Finite Group Databasebeta

← #31763991

Subgroups — #31763991

Order 17152.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574280C218yesmaximal, complemented
2#22574188C214yesmaximal, complemented
3#22574171C214yesmaximal, complemented
4#22574076C212yesmaximal, complemented
5#22574050C214yesmaximal, complemented
6#22573973C211yesmaximal, characteristic, complemented
7#22573930C212yesmaximal, complemented
8#22573908C214yesmaximal, complemented
9#22573854C212yesmaximal, complemented
10#22573830C214yesmaximal, complemented
11#22573820C214yesmaximal, complemented
12#22573775C218yesmaximal, complemented
13#22573643C212yesmaximal, complemented
14#22573621C214yesmaximal, complemented
15#22573506C212yesmaximal, complemented
16C2×#16863932C214yesmaximal, complemented
17#22573413C212yesmaximal, complemented
18C2×C4×#11761627C211yesmaximal, characteristic, complemented
19C67×#3501C211yesmaximal, characteristic, complemented
20C2×#14524088C2212yes—
21C22×#11761627C2211yescharacteristic
22#16864131C2214yescomplemented
23#16864125C2214yescomplemented
24#16864120C2214yescomplemented
25#16864120C2218yescomplemented
26#16864119C2218yescomplemented
27#16864112C2218yescomplemented
28#16864107C2214yescomplemented
29#16864099C2218yescomplemented
30#16864094C2218yescomplemented
31#16864094C22116yescomplemented
32#16864088C22116yescomplemented
33#16864088C2218yescomplemented
34#16864088C22116yescomplemented
35#16864084C2218yescomplemented
36#16864084C2218yescomplemented
37#16864073C22116yescomplemented
38#16864073C22116yescomplemented
39#16864073C22116yescomplemented
40#16864057C2218yescomplemented
41#16864050C2218yescomplemented
42#16864050C2214yescomplemented
43#16864050C2218yescomplemented
44#16864041C2218yescomplemented
45#16864041C2218yescomplemented
46#16864041C2218yescomplemented
47#16864037C2218yescomplemented
48D4×D268C2214yescomplemented
49#16864020C2218yescomplemented
50#16864009C2218yescomplemented
51#16863995C2218yescomplemented
52#16863995C22116yescomplemented
53#16863995C2218yescomplemented
54#16863986C22116yescomplemented
55#16863986C2218yescomplemented
56#16863977C2212yes—
57#16863972C2214yescomplemented
58#16863958C2214yes—
59#16863958C2218yescomplemented
60#16863951C2212yescomplemented
61#16863951C2218yescomplemented
62#16863951C2212yescomplemented
63#16863947C2212yescomplemented
64#16863947C2212yescomplemented
65#16863946C2212yes—
66#16863933C2214yescomplemented
67#16863933C2214yescomplemented
68#16863932C22116yescomplemented
69#16863932C2218yescomplemented
70#16863932C2218yescomplemented
71#16863932C2214yescomplemented
72#16863932C2218yescomplemented
73#16863932C2218yescomplemented
74#16863932C2214yescomplemented
75#16863932C2218yescomplemented
76#16863932C2218yescomplemented
77#16863932C2218yescomplemented
78#16863931C2218yescomplemented
79#16863931C2214yescomplemented
80#16863931C2214yescomplemented
81C2×#14524038C2218yescomplemented
82C2×#14524034C2214yescomplemented
83C2×#14524032C2214yescomplemented
84#16863909C2214yescomplemented
85#16863909C22116yescomplemented
86#16863909C2214yescomplemented
87#16863908C2214yescomplemented
88C2×#14524027C2218yescomplemented
89C2×#14524017C2214yes—
90#16863876C2214yescomplemented
91#16863875C2218yescomplemented
92#16863869C2218yescomplemented
93#16863868C2218yescomplemented
94C4×#11761629C2214yescomplemented
95C4×#11761629C2214yescomplemented
96#16863864C2214yescomplemented
97C4×#11761627C2214yescomplemented
98C4×#11761627C2218yescomplemented
99C4×#11761627C2214yescomplemented
100C4×#11761627C2214yescomplemented
101C4×#11761627C2214yescomplemented
102C2×Q8×Dic67C2214yescomplemented
103C2×C4×Dic134C2211yescharacteristic, complemented
104C2×#14524008C2211yescharacteristic, complemented
105C2×D4×Dic67C2211yescharacteristic
106C2×#14524005C2214yescomplemented
107C2×C4×C22⋊D67C2212yescomplemented
108C2×(C22⋊D67)⋊C4C2212yescomplemented
109C2×(C22⋊D67)⋊C4C2218yescomplemented
110C4×D4×D67C2218yescomplemented
111C2×#14524001C2211yescharacteristic, complemented
112C2×#14524001C2218yescomplemented
113C2×#14523999C2212yescomplemented
114C22×C4×Dic67C2212yescomplemented
115C2×C42×D67C2211yescharacteristic, complemented
116#554×C67C2214yescomplemented
117#554×C67C2218yescomplemented
118D4×Q8×C67C2214yescomplemented
119#544×C67C2212yescomplemented
120#543×C67C2214yescomplemented
121#533×C67C2212yescomplemented
122C2×C22⋊Q8×C67C2214yescomplemented
123#518×C67C2212yes—
124C2×C4×D4×C67C2211yescharacteristic
125#14524088—216no—
126C2×#11761629C2314yes—
127C2×#11761629C2314yes—
128C2×#11761628C2314yes—
129C2×#11761627—28no—
130C2×#11761627C2314yes—
131C2×#11761627C2314yes—
132C2×#11761627C2318yes—
133C22×Dic134C2311yescharacteristic
134C22×D268C2314yes—
135C22×C22⋊D67C2312yes—
136C22×C22⋊D67C2318yes—
137C2×D4×D67C2318yes—
138C23×Dic67C2312yes—
139C23×Dic67C2312yes—
140C22×C4×D67C2311yescharacteristic
141C22×C4×D67C2311yescharacteristic
142C22×C4×D67C2311yescharacteristic
143C22×C4×D67C2318yes—
144#14524043C2318yes—
145#14524043C2312yes—
146#14524040C2312yes—
147#14524038C23116yes—
148#14524038C23116yes—
149#14524038C2318yes—
150#14524038C23116yes—
151#14524038C23116yes—
152#14524038C23116yes—
153#14524038C23116yes—
154#14524038C2318yes—
155#14524034C2318yes—
156#14524034C23116yes—
157#14524034C2318yes—
158#14524034C23116yes—
159#14524034C2314yes—
160#14524034C2318yes—
161#14524034C2314yes—
162#14524032C2318yes—
163#14524032C2318yes—
164#14524032C23116yes—
165#14524032C2314yes—
166#14524032C2318yes—
167#14524032C2314yes—
168#14524031C2318yes—
169#14524031C2314yes—
170#14524028C23116yes—
171#14524028C23116yes—
172#14524028C2318yes—
173#14524028C23116yes—
174#14524028C2318yes—
175#14524027C23116yes—
176#14524027C23116yes—
177#14524027C23116yes—
178#14524027C23116yes—
179#14524027C2318yes—
180#14524027C23116yes—
181#14524023C2318yes—
182#14524023C2318yes—
183#14524023C2318yes—
184#14524023C2314yes—
185#14524023C2314yes—
186#14524019C23116yes—
187#14524019C2314yes—
188#14524019C23116yes—
189#14524019C2314yes—
190#14524018C2318yes—
191#14524018C2314yes—
192#14524018C23116yes—
193#14524018C2314yes—
194#14524018C2314yes—
195#14524018C2314yes—
196#14524017C2318yes—
197#14524017C2318yes—
198#14524017C23116yes—
199#14524017C23116yes—
200#14524017C2314yes—
201#14524017C2318yes—
202#14524017C2314yes—
203#14524013C23116yes—
204#14524013C23116yes—
205#14524013C2318yes—
206Q8×Dic67C2318yes—
207Q8×Dic67C2314yes—
208Q8×Dic67C2318yes—
209Q8×Dic67C2314yes—
210Q8×Dic67C2318yes—
211C4×Dic134C2314yes—
212C4×Dic134C2318yes—
213C4×Dic134C2314yes—
214#14524008C2314yes—
215#14524008C2314yes—
216#14524008C2314yes—
217#14524008C2314yes—
218C4×D268C2314yes—
219C4×D268C2314yes—
220C4×D268C2318yes—
221C4×D268C2318yes—
222C4×D268C2318yes—
223D4×Dic67C2314yes—
224D4×Dic67C2314yes—
225#14524005C2314yes—
226#14524005C2318yes—
227#14524005C2314yes—
228#14524005C2318yes—
229#14524005C2318yes—
230#14524005C2314yes—
231#14524005C2314yes—
232#14524005C2318yes—
233#14524005C2318yes—
234C4×C22⋊D67C2318yes—
235C4×C22⋊D67C23116yes—
236C4×C22⋊D67C2318yes—
237C4×C22⋊D67C23116yes—
238(C22⋊D67)⋊C4C23116yes—
239(C22⋊D67)⋊C4C2318yes—
240(C22⋊D67)⋊C4C2318yes—
241(C22⋊D67)⋊C4C2318yes—
242(C22⋊D67)⋊C4C23116yes—
243(C22⋊D67)⋊C4C23116yes—
244(C22⋊D67)⋊C4C2318yes—
245#14524001C2318yes—
246#14524001C23116yes—
247#14524001C23116yes—
248#14524001C2314yes—
249#14524001C2318yes—
250#14524001C2314yes—
251#14524001C2314yes—
252#14524001C2318yes—
253#14524001C23116yes—
254#14524001C2314yes—
255#14524000C2318yes—
256#14523999C2318yes—
257#14523999C2318yes—
258#14523999C23116yes—
259C2×C4⋊Dic67C2318yes—
260C2×C4⋊Dic67C2314yes—
261C2×C4⋊Dic67C2318yes—
262C2×C4⋊Dic67C2311yescharacteristic
263C2×Dic67⋊C4C2312yes—
264C2×Dic67⋊C4C2312yes—
265C2×Dic67⋊C4C2318yes—
266C4⋊C4×D67C2318yes—
267C2×C22⋊Dic67C2312yes—
268C2×(C2×D67)⋊C4C2318yes—
269C2×(C2×D67)⋊C4C2318yes—
270C2×(C2×D67)⋊C4C2318yes—
271C2×(C2×D67)⋊C4C2312yes—
272C2×(C2×D67)⋊C4C2318yes—
273C22⋊C4×D67C23116yes—
274C2×C4×Dic67C2311yescharacteristic
275C2×C4×Dic67C2311yescharacteristic
276C2×C4×Dic67C2311yescharacteristic
277C2×C4×Dic67C2312yes—
278C2×C4×Dic67C2314yes—
279C2×C4×Dic67C2312yes—
280C2×C4×Dic67C2312yes—
281C2×C4×Dic67C2314yes—
282C2×C4×Dic67C2314yes—
283C2×C4×Dic67C2314yes—
284C2×C4×Dic67C2318yes—
285C42×D67C2312yes—
286C42×D67C2312yes—
287C42×D67C2312yes—
288C42×D67C2312yes—
289C42×D67C2318yes—
290C22×Q8×C67C2314yes—
291C22×D4×C67C2311yescharacteristic
292C23×C4×C67C2312yes—
293C4⋊Q8×C67C2318yes—
294C4⋊Q8×C67C2312yes—
295C4⋊Q8×C67C2312yes—
296#125×C67C2318yes—
297#125×C67C2314yes—
298C22⋊Q8×C67C2318yes—
299C22⋊Q8×C67C2318yes—
300C22⋊Q8×C67C23116yes—
301C22⋊Q8×C67C23116yes—
302C22⋊Q8×C67C2314yes—
303C22⋊Q8×C67C2318yes—
304C22⋊Q8×C67C2314yes—
305C4×Q8×C67C2314yes—
306C4×Q8×C67C2314yes—
307C4×D4×C67C2314yes—
308C4×D4×C67C2314yes—
309C4×D4×C67C2318yes—
310C4×D4×C67C2318yes—
311#117×C67C2314yes—
312C2×C4⋊C4×C67C2311yescharacteristic
313C2×C4⋊C4×C67C2318yes—
314C2×C4⋊C4×C67C2314yes—
315C2×C22⋊C4×C67C2312yes—
316C2×C22⋊C4×C67C2318yes—
317C2×C42×C67C2311yescharacteristic
318C23×D67C2418yes—
319C23×D67C2411yescharacteristic
320#11761629—48no—
321#11761629—48no—
322#11761628—216no—
323#11761627—216no—
324#11761627—216no—
325#11761627—232no—
326C2×Dic134—24no—
327C2×Dic134C2414yes—
328C2×Dic134C2414yes—
329C2×D268—48no—
330C2×D268C2414yes—
331C2×D268C2414yes—
332C2×D268C2418yes—
333C2×D268C2414yes—
334C2×D268C2418yes—
335C2×D268C2418yes—
336C2×C22⋊D67—28no—
337C2×C22⋊D67—232no—
338C2×C22⋊D67C2418yes—
339C2×C22⋊D67C2418yes—
340C2×C22⋊D67C24116yes—
341D4×D67—232no—
342C22×Dic67—28no—
343C22×Dic67—44no—
344C22×Dic67C2411yescharacteristic
345C22×Dic67C2414yes—
346C22×Dic67C2411yescharacteristic
347C22×Dic67C2414yes—
348C22×Dic67C2414yes—
349C22×Dic67C2412yes—
350C22×Dic67C2418yes—
351C22×Dic67C2414yes—
352C22×Dic67C2412yes—
353C22×Dic67C2411yescharacteristic
354C2×C4×D67—24no—
355C2×C4×D67—416no—
356C2×C4×D67—42no—
357C2×C4×D67—42no—
358C2×C4×D67C2412yes—
359C2×C4×D67C2412yes—
360C2×C4×D67C2412yes—
361C2×C4×D67C2412yes—
362C2×C4×D67C2418yes—
363C2×C4×D67C2418yes—
364C2×C4×D67C2412yes—
365C2×C4×D67C2412yes—
366C2×C4×D67C2418yes—
367C2×C4×D67C24116yes—
368C4⋊Dic67C2414yes—
369C4⋊Dic67C2418yes—
370C4⋊Dic67C2414yes—
371C4⋊Dic67C2418yes—
372C4⋊Dic67C24116yes—
373C4⋊Dic67C2418yes—
374C4⋊Dic67C24116yes—
375C4⋊Dic67C2414yes—
376Dic67⋊C4C24116yes—
377Dic67⋊C4C2418yes—
378Dic67⋊C4C2418yes—
379Dic67⋊C4C2418yes—
380Dic67⋊C4C2418yes—
381C22⋊Dic67C2418yes—
382(C2×D67)⋊C4C2418yes—
383(C2×D67)⋊C4C24116yes—
384(C2×D67)⋊C4C2418yes—
385(C2×D67)⋊C4C2418yes—
386(C2×D67)⋊C4C2418yes—
387(C2×D67)⋊C4C2418yes—
388(C2×D67)⋊C4C2418yes—
389(C2×D67)⋊C4C24116yes—
390(C2×D67)⋊C4C24116yes—
391(C2×D67)⋊C4C24116yes—
392(C2×D67)⋊C4C2418yes—
393(C2×D67)⋊C4C2418yes—
394(C2×D67)⋊C4C2418yes—
395C4×Dic67C2412yes—
396C4×Dic67C2411yescharacteristic
397C4×Dic67C2411yescharacteristic
398C4×Dic67C2411yescharacteristic
399C4×Dic67C2411yescharacteristic
400C4×Dic67C2412yes—
401C4×Dic67C2412yes—
402C4×Dic67C2412yes—
403C4×Dic67C2418yes—
404C4×Dic67C2418yes—
405C4×Dic67C2414yes—
406C4×Dic67C2414yes—
407C4×Dic67C2414yes—
408C4×Dic67C2414yes—
409C4×Dic67C2414yes—
410C4×Dic67C2414yes—
411C4×Dic67C24116yes—
412C24×C67C2412yes—
413C2×Q8×C67—48no—
414C2×Q8×C67C2414yes—
415C2×Q8×C67C2414yes—
416C2×Q8×C67C2418yes—
417C2×D4×C67#4118yescomplemented
418C2×D4×C67C2414yes—
419C22×C4×C67—44no—
420C22×C4×C67C2411yescharacteristic
421C22×C4×C67C2414yes—
422C22×C4×C67C2411yescharacteristic
423C22×C4×C67C2418yes—
424C22×C4×C67C2418yes—
425C22×C4×C67C2412yes—
426C22×C4×C67C2414yes—
427C22×C4×C67C2411yescharacteristic
428C4⋊C4×C67C2418yes—
429C4⋊C4×C67C2414yes—
430C4⋊C4×C67C2414yes—
431C4⋊C4×C67C2418yes—
432C4⋊C4×C67C24116yes—
433C4⋊C4×C67C2414yes—
434C4⋊C4×C67C2414yes—
435C4⋊C4×C67C2418yes—
436C4⋊C4×C67C2414yes—
437C22⋊C4×C67C2418yes—
438C22⋊C4×C67C24116yes—
439C22⋊C4×C67C2418yes—
440C42×C67C2412yes—
441C42×C67C2412yes—
442C42×C67C2418yes—
443C23×C67—42no—
444C23×C67—42no—
445C23×C67C2×#4118yes—
446C23×C67C2511yescharacteristic
447C23×C67C2514yes—
448C22×D67—22no—
449C22×D67—216no—
450C22×D67—41no—
451C22×D67—41no—
452C22×D67—48no—
453C22×D67—48no—
454C22×D67C2518yes—
455C22×D67C2512yes—
456Q8×C67—28no—
457Q8×C67—48no—
458Q8×C67—44no—
459D4×C67C2×#41116yes—
460C2×C4×C67—22no—
461C2×C4×C67—28no—
462C2×C4×C67—44no—
463C2×C4×C67—42no—
464C2×C4×C67—48no—
465C2×C4×C67—48no—
466C2×C4×C67—41no—
467C2×C4×C67C2×#4114yes—
468C2×C4×C67C2512yes—
469C2×C4×C67C2511yescharacteristic
470C2×C4×C67C2518yes—
471C2×C4×C67C2518yes—
472C2×C4×C67C2514yes—
473C2×C4×C67C2512yes—
474C2×C4×C67C2511yescharacteristic
475C22⋊D67—232no—
476C22⋊D67—216no—
477C22⋊D67—216no—
478C2×Dic67—22no—
479C2×Dic67—24no—
480C2×Dic67—28no—
481C2×Dic67—28no—
482C2×Dic67—216no—
483C2×Dic67—28no—
484C2×Dic67—22no—
485C2×Dic67—41no—
486C2×Dic67—42no—
487C2×Dic67—44no—
488C2×Dic67C2511yescharacteristic
489C2×Dic67C2511yescharacteristic
490C2×Dic67C2511yescharacteristic
491C2×Dic67C2514yes—
492C2×Dic67C2512yes—
493C2×Dic67C2514yes—
494C2×Dic67C2518yes—
495C2×Dic67C2511yescharacteristic
496D268—28no—
497D268—28no—
498D268—48no—
499D268—48no—
500D268—44no—
501D268—48no—
502C4×D67—24no—
503C4×D67—24no—
504C4×D67—216no—
505C4×D67—24no—
506C4×D67—216no—
507C4×D67—24no—
508C4×D67—42no—
509C4×D67—416no—
510C4×D67—42no—
511C4×D67—48no—
512Dic134—28no—
513Dic134—28no—
514C22×C67—21no—
515C22×C67—24no—
516C22×C67—21no—
517C22×C67—24no—
518C22×C67—48no—
519C22×C67C22×#4118yes—
520C22×C67C22×#4112yes—
521C22×C67C2611yescharacteristic
522C2×D67—22no—
523C2×D67—28no—
524C2×D67—28no—
525C2×D67—22no—
526C2×D67—22no—
527C2×D67—28no—
528C2×D67—44no—
529C2×D67—816no—
530C4×C67—28no—
531C4×C67—22no—
532C4×C67—21no—
533C4×C67—28no—
534C4×C67—24no—
535C4×C67C22×#4114yes—
536C4×C67#58512yes—
537Dic67—24no—
538Dic67—28no—
539Dic67—21no—
540Dic67—21no—
541Dic67—22no—
542Dic67—24no—
543Dic67—21no—
544Dic67#58512yes—
545#62781—671nomaximal, Sylow
546C2×C67—22no—
547C2×C67—28no—
548C2×C67C23×#4111yescharacteristic
549C2×C67C2×#58511yescharacteristic
550C2×C67C2×#58511yescharacteristic
551D67—42no—
552D67—48no—
553#3521—678no—
554#3515—674no—
555#3514—674no—
556#3507—672no—
557#3505—674no—
558#3501D6711yescharacteristic, complemented
559#3496—671no—
560#3493—672no—
561#3491—674no—
562#3485—672no—
563#3482—674no—
564#3481—674no—
565#3475—678no—
566#3461—672no—
567#3459—674no—
568#3444—672no—
569C2×#529—674no—
570C4×H(5,𝔽2)—672no—
571C2×C4×#41—671no—
572C67#6278111yescharacteristic, complemented, Sylow
573C2×H(5,𝔽2)—672no—
574C22×#41—671no—
575#559—674no—
576#557—674no—
577#556—678no—
578#556—674no—
579#556—678no—
580#555—678no—
581#554—674no—
582#554C2×D6718yescomplemented
583#554C2×D6714yescomplemented
584#553—678no—
585#553—6716no—
586#553—678no—
587#552—678no—
588#552—678no—
589#552—6716no—
590#552—6716no—
591#552—678no—
592#551—6716no—
593#551—6716no—
594#551—6716no—
595D4×Q8C2×D6714yescomplemented
596#548—678no—
597#547—678no—
598#547—678no—
599#547—674no—
600#546—678no—
601#546—678no—
602#546—678no—
603#546—678no—
604D42—674no—
605#544C2×D6712yescomplemented
606#543C2×D6714yescomplemented
607#542—678no—
608#541—678no—
609#539—678no—
610#539—6716no—
611#539—678no—
612#538—678no—
613#538—6716no—
614#537—672no—
615#536—674no—
616#534—678no—
617#534—674no—
618#533—672no—
619#533—672no—
620#533—678no—
621#533C2×D6712yescomplemented
622#532—672no—
623#532—672no—
624#532—672no—
625#529—674no—
626#529—674no—
627#529—678no—
628#529—674no—
629#529—678no—
630#529—678no—
631#529—678no—
632#529—678no—
633#529—678no—
634#529—678no—
635#529—678no—
636#529—674no—
637#529—6716no—
638#529—674no—
639#529—674no—
640C2×#126—678no—
641C2×#125—674no—
642C2×#124—674no—
643#525—674no—
644#525—674no—
645#525—6716no—
646#525—674no—
647C2×#123—678no—
648C2×C22⋊Q8C2×D6714yescomplemented
649C2×#121—674no—
650#520—678no—
651#520—674no—
652#518—678no—
653#518—678no—
654#518C2×D6712yes—
655C4×#41—674no—
656C4×#41—674no—
657C4×#41—674no—
658C4×#41—674no—
659C4×#41—674no—
660C4×#41—674no—
661C4×#41—678no—
662C4×#41—674no—
663C2×C4×Q8—674no—
664C2×C4×Q8—671no—
665C2×C4×Q8—671no—
666C2×C4×D4—671no—
667C2×C4×D4—672no—
668C2×C4×D4—678no—
669C2×C4×D4—674no—
670C2×C4×D4—672no—
671C2×C4×D4—678no—
672C2×C4×D4C2×D6711yescharacteristic
673C2×#117—671no—
674C2×#117—678no—
675C2×#117—672no—
676C22×C42—672no—
677C22×C42—671no—
678H(5,𝔽2)—13416no—
679C2×#41—674no—
680C2×#41—674no—
681C2×#41—674no—
682C2×#41—674no—
683C2×#41—678no—
684C2×#41—674no—
685C2×#41—1348no—
686C22×Q8—671no—
687C22×Q8C22×D6714yes—
688C22×D4—672no—
689C22×D4—678no—
690C22×D4—678no—
691C22×D4—674no—
692C22×D4C22×D6711yescharacteristic
693C23×C4—672no—
694C23×C4—678no—
695C23×C4—671no—
696C23×C4—671no—
697C23×C4—672no—
698C23×C4—671no—
699C23×C4C22×D6712yes—
700C4⋊Q8—672no—
701C4⋊Q8—678no—
702C4⋊Q8C22×D6712yes—
703C4⋊Q8C22×D6712yes—
704C4⋊Q8C22×D6718yes—
705#127—672no—
706#126—678no—
707#126—6716no—
708#126—6716no—
709#126—6716no—
710#126—678no—
711#126—6716no—
712#126—6716no—
713#126—6716no—
714#125—674no—
715#125—678no—
716#125—678no—
717#125—678no—
718#125—674no—
719#125—6716no—
720#125—6716no—
721#125C22×D6714yes—
722#125C22×D6718yes—
723#124—674no—
724#124—678no—
725#124—678no—
726#124—678no—
727#124—674no—
728#124—6716no—
729#124—674no—
730#124—678no—
731#123—678no—
732#123—678no—
733#123—6716no—
734#123—6716no—
735#123—6716no—
736#123—678no—
737#123—6716no—
738#123—6716no—
739#123—6716no—
740#123—6716no—
741#123—6716no—
742C22⋊Q8—674no—
743C22⋊Q8—674no—
744C22⋊Q8—6716no—
745C22⋊Q8—6716no—
746C22⋊Q8—674no—
747C22⋊Q8—674no—
748C22⋊Q8—678no—
749C22⋊Q8—678no—
750C22⋊Q8—678no—
751C22⋊Q8C22×D6714yes—
752C22⋊Q8C22×D6718yes—
753C22⋊Q8C22×D6718yes—
754C22⋊Q8C22×D6718yes—
755C22⋊Q8C22×D6714yes—
756C22⋊Q8C22×D67116yes—
757C22⋊Q8C22×D67116yes—
758#121—674no—
759#121—678no—
760#121—678no—
761#121—678no—
762#121—674no—
763#121—6716no—
764#121—6716no—
765#121—674no—
766#121—674no—
767#121—674no—
768#121—674no—
769#121—6716no—
770#121—678no—
771#120—678no—
772#120—6716no—
773#120—6716no—
774C4×Q8—674no—
775C4×Q8—678no—
776C4×Q8—678no—
777C4×Q8—678no—
778C4×Q8—674no—
779C4×Q8—674no—
780C4×Q8—674no—
781C4×Q8—674no—
782C4×Q8—674no—
783C4×Q8—674no—
784C4×Q8—674no—
785C4×Q8—678no—
786C4×Q8C22×D6714yes—
787C4×Q8C22×D6714yes—
788C4×D4—674no—
789C4×D4—674no—
790C4×D4—678no—
791C4×D4—678no—
792C4×D4—6716no—
793C4×D4—6716no—
794C4×D4—674no—
795C4×D4—674no—
796C4×D4—678no—
797C4×D4—678no—
798C4×D4—678no—
799C4×D4—674no—
800C4×D4—678no—
801C4×D4—678no—
802C4×D4—674no—
803C4×D4—6716no—
804C4×D4—678no—
805C4×D4—678no—
806C4×D4—678no—
807C4×D4—6716no—
808C4×D4—6716no—
809C4×D4—678no—
810C4×D4—678no—
811C4×D4—678no—
812C4×D4—678no—
813C4×D4—674no—
814C4×D4—674no—
815C4×D4C22×D6718yes—
816C4×D4C22×D6714yes—
817C4×D4C22×D6714yes—
818C4×D4C22×D6718yes—
819#117—678no—
820#117—674no—
821#117—674no—
822#117—6716no—
823#117—6716no—
824#117—6716no—
825#117—678no—
826#117—674no—
827#117—674no—
828#117—678no—
829#117—678no—
830#117—678no—
831#117—6716no—
832#117—678no—
833#117C22×D6714yes—
834C2×C4⋊C4—671no—
835C2×C4⋊C4—672no—
836C2×C4⋊C4—672no—
837C2×C4⋊C4—678no—
838C2×C4⋊C4—678no—
839C2×C4⋊C4—674no—
840C2×C4⋊C4—678no—
841C2×C4⋊C4—678no—
842C2×C4⋊C4C22×D6711yescharacteristic
843C2×C4⋊C4C22×D6718yes—
844C2×C4⋊C4C22×D6714yes—
845C2×C22⋊C4—672no—
846C2×C22⋊C4—672no—
847C2×C22⋊C4—678no—
848C2×C22⋊C4—678no—
849C2×C22⋊C4—678no—
850C2×C22⋊C4—678no—
851C2×C22⋊C4—6716no—
852C2×C22⋊C4C22×D6712yes—
853C2×C22⋊C4C22×D6718yes—
854C2×C42—674no—
855C2×C42—672no—
856C2×C42—671no—
857C2×C42—678no—
858C2×C42—671no—
859C2×C42—674no—
860C2×C42—672no—
861C2×C42—672no—
862C2×C42—674no—
863C2×C42—674no—
864C2×C42—671no—
865C2×C42—678no—
866C2×C42—672no—
867C2×C42—672no—
868C2×C42—672no—
869C2×C42—672no—
870C2×C42C22×D6711yescharacteristic
871C24—678no—
872C24—671no—
873C24C23×D6712yes—
874#41—2688no—
875#41—2688no—
876#41—13416no—
877#41—13416no—
878#41—13432no—
879#41—13416no—
880C2×Q8—48no—
881C2×Q8—674no—
882C2×Q8—674no—
883C2×Q8—1344no—
884C2×Q8C23×D6714yes—
885C2×Q8C23×D6718yes—
886C2×Q8C23×D6714yes—
887C2×D4—2688no—
888C2×D4—678no—
889C2×D4—6716no—
890C2×D4—678no—
891C2×D4—674no—
892C2×D4—678no—
893C2×D4—678no—
894C2×D4—678no—
895C2×D4—674no—
896C2×D4—674no—
897C2×D4—1348no—
898C2×D4—13432no—
899C2×D4—13432no—
900C2×D4#1176162918yescomplemented
901C2×D4C23×D6714yes—
902C22×C4—44no—
903C22×C4—2682no—
904C22×C4—26816no—
905C22×C4—2682no—
906C22×C4—2684no—
907C22×C4—674no—
908C22×C4—671no—
909C22×C4—672no—
910C22×C4—672no—
911C22×C4—672no—
912C22×C4—678no—
913C22×C4—6716no—
914C22×C4—674no—
915C22×C4—671no—
916C22×C4—671no—
917C22×C4—674no—
918C22×C4—674no—
919C22×C4—672no—
920C22×C4—678no—
921C22×C4—672no—
922C22×C4—672no—
923C22×C4—672no—
924C22×C4—672no—
925C22×C4—678no—
926C22×C4—678no—
927C22×C4—1348no—
928C22×C4—1344no—
929C22×C4C23×D6711yescharacteristic
930C22×C4C23×D6714yes—
931C22×C4C23×D6714yes—
932C22×C4C23×D6712yes—
933C22×C4C23×D6711yescharacteristic
934C22×C4C23×D6718yes—
935C22×C4C23×D6718yes—
936C22×C4C23×D6711yescharacteristic
937C4⋊C4—674no—
938C4⋊C4—678no—
939C4⋊C4—678no—
940C4⋊C4—6716no—
941C4⋊C4—674no—
942C4⋊C4—678no—
943C4⋊C4—678no—
944C4⋊C4—678no—
945C4⋊C4—6716no—
946C4⋊C4—678no—
947C4⋊C4—6716no—
948C4⋊C4—678no—
949C4⋊C4—674no—
950C4⋊C4C23×D6714yes—
951C4⋊C4C23×D6718yes—
952C4⋊C4C23×D6714yes—
953C4⋊C4C23×D6714yes—
954C4⋊C4C23×D67116yes—
955C4⋊C4C23×D6718yes—
956C4⋊C4C23×D6714yes—
957C4⋊C4C23×D6714yes—
958C4⋊C4C23×D6718yes—
959C22⋊C4—678no—
960C22⋊C4—678no—
961C22⋊C4—678no—
962C22⋊C4—678no—
963C22⋊C4—678no—
964C22⋊C4—678no—
965C22⋊C4—6716no—
966C22⋊C4—678no—
967C22⋊C4—6716no—
968C22⋊C4—6716no—
969C22⋊C4—6716no—
970C22⋊C4—678no—
971C22⋊C4—678no—
972C22⋊C4—678no—
973C22⋊C4C23×D67116yes—
974C22⋊C4C23×D6718yes—
975C22⋊C4C23×D6718yes—
976C42—671no—
977C42—672no—
978C42—671no—
979C42—671no—
980C42—671no—
981C42—674no—
982C42—672no—
983C42—674no—
984C42—678no—
985C42—672no—
986C42—674no—
987C42—672no—
988C42—674no—
989C42—674no—
990C42—674no—
991C42—678no—
992C42—6716no—
993C42C23×D6712yes—
994C42C23×D6712yes—
995C42C23×D6718yes—
996C23—42no—
997C23—42no—
998C23—2681no—
999C23—2681no—
1000C23—2688no—
1001C23—2688no—
1002C23—678no—
1003C23—672no—
1004C23—1342no—
1005C23—13416no—
1006C23C2×#1176162918yes—
1007C23C24×D6714yes—
1008C23C24×D6711yescharacteristic
1009Q8—28no—
1010Q8—48no—
1011Q8—44no—
1012Q8—1348no—
1013Q8—1348no—
1014D4—2688no—
1015D4—2688no—
1016D4—2684no—
1017D4—2688no—
1018D4—13432no—
1019D4—13416no—
1020D4—13416no—
1021D4—1348no—
1022D4—1348no—
1023D4C2×#11761629116yes—
1024C2×C4—22no—
1025C2×C4—28no—
1026C2×C4—44no—
1027C2×C4—42no—
1028C2×C4—48no—
1029C2×C4—41no—
1030C2×C4—48no—
1031C2×C4—26816no—
1032C2×C4—2682no—
1033C2×C4—2682no—
1034C2×C4—2688no—
1035C2×C4—2684no—
1036C2×C4—2682no—
1037C2×C4—2681no—
1038C2×C4—671no—
1039C2×C4—671no—
1040C2×C4—671no—
1041C2×C4—671no—
1042C2×C4—674no—
1043C2×C4—672no—
1044C2×C4—674no—
1045C2×C4—678no—
1046C2×C4—13416no—
1047C2×C4—1344no—
1048C2×C4—1348no—
1049C2×C4—1342no—
1050C2×C4—1342no—
1051C2×C4—1344no—
1052C2×C4—1348no—
1053C2×C4—1348no—
1054C2×C4—13416no—
1055C2×C4—1344no—
1056C2×C4—1344no—
1057C2×C4—13416no—
1058C2×C4—1344no—
1059C2×C4C2×#1176162914yes—
1060C2×C4C24×D6711yescharacteristic
1061C2×C4C24×D6714yes—
1062C2×C4C24×D6718yes—
1063C2×C4C24×D6712yes—
1064C2×C4C24×D6718yes—
1065C2×C4C24×D6712yes—
1066C2×C4C24×D6711yescharacteristic
1067C22—24no—
1068C22—21no—
1069C22—24no—
1070C22—21no—
1071C22—48no—
1072C22—2684no—
1073C22—53616no—
1074C22—1342no—
1075C22—1348no—
1076C22—1348no—
1077C22—1342no—
1078C22—1342no—
1079C22—1348no—
1080C22C22×#1176162918yes—
1081C22C22×#1176162912yes—
1082C22C25×D6711yescharacteristic
1083C4—28no—
1084C4—22no—
1085C4—21no—
1086C4—24no—
1087C4—28no—
1088C4—672no—
1089C4—1341no—
1090C4—1341no—
1091C4—1348no—
1092C4—1344no—
1093C4—1344no—
1094C4—1341no—
1095C4—1342no—
1096C4C22×#1176162914yes—
1097C4#1686423112yes—
1098C2—22no—
1099C2—28no—
1100C2—2682no—
1101C2—2688no—
1102C2C23×#1176162911yescharacteristic
1103C2#585×D6711yescharacteristic
1104C2C2×#1686423111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D67
commutator, socle, cosocleC22×C67C26
FittingC67×#3501C2
hypercenter#3501D67
hypocenterC67#62781
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #22574280C2semidirect
2. #22574188C2semidirect
3. #22574171C2semidirect
4. #22574076C2semidirect
5. #22574050C2semidirect
6. #22573973C2semidirect
7. #22573930C2semidirect
8. #22573908C2semidirect
9. #22573854C2semidirect
10. #22573830C2semidirect
11. #22573820C2semidirect
12. #22573775C2semidirect
13. #22573643C2semidirect
14. #22573621C2semidirect
15. #22573506C2semidirect
16. C2×#16863932C2semidirect
17. #22573413C2semidirect
18. C2×C4×#11761627C2semidirect
19. C67×#3501C2semidirect
22. #16864131C22semidirect
23. #16864125C22semidirect
24. #16864120C22semidirect
25. #16864120C22semidirect
26. #16864119C22semidirect
27. #16864112C22semidirect
28. #16864107C22semidirect
29. #16864099C22semidirect
30. #16864094C22semidirect
31. #16864094C22semidirect
32. #16864088C22semidirect
33. #16864088C22semidirect
34. #16864088C22semidirect
35. #16864084C22semidirect
36. #16864084C22semidirect
37. #16864073C22semidirect
38. #16864073C22semidirect
39. #16864073C22semidirect
40. #16864057C22semidirect
41. #16864050C22semidirect
42. #16864050C22semidirect
43. #16864050C22semidirect
44. #16864041C22semidirect
45. #16864041C22semidirect
46. #16864041C22semidirect
47. #16864037C22semidirect
48. D4×D268C22semidirect
49. #16864020C22semidirect
50. #16864009C22semidirect
51. #16863995C22semidirect
52. #16863995C22semidirect
53. #16863995C22semidirect
54. #16863986C22semidirect
55. #16863986C22semidirect
57. #16863972C22semidirect
59. #16863958C22semidirect
60. #16863951C22semidirect
61. #16863951C22semidirect
62. #16863951C22semidirect
63. #16863947C22semidirect
64. #16863947C22semidirect
66. #16863933C22semidirect
67. #16863933C22semidirect
68. #16863932C22semidirect
69. #16863932C22semidirect
70. #16863932C22semidirect
71. #16863932C22semidirect
72. #16863932C22semidirect
73. #16863932C22semidirect
74. #16863932C22semidirect
75. #16863932C22semidirect
76. #16863932C22semidirect
77. #16863932C22semidirect
78. #16863931C22semidirect
79. #16863931C22semidirect
80. #16863931C22semidirect
81. C2×#14524038C22semidirect
82. C2×#14524034C22semidirect
83. C2×#14524032C22semidirect
84. #16863909C22semidirect
85. #16863909C22semidirect
86. #16863909C22semidirect
87. #16863908C22semidirect
88. C2×#14524027C22semidirect
90. #16863876C22semidirect
91. #16863875C22semidirect
92. #16863869C22semidirect
93. #16863868C22semidirect
94. C4×#11761629C22semidirect
95. C4×#11761629C22semidirect
96. #16863864C22semidirect
97. C4×#11761627C22semidirect
98. C4×#11761627C22semidirect
99. C4×#11761627C22semidirect
100. C4×#11761627C22semidirect
101. C4×#11761627C22semidirect
102. C2×Q8×Dic67C22semidirect
103. C2×C4×Dic134C22semidirect
104. C2×#14524008C22semidirect
106. C2×#14524005C22semidirect
107. C2×C4×C22⋊D67C22semidirect
108. C2×(C22⋊D67)⋊C4C22semidirect
109. C2×(C22⋊D67)⋊C4C22semidirect
110. C4×D4×D67C22semidirect
111. C2×#14524001C22semidirect
112. C2×#14524001C22semidirect
113. C2×#14523999C22semidirect
114. C22×C4×Dic67C22semidirect
115. C2×C42×D67C22semidirect
116. #554×C67C22semidirect
117. #554×C67C22semidirect
118. D4×Q8×C67C22semidirect
119. #544×C67C22semidirect
120. #543×C67C22semidirect
121. #533×C67C22semidirect
122. C2×C22⋊Q8×C67C22semidirect
417. C2×D4×C67#41semidirect
558. #3501D67semidirect
572. C67#62781semidirect
582. #554C2×D67semidirect
583. #554C2×D67semidirect
595. D4×Q8C2×D67semidirect
605. #544C2×D67semidirect
606. #543C2×D67semidirect
621. #533C2×D67semidirect
648. C2×C22⋊Q8C2×D67semidirect
900. C2×D4#11761629semidirect

Maximal subgroups

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

subgroupindex
#225742802
#225741882
#225741712
#225740762
#225740502
#225739732
#225739302
#225739082
#225738542
#225738302
#225738202
#225737752
#225736432
#225736212
#225735062
C2×#168639322
#225734132
C2×C4×#117616272
C67×#35012
#6278167