Finite Group Databasebeta

← C2×#22574126 #31764332

Subgroups — C2×#22574126 #31764332

Order 17152.

7238 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574126C2132yesmaximal, direct product factor
2C2×#16864095C214yesmaximal, complemented
3C2×#16864094C212yesmaximal, complemented
4C2×#16864092C214yesmaximal, complemented
5C2×#16864090C212yesmaximal, complemented
6C2×#16864085C212yesmaximal, complemented
7C2×#16864081C212yesmaximal, complemented
8C2×#16864004C212yesmaximal, complemented
9C2×#16863997C212yesmaximal, complemented
10C2×#16863977C211yesmaximal, characteristic, complemented
11C2×#16863974C211yesmaximal, characteristic, complemented
12C2×#16863942C211yesmaximal, characteristic, complemented
13C2×#16863933C212yesmaximal, complemented
14C2×#16863928C212yesmaximal, complemented
15C22×#14524034C211yesmaximal, characteristic, complemented
16C2×#16863876C211yesmaximal, characteristic, complemented
17C2×#16863864C211yesmaximal, characteristic, complemented
18C2×#520×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2211yescharacteristic
20C22×#11761628C2211yescharacteristic
21#16864095C22164yescomplemented
22#16864094C22132yescomplemented
23#16864092C22164yescomplemented
24#16864090C22132yescomplemented
25#16864085C22132yescomplemented
26#16864081C22132yescomplemented
27#16864004C22132yescomplemented
28#16863997C22132yescomplemented
29#16863977C22116yescomplemented
30#16863974C22116yescomplemented
31#16863942C22116yescomplemented
32C2×#14524041C2211yescharacteristic
33C2×#14524039C2211yescharacteristic
34#16863933C22132yescomplemented
35#16863928C22132yescomplemented
36C2×#14524038C2214yes—
37C2×#14524038C2214yes—
38C2×#14524037C2214yes—
39C2×#14524036C2214yes—
40C2×#14524035C2214yes—
41C2×#14524034C2212yes—
42C2×#14524034C2212yes—
43C2×#14524034C2212yes—
44C2×#14524034C2212yes—
45C2×#14524034C22116yescomplemented
46C2×#14524033C2214yes—
47C2×#14524032C2211yescharacteristic
48C2×#14524030C2211yescharacteristic
49C2×#14524028C2214yes—
50C2×#14524026C2214yes—
51C2×#14524025C2214yes—
52C2×#14524025C2214yes—
53C2×#14524023C2212yes—
54C2×#14524023C2212yes—
55C2×#14524022C2212yes—
56C2×#14524019C2212yes—
57C2×#14524018C2212yes—
58C2×#14524018C2212yes—
59C2×#14524017C2212yes—
60C2×#14524017C2214yes—
61C2×#14524017C2214yes—
62C2×#14524016C2214yes—
63C2×#14524015C2212yes—
64C2×#14524015C2214yes—
65C2×#14524015C2212yes—
66C2×#14524014C2212yes—
67#16863876C22116yescomplemented
68#16863864C22116yescomplemented
69C2×C4×Dic134C2212yes—
70C2×#14524008C2211yescharacteristic
71C2×#14524008C2211yescharacteristic
72C2×C4×D268C2212yes—
73C2×C4×D268C2214yes—
74C2×#14524005C2211yescharacteristic
75C2×#14524005C2211yescharacteristic
76C2×C4×C22⋊D67C2212yes—
77C2×C4×C22⋊D67C2212yes—
78C2×C4×C22⋊D67C2214yes—
79C2×(C22⋊D67)⋊C4C2212yes—
80C2×(C22⋊D67)⋊C4C2212yes—
81C2×(C22⋊D67)⋊C4C2214yes—
82C2×#14524002C2214yes—
83C2×#14524001C2212yes—
84C2×#14524000C2212yes—
85C2×#14524000C2214yes—
86C22×C4⋊Dic67C2211yescharacteristic
87C22×C4⋊Dic67C2212yes—
88C22×Dic67⋊C4C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C22×C4×Dic67C2211yescharacteristic
91C2×C42×D67C2212yes—
92C22×#41×C67C2211yescharacteristic
93#520×C67C22116yescomplemented
94C2×C4×Q8×C67C2212yes—
95C2×C4×D4×C67C2214yes—
96C2×C4×D4×C67C2212yes—
97C2×#117×C67C2211yescharacteristic
98C2×#117×C67C2212yes—
99C22×C4⋊C4×C67C2212yes—
100C22×C4⋊C4×C67C2211yescharacteristic
101C2×#11761628—28no—
102C2×#11761628—28no—
103C2×#11761628C2318yes—
104C2×#11761628C2318yes—
105C22×Dic134C2311yescharacteristic
106C22×Dic134C2311yescharacteristic
107C22×D268C2311yescharacteristic
108C22×D268C2311yescharacteristic
109C22×D268C2314yes—
110C22×C22⋊D67C2312yes—
111C22×C22⋊D67C2312yes—
112C22×C22⋊D67C2314yes—
113C22×C22⋊D67C2312yes—
114C22×C22⋊D67C2312yes—
115C23×Dic67C2311yescharacteristic
116C23×Dic67C2311yescharacteristic
117C23×Dic67C2312yes—
118C22×C4×D67C2312yes—
119C22×C4×D67C2312yes—
120C22×C4×D67C2312yes—
121C22×C4×D67C2312yes—
122C22×C4×D67C2314yes—
123#14524041C2318yes—
124#14524039C2318yes—
125#14524038C23132yes—
126#14524038C23132yes—
127#14524037C23132yes—
128#14524036C23132yes—
129#14524035C23132yes—
130#14524034C23116yes—
131#14524034C23116yes—
132#14524034C23116yes—
133#14524034C23116yes—
134#14524033C23132yes—
135#14524032C2318yes—
136#14524030C2318yes—
137#14524028C23132yes—
138#14524026C23132yes—
139#14524025C23132yes—
140#14524025C23132yes—
141#14524023C23116yes—
142#14524023C23116yes—
143#14524022C23116yes—
144#14524019C23116yes—
145#14524018C23116yes—
146#14524018C23116yes—
147#14524017C23116yes—
148#14524017C23132yes—
149#14524017C23132yes—
150#14524016C23132yes—
151#14524015C23116yes—
152#14524015C23132yes—
153#14524015C23116yes—
154#14524014C23116yes—
155C4×Dic134C23116yes—
156#14524008C2318yes—
157#14524008C2318yes—
158C4×D268C23132yes—
159C4×D268C23116yes—
160#14524005C2318yes—
161#14524005C2318yes—
162C4×C22⋊D67C23116yes—
163C4×C22⋊D67C23116yes—
164C4×C22⋊D67C23132yes—
165(C22⋊D67)⋊C4C23116yes—
166(C22⋊D67)⋊C4C23132yes—
167(C22⋊D67)⋊C4C23116yes—
168#14524002C23132yes—
169#14524001C23116yes—
170#14524000C23116yes—
171#14524000C23132yes—
172C2×C4⋊Dic67C23116yes—
173C2×C4⋊Dic67C2312yes—
174C2×C4⋊Dic67C2314yes—
175C2×C4⋊Dic67C2312yes—
176C2×C4⋊Dic67C2318yes—
177C2×C4⋊Dic67C2314yes—
178C2×C4⋊Dic67C2314yes—
179C2×Dic67⋊C4C23116yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2314yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C4⋊C4×D67C23116yes—
189C2×C22⋊Dic67C2312yes—
190C2×C22⋊Dic67C2314yes—
191C2×C22⋊Dic67C2312yes—
192C2×(C2×D67)⋊C4C2312yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2314yes—
200C2×C4×Dic67C2311yescharacteristic
201C2×C4×Dic67C2312yes—
202C2×C4×Dic67C2312yes—
203C2×C4×Dic67C2311yescharacteristic
204C2×C4×Dic67C2311yescharacteristic
205C2×C4×Dic67C2311yescharacteristic
206C2×C4×Dic67C2318yes—
207C2×C4×Dic67C2314yes—
208C42×D67C23116yes—
209C2×#41×C67—28no—
210C2×#41×C67C2318yes—
211C22×Q8×C67C2311yescharacteristic
212C22×D4×C67C2311yescharacteristic
213C22×D4×C67C2312yes—
214C23×C4×C67C2312yes—
215C23×C4×C67C2312yes—
216C23×C4×C67C2314yes—
217C23×C4×C67C2311yescharacteristic
218C4×Q8×C67C23116yes—
219C4×D4×C67C23132yes—
220C4×D4×C67C23116yes—
221#117×C67C23116yes—
222#117×C67C2318yes—
223C2×C4⋊C4×C67C2311yescharacteristic
224C2×C4⋊C4×C67C2312yes—
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2314yes—
227C2×C4⋊C4×C67C23116yes—
228C2×C4⋊C4×C67C2318yes—
229C2×C4⋊C4×C67C2311yescharacteristic
230C2×C22⋊C4×C67C2312yes—
231C2×C22⋊C4×C67C2314yes—
232C2×C42×C67C2312yes—
233C2×C42×C67C2314yes—
234C23×D67C2412yes—
235C23×D67C2412yes—
236#11761628—232no—
237#11761628—232no—
238C2×Dic134—24no—
239C2×Dic134—24no—
240C2×Dic134C2414yes—
241C2×Dic134C2414yes—
242C2×D268—24no—
243C2×D268—24no—
244C2×D268—48no—
245C2×D268C2414yes—
246C2×D268C2414yes—
247C2×D268C24116yes—
248C2×C22⋊D67—28no—
249C2×C22⋊D67—28no—
250C2×C22⋊D67—48no—
251C2×C22⋊D67—44no—
252C2×C22⋊D67—44no—
253C2×C22⋊D67C2418yes—
254C2×C22⋊D67C2418yes—
255C2×C22⋊D67C24116yes—
256C2×C22⋊D67C2418yes—
257C2×C22⋊D67C2418yes—
258C22×Dic67—42no—
259C22×Dic67—42no—
260C22×Dic67—44no—
261C22×Dic67C2411yescharacteristic
262C22×Dic67C2411yescharacteristic
263C22×Dic67C2412yes—
264C22×Dic67C2412yes—
265C22×Dic67C2411yescharacteristic
266C22×Dic67C2411yescharacteristic
267C22×Dic67C2414yes—
268C22×Dic67C2414yes—
269C22×Dic67C2414yes—
270C22×Dic67C2418yes—
271C2×C4×D67—28no—
272C2×C4×D67—28no—
273C2×C4×D67—44no—
274C2×C4×D67—44no—
275C2×C4×D67—48no—
276C2×C4×D67C2418yes—
277C2×C4×D67C2418yes—
278C2×C4×D67C2418yes—
279C2×C4×D67C2418yes—
280C2×C4×D67C24116yes—
281C4⋊Dic67C2418yes—
282C4⋊Dic67C24116yes—
283C4⋊Dic67C2418yes—
284C4⋊Dic67C24116yes—
285C4⋊Dic67C24116yes—
286Dic67⋊C4C24116yes—
287Dic67⋊C4C24116yes—
288Dic67⋊C4C24116yes—
289Dic67⋊C4C2418yes—
290Dic67⋊C4C2418yes—
291Dic67⋊C4C24116yes—
292Dic67⋊C4C2418yes—
293Dic67⋊C4C2418yes—
294C22⋊Dic67C2418yes—
295C22⋊Dic67C24116yes—
296C22⋊Dic67C2418yes—
297(C2×D67)⋊C4C2418yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C24116yes—
301(C2×D67)⋊C4C24116yes—
302(C2×D67)⋊C4C2418yes—
303(C2×D67)⋊C4C24116yes—
304(C2×D67)⋊C4C24116yes—
305C4×Dic67C2414yes—
306C4×Dic67C2418yes—
307C4×Dic67C2418yes—
308C4×Dic67C2414yes—
309C4×Dic67C2414yes—
310C4×Dic67C2414yes—
311C4×Dic67C24116yes—
312C24×C67C2412yes—
313C24×C67C2411yescharacteristic
314#41×C67—232no—
315C2×Q8×C67—24no—
316C2×Q8×C67C2414yes—
317C2×D4×C67—28no—
318C2×D4×C67—24no—
319C2×D4×C67C2414yes—
320C2×D4×C67C2418yes—
321C22×C4×C67—28no—
322C22×C4×C67—48no—
323C22×C4×C67—44no—
324C22×C4×C67#4118yes—
325C22×C4×C67C2412yes—
326C22×C4×C67C2412yes—
327C22×C4×C67C2412yes—
328C22×C4×C67C2414yes—
329C22×C4×C67C2418yes—
330C22×C4×C67C2418yes—
331C22×C4×C67C24116yes—
332C22×C4×C67C2411yescharacteristic
333C22×C4×C67C2411yescharacteristic
334C22×C4×C67C2414yes—
335C4⋊C4×C67C2414yes—
336C4⋊C4×C67C2418yes—
337C4⋊C4×C67C2418yes—
338C4⋊C4×C67C24116yes—
339C4⋊C4×C67C2414yes—
340C22⋊C4×C67C2418yes—
341C22⋊C4×C67C24116yes—
342C42×C67C2418yes—
343C42×C67C24116yes—
344C23×C67—22no—
345C23×C67—22no—
346C23×C67—24no—
347C23×C67—24no—
348C23×C67—24no—
349C23×C67C2×#4114yes—
350C23×C67C2514yes—
351C23×C67C2512yes—
352C23×C67C2511yescharacteristic
353C22×D67—24no—
354C22×D67—24no—
355C22×D67—24no—
356C22×D67—24no—
357C22×D67—24no—
358C22×D67—24no—
359C22×D67C2514yes—
360C22×D67C2514yes—
361Q8×C67—28no—
362D4×C67—216no—
363D4×C67—28no—
364C2×C4×C67—24no—
365C2×C4×C67—24no—
366C2×C4×C67—28no—
367C2×C4×C67—24no—
368C2×C4×C67—216no—
369C2×C4×C67—416no—
370C2×C4×C67—48no—
371C2×C4×C67C2×#4114yes—
372C2×C4×C67C2×#4114yes—
373C2×C4×C67C2×#41116yes—
374C2×C4×C67C2514yes—
375C2×C4×C67C2514yes—
376C2×C4×C67C2514yes—
377C2×C4×C67C2518yes—
378C2×C4×C67C2512yes—
379C2×C4×C67C2512yes—
380C22⋊D67—216no—
381C22⋊D67—216no—
382C22⋊D67—416no—
383C22⋊D67—48no—
384C22⋊D67—48no—
385C2×Dic67—24no—
386C2×Dic67—24no—
387C2×Dic67—22no—
388C2×Dic67—22no—
389C2×Dic67—28no—
390C2×Dic67—22no—
391C2×Dic67—22no—
392C2×Dic67—44no—
393C2×Dic67—44no—
394C2×Dic67—48no—
395C2×Dic67C2512yes—
396C2×Dic67C2512yes—
397C2×Dic67C2514yes—
398C2×Dic67C2514yes—
399C2×Dic67C2512yes—
400C2×Dic67C2512yes—
401C2×Dic67C2518yes—
402D268—28no—
403D268—28no—
404D268—416no—
405C4×D67—216no—
406C4×D67—216no—
407C4×D67—48no—
408C4×D67—48no—
409C4×D67—416no—
410Dic134—28no—
411Dic134—28no—
412C22×C67—22no—
413C22×C67—22no—
414C22×C67—28no—
415C22×C67—24no—
416C22×C67—24no—
417C22×C67—24no—
418C22×C67—48no—
419C22×C67C22×#4114yes—
420C22×C67C22×#4112yes—
421C22×C67#58512yes—
422C22×C67#58512yes—
423C22×C67C2611yescharacteristic
424C2×D67—24no—
425C2×D67—24no—
426C2×D67—24no—
427C2×D67—24no—
428C2×D67—24no—
429C2×D67—24no—
430C2×D67—48no—
431C2×D67—48no—
432C4×C67—24no—
433C4×C67—24no—
434C4×C67—24no—
435C4×C67—28no—
436C4×C67C22×#4114yes—
437C4×C67C22×#4114yes—
438Dic67—24no—
439Dic67—24no—
440Dic67—22no—
441Dic67—22no—
442Dic67—28no—
443Dic67—22no—
444Dic67—22no—
445C2×#3512—671nomaximal, Sylow
446C2×C67—24no—
447C2×C67—44no—
448C2×C67#351214yescomplemented
449C2×C67C23×#4111yescharacteristic
450C2×C67C2×#58511yescharacteristic
451C2×C67C2×#58511yescharacteristic
452D67—44no—
453D67—44no—
454#3512—6732no—
455C2×#553—674no—
456C2×#553—674no—
457C2×#553—672no—
458C2×#553—672no—
459C2×#552—672no—
460C2×#552—672no—
461C2×#541—672no—
462C2×#540—672no—
463C2×#537—671no—
464C2×#537—671no—
465C2×#532—671no—
466C2×#529—672no—
467C2×#529—672no—
468C22×#125—671no—
469C2×#520—671no—
470C2×#520D6711yescharacteristic, complemented
471C2×C4×#41—671no—
472C67C2×#351211yescharacteristic, complemented, Sylow
473C22×#41—671no—
474C22×#41—671no—
475C22×#41C2×D6711yescharacteristic
476#553—6764no—
477#553—6764no—
478#553—6732no—
479#553—6732no—
480#552—6732no—
481#552—6732no—
482#541—6732no—
483#540—6732no—
484#537—6716no—
485#537—6716no—
486#532—6716no—
487C2×C4⋊Q8—671no—
488C2×#127—671no—
489#529—6732no—
490#529—6732no—
491C2×#126—674no—
492C2×#126—674no—
493C2×#126—674no—
494C2×#126—674no—
495C2×#125—672no—
496C2×#125—672no—
497C2×#125—672no—
498C2×#125—672no—
499C2×#125—6716no—
500C2×#125—674no—
501C2×#125—674no—
502C2×#124—671no—
503C2×#124—671no—
504C2×#123—674no—
505C2×#123—674no—
506C2×#123—674no—
507C2×#123—674no—
508C2×C22⋊Q8—672no—
509C2×C22⋊Q8—672no—
510C2×C22⋊Q8—672no—
511C2×C22⋊Q8—672no—
512C2×#121—672no—
513C2×#121—672no—
514C2×#121—672no—
515C2×#121—674no—
516C2×#121—674no—
517C2×#121—672no—
518C2×#121—674no—
519C2×#121—672no—
520C2×#121—672no—
521C2×#121—674no—
522#520—6716no—
523#520C2×D67116yescomplemented
524C4×#41—6716no—
525C2×C4×Q8—671no—
526C2×C4×Q8—671no—
527C2×C4×Q8—672no—
528C2×C4×Q8C2×D6712yes—
529C2×C4×D4—674no—
530C2×C4×D4—672no—
531C2×C4×D4—672no—
532C2×C4×D4—671no—
533C2×C4×D4—671no—
534C2×C4×D4—672no—
535C2×C4×D4—672no—
536C2×C4×D4—674no—
537C2×C4×D4—672no—
538C2×C4×D4—674no—
539C2×C4×D4C2×D6712yes—
540C2×C4×D4C2×D6714yes—
541C2×#117—674no—
542C2×#117—672no—
543C2×#117—672no—
544C2×#117—674no—
545C2×#117C2×D6711yescharacteristic
546C2×#117C2×D6712yes—
547C22×C4⋊C4—671no—
548C22×C4⋊C4—672no—
549C22×C4⋊C4—672no—
550C22×C4⋊C4—672no—
551C22×C4⋊C4C2×D6711yescharacteristic
552C22×C4⋊C4C2×D6712yes—
553C22×C42—671no—
554C22×C42—672no—
555C2×#41—28no—
556C2×#41—678no—
557C2×#41—678no—
558C2×#41—1348no—
559C2×#41—1348no—
560C2×#41C22×D6718yes—
561C22×Q8—671no—
562C22×Q8—671no—
563C22×Q8C22×D6711yescharacteristic
564C22×D4—674no—
565C22×D4—672no—
566C22×D4—672no—
567C22×D4—672no—
568C22×D4—672no—
569C22×D4—674no—
570C22×D4—671no—
571C22×D4—671no—
572C22×D4C22×D6712yes—
573C22×D4C22×D6711yescharacteristic
574C23×C4—672no—
575C23×C4—671no—
576C23×C4—671no—
577C23×C4—674no—
578C23×C4—672no—
579C23×C4—672no—
580C23×C4—672no—
581C23×C4—672no—
582C23×C4C22×D6712yes—
583C23×C4C22×D6712yes—
584C23×C4C22×D6714yes—
585C23×C4C22×D6711yescharacteristic
586C4⋊Q8—678no—
587#127—678no—
588#126—6732no—
589#126—6732no—
590#126—6732no—
591#126—6732no—
592#125—6716no—
593#125—6716no—
594#125—6716no—
595#125—6716no—
596#125—6732no—
597#125—6732no—
598#124—678no—
599#124—678no—
600#123—6732no—
601#123—6732no—
602#123—6732no—
603#123—6732no—
604C22⋊Q8—6716no—
605C22⋊Q8—6716no—
606C22⋊Q8—6716no—
607C22⋊Q8—6716no—
608#121—6716no—
609#121—6716no—
610#121—6716no—
611#121—6732no—
612#121—6732no—
613#121—6716no—
614#121—6732no—
615#121—6716no—
616#121—6716no—
617#121—6732no—
618C4×Q8—678no—
619C4×Q8—678no—
620C4×Q8—6716no—
621C4×Q8C22×D67116yes—
622C4×D4—6732no—
623C4×D4—6716no—
624C4×D4—6716no—
625C4×D4—678no—
626C4×D4—678no—
627C4×D4—6716no—
628C4×D4—6716no—
629C4×D4—6732no—
630C4×D4—6716no—
631C4×D4—6732no—
632C4×D4C22×D67116yes—
633C4×D4C22×D67132yes—
634#117—6732no—
635#117—6716no—
636#117—6716no—
637#117—6732no—
638#117C22×D6718yes—
639#117C22×D67116yes—
640C2×C4⋊C4—672no—
641C2×C4⋊C4—674no—
642C2×C4⋊C4—674no—
643C2×C4⋊C4—672no—
644C2×C4⋊C4—674no—
645C2×C4⋊C4—678no—
646C2×C4⋊C4—674no—
647C2×C4⋊C4—674no—
648C2×C4⋊C4—6716no—
649C2×C4⋊C4—6716no—
650C2×C4⋊C4—672no—
651C2×C4⋊C4—672no—
652C2×C4⋊C4—674no—
653C2×C4⋊C4—674no—
654C2×C4⋊C4—672no—
655C2×C4⋊C4—672no—
656C2×C4⋊C4—6716no—
657C2×C4⋊C4C22×D6711yescharacteristic
658C2×C4⋊C4C22×D6711yescharacteristic
659C2×C4⋊C4C22×D6712yes—
660C2×C4⋊C4C22×D6712yes—
661C2×C4⋊C4C22×D6714yes—
662C2×C4⋊C4C22×D6718yes—
663C2×C4⋊C4C22×D67116yes—
664C2×C22⋊C4—672no—
665C2×C22⋊C4—674no—
666C2×C22⋊C4—672no—
667C2×C22⋊C4—672no—
668C2×C22⋊C4—672no—
669C2×C22⋊C4—672no—
670C2×C22⋊C4—674no—
671C2×C22⋊C4—674no—
672C2×C22⋊C4—672no—
673C2×C22⋊C4—674no—
674C2×C22⋊C4—674no—
675C2×C22⋊C4C22×D6712yes—
676C2×C22⋊C4C22×D6714yes—
677C2×C42—674no—
678C2×C42—672no—
679C2×C42—672no—
680C2×C42—671no—
681C2×C42—671no—
682C2×C42—671no—
683C2×C42—678no—
684C2×C42—671no—
685C2×C42—6716no—
686C2×C42C22×D6712yes—
687C2×C42C22×D6714yes—
688C24—672no—
689C24—672no—
690C24C23×D6712yes—
691C24C23×D6711yescharacteristic
692#41—232no—
693#41—13432no—
694#41—13432no—
695C2×Q8—24no—
696C2×Q8—674no—
697C2×Q8—674no—
698C2×Q8—1344no—
699C2×Q8—1344no—
700C2×Q8C23×D6714yes—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—2688no—
704C2×D4—2684no—
705C2×D4—2688no—
706C2×D4—2684no—
707C2×D4—6716no—
708C2×D4—678no—
709C2×D4—678no—
710C2×D4—678no—
711C2×D4—678no—
712C2×D4—6716no—
713C2×D4—674no—
714C2×D4—674no—
715C2×D4—1348no—
716C2×D4—1348no—
717C2×D4—1344no—
718C2×D4—1344no—
719C2×D4C23×D6718yes—
720C2×D4C23×D6714yes—
721C22×C4—28no—
722C22×C4—48no—
723C22×C4—44no—
724C22×C4—2684no—
725C22×C4—2684no—
726C22×C4—2688no—
727C22×C4—2682no—
728C22×C4—2682no—
729C22×C4—2684no—
730C22×C4—674no—
731C22×C4—674no—
732C22×C4—678no—
733C22×C4—678no—
734C22×C4—678no—
735C22×C4—6716no—
736C22×C4—671no—
737C22×C4—671no—
738C22×C4—672no—
739C22×C4—672no—
740C22×C4—671no—
741C22×C4—671no—
742C22×C4—674no—
743C22×C4—678no—
744C22×C4—678no—
745C22×C4—1348no—
746C22×C4—1348no—
747C22×C4#1176162818yes—
748C22×C4C23×D6718yes—
749C22×C4C23×D6712yes—
750C22×C4C23×D6712yes—
751C22×C4C23×D6712yes—
752C22×C4C23×D6714yes—
753C22×C4C23×D6718yes—
754C22×C4C23×D67116yes—
755C22×C4C23×D6714yes—
756C22×C4C23×D6711yescharacteristic
757C22×C4C23×D6711yescharacteristic
758C4⋊C4—678no—
759C4⋊C4—6716no—
760C4⋊C4—6716no—
761C4⋊C4—678no—
762C4⋊C4—6716no—
763C4⋊C4—6716no—
764C4⋊C4—6716no—
765C4⋊C4—678no—
766C4⋊C4—678no—
767C4⋊C4—6716no—
768C4⋊C4—6716no—
769C4⋊C4—678no—
770C4⋊C4—678no—
771C4⋊C4C23×D6714yes—
772C4⋊C4C23×D6714yes—
773C4⋊C4C23×D6718yes—
774C4⋊C4C23×D6718yes—
775C4⋊C4C23×D67116yes—
776C22⋊C4—678no—
777C22⋊C4—6716no—
778C22⋊C4—678no—
779C22⋊C4—678no—
780C22⋊C4—678no—
781C22⋊C4—678no—
782C22⋊C4—6716no—
783C22⋊C4—6716no—
784C22⋊C4—678no—
785C22⋊C4—6716no—
786C22⋊C4—6716no—
787C22⋊C4C23×D6718yes—
788C22⋊C4C23×D67116yes—
789C42—674no—
790C42—678no—
791C42—678no—
792C42—674no—
793C42—674no—
794C42—674no—
795C42—6716no—
796C42C23×D6718yes—
797C42C23×D67116yes—
798C23—22no—
799C23—22no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—674no—
804C23—674no—
805C23—1344no—
806C23—1344no—
807C23—1344no—
808C23—1344no—
809C23—1344no—
810C23—1344no—
811C23C2×#1176162814yes—
812C23C24×D6714yes—
813C23C24×D6712yes—
814C23C24×D6711yescharacteristic
815Q8—28no—
816Q8—1348no—
817Q8—1348no—
818D4—216no—
819D4—28no—
820D4—26816no—
821D4—2688no—
822D4—26816no—
823D4—2688no—
824D4—13416no—
825D4—13416no—
826D4—1348no—
827D4—1348no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—28no—
831C2×C4—24no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—48no—
835C2×C4—2688no—
836C2×C4—2688no—
837C2×C4—26816no—
838C2×C4—2684no—
839C2×C4—2684no—
840C2×C4—2688no—
841C2×C4—672no—
842C2×C4—672no—
843C2×C4—674no—
844C2×C4—674no—
845C2×C4—672no—
846C2×C4—672no—
847C2×C4—678no—
848C2×C4—1344no—
849C2×C4—1344no—
850C2×C4—1342no—
851C2×C4—1342no—
852C2×C4—1342no—
853C2×C4—1348no—
854C2×C4—1342no—
855C2×C4—13416no—
856C2×C4—13416no—
857C2×C4C2×#1176162814yes—
858C2×C4C2×#1176162814yes—
859C2×C4C2×#11761628116yes—
860C2×C4C24×D6714yes—
861C2×C4C24×D6714yes—
862C2×C4C24×D6714yes—
863C2×C4C24×D6718yes—
864C2×C4C24×D6712yes—
865C2×C4C24×D6712yes—
866C22—28no—
867C22—22no—
868C22—22no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—48no—
873C22—2688no—
874C22—2688no—
875C22—1344no—
876C22—1344no—
877C22—1344no—
878C22—1344no—
879C22—1344no—
880C22—1344no—
881C22C22×#1176162814yes—
882C22C22×#1176162812yes—
883C22#1686423112yes—
884C22#1686423312yes—
885C22C25×D6711yescharacteristic
886C4—24no—
887C4—24no—
888C4—28no—
889C4—24no—
890C4—1344no—
891C4—1344no—
892C4—1342no—
893C4—1342no—
894C4—1342no—
895C4—1348no—
896C4—1342no—
897C4C22×#1176162814yes—
898C4C22×#1176162814yes—
899C2—24no—
900C2—44no—
901C2—2684no—
902C2—2684no—
903C2#2257412614yesdirect product factor
904C2C23×#1176162811yescharacteristic
905C2C2×#1686423111yescharacteristic
906C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#520×C67C2
socleC23×C67C25
hypercenterC2×#520D67
hypocenterC67C2×#3512
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22574126C2direct (N × H)
2. C2×#16864095C2semidirect
3. C2×#16864094C2semidirect
4. C2×#16864092C2semidirect
5. C2×#16864090C2semidirect
6. C2×#16864085C2semidirect
7. C2×#16864081C2semidirect
8. C2×#16864004C2semidirect
9. C2×#16863997C2semidirect
10. C2×#16863977C2semidirect
11. C2×#16863974C2semidirect
12. C2×#16863942C2semidirect
13. C2×#16863933C2semidirect
14. C2×#16863928C2semidirect
15. C22×#14524034C2semidirect
16. C2×#16863876C2semidirect
17. C2×#16863864C2semidirect
18. C2×#520×C67C2semidirect
21. #16864095C22semidirect
22. #16864094C22semidirect
23. #16864092C22semidirect
24. #16864090C22semidirect
25. #16864085C22semidirect
26. #16864081C22semidirect
27. #16864004C22semidirect
28. #16863997C22semidirect
29. #16863977C22semidirect
30. #16863974C22semidirect
31. #16863942C22semidirect
34. #16863933C22semidirect
35. #16863928C22semidirect
45. C2×#14524034C22semidirect
67. #16863876C22semidirect
68. #16863864C22semidirect
93. #520×C67C22semidirect
448. C2×C67#3512semidirect
470. C2×#520D67semidirect
472. C67C2×#3512semidirect
523. #520C2×D67semidirect
903. C2#22574126direct (N × H)

Maximal subgroups

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

subgroupindex
#225741262
C2×#168640952
C2×#168640942
C2×#168640922
C2×#168640902
C2×#168640852
C2×#168640812
C2×#168640042
C2×#168639972
C2×#168639772
C2×#168639742
C2×#168639422
C2×#168639332
C2×#168639282
C22×#145240342
C2×#168638762
C2×#168638642
C2×#520×C672
C2×#351267