Finite Group Databasebeta

← C2×#13082365 #15662200

Subgroups — C2×#13082365 #15662200

Order 2816.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082365C2132yesmaximal, direct product factor
2C2×#10623172C212yesmaximal, complemented
3C2×#10623166C212yesmaximal, complemented
4C2×#10623173C212yesmaximal, complemented
5C2×#10623181C214yesmaximal, complemented
6C2×#10623170C212yesmaximal, complemented
7C2×#10623189C214yesmaximal, complemented
8C2×#10623050C211yesmaximal, characteristic, complemented
9C2×#10623213C212yesmaximal, complemented
10C2×#10623262C212yesmaximal, complemented
11C2×#10623259C212yesmaximal, complemented
12C2×#10623211C212yesmaximal, complemented
13C2×#10623359C211yesmaximal, characteristic
14C22×#66999C211yesmaximal, characteristic, complemented
15C2×#10623358C211yesmaximal, characteristic, complemented
16C2×#10623343C211yesmaximal, characteristic, complemented
17C2×D11×#117C211yesmaximal, characteristic, complemented
18C2×C11×#536C211yesmaximal, characteristic, complemented
19C22×C11×#41C2211yescharacteristic
20C23×Q8×C11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C11×#536C22116yescomplemented
23C2×C11×C4⋊Q8C2212yescomplemented
24C2×C11×#124C2212yescomplemented
25C2×C11×#123C2214yes—
26C2×C11×C22⋊Q8C2212yescomplemented
27C2×C11×C22⋊Q8C2212yescomplemented
28C2×C11×#117C2211yescharacteristic
29#10623359C22116yes—
30#10623358C22116yescomplemented
31C2×#66999C2212yes—
32C2×#66999C2212yes—
33C2×#66999C2212yes—
34C2×#66999C2211yescharacteristic
35C2×#66999C2211yescharacteristic
36C2×#66999C2212yes—
37C2×#66999C22116yescomplemented
38#10623343C22116yescomplemented
39C2×Q8×Dic11C2212yescomplemented
40C2×Q8×Dic11C2212yescomplemented
41C2×Q8×Dic11C2212yescomplemented
42C2×Q8×Dic11C2212yescomplemented
43C2×Q8×Dic11C2212yescomplemented
44C2×#66991C2211yescharacteristic
45C2×#66991C2211yescharacteristic
46C2×#66990C2212yes—
47C2×#66988C2212yes—
48C2×D4×Dic11C2214yes—
49C2×D4×Dic11C2212yescomplemented
50C2×C4×C22⋊D11C2212yes—
51C2×C4×C22⋊D11C2212yes—
52C22×(C2×D11)⋊C4C2212yes—
53C2×#66979C2214yes—
54C2×#66979C2211yescharacteristic
55C2×#66979C2211yescharacteristic
56C2×#66979C2212yescomplemented
57C22×C4⋊Dic11C2211yescharacteristic
58C22×C4⋊Dic11C2212yescomplemented
59C22×Dic11⋊C4C2212yes—
60#10623262C22132yescomplemented
61#10623259C22132yescomplemented
62#10623213C22132yescomplemented
63#10623211C22132yescomplemented
64#10623189C22164yescomplemented
65#10623181C22164yescomplemented
66#10623173C22132yescomplemented
67#10623172C22132yescomplemented
68#10623170C22132yescomplemented
69#10623166C22132yescomplemented
70D11×#117C22116yescomplemented
71#10623050C22116yescomplemented
72C2×#66951C2214yes—
73C2×#66951C2214yes—
74C2×#66950C2214yes—
75C2×#66945C2214yes—
76C2×#66945C2211yescharacteristic
77C2×#66945C2211yescharacteristic
78C2×C4⋊C4×D11C2211yescharacteristic
79C2×C4⋊C4×D11C2211yescharacteristic
80C2×#66943C2212yescomplemented
81C2×#66943C2214yescomplemented
82C2×#66942C2214yescomplemented
83C2×#66942C2214yescomplemented
84C2×#66941C2212yescomplemented
85C2×#66940C2214yescomplemented
86C2×#66939C2214yes—
87C2×#66938C2214yes—
88C2×#66936C2214yes—
89C2×(C22⋊D11)⋊C4C2214yes—
90C2×C22⋊C4×D11C2212yes—
91C2×#66932C2214yescomplemented
92C2×#66932C2214yescomplemented
93C2×#66931C2214yes—
94C2×#66931C2214yescomplemented
95C2×#66930C2212yes—
96C2×#66930C2214yescomplemented
97C2×#66925C2212yes—
98C2×C42×D11C2212yes—
99C2×#66923C2212yescomplemented
100C2×#66922C2212yescomplemented
101C24×D11C2311yescharacteristic
102C2×C11×#41—28no—
103C2×C11×#41C2318yes—
104C22×Q8×C11—28no—
105C22×Q8×C11C2312yes—
106C22×Q8×C11C2312yes—
107C22×Q8×C11C2311yescharacteristic
108C22×Q8×C11C2318yes—
109C22×D4×C11C2312yes—
110C22×D4×C11C2311yescharacteristic
111C23×C4×C11C2312yes—
112C23×C4×C11C2312yes—
113C23×C4×C11C2311yescharacteristic
114C22×C22⋊D11C2312yes—
115C22×C22⋊D11C2312yes—
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2314yes—
118C23×Dic11C2312yes—
119C22×C4×D11—28no—
120C22×C4×D11C2311yescharacteristic
121C22×C4×D11C2312yes—
122C22×C4×D11C2311yescharacteristic
123C22×C4×D11C2311yescharacteristic
124C22×C4×D11C2311yescharacteristic
125C22×C4×D11C2318yes—
126C22×C4×D11C2312yes—
127C22×Dic22C2314yes—
128C11×C4⋊Q8C23116yescomplemented
129C11×#124C23116yescomplemented
130C11×#123C23132yes—
131C11×C22⋊Q8C23116yescomplemented
132C11×C22⋊Q8C23116yescomplemented
133C11×#117C2318yes—
134C2×C11×C4⋊C4C2314yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2314yes—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4C2312yes—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2314yes—
141C2×C42×C11C2312yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2312yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2314yes—
147#66999C2318yes—
148#66999C23116yes—
149#66999C2318yes—
150#66999C23116yes—
151#66999C23116yes—
152#66999C23116yes—
153Q8×Dic11C23116yescomplemented
154Q8×Dic11C23116yescomplemented
155Q8×Dic11C23116yescomplemented
156Q8×Dic11C23116yescomplemented
157Q8×Dic11C23116yescomplemented
158#66991C2318yes—
159#66991C2318yes—
160#66990C23116yes—
161#66988C23116yes—
162D4×Dic11C23132yes—
163D4×Dic11C23116yescomplemented
164C4×C22⋊D11C23116yes—
165C4×C22⋊D11C23116yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C23116yes—
173#66979C2318yes—
174#66979C2318yes—
175#66979C23132yes—
176#66979C23116yescomplemented
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2314yes—
180C2×C4⋊Dic11C2311yescharacteristic
181C2×C4⋊Dic11C2314yes—
182C2×C4⋊Dic11C2314yes—
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2314yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2311yescharacteristic
187C2×C4⋊Dic11C2318yes—
188C2×C4⋊Dic11C23116yescomplemented
189C2×Dic11⋊C4C2314yes—
190C2×Dic11⋊C4C2314yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2314yes—
194C2×Dic11⋊C4C2314yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×Dic11⋊C4C23116yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2314yes—
202C2×C4×Dic11C2314yes—
203C2×C4×Dic11C2314yes—
204C2×C4×Dic11C2312yes—
205#66951C23132yes—
206#66951C23132yes—
207#66950C23132yes—
208#66945C23132yes—
209#66945C2318yes—
210#66945C2318yes—
211C4⋊C4×D11C2318yes—
212C4⋊C4×D11C2318yes—
213#66943C23132yescomplemented
214#66943C23116yescomplemented
215#66942C23132yescomplemented
216#66942C23132yescomplemented
217#66941C23116yescomplemented
218#66940C23132yescomplemented
219#66939C23132yes—
220#66938C23132yes—
221#66936C23132yes—
222(C22⋊D11)⋊C4C23132yes—
223C22⋊C4×D11C23116yes—
224#66932C23132yescomplemented
225#66932C23132yescomplemented
226#66931C23132yes—
227#66931C23132yescomplemented
228#66930C23116yes—
229#66930C23132yescomplemented
230#66925C23116yes—
231C42×D11C23116yes—
232#66923C23116yescomplemented
233#66922C23116yescomplemented
234C2×#3495—111nomaximal, Sylow
235C24×C11C2412yes—
236C24×C11C2411yescharacteristic
237C23×D11—24no—
238C23×D11—24no—
239C23×D11—42no—
240C23×D11C2411yescharacteristic
241C23×D11C2414yes—
242C23×D11C2411yescharacteristic
243C11×#41—232no—
244C2×Q8×C11—28no—
245C2×Q8×C11—28no—
246C2×Q8×C11—232no—
247C2×Q8×C11—24no—
248C2×Q8×C11C2418yes—
249C2×Q8×C11C2418yes—
250C2×Q8×C11C2414yes—
251C2×D4×C11—28no—
252C2×D4×C11—24no—
253C2×D4×C11C2418yes—
254C2×D4×C11C2414yes—
255C22×C4×C11—28no—
256C22×C4×C11—28no—
257C22×C4×C11#4118yes—
258C22×C4×C11C2414yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2412yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2418yes—
263C22×C4×C11C2418yes—
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2414yes—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11C2418yes—
270C2×C22⋊D11C2418yes—
271C22×Dic11—24no—
272C22×Dic11—44no—
273C22×Dic11—48no—
274C22×Dic11C2414yes—
275C22×Dic11C2412yes—
276C22×Dic11C2411yescharacteristic
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2414yes—
281C22×Dic11C2411yescharacteristic
282C22×Dic11C24116yes—
283C22×Dic11C2418yes—
284C2×C4×D11—28no—
285C2×C4×D11—24no—
286C2×C4×D11—24no—
287C2×C4×D11—24no—
288C2×C4×D11—24no—
289C2×C4×D11—232no—
290C2×C4×D11—44no—
291C2×C4×D11C2414yes—
292C2×C4×D11C2418yes—
293C2×C4×D11C2414yes—
294C2×C4×D11C2414yes—
295C2×C4×D11C2414yes—
296C2×C4×D11C2418yes—
297C2×Dic22—48no—
298C2×Dic22C24116yes—
299C11×C4⋊C4C24116yes—
300C11×C4⋊C4C2414yes—
301C11×C4⋊C4C24116yes—
302C11×C4⋊C4C2414yes—
303C11×C22⋊C4C2418yes—
304C11×C22⋊C4C24116yes—
305C11×C22⋊C4C24116yes—
306C42×C11C2418yes—
307C22⋊Dic11C2418yes—
308C22⋊Dic11C2418yes—
309C22⋊Dic11C2418yes—
310C22⋊Dic11C2418yes—
311C22⋊Dic11C24116yes—
312(C2×D11)⋊C4C2418yes—
313(C2×D11)⋊C4C2418yes—
314(C2×D11)⋊C4C24116yes—
315(C2×D11)⋊C4C24116yes—
316(C2×D11)⋊C4C2418yes—
317(C2×D11)⋊C4C2418yes—
318C4⋊Dic11C2414yes—
319C4⋊Dic11C2418yes—
320C4⋊Dic11C24116yes—
321C4⋊Dic11C2414yes—
322C4⋊Dic11C24116yes—
323C4⋊Dic11C24116yes—
324C4⋊Dic11C2418yes—
325C4⋊Dic11C24116yes—
326C4⋊Dic11C2414yes—
327C4⋊Dic11C2414yes—
328Dic11⋊C4C24116yes—
329Dic11⋊C4C24116yes—
330Dic11⋊C4C2418yes—
331Dic11⋊C4C2418yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C24116yes—
334Dic11⋊C4C2418yes—
335Dic11⋊C4C2418yes—
336C4×Dic11C2418yes—
337C4×Dic11C2418yes—
338C4×Dic11C2418yes—
339C4×Dic11C24116yes—
340C4×Dic11C24116yes—
341C4×Dic11C24116yes—
342C4×Dic11C2418yes—
343#3495—1132no—
344C2×#556—112no—
345C2×#554—112no—
346C2×#552—114no—
347C2×#552—112no—
348C2×#552—112no—
349C2×#551—114no—
350C2×#544—111no—
351C2×#542—112no—
352C2×#541—112no—
353C2×#536D1111yescharacteristic, complemented
354C2×#533—112no—
355C2×#529—112no—
356C2×#525—111no—
357C22×C22⋊Q8—111no—
358C2×#520—111no—
359C2×#519—111no—
360C22×#117—111no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—24no—
364C23×C11—24no—
365C23×C11—24no—
366C23×C11C2×#4114yes—
367C23×C11C2514yes—
368C23×C11C2512yes—
369C23×C11C2511yescharacteristic
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—28no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—28no—
377C22×D11—44no—
378C22×D11—416no—
379C22×D112−1+414yes—
380C22×D11C2512yes—
381C22×D11C2512yes—
382Q8×C11—216no—
383Q8×C11—216no—
384Q8×C11—28no—
385D4×C11—216no—
386D4×C11—28no—
387C2×C4×C11—24no—
388C2×C4×C11—216no—
389C2×C4×C11—28no—
390C2×C4×C11—24no—
391C2×C4×C11—24no—
392C2×C4×C11—216no—
393C2×C4×C11C2×#4114yes—
394C2×C4×C11C2×#4114yes—
395C2×C4×C11C2×#41116yes—
396C2×C4×C11C2518yes—
397C2×C4×C11C2514yes—
398C2×C4×C11C2514yes—
399C2×C4×C11C2514yes—
400C2×C4×C11C2512yes—
401C2×C4×C11C2512yes—
402C22⋊D11—216no—
403C22⋊D11—48no—
404C2×Dic11—28no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—24no—
408C2×Dic11—24no—
409C2×Dic11—24no—
410C2×Dic11—28no—
411C2×Dic11—24no—
412C2×Dic11—48no—
413C2×Dic11—416no—
414C2×Dic11C2514yes—
415C2×Dic11C2512yes—
416C2×Dic11C2514yes—
417C2×Dic11C2514yes—
418C2×Dic11C2514yes—
419C2×Dic11C2518yes—
420C2×Dic11C2512yes—
421C4×D11—216no—
422C4×D11—28no—
423C4×D11—28no—
424C4×D11—28no—
425C4×D11—28no—
426C4×D11—48no—
427Dic22—416no—
428C22×#41C2×D1111yescharacteristic
429C23×Q8C2×D1111yescharacteristic
430C24×C4—111no—
431#556—1132no—
432#554—1132no—
433#552—1164no—
434#552—1132no—
435#552—1132no—
436#551—1164no—
437#544—1116no—
438#542—1132no—
439#541—1132no—
440#536C2×D11116yescomplemented
441#533—1132no—
442C2×C4⋊Q8—112no—
443C2×C4⋊Q8—112no—
444C2×C4⋊Q8C2×D1112yescomplemented
445#529—1132no—
446C2×#126—114no—
447C2×#126—114no—
448C2×#126—114no—
449C2×#126—114no—
450C2×#125—114no—
451C2×#125—114no—
452C2×#125—114no—
453C2×#125—112no—
454C2×#125—112no—
455C2×#124—114no—
456C2×#124C2×D1112yescomplemented
457#525—1116no—
458C2×#123—112no—
459C2×#123—114no—
460C2×#123—114no—
461C2×#123C2×D1114yes—
462C2×C22⋊Q8—112no—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—112no—
465C2×C22⋊Q8—112no—
466C2×C22⋊Q8—1116no—
467C2×C22⋊Q8—111no—
468C2×C22⋊Q8—111no—
469C2×C22⋊Q8—114no—
470C2×C22⋊Q8—114no—
471C2×C22⋊Q8—114no—
472C2×C22⋊Q8C2×D1112yescomplemented
473C2×C22⋊Q8C2×D1112yescomplemented
474C2×#121—111no—
475C2×#121—111no—
476C2×#120—112no—
477#520—1116no—
478#519—1116no—
479C2×C4×Q8—112no—
480C2×C4×Q8—112no—
481C2×C4×Q8—112no—
482C2×C4×Q8—112no—
483C2×C4×Q8—112no—
484C2×C4×Q8—114no—
485C2×C4×D4—114no—
486C2×C4×D4—112no—
487C2×C4×D4—112no—
488C2×C4×D4—112no—
489C2×C4×D4—114no—
490C2×#117—111no—
491C2×#117—111no—
492C2×#117—114no—
493C2×#117—112no—
494C2×#117—1116no—
495C2×#117—111no—
496C2×#117—111no—
497C2×#117—114no—
498C2×#117—112no—
499C2×#117—114no—
500C2×#117—112no—
501C2×#117C2×D1111yescharacteristic
502C22×C4⋊C4—112no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4—112no—
505C22×C4⋊C4—111no—
506C22×C4⋊C4—111no—
507C22×C22⋊C4—112no—
508C22×C22⋊C4—112no—
509C22×C42—112no—
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—28no—
513C22×C11—24no—
514C22×C11—24no—
515C22×C11—24no—
516C22×C11—48no—
517C22×C11C22×#4114yes—
518C22×C11C22×#4112yes—
519C22×C11C2×2−1+412yes—
520C22×C11#58512yes—
521C22×C11C2611yescharacteristic
522C2×D11—22no—
523C2×D11—22no—
524C2×D11—28no—
525C2×D11—22no—
526C2×D11—22no—
527C2×D11—22no—
528C2×D11—416no—
529C2×D11—44no—
530C2×D11C2×2−1+414yes—
531C4×C11—24no—
532C4×C11—28no—
533C4×C11—24no—
534C4×C11—24no—
535C4×C11C22×#4114yes—
536C4×C11C22×#4114yes—
537Dic11—22no—
538Dic11—22no—
539Dic11—24no—
540Dic11—24no—
541Dic11—24no—
542Dic11—28no—
543Dic11—24no—
544C25—111no—
545C2×#41—28no—
546C2×#41C22×D1118yes—
547C22×Q8—28no—
548C22×Q8—114no—
549C22×Q8C22×D1112yes—
550C22×Q8C22×D1112yes—
551C22×Q8C22×D1111yescharacteristic
552C22×Q8C22×D1118yes—
553C22×D4—112no—
554C22×D4—112no—
555C22×D4C22×D1112yes—
556C22×D4C22×D1111yescharacteristic
557C23×C4—111no—
558C23×C4—112no—
559C23×C4—114no—
560C23×C4—112no—
561C23×C4—111no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—118no—
565C23×C4—111no—
566C23×C4—112no—
567C23×C4—228no—
568C23×C4C22×D1112yes—
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C4⋊Q8—1116no—
572C4⋊Q8—1116no—
573C4⋊Q8C22×D11116yescomplemented
574#126—1132no—
575#126—1132no—
576#126—1132no—
577#126—1132no—
578#125—1132no—
579#125—1132no—
580#125—1132no—
581#125—1116no—
582#125—1116no—
583#124—1132no—
584#124C22×D11116yescomplemented
585#123—1116no—
586#123—1132no—
587#123—1132no—
588#123C22×D11132yes—
589C22⋊Q8—1116no—
590C22⋊Q8—1116no—
591C22⋊Q8—1116no—
592C22⋊Q8—1116no—
593C22⋊Q8—118no—
594C22⋊Q8—118no—
595C22⋊Q8—1132no—
596C22⋊Q8—1132no—
597C22⋊Q8—1132no—
598C22⋊Q8C22×D11116yescomplemented
599C22⋊Q8C22×D11116yescomplemented
600#121—118no—
601#121—118no—
602#120—1116no—
603C4×Q8—1116no—
604C4×Q8—1116no—
605C4×Q8—1116no—
606C4×Q8—1116no—
607C4×Q8—1116no—
608C4×Q8—1132no—
609C4×D4—1116no—
610C4×D4—1132no—
611C4×D4—1116no—
612C4×D4—1116no—
613C4×D4—1132no—
614#117—118no—
615#117—118no—
616#117—1132no—
617#117—1116no—
618#117—118no—
619#117—118no—
620#117—1132no—
621#117—1116no—
622#117—1132no—
623#117—1116no—
624#117C22×D1118yes—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—112no—
627C2×C4⋊C4—111no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—114no—
633C2×C4⋊C4—118no—
634C2×C4⋊C4—1116no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—1116no—
637C2×C4⋊C4—111no—
638C2×C4⋊C4—111no—
639C2×C4⋊C4—114no—
640C2×C4⋊C4—114no—
641C2×C4⋊C4—114no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—112no—
644C2×C4⋊C4—112no—
645C2×C4⋊C4—114no—
646C2×C4⋊C4—118no—
647C2×C4⋊C4—118no—
648C2×C4⋊C4C22×D1111yescharacteristic
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C4⋊C4C22×D1114yes—
651C2×C4⋊C4C22×D1114yes—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—112no—
657C2×C22⋊C4—112no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—114no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—1116no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—1116no—
665C2×C22⋊C4C22×D1112yes—
666C2×C22⋊C4C22×D1114yes—
667C2×C22⋊C4C22×D1114yes—
668C2×C42—112no—
669C2×C42—112no—
670C2×C42—114no—
671C2×C42—114no—
672C2×C42—114no—
673C2×C42—112no—
674C2×C42—112no—
675C2×C42—1116no—
676C2×C42C22×D1112yes—
677C2×C11—24no—
678C2×C11—44no—
679C2×C11#349514yescomplemented
680C2×C11C23×#4111yescharacteristic
681C2×C11C22×2−1+411yescharacteristic
682C2×C11C2×#58511yescharacteristic
683D11—24no—
684D11—42no—
685C24—111no—
686C24—111no—
687C24—114no—
688C24—224no—
689C24—224no—
690C24—442no—
691C24C23×D1112yes—
692C24C23×D1111yescharacteristic
693#41—232no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—232no—
697C2×Q8—24no—
698C2×Q8—1116no—
699C2×Q8—448no—
700C2×Q8C23×D1118yes—
701C2×Q8C23×D1118yes—
702C2×Q8C23×D1114yes—
703C2×D4—28no—
704C2×D4—24no—
705C2×D4—118no—
706C2×D4—118no—
707C2×D4—228no—
708C2×D4—444no—
709C2×D4C23×D1118yes—
710C2×D4C23×D1114yes—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—114no—
714C22×C4—112no—
715C22×C4—111no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—114no—
720C22×C4—111no—
721C22×C4—118no—
722C22×C4—1116no—
723C22×C4—114no—
724C22×C4—118no—
725C22×C4—114no—
726C22×C4—114no—
727C22×C4—114no—
728C22×C4—118no—
729C22×C4—228no—
730C22×C4—224no—
731C22×C4—224no—
732C22×C4—224no—
733C22×C4—224no—
734C22×C4—224no—
735C22×C4—2232no—
736C22×C4—444no—
737C22×C4—448no—
738C22×C4—444no—
739C22×C4#434118yes—
740C22×C4C23×D1118yes—
741C22×C4C23×D1118yes—
742C22×C4C23×D1114yes—
743C22×C4C23×D1112yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1112yes—
746C22×C4C23×D1114yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C4⋊C4—114no—
750C4⋊C4—118no—
751C4⋊C4—114no—
752C4⋊C4—118no—
753C4⋊C4—118no—
754C4⋊C4—1116no—
755C4⋊C4—118no—
756C4⋊C4—1116no—
757C4⋊C4—1116no—
758C4⋊C4—114no—
759C4⋊C4—114no—
760C4⋊C4—1116no—
761C4⋊C4—1116no—
762C4⋊C4—1116no—
763C4⋊C4—1116no—
764C4⋊C4—118no—
765C4⋊C4—118no—
766C4⋊C4—1116no—
767C4⋊C4C23×D1114yes—
768C4⋊C4C23×D1114yes—
769C4⋊C4C23×D11116yes—
770C4⋊C4C23×D11116yes—
771C22⋊C4—118no—
772C22⋊C4—118no—
773C22⋊C4—118no—
774C22⋊C4—1116no—
775C22⋊C4—118no—
776C22⋊C4—118no—
777C22⋊C4—118no—
778C22⋊C4—1116no—
779C22⋊C4—1116no—
780C22⋊C4—118no—
781C22⋊C4—118no—
782C22⋊C4C23×D1118yes—
783C22⋊C4C23×D11116yes—
784C22⋊C4C23×D11116yes—
785C42—118no—
786C42—118no—
787C42—118no—
788C42—1116no—
789C42—1116no—
790C42—1116no—
791C42—118no—
792C42C23×D1118yes—
793C11C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—114no—
800C23—112no—
801C23—112no—
802C23—228no—
803C23—222no—
804C23—222no—
805C23—228no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—444no—
810C23—4416no—
811C23C2×#434114yes—
812C23C24×D1114yes—
813C23C24×D1112yes—
814C23C24×D1111yescharacteristic
815Q8—216no—
816Q8—216no—
817Q8—28no—
818Q8—4416no—
819D4—216no—
820D4—28no—
821D4—2216no—
822D4—448no—
823C2×C4—24no—
824C2×C4—216no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—216no—
829C2×C4—114no—
830C2×C4—112no—
831C2×C4—114no—
832C2×C4—114no—
833C2×C4—114no—
834C2×C4—118no—
835C2×C4—112no—
836C2×C4—2216no—
837C2×C4—228no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—224no—
841C2×C4—224no—
842C2×C4—224no—
843C2×C4—228no—
844C2×C4—224no—
845C2×C4—228no—
846C2×C4—228no—
847C2×C4—228no—
848C2×C4—228no—
849C2×C4—448no—
850C2×C4—4416no—
851C2×C4—448no—
852C2×C4C2×#434114yes—
853C2×C4C2×#434114yes—
854C2×C4C2×#4341116yes—
855C2×C4C24×D1118yes—
856C2×C4C24×D1114yes—
857C2×C4C24×D1114yes—
858C2×C4C24×D1114yes—
859C2×C4C24×D1112yes—
860C2×C4C24×D1112yes—
861C22—22no—
862C22—22no—
863C22—28no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—114no—
869C22—222no—
870C22—222no—
871C22—228no—
872C22—222no—
873C22—222no—
874C22—222no—
875C22—4416no—
876C22—444no—
877C22C22×#434114yes—
878C22C22×#434112yes—
879C22D11×2−1+412yes—
880C22#1062345712yes—
881C22C25×D1111yescharacteristic
882C4—24no—
883C4—28no—
884C4—24no—
885C4—24no—
886C4—222no—
887C4—222no—
888C4—224no—
889C4—224no—
890C4—224no—
891C4—228no—
892C4—224no—
893C4C22×#434114yes—
894C4C22×#434114yes—
895C2—24no—
896C2—44no—
897C2—224no—
898C2—442no—
899C2#1308236514yesdirect product factor
900C2C23×#434111yescharacteristic
901C2C2×D11×2−1+411yescharacteristic
902C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#536C2
socleC23×C11C25
prime radicalC2×#10623359C2
hypercenterC2×#536D11
hypocenterC11C2×#3495
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #13082365C2direct (N × H)
2. C2×#10623172C2semidirect
3. C2×#10623166C2semidirect
4. C2×#10623173C2semidirect
5. C2×#10623181C2semidirect
6. C2×#10623170C2semidirect
7. C2×#10623189C2semidirect
8. C2×#10623050C2semidirect
9. C2×#10623213C2semidirect
10. C2×#10623262C2semidirect
11. C2×#10623259C2semidirect
12. C2×#10623211C2semidirect
14. C22×#66999C2semidirect
15. C2×#10623358C2semidirect
16. C2×#10623343C2semidirect
17. C2×D11×#117C2semidirect
18. C2×C11×#536C2semidirect
22. C11×#536C22semidirect
23. C2×C11×C4⋊Q8C22semidirect
24. C2×C11×#124C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
30. #10623358C22semidirect
37. C2×#66999C22semidirect
38. #10623343C22semidirect
39. C2×Q8×Dic11C22semidirect
40. C2×Q8×Dic11C22semidirect
41. C2×Q8×Dic11C22semidirect
42. C2×Q8×Dic11C22semidirect
43. C2×Q8×Dic11C22semidirect
49. C2×D4×Dic11C22semidirect
56. C2×#66979C22semidirect
58. C22×C4⋊Dic11C22semidirect
60. #10623262C22semidirect
61. #10623259C22semidirect
62. #10623213C22semidirect
63. #10623211C22semidirect
64. #10623189C22semidirect
65. #10623181C22semidirect
66. #10623173C22semidirect
67. #10623172C22semidirect
68. #10623170C22semidirect
69. #10623166C22semidirect
70. D11×#117C22semidirect
71. #10623050C22semidirect
80. C2×#66943C22semidirect
81. C2×#66943C22semidirect
82. C2×#66942C22semidirect
83. C2×#66942C22semidirect
84. C2×#66941C22semidirect
85. C2×#66940C22semidirect
91. C2×#66932C22semidirect
92. C2×#66932C22semidirect
94. C2×#66931C22semidirect
96. C2×#66930C22semidirect
99. C2×#66923C22semidirect
100. C2×#66922C22semidirect
128. C11×C4⋊Q8C23semidirect
129. C11×#124C23semidirect
131. C11×C22⋊Q8C23semidirect
132. C11×C22⋊Q8C23semidirect
153. Q8×Dic11C23semidirect
154. Q8×Dic11C23semidirect
155. Q8×Dic11C23semidirect
156. Q8×Dic11C23semidirect
157. Q8×Dic11C23semidirect
163. D4×Dic11C23semidirect
176. #66979C23semidirect
188. C2×C4⋊Dic11C23semidirect
213. #66943C23semidirect
214. #66943C23semidirect
215. #66942C23semidirect
216. #66942C23semidirect
217. #66941C23semidirect
218. #66940C23semidirect
224. #66932C23semidirect
225. #66932C23semidirect
227. #66931C23semidirect
229. #66930C23semidirect
232. #66923C23semidirect
233. #66922C23semidirect
353. C2×#536D11semidirect
440. #536C2×D11semidirect
444. C2×C4⋊Q8C2×D11semidirect
456. C2×#124C2×D11semidirect
472. C2×C22⋊Q8C2×D11semidirect
473. C2×C22⋊Q8C2×D11semidirect
573. C4⋊Q8C22×D11semidirect
584. #124C22×D11semidirect
598. C22⋊Q8C22×D11semidirect
599. C22⋊Q8C22×D11semidirect
679. C2×C11#3495semidirect
793. C11C2×#3495semidirect
899. C2#13082365direct (N × H)

Maximal subgroups

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

subgroupindex
#130823652
C2×#106231722
C2×#106231662
C2×#106231732
C2×#106231812
C2×#106231702
C2×#106231892
C2×#106230502
C2×#106232132
C2×#106232622
C2×#106232592
C2×#106232112
C2×#106233592
C22×#669992
C2×#106233582
C2×#106233432
C2×D11×#1172
C2×C11×#5362
C2×#349511