Finite Group Databasebeta

← C2×#13081088 #15632338

Subgroups — C2×#13081088 #15632338

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×#10623096C211yesmaximal, characteristic, complemented
2C2×#10623086C211yesmaximal, characteristic, complemented
3#13081088C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622348C211yesmaximal, characteristic, complemented
7C2×#10622350C211yesmaximal, characteristic, complemented
8C2×#10622349C211yesmaximal, characteristic, complemented
9C2×#10622460C211yesmaximal, characteristic, complemented
10C2×#10622455C211yesmaximal, characteristic, complemented
11C2×#10622748C211yesmaximal, characteristic, complemented
12C2×#10622728C211yesmaximal, characteristic, complemented
13C2×#10622324C211yesmaximal, characteristic, complemented
14C2×#10622734C211yesmaximal, characteristic, complemented
15C22×#66881C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66992—21no—
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66979C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×D88C2211yescharacteristic
31#10623096—24no—
32#10623096C2218yescomplemented
33#10623086—24no—
34#10623086C2218yescomplemented
35C2×#66951—21no—
36C2×#66950—21no—
37C2×#66939—21no—
38C2×#66939—21no—
39C2×#66936—21no—
40C2×(C22⋊D11)⋊C4—21no—
41C2×C4×D44C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×#66923C2211yescharacteristic
44C2×#66922C2211yescharacteristic
45C11×#435C2218yescomplemented
46C2×C11×C4⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50#10622748C2218yescomplemented
51#10622734C2218yescomplemented
52#10622728C2218yescomplemented
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66882C2211yescharacteristic
62C2×#66881C2211yescharacteristic
63C2×#66881C2211yescharacteristic
64C2×#66881C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×#66881C2211yescharacteristic
67C2×#66881C2211yescharacteristic
68C2×#66881C2218yescomplemented
69#10622460C2218yescomplemented
70#10622455C2218yescomplemented
71#10622350C2218yescomplemented
72#10622349C2218yescomplemented
73#10622348C2218yescomplemented
74#10622348C2218yescomplemented
75#10622324C2218yescomplemented
76#10622315C2218yescomplemented
77C22×D4×C11D411yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C2×#4341—28no—
88C2×#4341—48no—
89C22×D44C2311yescharacteristic
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×Dic22—21no—
94C2×C11×M16—24no—
95C2×C11×M16C2314yes—
96C22×C8×C11—24no—
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2314yes—
101C22×C8×C11C2311yescharacteristic
102C4×D4×C11D414yes—
103C4×D4×C11C2314yes—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C22⋊C4D411yescharacteristic
106C2×C11×C22⋊C4D411yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109#66992—28no—
110#66983—22no—
111#66983—22no—
112#66983—22no—
113#66983—22no—
114#66983C2314yes—
115#66983C2314yes—
116#66983C2314yes—
117#66983C2314yes—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124#66979—22no—
125#66979C2314yes—
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11—22no—
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2314yes—
140C2×C4⋊Dic11C2314yes—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—21no—
144C2×C4×Dic11—21no—
145C2×D88—24no—
146C2×D88C2314yes—
147#66951—28no—
148#66950—28no—
149#66939—28no—
150#66939—28no—
151#66936—28no—
152(C22⋊D11)⋊C4—28no—
153C4×D44—22no—
154C4×D44—22no—
155C4×D44C2314yes—
156C4×D44C2314yes—
157#66923—22no—
158#66923C2314yes—
159#66922—22no—
160#66922C2314yes—
161C11×C4⋊C8C2314yes—
162C11×C22⋊C8C2314yes—
163C11×C22⋊C8C2314yes—
164C11×#97C2314yes—
165#66885C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169#66885C2314yes—
170#66885C2314yes—
171#66882C2314yes—
172#66882C2314yes—
173#66882C2314yes—
174#66881C2314yes—
175#66881C2314yes—
176#66881C2314yes—
177#66881C2314yes—
178#66881C2314yes—
179#66881C2314yes—
180C2×#3345—111nomaximal, Sylow
181C24×C11C2×D411yescharacteristic
182C24×C11C2×D411yescharacteristic
183C23×D11—21no—
184C23×D11—21no—
185C2×D4×C11—24no—
186C2×D4×C11C2×D414yes—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11—44no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—82no—
208C22×Dic11—24no—
209C22×Dic11—24no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—24no—
217C22×Dic11—44no—
218C22×Dic11—44no—
219C22×Dic11—82no—
220#4341—432no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—22no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44C2412yes—
228C2×D44C2412yes—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—44no—
232C2×C4×D11—82no—
233C2×Dic22—24no—
234C2×Dic22—44no—
235C11×M16—28no—
236C2×C8×C11—28no—
237C2×C8×C11—22no—
238C2×C8×C11—22no—
239C2×C8×C11—22no—
240C2×C8×C11#4114yescomplemented
241C2×C8×C11C2412yes—
242C2×C8×C11C2412yes—
243C2×C8×C11C2412yes—
244C2×C8×C11C2412yes—
245C11×C4⋊C4C2×D414yes—
246C11×C22⋊C4C2×D414yes—
247C11×C22⋊C4C2×D414yes—
248C42×C11C2×D412yes—
249C42×C11C2412yes—
250C22⋊Dic11—24no—
251(C2×D11)⋊C4—24no—
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—
257C4⋊Dic11—21no—
258C4⋊Dic11—21no—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—24no—
265C4⋊Dic11—24no—
266C4⋊Dic11—24no—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269C4⋊Dic11C2412yes—
270C4⋊Dic11C2412yes—
271C4⋊Dic11C2412yes—
272C4⋊Dic11C2412yes—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275C4×Dic11—24no—
276D88—28no—
277C2×#553—111no—
278C2×#547—111no—
279#3345—1116no—
280C2×#501—111no—
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×#435D1111yescharacteristic, complemented
291C2×#428—111no—
292C22×#106—111no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11AGL(1,ℤ/8)14yes—
299C23×C11C22×D412yes—
300C23×C11C22×D412yes—
301C23×C11C22×D411yescharacteristic
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310D4×C11—28no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11C22×D412yes—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C2×#4112yes—
327C2×C4×C112−1+412yes—
328C2×C4×C11C2511yescharacteristic
329C22⋊D11—48no—
330C22⋊D11—48no—
331C22⋊D11—48no—
332C22⋊D11—84no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—48no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—48no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—84no—
348D44—22no—
349D44—22no—
350D44—22no—
351D44—22no—
352D44—42no—
353D44—42no—
354C4×D11—48no—
355C4×D11—84no—
356Dic22—48no—
357C8×C11—22no—
358C8×C11—22no—
359C8×C11—22no—
360C8×C11C2×#4114yescomplemented
361C22×#41—221no—
362C22×D8—111no—
363C22×M16C2×D1111yescharacteristic
364C23×C8C2×D1111yescharacteristic
365#553—118no—
366#553—224no—
367#547—118no—
368#547—224no—
369C2×C4⋊Q8—111no—
370C2×#126—221no—
371C2×#125—111no—
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—221no—
384C2×C4×D4C2×D1111yescharacteristic
385C2×#117—111no—
386C22×C4⋊C4—111no—
387C22×C4⋊C4—111no—
388C22×C4⋊C4—111no—
389#501—118no—
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#435C2×D1118yescomplemented
400#428—118no—
401C2×#107—111no—
402C2×#107—111no—
403C2×#107—111no—
404C2×#106—111no—
405C2×#106—111no—
406C2×#106—111no—
407C2×#106—111no—
408C2×#106—118no—
409C2×#106—111no—
410C2×#106—111no—
411C2×C4⋊C8C2×D1111yescharacteristic
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×C22⋊C8C2×D1111yescharacteristic
419C2×C22⋊C8C2×D1111yescharacteristic
420C2×#97C2×D1111yescharacteristic
421C22×C11—28no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—44no—
428C22×C11#54712yes—
429C22×C11C2×AGL(1,ℤ/8)14yes—
430C22×C11C2×AGL(1,ℤ/8)12yes—
431C22×C11#57712yes—
432C22×C11C23×D411yescharacteristic
433C2×D11—42no—
434C2×D11—42no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—84no—
440C2×D11—84no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—22no—
445C4×C11#54712yes—
446C4×C11C22×#4111yescharacteristic
447C4×C11C2×2−1+411yescharacteristic
448Dic11—42no—
449Dic11—42no—
450Dic11—42no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454C2×#41—228no—
455C2×#41—448no—
456C22×Q8—221no—
457C22×D4—111no—
458C22×D4—111no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4—221no—
463C22×D4D4411yescharacteristic
464C23×C4—221no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C2×D8—114no—
472C2×D8—224no—
473C2×M16—24no—
474C2×M16C22×D1114yes—
475C22×C8—24no—
476C22×C8C22×D1111yescharacteristic
477C22×C8C22×D1114yes—
478C22×C8C22×D1111yescharacteristic
479C22×C8C22×D1111yescharacteristic
480C22×C8C22×D1111yescharacteristic
481C4⋊Q8—114no—
482C4⋊Q8—222no—
483#126—228no—
484#125—114no—
485#125—222no—
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—228no—
495#121—222no—
496#121—222no—
497#121—222no—
498#121—222no—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—228no—
502C4×D4—222no—
503C4×D4—222no—
504C4×D4D4414yes—
505C4×D4C22×D1114yes—
506#117—114no—
507#117—222no—
508C2×C4⋊C4—111no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—222no—
521C2×C4⋊C4—222no—
522C2×C4⋊C4—222no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—221no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4D4411yescharacteristic
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4D4411yescharacteristic
535C2×C22⋊C4D4411yescharacteristic
536C2×C42—221no—
537C2×C42C22×D1111yescharacteristic
538#107—114no—
539#107—114no—
540#107—114no—
541#106—114no—
542#106—114no—
543#106—114no—
544#106—114no—
545#106—114no—
546#106—114no—
547C4⋊C8C22×D1114yes—
548#102—114no—
549#102—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553#102—114no—
554C22⋊C8C22×D1114yes—
555C22⋊C8C22×D1114yes—
556#97C22×D1114yes—
557C2×C11—24no—
558C2×C11—42no—
559C2×C11#334514yescomplemented
560C2×C11C2×#54711yescharacteristic
561C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
562C2×C11C2×#57711yescharacteristic
563D11—82no—
564D11—82no—
565C24—221no—
566C24—221no—
567C24C2×D4411yescharacteristic
568C24C2×D4411yescharacteristic
569#41—4432no—
570C2×Q8—224no—
571C2×Q8—444no—
572C2×D4—24no—
573C2×D4—112no—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—224no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—444no—
586C2×D4—444no—
587C2×D4—444no—
588C2×D4—882no—
589C2×D4C2×D4414yes—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—224no—
595C22×C4—224no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—224no—
603C22×C4—224no—
604C22×C4—224no—
605C22×C4—444no—
606C22×C4—444no—
607C22×C4—444no—
608C22×C4—882no—
609C22×C4—882no—
610C22×C4C2×D4412yes—
611C22×C4C2×D4412yes—
612C22×C4C2×D4411yescharacteristic
613C22×C4C2×D4411yescharacteristic
614C22×C4C2×D4411yescharacteristic
615C22×C4C2×D4411yescharacteristic
616C22×C4C23×D1112yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619D8—228no—
620M16—28no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—28no—
625C2×C8#434114yescomplemented
626C2×C8C23×D1112yes—
627C2×C8C23×D1112yes—
628C2×C8C23×D1112yes—
629C2×C8C23×D1112yes—
630C4⋊C4—112no—
631C4⋊C4—112no—
632C4⋊C4—112no—
633C4⋊C4—112no—
634C4⋊C4—112no—
635C4⋊C4—112no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—221no—
639C4⋊C4—221no—
640C4⋊C4—221no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—224no—
644C4⋊C4—221no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4C2×D4414yes—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—224no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4C2×D4414yes—
657C22⋊C4C2×D4414yes—
658C42—224no—
659C42C2×D4412yes—
660C42C23×D1112yes—
661C11C2×#334511yescharacteristic, complemented, Sylow
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—222no—
668C23—222no—
669C23—442no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23#6696114yes—
676C23C22×D4412yes—
677C23C22×D4412yes—
678C23C22×D4411yescharacteristic
679Q8—448no—
680D4—28no—
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—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—448no—
708C2×C4—448no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—448no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—884no—
717C2×C4—884no—
718C2×C4C22×D4412yes—
719C2×C4C22×D4412yes—
720C2×C4C22×D4412yes—
721C2×C4C22×D4412yes—
722C2×C4C22×D4411yescharacteristic
723C2×C4C2×#434112yes—
724C2×C4#6704312yes—
725C2×C4C24×D1111yescharacteristic
726C8—22no—
727C8—22no—
728C8—22no—
729C8C2×#434114yescomplemented
730C22—28no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—884no—
744C22—884no—
745C22#1062308612yes—
746C22C2×#6696114yes—
747C22C2×#6696112yes—
748C22#1062328212yes—
749C22C23×D4411yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—442no—
755C4—442no—
756C4—442no—
757C4—442no—
758C4—442no—
759C4—442no—
760C4#1062308612yes—
761C4C22×#434111yescharacteristic
762C4C2×#6704311yescharacteristic
763C2—24no—
764C2—42no—
765C2—882no—
766C2—882no—
767C2#1308108814yesdirect product factor
768C2C2×#1062308611yescharacteristic
769C2C22×#6696111yescharacteristic
770C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
hypercenterC2×#435D11
hypocenterC11C2×#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10623096C2semidirect
2. C2×#10623086C2semidirect
3. #13081088C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622348C2semidirect
7. C2×#10622350C2semidirect
8. C2×#10622349C2semidirect
9. C2×#10622460C2semidirect
10. C2×#10622455C2semidirect
11. C2×#10622748C2semidirect
12. C2×#10622728C2semidirect
13. C2×#10622324C2semidirect
14. C2×#10622734C2semidirect
15. C22×#66881C2semidirect
16. C2×C11×#435C2semidirect
32. #10623096C22semidirect
34. #10623086C22semidirect
45. C11×#435C22semidirect
50. #10622748C22semidirect
51. #10622734C22semidirect
52. #10622728C22semidirect
68. C2×#66881C22semidirect
69. #10622460C22semidirect
70. #10622455C22semidirect
71. #10622350C22semidirect
72. #10622349C22semidirect
73. #10622348C22semidirect
74. #10622348C22semidirect
75. #10622324C22semidirect
76. #10622315C22semidirect
240. C2×C8×C11#41semidirect
290. C2×#435D11semidirect
360. C8×C11C2×#41semidirect
399. #435C2×D11semidirect
559. C2×C11#3345semidirect
625. C2×C8#4341semidirect
661. C11C2×#3345semidirect
729. C8C2×#4341semidirect
767. C2#13081088direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
C2×#106230862
#130810882
C2×#106223152
C2×#106223482
C2×#106223502
C2×#106223492
C2×#106224602
C2×#106224552
C2×#106227482
C2×#106227282
C2×#106223242
C2×#106227342
C22×#668812
C2×C11×#4352
C2×#334511