Finite Group Databasebeta

← C2×#13079470 #15624428

Subgroups — C2×#13079470 #15624428

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×#10623364C211yesmaximal, characteristic, complemented
2C2×#10623361C211yesmaximal, characteristic, complemented
3#13079470C2116yesmaximal, direct product factor
4C2×#10622348C211yesmaximal, characteristic, complemented
5C2×#10622336C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622349C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622747C211yesmaximal, characteristic, complemented
10C2×#10622728C211yesmaximal, characteristic, complemented
11C2×#10622727C211yesmaximal, characteristic, complemented
12C2×#10622347C211yesmaximal, characteristic, complemented
13C2×#10622347C211yesmaximal, characteristic, complemented
14C2×#10622344C211yesmaximal, characteristic, complemented
15C2×#10622345C211yesmaximal, characteristic, complemented
16C2×C11×#408C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4339C2211yescharacteristic, complemented
19C23×D44C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C23×C8×C11C2211yescharacteristic, complemented
22#10623364—24no—
23#10623364C2218yescomplemented
24#10623361—24no—
25#10623361C2218yescomplemented
26C2×#67000—21no—
27C2×#66999—21no—
28C2×#66993—21no—
29C2×#66992—21no—
30C2×#66992—21no—
31C2×#66991—21no—
32C2×#66990—21no—
33C2×#66990—21no—
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36C2×#66983C2211yescharacteristic
37C2×#66983C2211yescharacteristic
38C2×#66983C2211yescharacteristic
39C2×#66983C2211yescharacteristic, complemented
40C2×#66979C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic, complemented
42C2×#66977C2211yescharacteristic
43C2×#66977C2211yescharacteristic, complemented
44C22×D88C2211yescharacteristic
45C22×D88C2211yescharacteristic
46C22×#4314C2211yescharacteristic
47C22×#4314C2211yescharacteristic
48C11×#408C2218yescomplemented
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×C11×C22⋊C8C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic, complemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53#10622748C2218yescomplemented
54#10622747C2218yescomplemented
55#10622728C2218yescomplemented
56#10622727C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic
60C2×#66885C2211yescharacteristic
61C2×#66885C2211yescharacteristic, complemented
62C2×#66885C2211yescharacteristic, complemented
63C2×#66882C2211yescharacteristic, complemented
64C2×#66882C2211yescharacteristic, complemented
65C2×#66881C2211yescharacteristic, complemented
66C2×#66881C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68C2×#66880C2211yescharacteristic, complemented
69#10622350C2218yescomplemented
70#10622349C2218yescomplemented
71#10622348C2218yescomplemented
72#10622347C2218yescomplemented
73#10622347C2218yescomplemented
74#10622345C2218yescomplemented
75#10622344C2218yescomplemented
76#10622336C2218yescomplemented
77C24×D11—21no—
78C2×C11×#41—42no—
79C2×C11×#41—42no—
80C2×C11×#41D414yes—
81C2×C11×#41C2314yes—
82C22×Q8×C11D411yescharacteristic
83C22×D4×C11D411yescharacteristic
84C22×D4×C11D411yescharacteristic
85C22×D4×C11D411yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C23×Dic11—21no—
97C2×#4339—22no—
98C2×#4339—42no—
99C2×#4339—42no—
100C2×#4339C2314yescomplemented
101C22×D44—21no—
102C22×D44—22no—
103C22×D44—42no—
104C22×D44—42no—
105C22×D44C2311yescharacteristic
106C22×D44C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C22×D44C2314yes—
109C22×C4×D11—21no—
110C22×Dic22C2311yescharacteristic
111C2×C11×M16—42no—
112C2×C11×M16C2314yescomplemented
113C22×C8×C11—42no—
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C22×C8×C11C2311yescharacteristic
118C22×C8×C11C2314yescomplemented
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122#67000—28no—
123#66999—28no—
124#66993—28no—
125#66992—28no—
126#66992—28no—
127#66991—28no—
128#66990—28no—
129#66990—28no—
130#66983—22no—
131#66983—22no—
132#66983—22no—
133#66983—22no—
134#66983—22no—
135#66983—22no—
136#66983C2314yes—
137#66983C2314yes—
138#66983C2314yes—
139#66983C2314yes—
140#66983C2314yes—
141#66983C2314yescomplemented
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×(C2×D11)⋊C4—21no—
148#66979—22no—
149#66979C2314yes—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11—22no—
152C2×C4⋊Dic11C2311yescharacteristic
153C2×C4⋊Dic11C2311yescharacteristic
154C2×C4⋊Dic11C2311yescharacteristic
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2314yescomplemented
157#66977—22no—
158#66977—22no—
159#66977C2314yes—
160#66977C2314yescomplemented
161C2×Dic11⋊C4—21no—
162C2×Dic11⋊C4—21no—
163C2×C4×Dic11—21no—
164C2×D88—42no—
165C2×D88—42no—
166C2×D88C2314yes—
167C2×D88C2314yes—
168C2×#4314—42no—
169C2×#4314—42no—
170C2×#4314C2314yes—
171C2×#4314C2314yes—
172C11×C22⋊C8C2314yes—
173C11×C22⋊C8C2314yes—
174C11×C22⋊C8C2314yescomplemented
175C11×C22⋊C8C2314yescomplemented
176#66885C2314yes—
177#66885C2314yes—
178#66885C2314yes—
179#66885C2314yes—
180#66885C2314yescomplemented
181#66885C2314yescomplemented
182#66882C2314yescomplemented
183#66882C2314yescomplemented
184#66881C2314yescomplemented
185#66881C2314yescomplemented
186#66880C2314yescomplemented
187#66880C2314yescomplemented
188C2×#3198—111nomaximal, Sylow
189C24×C11C2×D411yescharacteristic
190C24×C11C2×D411yescharacteristic
191C24×C11C2×D411yescharacteristic
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—24no—
196C23×D11—44no—
197C23×D11—82no—
198C23×D11—82no—
199C11×#41—48no—
200C11×#41—44no—
201C11×#41—44no—
202C2×Q8×C11—42no—
203C2×Q8×C11C2×D414yes—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11C2×D414yes—
208C2×D4×C11C2×D414yes—
209C2×D4×C11C2×D414yes—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D412yes—
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—82no—
235C2×C22⋊D11—82no—
236C2×C22⋊D11—82no—
237C2×C22⋊D11—82no—
238C2×C22⋊D11—82no—
239C2×C22⋊D11—82no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—24no—
246C22×Dic11—82no—
247#4339—44no—
248#4339—44no—
249#4339—48no—
250C2×D44—21no—
251C2×D44—21no—
252C2×D44—21no—
253C2×D44—24no—
254C2×D44—22no—
255C2×D44—22no—
256C2×D44—22no—
257C2×D44—22no—
258C2×D44—22no—
259C2×D44—22no—
260C2×D44—44no—
261C2×D44—44no—
262C2×D44—44no—
263C2×D44—48no—
264C2×D44C2412yes—
265C2×D44C2412yes—
266C2×D44C2412yes—
267C2×C4×D11—24no—
268C2×C4×D11—44no—
269C2×Dic22—21no—
270C2×Dic22—22no—
271C2×Dic22—22no—
272C2×Dic22C2412yes—
273C11×M16—44no—
274C2×C8×C11—22no—
275C2×C8×C11—22no—
276C2×C8×C11—22no—
277C2×C8×C11—22no—
278C2×C8×C11—44no—
279C2×C8×C11C2412yes—
280C2×C8×C11C2412yes—
281C2×C8×C11C2412yes—
282C2×C8×C11C2412yes—
283C22⋊Dic11—24no—
284C22⋊Dic11—24no—
285C22⋊Dic11—24no—
286(C2×D11)⋊C4—24no—
287(C2×D11)⋊C4—24no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4—24no—
291(C2×D11)⋊C4—24no—
292C4⋊Dic11—21no—
293C4⋊Dic11—21no—
294C4⋊Dic11—24no—
295C4⋊Dic11—21no—
296C4⋊Dic11—21no—
297C4⋊Dic11C2412yes—
298C4⋊Dic11C2412yes—
299C4⋊Dic11C2412yes—
300C4⋊Dic11C2412yes—
301Dic11⋊C4—24no—
302Dic11⋊C4—24no—
303C4×Dic11—24no—
304D88—44no—
305D88—44no—
306#4314—44no—
307#4314—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×#450—111no—
322C2×#447—111no—
323C2×#408D1111yescharacteristic, complemented
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11C22×D412yes—
334C23×C11C22×D412yes—
335C23×C11C22×D412yes—
336C23×C11C22×D411yescharacteristic
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—48no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—84no—
351C22×D11—84no—
352C22×D11—816no—
353Q8×C11—44no—
354D4×C11—44no—
355D4×C11—44no—
356D4×C11—44no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—24no—
361C2×C4×C11—24no—
362C2×C4×C11—24no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D412yes—
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—48no—
377C22⋊D11—84no—
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×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—84no—
394D44—22no—
395D44—22no—
396D44—22no—
397D44—22no—
398D44—22no—
399D44—22no—
400D44—48no—
401D44—42no—
402D44—42no—
403D44—42no—
404C4×D11—48no—
405Dic22—22no—
406Dic22—22no—
407Dic22—42no—
408C8×C11—22no—
409C8×C11—22no—
410C8×C11—22no—
411C8×C11—22no—
412C22×#41—111no—
413C22×#41C2×D1111yescharacteristic
414C23×D4—111no—
415C22×SD16—111no—
416C22×SD16—111no—
417C22×D8—111no—
418C22×D8—111no—
419C22×M16C2×D1111yescharacteristic, complemented
420C23×C8C2×D1111yescharacteristic, complemented
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—111no—
429C2×C22⋊Q8—221no—
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#450—118no—
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×#102—111no—
466C2×#102—111no—
467#408C2×D1118yescomplemented
468C2×C22⋊C8C2×D1111yescharacteristic
469C2×C22⋊C8C2×D1111yescharacteristic
470C2×C22⋊C8C2×D1111yescharacteristic, complemented
471C2×C22⋊C8C2×D1111yescharacteristic, complemented
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—44no—
482C22×C11—44no—
483C22×C11—44no—
484C22×C11#53412yes—
485C22×C11#57612yes—
486C22×C11#57712yes—
487C22×C11C23×D411yescharacteristic
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—816no—
498C2×D11—84no—
499C2×D11—84no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11#53412yes—
505C4×C11C2×H(5,𝔽2)11yescharacteristic
506C4×C11C2×H(5,𝔽2)11yescharacteristic
507Dic11—42no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—221no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—114no—
516C2×#41—222no—
517C2×#41—442no—
518C2×#41—442no—
519C2×#41D4414yes—
520C2×#41C22×D1114yes—
521C22×Q8—111no—
522C22×Q8D4411yescharacteristic
523C22×D4—111no—
524C22×D4—111no—
525C22×D4—111no—
526C22×D4—114no—
527C22×D4—221no—
528C22×D4—221no—
529C22×D4—221no—
530C22×D4—221no—
531C22×D4—221no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—221no—
535C22×D4—222no—
536C22×D4—442no—
537C22×D4—442no—
538C22×D4D4411yescharacteristic
539C22×D4D4411yescharacteristic
540C22×D4D4411yescharacteristic
541C23×C4—221no—
542C23×C4—221no—
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C2×SD16—114no—
547C2×SD16—114no—
548C2×SD16—442no—
549C2×SD16—442no—
550C2×D8—114no—
551C2×D8—114no—
552C2×D8—442no—
553C2×D8—442no—
554C2×M16—42no—
555C2×M16C22×D1114yescomplemented
556C22×C8—42no—
557C22×C8C22×D1111yescharacteristic
558C22×C8C22×D1111yescharacteristic
559C22×C8C22×D1111yescharacteristic
560C22×C8C22×D1111yescharacteristic
561C22×C8C22×D1114yescomplemented
562#127—228no—
563#124—228no—
564C22⋊Q8—114no—
565C22⋊Q8—114no—
566C22⋊Q8—228no—
567C22⋊Q8—222no—
568C22⋊Q8—222no—
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—228no—
578#121—222no—
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—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—111no—
592C2×C4⋊C4—111no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—221no—
596C2×C4⋊C4—221no—
597C2×C22⋊C4—221no—
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#102—114no—
618#102—114no—
619C22⋊C8C22×D1114yes—
620C22⋊C8C22×D1114yes—
621C22⋊C8C22×D1114yescomplemented
622C22⋊C8C22×D1114yescomplemented
623C2×C11—42no—
624C2×C11—42no—
625C2×C11—42no—
626C2×C11#319814yescomplemented
627C2×C11C2×#53411yescharacteristic
628C2×C11C2×#57611yescharacteristic
629C2×C11C2×#57711yescharacteristic
630D11—82no—
631D11—82no—
632D11—82no—
633C24—221no—
634C24—221no—
635C24—221no—
636C24—224no—
637C24—444no—
638C24—882no—
639C24—882no—
640C24C2×D4411yescharacteristic
641C24C2×D4411yescharacteristic
642C24C2×D4411yescharacteristic
643#41—44no—
644#41—44no—
645#41—48no—
646#41—444no—
647#41—444no—
648#41—448no—
649C2×Q8—42no—
650C2×Q8—112no—
651C2×Q8—221no—
652C2×Q8—222no—
653C2×Q8—222no—
654C2×Q8C2×D4414yes—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—112no—
659C2×D4—112no—
660C2×D4—112no—
661C2×D4—224no—
662C2×D4—224no—
663C2×D4—224no—
664C2×D4—224no—
665C2×D4—224no—
666C2×D4—224no—
667C2×D4—224no—
668C2×D4—221no—
669C2×D4—221no—
670C2×D4—221no—
671C2×D4—224no—
672C2×D4—222no—
673C2×D4—222no—
674C2×D4—222no—
675C2×D4—222no—
676C2×D4—222no—
677C2×D4—222no—
678C2×D4—444no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—448no—
682C2×D4—444no—
683C2×D4—882no—
684C2×D4—882no—
685C2×D4—882no—
686C2×D4—882no—
687C2×D4—882no—
688C2×D4—882no—
689C2×D4C2×D4414yes—
690C2×D4C2×D4414yes—
691C2×D4C2×D4414yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—224no—
704C22×C4—224no—
705C22×C4—444no—
706C22×C4—882no—
707C22×C4C2×D4412yes—
708C22×C4C2×D4412yes—
709C22×C4C2×D4412yes—
710C22×C4C2×D4411yescharacteristic
711C22×C4C2×D4411yescharacteristic
712C22×C4C2×D4411yescharacteristic
713C22×C4C23×D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717SD16—444no—
718SD16—444no—
719D8—444no—
720D8—444no—
721M16—44no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—44no—
727C2×C8C23×D1112yes—
728C2×C8C23×D1112yes—
729C2×C8C23×D1112yes—
730C2×C8C23×D1112yes—
731C4⋊C4—112no—
732C4⋊C4—112no—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—224no—
736C4⋊C4—221no—
737C4⋊C4—221no—
738C4⋊C4—221no—
739C4⋊C4—221no—
740C4⋊C4—224no—
741C4⋊C4—224no—
742C22⋊C4—224no—
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—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—448no—
766C23—442no—
767C23—442no—
768C23—442no—
769C23—442no—
770C23—442no—
771C23—442no—
772C23—442no—
773C23—442no—
774C23—442no—
775C23—884no—
776C23—884no—
777C23—8816no—
778C23C22×D4412yes—
779C23C22×D4412yes—
780C23C22×D4412yes—
781C23C22×D4411yescharacteristic
782Q8—44no—
783Q8—222no—
784Q8—222no—
785Q8—442no—
786D4—44no—
787D4—44no—
788D4—44no—
789D4—222no—
790D4—222no—
791D4—222no—
792D4—222no—
793D4—222no—
794D4—222no—
795D4—448no—
796D4—448no—
797D4—442no—
798D4—442no—
799D4—442no—
800D4—884no—
801D4—884no—
802D4—884no—
803D4—884no—
804D4—884no—
805D4—884no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—448no—
824C2×C4—442no—
825C2×C4—442no—
826C2×C4—442no—
827C2×C4—442no—
828C2×C4—442no—
829C2×C4—884no—
830C2×C4C22×D4412yes—
831C2×C4C22×D4412yes—
832C2×C4C22×D4412yes—
833C2×C4C22×D4411yescharacteristic
834C2×C4#6703712yes—
835C2×C4#6703712yes—
836C2×C4C24×D1111yescharacteristic
837C8—22no—
838C8—22no—
839C8—22no—
840C8—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—442no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—8816no—
863C22—884no—
864C22—884no—
865C22—884no—
866C22#1062302412yes—
867C22#1062328212yes—
868C22#1062328312yes—
869C22C23×D4411yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—442no—
874C4—442no—
875C4—442no—
876C4—442no—
877C4—442no—
878C4#1062302412yes—
879C4C2×#6703711yescharacteristic
880C4C2×#6703711yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—882no—
885C2—882no—
886C2—882no—
887C2#1307947014yesdirect product factor
888C2C2×#1062302411yescharacteristic
889C2C2×#1062328311yescharacteristic
890C2C2×#1062328211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#408C2
socleC23×C11C22×D4
hypercenterC2×#408D11
hypocenterC11C2×#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#10623364C2semidirect
2. C2×#10623361C2semidirect
3. #13079470C2direct (N × H)
4. C2×#10622348C2semidirect
5. C2×#10622336C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622349C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622747C2semidirect
10. C2×#10622728C2semidirect
11. C2×#10622727C2semidirect
12. C2×#10622347C2semidirect
13. C2×#10622347C2semidirect
14. C2×#10622344C2semidirect
15. C2×#10622345C2semidirect
16. C2×C11×#408C2semidirect
18. C22×#4339C22semidirect
20. C22×C11×M16C22semidirect
21. C23×C8×C11C22semidirect
23. #10623364C22semidirect
25. #10623361C22semidirect
39. C2×#66983C22semidirect
41. C22×C4⋊Dic11C22semidirect
43. C2×#66977C22semidirect
48. C11×#408C22semidirect
51. C2×C11×C22⋊C8C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. #10622748C22semidirect
54. #10622747C22semidirect
55. #10622728C22semidirect
56. #10622727C22semidirect
61. C2×#66885C22semidirect
62. C2×#66885C22semidirect
63. C2×#66882C22semidirect
64. C2×#66882C22semidirect
65. C2×#66881C22semidirect
66. C2×#66881C22semidirect
67. C2×#66880C22semidirect
68. C2×#66880C22semidirect
69. #10622350C22semidirect
70. #10622349C22semidirect
71. #10622348C22semidirect
72. #10622347C22semidirect
73. #10622347C22semidirect
74. #10622345C22semidirect
75. #10622344C22semidirect
76. #10622336C22semidirect
100. C2×#4339C23semidirect
112. C2×C11×M16C23semidirect
118. C22×C8×C11C23semidirect
141. #66983C23semidirect
156. C2×C4⋊Dic11C23semidirect
160. #66977C23semidirect
174. C11×C22⋊C8C23semidirect
175. C11×C22⋊C8C23semidirect
180. #66885C23semidirect
181. #66885C23semidirect
182. #66882C23semidirect
183. #66882C23semidirect
184. #66881C23semidirect
185. #66881C23semidirect
186. #66880C23semidirect
187. #66880C23semidirect
323. C2×#408D11semidirect
419. C22×M16C2×D11semidirect
420. C23×C8C2×D11semidirect
467. #408C2×D11semidirect
470. C2×C22⋊C8C2×D11semidirect
471. C2×C22⋊C8C2×D11semidirect
555. C2×M16C22×D11semidirect
561. C22×C8C22×D11semidirect
621. C22⋊C8C22×D11semidirect
622. C22⋊C8C22×D11semidirect
626. C2×C11#3198semidirect
752. C11C2×#3198semidirect
887. C2#13079470direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106233612
#130794702
C2×#106223482
C2×#106223362
C2×#106223502
C2×#106223492
C2×#106227482
C2×#106227472
C2×#106227282
C2×#106227272
C2×#106223472
C2×#106223442
C2×#106223452
C2×C11×#4082
C2×#319811