Finite Group Databasebeta

← C2×#13079472 #15624430

Subgroups — C2×#13079472 #15624430

Order 2816.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623160C211yesmaximal, characteristic, complemented
2C2×#10623336C211yesmaximal, characteristic, complemented
3#13079472C2116yesmaximal, direct product factor
4C2×#10622390C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622387C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622787C211yesmaximal, characteristic, complemented
10C2×#10622388C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×#10622785C211yesmaximal, characteristic, complemented
13C2×#10622785C211yesmaximal, characteristic, complemented
14C2×#10622830C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#450C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×#4343C2211yescharacteristic, complemented
19C22×#4339C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×#67006—21no—
24C2×#67006—21no—
25C2×#66999C2211yescharacteristic, complemented
26#10623336—24no—
27#10623336C2218yescomplemented
28C2×#66993—21no—
29C2×#66991C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C2×#66989—21no—
34C22×#4323C2211yescharacteristic
35C22×#4323C2211yescharacteristic
36C2×#66983C2211yescharacteristic
37C2×#66979C2211yescharacteristic
38C22×#4313C2211yescharacteristic, complemented
39C22×C8×D11C2211yescharacteristic, complemented
40#10623160—24no—
41#10623160C2218yescomplemented
42C2×#66949—21no—
43C2×#66948—21no—
44C2×#66948C2211yescharacteristic, complemented
45C2×C4⋊C4×D11C2211yescharacteristic, complemented
46C2×#66937—21no—
47C2×#66937—21no—
48C11×#450C2218yescomplemented
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×#66899C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54#10622830C2218yescomplemented
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57C2×C22⋊(C11⋊C8)C2211yescharacteristic
58#10622787C2218yescomplemented
59#10622785C2218yescomplemented
60#10622785C2218yescomplemented
61#10622784C2218yescomplemented
62C2×#66885C2211yescharacteristic, complemented
63C2×#66885C2211yescharacteristic, complemented
64C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
65C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
66C2×#66882C2211yescharacteristic, complemented
67C2×#66881C2211yescharacteristic, complemented
68#10622658C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622395C2218yescomplemented
72#10622390C2218yescomplemented
73#10622388C2218yescomplemented
74#10622387C2218yescomplemented
75#10622350C2218yescomplemented
76#10622340C2218yescomplemented
77C25×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11—22no—
81C22×D4×C11—42no—
82C22×D4×C11—42no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C22×D4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11D411yescharacteristic
93C22×C22⋊D11D411yescharacteristic
94C2×#4343—22no—
95C2×#4343—42no—
96C2×#4343—42no—
97C2×#4343C2314yescomplemented
98C2×#4339—42no—
99C2×#4339—42no—
100C2×#4339D414yes—
101C2×#4339C2314yes—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44D411yescharacteristic
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11C2311yescharacteristic
109C22×C4×D11C2311yescharacteristic
110C22×Dic22D411yescharacteristic
111C2×C11×SD16—42no—
112C2×C11×SD16—42no—
113C2×C11×SD16C2314yes—
114C2×C11×SD16C2314yes—
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8C2314yes—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4—21no—
122#67006—28no—
123#67006—28no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129#66999—22no—
130#66999C2314yescomplemented
131#66993—28no—
132#66991—22no—
133#66991—22no—
134#66991—22no—
135#66991—22no—
136#66991C2314yes—
137#66991C2314yes—
138#66991C2314yes—
139#66991C2314yes—
140#66989—28no—
141C2×#4323—42no—
142C2×#4323—42no—
143C2×#4323C2314yes—
144C2×#4323C2314yes—
145#66983—22no—
146#66983C2314yes—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150#66979—22no—
151#66979C2314yes—
152C2×C4⋊Dic11C2311yescharacteristic
153C2×C4⋊Dic11C2311yescharacteristic
154C2×C4⋊Dic11C2311yescharacteristic
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4—21no—
157C2×C4×Dic11—21no—
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C2×#4313—42no—
161C2×#4313C2314yescomplemented
162C2×C8×D11—42no—
163C2×C8×D11C2314yescomplemented
164#66949—28no—
165#66948—28no—
166#66948—22no—
167#66948C2314yescomplemented
168C4⋊C4×D11—22no—
169C4⋊C4×D11C2314yescomplemented
170#66937—28no—
171#66937—28no—
172C11×#102C2314yes—
173C11×#102C2314yes—
174C11×C22⋊C8C2314yes—
175#66899C2314yescomplemented
176#66899C2314yescomplemented
177#66896C2314yes—
178#66896C2314yes—
179C22⋊(C11⋊C8)C2314yes—
180#66885C2314yescomplemented
181#66885C2314yescomplemented
182(C2×D11)⋊C8C2314yescomplemented
183(C2×D11)⋊C8C2314yescomplemented
184#66882C2314yescomplemented
185#66881C2314yescomplemented
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3198—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—24no—
192C24×C11—44no—
193C24×C11—82no—
194C24×C11—82no—
195C24×C11C2×D411yescharacteristic
196C23×D11—21no—
197C23×D11C2×D411yescharacteristic
198C23×D11C2×D411yescharacteristic
199C2×Q8×C11—21no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11C2412yes—
203C2×D4×C11—24no—
204C2×D4×C11—21no—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—22no—
209C2×D4×C11—22no—
210C2×D4×C11—44no—
211C2×D4×C11—44no—
212C2×D4×C11—44no—
213C2×D4×C11—48no—
214C2×D4×C11C2412yes—
215C2×D4×C11C2412yes—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2411yescharacteristic
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—42no—
230C2×C22⋊D11—42no—
231C2×C22⋊D11—82no—
232C2×C22⋊D11—82no—
233C2×C22⋊D11—82no—
234C2×C22⋊D11—82no—
235C2×C22⋊D11—82no—
236C2×C22⋊D11C2×D414yes—
237C2×C22⋊D11C2×D414yes—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11C2×D411yescharacteristic
242C22×Dic11C2×D411yescharacteristic
243#4343—44no—
244#4343—44no—
245#4343—48no—
246#4339—48no—
247#4339—44no—
248#4339—44no—
249C2×D44—24no—
250C2×D44—24no—
251C2×D44—21no—
252C2×D44—22no—
253C2×D44—22no—
254C2×D44—42no—
255C2×D44—44no—
256C2×D44—82no—
257C2×D44C2×D414yes—
258C2×D44C2412yes—
259C2×C4×D11—24no—
260C2×C4×D11—24no—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—44no—
266C2×C4×D11—82no—
267C2×C4×D11C2×D412yes—
268C2×C4×D11C2×D412yes—
269C2×C4×D11C2412yes—
270C2×C4×D11C2412yes—
271C2×Dic22—42no—
272C2×Dic22C2×D414yes—
273C11×SD16—44no—
274C11×SD16—44no—
275C2×C8×C11—22no—
276C2×C8×C11—22no—
277C2×C8×C11C2412yes—
278C2×C8×C11C2412yes—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—24no—
281C11×C4⋊C4C2412yes—
282C11×C22⋊C4—24no—
283C22⋊Dic11—24no—
284C22⋊Dic11—24no—
285C22⋊Dic11—24no—
286C22⋊Dic11—24no—
287C22⋊Dic11—24no—
288#4323—44no—
289#4323—44no—
290(C2×D11)⋊C4—24no—
291(C2×D11)⋊C4—24no—
292(C2×D11)⋊C4—24no—
293C4⋊Dic11—21no—
294C4⋊Dic11—21no—
295C4⋊Dic11—21no—
296C4⋊Dic11C2412yes—
297C4⋊Dic11C2412yes—
298C4⋊Dic11C2412yes—
299Dic11⋊C4—24no—
300Dic11⋊C4—24no—
301C4×Dic11—24no—
302C2×C11⋊C8—22no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8C2412yes—
305C2×C11⋊C8C2412yes—
306#4313—44no—
307C8×D11—44no—
308C2×#537—111no—
309C2×#535—111no—
310#3198—1116no—
311C2×#481—111no—
312C2×#485—111no—
313C2×#482—111no—
314C2×#480—111no—
315C2×#469—111no—
316C2×#468—111no—
317C2×#466—111no—
318C2×#465—111no—
319C2×#449—111no—
320C2×#449—111no—
321C2×#450D1111yescharacteristic, complemented
322C2×#447—111no—
323C2×#408—111no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—48no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11—42no—
336C23×C11—84no—
337C23×C11—84no—
338C23×C11—816no—
339C23×C11C22×D412yes—
340C23×C11C22×D411yescharacteristic
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11C22×D412yes—
352C22×D11C22×D412yes—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—42no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—48no—
361D4×C11—42no—
362D4×C11—42no—
363C2×C4×C11—22no—
364C2×C4×C11—24no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
371C2×C4×C11C22×D412yes—
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11H(5,𝔽2)12yes—
374C2×C4×C11H(5,𝔽2)12yes—
375C2×C4×C11C2511yescharacteristic
376C22⋊D11—44no—
377C22⋊D11—44no—
378C22⋊D11—84no—
379C22⋊D11—84no—
380C22⋊D11—84no—
381C22⋊D11—84no—
382C22⋊D11—84no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11C22×D412yes—
392C2×Dic11C22×D412yes—
393D44—22no—
394D44—22no—
395D44—44no—
396D44—48no—
397D44—42no—
398D44—84no—
399C4×D11—24no—
400C4×D11—24no—
401C4×D11—22no—
402C4×D11—22no—
403C4×D11—22no—
404C4×D11—22no—
405C4×D11—48no—
406C4×D11—84no—
407Dic22—44no—
408C8×C11—22no—
409C8×C11—22no—
410C11⋊C8—22no—
411C11⋊C8—22no—
412C22×#41—111no—
413C22×#41—111no—
414C23×D4C2×D1111yescharacteristic
415C22×SD16C2×D1111yescharacteristic
416C22×SD16C2×D1111yescharacteristic
417C22×D8—111no—
418C22×D8—111no—
419C22×M16—111no—
420C23×C8—111no—
421#537—118no—
422#537—224no—
423#535—118no—
424#535—224no—
425C2×#127—221no—
426C2×#124—221no—
427C2×C22⋊Q8—111no—
428C2×C22⋊Q8—221no—
429C2×C22⋊Q8C2×D1111yescharacteristic
430C2×#121—111no—
431C2×#121—111no—
432C2×#121—111no—
433C2×#121—111no—
434C2×#121—111no—
435C2×#121—111no—
436C2×#121—221no—
437C2×#121—221no—
438C2×#121—221no—
439C2×#120—221no—
440C2×#120—221no—
441C2×#117—111no—
442C22×C4⋊C4—111no—
443#485—118no—
444#482—118no—
445#481—118no—
446#480—118no—
447#469—118no—
448#468—118no—
449#466—118no—
450#465—118no—
451#450C2×D1118yescomplemented
452#449—118no—
453#449—118no—
454#447—118no—
455C2×#107—111no—
456C2×#107—111no—
457C2×#106—111no—
458C2×#106—111no—
459C2×#103—111no—
460C2×#103—111no—
461C2×#102—111no—
462C2×#102—111no—
463C2×#102—111no—
464C2×#102—111no—
465C2×#102C2×D1111yescharacteristic
466C2×#102C2×D1111yescharacteristic
467#408—118no—
468C2×C22⋊C8—111no—
469C2×C22⋊C8—111no—
470C2×C22⋊C8—111no—
471C2×C22⋊C8C2×D1111yescharacteristic
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—44no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—816no—
483C22×C11—84no—
484C22×C11—84no—
485C22×C11#53412yes—
486C22×C11#57612yes—
487C22×C11#57712yes—
488C22×C11C23×D411yescharacteristic
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—22no—
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—44no—
496C2×D11—44no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11#53412yes—
505C4×C11C2×H(5,𝔽2)11yescharacteristic
506C4×C11C2×H(5,𝔽2)11yescharacteristic
507Dic11—22no—
508Dic11—22no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—21no—
513C2×#41—114no—
514C2×#41—114no—
515C2×#41—114no—
516C2×#41—222no—
517C2×#41—442no—
518C2×#41—442no—
519C2×#41—442no—
520C2×#41—442no—
521C22×Q8—111no—
522C22×Q8C22×D1111yescharacteristic
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—42no—
526C22×D4—42no—
527C22×D4—111no—
528C22×D4—111no—
529C22×D4—111no—
530C22×D4—111no—
531C22×D4—221no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—221no—
535C22×D4—221no—
536C22×D4—221no—
537C22×D4—221no—
538C22×D4C22×D1111yescharacteristic
539C22×D4C22×D1111yescharacteristic
540C22×D4C22×D1114yes—
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—221no—
544C23×C4—221no—
545C23×C4C22×D1111yescharacteristic
546C2×SD16—42no—
547C2×SD16—42no—
548C2×SD16C22×D1114yes—
549C2×SD16C22×D1114yes—
550C2×D8—114no—
551C2×D8—114no—
552C2×D8—442no—
553C2×D8—442no—
554C2×M16—114no—
555C2×M16—442no—
556C22×C8—111no—
557C22×C8—111no—
558C22×C8—114no—
559C22×C8—442no—
560C22×C8C22×D1111yescharacteristic
561C22×C8C22×D1111yescharacteristic
562#127—228no—
563#124—228no—
564C22⋊Q8—22no—
565C22⋊Q8—114no—
566C22⋊Q8—228no—
567C22⋊Q8—222no—
568C22⋊Q8C22×D1114yes—
569#121—114no—
570#121—114no—
571#121—114no—
572#121—114no—
573#121—114no—
574#121—114no—
575#121—228no—
576#121—228no—
577#121—222no—
578#121—228no—
579#121—222no—
580#121—222no—
581#121—222no—
582#121—222no—
583#121—222no—
584#120—228no—
585#120—228no—
586#117—114no—
587#117—222no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—111no—
592C2×C4⋊C4—114no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4—221no—
596C2×C4⋊C4C22×D1111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—221no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C42—221no—
607#107—114no—
608#107—114no—
609#106—114no—
610#106—114no—
611#103—114no—
612#103—114no—
613#102—114no—
614#102—114no—
615#102—114no—
616#102—114no—
617#102C22×D1114yes—
618#102C22×D1114yes—
619C22⋊C8—114no—
620C22⋊C8—114no—
621C22⋊C8—114no—
622C22⋊C8C22×D1114yes—
623C2×C11—42no—
624C2×C11—82no—
625C2×C11—82no—
626C2×C11#319814yescomplemented
627C2×C11C2×#53411yescharacteristic
628C2×C11C2×#57611yescharacteristic
629C2×C11C2×#57711yescharacteristic
630D11—42no—
631D11—42no—
632D11—82no—
633C24—21no—
634C24—21no—
635C24—24no—
636C24—44no—
637C24—82no—
638C24—82no—
639C24—111no—
640C24—111no—
641C24—221no—
642C24D4×D1111yescharacteristic
643#41—448no—
644#41—444no—
645#41—444no—
646#41—444no—
647#41—444no—
648#41—448no—
649C2×Q8—21no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—114no—
653C2×Q8—442no—
654C2×Q8C23×D1112yes—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—44no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—48no—
666C2×D4—114no—
667C2×D4—114no—
668C2×D4—114no—
669C2×D4—112no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—221no—
678C2×D4—222no—
679C2×D4—222no—
680C2×D4—442no—
681C2×D4—444no—
682C2×D4—442no—
683C2×D4—442no—
684C2×D4—882no—
685C2×D4—882no—
686C2×D4—882no—
687C2×D4—882no—
688C2×D4—882no—
689C2×D4—882no—
690C2×D4C23×D1112yes—
691C2×D4C23×D1112yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—111no—
697C22×C4—111no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—224no—
703C22×C4—224no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—444no—
712C22×C4—882no—
713C22×C4D4×D1112yes—
714C22×C4D4×D1111yescharacteristic
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717SD16—44no—
718SD16—44no—
719D8—444no—
720D8—444no—
721M16—444no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—112no—
725C2×C8—112no—
726C2×C8—222no—
727C2×C8—222no—
728C2×C8—444no—
729C2×C8C23×D1112yes—
730C2×C8C23×D1112yes—
731C4⋊C4—24no—
732C4⋊C4—21no—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—112no—
736C4⋊C4—224no—
737C4⋊C4—224no—
738C4⋊C4—221no—
739C4⋊C4—221no—
740C4⋊C4—221no—
741C4⋊C4C23×D1112yes—
742C22⋊C4—24no—
743C22⋊C4—224no—
744C22⋊C4—224no—
745C22⋊C4—224no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C42—224no—
752C11C2×#319811yescharacteristic, complemented, Sylow
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—48no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—84no—
766C23—84no—
767C23—816no—
768C23—112no—
769C23—112no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—442no—
778C23—442no—
779C23—442no—
780C23C2×D4×D1112yes—
781C23C2×D4×D1111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—444no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—222no—
794D4—222no—
795D4—444no—
796D4—448no—
797D4—444no—
798D4—444no—
799D4—442no—
800D4—884no—
801D4—884no—
802D4—884no—
803D4—884no—
804D4—884no—
805D4—884no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—112no—
815C2×C4—112no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—224no—
819C2×C4—224no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—448no—
828C2×C4—442no—
829C2×C4—442no—
830C2×C4—442no—
831C2×C4—884no—
832C2×C4C2×D4×D1112yes—
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4#6703712yes—
835C2×C4#6703712yes—
836C2×C4C24×D1111yescharacteristic
837C8—22no—
838C8—22no—
839C8—222no—
840C8—222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—84no—
853C22—84no—
854C22—222no—
855C22—222no—
856C22—222no—
857C22—222no—
858C22—222no—
859C22—222no—
860C22—444no—
861C22—444no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—884no—
866C22#1062312012yes—
867C22#1062329312yes—
868C22#1062330512yes—
869C22C22×D4×D1111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—222no—
874C4—222no—
875C4—442no—
876C4—442no—
877C4—442no—
878C4#1062312012yes—
879C4C2×#6703711yescharacteristic
880C4C2×#6703711yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—442no—
885C2—442no—
886C2—882no—
887C2#1307947214yesdirect product factor
888C2C2×#1062312011yescharacteristic
889C2C2×#1062330511yescharacteristic
890C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
hypercenterC2×#450D11
hypocenterC11C2×#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#10623160C2semidirect
2. C2×#10623336C2semidirect
3. #13079472C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622387C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622787C2semidirect
10. C2×#10622388C2semidirect
11. C2×#10622784C2semidirect
12. C2×#10622785C2semidirect
13. C2×#10622785C2semidirect
14. C2×#10622830C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#450C2semidirect
18. C22×#4343C22semidirect
25. C2×#66999C22semidirect
27. #10623336C22semidirect
38. C22×#4313C22semidirect
39. C22×C8×D11C22semidirect
41. #10623160C22semidirect
44. C2×#66948C22semidirect
45. C2×C4⋊C4×D11C22semidirect
48. C11×#450C22semidirect
52. C2×#66899C22semidirect
53. C2×#66899C22semidirect
54. #10622830C22semidirect
58. #10622787C22semidirect
59. #10622785C22semidirect
60. #10622785C22semidirect
61. #10622784C22semidirect
62. C2×#66885C22semidirect
63. C2×#66885C22semidirect
64. C2×(C2×D11)⋊C8C22semidirect
65. C2×(C2×D11)⋊C8C22semidirect
66. C2×#66882C22semidirect
67. C2×#66881C22semidirect
68. #10622658C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622395C22semidirect
72. #10622390C22semidirect
73. #10622388C22semidirect
74. #10622387C22semidirect
75. #10622350C22semidirect
76. #10622340C22semidirect
97. C2×#4343C23semidirect
130. #66999C23semidirect
161. C2×#4313C23semidirect
163. C2×C8×D11C23semidirect
167. #66948C23semidirect
169. C4⋊C4×D11C23semidirect
175. #66899C23semidirect
176. #66899C23semidirect
180. #66885C23semidirect
181. #66885C23semidirect
182. (C2×D11)⋊C8C23semidirect
183. (C2×D11)⋊C8C23semidirect
184. #66882C23semidirect
185. #66881C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
321. C2×#450D11semidirect
451. #450C2×D11semidirect
626. C2×C11#3198semidirect
752. C11C2×#3198semidirect
887. C2#13079472direct (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×#106233362
#130794722
C2×#106223902
C2×#106226582
C2×#106223502
C2×#106223872
C2×#106223952
C2×#106227872
C2×#106223882
C2×#106227842
C2×#106227852
C2×#106228302
C2×#106223402
C2×C11×#4502
C2×#319811