Finite Group Databasebeta

← C2×#13079444 #15624389

Subgroups — C2×#13079444 #15624389

Order 2816.

2342 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C2×D11×C22⋊Q8C211yesmaximal, characteristic, complemented
3#13079444C2116yesmaximal, direct product factor
4C2×#10622422C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622336C211yesmaximal, characteristic, complemented
7C2×#10622658C211yesmaximal, characteristic, complemented
8C2×#10622429C211yesmaximal, characteristic, complemented
9C2×#10622802C211yesmaximal, characteristic, complemented
10C2×#10622393C211yesmaximal, characteristic, complemented
11C2×#10622787C211yesmaximal, characteristic, complemented
12C2×#10622852C211yesmaximal, characteristic, complemented
13C2×#10622799C211yesmaximal, characteristic, complemented
14C2×#10622783C211yesmaximal, characteristic, complemented
15C2×#10622339C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic, complemented
21C22×C11×SD16C2211yescharacteristic, complemented
22C2×C11×C22⋊Q8C2211yescharacteristic
23#10623359—24no—
24#10623359C2218yes—
25C2×#66999C2211yescharacteristic
26C2×#66999C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C22×#4326C2211yescharacteristic, complemented
29C2×#66991C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66990—21no—
32C2×#66988—21no—
33C22×#4324C2211yescharacteristic, complemented
34C2×C4×C22⋊D11—21no—
35C2×C4×C22⋊D11—21no—
36C2×#66979C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4313C2211yescharacteristic
39C22×#4313C2211yescharacteristic
40D11×C22⋊Q8—24no—
41D11×C22⋊Q8C2218yescomplemented
42C2×#66950C2211yescharacteristic
43C2×#66949—21no—
44C2×C4⋊C4×D11—21no—
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×C22⋊C4×D11—21no—
47C2×#66931—21no—
48C11×#452C2218yescomplemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×C22⋊C8C2211yescharacteristic
52#10622852C2218yescomplemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66899C2211yescharacteristic, complemented
55C2×#66899C2211yescharacteristic, complemented
56C2×#66896C2211yescharacteristic, complemented
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622802C2218yescomplemented
59#10622799C2218yescomplemented
60#10622787C2218yescomplemented
61#10622783C2218yescomplemented
62C2×(C2×D11)⋊C8C2211yescharacteristic
63C2×(C2×D11)⋊C8C2211yescharacteristic
64C2×#66882C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×#66880C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622429C2218yescomplemented
72#10622422C2218yescomplemented
73#10622393C2218yescomplemented
74#10622390C2218yescomplemented
75#10622339C2218yescomplemented
76#10622336C2218yescomplemented
77C24×D11D411yescharacteristic
78C2×C11×#41—22no—
79C2×C11×#41—42no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×Q8×C11C2311yescharacteristic
84C22×D4×C11—21no—
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C23×Dic11D411yescharacteristic
91C2×Q8×D11—22no—
92C2×Q8×D11—42no—
93C2×Q8×D11—42no—
94C2×Q8×D11C2314yes—
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11—42no—
98C22×C4×D11—42no—
99C22×C4×D11D411yescharacteristic
100C22×C4×D11D411yescharacteristic
101C22×C4×D11D414yes—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2314yes—
105C22×Dic22—21no—
106C22×Dic22C2311yescharacteristic
107C2×C11×Q16—42no—
108C2×C11×Q16C2314yescomplemented
109C2×C11×SD16—42no—
110C2×C11×SD16C2314yescomplemented
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8C2314yes—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C22⋊C4—21no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122#66999—22no—
123#66999—22no—
124#66999—22no—
125#66999C2314yes—
126#66999C2314yes—
127#66999C2314yes—
128C2×#4326—42no—
129C2×#4326C2314yescomplemented
130#66991—22no—
131#66991—22no—
132#66991C2314yes—
133#66991C2314yes—
134#66990—28no—
135#66988—28no—
136C2×#4324—42no—
137C2×#4324C2314yescomplemented
138C4×C22⋊D11—28no—
139C4×C22⋊D11—28no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144#66979—22no—
145#66979C2314yes—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150#66977—22no—
151#66977C2314yes—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×C4×Dic11—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×#4313—42no—
161C2×#4313—42no—
162C2×#4313C2314yes—
163C2×#4313C2314yes—
164#66950—22no—
165#66950C2314yes—
166#66949—28no—
167C4⋊C4×D11—28no—
168C4⋊C4×D11—22no—
169C4⋊C4×D11C2314yes—
170C22⋊C4×D11—28no—
171#66931—28no—
172C11×#103C2314yescomplemented
173C11×#102C2314yescomplemented
174C11×C22⋊C8C2314yes—
175#66899C2314yescomplemented
176#66899C2314yescomplemented
177#66899C2314yescomplemented
178#66896C2314yescomplemented
179C22⋊(C11⋊C8)C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182#66882C2314yescomplemented
183#66881C2314yescomplemented
184#66880C2314yescomplemented
185#66880C2314yescomplemented
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3196—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—24no—
192C23×D11—42no—
193C23×D11—42no—
194C23×D11C2×D411yescharacteristic
195C23×D11C2×D411yescharacteristic
196C23×D11C2×D414yes—
197C11×#41—44no—
198C11×#41—44no—
199C11×#41—48no—
200C2×Q8×C11—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—22no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11—22no—
206C2×Q8×C11C2412yes—
207C2×Q8×C11C2412yes—
208C2×D4×C11—24no—
209C2×D4×C11—21no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—44no—
213C2×D4×C11C2412yes—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—24no—
220C22×C4×C11—44no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—42no—
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D414yes—
237Q8×D11—44no—
238Q8×D11—44no—
239Q8×D11—48no—
240C2×C4×D11—24no—
241C2×C4×D11—24no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—22no—
246C2×C4×D11—42no—
247C2×C4×D11—42no—
248C2×C4×D11—48no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—44no—
252C2×C4×D11—44no—
253C2×C4×D11C2×D412yes—
254C2×C4×D11C2×D412yes—
255C2×C4×D11C2×D414yes—
256C2×C4×D11C2×D414yes—
257C2×C4×D11C2412yes—
258C2×C4×D11C2412yes—
259C2×Dic22—24no—
260C2×Dic22—21no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—44no—
264C2×Dic22C2412yes—
265C11×Q16—44no—
266C11×SD16—44no—
267C2×C8×C11—22no—
268C2×C8×C11—22no—
269C2×C8×C11C2412yes—
270C2×C8×C11C2412yes—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4C2412yes—
274C11×C22⋊C4—24no—
275C22⋊Dic11—24no—
276C22⋊Dic11—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11—24no—
279#4326—44no—
280#4324—44no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285C4⋊Dic11—24no—
286C4⋊Dic11—21no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11C2412yes—
290C4⋊Dic11C2412yes—
291C4⋊Dic11C2412yes—
292Dic11⋊C4—24no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295Dic11⋊C4—24no—
296Dic11⋊C4—24no—
297C4×Dic11—24no—
298C2×C11⋊C8—22no—
299C2×C11⋊C8—22no—
300C2×C11⋊C8C2412yes—
301C2×C11⋊C8C2412yes—
302#4313—44no—
303#4313—44no—
304C2×#525—111no—
305C22×C22⋊Q8—111no—
306#3196—1116no—
307C2×#484—111no—
308C2×#481—111no—
309C2×#485—111no—
310C2×#485—111no—
311C2×#470—111no—
312C2×#470—111no—
313C2×#468—111no—
314C2×#468—111no—
315C2×#452—111no—
316C2×#452D1111yescharacteristic, complemented
317C2×#451—111no—
318C2×#448—111no—
319C2×#407—111no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11C22×D412yes—
328C23×C11C22×D411yescharacteristic
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—28no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—416no—
338C22×D11#13714yes—
339C22×D11C22×D412yes—
340C22×D11C22×D412yes—
341Q8×C11—22no—
342Q8×C11—22no—
343Q8×C11—22no—
344Q8×C11—22no—
345Q8×C11—42no—
346Q8×C11—42no—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—48no—
350D4×C11—42no—
351C2×C4×C11—22no—
352C2×C4×C11—24no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—48no—
359C2×C4×C11—42no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11C22×D412yes—
363C2×C4×C11C22×D411yescharacteristic
364C2×C4×C11H(5,𝔽2)12yes—
365C2×C4×C11H(5,𝔽2)12yes—
366C2×C4×C11C2511yescharacteristic
367C22⋊D11—48no—
368C22⋊D11—48no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—44no—
376C2×Dic11—42no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11C22×D412yes—
381C2×Dic11C22×D412yes—
382C4×D11—24no—
383C4×D11—24no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—44no—
389C4×D11—44no—
390C4×D11—48no—
391C4×D11—48no—
392Dic22—22no—
393Dic22—22no—
394Dic22—48no—
395Dic22—42no—
396C8×C11—22no—
397C8×C11—22no—
398C11⋊C8—22no—
399C11⋊C8—22no—
400C22×#41C2×D1111yescharacteristic
401C23×Q8—111no—
402C24×C4—111no—
403C22×Q16—111no—
404C22×Q16C2×D1111yescharacteristic, complemented
405C22×SD16—111no—
406C22×SD16C2×D1111yescharacteristic, complemented
407C22×M16—111no—
408C22×M16—111no—
409#525—118no—
410#525—224no—
411C2×#123—221no—
412C2×C22⋊Q8—111no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—111no—
415C2×C22⋊Q8—111no—
416C2×C22⋊Q8—118no—
417C2×C22⋊Q8—111no—
418C2×C22⋊Q8—221no—
419C2×C22⋊Q8—221no—
420C2×C22⋊Q8—224no—
421C2×C22⋊Q8C2×D1111yescharacteristic
422C2×#121—111no—
423C2×#121—111no—
424C2×#120—221no—
425C2×C4×D4—221no—
426C2×C4×D4—221no—
427C2×#117—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—221no—
430C22×C22⋊C4—221no—
431#485—118no—
432#485—118no—
433#484—118no—
434#481—118no—
435#470—118no—
436#470—118no—
437#468—118no—
438#468—118no—
439#452—118no—
440#452C2×D1118yescomplemented
441#451—118no—
442#448—118no—
443C2×#107—111no—
444C2×#107—111no—
445C2×#106—111no—
446C2×#106—111no—
447C2×#103—111no—
448C2×#103—111no—
449C2×#103—111no—
450C2×#103—111no—
451C2×#103—111no—
452C2×#103C2×D1111yescharacteristic, complemented
453C2×#102—111no—
454C2×#102C2×D1111yescharacteristic, complemented
455#407—118no—
456C2×C22⋊C8—111no—
457C2×C22⋊C8—111no—
458C2×C22⋊C8—111no—
459C2×C22⋊C8C2×D1111yescharacteristic
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—44no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—84no—
468C22×C11#53412yes—
469C22×C11C2×#13712yes—
470C22×C11#57512yes—
471C22×C11C23×D411yescharacteristic
472C2×D11—22no—
473C2×D11—28no—
474C2×D11—22no—
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—416no—
479C2×D11—44no—
480C2×D11C2×#13714yes—
481C4×C11—22no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11#53412yes—
486C4×C11C2×H(5,𝔽2)11yescharacteristic
487C4×C11C2×H(5,𝔽2)11yescharacteristic
488Dic11—22no—
489Dic11—22no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494C25—111no—
495C2×#41—22no—
496C2×#41—42no—
497C2×#41—42no—
498C2×#41C22×D1114yes—
499C22×Q8—114no—
500C22×Q8—111no—
501C22×Q8—221no—
502C22×Q8—222no—
503C22×Q8—442no—
504C22×Q8—442no—
505C22×Q8C22×D1111yescharacteristic
506C22×Q8C22×D1111yescharacteristic
507C22×D4—21no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4C22×D1111yescharacteristic
511C23×C4—21no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—114no—
518C23×C4—114no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4—442no—
522C23×C4—442no—
523C23×C4C22×D1111yescharacteristic
524C2×Q16—42no—
525C2×Q16—114no—
526C2×Q16—442no—
527C2×Q16C22×D1114yescomplemented
528C2×SD16—42no—
529C2×SD16—114no—
530C2×SD16—442no—
531C2×SD16C22×D1114yescomplemented
532C2×M16—114no—
533C2×M16—114no—
534C2×M16—442no—
535C2×M16—442no—
536C22×C8—111no—
537C22×C8—111no—
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540#123—228no—
541C22⋊Q8—22no—
542C22⋊Q8—114no—
543C22⋊Q8—114no—
544C22⋊Q8—114no—
545C22⋊Q8—114no—
546C22⋊Q8—114no—
547C22⋊Q8—228no—
548C22⋊Q8—228no—
549C22⋊Q8—222no—
550C22⋊Q8—222no—
551C22⋊Q8—222no—
552C22⋊Q8—222no—
553C22⋊Q8—222no—
554C22⋊Q8C22×D1114yes—
555#121—114no—
556#121—114no—
557#121—222no—
558#121—222no—
559#120—228no—
560C4×D4—228no—
561C4×D4—228no—
562#117—114no—
563#117—222no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—111no—
566C2×C4⋊C4—111no—
567C2×C4⋊C4—111no—
568C2×C4⋊C4—114no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—228no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4—221no—
573C2×C4⋊C4—221no—
574C2×C4⋊C4—221no—
575C2×C4⋊C4—221no—
576C2×C4⋊C4—221no—
577C2×C4⋊C4C22×D1111yescharacteristic
578C2×C22⋊C4—21no—
579C2×C22⋊C4—228no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4—221no—
583C2×C22⋊C4—221no—
584C2×C22⋊C4—221no—
585C2×C22⋊C4—221no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C42—221no—
589#107—114no—
590#107—114no—
591#106—114no—
592#106—114no—
593#103—114no—
594#103—114no—
595#103—114no—
596#103—114no—
597#103—114no—
598#103C22×D1114yescomplemented
599#102—114no—
600#102C22×D1114yescomplemented
601C22⋊C8—114no—
602C22⋊C8—114no—
603C22⋊C8—114no—
604C22⋊C8C22×D1114yes—
605C2×C11—42no—
606C2×C11—82no—
607C2×C11#319614yescomplemented
608C2×C11C2×#53411yescharacteristic
609C2×C11C22×#13711yescharacteristic
610C2×C11C2×#57511yescharacteristic
611D11—24no—
612D11—42no—
613C24—21no—
614C24—111no—
615C24—111no—
616C24—114no—
617C24—224no—
618C24—442no—
619C24—442no—
620C24D4×D1111yescharacteristic
621#41—44no—
622#41—44no—
623#41—48no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—112no—
631C2×Q8—224no—
632C2×Q8—221no—
633C2×Q8—222no—
634C2×Q8—222no—
635C2×Q8—444no—
636C2×Q8—444no—
637C2×Q8—444no—
638C2×Q8—448no—
639C2×Q8C23×D1112yes—
640C2×Q8C23×D1112yes—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—44no—
646C2×D4—224no—
647C2×D4—224no—
648C2×D4—444no—
649C2×D4—444no—
650C2×D4C23×D1112yes—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—44no—
658C22×C4—111no—
659C22×C4—111no—
660C22×C4—114no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—114no—
666C22×C4—114no—
667C22×C4—224no—
668C22×C4—224no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—448no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—442no—
681C22×C4—442no—
682C22×C4—444no—
683C22×C4—444no—
684C22×C4—442no—
685C22×C4D4×D1112yes—
686C22×C4D4×D1111yescharacteristic
687C22×C4C23×D1112yes—
688C22×C4C23×D1111yescharacteristic
689Q16—44no—
690Q16—444no—
691SD16—44no—
692SD16—444no—
693M16—444no—
694M16—444no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—112no—
698C2×C8—112no—
699C2×C8—222no—
700C2×C8—222no—
701C2×C8C23×D1112yes—
702C2×C8C23×D1112yes—
703C4⋊C4—24no—
704C4⋊C4—21no—
705C4⋊C4—112no—
706C4⋊C4—112no—
707C4⋊C4—112no—
708C4⋊C4—224no—
709C4⋊C4—224no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—221no—
714C4⋊C4—221no—
715C4⋊C4—221no—
716C4⋊C4—224no—
717C4⋊C4C23×D1112yes—
718C22⋊C4—24no—
719C22⋊C4—224no—
720C22⋊C4—224no—
721C22⋊C4—224no—
722C22⋊C4—224no—
723C22⋊C4—224no—
724C22⋊C4—224no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C42—224no—
728C11C2×#319611yescharacteristic, complemented, Sylow
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—114no—
737C23—112no—
738C23—112no—
739C23—228no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—444no—
746C23—444no—
747C23—4416no—
748C23C2×D4×D1112yes—
749C23C2×D4×D1111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—222no—
757Q8—222no—
758Q8—448no—
759Q8—442no—
760D4—22no—
761D4—22no—
762D4—48no—
763D4—42no—
764D4—448no—
765D4—448no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—112no—
778C2×C4—112no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—224no—
782C2×C4—224no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—444no—
792C2×C4—444no—
793C2×C4—448no—
794C2×C4—448no—
795C2×C4—444no—
796C2×C4—442no—
797C2×C4—442no—
798C2×C4—442no—
799C2×C4—442no—
800C2×C4C2×D4×D1112yes—
801C2×C4C2×D4×D1111yescharacteristic
802C2×C4#6703712yes—
803C2×C4#6703712yes—
804C2×C4C24×D1111yescharacteristic
805C8—22no—
806C8—22no—
807C8—222no—
808C8—222no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—84no—
817C22—114no—
818C22—222no—
819C22—228no—
820C22—222no—
821C22—222no—
822C22—222no—
823C22—222no—
824C22—4416no—
825C22—444no—
826C22#1062312012yes—
827C22#1062329912yes—
828C22D11×#13712yes—
829C22C22×D4×D1111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—222no—
835C4—222no—
836C4—442no—
837C4—442no—
838C4—442no—
839C4—442no—
840C4#1062312012yes—
841C4C2×#6703711yescharacteristic
842C4C2×#6703711yescharacteristic
843C2—42no—
844C2—82no—
845C2—224no—
846C2—442no—
847C2#1307944414yesdirect product factor
848C2C2×#1062312011yescharacteristic
849C2C2×D11×#13711yescharacteristic
850C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
prime radicalC2×#10623359C2
hypercenterC2×#452D11
hypocenterC11C2×#3196
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊Q8C2semidirect
3. #13079444C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622336C2semidirect
7. C2×#10622658C2semidirect
8. C2×#10622429C2semidirect
9. C2×#10622802C2semidirect
10. C2×#10622393C2semidirect
11. C2×#10622787C2semidirect
12. C2×#10622852C2semidirect
13. C2×#10622799C2semidirect
14. C2×#10622783C2semidirect
15. C2×#10622339C2semidirect
16. C2×C11×#452C2semidirect
20. C22×C11×Q16C22semidirect
21. C22×C11×SD16C22semidirect
28. C22×#4326C22semidirect
33. C22×#4324C22semidirect
41. D11×C22⋊Q8C22semidirect
48. C11×#452C22semidirect
49. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
52. #10622852C22semidirect
53. C2×#66899C22semidirect
54. C2×#66899C22semidirect
55. C2×#66899C22semidirect
56. C2×#66896C22semidirect
58. #10622802C22semidirect
59. #10622799C22semidirect
60. #10622787C22semidirect
61. #10622783C22semidirect
64. C2×#66882C22semidirect
65. C2×#66881C22semidirect
66. C2×#66880C22semidirect
67. C2×#66880C22semidirect
68. #10622658C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622429C22semidirect
72. #10622422C22semidirect
73. #10622393C22semidirect
74. #10622390C22semidirect
75. #10622339C22semidirect
76. #10622336C22semidirect
108. C2×C11×Q16C23semidirect
110. C2×C11×SD16C23semidirect
129. C2×#4326C23semidirect
137. C2×#4324C23semidirect
172. C11×#103C23semidirect
173. C11×#102C23semidirect
175. #66899C23semidirect
176. #66899C23semidirect
177. #66899C23semidirect
178. #66896C23semidirect
182. #66882C23semidirect
183. #66881C23semidirect
184. #66880C23semidirect
185. #66880C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
316. C2×#452D11semidirect
404. C22×Q16C2×D11semidirect
406. C22×SD16C2×D11semidirect
440. #452C2×D11semidirect
452. C2×#103C2×D11semidirect
454. C2×#102C2×D11semidirect
527. C2×Q16C22×D11semidirect
531. C2×SD16C22×D11semidirect
598. #103C22×D11semidirect
600. #102C22×D11semidirect
607. C2×C11#3196semidirect
728. C11C2×#3196semidirect
847. C2#13079444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×D11×C22⋊Q82
#130794442
C2×#106224222
C2×#106223902
C2×#106223362
C2×#106226582
C2×#106224292
C2×#106228022
C2×#106223932
C2×#106227872
C2×#106228522
C2×#106227992
C2×#106227832
C2×#106223392
C2×C11×#4522
C2×#319611