Finite Group Databasebeta

← C2×#13080085 #15626747

Subgroups — C2×#13080085 #15626747

Order 2816.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623264C211yesmaximal, characteristic, complemented
2C2×#10623113C211yesmaximal, characteristic, complemented
3#13080085C2116yesmaximal, direct product factor
4C2×#10622467C211yesmaximal, characteristic, complemented
5C2×#10622483C211yesmaximal, characteristic, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622429C211yesmaximal, characteristic, complemented
8C2×#10622478C211yesmaximal, characteristic
9C2×#10622420C211yesmaximal, characteristic, complemented
10C2×#10622477C211yesmaximal, characteristic, complemented
11C2×#10622411C211yesmaximal, characteristic, complemented
12C2×#10622641C211yesmaximal, characteristic, complemented
13C2×#10622432C211yesmaximal, characteristic, complemented
14C2×#10622457C211yesmaximal, characteristic, complemented
15C2×#10622452C211yesmaximal, characteristic, complemented
16C2×C11×#475C211yesmaximal, characteristic, complemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000—21no—
20C2×#67000C2211yescharacteristic
21C2×#66999—21no—
22C2×#66999C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C22×D88C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623264—24no—
30#10623264C2218yescomplemented
31#10623113—24no—
32#10623113C2218yescomplemented
33C2×#66951—21no—
34C2×#66950C2211yescharacteristic
35C2×#66949—21no—
36C2×#66948C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66947—21no—
39C2×#66947—21no—
40C2×#66946C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66929—21no—
44C2×#66928—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66925C2211yescharacteristic
48C11×#475C2218yescomplemented
49C2×C11×#106C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622697C2218yescomplemented
59#10622641C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622483C2218yescomplemented
68#10622478C2218yes—
69#10622477C2218yescomplemented
70#10622467C2218yescomplemented
71#10622457C2218yescomplemented
72#10622452C2218yescomplemented
73#10622432C2218yescomplemented
74#10622429C2218yescomplemented
75#10622420C2218yescomplemented
76#10622411C2218yescomplemented
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D44—21no—
80C22×D44—21no—
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11C2311yescharacteristic
86C22×Dic22—21no—
87C22×Dic22C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C11×C4⋊Q8—22no—
91C11×C4⋊Q8C2314yes—
92C4×Q8×C11—22no—
93C4×Q8×C11C2314yes—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101#67000—28no—
102#67000—22no—
103#67000C2314yes—
104#66999—22no—
105#66999—28no—
106#66999C2314yes—
107C2×#4326—42no—
108C2×#4326C2314yes—
109C2×#4325—42no—
110C2×#4325C2314yes—
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)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4D411yescharacteristic
122C2×(C2×D11)⋊C4D411yescharacteristic
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4D411yescharacteristic
129C2×Dic11⋊C4D411yescharacteristic
130C2×C4×Dic11—21no—
131C2×C4×Dic11C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C2×D88—42no—
135C2×D88C2314yes—
136C2×#4314—42no—
137C2×#4314C2314yes—
138C2×#4313—42no—
139C2×#4313C2314yes—
140C2×C8×D11—42no—
141C2×C8×D11C2314yes—
142#66951—28no—
143#66950—22no—
144#66950C2314yes—
145#66949—28no—
146#66948—22no—
147#66948—22no—
148#66948C2314yes—
149#66948C2314yes—
150#66947—28no—
151#66947—28no—
152#66946—22no—
153#66946C2314yes—
154#66941—22no—
155#66941C2314yes—
156#66940—22no—
157#66940C2314yes—
158#66929—28no—
159#66928—22no—
160#66928—28no—
161#66928C2314yes—
162C4×D44—22no—
163C4×D44C2314yes—
164#66925D414yes—
165#66925C2314yes—
166C11×#106C2314yes—
167C11×#106C2314yes—
168C11×C4⋊C8C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171#66885C2314yes—
172#66880C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175#66874C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66872C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3263—111nomaximal, Sylow
183C23×D11—21no—
184C23×D11—21no—
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—21no—
187C2×Q8×C11—24no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—82no—
191C2×Q8×C11C2412yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11C2×D411yescharacteristic
202C22×Dic11C2×D411yescharacteristic
203C22×Dic11C2×D411yescharacteristic
204C2×D44—24no—
205C2×D44—24no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—22no—
212C2×D44—82no—
213C2×D44—82no—
214C2×D44C2412yes—
215C2×D44C2412yes—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—82no—
221C2×C4×D11—82no—
222C2×C4×D11C2×D412yes—
223C2×C4×D11C2412yes—
224C2×Dic22—24no—
225C2×Dic22—21no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—82no—
229C2×Dic22C2412yes—
230C2×C8×C11—22no—
231C2×C8×C11—22no—
232C2×C8×C11C2412yes—
233C2×C8×C11C2412yes—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C11×C4⋊C4C2412yes—
242C42×C11—24no—
243C42×C11C2×D412yes—
244C42×C11C2412yes—
245#4326—44no—
246#4325—44no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—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—
257(C2×D11)⋊C4C2×D414yes—
258(C2×D11)⋊C4C2×D414yes—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11C2412yes—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4—24no—
265Dic11⋊C4C2×D414yes—
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—
274D88—44no—
275#4314—44no—
276#4313—44no—
277C8×D11—44no—
278C2×#542—111no—
279C2×#542—111no—
280#3263—1116no—
281C2×#475—111no—
282C2×#475D1111yescharacteristic, complemented
283C2×#476—111no—
284C2×#476—111no—
285C2×#470—111no—
286C2×#469—111no—
287C2×#465—111no—
288C2×#465—111no—
289C2×#464—111no—
290C2×#464—111no—
291C2×#463—111no—
292C2×#463—111no—
293C2×#424—111no—
294C23×C11C22×D411yescharacteristic
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11C22×D412yes—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310Q8×C11—84no—
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×C11H(5,𝔽2)12yes—
325C2×C4×C112−1+412yes—
326C2×C4×C11C2511yescharacteristic
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11C22×D412yes—
335C2×Dic11C22×D412yes—
336C2×Dic11C22×D412yes—
337D44—22no—
338D44—22no—
339D44—22no—
340D44—22no—
341D44—42no—
342D44—42no—
343D44—84no—
344D44—84no—
345C4×D11—24no—
346C4×D11—22no—
347C4×D11—22no—
348C4×D11—84no—
349C4×D11—84no—
350Dic22—22no—
351Dic22—22no—
352Dic22—42no—
353Dic22—84no—
354C8×C11—22no—
355C8×C11—22no—
356C11⋊C8—22no—
357C11⋊C8—22no—
358C22×Q16—111no—
359C22×SD16—111no—
360C22×SD16—111no—
361C22×D8—111no—
362C22×M16—111no—
363C23×C8—111no—
364#542—118no—
365#542—118no—
366#542—224no—
367#542—224no—
368C2×C4⋊Q8—111no—
369C2×C4⋊Q8C2×D1111yescharacteristic
370C2×#126—221no—
371C2×#126—221no—
372C2×#124—111no—
373C2×#124—111no—
374C2×#124—221no—
375C2×#124—221no—
376C2×#123—221no—
377C2×#123—221no—
378C2×C22⋊Q8—111no—
379C2×C22⋊Q8—111no—
380C2×C22⋊Q8—221no—
381C2×C22⋊Q8—221no—
382C2×#121—111no—
383C2×#121—111no—
384C2×C4×Q8—111no—
385C2×C4×Q8C2×D1111yescharacteristic
386C2×C4×D4—111no—
387C2×C4×D4—111no—
388C2×#117—111no—
389#476—118no—
390#476—118no—
391#475—118no—
392#475C2×D1118yescomplemented
393#470—118no—
394#469—118no—
395#465—118no—
396#465—118no—
397#464—118no—
398#464—118no—
399#463—118no—
400#463—118no—
401C2×#106—111no—
402C2×#106—111no—
403C2×#106C2×D1111yescharacteristic
404C2×#106C2×D1111yescharacteristic
405#424—118no—
406C2×C4⋊C8—111no—
407C2×C4⋊C8—111no—
408C2×C4⋊C8—111no—
409C2×C4⋊C8C2×D1111yescharacteristic
410C2×#103—111no—
411C2×#103—111no—
412C2×#103C2×D1111yescharacteristic
413C2×#103C2×D1111yescharacteristic
414C2×#102—111no—
415C2×#102—111no—
416C2×#102—111no—
417C2×#102—111no—
418C22×C11#53712yes—
419C22×C11#57712yes—
420C22×C11#57712yes—
421C22×C11C23×D411yescharacteristic
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—44no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—84no—
433C2×D11—84no—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11—42no—
440C4×C11#53712yes—
441C4×C11C2×H(5,𝔽2)11yescharacteristic
442C4×C11C2×2−1+411yescharacteristic
443Dic11—22no—
444Dic11—22no—
445Dic11—22no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—21no—
449C22×Q8—111no—
450C22×Q8—221no—
451C22×Q8C22×D1111yescharacteristic
452C22×D4—111no—
453C22×D4—111no—
454C22×D4—221no—
455C22×D4—221no—
456C23×C4—111no—
457C23×C4—221no—
458C23×C4—221no—
459C2×Q16—114no—
460C2×Q16—442no—
461C2×SD16—114no—
462C2×SD16—114no—
463C2×SD16—442no—
464C2×SD16—442no—
465C2×D8—114no—
466C2×D8—442no—
467C2×M16—114no—
468C2×M16—442no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—114no—
472C22×C8—442no—
473C22×C8C22×D1111yescharacteristic
474C22×C8C22×D1111yescharacteristic
475C4⋊Q8—22no—
476C4⋊Q8—114no—
477C4⋊Q8—222no—
478C4⋊Q8C22×D1114yes—
479#126—228no—
480#126—228no—
481#124—114no—
482#124—114no—
483#124—228no—
484#124—222no—
485#124—228no—
486#124—222no—
487#123—228no—
488#123—228no—
489C22⋊Q8—114no—
490C22⋊Q8—114no—
491C22⋊Q8—228no—
492C22⋊Q8—222no—
493C22⋊Q8—228no—
494C22⋊Q8—222no—
495#121—114no—
496#121—114no—
497#121—222no—
498#121—222no—
499C4×Q8—22no—
500C4×Q8—114no—
501C4×Q8—222no—
502C4×Q8C22×D1114yes—
503C4×D4—114no—
504C4×D4—114no—
505C4×D4—222no—
506C4×D4—222no—
507#117—114no—
508#117—114no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4—221no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C22⋊C4—111no—
522C2×C22⋊C4—111no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C22⋊C4—221no—
526C2×C22⋊C4—221no—
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×C42—21no—
534C2×C42—111no—
535C2×C42—221no—
536C2×C42C22×D1111yescharacteristic
537#106—114no—
538#106—114no—
539#106C22×D1114yes—
540#106C22×D1114yes—
541C4⋊C8—114no—
542C4⋊C8—114no—
543C4⋊C8—114no—
544C4⋊C8C22×D1114yes—
545#103—114no—
546#103—114no—
547#103C22×D1114yes—
548#103C22×D1114yes—
549#102—114no—
550#102—114no—
551#102—114no—
552#102—114no—
553C2×C11#326314yescomplemented
554C2×C11C2×#53711yescharacteristic
555C2×C11C2×#57711yescharacteristic
556C2×C11C2×#57711yescharacteristic
557D11—42no—
558D11—82no—
559D11—82no—
560C24—111no—
561C24—221no—
562C24—221no—
563C2×Q8—21no—
564C2×Q8—24no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—82no—
568C2×Q8—112no—
569C2×Q8—224no—
570C2×Q8—221no—
571C2×Q8—222no—
572C2×Q8—222no—
573C2×Q8—882no—
574C2×Q8C23×D1112yes—
575C2×D4—112no—
576C2×D4—112no—
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—882no—
586C2×D4—882no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—111no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—224no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—224no—
602C22×C4—882no—
603C22×C4—882no—
604C22×C4D4×D1111yescharacteristic
605C22×C4D4×D1111yescharacteristic
606C22×C4C23×D1111yescharacteristic
607Q16—444no—
608SD16—444no—
609SD16—444no—
610D8—444no—
611M16—444no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—112no—
615C2×C8—112no—
616C2×C8—222no—
617C2×C8—222no—
618C2×C8—444no—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—114no—
627C4⋊C4—114no—
628C4⋊C4—112no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—221no—
634C4⋊C4C23×D1112yes—
635C4⋊C4C23×D1112yes—
636C4⋊C4C23×D1112yes—
637C22⋊C4—114no—
638C22⋊C4—114no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—224no—
649C42—24no—
650C42—112no—
651C42—112no—
652C42—224no—
653C42D4×D1112yes—
654C42C23×D1112yes—
655C11C2×#326311yescharacteristic, complemented, Sylow
656C23—112no—
657C23—222no—
658C23—222no—
659C23—222no—
660C23—222no—
661C23—222no—
662C23—442no—
663C23—442no—
664C23—442no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—222no—
674Q8—222no—
675Q8—442no—
676Q8—884no—
677D4—222no—
678D4—222no—
679D4—222no—
680D4—222no—
681D4—442no—
682D4—442no—
683D4—884no—
684D4—884no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—112no—
696C2×C4—112no—
697C2×C4—112no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—884no—
709C2×C4—884no—
710C2×C4C2×D4×D1112yes—
711C2×C4C2×D4×D1112yes—
712C2×C4C2×D4×D1111yescharacteristic
713C2×C4#6704012yes—
714C2×C4#6704212yes—
715C2×C4C24×D1111yescharacteristic
716C8—22no—
717C8—22no—
718C8—222no—
719C8—222no—
720C22—222no—
721C22—222no—
722C22—222no—
723C22—444no—
724C22—442no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—442no—
730C22—884no—
731C22—884no—
732C22#1062316012yes—
733C22#1062329312yes—
734C22#1062330912yes—
735C22C22×D4×D1111yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—222no—
743C4—222no—
744C4—222no—
745C4—442no—
746C4—442no—
747C4#1062316012yes—
748C4C2×#6704011yescharacteristic
749C4C2×#6704211yescharacteristic
750C2—442no—
751C2—882no—
752C2—882no—
753C2#1308008514yesdirect product factor
754C2C2×#1062316011yescharacteristic
755C2C2×#1062329311yescharacteristic
756C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#10622478C2
hypercenterC2×#475D11
hypocenterC11C2×#3263
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623264C2semidirect
2. C2×#10623113C2semidirect
3. #13080085C2direct (N × H)
4. C2×#10622467C2semidirect
5. C2×#10622483C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622429C2semidirect
9. C2×#10622420C2semidirect
10. C2×#10622477C2semidirect
11. C2×#10622411C2semidirect
12. C2×#10622641C2semidirect
13. C2×#10622432C2semidirect
14. C2×#10622457C2semidirect
15. C2×#10622452C2semidirect
16. C2×C11×#475C2semidirect
30. #10623264C22semidirect
32. #10623113C22semidirect
48. C11×#475C22semidirect
58. #10622697C22semidirect
59. #10622641C22semidirect
67. #10622483C22semidirect
69. #10622477C22semidirect
70. #10622467C22semidirect
71. #10622457C22semidirect
72. #10622452C22semidirect
73. #10622432C22semidirect
74. #10622429C22semidirect
75. #10622420C22semidirect
76. #10622411C22semidirect
282. C2×#475D11semidirect
392. #475C2×D11semidirect
553. C2×C11#3263semidirect
655. C11C2×#3263semidirect
753. C2#13080085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232642
C2×#106231132
#130800852
C2×#106224672
C2×#106224832
C2×#106226972
C2×#106224292
C2×#106224782
C2×#106224202
C2×#106224772
C2×#106224112
C2×#106226412
C2×#106224322
C2×#106224572
C2×#106224522
C2×C11×#4752
C2×#326311