊D11C2×Q8semidirect
267. #4339C2×Q8semidirect
268. C2×D44C2×Q8semidirect
274. C2×C4×D11C2×Q8semidirect
286. C2×Dic22C2×Q8semidirect
349. C2×#544D11semidirect
375. C2×C4×C11C22×Q8semidirect
383. C22⋊D11C22×Q8semidirect
403. D44C22×Q8semidirect
408. C4×D11C22×Q8semidirect
414. Dic22C22×Q8semidirect
427. #544C2×D11semidirect
658. C2×C11#3503semidirect
711. C22×C4Q8×D11semidirect
767. C11C2×#3503semidirect
818. C2×C4C2×Q8×D11semidirect
855. C2#13082431direct (N × H)

Maximal subgroups

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

subgroupindex
#130824312
C2×#106232532
C2×#106232162
C2×#106232212
C2×#106231672
C2×#106232582
C2×#106231632
C2×#106232202
C2×#106230502
C2×#106232602
C2×#106232192
C2×#106230482
C22×#669412
C2×D11×C4⋊Q82
C2×#106230352
C2×#106230542
C2×#106230532
C2×C11×#5442
C2×#350311