Finite Group Databasebeta

← C2×#13082523 #15662149

Subgroups — C2×#13082523 #15662149

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#13082523C2132yesmaximal, direct product factor
2C2×#10623073C212yesmaximal, complemented
3C2×#10623094C212yesmaximal, complemented
4C2×#10623074C212yesmaximal, complemented
5C2×#10623149C214yesmaximal, complemented
6C2×#10623129C214yesmaximal, complemented
7C2×#10623086C212yesmaximal, complemented
8C2×#10623213C214yesmaximal, complemented
9C2×#10623364C212yesmaximal, complemented
10C2×#10623259C212yesmaximal, complemented
11C2×#10623247C212yesmaximal, complemented
12C22×#66922C211yesmaximal, characteristic, complemented
13C2×#10623358C212yesmaximal, complemented
14C2×C4×#4339C211yesmaximal, characteristic, complemented
15C2×C11×#532C211yesmaximal, characteristic, complemented
16C22×C11×#41C2212yes—
17C22×#4341C2214yes—
18C22×#4339C2211yescharacteristic
19C23×Dic22C2212yes—
20C11×#532C22116yescomplemented
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#127C2211yescharacteristic
23C2×C11×#124C2212yes—
24C2×C11×#121C2212yes—
25C2×C11×#121C2212yes—
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2212yes—
28C22×C42×C11C2211yescharacteristic
29#10623364C22132yescomplemented
30#10623358C22132yescomplemented
31C2×#66999C2214yes—
32C2×Q8×Dic11C2214yes—
33C2×#66992C2218yes—
34C2×#66991C2214yes—
35C2×#66991C2214yes—
36C2×#66989C2214yes—
37C2×D4×Dic11C2214yes—
38C2×D4×Dic11C2218yes—
39C2×D4×Dic11C2214yes—
40C2×#66983C2214yes—
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2212yes—
43C2×#66979C2214yes—
44C2×#66979C2211yescharacteristic
45C22×C4⋊Dic11C2212yes—
46C22×C4⋊Dic11C2214yes—
47C22×C4⋊Dic11C2212yes—
48C2×#66977C2214yes—
49#10623259C22132yescomplemented
50#10623247C22132yescomplemented
51#10623213C22164yescomplemented
52#10623149C22164yescomplemented
53#10623129C22164yescomplemented
54#10623094C22132yescomplemented
55#10623086C22132yescomplemented
56#10623074C22132yescomplemented
57#10623073C22132yescomplemented
58C2×#66950C2214yes—
59C2×#66945C2214yes—
60C2×#66943C2214yes—
61C2×#66940C2214yes—
62C2×#66939C2218yes—
63C2×#66938C2218yes—
64C2×#66932C2218yes—
65C2×#66931C2218yes—
66C4×#4339C22116yescomplemented
67C2×C4×D44C2211yescharacteristic
68C2×C4×D44C2211yescharacteristic
69C2×#66925C2212yes—
70C2×C42×D11C2212yes—
71C2×#66922C2212yes—
72C2×#66922C2212yes—
73C2×#66922C2212yes—
74C2×#66922C2212yes—
75C2×#66922C22116yescomplemented
76C2×C4×Dic22C2211yescharacteristic
77C2×C4×Dic22C2211yescharacteristic
78C2×C11×#41—216no—
79C2×C11×#41C23116yes—
80C22×Q8×C11C2312yes—
81C22×D4×C11C2312yes—
82C22×D4×C11C2312yes—
83C22×D4×C11C2314yes—
84C22×D4×C11C2312yes—
85C23×C4×C11C2314yes—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2318yes—
91C23×Dic11C2318yes—
92C23×Dic11C2314yes—
93C2×#4341—416no—
94C2×#4341C23132yes—
95C2×#4339—28no—
96C2×#4339C2318yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11C2312yes—
99C22×C4×D11C2312yes—
100C22×C4×D11C2312yes—
101C22×Dic22—48no—
102C22×Dic22C2311yescharacteristic
103C22×Dic22C2314yes—
104C22×Dic22C2314yes—
105C22×Dic22C23116yes—
106C11×C4⋊Q8C2318yes—
107C11×#127C2318yes—
108C11×#124C23116yes—
109C11×#121C23116yes—
110C11×#121C23116yes—
111C4×D4×C11C23116yes—
112C4×D4×C11C23116yes—
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2318yes—
122C2×C22⋊Dic11C2318yes—
123C2×C22⋊Dic11C2318yes—
124C2×C22⋊Dic11C2312yes—
125#66999C23132yes—
126Q8×Dic11C23132yes—
127#66992C23164yes—
128#66991C23132yes—
129#66991C23132yes—
130#66989C23132yes—
131D4×Dic11C23132yes—
132D4×Dic11C23132yes—
133D4×Dic11C23164yes—
134#66983C23132yes—
135C4×C22⋊D11C23116yes—
136C4×C22⋊D11C23116yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2318yes—
140#66979C2318yes—
141#66979C23132yes—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2314yes—
145C2×C4⋊Dic11C2314yes—
146C2×C4⋊Dic11C2314yes—
147C2×C4⋊Dic11C2314yes—
148C2×C4⋊Dic11C23116yes—
149C2×C4⋊Dic11C23116yes—
150C2×C4⋊Dic11C2318yes—
151C2×C4⋊Dic11C23132yes—
152#66977C23132yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2318yes—
156C2×C4×Dic11C2312yes—
157C2×C4×Dic11C2312yes—
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2318yes—
160#66950C23132yes—
161#66945C23132yes—
162#66943C23132yes—
163#66940C23132yes—
164#66939C23164yes—
165#66938C23164yes—
166#66932C23164yes—
167#66931C23164yes—
168C4×D44C2318yes—
169C4×D44C2318yes—
170#66925C23116yes—
171C42×D11C23116yes—
172#66922C23116yes—
173#66922C23116yes—
174#66922C23116yes—
175#66922C23116yes—
176C4×Dic22C2318yes—
177C4×Dic22C2318yes—
178C2×#3511—111nomaximal, Sylow
179C24×C11C2414yes—
180C24×C11C2411yescharacteristic
181C23×D11C2412yes—
182C11×#41—264no—
183C2×Q8×C11—28no—
184C2×Q8×C11C2418yes—
185C2×D4×C11—216no—
186C2×D4×C11—28no—
187C2×D4×C11—28no—
188C2×D4×C11—28no—
189C2×D4×C11C2418yes—
190C2×D4×C11C2418yes—
191C2×D4×C11C24116yes—
192C2×D4×C11C2418yes—
193C22×C4×C11—216no—
194C22×C4×C11—24no—
195C22×C4×C11—24no—
196C22×C4×C11#4118yescomplemented
197C22×C4×C11C2414yes—
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C24116yes—
201C22×C4×C11C2414yes—
202C22×C4×C11C2414yes—
203C22×C4×C11C2411yescharacteristic
204C22×C4×C11C2411yescharacteristic
205C22×C4×C11C2414yes—
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—28no—
209C2×C22⋊D11—416no—
210C2×C22⋊D11C2418yes—
211C2×C22⋊D11C24132yes—
212C22×Dic11—48no—
213C22×Dic11—416no—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2418yes—
218C22×Dic11C24132yes—
219C22×Dic11C24116yes—
220#4341—464no—
221#4339—232no—
222C2×D44—24no—
223C2×D44C2414yes—
224C2×C4×D11—28no—
225C2×C4×D11—28no—
226C2×C4×D11—28no—
227C2×C4×D11C2418yes—
228C2×C4×D11C2418yes—
229C2×C4×D11C2418yes—
230C2×Dic22—24no—
231C2×Dic22—216no—
232C2×Dic22—432no—
233C2×Dic22—48no—
234C2×Dic22C2414yes—
235C2×Dic22C24116yes—
236C2×Dic22C24116yes—
237C11×C4⋊C4C2418yes—
238C11×C4⋊C4C2418yes—
239C11×C22⋊C4C24116yes—
240C11×C22⋊C4C24116yes—
241C42×C11C2414yes—
242C42×C11C2414yes—
243C42×C11C2414yes—
244C42×C11C2414yes—
245C22⋊Dic11C24132yes—
246C22⋊Dic11C24132yes—
247C22⋊Dic11C2418yes—
248(C2×D11)⋊C4C2418yes—
249(C2×D11)⋊C4C2418yes—
250(C2×D11)⋊C4C24132yes—
251C4⋊Dic11C2414yes—
252C4⋊Dic11C2414yes—
253C4⋊Dic11C24116yes—
254C4⋊Dic11C24116yes—
255C4⋊Dic11C24116yes—
256C4⋊Dic11C24116yes—
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—112no—
276C2×#532D1111yescharacteristic, complemented
277C22×C4⋊Q8—111no—
278C2×#520—112no—
279C2×C4×#41—111no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—28no—
283C23×C11—28no—
284C23×C11—28no—
285C23×C11C2×#4114yes—
286C23×C11C2518yes—
287C23×C11C2512yes—
288C23×C11C2511yescharacteristic
289C22×D11—24no—
290C22×D11—24no—
291C22×D11—24no—
292C22×D11C2514yes—
293Q8×C11—216no—
294D4×C11—232no—
295D4×C11—216no—
296D4×C11—216no—
297D4×C11—216no—
298C2×C4×C11—28no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—232no—
302C2×C4×C11—28no—
303C2×C4×C11—28no—
304C2×C4×C11C2×#4114yes—
305C2×C4×C11C2×#4114yes—
306C2×C4×C11C2×#41116yescomplemented
307C2×C4×C11H(5,𝔽2)14yes—
308C2×C4×C112−1+414yes—
309C2×C4×C11C2518yes—
310C2×C4×C11C2512yes—
311C2×C4×C11C2512yes—
312C2×C4×C11C2512yes—
313C2×C4×C11C2512yes—
314C2×C4×C11C2512yes—
315C2×C4×C11C2512yes—
316C22⋊D11—216no—
317C22⋊D11—432no—
318C2×Dic11—24no—
319C2×Dic11—216no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—416no—
323C2×Dic11—432no—
324C2×Dic11C2514yes—
325C2×Dic11C2514yes—
326C2×Dic11C2514yes—
327C2×Dic11C25116yes—
328D44—28no—
329C4×D11—216no—
330C4×D11—216no—
331C4×D11—216no—
332Dic22—28no—
333Dic22—232no—
334Dic22—416no—
335C22×#41—114no—
336C22×#41—111no—
337C22×#41C2×D1112yes—
338C23×Q8—112no—
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#532C2×D11116yescomplemented
350C2×C4⋊Q8—112no—
351C2×C4⋊Q8—112no—
352C2×C4⋊Q8—112no—
353C2×C4⋊Q8—112no—
354C2×C4⋊Q8—1116no—
355C2×C4⋊Q8C2×D1111yescharacteristic
356C2×#127C2×D1111yescharacteristic
357C2×#126—118no—
358C2×#125—114no—
359C2×#124—114no—
360C2×#124—118no—
361C2×#124C2×D1112yes—
362C2×#123—118no—
363C2×C22⋊Q8—114no—
364C2×C22⋊Q8—114no—
365C2×C22⋊Q8—114no—
366C2×C22⋊Q8—118no—
367C2×#121—114no—
368C2×#121—114no—
369C2×#121—118no—
370C2×#121—114no—
371C2×#121C2×D1112yes—
372C2×#121C2×D1112yes—
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—114no—
380C2×C4×D4—118no—
381C2×C4×D4—114no—
382C2×C4×D4—112no—
383C2×C4×D4—112no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4C2×D1112yes—
387C2×C4×D4C2×D1112yes—
388C2×#117—111no—
389C2×#117—114no—
390C2×#117—114no—
391C2×#117—112no—
392C22×C4⋊C4—112no—
393C22×C4⋊C4—114no—
394C22×C4⋊C4—112no—
395C22×C42—112no—
396C22×C42C2×D1111yescharacteristic
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—28no—
400C22×C11—28no—
401C22×C11—28no—
402C22×C11—28no—
403C22×C11—416no—
404C22×C11C22×#4114yes—
405C22×C11C22×#4112yes—
406C22×C11C2×H(5,𝔽2)12yes—
407C22×C11C2×2−1+412yes—
408C22×C11C2611yescharacteristic
409C2×D11—24no—
410C2×D11—24no—
411C2×D11—24no—
412C2×D11—48no—
413C4×C11—28no—
414C4×C11—22no—
415C4×C11—22no—
416C4×C11C22×#4114yes—
417C4×C11C22×#4114yes—
418C4×C11C2×H(5,𝔽2)14yes—
419C4×C11C2×2−1+414yes—
420Dic11—24no—
421Dic11—216no—
422Dic11—24no—
423Dic11—24no—
424C2×#41—216no—
425C2×#41—1132no—
426C2×#41—118no—
427C2×#41—228no—
428C2×#41—4416no—
429C2×#41C22×D11116yes—
430C22×Q8—111no—
431C22×Q8—114no—
432C22×Q8—114no—
433C22×Q8—1116no—
434C22×Q8—448no—
435C22×Q8C22×D1112yes—
436C22×D4—112no—
437C22×D4—118no—
438C22×D4—111no—
439C22×D4C22×D1112yes—
440C22×D4C22×D1114yes—
441C22×D4C22×D1112yes—
442C22×D4C22×D1112yes—
443C23×C4—114no—
444C23×C4—118no—
445C23×C4—112no—
446C23×C4—112no—
447C23×C4—112no—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1114yes—
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1111yescharacteristic
452C4⋊Q8—1116no—
453C4⋊Q8—1116no—
454C4⋊Q8—1116no—
455C4⋊Q8—1116no—
456C4⋊Q8C22×D1118yes—
457#127C22×D1118yes—
458#126—1164no—
459#125—1132no—
460#124—1132no—
461#124—1164no—
462#124C22×D11116yes—
463#123—1164no—
464C22⋊Q8—1132no—
465C22⋊Q8—1132no—
466C22⋊Q8—1132no—
467C22⋊Q8—1164no—
468#121—1132no—
469#121—1132no—
470#121—1164no—
471#121—1132no—
472#121C22×D11116yes—
473#121C22×D11116yes—
474C4×Q8—1132no—
475C4×Q8—1132no—
476C4×Q8—118no—
477C4×Q8—118no—
478C4×D4—1132no—
479C4×D4—1164no—
480C4×D4—1132no—
481C4×D4—1116no—
482C4×D4—1116no—
483C4×D4—118no—
484C4×D4—118no—
485C4×D4C22×D11116yes—
486C4×D4C22×D11116yes—
487#117—118no—
488#117—1132no—
489#117—1132no—
490#117—1116no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4—118no—
496C2×C4⋊C4—1116no—
497C2×C4⋊C4—1132no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—1116no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—112no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—118no—
504C2×C4⋊C4C22×D1112yes—
505C2×C4⋊C4C22×D1112yes—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—118no—
508C2×C22⋊C4—118no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—112no—
511C2×C22⋊C4—118no—
512C2×C22⋊C4C22×D1114yes—
513C2×C22⋊C4C22×D1114yes—
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—48no—
526C2×C11#351114yescomplemented
527C2×C11C23×#4111yescharacteristic
528C2×C11C22×H(5,𝔽2)11yescharacteristic
529C2×C11C22×2−1+411yescharacteristic
530D11—44no—
531C24—112no—
532C24C23×D1114yes—
533C24C23×D1111yescharacteristic
534#41—264no—
535#41—2232no—
536#41—4464no—
537C2×Q8—28no—
538C2×Q8—114no—
539C2×Q8—1116no—
540C2×Q8—1116no—
541C2×Q8—224no—
542C2×Q8—2216no—
543C2×Q8—448no—
544C2×Q8—4432no—
545C2×Q8C23×D1118yes—
546C2×D4—216no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—118no—
551C2×D4—1132no—
552C2×D4—114no—
553C2×D4—228no—
554C2×D4—224no—
555C2×D4—4416no—
556C2×D4C23×D1118yes—
557C2×D4C23×D11116yes—
558C2×D4C23×D1118yes—
559C2×D4C23×D1118yes—
560C22×C4—216no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—118no—
567C22×C4—1116no—
568C22×C4—1132no—
569C22×C4—118no—
570C22×C4—118no—
571C22×C4—118no—
572C22×C4—228no—
573C22×C4—228no—
574C22×C4—228no—
575C22×C4—448no—
576C22×C4—4416no—
577C22×C4#434118yescomplemented
578C22×C4C23×D1114yes—
579C22×C4C23×D1114yes—
580C22×C4C23×D11116yes—
581C22×C4C23×D1114yes—
582C22×C4C23×D1111yescharacteristic
583C22×C4C23×D1111yescharacteristic
584C22×C4C23×D1111yescharacteristic
585C22×C4C23×D1111yescharacteristic
586C22×C4C23×D1114yes—
587C22×C4C23×D1111yescharacteristic
588C22×C4C23×D1111yescharacteristic
589C4⋊C4—114no—
590C4⋊C4—1116no—
591C4⋊C4—1116no—
592C4⋊C4—1116no—
593C4⋊C4—1132no—
594C4⋊C4—1116no—
595C4⋊C4—114no—
596C4⋊C4—118no—
597C4⋊C4—118no—
598C4⋊C4—1132no—
599C4⋊C4C23×D1118yes—
600C4⋊C4C23×D1118yes—
601C22⋊C4—118no—
602C22⋊C4—1132no—
603C22⋊C4—1132no—
604C22⋊C4—118no—
605C22⋊C4—118no—
606C22⋊C4—1132no—
607C22⋊C4C23×D11116yes—
608C22⋊C4C23×D11116yes—
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—28no—
621C23—28no—
622C23—28no—
623C23—114no—
624C23—224no—
625C23—224no—
626C23—224no—
627C23C2×#434114yes—
628C23C24×D1118yes—
629C23C24×D1112yes—
630C23C24×D1111yescharacteristic
631Q8—216no—
632Q8—228no—
633Q8—2232no—
634Q8—4416no—
635D4—232no—
636D4—216no—
637D4—216no—
638D4—216no—
639D4—2216no—
640D4—228no—
641D4—4432no—
642C2×C4—28no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—232no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—114no—
649C2×C4—114no—
650C2×C4—114no—
651C2×C4—1116no—
652C2×C4—224no—
653C2×C4—224no—
654C2×C4—2216no—
655C2×C4—224no—
656C2×C4—2216no—
657C2×C4—2216no—
658C2×C4—2216no—
659C2×C4—4416no—
660C2×C4—4432no—
661C2×C4C2×#434114yes—
662C2×C4C2×#434114yes—
663C2×C4C2×#4341116yescomplemented
664C2×C4#6704214yes—
665C2×C4#6704314yes—
666C2×C4C24×D1118yes—
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—28no—
677C22—28no—
678C22—28no—
679C22—416no—
680C22—224no—
681C22—224no—
682C22—224no—
683C22—448no—
684C22C22×#434114yes—
685C22C22×#434112yes—
686C22C2×#6704212yes—
687C22C2×#6704312yes—
688C22C25×D1111yescharacteristic
689C4—28no—
690C4—22no—
691C4—22no—
692C4—224no—
693C4—224no—
694C4—2216no—
695C4—224no—
696C4C22×#434114yes—
697C4C22×#434114yes—
698C4C2×#6704214yes—
699C4C2×#6704314yes—
700C2—24no—
701C2—48no—
702C2—444no—
703C2#1308252314yesdirect product factor
704C2C23×#434111yescharacteristic
705C2C22×#6704211yescharacteristic
706C2C22×#6704311yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#532C2
socleC23×C11C25
hypercenterC2×#532D11
hypocenterC11C2×#3511
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13082523C2direct (N × H)
2. C2×#10623073C2semidirect
3. C2×#10623094C2semidirect
4. C2×#10623074C2semidirect
5. C2×#10623149C2semidirect
6. C2×#10623129C2semidirect
7. C2×#10623086C2semidirect
8. C2×#10623213C2semidirect
9. C2×#10623364C2semidirect
10. C2×#10623259C2semidirect
11. C2×#10623247C2semidirect
12. C22×#66922C2semidirect
13. C2×#10623358C2semidirect
14. C2×C4×#4339C2semidirect
15. C2×C11×#532C2semidirect
20. C11×#532C22semidirect
29. #10623364C22semidirect
30. #10623358C22semidirect
49. #10623259C22semidirect
50. #10623247C22semidirect
51. #10623213C22semidirect
52. #10623149C22semidirect
53. #10623129C22semidirect
54. #10623094C22semidirect
55. #10623086C22semidirect
56. #10623074C22semidirect
57. #10623073C22semidirect
66. C4×#4339C22semidirect
75. C2×#66922C22semidirect
196. C22×C4×C11#41semidirect
276. C2×#532D11semidirect
306. C2×C4×C11C2×#41semidirect
349. #532C2×D11semidirect
526. C2×C11#3511semidirect
577. C22×C4#4341semidirect
617. C11C2×#3511semidirect
663. C2×C4C2×#4341semidirect
703. C2#13082523direct (N × H)

Maximal subgroups

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

subgroupindex
#130825232
C2×#106230732
C2×#106230942
C2×#106230742
C2×#106231492
C2×#106231292
C2×#106230862
C2×#106232132
C2×#106233642
C2×#106232592
C2×#106232472
C22×#669222
C2×#106233582
C2×C4×#43392
C2×C11×#5322
C2×#351111