Finite Group Databasebeta

← C2×#13080969 #15632192

Subgroups — C2×#13080969 #15632192

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623042C211yesmaximal, characteristic, complemented
2C2×#10623038C211yesmaximal, characteristic
3#13080969C2116yesmaximal, direct product factor
4C2×#10622468C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622581C211yesmaximal, characteristic, complemented
7C2×#10622475C211yesmaximal, characteristic, complemented
8C2×#10622584C211yesmaximal, characteristic, complemented
9C2×#10622467C211yesmaximal, characteristic, complemented
10C2×#10622483C211yesmaximal, characteristic, complemented
11C2×#10622477C211yesmaximal, characteristic, complemented
12C2×#10622727C211yesmaximal, characteristic, complemented
13C2×#10622465C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
15C2×D11×#106C211yesmaximal, characteristic, complemented
16C22×C11×#106C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C23×C8×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66982—21no—
23C2×C4×C22⋊D11—21no—
24C2×C4×C22⋊D11C2211yescharacteristic
25C2×#66977—21no—
26C2×#66977C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623042—24no—
30#10623042C2218yescomplemented
31C2×#66950C2211yescharacteristic
32C2×#66949—21no—
33C2×#66949—21no—
34#10623038—24no—
35#10623038C2218yes—
36C2×#66948C2211yescharacteristic
37C2×#66947—21no—
38C2×#66946C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66942—21no—
42C2×#66941C2211yescharacteristic
43C2×#66941C2211yescharacteristic
44C2×#66940C2211yescharacteristic
45C2×C11×#106C2211yescharacteristic
46C2×C11×#106C2211yescharacteristic
47C2×C11×#106C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#106C2218yescomplemented
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51#10622727C2218yescomplemented
52C2×#66885C2211yescharacteristic
53C8×C22⋊D11C2218yescomplemented
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66881C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×C8×Dic11C2211yescharacteristic
59#10622584C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62#10622581C2218yescomplemented
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69#10622483C2218yescomplemented
70#10622477C2218yescomplemented
71#10622476C2218yescomplemented
72#10622475C2218yescomplemented
73D11×#106C2218yescomplemented
74#10622468C2218yescomplemented
75#10622467C2218yescomplemented
76#10622465C2218yescomplemented
77C23×C4×C11—21no—
78C23×C4×C11—21no—
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11D411yescharacteristic
82C2×#4339—28no—
83C2×#4339—48no—
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11C2311yescharacteristic
90C22×Dic22—21no—
91C22×Dic22—21no—
92C22×Dic22C2311yescharacteristic
93C22×C8×C11—24no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2314yes—
96C22×C8×C11C2311yescharacteristic
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—22no—
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11D411yescharacteristic
109#66983—22no—
110#66983C2314yes—
111#66982—28no—
112C4×C22⋊D11—28no—
113C4×C22⋊D11D414yes—
114C4×C22⋊D11C2314yes—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123#66977—22no—
124#66977—28no—
125#66977C2314yes—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4D411yescharacteristic
133C2×C4×Dic11—21no—
134C2×C4×Dic11C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C22×C11⋊C8C2311yescharacteristic
137C2×#4314—24no—
138C2×#4314C2314yes—
139C2×C8×D11—24no—
140C2×C8×D11C2314yes—
141#66950—22no—
142#66950C2314yes—
143#66949—28no—
144#66949—28no—
145#66948—22no—
146#66948C2314yes—
147#66947—28no—
148#66946—22no—
149#66946C2314yes—
150C4⋊C4×D11—22no—
151C4⋊C4×D11—22no—
152C4⋊C4×D11C2314yes—
153C4⋊C4×D11C2314yes—
154#66942—28no—
155#66941—22no—
156#66941—22no—
157#66941C2314yes—
158#66941C2314yes—
159#66940—22no—
160#66940C2314yes—
161C11×#106C2314yes—
162C11×#106C2314yes—
163C11×#106C2314yes—
164C11×#106C2314yes—
165C22⋊(C11⋊C8)C2314yes—
166#66885C2314yes—
167(C2×D11)⋊C8C2314yes—
168#66881C2314yes—
169#66880C2314yes—
170Dic11⋊C8C2314yes—
171C8×Dic11C2314yes—
172#66874C2314yes—
173#66874C2314yes—
174#66873C2314yes—
175#66873C2314yes—
176#66872C2314yes—
177#66872C2314yes—
178#66872C2314yes—
179#66872C2314yes—
180C2×#3335—111nomaximal, Sylow
181C24×C11C2×D411yescharacteristic
182C23×D11—21no—
183C23×D11C2×D411yescharacteristic
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—24no—
191C22×C4×C11—24no—
192C22×C4×C11—44no—
193C22×C4×C11—82no—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—44no—
200C2×C22⋊D11SD1618yescomplemented
201C2×C22⋊D11C2×D414yes—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208#4339—432no—
209C2×D44—24no—
210C2×D44—21no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44—44no—
214C2×D44C2412yes—
215C2×C4×D11—24no—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11—82no—
223C2×C4×D11C2×D412yes—
224C2×C4×D11C2412yes—
225C2×Dic22—24no—
226C2×Dic22—24no—
227C2×Dic22—21no—
228C2×Dic22—22no—
229C2×Dic22—22no—
230C2×Dic22—44no—
231C2×Dic22—82no—
232C2×Dic22C2412yes—
233C2×C8×C11—28no—
234C2×C8×C11—22no—
235C2×C8×C11#4114yescomplemented
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C4⋊C4C2412yes—
247C11×C4⋊C4C2412yes—
248C22⋊Dic11—24no—
249C22⋊Dic11C2×D414yes—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4C2×D414yes—
255C4⋊Dic11—24no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4C2×D414yes—
267C4×Dic11—24no—
268C4×Dic11C2×D412yes—
269C4×Dic11C2412yes—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274#4314—28no—
275C8×D11—28no—
276C2×#554—111no—
277C2×#547—111no—
278#3335—1116no—
279C2×#498—111no—
280C2×#481—111no—
281C2×#481—111no—
282C2×#483—111no—
283C2×#483—111no—
284C2×#475—111no—
285C2×#476—111no—
286C2×#465—111no—
287C2×#465—111no—
288C2×C4×SD16—111no—
289C2×C8×D4—111no—
290C22×#106—111no—
291C22×#106D1111yescharacteristic, complemented
292C23×C11—22no—
293C23×C11—22no—
294C23×C11C2×SD1614yes—
295C23×C11C22×D412yes—
296C23×C11C22×D411yescharacteristic
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11C2×SD1614yes—
304C22×D11C22×D412yes—
305C2×C4×C11—22no—
306C2×C4×C11—24no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—48no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—84no—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C2×#4112yes—
322C2×C4×C112−1+412yes—
323C2×C4×C11C2511yescharacteristic
324C22⋊D11—48no—
325C22⋊D11C2×SD16116yescomplemented
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11C2×SD1614yes—
335C2×Dic11C22×D412yes—
336C2×Dic11C22×D412yes—
337C2×Dic11C22×D412yes—
338D44—22no—
339D44—22no—
340D44—48no—
341D44—42no—
342C4×D11—24no—
343C4×D11—22no—
344C4×D11—22no—
345C4×D11—48no—
346C4×D11—48no—
347C4×D11—84no—
348Dic22—22no—
349Dic22—22no—
350Dic22—42no—
351Dic22—48no—
352Dic22—84no—
353C8×C11—22no—
354C8×C11C2×#4114yescomplemented
355C11⋊C8—22no—
356C11⋊C8—22no—
357C22×#41—221no—
358C22×SD16—111no—
359C23×C8—111no—
360C23×C8C2×D1111yescharacteristic
361#554—118no—
362#554—224no—
363#547—118no—
364#547—224no—
365C2×C4⋊Q8—111no—
366C2×C4⋊Q8—111no—
367C2×#125—221no—
368C2×#123—221no—
369C2×#123—221no—
370C2×C22⋊Q8—111no—
371C2×C22⋊Q8—111no—
372C2×C22⋊Q8—221no—
373C2×C22⋊Q8—221no—
374C2×C22⋊Q8—221no—
375C2×#121—111no—
376C2×#121—111no—
377C2×C4×Q8—111no—
378C2×C4×D4—111no—
379C2×C4×D4—111no—
380C2×C4×D4—221no—
381C22×C4⋊C4—111no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4C2×D1111yescharacteristic
384C22×C4⋊C4C2×D1111yescharacteristic
385#498—118no—
386#483—118no—
387#483—118no—
388#481—118no—
389#481—118no—
390#476—118no—
391#475—118no—
392#465—118no—
393#465—118no—
394C4×SD16—118no—
395C8×D4—118no—
396C2×#106—111no—
397C2×#106—111no—
398C2×#106—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×#106—118no—
402C2×#106C2×D1111yescharacteristic
403C2×#106C2×D1111yescharacteristic
404C2×#106C2×D1111yescharacteristic
405C2×#106C2×D1111yescharacteristic
406C2×#106C2×D1118yescomplemented
407C2×C4⋊C8—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#102—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×C22⋊C8—111no—
415C2×C22⋊C8—111no—
416C2×C4×C8—111no—
417C22×C11—28no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11#54712yes—
421C22×C11C22×SD1614yes—
422C22×C11C22×SD1612yes—
423C22×C11#57712yes—
424C22×C11C23×D411yescharacteristic
425C2×D11—28no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—84no—
432C2×D11C22×SD1614yes—
433C4×C11—22no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11#54712yes—
439C4×C11C22×#4111yescharacteristic
440C4×C11C2×2−1+411yescharacteristic
441Dic11—22no—
442Dic11—22no—
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446Dic11C22×SD1614yes—
447C2×#41—228no—
448C2×#41—448no—
449C22×Q8—111no—
450C22×Q8—221no—
451C22×Q8—221no—
452C22×D4—111no—
453C22×D4—111no—
454C22×D4—221no—
455C22×D4—221no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—111no—
459C23×C4—221no—
460C23×C4—221no—
461C23×C4—221no—
462C23×C4C22×D1111yescharacteristic
463C2×SD16—114no—
464C2×SD16—224no—
465C22×C8—24no—
466C22×C8—111no—
467C22×C8—111no—
468C22×C8—114no—
469C22×C8—224no—
470C22×C8C22×D1111yescharacteristic
471C22×C8C22×D1114yes—
472C22×C8C22×D1111yescharacteristic
473C4⋊Q8—114no—
474C4⋊Q8—114no—
475C4⋊Q8—222no—
476C4⋊Q8—222no—
477#125—228no—
478#123—228no—
479#123—228no—
480C22⋊Q8—114no—
481C22⋊Q8—114no—
482C22⋊Q8—228no—
483C22⋊Q8—228no—
484C22⋊Q8—228no—
485C22⋊Q8—222no—
486C22⋊Q8—222no—
487#121—114no—
488#121—114no—
489#121—222no—
490#121—222no—
491C4×Q8—114no—
492C4×Q8—222no—
493C4×D4—114no—
494C4×D4—114no—
495C4×D4—114no—
496C4×D4—222no—
497C4×D4—228no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C4⋊C4C22×D1111yescharacteristic
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C4⋊C4C22×D1114yes—
521C2×C4⋊C4C22×D1114yes—
522C2×C22⋊C4—111no—
523C2×C22⋊C4—111no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C42—111no—
530C2×C42—221no—
531#106—114no—
532#106—114no—
533#106—114no—
534#106—114no—
535#106—114no—
536#106C22×D1114yes—
537#106C22×D1114yes—
538#106C22×D1114yes—
539#106C22×D1114yes—
540C4⋊C8—114no—
541#103—114no—
542#103—114no—
543#103—114no—
544#102—114no—
545#102—114no—
546#102—114no—
547C22⋊C8—114no—
548C22⋊C8—114no—
549C4×C8—114no—
550C2×C11—24no—
551C2×C11#333514yescomplemented
552C2×C11C2×#54711yescharacteristic
553C2×C11C23×SD1611yescharacteristic
554C2×C11C2×#57711yescharacteristic
555D11—24no—
556D11—82no—
557C24—111no—
558C24—221no—
559C24D4×D1111yescharacteristic
560#41—4432no—
561C2×Q8—112no—
562C2×Q8—224no—
563C2×Q8—224no—
564C2×Q8—221no—
565C2×Q8—222no—
566C2×Q8—222no—
567C2×Q8—444no—
568C2×Q8—882no—
569C2×D4—118no—
570C2×D4—114no—
571C2×D4—112no—
572C2×D4—224no—
573C2×D4—224no—
574C2×D4—222no—
575C2×D4—221no—
576C2×D4—222no—
577C2×D4—444no—
578C2×D4—444no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—44no—
588C22×C4—82no—
589C22×C4—111no—
590C22×C4—111no—
591C22×C4—111no—
592C22×C4—112no—
593C22×C4—112no—
594C22×C4—224no—
595C22×C4—224no—
596C22×C4—224no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—444no—
603C22×C4—444no—
604C22×C4—882no—
605C22×C4D4×D1112yes—
606C22×C4D4×D1111yescharacteristic
607C22×C4C23×D1112yes—
608C22×C4C23×D1111yescharacteristic
609SD16—228no—
610C2×C8—22no—
611C2×C8—28no—
612C2×C8—112no—
613C2×C8—112no—
614C2×C8—222no—
615C2×C8—222no—
616C2×C8—228no—
617C2×C8#433914yescomplemented
618C2×C8C23×D1112yes—
619C2×C8C23×D1112yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—114no—
627C4⋊C4—112no—
628C4⋊C4—112no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—224no—
638C4⋊C4C23×D1112yes—
639C4⋊C4C23×D1112yes—
640C4⋊C4C23×D1112yes—
641C4⋊C4C23×D1112yes—
642C22⋊C4—114no—
643C22⋊C4—114no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—112no—
650C42—112no—
651C42—224no—
652C11C2×#333511yescharacteristic, complemented, Sylow
653C23—22no—
654C23—22no—
655C23—114no—
656C23—112no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23SD16×D1114yes—
664C23C2×D4×D1112yes—
665C23C2×D4×D1111yescharacteristic
666Q8—222no—
667Q8—222no—
668Q8—448no—
669Q8—442no—
670Q8—884no—
671D4—1116no—
672D4—222no—
673D4—222no—
674D4—448no—
675D4—448no—
676D4—442no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—114no—
692C2×C4—112no—
693C2×C4—112no—
694C2×C4—112no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—224no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—448no—
704C2×C4—448no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—884no—
709C2×C4C2×#433912yes—
710C2×C4C2×D4×D1112yes—
711C2×C4C2×D4×D1111yescharacteristic
712C2×C4#6704012yes—
713C2×C4C24×D1111yescharacteristic
714C8—22no—
715C8—222no—
716C8—222no—
717C8C2×#433914yescomplemented
718C22—28no—
719C22—22no—
720C22—22no—
721C22—114no—
722C22—228no—
723C22—222no—
724C22—222no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—884no—
729C22#1062303812yes—
730C22C2×SD16×D1114yes—
731C22C2×SD16×D1112yes—
732C22#1062329312yes—
733C22C22×D4×D1111yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—114no—
740C4—222no—
741C4—222no—
742C4—442no—
743C4—442no—
744C4—442no—
745C4#1062303812yes—
746C4C22×#433911yescharacteristic
747C4C2×#6704011yescharacteristic
748C2—24no—
749C2—224no—
750C2—882no—
751C2#1308096914yesdirect product factor
752C2C2×#1062303811yescharacteristic
753C2C22×SD16×D1111yescharacteristic
754C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#106C2
socleC23×C11C22×D4
prime radicalC2×#10623038C2
hypercenterC22×#106D11
hypocenterC11C2×#3335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#10623042C2semidirect
3. #13080969C2direct (N × H)
4. C2×#10622468C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622581C2semidirect
7. C2×#10622475C2semidirect
8. C2×#10622584C2semidirect
9. C2×#10622467C2semidirect
10. C2×#10622483C2semidirect
11. C2×#10622477C2semidirect
12. C2×#10622727C2semidirect
13. C2×#10622465C2semidirect
14. C2×C8×C22⋊D11C2semidirect
15. C2×D11×#106C2semidirect
16. C22×C11×#106C2semidirect
30. #10623042C22semidirect
49. C2×C11×#106C22semidirect
51. #10622727C22semidirect
53. C8×C22⋊D11C22semidirect
59. #10622584C22semidirect
62. #10622581C22semidirect
69. #10622483C22semidirect
70. #10622477C22semidirect
71. #10622476C22semidirect
72. #10622475C22semidirect
73. D11×#106C22semidirect
74. #10622468C22semidirect
75. #10622467C22semidirect
76. #10622465C22semidirect
200. C2×C22⋊D11SD16semidirect
235. C2×C8×C11#41semidirect
291. C22×#106D11semidirect
325. C22⋊D11C2×SD16semidirect
354. C8×C11C2×#41semidirect
406. C2×#106C2×D11semidirect
551. C2×C11#3335semidirect
617. C2×C8#4339semidirect
652. C11C2×#3335semidirect
717. C8C2×#4339semidirect
751. C2#13080969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230422
C2×#106230382
#130809692
C2×#106224682
C2×#106224762
C2×#106225812
C2×#106224752
C2×#106225842
C2×#106224672
C2×#106224832
C2×#106224772
C2×#106227272
C2×#106224652
C2×C8×C22⋊D112
C2×D11×#1062
C22×C11×#1062
C2×#333511