Finite Group Databasebeta

← C2×#13081085 #15632335

Subgroups — C2×#13081085 #15632335

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623226C211yesmaximal, characteristic, complemented
2C2×#10623257C211yesmaximal, characteristic, complemented
3#13081085C2116yesmaximal, direct product factor
4C2×#10622476C211yesmaximal, characteristic, complemented
5C2×#10622476C211yesmaximal, characteristic, complemented
6C2×#10622498C211yesmaximal, characteristic, complemented
7C2×#10622495C211yesmaximal, characteristic, complemented
8C2×#10622679C211yesmaximal, characteristic, complemented
9C2×#10622697C211yesmaximal, characteristic, complemented
10C2×#10622478C211yesmaximal, characteristic, complemented
11C2×#10622496C211yesmaximal, characteristic, complemented
12C2×#10622324C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622494C211yesmaximal, characteristic, complemented
15C2×D11×#106C211yesmaximal, characteristic, complemented
16C2×C11×#501C211yesmaximal, characteristic, complemented
17C22×#4343—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×#66999—21no—
21C22×D88C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic
24#10623257—24no—
25#10623257C2218yescomplemented
26#10623226—24no—
27#10623226C2218yescomplemented
28C2×#66951—21no—
29C2×#66948—21no—
30C2×#66948C2211yescharacteristic
31C2×#66948C2211yescharacteristic
32C2×#66948C2211yescharacteristic
33C2×#66948C2211yescharacteristic
34C2×#66947—21no—
35C2×#66947—21no—
36C2×#66947—21no—
37C2×#66946—21no—
38C2×#66945C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C11×#501C2218yescomplemented
46C2×C11×#107C2211yescharacteristic
47C2×C11×#107C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#106C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66885C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66881C2211yescharacteristic
56#10622697C2218yescomplemented
57#10622679C2218yescomplemented
58C2×#66873C2211yescharacteristic
59C2×#66873C2211yescharacteristic
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622498C2218yescomplemented
68#10622496C2218yescomplemented
69#10622495C2218yescomplemented
70#10622494C2218yescomplemented
71#10622478C2218yescomplemented
72#10622476C2218yescomplemented
73#10622476C2218yescomplemented
74D11×#106C2218yescomplemented
75#10622324C2218yescomplemented
76#10622319C2218yescomplemented
77C22×Q8×C11—21no—
78C2×#4343—28no—
79C2×#4343—48no—
80C22×D44—21no—
81C22×D44—21no—
82C22×D44—21no—
83C22×D44—21no—
84C22×D44D411yescharacteristic
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11—21no—
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C11×C4⋊Q8—22no—
97C11×C4⋊Q8C2314yes—
98C11×#125—22no—
99C11×#125C2314yes—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108#66999—28no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4D411yescharacteristic
117C2×(C2×D11)⋊C4D411yescharacteristic
118C2×C4⋊Dic11D411yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C2×D88—24no—
128C2×D88C2314yes—
129C2×#4313—24no—
130C2×#4313C2314yes—
131C2×C8×D11—24no—
132C2×C8×D11C2314yes—
133#66951—28no—
134#66948—28no—
135#66948—22no—
136#66948—22no—
137#66948—22no—
138#66948—22no—
139#66948C2314yes—
140#66948C2314yes—
141#66948C2314yes—
142#66948C2314yes—
143#66947—28no—
144#66947—28no—
145#66947—28no—
146#66946—28no—
147#66945—22no—
148#66945C2314yes—
149C4⋊C4×D11—22no—
150C4⋊C4×D11—22no—
151C4⋊C4×D11—22no—
152C4⋊C4×D11C2314yes—
153C4⋊C4×D11C2314yes—
154C4⋊C4×D11C2314yes—
155C4×D44—22no—
156C4×D44—22no—
157C4×D44D414yes—
158C4×D44C2314yes—
159C4×D44C2314yes—
160C4×D44C2314yes—
161C11×#107C2314yes—
162C11×#107C2314yes—
163C11×#106C2314yes—
164C11×#106C2314yes—
165C11×#97C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168(C2×D11)⋊C8C2314yes—
169(C2×D11)⋊C8C2314yes—
170#66881C2314yes—
171#66873C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66873C2314yes—
175#66872C2314yes—
176#66872C2314yes—
177#66872C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C2×#3345—111nomaximal, Sylow
181C23×D11—21no—
182C23×D11—21no—
183C23×D11C2×D411yescharacteristic
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—24no—
186C2×Q8×C11—44no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11C2×D411yescharacteristic
197C22×Dic11C2×D411yescharacteristic
198#4343—432no—
199C2×D44—24no—
200C2×D44—24no—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—24no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—44no—
211C2×D44—44no—
212C2×D44—44no—
213C2×D44—82no—
214C2×D44C2×D414yes—
215C2×D44C2412yes—
216C2×D44C2412yes—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—22no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—22no—
226C2×C4×D11—44no—
227C2×C4×D11—44no—
228C2×C4×D11—44no—
229C2×C4×D11—82no—
230C2×C4×D11—82no—
231C2×C4×D11C2×D412yes—
232C2×C4×D11C2×D412yes—
233C2×C4×D11C2412yes—
234C2×C4×D11C2412yes—
235C2×C8×C11—22no—
236C2×C8×C11#4114yescomplemented
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—24no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C4⋊C4C2412yes—
247C11×C4⋊C4C2412yes—
248C11×C4⋊C4C2412yes—
249C11×C4⋊C4C2412yes—
250C42×C11C2×D412yes—
251C42×C11C2412yes—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4C2×D414yes—
260(C2×D11)⋊C4C2×D414yes—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11C2×D414yes—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269C4×Dic11—24no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274D88—28no—
275#4313—28no—
276C8×D11—28no—
277C2×#553—111no—
278C2×#547—111no—
279#3345—1116no—
280C2×#501D1111yescharacteristic, complemented
281C2×#481—111no—
282C2×#481—111no—
283C2×#482—111no—
284C2×#480—111no—
285C2×#478—111no—
286C2×#476—111no—
287C2×#469—111no—
288C2×#466—111no—
289C2×#442—111no—
290C2×#435—111no—
291C2×#428—111no—
292C22×#106—111no—
293C23×C11C22×D411yescharacteristic
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11AGL(1,ℤ/8)14yes—
308C22×D11C22×D412yes—
309C22×D11C22×D412yes—
310Q8×C11—48no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4112yes—
325C2×C4×C112−1+412yes—
326C2×C4×C11C2511yescharacteristic
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11C22×D412yes—
334C2×Dic11C22×D412yes—
335D44—28no—
336D44—22no—
337D44—22no—
338D44—22no—
339D44—22no—
340D44—48no—
341D44—48no—
342D44—48no—
343D44—42no—
344D44—42no—
345D44—84no—
346C4×D11—24no—
347C4×D11—24no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—22no—
352C4×D11—48no—
353C4×D11—48no—
354C4×D11—48no—
355C4×D11—84no—
356C4×D11—84no—
357C8×C11—22no—
358C8×C11C2×#4114yescomplemented
359C11⋊C8—22no—
360C11⋊C8—22no—
361C22×#41—221no—
362C22×D8—111no—
363C22×M16—111no—
364C23×C8—111no—
365#553—118no—
366#553—224no—
367#547—118no—
368#547—224no—
369C2×C4⋊Q8C2×D1111yescharacteristic
370C2×#126—221no—
371C2×#125C2×D1111yescharacteristic
372C2×#123—221no—
373C2×#123—221no—
374C2×#123—221no—
375C2×C22⋊Q8—221no—
376C2×#121—111no—
377C2×#121—111no—
378C2×#121—111no—
379C2×#121—111no—
380C2×#121—221no—
381C2×C4×D4—111no—
382C2×C4×D4—111no—
383C2×C4×D4—111no—
384C2×C4×D4—221no—
385C2×#117—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389#501C2×D1118yescomplemented
390#482—118no—
391#481—118no—
392#481—118no—
393#480—118no—
394#478—118no—
395#476—118no—
396#469—118no—
397#466—118no—
398#442—118no—
399#435—118no—
400#428—118no—
401C2×#107—111no—
402C2×#107C2×D1111yescharacteristic
403C2×#107C2×D1111yescharacteristic
404C2×#106—111no—
405C2×#106—111no—
406C2×#106—111no—
407C2×#106—111no—
408C2×#106—118no—
409C2×#106C2×D1111yescharacteristic
410C2×#106C2×D1111yescharacteristic
411C2×C4⋊C8—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×C22⋊C8—111no—
419C2×C22⋊C8—111no—
420C2×#97C2×D1111yescharacteristic
421C22×C11#54712yes—
422C22×C11C2×AGL(1,ℤ/8)12yes—
423C22×C11#57712yes—
424C22×C11C23×D411yescharacteristic
425C2×D11—28no—
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—44no—
432C2×D11—42no—
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—84no—
439C2×D11—84no—
440C2×D11C2×AGL(1,ℤ/8)14yes—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11#54712yes—
448C4×C11C22×#4111yescharacteristic
449C4×C11C2×2−1+411yescharacteristic
450Dic11—22no—
451Dic11—22no—
452Dic11—42no—
453Dic11—42no—
454C2×#41—228no—
455C2×#41—448no—
456C22×Q8—21no—
457C22×D4—111no—
458C22×D4—111no—
459C22×D4—111no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4—221no—
463C22×D4—221no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4—221no—
470C23×C4—221no—
471C2×D8—114no—
472C2×D8—224no—
473C2×M16—114no—
474C2×M16—224no—
475C22×C8—111no—
476C22×C8—111no—
477C22×C8—114no—
478C22×C8—224no—
479C22×C8C22×D1111yescharacteristic
480C22×C8C22×D1111yescharacteristic
481C4⋊Q8—22no—
482C4⋊Q8C22×D1114yes—
483#126—228no—
484#125—22no—
485#125C22×D1114yes—
486#123—228no—
487#123—228no—
488#123—228no—
489C22⋊Q8—228no—
490#121—114no—
491#121—114no—
492#121—114no—
493#121—114no—
494#121—222no—
495#121—222no—
496#121—222no—
497#121—222no—
498#121—228no—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—114no—
503C4×D4—228no—
504C4×D4—222no—
505C4×D4—222no—
506#117—114no—
507#117—222no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—222no—
518C2×C4⋊C4—222no—
519C2×C4⋊C4—222no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C4⋊C4C22×D1111yescharacteristic
527C2×C22⋊C4—111no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C42—221no—
537C2×C42C22×D1111yescharacteristic
538#107—114no—
539#107C22×D1114yes—
540#107C22×D1114yes—
541#106—114no—
542#106—114no—
543#106—114no—
544#106—114no—
545#106C22×D1114yes—
546#106C22×D1114yes—
547C4⋊C8—114no—
548#102—114no—
549#102—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554C22⋊C8—114no—
555C22⋊C8—114no—
556#97C22×D1114yes—
557C2×C11#334514yescomplemented
558C2×C11C2×#54711yescharacteristic
559C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
560C2×C11C2×#57711yescharacteristic
561D11—24no—
562D11—42no—
563D11—82no—
564D11—82no—
565C24—111no—
566C24—111no—
567C24—221no—
568C24—221no—
569#41—4432no—
570C2×Q8—24no—
571C2×Q8—44no—
572C2×D4—114no—
573C2×D4—112no—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—224no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—444no—
587C2×D4—444no—
588C2×D4—444no—
589C2×D4—882no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—224no—
601C22×C4—224no—
602C22×C4—224no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—224no—
610C22×C4—224no—
611C22×C4—444no—
612C22×C4—444no—
613C22×C4—444no—
614C22×C4—882no—
615C22×C4—882no—
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619D8—228no—
620M16—228no—
621C2×C8—22no—
622C2×C8—112no—
623C2×C8—112no—
624C2×C8—222no—
625C2×C8—222no—
626C2×C8—228no—
627C2×C8#434314yescomplemented
628C2×C8C23×D1112yes—
629C2×C8C23×D1112yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—114no—
638C4⋊C4—112no—
639C4⋊C4—112no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4C23×D1112yes—
646C4⋊C4C23×D1112yes—
647C4⋊C4C23×D1112yes—
648C4⋊C4C23×D1112yes—
649C22⋊C4—114no—
650C22⋊C4—114no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C42—224no—
659C42D4×D1112yes—
660C42C23×D1112yes—
661C11C2×#334511yescharacteristic, complemented, Sylow
662C23—114no—
663C23—112no—
664C23—112no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—222no—
671C23—222no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23—442no—
677C23—442no—
678C23C2×D4×D1111yescharacteristic
679Q8—48no—
680D4—228no—
681D4—222no—
682D4—222no—
683D4—222no—
684D4—222no—
685D4—448no—
686D4—448no—
687D4—448no—
688D4—442no—
689D4—442no—
690D4—884no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—112no—
702C2×C4—112no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—448no—
714C2×C4—448no—
715C2×C4—448no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—884no—
719C2×C4—884no—
720C2×C4C2×D4×D1112yes—
721C2×C4C2×D4×D1112yes—
722C2×C4C2×D4×D1111yescharacteristic
723C2×C4C2×#434312yes—
724C2×C4#6704012yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—222no—
728C8—222no—
729C8C2×#434314yescomplemented
730C22—114no—
731C22—222no—
732C22—222no—
733C22—228no—
734C22—222no—
735C22—222no—
736C22—222no—
737C22—444no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22—884no—
745C22—884no—
746C22#1062325712yes—
747C22D11×AGL(1,ℤ/8)12yes—
748C22#1062330912yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—222no—
757C4—222no—
758C4—442no—
759C4—442no—
760C4#1062325712yes—
761C4C22×#434311yescharacteristic
762C4C2×#6704011yescharacteristic
763C2—224no—
764C2—442no—
765C2—882no—
766C2—882no—
767C2#1308108514yesdirect product factor
768C2C2×#1062325711yescharacteristic
769C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
770C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#501C2
socleC23×C11C22×D4
hypercenterC2×#501D11
hypocenterC11C2×#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#10623226C2semidirect
2. C2×#10623257C2semidirect
3. #13081085C2direct (N × H)
4. C2×#10622476C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622495C2semidirect
8. C2×#10622679C2semidirect
9. C2×#10622697C2semidirect
10. C2×#10622478C2semidirect
11. C2×#10622496C2semidirect
12. C2×#10622324C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622494C2semidirect
15. C2×D11×#106C2semidirect
16. C2×C11×#501C2semidirect
25. #10623257C22semidirect
27. #10623226C22semidirect
45. C11×#501C22semidirect
56. #10622697C22semidirect
57. #10622679C22semidirect
67. #10622498C22semidirect
68. #10622496C22semidirect
69. #10622495C22semidirect
70. #10622494C22semidirect
71. #10622478C22semidirect
72. #10622476C22semidirect
73. #10622476C22semidirect
74. D11×#106C22semidirect
75. #10622324C22semidirect
76. #10622319C22semidirect
236. C2×C8×C11#41semidirect
280. C2×#501D11semidirect
358. C8×C11C2×#41semidirect
389. #501C2×D11semidirect
557. C2×C11#3345semidirect
627. C2×C8#4343semidirect
661. C11C2×#3345semidirect
729. C8C2×#4343semidirect
767. C2#13081085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232262
C2×#106232572
#130810852
C2×#106224762
C2×#106224982
C2×#106224952
C2×#106226792
C2×#106226972
C2×#106224782
C2×#106224962
C2×#106223242
C2×#106223192
C2×#106224942
C2×D11×#1062
C2×C11×#5012
C2×#334511