Finite Group Databasebeta

← C2×#13078846 #15622053

Subgroups — C2×#13078846 #15622053

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623174C211yesmaximal, characteristic
2C2×#10623343C211yesmaximal, characteristic, complemented
3#13078846C2116yesmaximal, direct product factor
4C2×#10622658C211yesmaximal, characteristic, complemented
5C2×#10622350C211yesmaximal, characteristic
6C2×#10622407C211yesmaximal, characteristic, complemented
7C2×#10622404C211yesmaximal, characteristic, complemented
8C2×#10622798C211yesmaximal, characteristic, complemented
9C2×#10622798C211yesmaximal, characteristic, complemented
10C2×#10622840C211yesmaximal, characteristic
11C2×#10622797C211yesmaximal, characteristic, complemented
12C2×#10622430C211yesmaximal, characteristic, complemented
13C2×Q16×Dic11C211yesmaximal, characteristic, complemented
14C2×#10622401C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#451C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22#10623343—24no—
23#10623343C2218yescomplemented
24C2×Q8×Dic11—21no—
25C2×Q8×Dic11—21no—
26C2×Q8×Dic11C2211yescharacteristic
27C2×Q8×Dic11C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2211yescharacteristic
30C2×Q8×Dic11C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×#4325C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×#66979—21no—
35C2×#66979—21no—
36C2×#66979C2211yescharacteristic
37C2×#66979C2211yescharacteristic
38#10623174—24no—
39#10623174C2218yes—
40C2×#66951—21no—
41C2×#66950—21no—
42C2×#66946C2211yescharacteristic
43C2×#66941C2211yescharacteristic
44C2×#66938—21no—
45C2×#66936—21no—
46C11×#451C2218yescomplemented
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50#10622840C2218yes—
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622798C2218yescomplemented
57#10622798C2218yescomplemented
58#10622797C2218yescomplemented
59Q16×Dic11C2218yescomplemented
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic
62C2×#66882C2211yescharacteristic
63C2×#66881C2211yescharacteristic
64C2×#66879C2211yescharacteristic
65C2×Dic11⋊C8C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67C2×C8×Dic11C2211yescharacteristic
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622430C2218yescomplemented
72#10622407C2218yescomplemented
73#10622404C2218yescomplemented
74#10622401C2218yescomplemented
75#10622350C2218yes—
76#10622333C2218yescomplemented
77C22×Q8×C11—24no—
78C22×Q8×C11—24no—
79C22×Q8×C11—21no—
80C22×Q8×C11—22no—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2314yes—
83C22×Q8×C11C2311yescharacteristic
84C22×Q8×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×Dic22—21no—
91C2×C11×Q16—24no—
92C2×C11×Q16—24no—
93C2×C11×Q16C2314yes—
94C2×C11×Q16C2314yes—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8C2314yes—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D411yescharacteristic
104C2×C22⋊Dic11D411yescharacteristic
105#67000—22no—
106#67000C2314yes—
107Q8×Dic11—28no—
108Q8×Dic11—28no—
109Q8×Dic11—22no—
110Q8×Dic11—22no—
111Q8×Dic11—22no—
112Q8×Dic11—22no—
113Q8×Dic11—22no—
114Q8×Dic11C2314yes—
115Q8×Dic11C2314yes—
116Q8×Dic11C2314yes—
117Q8×Dic11C2314yes—
118Q8×Dic11C2314yes—
119C2×#4325—24no—
120C2×#4325—24no—
121C2×#4325C2314yes—
122C2×#4325C2314yes—
123#66983—22no—
124#66983C2314yes—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129#66979—22no—
130#66979—28no—
131#66979—28no—
132#66979D414yes—
133#66979C2314yes—
134#66979C2314yes—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11D411yescharacteristic
141C2×C4⋊Dic11D411yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×Dic11⋊C4—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11—21no—
148C2×C4×Dic11—21no—
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156#66951—28no—
157#66950—28no—
158#66946—22no—
159#66946C2314yes—
160#66941—22no—
161#66941C2314yes—
162#66938—28no—
163#66936—28no—
164C11×#103C2314yes—
165C11×#103C2314yes—
166C11×C22⋊C8C2314yes—
167#66899C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66899C2314yes—
171C22⋊(C11⋊C8)C2314yes—
172#66885C2314yes—
173#66885C2314yes—
174#66882C2314yes—
175#66881C2314yes—
176#66879C2314yes—
177Dic11⋊C8C2314yes—
178Dic11⋊C8C2314yes—
179C8×Dic11C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3121—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C2×Q8×C11—216no—
186C2×Q8×C11—28no—
187C2×Q8×C11—28no—
188C2×Q8×C11—28no—
189C2×Q8×C11—24no—
190C2×Q8×C11—21no—
191C2×Q8×C11—21no—
192C2×Q8×C11—21no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11#4114yes—
198C2×Q8×C11#4114yes—
199C2×Q8×C11C2412yes—
200C2×Q8×C11C2412yes—
201C2×Q8×C11C2412yes—
202C22×C4×C11—28no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—24no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—82no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223C2×D44—21no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44C2412yes—
227C2×C4×D11—24no—
228C2×C4×D11—82no—
229C2×Dic22—24no—
230C2×Dic22—82no—
231C11×Q16—28no—
232C11×Q16—28no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4C2412yes—
240C11×C22⋊C4—24no—
241C22⋊Dic11—24no—
242C22⋊Dic11C2×D414yes—
243C22⋊Dic11C2×D414yes—
244#4325—28no—
245#4325—28no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250C4⋊Dic11—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11C2×D414yes—
259C4⋊Dic11C2×D414yes—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263Dic11⋊C4—24no—
264C4×Dic11—24no—
265C4×Dic11—24no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11—24no—
269C4×Dic11—24no—
270C4×Dic11C2×D412yes—
271C4×Dic11C2×D412yes—
272C4×Dic11C2412yes—
273C4×Dic11C2412yes—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8C2412yes—
277C2×C11⋊C8C2412yes—
278C2×#542—111no—
279C2×#519—111no—
280#3121—1116no—
281C2×#485—111no—
282C2×#482—111no—
283C2×#477—111no—
284C2×#475—111no—
285C2×#464—111no—
286C2×#464—111no—
287C2×#451D1111yescharacteristic, complemented
288C2×#448—111no—
289C2×#441—111no—
290C2×#440—111no—
291C2×C4×Q16—111no—
292C2×C4×SD16—111no—
293C2×#433—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11C22×D412yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303Q8×C11—216no—
304Q8×C11—24no—
305Q8×C11—24no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—22no—
310Q8×C11—42no—
311Q8×C11C2×#4114yes—
312Q8×C11C2×#4114yes—
313C2×C4×C11—216no—
314C2×C4×C11—24no—
315C2×C4×C11—24no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4112yes—
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2511yescharacteristic
331C22⋊D11—84no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346D44—22no—
347D44—22no—
348D44—42no—
349C4×D11—84no—
350Dic22—84no—
351C8×C11—22no—
352C8×C11—22no—
353C11⋊C8—22no—
354C11⋊C8—22no—
355C23×Q8C2×D1111yescharacteristic
356C22×Q16C2×D1111yescharacteristic
357C22×Q16C2×D1111yescharacteristic
358C22×SD16—111no—
359C22×SD16—111no—
360#542—118no—
361#542—224no—
362C2×C4⋊Q8—111no—
363C2×#126—221no—
364C2×#124—111no—
365C2×#124—221no—
366C2×#123—221no—
367C2×C22⋊Q8—221no—
368C2×C22⋊Q8C2×D1111yescharacteristic
369C2×#121—111no—
370#519—118no—
371#519—224no—
372C2×C4×Q8—111no—
373C2×C4×Q8—111no—
374C2×C4×Q8—111no—
375C2×C4×Q8—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—221no—
378C2×C4×Q8—221no—
379C2×C4×D4—111no—
380C2×#117—111no—
381C2×#117—111no—
382C2×#117—221no—
383C2×#117—221no—
384#485—118no—
385#482—118no—
386#477—118no—
387#475—118no—
388#464—118no—
389#464—118no—
390#451C2×D1118yescomplemented
391#448—118no—
392#441—118no—
393#440—118no—
394C4×Q16—118no—
395C4×SD16—118no—
396#433—118no—
397C2×#107—111no—
398C2×#107—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×C4⋊C8—111no—
402C2×C4⋊C8—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103C2×D1111yescharacteristic
408C2×#103C2×D1111yescharacteristic
409C2×#102—111no—
410C2×#102—111no—
411C2×C22⋊C8—111no—
412C2×C22⋊C8C2×D1111yescharacteristic
413C2×#97—111no—
414C2×C4×C8—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—44no—
419C22×C11#52512yes—
420C22×C11#57712yes—
421C22×C11#57812yes—
422C22×C11C23×D411yescharacteristic
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—84no—
427C4×C11—24no—
428C4×C11—24no—
429C4×C11—22no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11#52512yes—
433C4×C11C22×#4111yescharacteristic
434C4×C11C22×#4111yescharacteristic
435Dic11—22no—
436Dic11—22no—
437Dic11—22no—
438Dic11—22no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442C22×Q8—24no—
443C22×Q8—24no—
444C22×Q8—21no—
445C22×Q8—22no—
446C22×Q8—221no—
447C22×Q8C22×D1111yescharacteristic
448C22×Q8C22×D1114yes—
449C22×Q8C22×D1111yescharacteristic
450C22×Q8C22×D1111yescharacteristic
451C22×D4—111no—
452C22×D4—221no—
453C23×C4—21no—
454C23×C4—221no—
455C23×C4C22×D1111yescharacteristic
456C2×Q16—24no—
457C2×Q16—24no—
458C2×Q16C22×D1114yes—
459C2×Q16C22×D1114yes—
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—224no—
463C2×SD16—224no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8C22×D1111yescharacteristic
467C22×C8C22×D1111yescharacteristic
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470#126—228no—
471#124—114no—
472#124—222no—
473#124—228no—
474#123—228no—
475C22⋊Q8—22no—
476C22⋊Q8—228no—
477C22⋊Q8C22×D1114yes—
478#121—114no—
479#121—222no—
480C4×Q8—114no—
481C4×Q8—114no—
482C4×Q8—114no—
483C4×Q8—114no—
484C4×Q8—114no—
485C4×Q8—222no—
486C4×Q8—222no—
487C4×Q8—222no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—228no—
491C4×Q8—228no—
492C4×D4—114no—
493C4×D4—222no—
494#117—114no—
495#117—114no—
496#117—114no—
497#117—228no—
498#117—228no—
499#117—222no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—111no—
515C2×C22⋊C4—111no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—111no—
522C2×C42—111no—
523C2×C42—221no—
524C2×C42—221no—
525C2×C42—221no—
526C2×C42—221no—
527C2×C42—221no—
528C2×C42—221no—
529#107—114no—
530#107—114no—
531#106—114no—
532#106—114no—
533C4⋊C8—114no—
534C4⋊C8—114no—
535#103—114no—
536#103—114no—
537#103—114no—
538#103—114no—
539#103C22×D1114yes—
540#103C22×D1114yes—
541#102—114no—
542#102—114no—
543C22⋊C8—114no—
544C22⋊C8C22×D1114yes—
545#97—114no—
546C4×C8—114no—
547C2×C11—42no—
548C2×C11#312114yescomplemented
549C2×C11C2×#52511yescharacteristic
550C2×C11C2×#57711yescharacteristic
551C2×C11C2×#57811yescharacteristic
552D11—82no—
553C24—221no—
554C24D4×D1111yescharacteristic
555C2×Q8—216no—
556C2×Q8—28no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—24no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—224no—
568C2×Q8—882no—
569C2×Q8#434114yes—
570C2×Q8#434114yes—
571C2×Q8C23×D1112yes—
572C2×Q8C23×D1112yes—
573C2×Q8C23×D1112yes—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—221no—
577C2×D4—222no—
578C2×D4—222no—
579C2×D4—882no—
580C22×C4—28no—
581C22×C4—24no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—111no—
589C22×C4—111no—
590C22×C4—111no—
591C22×C4—111no—
592C22×C4—224no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—882no—
597C22×C4D4×D1112yes—
598C22×C4D4×D1111yescharacteristic
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601Q16—28no—
602Q16—28no—
603SD16—228no—
604SD16—228no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—112no—
608C2×C8—112no—
609C2×C8—222no—
610C2×C8—222no—
611C2×C8C23×D1112yes—
612C2×C8C23×D1112yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—114no—
616C4⋊C4—114no—
617C4⋊C4—112no—
618C4⋊C4—112no—
619C4⋊C4—112no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4C23×D1112yes—
630C22⋊C4—24no—
631C22⋊C4—114no—
632C22⋊C4—114no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—112no—
639C42—112no—
640C42—112no—
641C42—112no—
642C42—224no—
643C42—224no—
644C42—224no—
645C42—224no—
646C42—224no—
647C42—224no—
648C11C2×#312111yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—222no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23C2×D4×D1112yes—
657C23C2×D4×D1111yescharacteristic
658Q8—216no—
659Q8—24no—
660Q8—24no—
661Q8—22no—
662Q8—22no—
663Q8—22no—
664Q8—22no—
665Q8—42no—
666Q8—884no—
667Q8C2×#434114yes—
668Q8C2×#434114yes—
669D4—222no—
670D4—222no—
671D4—442no—
672D4—884no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—112no—
687C2×C4—112no—
688C2×C4—112no—
689C2×C4—112no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—884no—
701C2×C4C2×D4×D1112yes—
702C2×C4C2×D4×D1111yescharacteristic
703C2×C4C2×#434112yes—
704C2×C4C2×#434112yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—222no—
709C8—222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—884no—
718C22#1062311712yes—
719C22#1062329712yes—
720C22#1062330912yes—
721C22C22×D4×D1111yescharacteristic
722C4—24no—
723C4—24no—
724C4—22no—
725C4—42no—
726C4—42no—
727C4—222no—
728C4—222no—
729C4—222no—
730C4—222no—
731C4—442no—
732C4—442no—
733C4—442no—
734C4#1062311712yes—
735C4C22×#434111yescharacteristic
736C4C22×#434111yescharacteristic
737C2—42no—
738C2—882no—
739C2#1307884614yesdirect product factor
740C2C2×#1062311711yescharacteristic
741C2C2×#1062330911yescharacteristic
742C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#451D11
hypocenterC11C2×#3121
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#10623343C2semidirect
3. #13078846C2direct (N × H)
4. C2×#10622658C2semidirect
6. C2×#10622407C2semidirect
7. C2×#10622404C2semidirect
8. C2×#10622798C2semidirect
9. C2×#10622798C2semidirect
11. C2×#10622797C2semidirect
12. C2×#10622430C2semidirect
13. C2×Q16×Dic11C2semidirect
14. C2×#10622401C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#451C2semidirect
23. #10623343C22semidirect
46. C11×#451C22semidirect
56. #10622798C22semidirect
57. #10622798C22semidirect
58. #10622797C22semidirect
59. Q16×Dic11C22semidirect
68. #10622658C22semidirect
71. #10622430C22semidirect
72. #10622407C22semidirect
73. #10622404C22semidirect
74. #10622401C22semidirect
76. #10622333C22semidirect
287. C2×#451D11semidirect
390. #451C2×D11semidirect
548. C2×C11#3121semidirect
648. C11C2×#3121semidirect
739. C2#13078846direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231742
C2×#106233432
#130788462
C2×#106226582
C2×#106223502
C2×#106224072
C2×#106224042
C2×#106227982
C2×#106228402
C2×#106227972
C2×#106224302
C2×Q16×Dic112
C2×#106224012
C2×#106223332
C2×C11×#4512
C2×#312111