Finite Group Databasebeta

← C2×#13082228 #15660870

Subgroups — C2×#13082228 #15660870

Order 2816.

7706 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082228C2132yesmaximal, direct product factor
2C2×#10623252C211yesmaximal, characteristic, complemented
3C2×#10623172C212yesmaximal, complemented
4C2×#10623073C211yesmaximal, characteristic, complemented
5C2×#10623181C214yesmaximal, complemented
6C2×#10623044C212yesmaximal, complemented
7C2×D4×Dic22C211yesmaximal, characteristic, complemented
8C2×#10623129C212yesmaximal, complemented
9C2×#10623355C212yesmaximal, complemented
10C2×#10623259C211yesmaximal, characteristic, complemented
11C2×#10623153C212yesmaximal, complemented
12C2×#10623131C212yesmaximal, complemented
13C2×#10623180C214yesmaximal, complemented
14C2×#41×Dic11C212yesmaximal, complemented
15C2×C4×#4341C211yesmaximal, characteristic, complemented
16C2×C4×#4341C211yesmaximal, characteristic, complemented
17C22×#66940C212yesmaximal, complemented
18C2×C11×#547C211yesmaximal, characteristic, complemented
19C22×C11×#41C2212yes—
20C22×#4341C2211yescharacteristic
21C22×#4341C2211yescharacteristic
22C23×Dic22C2212yes—
23C11×#547C22116yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#123C2214yes—
26C2×C11×C22⋊Q8C2212yes—
27C2×C11×#121C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C22×C11×C4⋊C4C2212yes—
31#41×Dic11C22132yescomplemented
32#10623355C22132yescomplemented
33C2×#66999C2212yes—
34C2×Q8×Dic11C2212yes—
35C2×Q8×Dic11C2212yes—
36C2×#66997C2212yes—
37C2×#66992C2214yes—
38C2×#66989C2212yes—
39C2×#66988C2214yes—
40C2×D4×Dic11C2214yes—
41C2×D4×Dic11C2214yes—
42C2×D4×Dic11C2211yescharacteristic
43C2×D4×Dic11C2211yescharacteristic
44C2×D4×Dic11C2212yes—
45C2×#66982C2214yes—
46C2×C4×C22⋊D11C2212yes—
47C2×C4×C22⋊D11C2212yes—
48C2×#66979C2214yes—
49C2×#66979C2212yes—
50C2×#66977C2212yes—
51C2×#66977C2212yes—
52C22×Dic11⋊C4C2214yes—
53C22×C4×Dic11C2214yes—
54C22×C4×Dic11C2212yes—
55C22×C4×Dic11C2212yes—
56#10623259C22116yescomplemented
57#10623252C22116yescomplemented
58#10623181C22164yescomplemented
59#10623180C22164yescomplemented
60#10623172C22132yescomplemented
61#10623153C22132yescomplemented
62#10623131C22132yescomplemented
63#10623129C22132yescomplemented
64#10623073C22116yescomplemented
65D4×Dic22C22116yescomplemented
66C4×#4341C22116yescomplemented
67C4×#4341C22116yescomplemented
68#10623044C22132yescomplemented
69C2×#66951C2214yes—
70C2×#66950C2212yes—
71C2×#66945C2211yescharacteristic
72C2×#66945C2212yes—
73C2×#66945C2211yescharacteristic
74C2×#66943C2212yes—
75C2×#66943C2212yes—
76C2×#66942C2214yes—
77C2×#66942C2214yes—
78C2×#66941C2212yes—
79C2×#66940C2212yes—
80C2×#66940C2214yes—
81C2×#66940C2214yes—
82C2×#66940C2212yes—
83C2×#66940C2211yescharacteristic
84C2×#66940C2212yes—
85C2×#66940C2211yescharacteristic
86C2×#66940C22132yescomplemented
87C2×#66938C2214yes—
88C2×(C22⋊D11)⋊C4C2212yes—
89C2×(C22⋊D11)⋊C4C2212yes—
90C2×#66932C2214yes—
91C2×#66932C2214yes—
92C2×#66931C2214yes—
93C2×#66931C2214yes—
94C2×#66930C2212yes—
95C2×#66930C2212yes—
96C2×#66930C2214yes—
97C2×C42×D11C2211yescharacteristic
98C2×#66922C2211yescharacteristic
99C2×C4×Dic22C2211yescharacteristic
100C2×C4×Dic22C2211yescharacteristic
101C2×C11×#41—216no—
102C2×C11×#41C23116yes—
103C22×Q8×C11C2312yes—
104C22×D4×C11C2314yes—
105C22×D4×C11C2311yescharacteristic
106C22×D4×C11C2311yescharacteristic
107C23×C4×C11C2314yes—
108C23×C4×C11C2312yes—
109C23×C4×C11C2312yes—
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2312yes—
112C23×Dic11C2312yes—
113C23×Dic11C2312yes—
114C23×Dic11C2312yes—
115C23×Dic11C2314yes—
116C23×Dic11C2312yes—
117C2×#4341—28no—
118C2×#4341—28no—
119C2×#4341C2318yes—
120C2×#4341C2318yes—
121C22×C4×D11C2311yescharacteristic
122C22×C4×D11C2311yescharacteristic
123C22×C4×D11C2311yescharacteristic
124C22×Dic22—216no—
125C22×Dic22C2311yescharacteristic
126C22×Dic22C2312yes—
127C22×Dic22C2314yes—
128C22×Dic22C23116yes—
129C22×Dic22C2311yescharacteristic
130C11×C4⋊Q8C2318yes—
131C11×#123C23132yes—
132C11×C22⋊Q8C23116yes—
133C11×#121C23116yes—
134C4×D4×C11C2318yes—
135C4×D4×C11C2318yes—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2314yes—
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C23116yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C42×C11C2311yescharacteristic
146C2×C22⋊Dic11C2314yes—
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2314yes—
150C2×C22⋊Dic11C2314yes—
151#66999C23116yes—
152Q8×Dic11C23116yes—
153Q8×Dic11C23116yes—
154#66997C23116yes—
155#66992C23132yes—
156#66989C23116yes—
157#66988C23132yes—
158D4×Dic11C2318yes—
159D4×Dic11C2318yes—
160D4×Dic11C23116yes—
161D4×Dic11C23132yes—
162D4×Dic11C23132yes—
163#66982C23132yes—
164C4×C22⋊D11C23116yes—
165C4×C22⋊D11C23116yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2314yes—
169#66979C23132yes—
170#66979C23116yes—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2312yes—
175C2×C4⋊Dic11C2314yes—
176C2×C4⋊Dic11C2314yes—
177#66977C23116yes—
178#66977C23116yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2314yes—
186C2×Dic11⋊C4C2314yes—
187C2×Dic11⋊C4C2314yes—
188C2×Dic11⋊C4C23132yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2314yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2314yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2314yes—
201C2×C4×Dic11C23116yes—
202C2×C4×Dic11C23132yes—
203C2×C4×Dic11C23116yes—
204#66951C23132yes—
205#66950C23116yes—
206#66945C23116yes—
207#66945C2318yes—
208#66945C2318yes—
209#66943C23116yes—
210#66943C23116yes—
211#66942C23132yes—
212#66942C23132yes—
213#66941C23116yes—
214#66940C23116yes—
215#66940C23116yes—
216#66940C2318yes—
217#66940C23116yes—
218#66940C23132yes—
219#66940C23132yes—
220#66940C2318yes—
221#66938C23132yes—
222(C22⋊D11)⋊C4C23116yes—
223(C22⋊D11)⋊C4C23116yes—
224#66932C23132yes—
225#66932C23132yes—
226#66931C23132yes—
227#66931C23132yes—
228#66930C23116yes—
229#66930C23116yes—
230#66930C23132yes—
231C42×D11C2318yes—
232#66922C2318yes—
233C4×Dic22C2318yes—
234C4×Dic22C2318yes—
235C2×#3482—111nomaximal, Sylow
236C24×C11C2412yes—
237C24×C11C2412yes—
238C23×D11C2411yescharacteristic
239C11×#41—264no—
240C2×Q8×C11—28no—
241C2×Q8×C11C2418yes—
242C2×D4×C11—216no—
243C2×D4×C11—24no—
244C2×D4×C11#4118yescomplemented
245C2×D4×C11C24116yes—
246C2×D4×C11C2414yes—
247C2×D4×C11C2414yes—
248C22×C4×C11—216no—
249C22×C4×C11—28no—
250C22×C4×C11—28no—
251C22×C4×C11C2412yes—
252C22×C4×C11C2414yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C24116yes—
255C22×C4×C11C2418yes—
256C22×C4×C11C2418yes—
257C22×C4×C11C2411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11C2418yes—
263C2×C22⋊D11C2418yes—
264C22×Dic11—216no—
265C22×Dic11—28no—
266C22×Dic11—28no—
267C22×Dic11—28no—
268C22×Dic11—28no—
269C22×Dic11C2418yes—
270C22×Dic11C2418yes—
271C22×Dic11C2418yes—
272C22×Dic11C24116yes—
273C22×Dic11C2418yes—
274C22×Dic11C2412yes—
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2414yes—
280C22×Dic11C2412yes—
281C22×Dic11C2411yescharacteristic
282#4341—232no—
283#4341—232no—
284C2×C4×D11—24no—
285C2×C4×D11—24no—
286C2×C4×D11—24no—
287C2×C4×D11C2414yes—
288C2×C4×D11C2414yes—
289C2×C4×D11C2414yes—
290C2×Dic22—216no—
291C2×Dic22—264no—
292C2×Dic22—28no—
293C2×Dic22—24no—
294C2×Dic22#4118yescomplemented
295C2×Dic22C2414yes—
296C2×Dic22C2418yes—
297C2×Dic22C24116yes—
298C2×Dic22C2414yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C24116yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C2414yes—
303C11×C4⋊C4C2418yes—
304C11×C22⋊C4C2418yes—
305C11×C22⋊C4C24116yes—
306C11×C22⋊C4C2418yes—
307C42×C11C2414yes—
308C22⋊Dic11C24116yes—
309C22⋊Dic11C2418yes—
310C22⋊Dic11C2418yes—
311C22⋊Dic11C24116yes—
312C22⋊Dic11C24116yes—
313(C2×D11)⋊C4C2418yes—
314(C2×D11)⋊C4C2418yes—
315(C2×D11)⋊C4C24116yes—
316C4⋊Dic11C2414yes—
317C4⋊Dic11C2414yes—
318C4⋊Dic11C2418yes—
319C4⋊Dic11C2418yes—
320C4⋊Dic11C24116yes—
321C4⋊Dic11C24116yes—
322Dic11⋊C4C2418yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C2418yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C24116yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C24116yes—
331C4×Dic11C2418yes—
332C4×Dic11C2418yes—
333C4×Dic11C2414yes—
334C4×Dic11C2414yes—
335C4×Dic11C2414yes—
336C4×Dic11C2418yes—
337C4×Dic11C2418yes—
338C4×Dic11C24116yes—
339C4×Dic11C2418yes—
340C4×Dic11C24116yes—
341C4×Dic11C2418yes—
342C4×Dic11C24116yes—
343#3482—1132no—
344C2×#557—111no—
345C2×#556—112no—
346C2×#556—111no—
347C2×#552—114no—
348C2×#552—112no—
349C2×D4×Q8—111no—
350C2×#548—112no—
351C2×#547—112no—
352C2×#547D1111yescharacteristic, complemented
353C2×#533—111no—
354C2×#533—112no—
355C2×#529—114no—
356C2×#529—112no—
357C2×C4×#41—112no—
358C2×C4×#41—111no—
359C2×C4×#41—111no—
360C22×C4×Q8—112no—
361C23×C11—24no—
362C23×C11—24no—
363C23×C11—24no—
364C23×C11—24no—
365C23×C11—24no—
366C23×C11C2×#4118yes—
367C23×C11C2514yes—
368C23×C11C2514yes—
369C23×C11C2511yescharacteristic
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11C2512yes—
374Q8×C11—216no—
375D4×C11—232no—
376D4×C11—28no—
377D4×C11C2×#41116yescomplemented
378C2×C4×C11—24no—
379C2×C4×C11—24no—
380C2×C4×C11—28no—
381C2×C4×C11—232no—
382C2×C4×C11—22no—
383C2×C4×C11—216no—
384C2×C4×C11—216no—
385C2×C4×C11C2×#4114yes—
386C2×C4×C11C2×#4114yes—
387C2×C4×C11C2514yes—
388C2×C4×C11C2518yes—
389C2×C4×C11C2514yes—
390C2×C4×C11C2512yes—
391C2×C4×C11C2512yes—
392C2×C4×C11C2512yes—
393C22⋊D11—216no—
394C22⋊D11—216no—
395C2×Dic11—28no—
396C2×Dic11—24no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—216no—
400C2×Dic11—24no—
401C2×Dic11—24no—
402C2×Dic11—232no—
403C2×Dic11—216no—
404C2×Dic11—216no—
405C2×Dic11—216no—
406C2×Dic11C2×#4118yes—
407C2×Dic112−1+414yes—
408C2×Dic11C2514yes—
409C2×Dic11C2512yes—
410C2×Dic11C2512yes—
411C2×Dic11C2514yes—
412C2×Dic11C2514yes—
413C2×Dic11C2518yes—
414C2×Dic11C2514yes—
415C2×Dic11C2512yes—
416C4×D11—28no—
417C4×D11—28no—
418C4×D11—28no—
419Dic22—216no—
420Dic22—28no—
421Dic22—232no—
422Dic22C2×#41116yescomplemented
423C22×#41—111no—
424C22×#41—111no—
425C22×#41C2×D1112yes—
426C23×Q8—112no—
427#557—1116no—
428#556—1132no—
429#556—1116no—
430#552—1164no—
431#552—1132no—
432D4×Q8—1116no—
433#548—1132no—
434#547—1132no—
435#547C2×D11116yescomplemented
436#533—1116no—
437#533—1132no—
438C2×C4⋊Q8—112no—
439C2×C4⋊Q8—112no—
440C2×C4⋊Q8—111no—
441C2×C4⋊Q8C2×D1111yescharacteristic
442#529—1164no—
443#529—1132no—
444C2×#126—114no—
445C2×#126—114no—
446C2×#126—114no—
447C2×#125—114no—
448C2×#125—114no—
449C2×#125—112no—
450C2×#125—112no—
451C2×#124—112no—
452C2×#124—114no—
453C2×#123—114no—
454C2×#123—114no—
455C2×#123C2×D1114yes—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—112no—
458C2×C22⋊Q8—112no—
459C2×C22⋊Q8—112no—
460C2×C22⋊Q8—114no—
461C2×C22⋊Q8—114no—
462C2×C22⋊Q8C2×D1112yes—
463C2×#121—114no—
464C2×#121C2×D1112yes—
465C4×#41—1132no—
466C4×#41—1116no—
467C4×#41—1116no—
468C2×C4×Q8—112no—
469C2×C4×Q8—112no—
470C2×C4×Q8—111no—
471C2×C4×Q8—114no—
472C2×C4×Q8—112no—
473C2×C4×Q8—112no—
474C2×C4×Q8—114no—
475C2×C4×Q8—112no—
476C2×C4×Q8—111no—
477C2×C4×Q8—1132no—
478C2×C4×Q8—111no—
479C2×C4×Q8—111no—
480C2×C4×D4—111no—
481C2×C4×D4—114no—
482C2×C4×D4—111no—
483C2×C4×D4—112no—
484C2×C4×D4—114no—
485C2×C4×D4—112no—
486C2×C4×D4—112no—
487C2×C4×D4—112no—
488C2×C4×D4—112no—
489C2×C4×D4C2×D1111yescharacteristic
490C2×C4×D4C2×D1111yescharacteristic
491C2×#117—114no—
492C2×#117—112no—
493C2×#117—111no—
494C2×#117—111no—
495C2×#117—112no—
496C2×#117—112no—
497C2×#117—112no—
498C2×#117—114no—
499C22×C4⋊C4—114no—
500C22×C4⋊C4C2×D1112yes—
501C22×C42—112no—
502C22×C42—114no—
503C22×C42—112no—
504C22×C42—111no—
505C22×C11—24no—
506C22×C11—24no—
507C22×C11—216no—
508C22×C11—24no—
509C22×C11—24no—
510C22×C11—24no—
511C22×C11—48no—
512C22×C11C22×#4118yes—
513C22×C11C22×#4112yes—
514C22×C11C22×#4112yes—
515C22×C11C2×2−1+412yes—
516C22×C11C2611yescharacteristic
517C2×D11—22no—
518C2×D11—22no—
519C2×D11—22no—
520C2×D11—44no—
521C4×C11—24no—
522C4×C11—28no—
523C4×C11—24no—
524C4×C11—22no—
525C4×C11C22×#4114yes—
526C4×C11C22×#4114yes—
527Dic11—28no—
528Dic11—24no—
529Dic11—22no—
530Dic11—22no—
531Dic11—24no—
532Dic11—24no—
533Dic11C22×#4118yes—
534Dic11C2×2−1+414yes—
535C2×#41—216no—
536C2×#41—118no—
537C2×#41—118no—
538C2×#41—228no—
539C2×#41—228no—
540C2×#41C22×D11116yes—
541C22×Q8—111no—
542C22×Q8—114no—
543C22×Q8—112no—
544C22×Q8—111no—
545C22×Q8—1116no—
546C22×Q8—2216no—
547C22×Q8C22×D1112yes—
548C22×D4—112no—
549C22×D4—112no—
550C22×D4C22×D1114yes—
551C22×D4C22×D1111yescharacteristic
552C22×D4C22×D1111yescharacteristic
553C23×C4—112no—
554C23×C4—114no—
555C23×C4—112no—
556C23×C4—112no—
557C23×C4—112no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4C22×D1114yes—
562C23×C4C22×D1112yes—
563C23×C4C22×D1112yes—
564C4⋊Q8—1116no—
565C4⋊Q8—1116no—
566C4⋊Q8—118no—
567C4⋊Q8C22×D1118yes—
568#126—1132no—
569#126—1132no—
570#126—1132no—
571#125—1132no—
572#125—1116no—
573#125—1132no—
574#125—1116no—
575#124—1116no—
576#124—1132no—
577#123—1132no—
578#123—1132no—
579#123C22×D11132yes—
580C22⋊Q8—1116no—
581C22⋊Q8—1116no—
582C22⋊Q8—1116no—
583C22⋊Q8—1116no—
584C22⋊Q8—1132no—
585C22⋊Q8—1132no—
586C22⋊Q8C22×D11116yes—
587#121—1132no—
588#121C22×D11116yes—
589C4×Q8—1116no—
590C4×Q8—1116no—
591C4×Q8—118no—
592C4×Q8—1132no—
593C4×Q8—1116no—
594C4×Q8—1116no—
595C4×Q8—1132no—
596C4×Q8—1116no—
597C4×Q8—118no—
598C4×Q8—118no—
599C4×Q8—118no—
600C4×D4—118no—
601C4×D4—118no—
602C4×D4—1132no—
603C4×D4—1116no—
604C4×D4—1132no—
605C4×D4—1116no—
606C4×D4—1116no—
607C4×D4—1116no—
608C4×D4—1116no—
609C4×D4C22×D1118yes—
610C4×D4C22×D1118yes—
611#117—1132no—
612#117—1116no—
613#117—118no—
614#117—118no—
615#117—1116no—
616#117—1116no—
617#117—1116no—
618#117—1132no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—114no—
621C2×C4⋊C4—114no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—1132no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—112no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—114no—
628C2×C4⋊C4—111no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—114no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4C22×D1111yescharacteristic
636C2×C4⋊C4C22×D1112yes—
637C2×C4⋊C4C22×D1114yes—
638C2×C4⋊C4C22×D11116yes—
639C2×C4⋊C4C22×D1111yescharacteristic
640C2×C4⋊C4C22×D1112yes—
641C2×C22⋊C4—112no—
642C2×C22⋊C4—114no—
643C2×C22⋊C4—112no—
644C2×C22⋊C4—114no—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4—112no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4C22×D1112yes—
650C2×C22⋊C4C22×D1112yes—
651C2×C22⋊C4C22×D1114yes—
652C2×C42—111no—
653C2×C42—112no—
654C2×C42—114no—
655C2×C42—112no—
656C2×C42—112no—
657C2×C42—114no—
658C2×C42—112no—
659C2×C42—114no—
660C2×C42—112no—
661C2×C42—112no—
662C2×C42—111no—
663C2×C42—111no—
664C2×C42—1116no—
665C2×C42—1132no—
666C2×C42—1116no—
667C2×C42—118no—
668C2×C42C22×D1111yescharacteristic
669C2×C11—28no—
670C2×C11—44no—
671C2×C11#348214yescomplemented
672C2×C11C23×#4111yescharacteristic
673C2×C11C23×#4111yescharacteristic
674C2×C11C22×2−1+411yescharacteristic
675D11—42no—
676C24—111no—
677C24C23×D1112yes—
678C24C23×D1112yes—
679#41—264no—
680#41—2232no—
681#41—2232no—
682C2×Q8—28no—
683C2×Q8—118no—
684C2×Q8—114no—
685C2×Q8—1116no—
686C2×Q8—118no—
687C2×Q8—114no—
688C2×Q8—2216no—
689C2×Q8—2264no—
690C2×Q8—224no—
691C2×Q8—228no—
692C2×Q8C23×D1118yes—
693C2×D4—216no—
694C2×D4—24no—
695C2×D4—118no—
696C2×D4—118no—
697C2×D4—228no—
698C2×D4—228no—
699C2×D4#434118yescomplemented
700C2×D4C23×D11116yes—
701C2×D4C23×D1114yes—
702C2×D4C23×D1114yes—
703C22×C4—216no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—111no—
707C22×C4—112no—
708C22×C4—118no—
709C22×C4—118no—
710C22×C4—1116no—
711C22×C4—118no—
712C22×C4—118no—
713C22×C4—112no—
714C22×C4—111no—
715C22×C4—111no—
716C22×C4—112no—
717C22×C4—114no—
718C22×C4—112no—
719C22×C4—114no—
720C22×C4—114no—
721C22×C4—114no—
722C22×C4—224no—
723C22×C4—2216no—
724C22×C4—228no—
725C22×C4—228no—
726C22×C4—228no—
727C22×C4—228no—
728C22×C4—224no—
729C22×C4—224no—
730C22×C4C23×D11116yes—
731C22×C4C23×D1118yes—
732C22×C4C23×D1118yes—
733C22×C4C23×D1112yes—
734C22×C4C23×D1112yes—
735C22×C4C23×D1114yes—
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738C22×C4C23×D1111yescharacteristic
739C4⋊C4—118no—
740C4⋊C4—1116no—
741C4⋊C4—1116no—
742C4⋊C4—1116no—
743C4⋊C4—114no—
744C4⋊C4—118no—
745C4⋊C4—118no—
746C4⋊C4—1116no—
747C4⋊C4—114no—
748C4⋊C4—118no—
749C4⋊C4—118no—
750C4⋊C4—1116no—
751C4⋊C4—1116no—
752C4⋊C4—118no—
753C4⋊C4—1116no—
754C4⋊C4C23×D1114yes—
755C4⋊C4C23×D1118yes—
756C4⋊C4C23×D11116yes—
757C4⋊C4C23×D1114yes—
758C4⋊C4C23×D1118yes—
759C22⋊C4—118no—
760C22⋊C4—1116no—
761C22⋊C4—118no—
762C22⋊C4—1116no—
763C22⋊C4—1116no—
764C22⋊C4—118no—
765C22⋊C4—118no—
766C22⋊C4—1116no—
767C22⋊C4C23×D1118yes—
768C22⋊C4C23×D1118yes—
769C22⋊C4C23×D11116yes—
770C42—118no—
771C42—114no—
772C42—114no—
773C42—114no—
774C42—118no—
775C42—1116no—
776C42—118no—
777C42—118no—
778C42—1116no—
779C42—118no—
780C42—1116no—
781C42—118no—
782C42C23×D1114yes—
783C11C2×#348211yescharacteristic, complemented, Sylow
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—112no—
790C23—222no—
791C23—222no—
792C23—222no—
793C23C2×#434118yes—
794C23C24×D1114yes—
795C23C24×D1114yes—
796C23C24×D1111yescharacteristic
797Q8—216no—
798Q8—1116no—
799Q8—2232no—
800Q8—228no—
801Q8—2216no—
802D4—232no—
803D4—28no—
804D4—2216no—
805D4—2216no—
806D4C2×#4341116yescomplemented
807C2×C4—24no—
808C2×C4—28no—
809C2×C4—232no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—216no—
813C2×C4—216no—
814C2×C4—118no—
815C2×C4—114no—
816C2×C4—112no—
817C2×C4—114no—
818C2×C4—114no—
819C2×C4—112no—
820C2×C4—112no—
821C2×C4—114no—
822C2×C4—118no—
823C2×C4—114no—
824C2×C4—228no—
825C2×C4—2232no—
826C2×C4—2216no—
827C2×C4—2216no—
828C2×C4—2216no—
829C2×C4—222no—
830C2×C4—224no—
831C2×C4—2216no—
832C2×C4—222no—
833C2×C4—228no—
834C2×C4—224no—
835C2×C4—224no—
836C2×C4—228no—
837C2×C4—228no—
838C2×C4C2×#434114yes—
839C2×C4#41×D1114yes—
840C2×C4C24×D1114yes—
841C2×C4C24×D1114yes—
842C2×C4C24×D1118yes—
843C2×C4C24×D1112yes—
844C2×C4C24×D1112yes—
845C2×C4C24×D1112yes—
846C22—24no—
847C22—24no—
848C22—216no—
849C22—24no—
850C22—24no—
851C22—24no—
852C22—48no—
853C22—222no—
854C22—222no—
855C22—222no—
856C22—444no—
857C22C22×#434118yes—
858C22C22×#434112yes—
859C22C2×#41×D1112yes—
860C22D11×2−1+412yes—
861C22C25×D1111yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—22no—
866C4—118no—
867C4—114no—
868C4—222no—
869C4—228no—
870C4—222no—
871C4—224no—
872C4—224no—
873C4—224no—
874C4C22×#434114yes—
875C4C2×#41×D1114yes—
876C2—28no—
877C2—44no—
878C2—442no—
879C2#1308222814yesdirect product factor
880C2C22×#41×D1111yescharacteristic
881C2C23×#434111yescharacteristic
882C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#547C2
socleC23×C11C25
hypercenterC2×#547D11
hypocenterC11C2×#3482
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13082228C2direct (N × H)
2. C2×#10623252C2semidirect
3. C2×#10623172C2semidirect
4. C2×#10623073C2semidirect
5. C2×#10623181C2semidirect
6. C2×#10623044C2semidirect
7. C2×D4×Dic22C2semidirect
8. C2×#10623129C2semidirect
9. C2×#10623355C2semidirect
10. C2×#10623259C2semidirect
11. C2×#10623153C2semidirect
12. C2×#10623131C2semidirect
13. C2×#10623180C2semidirect
14. C2×#41×Dic11C2semidirect
15. C2×C4×#4341C2semidirect
16. C2×C4×#4341C2semidirect
17. C22×#66940C2semidirect
18. C2×C11×#547C2semidirect
23. C11×#547C22semidirect
31. #41×Dic11C22semidirect
32. #10623355C22semidirect
56. #10623259C22semidirect
57. #10623252C22semidirect
58. #10623181C22semidirect
59. #10623180C22semidirect
60. #10623172C22semidirect
61. #10623153C22semidirect
62. #10623131C22semidirect
63. #10623129C22semidirect
64. #10623073C22semidirect
65. D4×Dic22C22semidirect
66. C4×#4341C22semidirect
67. C4×#4341C22semidirect
68. #10623044C22semidirect
86. C2×#66940C22semidirect
244. C2×D4×C11#41semidirect
294. C2×Dic22#41semidirect
352. C2×#547D11semidirect
377. D4×C11C2×#41semidirect
422. Dic22C2×#41semidirect
435. #547C2×D11semidirect
671. C2×C11#3482semidirect
699. C2×D4#4341semidirect
783. C11C2×#3482semidirect
806. D4C2×#4341semidirect
879. C2#13082228direct (N × H)

Maximal subgroups

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

subgroupindex
#130822282
C2×#106232522
C2×#106231722
C2×#106230732
C2×#106231812
C2×#106230442
C2×D4×Dic222
C2×#106231292
C2×#106233552
C2×#106232592
C2×#106231532
C2×#106231312
C2×#106231802
C2×#41×Dic112
C2×C4×#43412
C22×#669402
C2×C11×#5472
C2×#348211