Finite Group Databasebeta

← C2×#13082529 #15662139

Subgroups — C2×#13082529 #15662139

Order 2816.

7758 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082529C2132yesmaximal, direct product factor
2C2×#10623263C212yesmaximal, complemented
3C2×#10623265C212yesmaximal, complemented
4C2×#10623261C212yesmaximal, complemented
5C2×#10623045C214yesmaximal, complemented
6C2×#10623348C214yesmaximal, complemented
7C2×#10623257C212yesmaximal, complemented
8C2×#10623264C214yesmaximal, complemented
9C2×#10623041C212yesmaximal, complemented
10C2×#10623259C212yesmaximal, complemented
11C2×#10623256C212yesmaximal, complemented
12C2×#10623008C211yesmaximal, characteristic, complemented
13C2×#10623035C212yesmaximal, complemented
14C2×C4×#4339C211yesmaximal, characteristic, complemented
15C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2212yes—
17C22×#4343C2214yes—
18C22×#4339C2212yes—
19C22×#4339C2211yescharacteristic
20C2×C11×C4⋊Q8C2212yes—
21C2×C11×C4⋊Q8C2212yes—
22C2×C11×C4⋊Q8C2212yes—
23C2×C11×C4⋊Q8C2212yes—
24C2×C11×C4⋊Q8C22116yescomplemented
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C22×C42×C11C2211yescharacteristic
28#10623348C22164yescomplemented
29C2×#67000C2214yes—
30C2×#67000C2218yes—
31C2×#66999C2218yes—
32C2×#66999C2214yes—
33C2×Q8×Dic11C2214yes—
34C2×#66983C2212yes—
35C2×#66983C2218yes—
36C2×#66983C2212yes—
37C2×C4×C22⋊D11C2212yes—
38C2×C4×C22⋊D11C2218yes—
39C2×C4×C22⋊D11C2212yes—
40C2×#66979C2211yescharacteristic
41#10623265C22132yescomplemented
42#10623264C22164yescomplemented
43#10623263C22132yescomplemented
44#10623261C22132yescomplemented
45#10623259C22132yescomplemented
46#10623257C22132yescomplemented
47#10623256C22132yescomplemented
48#10623045C22164yescomplemented
49C2×#66951C2218yes—
50#10623041C22132yescomplemented
51C2×#66950C2214yes—
52C2×#66950C2214yes—
53C2×#66948C2214yes—
54C2×#66948C2214yes—
55C2×#66948C2214yes—
56C2×#66947C2218yes—
57#10623035C22132yescomplemented
58C2×#66946C2214yes—
59C2×#66946C2214yes—
60C2×#66945C2214yes—
61C2×#66945C2214yes—
62C2×C4⋊C4×D11C2214yes—
63C2×#66943C2214yes—
64C2×#66940C2214yes—
65#10623008C22116yescomplemented
66C2×#66928C2212yes—
67C2×#66927C2211yescharacteristic
68C4×#4339C22116yescomplemented
69C2×C4×D44C2212yes—
70C2×C4×D44C2212yes—
71C2×C4×D44C2211yescharacteristic
72C2×C4×D44C2211yescharacteristic
73C2×#66925C2212yes—
74C2×C42×D11C2212yes—
75C2×#66922C2211yescharacteristic
76C2×C4×Dic22C2211yescharacteristic
77C2×C4×Dic22C2211yescharacteristic
78C22×Q8×C11—48no—
79C22×Q8×C11C2314yes—
80C22×Q8×C11C2314yes—
81C22×Q8×C11C23116yes—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11C2312yes—
87C22×C22⋊D11C2314yes—
88C2×#4343—416no—
89C2×#4343C23132yes—
90C2×#4339—216no—
91C2×#4339—28no—
92C2×#4339C2318yes—
93C2×#4339C23116yes—
94C22×D44C2311yescharacteristic
95C22×D44C2312yes—
96C22×D44C2312yes—
97C22×D44C2312yes—
98C22×D44C2318yes—
99C22×C4×D11C2312yes—
100C22×C4×D11C2312yes—
101C22×C4×D11C2312yes—
102C22×C4×D11C2314yes—
103C22×C4×D11C2318yes—
104C22×Dic22C2311yescharacteristic
105C22×Dic22C2312yes—
106C11×C4⋊Q8C23116yes—
107C11×C4⋊Q8C23116yes—
108C11×C4⋊Q8C23116yes—
109C11×C4⋊Q8C23116yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2314yes—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C23116yes—
114C2×C11×C4⋊C4C2314yes—
115C2×C11×C4⋊C4C23116yes—
116C2×C42×C11C2311yescharacteristic
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2318yes—
121C2×C22⋊Dic11C2312yes—
122#67000C23132yes—
123#67000C23164yes—
124#66999C23132yes—
125#66999C23164yes—
126Q8×Dic11C23132yes—
127#66983C23116yes—
128#66983C23116yes—
129#66983C23164yes—
130C4×C22⋊D11C23116yes—
131C4×C22⋊D11C23116yes—
132C4×C22⋊D11C23164yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2318yes—
138C2×(C2×D11)⋊C4C2318yes—
139C2×(C2×D11)⋊C4C2318yes—
140#66979C2318yes—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2318yes—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2318yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2312yes—
151C2×C4×Dic11C2312yes—
152C2×C4×Dic11C2318yes—
153#66951C23164yes—
154#66950C23132yes—
155#66950C23132yes—
156#66948C23132yes—
157#66948C23132yes—
158#66948C23132yes—
159#66947C23164yes—
160#66946C23132yes—
161#66946C23132yes—
162#66945C23132yes—
163#66945C23132yes—
164C4⋊C4×D11C23132yes—
165#66943C23132yes—
166#66940C23132yes—
167#66928C23116yes—
168#66927C2318yes—
169C4×D44C2318yes—
170C4×D44C23116yes—
171C4×D44C2318yes—
172C4×D44C23116yes—
173#66925C23116yes—
174C42×D11C23116yes—
175#66922C2318yes—
176C4×Dic22C2318yes—
177C4×Dic22C2318yes—
178C2×#3511—111nomaximal, Sylow
179C24×C11C2411yescharacteristic
180C23×D11C2412yes—
181C23×D11C2414yes—
182C2×Q8×C11—216no—
183C2×Q8×C11—48no—
184C2×Q8×C11—432no—
185C2×Q8×C11C24116yes—
186C2×Q8×C11C24116yes—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—48no—
190C22×C4×C11#4118yescomplemented
191C22×C4×C11C2418yes—
192C22×C4×C11C2411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2414yes—
195C22×C4×C11C2414yes—
196C22×C4×C11C24116yes—
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2414yes—
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—216no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11C2418yes—
205C2×C22⋊D11C24116yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2414yes—
210#4343—464no—
211#4339—232no—
212#4339—264no—
213C2×D44—28no—
214C2×D44—24no—
215C2×D44—28no—
216C2×D44—28no—
217C2×D44—416no—
218C2×D44C2414yes—
219C2×D44C2418yes—
220C2×D44C2418yes—
221C2×D44C2418yes—
222C2×D44C24132yes—
223C2×C4×D11—28no—
224C2×C4×D11—216no—
225C2×C4×D11—28no—
226C2×C4×D11—28no—
227C2×C4×D11—416no—
228C2×C4×D11C2418yes—
229C2×C4×D11C2418yes—
230C2×C4×D11C2418yes—
231C2×C4×D11C24116yes—
232C2×C4×D11C24132yes—
233C2×Dic22—28no—
234C2×Dic22—24no—
235C2×Dic22C2414yes—
236C2×Dic22C2418yes—
237C11×C4⋊C4C24116yes—
238C11×C4⋊C4C24116yes—
239C11×C4⋊C4C24116yes—
240C11×C4⋊C4C24116yes—
241C42×C11C2414yes—
242C42×C11C2414yes—
243C42×C11C2414yes—
244C42×C11C2414yes—
245C22⋊Dic11C2418yes—
246(C2×D11)⋊C4C2418yes—
247(C2×D11)⋊C4C2418yes—
248(C2×D11)⋊C4C24116yes—
249(C2×D11)⋊C4C24116yes—
250(C2×D11)⋊C4C24132yes—
251(C2×D11)⋊C4C24132yes—
252(C2×D11)⋊C4C24132yes—
253C4⋊Dic11C2414yes—
254C4⋊Dic11C2414yes—
255C4⋊Dic11C2418yes—
256C4⋊Dic11C2418yes—
257C4⋊Dic11C24132yes—
258Dic11⋊C4C2418yes—
259Dic11⋊C4C2418yes—
260Dic11⋊C4C24132yes—
261C4×Dic11C2418yes—
262C4×Dic11C2418yes—
263C4×Dic11C2418yes—
264C4×Dic11C24132yes—
265#3511—1132no—
266C2×#556—112no—
267C2×#555—112no—
268C2×#554—112no—
269C2×#553—114no—
270C2×#548—114no—
271C2×#547—112no—
272C2×#542—114no—
273C2×#537—112no—
274C2×#533—112no—
275C2×#532—111no—
276C2×#532—112no—
277C22×C4⋊Q8D1111yescharacteristic, complemented
278C2×#520—112no—
279C2×C4×#41—111no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11C2×#4114yes—
283C23×C11C2512yes—
284C23×C11C2511yescharacteristic
285C22×D11—24no—
286C22×D11—28no—
287C22×D11—24no—
288C22×D11—28no—
289C22×D11—24no—
290C22×D11—28no—
291C22×D11C2514yes—
292C22×D11C2518yes—
293Q8×C11—232no—
294Q8×C11—416no—
295C2×C4×C11—216no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—28no—
299C2×C4×C11—28no—
300C2×C4×C11—416no—
301C2×C4×C11C2×#4114yes—
302C2×C4×C11C2×#4114yes—
303C2×C4×C11C2×#41116yescomplemented
304C2×C4×C11H(5,𝔽2)14yes—
305C2×C4×C112−1+414yes—
306C2×C4×C11C25116yes—
307C2×C4×C11C2512yes—
308C2×C4×C11C2512yes—
309C2×C4×C11C2512yes—
310C2×C4×C11C2512yes—
311C2×C4×C11C2512yes—
312C2×C4×C11C2512yes—
313C22⋊D11—216no—
314C22⋊D11—232no—
315C2×Dic11—28no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11C2514yes—
320C2×Dic11C2514yes—
321C2×Dic11C2514yes—
322C2×Dic11C2518yes—
323D44—216no—
324D44—28no—
325D44—216no—
326D44—216no—
327D44—432no—
328C4×D11—216no—
329C4×D11—232no—
330C4×D11—216no—
331C4×D11—216no—
332C4×D11—432no—
333Dic22—216no—
334Dic22—28no—
335C22×#41—114no—
336C22×#41—111no—
337C22×#41—112no—
338C23×Q8C2×D1112yes—
339#556—1132no—
340#555—1132no—
341#554—1132no—
342#553—1164no—
343#548—1164no—
344#547—1132no—
345#542—1164no—
346#537—1132no—
347#533—1132no—
348#532—1132no—
349#532—1116no—
350C2×C4⋊Q8—111no—
351C2×C4⋊Q8C2×D1112yes—
352C2×C4⋊Q8C2×D1112yes—
353C2×C4⋊Q8C2×D1112yes—
354C2×C4⋊Q8C2×D1112yes—
355C2×C4⋊Q8C2×D11116yescomplemented
356C2×#127—111no—
357C2×#126—118no—
358C2×#125—114no—
359C2×#124—114no—
360C2×#124—118no—
361C2×#124—112no—
362C2×#123—118no—
363C2×C22⋊Q8—114no—
364C2×C22⋊Q8—118no—
365C2×C22⋊Q8—114no—
366C2×C22⋊Q8—114no—
367C2×#121—112no—
368C2×#121—112no—
369C2×#121—118no—
370C2×#121—114no—
371C2×#121—114no—
372C2×#121—114no—
373#520—1132no—
374C4×#41—1116no—
375C2×C4×Q8—114no—
376C2×C4×Q8—114no—
377C2×C4×Q8—111no—
378C2×C4×Q8—111no—
379C2×C4×D4—112no—
380C2×C4×D4—112no—
381C2×C4×D4—118no—
382C2×C4×D4—114no—
383C2×C4×D4—114no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—112no—
387C2×C4×D4—112no—
388C2×#117—111no—
389C2×#117—114no—
390C2×#117—114no—
391C2×#117—112no—
392C22×C4⋊C4—114no—
393C22×C4⋊C4C2×D1112yes—
394C22×C4⋊C4C2×D1112yes—
395C22×C42—112no—
396C22×C42C2×D1111yescharacteristic
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—28no—
400C22×C11C22×#4114yes—
401C22×C11C22×#4112yes—
402C22×C11C2×H(5,𝔽2)12yes—
403C22×C11C2×2−1+412yes—
404C22×C11C2611yescharacteristic
405C2×D11—24no—
406C2×D11—28no—
407C2×D11—24no—
408C2×D11—28no—
409C2×D11—24no—
410C2×D11—28no—
411C2×D11—48no—
412C2×D11—416no—
413C4×C11—22no—
414C4×C11—216no—
415C4×C11—22no—
416C4×C11C22×#4114yes—
417C4×C11C22×#4114yes—
418C4×C11C2×H(5,𝔽2)14yes—
419C4×C11C2×2−1+414yes—
420Dic11—28no—
421Dic11—24no—
422Dic11—24no—
423Dic11—24no—
424C2×#41—1132no—
425C2×#41—118no—
426C2×#41—1116no—
427C2×#41—228no—
428C2×#41—2216no—
429C2×#41—4416no—
430C22×Q8—48no—
431C22×Q8—111no—
432C22×Q8—112no—
433C22×Q8C22×D1114yes—
434C22×Q8C22×D1114yes—
435C22×Q8C22×D11116yes—
436C22×D4—112no—
437C22×D4—114no—
438C22×D4—112no—
439C22×D4—111no—
440C22×D4—112no—
441C22×D4—112no—
442C22×D4—118no—
443C23×C4—114no—
444C23×C4—112no—
445C23×C4—112no—
446C23×C4—112no—
447C23×C4—118no—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1114yes—
451C23×C4C22×D1111yescharacteristic
452C4⋊Q8—118no—
453C4⋊Q8C22×D11116yes—
454C4⋊Q8C22×D11116yes—
455C4⋊Q8C22×D11116yes—
456C4⋊Q8C22×D11116yes—
457#127—118no—
458#126—1164no—
459#125—1132no—
460#124—1132no—
461#124—1164no—
462#124—1116no—
463#123—1164no—
464C22⋊Q8—1132no—
465C22⋊Q8—1164no—
466C22⋊Q8—1132no—
467C22⋊Q8—1132no—
468#121—1116no—
469#121—1116no—
470#121—1164no—
471#121—1132no—
472#121—1132no—
473#121—1132no—
474C4×Q8—1132no—
475C4×Q8—1132no—
476C4×Q8—118no—
477C4×Q8—118no—
478C4×D4—1116no—
479C4×D4—1116no—
480C4×D4—1164no—
481C4×D4—1132no—
482C4×D4—1132no—
483C4×D4—118no—
484C4×D4—118no—
485C4×D4—1116no—
486C4×D4—1116no—
487#117—118no—
488#117—1132no—
489#117—1132no—
490#117—1116no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—118no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—112no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—112no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—118no—
499C2×C4⋊C4—1132no—
500C2×C4⋊C4C22×D1114yes—
501C2×C4⋊C4C22×D1114yes—
502C2×C4⋊C4C22×D1114yes—
503C2×C4⋊C4C22×D11116yes—
504C2×C4⋊C4C22×D1114yes—
505C2×C4⋊C4C22×D11116yes—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—118no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—118no—
511C2×C22⋊C4—118no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—114no—
514C2×C42—112no—
515C2×C42—118no—
516C2×C42—112no—
517C2×C42—112no—
518C2×C42—1116no—
519C2×C42C22×D1111yescharacteristic
520C2×C42C22×D1111yescharacteristic
521C2×C42C22×D1111yescharacteristic
522C2×C42C22×D1118yes—
523C2×C42C22×D1111yescharacteristic
524C2×C11—24no—
525C2×C11#351114yescomplemented
526C2×C11C23×#4111yescharacteristic
527C2×C11C22×H(5,𝔽2)11yescharacteristic
528C2×C11C22×2−1+411yescharacteristic
529D11—44no—
530D11—48no—
531C24—112no—
532C24—114no—
533C24C23×D1111yescharacteristic
534#41—2232no—
535#41—2264no—
536#41—4464no—
537C2×Q8—216no—
538C2×Q8—48no—
539C2×Q8—432no—
540C2×Q8—114no—
541C2×Q8—118no—
542C2×Q8—224no—
543C2×Q8—228no—
544C2×Q8C23×D11116yes—
545C2×Q8C23×D11116yes—
546C2×D4—118no—
547C2×D4—1116no—
548C2×D4—118no—
549C2×D4—114no—
550C2×D4—118no—
551C2×D4—118no—
552C2×D4—1132no—
553C2×D4—228no—
554C2×D4—2216no—
555C2×D4—228no—
556C2×D4—224no—
557C2×D4—228no—
558C2×D4—228no—
559C2×D4—4416no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—48no—
563C22×C4—112no—
564C22×C4—114no—
565C22×C4—112no—
566C22×C4—112no—
567C22×C4—118no—
568C22×C4—118no—
569C22×C4—118no—
570C22×C4—1116no—
571C22×C4—1132no—
572C22×C4—228no—
573C22×C4—2216no—
574C22×C4—228no—
575C22×C4—228no—
576C22×C4—4416no—
577C22×C4#434318yescomplemented
578C22×C4C23×D1114yes—
579C22×C4C23×D1114yes—
580C22×C4C23×D1118yes—
581C22×C4C23×D1111yescharacteristic
582C22×C4C23×D1111yescharacteristic
583C22×C4C23×D11116yes—
584C22×C4C23×D1111yescharacteristic
585C22×C4C23×D1111yescharacteristic
586C22×C4C23×D1111yescharacteristic
587C22×C4C23×D1114yes—
588C22×C4C23×D1111yescharacteristic
589C4⋊C4—114no—
590C4⋊C4—1132no—
591C4⋊C4—114no—
592C4⋊C4—118no—
593C4⋊C4—118no—
594C4⋊C4—118no—
595C4⋊C4—118no—
596C4⋊C4—1132no—
597C4⋊C4C23×D11116yes—
598C4⋊C4C23×D11116yes—
599C4⋊C4C23×D11116yes—
600C4⋊C4C23×D11116yes—
601C22⋊C4—118no—
602C22⋊C4—1132no—
603C22⋊C4—118no—
604C22⋊C4—118no—
605C22⋊C4—1132no—
606C22⋊C4—1132no—
607C22⋊C4—1116no—
608C22⋊C4—1116no—
609C42—118no—
610C42—118no—
611C42—118no—
612C42—1132no—
613C42C23×D1114yes—
614C42C23×D1114yes—
615C42C23×D1114yes—
616C42C23×D1114yes—
617C11C2×#351111yescharacteristic, complemented, Sylow
618C23—22no—
619C23—22no—
620C23—114no—
621C23—118no—
622C23—224no—
623C23—228no—
624C23—224no—
625C23—228no—
626C23—224no—
627C23—228no—
628C23C2×#434314yes—
629C23C24×D1112yes—
630C23C24×D1111yescharacteristic
631Q8—232no—
632Q8—416no—
633Q8—228no—
634Q8—2216no—
635D4—2216no—
636D4—2232no—
637D4—2216no—
638D4—228no—
639D4—2216no—
640D4—2216no—
641D4—4432no—
642C2×C4—22no—
643C2×C4—216no—
644C2×C4—22no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—416no—
648C2×C4—114no—
649C2×C4—114no—
650C2×C4—118no—
651C2×C4—114no—
652C2×C4—224no—
653C2×C4—228no—
654C2×C4—224no—
655C2×C4—224no—
656C2×C4—2216no—
657C2×C4—2232no—
658C2×C4—2216no—
659C2×C4—2216no—
660C2×C4—4432no—
661C2×C4#6703714yes—
662C2×C4C2×#434314yes—
663C2×C4C2×#434314yes—
664C2×C4C2×#4343116yescomplemented
665C2×C4#6704014yes—
666C2×C4C24×D11116yes—
667C2×C4C24×D1112yes—
668C2×C4C24×D1112yes—
669C2×C4C24×D1112yes—
670C2×C4C24×D1112yes—
671C2×C4C24×D1112yes—
672C2×C4C24×D1112yes—
673C22—22no—
674C22—22no—
675C22—28no—
676C22—224no—
677C22—228no—
678C22—224no—
679C22—228no—
680C22—224no—
681C22—228no—
682C22—448no—
683C22—4416no—
684C22C2×#6703712yes—
685C22C22×#434314yes—
686C22C22×#434312yes—
687C22C2×#6704012yes—
688C22C25×D1111yescharacteristic
689C4—22no—
690C4—216no—
691C4—22no—
692C4—224no—
693C4—228no—
694C4—224no—
695C4—224no—
696C4C2×#6703714yes—
697C4C22×#434314yes—
698C4C22×#434314yes—
699C4C2×#6704014yes—
700C2—24no—
701C2—444no—
702C2—448no—
703C2#1308252914yesdirect product factor
704C2C23×#434311yescharacteristic
705C2C22×#6703711yescharacteristic
706C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11C25
hypercenterC22×C4⋊Q8D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13082529C2direct (N × H)
2. C2×#10623263C2semidirect
3. C2×#10623265C2semidirect
4. C2×#10623261C2semidirect
5. C2×#10623045C2semidirect
6. C2×#10623348C2semidirect
7. C2×#10623257C2semidirect
8. C2×#10623264C2semidirect
9. C2×#10623041C2semidirect
10. C2×#10623259C2semidirect
11. C2×#10623256C2semidirect
12. C2×#10623008C2semidirect
13. C2×#10623035C2semidirect
14. C2×C4×#4339C2semidirect
15. C22×C11×C4⋊Q8C2semidirect
24. C2×C11×C4⋊Q8C22semidirect
28. #10623348C22semidirect
41. #10623265C22semidirect
42. #10623264C22semidirect
43. #10623263C22semidirect
44. #10623261C22semidirect
45. #10623259C22semidirect
46. #10623257C22semidirect
47. #10623256C22semidirect
48. #10623045C22semidirect
50. #10623041C22semidirect
57. #10623035C22semidirect
65. #10623008C22semidirect
68. C4×#4339C22semidirect
190. C22×C4×C11#41semidirect
277. C22×C4⋊Q8D11semidirect
303. C2×C4×C11C2×#41semidirect
355. C2×C4⋊Q8C2×D11semidirect
525. C2×C11#3511semidirect
577. C22×C4#4343semidirect
617. C11C2×#3511semidirect
664. C2×C4C2×#4343semidirect
703. C2#13082529direct (N × H)

Maximal subgroups

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

subgroupindex
#130825292
C2×#106232632
C2×#106232652
C2×#106232612
C2×#106230452
C2×#106233482
C2×#106232572
C2×#106232642
C2×#106230412
C2×#106232592
C2×#106232562
C2×#106230082
C2×#106230352
C2×C4×#43392
C22×C11×C4⋊Q82
C2×#351111