Finite Group Databasebeta

← C2×#13080064 #15626723

Subgroups — C2×#13080064 #15626723

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×#10623228C211yesmaximal, characteristic, complemented
2C2×#10623093C211yesmaximal, characteristic
3#13080064C2116yesmaximal, direct product factor
4C2×#10622470C211yesmaximal, characteristic, complemented
5C2×#10622490C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622499C211yesmaximal, characteristic, complemented
8C2×#10622393C211yesmaximal, characteristic, complemented
9C2×#10622477C211yesmaximal, characteristic, complemented
10C2×#10622391C211yesmaximal, characteristic, complemented
11C2×#10622375C211yesmaximal, characteristic, complemented
12C2×#10622375C211yesmaximal, characteristic, complemented
13C2×#10622454C211yesmaximal, characteristic, complemented
14C2×#10622632C211yesmaximal, characteristic, complemented
15C2×#10622452C211yesmaximal, characteristic, complemented
16C2×C11×#478C211yesmaximal, characteristic, complemented
17C2×C11×#125C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66993C2211yescharacteristic
20C2×#66991C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×#66983—21no—
24C2×#66982—21no—
25C22×#4314C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28C22×C8×D11C2211yescharacteristic
29#10623228—24no—
30#10623228C2218yescomplemented
31#10623093—24no—
32#10623093C2218yes—
33C2×#66951—21no—
34C2×#66951—21no—
35C2×#66950C2211yescharacteristic
36C2×#66950C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66943—21no—
39C2×#66943—21no—
40C2×#66943C2211yescharacteristic
41C2×#66940C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66937—21no—
44C2×#66936—21no—
45C2×C4×D44C2211yescharacteristic
46C2×#66925C2211yescharacteristic
47C2×#66922C2211yescharacteristic
48C11×#478C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#102C2211yescharacteristic
53C2×C11×#102C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622679C2218yescomplemented
59#10622632C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622499C2218yescomplemented
68#10622490C2218yescomplemented
69#10622477C2218yescomplemented
70#10622470C2218yescomplemented
71#10622454C2218yescomplemented
72#10622452C2218yescomplemented
73#10622393C2218yescomplemented
74#10622391C2218yescomplemented
75#10622375C2218yescomplemented
76#10622375C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×D44—21no—
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×C4×D11C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C11×#125—22no—
91C11×#125C2314yes—
92C4×D4×C11—22no—
93C4×D4×C11C2314yes—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102#66993—22no—
103#66993C2314yes—
104#66991—22no—
105#66991C2314yes—
106C2×#4324—42no—
107C2×#4324—42no—
108C2×#4324C2314yes—
109C2×#4324C2314yes—
110#66983—28no—
111#66982—28no—
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⋊Dic11—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4D411yescharacteristic
128C2×Dic11⋊C4D411yescharacteristic
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C2×#4314—42no—
135C2×#4314—42no—
136C2×#4314C2314yes—
137C2×#4314C2314yes—
138C2×#4313—42no—
139C2×#4313C2314yes—
140C2×C8×D11—42no—
141C2×C8×D11C2314yes—
142#66951—28no—
143#66951—28no—
144#66950—22no—
145#66950—22no—
146#66950C2314yes—
147#66950C2314yes—
148#66948—22no—
149#66948C2314yes—
150#66943—28no—
151#66943—28no—
152#66943—22no—
153#66943C2314yes—
154#66940—22no—
155#66940—22no—
156#66940C2314yes—
157#66940C2314yes—
158#66937—28no—
159#66936—28no—
160C4×D44—22no—
161C4×D44C2314yes—
162#66925D414yes—
163#66925C2314yes—
164#66922—22no—
165#66922C2314yes—
166C11×#107C2314yes—
167C11×#106C2314yes—
168C11×C4⋊C8C2314yes—
169C11×#102C2314yes—
170C11×#102C2314yes—
171#66880C2314yes—
172#66880C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3260—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11C2×D411yescharacteristic
186C2×D4×C11—21no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11C2412yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—24no—
194C22×C4×C11—82no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—82no—
202C2×C22⋊D11—82no—
203C2×C22⋊D11—82no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C2×D44—24no—
211C2×D44—21no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—82no—
215C2×D44C2412yes—
216C2×C4×D11—24no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—82no—
220C2×C4×D11C2×D412yes—
221C2×C4×D11C2412yes—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22C2412yes—
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—
242C11×C22⋊C4—24no—
243C42×C11C2×D412yes—
244C42×C11C2412yes—
245C22⋊Dic11—24no—
246#4324—44no—
247#4324—44no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4C2×D414yes—
253(C2×D11)⋊C4C2×D414yes—
254C4⋊Dic11—24no—
255C4⋊Dic11—24no—
256C4⋊Dic11—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—21no—
260C4⋊Dic11C2412yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—24no—
264Dic11⋊C4C2×D414yes—
265Dic11⋊C4C2×D414yes—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11C2×D412yes—
269C4×Dic11C2412yes—
270C2×C11⋊C8—22no—
271C2×C11⋊C8—22no—
272C2×C11⋊C8C2412yes—
273C2×C11⋊C8C2412yes—
274#4314—44no—
275#4314—44no—
276#4313—44no—
277C8×D11—44no—
278C2×#541—111no—
279C2×#540—111no—
280#3260—1116no—
281C2×#479—111no—
282C2×#479—111no—
283C2×#478—111no—
284C2×#478D1111yescharacteristic, complemented
285C2×#468—111no—
286C2×#468—111no—
287C2×#465—111no—
288C2×#465—111no—
289C2×#460—111no—
290C2×#460—111no—
291C2×#461—111no—
292C2×#461—111no—
293C2×#424—111no—
294C23×C11—22no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11C22×D411yescharacteristic
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11C22×D412yes—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—42no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—84no—
319C2×C4×C11C22×D412yes—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11H(5,𝔽2)12yes—
323C2×C4×C112−1+412yes—
324C2×C4×C11C2511yescharacteristic
325C22⋊D11—84no—
326C22⋊D11—84no—
327C22⋊D11—84no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11C22×D412yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340D44—22no—
341D44—22no—
342D44—42no—
343D44—84no—
344C4×D11—24no—
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—84no—
348Dic22—22no—
349Dic22—22no—
350Dic22—22no—
351Dic22—22no—
352Dic22—42no—
353Dic22—42no—
354C8×C11—22no—
355C8×C11—22no—
356C11⋊C8—22no—
357C11⋊C8—22no—
358C22×SD16—111no—
359C22×SD16—111no—
360C22×SD16—111no—
361C22×SD16—111no—
362C22×M16—111no—
363C23×C8—111no—
364#541—118no—
365#541—224no—
366#540—118no—
367#540—224no—
368C2×C4⋊Q8—111no—
369C2×#127—111no—
370C2×#126—221no—
371C2×#126—221no—
372C2×#125—111no—
373C2×#125—221no—
374C2×#125—221no—
375C2×#125C2×D1111yescharacteristic
376C2×#123—221no—
377C2×#123—221no—
378C2×C22⋊Q8—111no—
379C2×C22⋊Q8—111no—
380C2×#121—111no—
381C2×#121—111no—
382C2×#121—221no—
383C2×#121—221no—
384C2×C4×Q8—111no—
385C2×C4×Q8—111no—
386C2×C4×D4—111no—
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117—111no—
389#479—118no—
390#479—118no—
391#478—118no—
392#478C2×D1118yescomplemented
393#468—118no—
394#468—118no—
395#465—118no—
396#465—118no—
397#461—118no—
398#461—118no—
399#460—118no—
400#460—118no—
401C2×#107—111no—
402C2×#107C2×D1111yescharacteristic
403C2×#106—111no—
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×#103—111no—
413C2×#103—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×#102C2×D1111yescharacteristic
417C2×#102C2×D1111yescharacteristic
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—84no—
422C22×C11#53712yes—
423C22×C11#57712yes—
424C22×C11#57712yes—
425C22×C11C23×D411yescharacteristic
426C2×D11—22no—
427C2×D11—22no—
428C2×D11—22no—
429C2×D11—44no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—42no—
433C2×D11—84no—
434C4×C11—22no—
435C4×C11—22no—
436C4×C11—42no—
437C4×C11—42no—
438C4×C11—42no—
439C4×C11#53712yes—
440C4×C11C2×H(5,𝔽2)11yescharacteristic
441C4×C11C2×2−1+411yescharacteristic
442Dic11—22no—
443Dic11—22no—
444Dic11—22no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8—111no—
450C22×D4—111no—
451C22×D4—221no—
452C22×D4—221no—
453C22×D4—221no—
454C22×D4—221no—
455C22×D4C22×D1111yescharacteristic
456C23×C4—21no—
457C23×C4—111no—
458C23×C4—221no—
459C2×SD16—114no—
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—114no—
463C2×SD16—442no—
464C2×SD16—442no—
465C2×SD16—442no—
466C2×SD16—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—114no—
476C4⋊Q8—222no—
477#127—114no—
478#127—222no—
479#126—228no—
480#126—228no—
481#125—22no—
482#125—114no—
483#125—222no—
484#125—228no—
485#125—228no—
486#125C22×D1114yes—
487#123—228no—
488#123—228no—
489C22⋊Q8—114no—
490C22⋊Q8—114no—
491C22⋊Q8—222no—
492C22⋊Q8—222no—
493#121—114no—
494#121—114no—
495#121—228no—
496#121—228no—
497#121—222no—
498#121—222no—
499C4×Q8—114no—
500C4×Q8—114no—
501C4×Q8—222no—
502C4×Q8—222no—
503C4×D4—22no—
504C4×D4—114no—
505C4×D4—222no—
506C4×D4C22×D1114yes—
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⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4C22×D1111yescharacteristic
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—111no—
527C2×C22⋊C4—111no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C42—111no—
534C2×C42—221no—
535C2×C42—221no—
536C2×C42C22×D1111yescharacteristic
537#107—114no—
538#107C22×D1114yes—
539#106—114no—
540#106C22×D1114yes—
541C4⋊C8—114no—
542C4⋊C8—114no—
543C4⋊C8—114no—
544C4⋊C8C22×D1114yes—
545#103—114no—
546#103—114no—
547#103—114no—
548#103—114no—
549#102—114no—
550#102—114no—
551#102C22×D1114yes—
552#102C22×D1114yes—
553C2×C11—82no—
554C2×C11#326014yescomplemented
555C2×C11C2×#53711yescharacteristic
556C2×C11C2×#57711yescharacteristic
557C2×C11C2×#57711yescharacteristic
558D11—42no—
559D11—82no—
560C24—21no—
561C24—111no—
562C24—221no—
563C2×Q8—112no—
564C2×Q8—112no—
565C2×Q8—221no—
566C2×Q8—221no—
567C2×Q8—222no—
568C2×Q8—222no—
569C2×Q8—222no—
570C2×Q8—222no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—224no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—221no—
580C2×D4—222no—
581C2×D4—222no—
582C2×D4—882no—
583C2×D4—882no—
584C2×D4—882no—
585C2×D4—882no—
586C2×D4C23×D1112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—82no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—111no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—224no—
603C22×C4—882no—
604C22×C4D4×D1111yescharacteristic
605C22×C4D4×D1111yescharacteristic
606C22×C4C23×D1111yescharacteristic
607SD16—444no—
608SD16—444no—
609SD16—444no—
610SD16—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—224no—
634C4⋊C4—224no—
635C4⋊C4—221no—
636C4⋊C4—224no—
637C4⋊C4—224no—
638C4⋊C4C23×D1112yes—
639C4⋊C4C23×D1112yes—
640C4⋊C4C23×D1112yes—
641C22⋊C4—24no—
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—
652C42—224no—
653C42D4×D1112yes—
654C42C23×D1112yes—
655C11C2×#326011yescharacteristic, complemented, Sylow
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—112no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—222no—
665C23—442no—
666C23—442no—
667C23—442no—
668C23C2×D4×D1111yescharacteristic
669Q8—222no—
670Q8—222no—
671Q8—222no—
672Q8—222no—
673Q8—442no—
674Q8—442no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—222no—
679D4—222no—
680D4—442no—
681D4—884no—
682D4—884no—
683D4—884no—
684D4—884no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—84no—
694C2×C4—112no—
695C2×C4—112no—
696C2×C4—112no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—224no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
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—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—222no—
725C22—222no—
726C22—222no—
727C22—444no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—884no—
732C22#1062316012yes—
733C22#1062330112yes—
734C22#1062330612yes—
735C22C22×D4×D1111yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—222no—
742C4—222no—
743C4—222no—
744C4—442no—
745C4—442no—
746C4—442no—
747C4#1062316012yes—
748C4C2×#6704011yescharacteristic
749C4C2×#6704211yescharacteristic
750C2—82no—
751C2—442no—
752C2—882no—
753C2#1308006414yesdirect product factor
754C2C2×#1062316011yescharacteristic
755C2C2×#1062330111yescharacteristic
756C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radicalC2×#10623093C2
hypercenterC2×#478D11
hypocenterC11C2×#3260
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#10623228C2semidirect
3. #13080064C2direct (N × H)
4. C2×#10622470C2semidirect
5. C2×#10622490C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622393C2semidirect
9. C2×#10622477C2semidirect
10. C2×#10622391C2semidirect
11. C2×#10622375C2semidirect
12. C2×#10622375C2semidirect
13. C2×#10622454C2semidirect
14. C2×#10622632C2semidirect
15. C2×#10622452C2semidirect
16. C2×C11×#478C2semidirect
30. #10623228C22semidirect
48. C11×#478C22semidirect
58. #10622679C22semidirect
59. #10622632C22semidirect
67. #10622499C22semidirect
68. #10622490C22semidirect
69. #10622477C22semidirect
70. #10622470C22semidirect
71. #10622454C22semidirect
72. #10622452C22semidirect
73. #10622393C22semidirect
74. #10622391C22semidirect
75. #10622375C22semidirect
76. #10622375C22semidirect
284. C2×#478D11semidirect
392. #478C2×D11semidirect
554. C2×C11#3260semidirect
655. C11C2×#3260semidirect
753. C2#13080064direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232282
C2×#106230932
#130800642
C2×#106224702
C2×#106224902
C2×#106226792
C2×#106224992
C2×#106223932
C2×#106224772
C2×#106223912
C2×#106223752
C2×#106224542
C2×#106226322
C2×#106224522
C2×C11×#4782
C2×#326011