Finite Group Databasebeta

← C2×#22574112 #31764200

Subgroups — C2×#22574112 #31764200

Order 17152.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574112C2132yesmaximal, direct product factor
2C2×#16864114C212yesmaximal, complemented
3C2×#16864109C212yesmaximal, complemented
4C2×#16864101C212yesmaximal, complemented
5C2×#16864095C214yesmaximal, complemented
6C2×#16864055C214yesmaximal, complemented
7C2×#16864047C212yesmaximal, complemented
8C2×#16864018C212yesmaximal, complemented
9C2×#16864011C212yesmaximal, complemented
10C2×#16863977C211yesmaximal, characteristic, complemented
11C2×#16863974C211yesmaximal, characteristic, complemented
12C2×#16863950C212yesmaximal, complemented
13C2×#16863943C212yesmaximal, complemented
14C2×#16863942C211yesmaximal, characteristic, complemented
15C22×#14524042C211yesmaximal, characteristic, complemented
16C2×#16863876C211yesmaximal, characteristic, complemented
17C2×#16863864C211yesmaximal, characteristic, complemented
18C2×#520×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2211yescharacteristic
20C22×#11761628C2211yescharacteristic
21C22×#11761628C2214yes—
22C23×Dic134C2212yes—
23#16864114C22132yescomplemented
24#16864109C22132yescomplemented
25#16864101C22132yescomplemented
26#16864095C22164yescomplemented
27#16864055C22164yescomplemented
28#16864047C22132yescomplemented
29#16864018C22132yescomplemented
30#16864011C22132yescomplemented
31#16863977C22116yescomplemented
32#16863974C22116yescomplemented
33#16863950C22132yescomplemented
34#16863943C22132yescomplemented
35#16863942C22116yescomplemented
36C2×#14524042C2212yes—
37C2×#14524042C2212yes—
38C2×#14524042C2212yes—
39C2×#14524042C2212yes—
40C2×#14524042C22116yescomplemented
41C2×#14524041C2211yescharacteristic
42C2×#14524039C2211yescharacteristic
43C2×#14524037C2214yes—
44C2×#14524036C2214yes—
45C2×#14524033C2214yes—
46C2×#14524032C2211yescharacteristic
47C2×#14524031C2214yes—
48C2×#14524030C2211yescharacteristic
49C2×#14524029C2214yes—
50C2×#14524029C2214yes—
51C2×#14524028C2214yes—
52C2×#14524026C2214yes—
53C2×#14524023C2212yes—
54C2×#14524023C2212yes—
55C2×#14524022C2214yes—
56C2×#14524022C2212yes—
57C2×#14524021C2214yes—
58C2×#14524021C2214yes—
59C2×#14524019C2212yes—
60C2×#14524018C2212yes—
61C2×#14524018C2212yes—
62C2×#14524017C2212yes—
63C2×#14524017C2214yes—
64C2×#14524016C2214yes—
65C2×#14524015C2212yes—
66C2×#14524015C2214yes—
67C2×#14524015C2212yes—
68C2×#14524014C2212yes—
69#16863876C22116yescomplemented
70#16863864C22116yescomplemented
71C2×C4×Dic134C2212yes—
72C2×C4×Dic134C2214yes—
73C2×#14524008C2211yescharacteristic
74C2×#14524008C2211yescharacteristic
75C2×C4×D268C2212yes—
76C2×#14524005C2211yescharacteristic
77C2×#14524005C2211yescharacteristic
78C2×C4×C22⋊D67C2212yes—
79C2×C4×C22⋊D67C2214yes—
80C2×C4×C22⋊D67C2212yes—
81C2×(C22⋊D67)⋊C4C2212yes—
82C2×(C22⋊D67)⋊C4C2212yes—
83C2×(C22⋊D67)⋊C4C2214yes—
84C2×#14524001C2212yes—
85C2×#14524000C2212yes—
86C2×#14524000C2214yes—
87C22×C4⋊Dic67C2211yescharacteristic
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×C67C2212yes—
96C2×C4×D4×C67C2214yes—
97C2×#117×C67C2211yescharacteristic
98C2×#117×C67C2212yes—
99C22×C4⋊C4×C67C2212yes—
100C22×C4⋊C4×C67C2211yescharacteristic
101C2×#11761628—28no—
102C2×#11761628—28no—
103C2×#11761628—416no—
104C2×#11761628C2318yes—
105C2×#11761628C2318yes—
106C2×#11761628C23132yes—
107C22×Dic134—48no—
108C22×Dic134C2311yescharacteristic
109C22×Dic134C2311yescharacteristic
110C22×Dic134C2314yes—
111C22×Dic134C23116yes—
112C22×Dic134C2314yes—
113C22×D268C2311yescharacteristic
114C22×D268C2311yescharacteristic
115C22×D268C2314yes—
116C22×C22⋊D67C2312yes—
117C22×C22⋊D67C2312yes—
118C22×C22⋊D67C2312yes—
119C22×C22⋊D67C2312yes—
120C22×C22⋊D67C2314yes—
121C23×Dic67C2311yescharacteristic
122C23×Dic67C2311yescharacteristic
123C23×Dic67C2312yes—
124C22×C4×D67C2312yes—
125C22×C4×D67C2312yes—
126C22×C4×D67C2312yes—
127C22×C4×D67C2312yes—
128C22×C4×D67C2314yes—
129#14524042C23116yes—
130#14524042C23116yes—
131#14524042C23116yes—
132#14524042C23116yes—
133#14524041C2318yes—
134#14524039C2318yes—
135#14524037C23132yes—
136#14524036C23132yes—
137#14524033C23132yes—
138#14524032C2318yes—
139#14524031C23132yes—
140#14524030C2318yes—
141#14524029C23132yes—
142#14524029C23132yes—
143#14524028C23132yes—
144#14524026C23132yes—
145#14524023C23116yes—
146#14524023C23116yes—
147#14524022C23132yes—
148#14524022C23116yes—
149#14524021C23132yes—
150#14524021C23132yes—
151#14524019C23116yes—
152#14524018C23116yes—
153#14524018C23116yes—
154#14524017C23116yes—
155#14524017C23132yes—
156#14524016C23132yes—
157#14524015C23116yes—
158#14524015C23132yes—
159#14524015C23116yes—
160#14524014C23116yes—
161C4×Dic134C23116yes—
162C4×Dic134C23132yes—
163#14524008C2318yes—
164#14524008C2318yes—
165C4×D268C23116yes—
166#14524005C2318yes—
167#14524005C2318yes—
168C4×C22⋊D67C23116yes—
169C4×C22⋊D67C23132yes—
170C4×C22⋊D67C23116yes—
171(C22⋊D67)⋊C4C23116yes—
172(C22⋊D67)⋊C4C23132yes—
173(C22⋊D67)⋊C4C23116yes—
174#14524001C23116yes—
175#14524000C23116yes—
176#14524000C23132yes—
177C2×C4⋊Dic67C2312yes—
178C2×C4⋊Dic67C2312yes—
179C2×C4⋊Dic67C2318yes—
180C2×C4⋊Dic67C2314yes—
181C2×Dic67⋊C4C23116yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C2×Dic67⋊C4C2312yes—
189C2×Dic67⋊C4C2314yes—
190C4⋊C4×D67C23116yes—
191C2×C22⋊Dic67C2314yes—
192C2×C22⋊Dic67C2312yes—
193C2×C22⋊Dic67C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2312yes—
200C2×(C2×D67)⋊C4C2312yes—
201C2×(C2×D67)⋊C4C2314yes—
202C2×C4×Dic67C2311yescharacteristic
203C2×C4×Dic67C2312yes—
204C2×C4×Dic67C2312yes—
205C2×C4×Dic67C2311yescharacteristic
206C2×C4×Dic67C2311yescharacteristic
207C2×C4×Dic67C2311yescharacteristic
208C2×C4×Dic67C2318yes—
209C2×C4×Dic67C2314yes—
210C42×D67C23116yes—
211C2×#41×C67—28no—
212C2×#41×C67C2318yes—
213C22×Q8×C67C2311yescharacteristic
214C22×D4×C67C2311yescharacteristic
215C22×D4×C67C2312yes—
216C23×C4×C67C2312yes—
217C23×C4×C67C2312yes—
218C23×C4×C67C2314yes—
219C23×C4×C67C2311yescharacteristic
220C4×Q8×C67C23116yes—
221C4×D4×C67C23116yes—
222C4×D4×C67C23132yes—
223#117×C67C23116yes—
224#117×C67C2318yes—
225C2×C4⋊C4×C67C23116yes—
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2312yes—
228C2×C4⋊C4×C67C2312yes—
229C2×C4⋊C4×C67C2314yes—
230C2×C4⋊C4×C67C2318yes—
231C2×C4⋊C4×C67C2311yescharacteristic
232C2×C22⋊C4×C67C2312yes—
233C2×C22⋊C4×C67C2314yes—
234C2×C42×C67C2312yes—
235C2×C42×C67C2314yes—
236C23×D67C2412yes—
237C23×D67C2412yes—
238#11761628—232no—
239#11761628—232no—
240#11761628—464no—
241C2×Dic134—24no—
242C2×Dic134—24no—
243C2×Dic134—216no—
244C2×Dic134—432no—
245C2×Dic134—48no—
246C2×Dic134C2414yes—
247C2×Dic134C2414yes—
248C2×Dic134C24116yes—
249C2×Dic134C24116yes—
250C2×D268—24no—
251C2×D268—24no—
252C2×D268—48no—
253C2×D268C2414yes—
254C2×D268C2414yes—
255C2×D268C24116yes—
256C2×C22⋊D67—28no—
257C2×C22⋊D67—28no—
258C2×C22⋊D67—28no—
259C2×C22⋊D67—28no—
260C2×C22⋊D67—48no—
261C2×C22⋊D67C2418yes—
262C2×C22⋊D67C2418yes—
263C2×C22⋊D67C2418yes—
264C2×C22⋊D67C2418yes—
265C2×C22⋊D67C24116yes—
266C22×Dic67—24no—
267C22×Dic67—24no—
268C22×Dic67—44no—
269C22×Dic67C2411yescharacteristic
270C22×Dic67C2411yescharacteristic
271C22×Dic67C2412yes—
272C22×Dic67C2412yes—
273C22×Dic67C2414yes—
274C22×Dic67C2414yes—
275C22×Dic67C2414yes—
276C22×Dic67C2418yes—
277C22×Dic67C2411yescharacteristic
278C22×Dic67C2411yescharacteristic
279C2×C4×D67—28no—
280C2×C4×D67—28no—
281C2×C4×D67—28no—
282C2×C4×D67—28no—
283C2×C4×D67—48no—
284C2×C4×D67C2418yes—
285C2×C4×D67C2418yes—
286C2×C4×D67C2418yes—
287C2×C4×D67C2418yes—
288C2×C4×D67C24116yes—
289C4⋊Dic67C2418yes—
290C4⋊Dic67C2418yes—
291C4⋊Dic67C24116yes—
292Dic67⋊C4C24116yes—
293Dic67⋊C4C24116yes—
294Dic67⋊C4C24116yes—
295Dic67⋊C4C2418yes—
296Dic67⋊C4C2418yes—
297Dic67⋊C4C2418yes—
298Dic67⋊C4C2418yes—
299Dic67⋊C4C24116yes—
300C22⋊Dic67C24116yes—
301C22⋊Dic67C2418yes—
302C22⋊Dic67C2418yes—
303(C2×D67)⋊C4C2418yes—
304(C2×D67)⋊C4C2418yes—
305(C2×D67)⋊C4C24116yes—
306(C2×D67)⋊C4C24116yes—
307(C2×D67)⋊C4C24116yes—
308(C2×D67)⋊C4C2418yes—
309(C2×D67)⋊C4C2418yes—
310(C2×D67)⋊C4C24116yes—
311C4×Dic67C2414yes—
312C4×Dic67C2418yes—
313C4×Dic67C2418yes—
314C4×Dic67C2414yes—
315C4×Dic67C2414yes—
316C4×Dic67C2414yes—
317C4×Dic67C24116yes—
318C24×C67C2412yes—
319C24×C67C2411yescharacteristic
320#41×C67—232no—
321C2×Q8×C67—24no—
322C2×Q8×C67C2414yes—
323C2×D4×C67—28no—
324C2×D4×C67—24no—
325C2×D4×C67C2414yes—
326C2×D4×C67C2418yes—
327C22×C4×C67—28no—
328C22×C4×C67—44no—
329C22×C4×C67—48no—
330C22×C4×C67#4118yescomplemented
331C22×C4×C67C2412yes—
332C22×C4×C67C2412yes—
333C22×C4×C67C2412yes—
334C22×C4×C67C2414yes—
335C22×C4×C67C2418yes—
336C22×C4×C67C2418yes—
337C22×C4×C67C24116yes—
338C22×C4×C67C2411yescharacteristic
339C22×C4×C67C2411yescharacteristic
340C22×C4×C67C2414yes—
341C4⋊C4×C67C2414yes—
342C4⋊C4×C67C2418yes—
343C4⋊C4×C67C2418yes—
344C4⋊C4×C67C24116yes—
345C4⋊C4×C67C2414yes—
346C22⋊C4×C67C2418yes—
347C22⋊C4×C67C24116yes—
348C42×C67C2418yes—
349C42×C67C24116yes—
350C23×C67—22no—
351C23×C67—22no—
352C23×C67—24no—
353C23×C67—24no—
354C23×C67—24no—
355C23×C67C2×#4114yes—
356C23×C67C2514yes—
357C23×C67C2512yes—
358C23×C67C2511yescharacteristic
359C22×D67—24no—
360C22×D67—24no—
361C22×D67—24no—
362C22×D67—24no—
363C22×D67—24no—
364C22×D67—24no—
365C22×D67C2514yes—
366C22×D67C2514yes—
367Q8×C67—28no—
368D4×C67—216no—
369D4×C67—28no—
370C2×C4×C67—24no—
371C2×C4×C67—24no—
372C2×C4×C67—28no—
373C2×C4×C67—24no—
374C2×C4×C67—216no—
375C2×C4×C67—48no—
376C2×C4×C67—416no—
377C2×C4×C67C2×#4114yes—
378C2×C4×C67C2×#4114yes—
379C2×C4×C67C2×#41116yescomplemented
380C2×C4×C67C2514yes—
381C2×C4×C67C2514yes—
382C2×C4×C67C2514yes—
383C2×C4×C67C2518yes—
384C2×C4×C67C2512yes—
385C2×C4×C67C2512yes—
386C22⋊D67—216no—
387C22⋊D67—216no—
388C22⋊D67—216no—
389C22⋊D67—216no—
390C22⋊D67—416no—
391C2×Dic67—24no—
392C2×Dic67—24no—
393C2×Dic67—28no—
394C2×Dic67—22no—
395C2×Dic67—22no—
396C2×Dic67—28no—
397C2×Dic67—28no—
398C2×Dic67—48no—
399C2×Dic67H(5,𝔽2)14yes—
400C2×Dic672−1+414yes—
401C2×Dic67C2512yes—
402C2×Dic67C2512yes—
403C2×Dic67C2514yes—
404C2×Dic67C2514yes—
405C2×Dic67C2518yes—
406C2×Dic67C2512yes—
407C2×Dic67C2512yes—
408D268—28no—
409D268—28no—
410D268—416no—
411C4×D67—216no—
412C4×D67—216no—
413C4×D67—216no—
414C4×D67—216no—
415C4×D67—416no—
416Dic134—28no—
417Dic134—28no—
418Dic134—232no—
419Dic134—416no—
420C22×C67—22no—
421C22×C67—22no—
422C22×C67—28no—
423C22×C67—24no—
424C22×C67—24no—
425C22×C67—24no—
426C22×C67—48no—
427C22×C67C22×#4114yes—
428C22×C67C22×#4112yes—
429C22×C67C2×H(5,𝔽2)12yes—
430C22×C67C2×2−1+412yes—
431C22×C67C2611yescharacteristic
432C2×D67—24no—
433C2×D67—24no—
434C2×D67—24no—
435C2×D67—24no—
436C2×D67—24no—
437C2×D67—24no—
438C2×D67—48no—
439C2×D67—48no—
440C4×C67—24no—
441C4×C67—28no—
442C4×C67—24no—
443C4×C67—24no—
444C4×C67C22×#4114yes—
445C4×C67C22×#4114yes—
446Dic67—24no—
447Dic67—24no—
448Dic67—28no—
449Dic67—22no—
450Dic67—22no—
451Dic67C2×H(5,𝔽2)14yes—
452Dic67C2×2−1+414yes—
453C2×#3511—671nomaximal, Sylow
454C2×C67—24no—
455C2×C67—44no—
456C2×C67#351114yescomplemented
457C2×C67C23×#4111yescharacteristic
458C2×C67C22×H(5,𝔽2)11yescharacteristic
459C2×C67C22×2−1+411yescharacteristic
460D67—44no—
461D67—44no—
462#3511—6732no—
463C2×#556—672no—
464C2×#555—672no—
465C2×#554—672no—
466C2×#553—674no—
467C2×#548—674no—
468C2×#547—672no—
469C2×#542—672no—
470C2×#542—672no—
471C2×#537—671no—
472C2×#537—671no—
473C2×#533—672no—
474C2×#532—671no—
475C2×#532—672no—
476C22×C4⋊Q8—671no—
477C2×#520—671no—
478C2×#520D6711yescharacteristic, complemented
479C2×C4×#41—671no—
480C67C2×#351111yescharacteristic, complemented, Sylow
481C22×#41—674no—
482C22×#41—671no—
483C22×#41—671no—
484C22×#41C2×D6711yescharacteristic
485C23×Q8—672no—
486#556—6732no—
487#555—6732no—
488#554—6732no—
489#553—6764no—
490#548—6764no—
491#547—6732no—
492#542—6732no—
493#542—6732no—
494#537—6716no—
495#537—6716no—
496#533—6732no—
497#532—6716no—
498#532—6732no—
499C2×C4⋊Q8—671no—
500C2×C4⋊Q8—672no—
501C2×C4⋊Q8—672no—
502C2×C4⋊Q8—672no—
503C2×C4⋊Q8—672no—
504C2×C4⋊Q8—6716no—
505C2×#127—671no—
506C2×#126—674no—
507C2×#126—674no—
508C2×#125—674no—
509C2×#124—671no—
510C2×#124—671no—
511C2×#124—674no—
512C2×#124—674no—
513C2×#124—674no—
514C2×#123—674no—
515C2×#123—674no—
516C2×C22⋊Q8—672no—
517C2×C22⋊Q8—672no—
518C2×C22⋊Q8—674no—
519C2×C22⋊Q8—672no—
520C2×C22⋊Q8—674no—
521C2×C22⋊Q8—672no—
522C2×C22⋊Q8—674no—
523C2×#121—672no—
524C2×#121—672no—
525C2×#121—672no—
526C2×#121—674no—
527C2×#121—672no—
528C2×#121—674no—
529C2×#121—672no—
530C2×#121—672no—
531C2×#121—674no—
532#520—6716no—
533#520C2×D67116yescomplemented
534C4×#41—6716no—
535C2×C4×Q8—671no—
536C2×C4×Q8—671no—
537C2×C4×Q8—672no—
538C2×C4×Q8—674no—
539C2×C4×Q8C2×D6712yes—
540C2×C4×D4—672no—
541C2×C4×D4—674no—
542C2×C4×D4—672no—
543C2×C4×D4—671no—
544C2×C4×D4—671no—
545C2×C4×D4—672no—
546C2×C4×D4—672no—
547C2×C4×D4—674no—
548C2×C4×D4—672no—
549C2×C4×D4C2×D6712yes—
550C2×C4×D4C2×D6714yes—
551C2×#117—672no—
552C2×#117—672no—
553C2×#117—674no—
554C2×#117C2×D6711yescharacteristic
555C2×#117C2×D6712yes—
556C22×C4⋊C4—671no—
557C22×C4⋊C4—672no—
558C22×C4⋊C4—672no—
559C22×C4⋊C4C2×D6711yescharacteristic
560C22×C4⋊C4C2×D6712yes—
561C22×C42—671no—
562C22×C42—672no—
563C2×#41—28no—
564C2×#41—26816no—
565C2×#41—6732no—
566C2×#41—678no—
567C2×#41—678no—
568C2×#41—1348no—
569C2×#41—1348no—
570C2×#41C22×D6718yes—
571C22×Q8—2688no—
572C22×Q8—674no—
573C22×Q8—6716no—
574C22×Q8—671no—
575C22×Q8—671no—
576C22×Q8—674no—
577C22×Q8C22×D6711yescharacteristic
578C22×D4—674no—
579C22×D4—672no—
580C22×D4—672no—
581C22×D4—672no—
582C22×D4—672no—
583C22×D4—674no—
584C22×D4—671no—
585C22×D4—671no—
586C22×D4C22×D6712yes—
587C22×D4C22×D6711yescharacteristic
588C23×C4—672no—
589C23×C4—674no—
590C23×C4—671no—
591C23×C4—671no—
592C23×C4—672no—
593C23×C4—672no—
594C23×C4—672no—
595C23×C4—672no—
596C23×C4C22×D6712yes—
597C23×C4C22×D6712yes—
598C23×C4C22×D6714yes—
599C23×C4C22×D6711yescharacteristic
600C4⋊Q8—678no—
601C4⋊Q8—6716no—
602C4⋊Q8—6716no—
603C4⋊Q8—6716no—
604C4⋊Q8—6716no—
605#127—678no—
606#126—6732no—
607#126—6732no—
608#125—6732no—
609#124—678no—
610#124—678no—
611#124—6732no—
612#124—6732no—
613#124—6732no—
614#123—6732no—
615#123—6732no—
616C22⋊Q8—6716no—
617C22⋊Q8—6716no—
618C22⋊Q8—6732no—
619C22⋊Q8—6716no—
620C22⋊Q8—6732no—
621C22⋊Q8—6716no—
622C22⋊Q8—6732no—
623#121—6716no—
624#121—6716no—
625#121—6716no—
626#121—6732no—
627#121—6716no—
628#121—6732no—
629#121—6716no—
630#121—6716no—
631#121—6732no—
632C4×Q8—678no—
633C4×Q8—678no—
634C4×Q8—6716no—
635C4×Q8—6732no—
636C4×Q8C22×D67116yes—
637C4×D4—6716no—
638C4×D4—6732no—
639C4×D4—6716no—
640C4×D4—678no—
641C4×D4—678no—
642C4×D4—6716no—
643C4×D4—6716no—
644C4×D4—6732no—
645C4×D4—6716no—
646C4×D4C22×D67116yes—
647C4×D4C22×D67132yes—
648#117—6716no—
649#117—6716no—
650#117—6732no—
651#117C22×D6718yes—
652#117C22×D67116yes—
653C2×C4⋊C4—672no—
654C2×C4⋊C4—674no—
655C2×C4⋊C4—672no—
656C2×C4⋊C4—674no—
657C2×C4⋊C4—678no—
658C2×C4⋊C4—674no—
659C2×C4⋊C4—6716no—
660C2×C4⋊C4—672no—
661C2×C4⋊C4—672no—
662C2×C4⋊C4—672no—
663C2×C4⋊C4—672no—
664C2×C4⋊C4—674no—
665C2×C4⋊C4—674no—
666C2×C4⋊C4—6716no—
667C2×C4⋊C4C22×D6711yescharacteristic
668C2×C4⋊C4C22×D6712yes—
669C2×C4⋊C4C22×D6712yes—
670C2×C4⋊C4C22×D6714yes—
671C2×C4⋊C4C22×D6718yes—
672C2×C4⋊C4C22×D67116yes—
673C2×C4⋊C4C22×D6711yescharacteristic
674C2×C22⋊C4—674no—
675C2×C22⋊C4—672no—
676C2×C22⋊C4—672no—
677C2×C22⋊C4—674no—
678C2×C22⋊C4—672no—
679C2×C22⋊C4—672no—
680C2×C22⋊C4—674no—
681C2×C22⋊C4—674no—
682C2×C22⋊C4—674no—
683C2×C22⋊C4—672no—
684C2×C22⋊C4—672no—
685C2×C22⋊C4C22×D6712yes—
686C2×C22⋊C4C22×D6714yes—
687C2×C42—674no—
688C2×C42—671no—
689C2×C42—672no—
690C2×C42—671no—
691C2×C42—671no—
692C2×C42—672no—
693C2×C42—678no—
694C2×C42—671no—
695C2×C42—6716no—
696C2×C42C22×D6712yes—
697C2×C42C22×D6714yes—
698C24—672no—
699C24—672no—
700C24C23×D6712yes—
701C24C23×D6711yescharacteristic
702#41—232no—
703#41—26864no—
704#41—13432no—
705#41—13432no—
706C2×Q8—24no—
707C2×Q8—2688no—
708C2×Q8—26832no—
709C2×Q8—6716no—
710C2×Q8—674no—
711C2×Q8—674no—
712C2×Q8—6716no—
713C2×Q8—13416no—
714C2×Q8—1344no—
715C2×Q8—1344no—
716C2×Q8C23×D6714yes—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—2688no—
720C2×D4—2688no—
721C2×D4—6716no—
722C2×D4—678no—
723C2×D4—678no—
724C2×D4—678no—
725C2×D4—678no—
726C2×D4—6716no—
727C2×D4—674no—
728C2×D4—674no—
729C2×D4—1348no—
730C2×D4—1348no—
731C2×D4—1348no—
732C2×D4—1348no—
733C2×D4—1344no—
734C2×D4—1344no—
735C2×D4C23×D6718yes—
736C2×D4C23×D6714yes—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—48no—
740C22×C4—2688no—
741C22×C4—2684no—
742C22×C4—678no—
743C22×C4—6716no—
744C22×C4—671no—
745C22×C4—671no—
746C22×C4—674no—
747C22×C4—674no—
748C22×C4—671no—
749C22×C4—671no—
750C22×C4—672no—
751C22×C4—672no—
752C22×C4—674no—
753C22×C4—678no—
754C22×C4—678no—
755C22×C4—678no—
756C22×C4—678no—
757C22×C4—1348no—
758C22×C4—1348no—
759C22×C4—1344no—
760C22×C4—1344no—
761C22×C4—1348no—
762C22×C4—1348no—
763C22×C4#1176162818yescomplemented
764C22×C4C23×D6718yes—
765C22×C4C23×D6712yes—
766C22×C4C23×D6712yes—
767C22×C4C23×D6712yes—
768C22×C4C23×D6714yes—
769C22×C4C23×D6718yes—
770C22×C4C23×D67116yes—
771C22×C4C23×D6711yescharacteristic
772C22×C4C23×D6711yescharacteristic
773C22×C4C23×D6714yes—
774C4⋊C4—678no—
775C4⋊C4—6716no—
776C4⋊C4—678no—
777C4⋊C4—6716no—
778C4⋊C4—6716no—
779C4⋊C4—678no—
780C4⋊C4—678no—
781C4⋊C4—678no—
782C4⋊C4—678no—
783C4⋊C4—6716no—
784C4⋊C4—6716no—
785C4⋊C4C23×D6714yes—
786C4⋊C4C23×D6718yes—
787C4⋊C4C23×D6718yes—
788C4⋊C4C23×D67116yes—
789C4⋊C4C23×D6714yes—
790C22⋊C4—6716no—
791C22⋊C4—678no—
792C22⋊C4—678no—
793C22⋊C4—6716no—
794C22⋊C4—678no—
795C22⋊C4—678no—
796C22⋊C4—6716no—
797C22⋊C4—6716no—
798C22⋊C4—6716no—
799C22⋊C4—678no—
800C22⋊C4—678no—
801C22⋊C4C23×D6718yes—
802C22⋊C4C23×D67116yes—
803C42—674no—
804C42—674no—
805C42—678no—
806C42—674no—
807C42—674no—
808C42—678no—
809C42—6716no—
810C42C23×D6718yes—
811C42C23×D67116yes—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—674no—
818C23—674no—
819C23—1344no—
820C23—1344no—
821C23—1344no—
822C23—1344no—
823C23—1344no—
824C23—1344no—
825C23C2×#1176162814yes—
826C23C24×D6714yes—
827C23C24×D6712yes—
828C23C24×D6711yescharacteristic
829Q8—28no—
830Q8—26816no—
831Q8—13432no—
832Q8—1348no—
833Q8—1348no—
834D4—216no—
835D4—28no—
836D4—26816no—
837D4—26816no—
838D4—13416no—
839D4—13416no—
840D4—13416no—
841D4—13416no—
842D4—1348no—
843D4—1348no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—26816no—
852C2×C4—2688no—
853C2×C4—674no—
854C2×C4—674no—
855C2×C4—672no—
856C2×C4—672no—
857C2×C4—672no—
858C2×C4—672no—
859C2×C4—674no—
860C2×C4—674no—
861C2×C4—678no—
862C2×C4—13416no—
863C2×C4—13416no—
864C2×C4—1348no—
865C2×C4—1348no—
866C2×C4—1344no—
867C2×C4—1344no—
868C2×C4—1348no—
869C2×C4—1342no—
870C2×C4—1342no—
871C2×C4—13416no—
872C2×C4—13416no—
873C2×C4C2×#1176162814yes—
874C2×C4C2×#1176162814yes—
875C2×C4C2×#11761628116yescomplemented
876C2×C4C24×D6714yes—
877C2×C4C24×D6714yes—
878C2×C4C24×D6714yes—
879C2×C4C24×D6718yes—
880C2×C4C24×D6712yes—
881C2×C4C24×D6712yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—48no—
889C22—2688no—
890C22—2688no—
891C22—1344no—
892C22—1344no—
893C22—1344no—
894C22—1344no—
895C22—1344no—
896C22—1344no—
897C22C22×#1176162814yes—
898C22C22×#1176162812yes—
899C22H(5,𝔽2)×D6712yes—
900C222−1+4×D6712yes—
901C22C25×D6711yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—24no—
906C4—674no—
907C4—674no—
908C4—1344no—
909C4—1344no—
910C4—1348no—
911C4—1342no—
912C4—1342no—
913C4C22×#1176162814yes—
914C4C22×#1176162814yes—
915C2—24no—
916C2—44no—
917C2—2684no—
918C2—2684no—
919C2#2257411214yesdirect product factor
920C2C23×#1176162811yescharacteristic
921C2C2×H(5,𝔽2)×D6711yescharacteristic
922C2C2×2−1+4×D6711yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#520×C67C2
socleC23×C67C25
hypercenterC2×#520D67
hypocenterC67C2×#3511
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22574112C2direct (N × H)
2. C2×#16864114C2semidirect
3. C2×#16864109C2semidirect
4. C2×#16864101C2semidirect
5. C2×#16864095C2semidirect
6. C2×#16864055C2semidirect
7. C2×#16864047C2semidirect
8. C2×#16864018C2semidirect
9. C2×#16864011C2semidirect
10. C2×#16863977C2semidirect
11. C2×#16863974C2semidirect
12. C2×#16863950C2semidirect
13. C2×#16863943C2semidirect
14. C2×#16863942C2semidirect
15. C22×#14524042C2semidirect
16. C2×#16863876C2semidirect
17. C2×#16863864C2semidirect
18. C2×#520×C67C2semidirect
23. #16864114C22semidirect
24. #16864109C22semidirect
25. #16864101C22semidirect
26. #16864095C22semidirect
27. #16864055C22semidirect
28. #16864047C22semidirect
29. #16864018C22semidirect
30. #16864011C22semidirect
31. #16863977C22semidirect
32. #16863974C22semidirect
33. #16863950C22semidirect
34. #16863943C22semidirect
35. #16863942C22semidirect
40. C2×#14524042C22semidirect
69. #16863876C22semidirect
70. #16863864C22semidirect
93. #520×C67C22semidirect
330. C22×C4×C67#41semidirect
379. C2×C4×C67C2×#41semidirect
456. C2×C67#3511semidirect
478. C2×#520D67semidirect
480. C67C2×#3511semidirect
533. #520C2×D67semidirect
763. C22×C4#11761628semidirect
875. C2×C4C2×#11761628semidirect
919. C2#22574112direct (N × H)

Maximal subgroups

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

subgroupindex
#225741122
C2×#168641142
C2×#168641092
C2×#168641012
C2×#168640952
C2×#168640552
C2×#168640472
C2×#168640182
C2×#168640112
C2×#168639772
C2×#168639742
C2×#168639502
C2×#168639432
C2×#168639422
C22×#145240422
C2×#168638762
C2×#168638642
C2×#520×C672
C2×#351167