Finite Group Databasebeta

← C2×#13080645 #15630436

Subgroups — C2×#13080645 #15630436

Order 2816.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623172C211yesmaximal, characteristic, complemented
2C2×#10623337C211yesmaximal, characteristic
3#13080645C2116yesmaximal, direct product factor
4C2×#10622378C211yesmaximal, characteristic, complemented
5C2×#10622336C211yesmaximal, characteristic, complemented
6C2×#10622397C211yesmaximal, characteristic, complemented
7C2×#10622374C211yesmaximal, characteristic, complemented
8C2×#10622665C211yesmaximal, characteristic, complemented
9C2×#10622784C211yesmaximal, characteristic, complemented
10C2×#10622779C211yesmaximal, characteristic, complemented
11C2×#10622786C211yesmaximal, characteristic, complemented
12C2×#10622777C211yesmaximal, characteristic, complemented
13C2×#10622341C211yesmaximal, characteristic, complemented
14C2×#10622828C211yesmaximal, characteristic, complemented
15C2×#10622385C211yesmaximal, characteristic, complemented
16C2×C11×#450C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×C11×SD16C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×#67006—21no—
23C22×C22⋊Dic11—21no—
24C2×#66999C2211yescharacteristic, complemented
25C2×Q8×Dic11C2211yescharacteristic, complemented
26C22×#4326C2211yescharacteristic, complemented
27#10623337—24no—
28#10623337C2218yes—
29C2×#66992—21no—
30C2×#66991C2211yescharacteristic
31C2×#66989C2211yescharacteristic
32C2×#66988—21no—
33C2×D4×Dic11C2211yescharacteristic
34C2×C4×C22⋊D11C2211yescharacteristic
35C2×#66979C2211yescharacteristic
36C2×#66977C2211yescharacteristic
37C22×#4318C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic, complemented
39#10623172—24no—
40#10623172C2218yescomplemented
41C2×#66951—21no—
42C2×#66945C2211yescharacteristic, complemented
43C2×#66941C2211yescharacteristic, complemented
44C2×#66940—21no—
45C2×#66938—21no—
46C2×#66932—21no—
47C11×#450C2218yescomplemented
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×#66899C2211yescharacteristic, complemented
52#10622828C2218yescomplemented
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic
57#10622786C2218yescomplemented
58#10622784C2218yescomplemented
59#10622779C2218yescomplemented
60#10622777C2218yescomplemented
61C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
62C2×#66882C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66880C2211yescharacteristic, complemented
65C2×#66880C2211yescharacteristic, complemented
66C2×#66879C2211yescharacteristic, complemented
67C2×Dic11⋊C8C2211yescharacteristic, complemented
68#10622665C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66872C2211yescharacteristic, complemented
71#10622397C2218yescomplemented
72#10622385C2218yescomplemented
73#10622378C2218yescomplemented
74#10622374C2218yescomplemented
75#10622341C2218yescomplemented
76#10622336C2218yescomplemented
77C25×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—24no—
80C22×D4×C11—21no—
81C22×D4×C11—22no—
82C22×D4×C11—42no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2314yes—
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11D411yescharacteristic
90C23×Dic11—21no—
91C23×Dic11—21no—
92C2×#4341—24no—
93C2×#4341—22no—
94C2×#4341—42no—
95C2×#4341C2314yes—
96C22×C4×D11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22C2311yescharacteristic
99C2×C11×SD16—24no—
100C2×C11×SD16—42no—
101C2×C11×SD16C2314yes—
102C2×C11×SD16C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110#67006—28no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11—21no—
117C2×C22⋊Dic11—28no—
118C2×C22⋊Dic11D411yescharacteristic
119#66999—22no—
120#66999C2314yescomplemented
121Q8×Dic11—22no—
122Q8×Dic11C2314yescomplemented
123C2×#4326—42no—
124C2×#4326C2314yescomplemented
125#66992—28no—
126#66991—22no—
127#66991C2314yes—
128#66989—22no—
129#66989C2314yes—
130#66988—28no—
131D4×Dic11—22no—
132D4×Dic11C2314yes—
133C4×C22⋊D11D414yes—
134C4×C22⋊D11C2314yes—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×(C2×D11)⋊C4D411yescharacteristic
138#66979—22no—
139#66979C2314yes—
140C2×C4⋊Dic11—21no—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144#66977—22no—
145#66977C2314yes—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4D411yescharacteristic
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11C2311yescharacteristic
154C2×#4318—42no—
155C2×#4318C2314yes—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C2×C8×D11—42no—
159C2×C8×D11C2314yescomplemented
160#66951—28no—
161#66945—22no—
162#66945C2314yescomplemented
163#66941—22no—
164#66941C2314yescomplemented
165#66940—28no—
166#66938—28no—
167#66932—28no—
168C11×#102C2314yes—
169C11×#102C2314yes—
170C11×C22⋊C8C2314yes—
171#66899C2314yescomplemented
172#66896C2314yes—
173#66896C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176(C2×D11)⋊C8C2314yescomplemented
177#66882C2314yescomplemented
178#66881C2314yescomplemented
179#66880C2314yescomplemented
180#66880C2314yescomplemented
181#66879C2314yescomplemented
182Dic11⋊C8C2314yescomplemented
183#66874C2314yescomplemented
184#66872C2314yescomplemented
185C2×#3311—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—24no—
189C24×C11—44no—
190C24×C11—44no—
191C24×C11—82no—
192C24×C11C2×D411yescharacteristic
193C23×D11C2×D411yescharacteristic
194C2×Q8×C11—21no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11C2412yes—
198C2×D4×C11—28no—
199C2×D4×C11—21no—
200C2×D4×C11—24no—
201C2×D4×C11—21no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—44no—
206C2×D4×C11—48no—
207C2×D4×C11—44no—
208C2×D4×C11#4114yes—
209C2×D4×C11C2412yes—
210C2×D4×C11C2412yes—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—42no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—82no—
224C2×C22⋊D11C2×D414yes—
225C22×Dic11—24no—
226C22×Dic11—24no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—44no—
232C22×Dic11—82no—
233C22×Dic11C2×D411yescharacteristic
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236#4341—28no—
237#4341—44no—
238#4341—48no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11C2×D412yes—
242C2×C4×D11C2412yes—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22—44no—
248C2×Dic22C2412yes—
249C11×SD16—28no—
250C11×SD16—44no—
251C2×C8×C11—22no—
252C2×C8×C11—22no—
253C2×C8×C11C2412yes—
254C2×C8×C11C2412yes—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264C22⋊Dic11—24no—
265C22⋊Dic11C2×D414yes—
266#4326—44no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4C2×D414yes—
270C4⋊Dic11—24no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4C2×D414yes—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2412yes—
286#4318—44no—
287C2×C11⋊C8—22no—
288C2×C11⋊C8—22no—
289C2×C11⋊C8C2412yes—
290C2×C11⋊C8C2412yes—
291C8×D11—44no—
292C2×#556—111no—
293C2×#546—111no—
294#3311—1116no—
295C2×#489—111no—
296C2×#485—111no—
297C2×#482—111no—
298C2×#476—111no—
299C2×#470—111no—
300C2×#465—111no—
301C2×#464—111no—
302C2×#452—111no—
303C2×#450D1111yescharacteristic, complemented
304C2×#440—111no—
305C2×#435—111no—
306C2×#418—111no—
307C2×#416—111no—
308C23×C11—24no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—48no—
315C23×C11—48no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—84no—
322C23×C11—816no—
323C23×C11C22×D412yes—
324C23×C11C22×D411yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11C22×D412yes—
329Q8×C11—22no—
330Q8×C11—22no—
331Q8×C11—42no—
332D4×C11—24no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—48no—
337D4×C11—42no—
338D4×C11C2×#4114yes—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—42no—
346C2×C4×C11—42no—
347C2×C4×C11C22×D412yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C2×#4112yes—
350C2×C4×C11H(5,𝔽2)12yes—
351C2×C4×C11C2511yescharacteristic
352C22⋊D11—44no—
353C22⋊D11—48no—
354C22⋊D11—84no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—48no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—84no—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371C4×D11—24no—
372C4×D11—22no—
373C4×D11—22no—
374Dic22—22no—
375Dic22—22no—
376Dic22—48no—
377Dic22—42no—
378C8×C11—22no—
379C8×C11—22no—
380C11⋊C8—22no—
381C11⋊C8—22no—
382C22×#41—111no—
383C23×D4C2×D1111yescharacteristic
384C22×Q16—111no—
385C22×SD16C2×D1111yescharacteristic
386C22×SD16C2×D1111yescharacteristic
387C22×M16—111no—
388C23×C8—111no—
389#556—118no—
390#556—224no—
391#546—118no—
392#546—224no—
393C2×C4⋊Q8—111no—
394C2×#126—221no—
395C2×#126—221no—
396C2×#124—111no—
397C2×#124—221no—
398C2×#123—221no—
399C2×C22⋊Q8—111no—
400C2×C22⋊Q8—111no—
401C2×C22⋊Q8C2×D1111yescharacteristic
402C2×#121—111no—
403C2×#121—221no—
404C2×#120—221no—
405C2×C4×Q8—111no—
406C2×C4×Q8—221no—
407C2×C4×D4—111no—
408C2×C4×D4—111no—
409C2×#117—111no—
410C2×#117—111no—
411C22×C22⋊C4—221no—
412#489—118no—
413#485—118no—
414#482—118no—
415#476—118no—
416#470—118no—
417#465—118no—
418#464—118no—
419#452—118no—
420#450C2×D1118yescomplemented
421#440—118no—
422#435—118no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
426C2×C4⋊C8—111no—
427#418—118no—
428#416—118no—
429C2×#103—111no—
430C2×#103—111no—
431C2×#103—111no—
432C2×#103—111no—
433C2×#102—111no—
434C2×#102—111no—
435C2×#102—111no—
436C2×#102—111no—
437C2×#102C2×D1111yescharacteristic
438C2×#102C2×D1111yescharacteristic
439C2×C22⋊C8—111no—
440C2×C22⋊C8C2×D1111yescharacteristic
441C2×#97—111no—
442C22×C11—22no—
443C22×C11—24no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—44no—
447C22×C11—48no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—816no—
454C22×C11—84no—
455C22×C11#54612yes—
456C22×C11#57512yes—
457C22×C11#57712yes—
458C22×C11C23×D411yescharacteristic
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—44no—
463C4×C11—22no—
464C4×C11—42no—
465C4×C11—42no—
466C4×C11#54612yes—
467C4×C11C22×#4111yescharacteristic
468C4×C11C2×H(5,𝔽2)11yescharacteristic
469Dic11—22no—
470Dic11—22no—
471Dic11—22no—
472Dic11—42no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476C25—21no—
477C2×#41—114no—
478C2×#41—222no—
479C2×#41—224no—
480C2×#41—442no—
481C22×Q8—111no—
482C22×Q8—221no—
483C22×Q8C22×D1111yescharacteristic
484C22×D4—24no—
485C22×D4—21no—
486C22×D4—22no—
487C22×D4—42no—
488C22×D4—111no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4C22×D1111yescharacteristic
492C22×D4C22×D1114yes—
493C22×D4C22×D1111yescharacteristic
494C23×C4—111no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×Q16—114no—
499C2×Q16—442no—
500C2×SD16—24no—
501C2×SD16—42no—
502C2×SD16C22×D1114yes—
503C2×SD16C22×D1114yes—
504C2×M16—114no—
505C2×M16—442no—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8—114no—
509C22×C8—442no—
510C22×C8C22×D1111yescharacteristic
511C22×C8C22×D1111yescharacteristic
512C4⋊Q8—114no—
513C4⋊Q8—222no—
514#126—228no—
515#126—228no—
516#124—114no—
517#124—222no—
518#124—228no—
519#123—228no—
520C22⋊Q8—22no—
521C22⋊Q8—114no—
522C22⋊Q8—114no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8C22×D1114yes—
526#121—114no—
527#121—228no—
528#121—222no—
529#120—228no—
530C4×Q8—114no—
531C4×Q8—222no—
532C4×Q8—228no—
533C4×D4—114no—
534C4×D4—114no—
535C4×D4—114no—
536C4×D4—222no—
537#117—114no—
538#117—114no—
539#117—222no—
540#117—222no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—228no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C42—111no—
564C2×C42—221no—
565C2×C42—221no—
566C2×C42—221no—
567#107—114no—
568#106—114no—
569#106—114no—
570C4⋊C8—114no—
571#103—114no—
572#103—114no—
573#103—114no—
574#103—114no—
575#102—114no—
576#102—114no—
577#102—114no—
578#102—114no—
579#102C22×D1114yes—
580#102C22×D1114yes—
581C22⋊C8—114no—
582C22⋊C8C22×D1114yes—
583#97—114no—
584C2×C11—42no—
585C2×C11—44no—
586C2×C11—82no—
587C2×C11#331114yescomplemented
588C2×C11C2×#54611yescharacteristic
589C2×C11C2×#57511yescharacteristic
590C2×C11C2×#57711yescharacteristic
591D11—42no—
592C24—21no—
593C24—21no—
594C24—24no—
595C24—44no—
596C24—44no—
597C24—82no—
598C24—111no—
599C24D4×D1111yescharacteristic
600#41—228no—
601#41—444no—
602#41—448no—
603C2×Q8—21no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—112no—
607C2×Q8—224no—
608C2×Q8—221no—
609C2×Q8—222no—
610C2×Q8—222no—
611C2×Q8—444no—
612C2×Q8C23×D1112yes—
613C2×D4—28no—
614C2×D4—21no—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—44no—
621C2×D4—48no—
622C2×D4—44no—
623C2×D4—114no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—442no—
627C2×D4—444no—
628C2×D4—882no—
629C2×D4#434114yes—
630C2×D4C23×D1112yes—
631C2×D4C23×D1112yes—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—111no—
637C22×C4—111no—
638C22×C4—111no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—221no—
646C22×C4—221no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—444no—
650C22×C4—882no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655Q16—444no—
656SD16—28no—
657SD16—44no—
658M16—444no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8—444no—
666C2×C8C23×D1112yes—
667C2×C8C23×D1112yes—
668C4⋊C4—24no—
669C4⋊C4—21no—
670C4⋊C4—114no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—112no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—221no—
678C4⋊C4—221no—
679C4⋊C4—221no—
680C4⋊C4—224no—
681C4⋊C4C23×D1112yes—
682C22⋊C4—24no—
683C22⋊C4—114no—
684C22⋊C4—114no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C22⋊C4—224no—
691C22⋊C4—224no—
692C22⋊C4—224no—
693C42—112no—
694C42—112no—
695C42—224no—
696C42—224no—
697C42—224no—
698C11C2×#331111yescharacteristic, complemented, Sylow
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—22no—
705C23—48no—
706C23—48no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—84no—
713C23—816no—
714C23—112no—
715C23—222no—
716C23—222no—
717C23—222no—
718C23C2×D4×D1112yes—
719C23C2×D4×D1111yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—222no—
724Q8—222no—
725Q8—448no—
726Q8—442no—
727D4—24no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—48no—
732D4—42no—
733D4—444no—
734D4—448no—
735D4—884no—
736D4C2×#434114yes—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—112no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—224no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—448no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—884no—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4C2×#434112yes—
767C2×C4#6703712yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—44no—
778C22—48no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—816no—
785C22—84no—
786C22—222no—
787C22—222no—
788C22—222no—
789C22—444no—
790C22#1062312212yes—
791C22#1062329312yes—
792C22#1062330412yes—
793C22C22×D4×D1111yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—222no—
798C4—222no—
799C4—222no—
800C4—442no—
801C4—442no—
802C4—442no—
803C4—442no—
804C4#1062312212yes—
805C4C22×#434111yescharacteristic
806C4C2×#6703711yescharacteristic
807C2—42no—
808C2—44no—
809C2—82no—
810C2—442no—
811C2#1308064514yesdirect product factor
812C2C2×#1062312211yescharacteristic
813C2C2×#1062330411yescharacteristic
814C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC2×#10623337C2
hypercenterC2×#450D11
hypocenterC11C2×#3311
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×#10623172C2semidirect
3. #13080645C2direct (N × H)
4. C2×#10622378C2semidirect
5. C2×#10622336C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622374C2semidirect
8. C2×#10622665C2semidirect
9. C2×#10622784C2semidirect
10. C2×#10622779C2semidirect
11. C2×#10622786C2semidirect
12. C2×#10622777C2semidirect
13. C2×#10622341C2semidirect
14. C2×#10622828C2semidirect
15. C2×#10622385C2semidirect
16. C2×C11×#450C2semidirect
24. C2×#66999C22semidirect
25. C2×Q8×Dic11C22semidirect
26. C22×#4326C22semidirect
38. C22×C8×D11C22semidirect
40. #10623172C22semidirect
42. C2×#66945C22semidirect
43. C2×#66941C22semidirect
47. C11×#450C22semidirect
51. C2×#66899C22semidirect
52. #10622828C22semidirect
57. #10622786C22semidirect
58. #10622784C22semidirect
59. #10622779C22semidirect
60. #10622777C22semidirect
61. C2×(C2×D11)⋊C8C22semidirect
62. C2×#66882C22semidirect
63. C2×#66881C22semidirect
64. C2×#66880C22semidirect
65. C2×#66880C22semidirect
66. C2×#66879C22semidirect
67. C2×Dic11⋊C8C22semidirect
68. #10622665C22semidirect
69. C2×#66874C22semidirect
70. C2×#66872C22semidirect
71. #10622397C22semidirect
72. #10622385C22semidirect
73. #10622378C22semidirect
74. #10622374C22semidirect
75. #10622341C22semidirect
76. #10622336C22semidirect
120. #66999C23semidirect
122. Q8×Dic11C23semidirect
124. C2×#4326C23semidirect
159. C2×C8×D11C23semidirect
162. #66945C23semidirect
164. #66941C23semidirect
171. #66899C23semidirect
176. (C2×D11)⋊C8C23semidirect
177. #66882C23semidirect
178. #66881C23semidirect
179. #66880C23semidirect
180. #66880C23semidirect
181. #66879C23semidirect
182. Dic11⋊C8C23semidirect
183. #66874C23semidirect
184. #66872C23semidirect
303. C2×#450D11semidirect
420. #450C2×D11semidirect
587. C2×C11#3311semidirect
698. C11C2×#3311semidirect
811. C2#13080645direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231722
C2×#106233372
#130806452
C2×#106223782
C2×#106223362
C2×#106223972
C2×#106223742
C2×#106226652
C2×#106227842
C2×#106227792
C2×#106227862
C2×#106227772
C2×#106223412
C2×#106228282
C2×#106223852
C2×C11×#4502
C2×#331111