Finite Group Databasebeta

← C2×#13079242 #15623581

Subgroups — C2×#13079242 #15623581

Order 2816.

1970 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×#10623114C211yesmaximal, characteristic, complemented
2C2×#10623093C211yesmaximal, characteristic
3#13079242C2116yesmaximal, direct product factor
4C2×#10622491C211yesmaximal, characteristic, complemented
5C2×#10622788C211yesmaximal, characteristic, complemented
6C2×#10622410C211yesmaximal, characteristic, complemented
7C2×#10622377C211yesmaximal, characteristic, complemented
8C2×#10622499C211yesmaximal, characteristic, complemented
9C2×#10622787C211yesmaximal, characteristic, complemented
10C2×#10622420C211yesmaximal, characteristic, complemented
11C2×#10622391C211yesmaximal, characteristic, complemented
12C2×#10622323C211yesmaximal, characteristic, complemented
13C2×C4×#4325C211yesmaximal, characteristic, complemented
14C2×C4×#4324C211yesmaximal, characteristic, complemented
15C2×#10622321C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×C11×SD16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66993C2211yescharacteristic
24C2×#66991C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C2×#66983—21no—
27C2×#66982—21no—
28C22×#4314C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623114—24no—
32#10623114C2218yescomplemented
33#10623093—24no—
34#10623093C2218yes—
35C2×#66951—21no—
36C2×#66950C2211yescharacteristic
37C2×#66948C2211yescharacteristic
38C2×#66943C2211yescharacteristic
39C2×#66943C2211yescharacteristic
40C2×#66942—21no—
41C2×#66937—21no—
42C2×#66936—21no—
43C2×#66929—21no—
44C2×C4×D44C2211yescharacteristic
45C2×#66925C2211yescharacteristic
46C2×#66923—21no—
47C2×C4×Dic22C2211yescharacteristic
48C11×#440C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55#10622788C2218yescomplemented
56#10622787C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×#66879C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62C4×#4325C2218yescomplemented
63C4×#4324C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×C4×C11⋊C8C2211yescharacteristic
69#10622499C2218yescomplemented
70#10622491C2218yescomplemented
71#10622420C2218yescomplemented
72#10622410C2218yescomplemented
73#10622391C2218yescomplemented
74#10622377C2218yescomplemented
75#10622323C2218yescomplemented
76#10622321C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×D44—21no—
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C2×C11×SD16—24no—
89C2×C11×SD16C2314yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×Q8×C11—22no—
93C4×Q8×C11C2314yes—
94C4×D4×C11—22no—
95C4×D4×C11C2314yes—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103#66999—22no—
104#66999C2314yes—
105#66997—22no—
106#66997C2314yes—
107C2×#4325—24no—
108C2×#4325C2314yes—
109#66993—22no—
110#66993C2314yes—
111#66991—22no—
112#66991C2314yes—
113C2×#4324—24no—
114C2×#4324C2314yes—
115#66983—28no—
116#66982—28no—
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⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4D411yescharacteristic
135C2×Dic11⋊C4D411yescharacteristic
136C2×C4×Dic11—21no—
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×#4314—24no—
141C2×#4314C2314yes—
142C2×#4313—24no—
143C2×#4313C2314yes—
144C2×C8×D11—24no—
145C2×C8×D11C2314yes—
146#66951—28no—
147#66950—22no—
148#66950C2314yes—
149#66948—22no—
150#66948C2314yes—
151#66943—22no—
152#66943—22no—
153#66943C2314yes—
154#66943C2314yes—
155#66942—28no—
156#66937—28no—
157#66936—28no—
158#66929—28no—
159C4×D44—22no—
160C4×D44C2314yes—
161#66925D414yes—
162#66925C2314yes—
163#66923—28no—
164C4×Dic22—22no—
165C4×Dic22C2314yes—
166C11×#107C2314yes—
167C11×#103C2314yes—
168C11×#102C2314yes—
169C11×#97C2314yes—
170#66899C2314yes—
171#66896C2314yes—
172#66885C2314yes—
173#66882C2314yes—
174#66880C2314yes—
175#66879C2314yes—
176C8×Dic11C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66872C2314yes—
181C4×C11⋊C8C2314yes—
182C2×#3174—111nomaximal, Sylow
183C24×C11—21no—
184C23×D11—21no—
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C2×D4×C11—21no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11C2412yes—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—24no—
198C22×C4×C11—82no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—82no—
206C2×C22⋊D11—82no—
207C2×C22⋊D11—82no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C2×D44—24no—
215C2×D44—21no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44—82no—
219C2×D44C2412yes—
220C2×C4×D11—24no—
221C2×C4×D11—22no—
222C2×C4×D11—22no—
223C2×C4×D11—82no—
224C2×C4×D11C2×D412yes—
225C2×C4×D11C2412yes—
226C2×Dic22—21no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22C2412yes—
230C11×SD16—28no—
231C2×C8×C11—22no—
232C2×C8×C11#4114yes—
233C2×C8×C11C2412yes—
234C2×C8×C11C2412yes—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C22⋊C4—24no—
241C42×C11—24no—
242C42×C11C2×D412yes—
243C42×C11C2412yes—
244C22⋊Dic11—24no—
245#4325—28no—
246#4324—28no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4C2×D414yes—
252(C2×D11)⋊C4C2×D414yes—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
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—
267Dic11⋊C4C2×D414yes—
268C4×Dic11—24no—
269C4×Dic11C2×D412yes—
270C4×Dic11C2412yes—
271C2×C11⋊C8—22no—
272C2×C11⋊C8#4114yes—
273C2×C11⋊C8C2412yes—
274C2×C11⋊C8C2412yes—
275#4314—28no—
276#4313—28no—
277C8×D11—28no—
278C2×#541—111no—
279C2×#540—111no—
280#3174—1116no—
281C2×#499—111no—
282C2×#492—111no—
283C2×#491—111no—
284C2×#490—111no—
285C2×#468—111no—
286C2×#468—111no—
287C2×#465—111no—
288C2×#465—111no—
289C2×#440—111no—
290C2×#440D1111yescharacteristic, complemented
291C2×C4×SD16—111no—
292C2×C4×SD16—111no—
293C2×#405—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—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310D4×C11—22no—
311D4×C11—22no—
312D4×C11—42no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—84no—
322C2×C4×C11C22×D412yes—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4112yes—
326C2×C4×C11C2×#4112yes—
327C2×C4×C11C2511yescharacteristic
328C22⋊D11—84no—
329C22⋊D11—84no—
330C22⋊D11—84no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11C22×D412yes—
341C2×Dic11C22×D412yes—
342C2×Dic11C22×D412yes—
343D44—22no—
344D44—22no—
345D44—42no—
346D44—84no—
347C4×D11—24no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—84no—
351Dic22—22no—
352Dic22—22no—
353Dic22—42no—
354C8×C11—22no—
355C8×C11C2×#4114yes—
356C11⋊C8—22no—
357C11⋊C8C2×#4114yes—
358C22×SD16—111no—
359C22×SD16—111no—
360C22×SD16—111no—
361C22×SD16C2×D1111yescharacteristic
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—111no—
374C2×#125—221no—
375C2×#125—221no—
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×Q8C2×D1111yescharacteristic
386C2×C4×D4—111no—
387C2×C4×D4C2×D1111yescharacteristic
388C2×#117—111no—
389#499—118no—
390#492—118no—
391#491—118no—
392#490—118no—
393#468—118no—
394#468—118no—
395#465—118no—
396#465—118no—
397#440—118no—
398#440C2×D1118yescomplemented
399C4×SD16—118no—
400C4×SD16—118no—
401C2×#107—111no—
402C2×#107C2×D1111yescharacteristic
403C2×#106—111no—
404C2×#106—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103C2×D1111yescharacteristic
409C2×#102—111no—
410C2×#102—111no—
411C2×#102—111no—
412C2×#102C2×D1111yescharacteristic
413#405—118no—
414C2×#97—111no—
415C2×#97C2×D1111yescharacteristic
416C2×C4×C8—111no—
417C2×C4×C8—111no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—84no—
422C22×C11#53212yes—
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#53212yes—
440C4×C11C22×#4111yescharacteristic
441C4×C11C22×#4111yescharacteristic
442Dic11—22no—
443Dic11—22no—
444Dic11—22no—
445Dic11—42no—
446Dic11—42no—
447Dic11—42no—
448C22×Q8—111no—
449C22×Q8C22×D1111yescharacteristic
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—24no—
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—114no—
463C2×SD16—224no—
464C2×SD16—224no—
465C2×SD16—224no—
466C2×SD16C22×D1114yes—
467C2×M16—114no—
468C2×M16—224no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8—114no—
472C22×C8—224no—
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—114no—
482#125—114no—
483#125—228no—
484#125—222no—
485#125—222no—
486#125—228no—
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—22no—
500C4×Q8—114no—
501C4×Q8—222no—
502C4×Q8C22×D1114yes—
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—111no—
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⋊C4—221no—
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—21no—
534C2×C42—111no—
535C2×C42—221no—
536C2×C42C22×D1111yescharacteristic
537#107—114no—
538#107C22×D1114yes—
539#106—114no—
540#106—114no—
541#103—114no—
542#103—114no—
543#103—114no—
544#103C22×D1114yes—
545#102—114no—
546#102—114no—
547#102—114no—
548#102C22×D1114yes—
549#97—114no—
550#97C22×D1114yes—
551C4×C8—114no—
552C4×C8—114no—
553C2×C11—82no—
554C2×C11#317414yescomplemented
555C2×C11C2×#53211yescharacteristic
556C2×C11C2×#57711yescharacteristic
557C2×C11C2×#57711yescharacteristic
558D11—42no—
559D11—82no—
560C24—21no—
561C24—111no—
562C24—221no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—112no—
567C2×Q8—221no—
568C2×Q8—222no—
569C2×Q8—222no—
570C2×Q8C23×D1112yes—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—224no—
577C2×D4—224no—
578C2×D4—224no—
579C2×D4—222no—
580C2×D4—221no—
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—28no—
608SD16—228no—
609SD16—228no—
610SD16—228no—
611M16—228no—
612C2×C8—22no—
613C2×C8—114no—
614C2×C8—112no—
615C2×C8—112no—
616C2×C8—228no—
617C2×C8—222no—
618C2×C8#433914yes—
619C2×C8C23×D1112yes—
620C2×C8C23×D1112yes—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—114no—
625C4⋊C4—114no—
626C4⋊C4—112no—
627C4⋊C4—112no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—224no—
635C4⋊C4—224no—
636C4⋊C4—221no—
637C4⋊C4—221no—
638C4⋊C4—224no—
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—24no—
650C42—112no—
651C42—112no—
652C42—224no—
653C42D4×D1112yes—
654C42C23×D1112yes—
655C11C2×#317411yescharacteristic, 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—22no—
670Q8—22no—
671Q8—42no—
672Q8—222no—
673Q8—222no—
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×#433912yes—
711C2×C4C2×D4×D1112yes—
712C2×C4C2×D4×D1112yes—
713C2×C4C2×D4×D1111yescharacteristic
714C2×C4#41×D1112yes—
715C2×C4C24×D1111yescharacteristic
716C8—22no—
717C8—114no—
718C8—222no—
719C8C2×#433914yes—
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#1062307912yes—
733C22#1062330612yes—
734C22#1062330912yes—
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#1062307912yes—
748C4C22×#433911yescharacteristic
749C4C2×#41×D1111yescharacteristic
750C2—82no—
751C2—442no—
752C2—882no—
753C2#1307924214yesdirect product factor
754C2C2×#1062307911yescharacteristic
755C2C2×#1062330911yescharacteristic
756C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC2×#10623093C2
hypercenterC2×#440D11
hypocenterC11C2×#3174
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#10623114C2semidirect
3. #13079242C2direct (N × H)
4. C2×#10622491C2semidirect
5. C2×#10622788C2semidirect
6. C2×#10622410C2semidirect
7. C2×#10622377C2semidirect
8. C2×#10622499C2semidirect
9. C2×#10622787C2semidirect
10. C2×#10622420C2semidirect
11. C2×#10622391C2semidirect
12. C2×#10622323C2semidirect
13. C2×C4×#4325C2semidirect
14. C2×C4×#4324C2semidirect
15. C2×#10622321C2semidirect
16. C2×C11×#440C2semidirect
32. #10623114C22semidirect
48. C11×#440C22semidirect
55. #10622788C22semidirect
56. #10622787C22semidirect
62. C4×#4325C22semidirect
63. C4×#4324C22semidirect
69. #10622499C22semidirect
70. #10622491C22semidirect
71. #10622420C22semidirect
72. #10622410C22semidirect
73. #10622391C22semidirect
74. #10622377C22semidirect
75. #10622323C22semidirect
76. #10622321C22semidirect
290. C2×#440D11semidirect
398. #440C2×D11semidirect
554. C2×C11#3174semidirect
655. C11C2×#3174semidirect
753. C2#13079242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231142
C2×#106230932
#130792422
C2×#106224912
C2×#106227882
C2×#106224102
C2×#106223772
C2×#106224992
C2×#106227872
C2×#106224202
C2×#106223912
C2×#106223232
C2×C4×#43252
C2×C4×#43242
C2×#106223212
C2×C11×#4402
C2×#317411