Finite Group Databasebeta

← C2×#13079524 #15624488

Subgroups — C2×#13079524 #15624488

Order 2816.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623160C211yesmaximal, characteristic, complemented
2C2×#10623364C211yesmaximal, characteristic, complemented
3#13079524C2116yesmaximal, direct product factor
4C2×#10622348C211yesmaximal, characteristic, complemented
5C2×#10622390C211yesmaximal, characteristic, complemented
6C2×#10622418C211yesmaximal, characteristic, complemented
7C2×#10622656C211yesmaximal, characteristic, complemented
8C2×#10622802C211yesmaximal, characteristic, complemented
9C2×#10622395C211yesmaximal, characteristic, complemented
10C2×#10622420C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×#10622800C211yesmaximal, characteristic, complemented
13C2×#10622851C211yesmaximal, characteristic, complemented
14C2×#10622785C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#452C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23#10623364—24no—
24#10623364C2218yescomplemented
25C2×#66999C2211yescharacteristic
26C2×#66999C2211yescharacteristic
27C2×#66999C2211yescharacteristic
28C22×#4325C2211yescharacteristic
29C2×#66992—21no—
30C2×#66992—21no—
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983—21no—
35C2×#66983C2211yescharacteristic
36C22×C4⋊Dic11C2211yescharacteristic
37C2×#66977—21no—
38C22×#4313C2211yescharacteristic
39C22×C8×D11C2211yescharacteristic
40#10623160—24no—
41#10623160C2218yescomplemented
42C2×#66949—21no—
43C2×#66948—21no—
44C2×#66948C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66937—21no—
47C2×#66937—21no—
48C11×#452C2218yescomplemented
49C2×C11×#103C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622802C2218yescomplemented
59#10622800C2218yescomplemented
60#10622785C2218yescomplemented
61#10622784C2218yescomplemented
62C2×#66885C2211yescharacteristic
63C2×#66885C2211yescharacteristic
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66881C2211yescharacteristic
67C2×#66881C2211yescharacteristic
68#10622656C2218yescomplemented
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71#10622420C2218yescomplemented
72#10622418C2218yescomplemented
73#10622395C2218yescomplemented
74#10622390C2218yescomplemented
75#10622348C2218yescomplemented
76#10622340C2218yescomplemented
77C2×C11×#41—22no—
78C2×C11×#41—42no—
79C2×C11×#41—42no—
80C2×C11×#41C2314yes—
81C22×Q8×C11C2311yescharacteristic
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11D411yescharacteristic
91C22×C22⋊D11D411yescharacteristic
92C23×Dic11—21no—
93C2×#4343—22no—
94C2×#4343—42no—
95C2×#4343—42no—
96C2×#4343C2314yes—
97C2×#4339—42no—
98C2×#4339—42no—
99C2×#4339D414yes—
100C2×#4339C2314yes—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44D411yescharacteristic
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C22×C4×D11C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×Dic22D411yescharacteristic
110C2×C11×Q16—42no—
111C2×C11×Q16C2314yes—
112C2×C11×SD16—42no—
113C2×C11×SD16C2314yes—
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8C2314yes—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123#66999—22no—
124#66999—22no—
125#66999—22no—
126#66999C2314yes—
127#66999C2314yes—
128#66999C2314yes—
129C2×#4325—42no—
130C2×#4325C2314yes—
131#66992—28no—
132#66992—28no—
133#66991—22no—
134#66991—22no—
135#66991C2314yes—
136#66991C2314yes—
137C2×#4323—42no—
138C2×#4323C2314yes—
139#66983—22no—
140#66983—28no—
141#66983C2314yes—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11—22no—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152C2×C4⋊Dic11C2314yes—
153#66977—28no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×Dic11⋊C4—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×#4313—42no—
161C2×#4313C2314yes—
162C2×C8×D11—42no—
163C2×C8×D11C2314yes—
164#66949—28no—
165#66948—28no—
166#66948—22no—
167#66948C2314yes—
168C4⋊C4×D11—22no—
169C4⋊C4×D11C2314yes—
170#66937—28no—
171#66937—28no—
172C11×#103C2314yes—
173C11×#102C2314yes—
174C11×C22⋊C8C2314yes—
175#66899C2314yes—
176#66899C2314yes—
177#66899C2314yes—
178#66896C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66885C2314yes—
181#66885C2314yes—
182(C2×D11)⋊C8C2314yes—
183(C2×D11)⋊C8C2314yes—
184#66881C2314yes—
185#66881C2314yes—
186#66872C2314yes—
187#66872C2314yes—
188C2×#3204—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C23×D11C2×D411yescharacteristic
193C23×D11C2×D411yescharacteristic
194C11×#41—44no—
195C11×#41—44no—
196C11×#41—48no—
197C2×Q8×C11—21no—
198C2×Q8×C11—21no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11—22no—
203C2×Q8×C11C2412yes—
204C2×Q8×C11C2412yes—
205C2×D4×C11—24no—
206C2×D4×C11—21no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—44no—
210C2×D4×C11C2412yes—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—24no—
217C22×C4×C11—44no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—42no—
226C2×C22⋊D11—42no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11—82no—
229C2×C22⋊D11—82no—
230C2×C22⋊D11C2×D414yes—
231C2×C22⋊D11C2×D414yes—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—24no—
236C22×Dic11—82no—
237C22×Dic11C2×D411yescharacteristic
238C22×Dic11C2×D411yescharacteristic
239#4343—44no—
240#4343—44no—
241#4343—48no—
242#4339—48no—
243#4339—44no—
244#4339—44no—
245C2×D44—24no—
246C2×D44—24no—
247C2×D44—21no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44—42no—
251C2×D44—44no—
252C2×D44—82no—
253C2×D44C2×D414yes—
254C2×D44C2412yes—
255C2×C4×D11—24no—
256C2×C4×D11—24no—
257C2×C4×D11—22no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—22no—
261C2×C4×D11—44no—
262C2×C4×D11—82no—
263C2×C4×D11C2×D412yes—
264C2×C4×D11C2×D412yes—
265C2×C4×D11C2412yes—
266C2×C4×D11C2412yes—
267C2×Dic22—42no—
268C2×Dic22C2×D414yes—
269C11×Q16—44no—
270C11×SD16—44no—
271C2×C8×C11—22no—
272C2×C8×C11—22no—
273C2×C8×C11C2412yes—
274C2×C8×C11C2412yes—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—24no—
277C11×C4⋊C4C2412yes—
278C11×C22⋊C4—24no—
279C22⋊Dic11—24no—
280C22⋊Dic11—24no—
281#4325—44no—
282#4323—44no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288C4⋊Dic11—21no—
289C4⋊Dic11—24no—
290C4⋊Dic11—21no—
291C4⋊Dic11—21no—
292C4⋊Dic11C2412yes—
293C4⋊Dic11C2412yes—
294C4⋊Dic11C2412yes—
295Dic11⋊C4—24no—
296Dic11⋊C4—24no—
297Dic11⋊C4—24no—
298Dic11⋊C4—24no—
299C2×C11⋊C8—22no—
300C2×C11⋊C8—22no—
301C2×C11⋊C8C2412yes—
302C2×C11⋊C8C2412yes—
303#4313—44no—
304C8×D11—44no—
305C2×#537—111no—
306C2×#537—111no—
307#3204—1116no—
308C2×#481—111no—
309C2×#481—111no—
310C2×#483—111no—
311C2×#483—111no—
312C2×#470—111no—
313C2×#469—111no—
314C2×#465—111no—
315C2×#465—111no—
316C2×#452—111no—
317C2×#452D1111yescharacteristic, complemented
318C2×#449—111no—
319C2×#449—111no—
320C2×#408—111no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11C22×D412yes—
329C23×C11C22×D411yescharacteristic
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11C22×D412yes—
341C22×D11C22×D412yes—
342Q8×C11—22no—
343Q8×C11—22no—
344Q8×C11—22no—
345Q8×C11—22no—
346Q8×C11—42no—
347Q8×C11—42no—
348D4×C11—22no—
349D4×C11—22no—
350D4×C11—48no—
351D4×C11—42no—
352C2×C4×C11—22no—
353C2×C4×C11—24no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—48no—
360C2×C4×C11—42no—
361C2×C4×C11—42no—
362C2×C4×C11—42no—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11H(5,𝔽2)12yes—
366C2×C4×C11H(5,𝔽2)12yes—
367C2×C4×C11C2511yescharacteristic
368C22⋊D11—44no—
369C22⋊D11—44no—
370C22⋊D11—84no—
371C22⋊D11—84no—
372C22⋊D11—84no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—42no—
381C2×Dic11—84no—
382C2×Dic11C22×D412yes—
383C2×Dic11C22×D412yes—
384D44—22no—
385D44—22no—
386D44—44no—
387D44—48no—
388D44—42no—
389D44—84no—
390C4×D11—24no—
391C4×D11—24no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—22no—
396C4×D11—48no—
397C4×D11—84no—
398Dic22—44no—
399C8×C11—22no—
400C8×C11—22no—
401C11⋊C8—22no—
402C11⋊C8—22no—
403C22×#41—111no—
404C22×#41—111no—
405C22×#41C2×D1111yescharacteristic
406C22×Q16C2×D1111yescharacteristic
407C22×SD16—111no—
408C22×SD16C2×D1111yescharacteristic
409C22×D8—111no—
410C22×M16—111no—
411C23×C8—111no—
412#537—118no—
413#537—118no—
414#537—224no—
415#537—224no—
416C2×C22⋊Q8—111no—
417C2×C22⋊Q8—111no—
418C2×C22⋊Q8—111no—
419C2×C22⋊Q8—221no—
420C2×C22⋊Q8—221no—
421C2×C22⋊Q8C2×D1111yescharacteristic
422C2×#121—111no—
423C2×#121—111no—
424C2×#121—111no—
425C2×#121—111no—
426C2×#121—221no—
427C2×#121—221no—
428C2×#121—221no—
429C2×#121—221no—
430C2×#121—221no—
431C2×#121—221no—
432C22×C4⋊C4—111no—
433C22×C4⋊C4—111no—
434#483—118no—
435#483—118no—
436#481—118no—
437#481—118no—
438#470—118no—
439#469—118no—
440#465—118no—
441#465—118no—
442#452—118no—
443#452C2×D1118yescomplemented
444#449—118no—
445#449—118no—
446C2×#106—111no—
447C2×#106—111no—
448C2×#106—111no—
449C2×#106—111no—
450C2×#103—111no—
451C2×#103—111no—
452C2×#103—111no—
453C2×#103C2×D1111yescharacteristic
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102C2×D1111yescharacteristic
458#408—118no—
459C2×C22⋊C8—111no—
460C2×C22⋊C8—111no—
461C2×C22⋊C8—111no—
462C2×C22⋊C8C2×D1111yescharacteristic
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—44no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—84no—
471C22×C11#53412yes—
472C22×C11#57712yes—
473C22×C11#57712yes—
474C22×C11C23×D411yescharacteristic
475C2×D11—22no—
476C2×D11—22no—
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—44no—
482C2×D11—44no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—84no—
487C4×C11—22no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11#53412yes—
492C4×C11C2×H(5,𝔽2)11yescharacteristic
493C4×C11C2×H(5,𝔽2)11yescharacteristic
494Dic11—22no—
495Dic11—22no—
496Dic11—42no—
497Dic11—42no—
498Dic11—42no—
499C2×#41—22no—
500C2×#41—42no—
501C2×#41—42no—
502C2×#41—114no—
503C2×#41—114no—
504C2×#41—114no—
505C2×#41—222no—
506C2×#41—442no—
507C2×#41—442no—
508C2×#41—442no—
509C2×#41—442no—
510C2×#41C22×D1114yes—
511C22×Q8—111no—
512C22×Q8C22×D1111yescharacteristic
513C22×Q8C22×D1111yescharacteristic
514C22×D4—21no—
515C22×D4—111no—
516C22×D4—111no—
517C22×D4—111no—
518C22×D4—111no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4—221no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4C22×D1111yescharacteristic
525C23×C4—21no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—221no—
529C23×C4—221no—
530C23×C4—221no—
531C23×C4C22×D1111yescharacteristic
532C2×Q16—42no—
533C2×Q16C22×D1114yes—
534C2×SD16—42no—
535C2×SD16—114no—
536C2×SD16—442no—
537C2×SD16C22×D1114yes—
538C2×D8—114no—
539C2×D8—442no—
540C2×M16—114no—
541C2×M16—442no—
542C22×C8—111no—
543C22×C8—111no—
544C22×C8—114no—
545C22×C8—442no—
546C22×C8C22×D1111yescharacteristic
547C22×C8C22×D1111yescharacteristic
548C22⋊Q8—22no—
549C22⋊Q8—114no—
550C22⋊Q8—114no—
551C22⋊Q8—114no—
552C22⋊Q8—228no—
553C22⋊Q8—228no—
554C22⋊Q8—222no—
555C22⋊Q8—222no—
556C22⋊Q8—222no—
557C22⋊Q8C22×D1114yes—
558#121—114no—
559#121—114no—
560#121—114no—
561#121—114no—
562#121—228no—
563#121—228no—
564#121—222no—
565#121—228no—
566#121—228no—
567#121—222no—
568#121—222no—
569#121—228no—
570#121—228no—
571#121—222no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—111no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—111no—
576C2×C4⋊C4—114no—
577C2×C4⋊C4—114no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—221no—
580C2×C4⋊C4—221no—
581C2×C4⋊C4—221no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4—221no—
584C2×C4⋊C4—222no—
585C2×C4⋊C4C22×D1111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594#106—114no—
595#106—114no—
596#106—114no—
597#106—114no—
598#103—114no—
599#103—114no—
600#103—114no—
601#103C22×D1114yes—
602#102—114no—
603#102—114no—
604#102—114no—
605#102C22×D1114yes—
606C22⋊C8—114no—
607C22⋊C8—114no—
608C22⋊C8—114no—
609C22⋊C8C22×D1114yes—
610C2×C11—42no—
611C2×C11—82no—
612C2×C11#320414yescomplemented
613C2×C11C2×#53411yescharacteristic
614C2×C11C2×#57711yescharacteristic
615C2×C11C2×#57711yescharacteristic
616D11—42no—
617D11—42no—
618D11—82no—
619C24—21no—
620C24—111no—
621C24—111no—
622C24—221no—
623C24D4×D1111yescharacteristic
624#41—44no—
625#41—44no—
626#41—48no—
627#41—448no—
628#41—444no—
629#41—444no—
630#41—444no—
631#41—444no—
632#41—448no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—22no—
638C2×Q8—22no—
639C2×Q8—114no—
640C2×Q8—442no—
641C2×Q8C23×D1112yes—
642C2×Q8C23×D1112yes—
643C2×D4—24no—
644C2×D4—21no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—44no—
648C2×D4—114no—
649C2×D4—114no—
650C2×D4—114no—
651C2×D4—112no—
652C2×D4—224no—
653C2×D4—224no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—221no—
658C2×D4—222no—
659C2×D4—222no—
660C2×D4—442no—
661C2×D4—444no—
662C2×D4—442no—
663C2×D4—442no—
664C2×D4—882no—
665C2×D4—882no—
666C2×D4—882no—
667C2×D4—882no—
668C2×D4C23×D1112yes—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—24no—
675C22×C4—44no—
676C22×C4—111no—
677C22×C4—111no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—224no—
683C22×C4—224no—
684C22×C4—222no—
685C22×C4—222no—
686C22×C4—222no—
687C22×C4—222no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—224no—
692C22×C4—444no—
693C22×C4—882no—
694C22×C4—882no—
695C22×C4D4×D1112yes—
696C22×C4D4×D1111yescharacteristic
697C22×C4C23×D1112yes—
698C22×C4C23×D1111yescharacteristic
699Q16—44no—
700SD16—44no—
701SD16—444no—
702D8—444no—
703M16—444no—
704C2×C8—22no—
705C2×C8—22no—
706C2×C8—112no—
707C2×C8—112no—
708C2×C8—222no—
709C2×C8—222no—
710C2×C8—444no—
711C2×C8C23×D1112yes—
712C2×C8C23×D1112yes—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—112no—
716C4⋊C4—112no—
717C4⋊C4—112no—
718C4⋊C4—224no—
719C4⋊C4—224no—
720C4⋊C4—224no—
721C4⋊C4—224no—
722C4⋊C4—224no—
723C4⋊C4—221no—
724C4⋊C4—221no—
725C4⋊C4—221no—
726C4⋊C4C23×D1112yes—
727C22⋊C4—24no—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C11C2×#320411yescharacteristic, complemented, Sylow
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—112no—
744C23—112no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—442no—
753C23—442no—
754C23—442no—
755C23C2×D4×D1112yes—
756C23C2×D4×D1111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8—22no—
761Q8—42no—
762Q8—42no—
763Q8—444no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—42no—
768D4—222no—
769D4—222no—
770D4—444no—
771D4—448no—
772D4—444no—
773D4—444no—
774D4—442no—
775D4—884no—
776D4—884no—
777D4—884no—
778D4—884no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—48no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—112no—
791C2×C4—112no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—224no—
795C2×C4—224no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—448no—
804C2×C4—442no—
805C2×C4—442no—
806C2×C4—442no—
807C2×C4—884no—
808C2×C4—884no—
809C2×C4C2×D4×D1112yes—
810C2×C4C2×D4×D1111yescharacteristic
811C2×C4#6703712yes—
812C2×C4#6703712yes—
813C2×C4C24×D1111yescharacteristic
814C8—22no—
815C8—22no—
816C8—222no—
817C8—222no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—84no—
826C22—222no—
827C22—222no—
828C22—222no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—444no—
833C22—444no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—884no—
838C22#1062312012yes—
839C22#1062330112yes—
840C22#1062330912yes—
841C22C22×D4×D1111yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—222no—
847C4—222no—
848C4—442no—
849C4—442no—
850C4—442no—
851C4#1062312012yes—
852C4C2×#6703711yescharacteristic
853C4C2×#6703711yescharacteristic
854C2—42no—
855C2—82no—
856C2—442no—
857C2—442no—
858C2—882no—
859C2#1307952414yesdirect product factor
860C2C2×#1062312011yescharacteristic
861C2C2×#1062330111yescharacteristic
862C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#452C2
socleC23×C11C22×D4
hypercenterC2×#452D11
hypocenterC11C2×#3204
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
1. C2×#10623160C2semidirect
2. C2×#10623364C2semidirect
3. #13079524C2direct (N × H)
4. C2×#10622348C2semidirect
5. C2×#10622390C2semidirect
6. C2×#10622418C2semidirect
7. C2×#10622656C2semidirect
8. C2×#10622802C2semidirect
9. C2×#10622395C2semidirect
10. C2×#10622420C2semidirect
11. C2×#10622784C2semidirect
12. C2×#10622800C2semidirect
13. C2×#10622851C2semidirect
14. C2×#10622785C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#452C2semidirect
24. #10623364C22semidirect
41. #10623160C22semidirect
48. C11×#452C22semidirect
52. #10622851C22semidirect
58. #10622802C22semidirect
59. #10622800C22semidirect
60. #10622785C22semidirect
61. #10622784C22semidirect
68. #10622656C22semidirect
71. #10622420C22semidirect
72. #10622418C22semidirect
73. #10622395C22semidirect
74. #10622390C22semidirect
75. #10622348C22semidirect
76. #10622340C22semidirect
317. C2×#452D11semidirect
443. #452C2×D11semidirect
612. C2×C11#3204semidirect
735. C11C2×#3204semidirect
859. C2#13079524direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231602
C2×#106233642
#130795242
C2×#106223482
C2×#106223902
C2×#106224182
C2×#106226562
C2×#106228022
C2×#106223952
C2×#106224202
C2×#106227842
C2×#106228002
C2×#106228512
C2×#106227852
C2×#106223402
C2×C11×#4522
C2×#320411