Finite Group Databasebeta

← #31763990

Subgroups — #31763990

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#22574277C218yesmaximal, complemented
2#22574187C214yesmaximal, complemented
3#22574170C214yesmaximal, complemented
4#22574074C212yesmaximal, complemented
5#22574048C214yesmaximal, complemented
6#22574012C211yesmaximal, characteristic, complemented
7#22573973C211yesmaximal, characteristic, complemented
8#22573929C212yesmaximal, complemented
9#22573907C214yesmaximal, complemented
10#22573853C212yesmaximal, complemented
11#22573824C214yesmaximal, complemented
12#22573819C214yesmaximal, complemented
13#22573771C218yesmaximal, complemented
14#22573642C212yesmaximal, complemented
15#22573618C214yesmaximal, complemented
16#22573505C212yesmaximal, complemented
17C2×#16863930C214yesmaximal, complemented
18C4×#14524088C212yesmaximal, complemented
19C2×C4×#41×C67C211yesmaximal, characteristic, complemented
20C2×#14524088C2212yes—
21#16864131C2214yescomplemented
22#16864124C2214yescomplemented
23#16864119C2214yescomplemented
24#16864118C2218yescomplemented
25#16864114C2218yescomplemented
26#16864109C2218yescomplemented
27#16864106C2214yescomplemented
28#16864105C2218yescomplemented
29#16864103C2214yescomplemented
30#16864095C22116yescomplemented
31#16864092C2218yescomplemented
32#16864090C2218yescomplemented
33#16864087C2218yescomplemented
34#16864086C2218yescomplemented
35#16864085C2218yescomplemented
36#16864079C22116yescomplemented
37#16864079C22116yescomplemented
38#16864075C22116yescomplemented
39#16864070C22116yescomplemented
40#16864070C22116yescomplemented
41D4×Dic134C2214yescomplemented
42#16864055C2218yescomplemented
43#16864050C2214yescomplemented
44#16864045C2218yescomplemented
45#16864045C2218yescomplemented
46#16864042C2218yescomplemented
47#16864041C2218yescomplemented
48#16864034C2218yescomplemented
49#16864034C2218yescomplemented
50D4×D268C2214yescomplemented
51#16864027C2212yescomplemented
52#16864022C2214yescomplemented
53#16864018C2218yescomplemented
54#16864004C2218yescomplemented
55#16863993C2218yescomplemented
56#16863993C2218yescomplemented
57#16863988C22116yescomplemented
58#16863984C2218yescomplemented
59#16863979C22116yescomplemented
60#16863977C2212yes—
61#16863970C2214yescomplemented
62#16863958C2214yes—
63#16863955C2218yescomplemented
64#16863953C2212yescomplemented
65#16863953C2212yescomplemented
66#16863953C2212yescomplemented
67#16863950C2218yescomplemented
68#16863946C2212yes—
69#16863946C2212yescomplemented
70#16863946C2212yescomplemented
71#16863933C2218yescomplemented
72#16863930C2218yescomplemented
73#16863930C2218yescomplemented
74#16863930C2214yescomplemented
75#16863930C2218yescomplemented
76#16863930C2218yescomplemented
77#16863930C2214yescomplemented
78#16863930C2214yescomplemented
79#16863930C2218yescomplemented
80#16863930C2218yescomplemented
81#16863930C2218yescomplemented
82#16863930C2214yescomplemented
83#16863930C2214yescomplemented
84#16863930C2214yescomplemented
85#16863926C22116yescomplemented
86C2×#14524037C2218yescomplemented
87C2×#14524035C2214yescomplemented
88C2×#14524031C2214yescomplemented
89#16863907C2214yescomplemented
90#16863907C2214yescomplemented
91#16863907C2214yescomplemented
92#16863905C22116yescomplemented
93C2×#14524026C2218yescomplemented
94C2×#14524022C2214yescomplemented
95C2×#14524017C2214yes—
96#16863877C2214yescomplemented
97#16863875C2218yescomplemented
98#16863871C2212yes—
99#16863869C2218yescomplemented
100#16863868C2218yescomplemented
101C4×#11761628C2214yescomplemented
102C4×#11761628C2214yescomplemented
103C4×#11761628C2214yescomplemented
104C4×#11761627C2218yescomplemented
105C2×C4×Dic134C2214yescomplemented
106C2×C4×D268C2214yescomplemented
107C2×C4×C22⋊D67C2218yescomplemented
108C4×D4×D67C2218yescomplemented
109C2×#14524000C2218yescomplemented
110C22×#41×C67C2211yescharacteristic
111C4×#41×C67C2214yescomplemented
112C4×#41×C67C2214yescomplemented
113C4×#41×C67C2214yescomplemented
114C4×#41×C67C2214yescomplemented
115C2×C4×Q8×C67C2211yescharacteristic, complemented
116C2×C4×Q8×C67C2211yescharacteristic, complemented
117C2×C4×D4×C67C2211yescharacteristic
118C2×C4×D4×C67C2211yescharacteristic
119C2×C4×D4×C67C2212yescomplemented
120C2×C4×D4×C67C2212yescomplemented
121C2×#117×C67C2212yescomplemented
122C2×#117×C67C2211yescharacteristic, complemented
123C22×C42×C67C2212yescomplemented
124C22×C42×C67C2211yescharacteristic, complemented
125#14524088—216no—
126C2×#11761628C2314yes—
127C2×#11761628C2314yes—
128C2×#11761628C2314yes—
129C2×#11761627C2318yes—
130C22×Dic134C2314yes—
131C22×D268C2314yes—
132C22×C22⋊D67C2318yes—
133C2×D4×D67C2318yes—
134C22×C4×D67C2318yes—
135#14524043C2312yes—
136#14524043C2312yes—
137#14524043C2312yes—
138#14524042C2318yes—
139#14524041C2318yes—
140#14524040C2312yes—
141#14524038C23116yes—
142#14524038C23116yes—
143#14524037C23116yes—
144#14524037C2318yes—
145#14524037C23116yes—
146#14524037C23116yes—
147#14524037C2318yes—
148#14524036C23116yes—
149#14524035C2318yes—
150#14524035C2314yes—
151#14524035C2318yes—
152#14524035C2318yes—
153#14524035C2314yes—
154#14524035C2314yes—
155#14524034C2318yes—
156#14524033C23116yes—
157#14524033C23116yes—
158#14524032C2318yes—
159#14524031C2318yes—
160#14524031C2314yes—
161#14524031C2318yes—
162#14524031C2314yes—
163#14524031C2318yes—
164#14524031C2314yes—
165#14524029C23116yes—
166#14524028C23116yes—
167#14524028C23116yes—
168#14524027C23116yes—
169#14524026C23116yes—
170#14524026C23116yes—
171#14524026C2318yes—
172#14524026C2318yes—
173#14524026C23116yes—
174#14524026C2318yes—
175#14524025C23116yes—
176#14524024C23116yes—
177#14524023C2318yes—
178#14524022C2314yes—
179#14524022C2318yes—
180#14524022C2318yes—
181#14524022C2314yes—
182#14524022C2314yes—
183#14524022C2314yes—
184#14524022C2318yes—
185#14524022C2314yes—
186#14524022C2314yes—
187#14524021C23116yes—
188#14524021C23116yes—
189#14524020C23116yes—
190#14524020C23116yes—
191#14524019C2318yes—
192#14524019C2318yes—
193#14524018C2318yes—
194#14524017C2318yes—
195#14524017C2314yes—
196#14524017C2314yes—
197#14524017C2318yes—
198#14524017C2314yes—
199#14524017C2314yes—
200#14524017C2318yes—
201#14524017C2314yes—
202#14524017C2314yes—
203#14524016C23116yes—
204#14524015C23116yes—
205#14524015C23116yes—
206#14524013C23116yes—
207#14524012C2318yes—
208#14524011C23116yes—
209C4×Dic134C2314yes—
210C4×Dic134C2318yes—
211C4×Dic134C2314yes—
212C4×Dic134C2314yes—
213C4×Dic134C2318yes—
214C4×Dic134C2314yes—
215C4×Dic134C2314yes—
216C4×Dic134C2318yes—
217C4×Dic134C2314yes—
218#14524008C2318yes—
219C4×D268C2314yes—
220C4×D268C2314yes—
221C4×D268C2314yes—
222C4×D268C2318yes—
223C4×D268C2314yes—
224C4×D268C2318yes—
225C4×D268C2314yes—
226C4×D268C2314yes—
227C4×D268C2318yes—
228D4×Dic67C2318yes—
229D4×Dic67C2318yes—
230#14524005C2318yes—
231C4×C22⋊D67C2318yes—
232C4×C22⋊D67C2318yes—
233C4×C22⋊D67C2318yes—
234C4×C22⋊D67C23116yes—
235C4×C22⋊D67C2318yes—
236C4×C22⋊D67C23116yes—
237C4×C22⋊D67C23116yes—
238C4×C22⋊D67C2318yes—
239C4×C22⋊D67C2318yes—
240(C22⋊D67)⋊C4C23116yes—
241(C22⋊D67)⋊C4C23116yes—
242#14524002C2314yes—
243#14524002C2314yes—
244#14524002C2314yes—
245#14524001C2318yes—
246#14524000C2318yes—
247#14524000C2318yes—
248#14524000C23116yes—
249#14524000C23116yes—
250#14524000C2318yes—
251#14524000C23116yes—
252#14523999C23116yes—
253C2×C4⋊Dic67C2314yes—
254C2×C4⋊Dic67C2314yes—
255C2×Dic67⋊C4C2318yes—
256C2×Dic67⋊C4C2318yes—
257C2×Dic67⋊C4C2318yes—
258C2×Dic67⋊C4C2318yes—
259C4⋊C4×D67C2318yes—
260C2×C22⋊Dic67C2318yes—
261C2×(C2×D67)⋊C4C2318yes—
262C2×(C2×D67)⋊C4C2318yes—
263C2×(C2×D67)⋊C4C2318yes—
264C2×(C2×D67)⋊C4C2318yes—
265C22⋊C4×D67C23116yes—
266C2×C4×Dic67C2318yes—
267C42×D67C2318yes—
268C2×#41×C67—28no—
269C2×#41×C67C2314yes—
270C2×#41×C67C2314yes—
271C22×Q8×C67C2311yescharacteristic
272C22×D4×C67C2312yes—
273C22×D4×C67C2311yescharacteristic
274C23×C4×C67C2312yes—
275C23×C4×C67C2311yescharacteristic
276C23×C4×C67C2312yes—
277C23×C4×C67C2312yes—
278C23×C4×C67C2311yescharacteristic
279C23×C4×C67C2311yescharacteristic
280C4×Q8×C67C2314yes—
281C4×Q8×C67C2314yes—
282C4×Q8×C67C2314yes—
283C4×Q8×C67C2314yes—
284C4×D4×C67C2314yes—
285C4×D4×C67C2314yes—
286C4×D4×C67C2318yes—
287C4×D4×C67C2314yes—
288C4×D4×C67C2314yes—
289C4×D4×C67C2318yes—
290C4×D4×C67C2318yes—
291C4×D4×C67C2318yes—
292#117×C67C2318yes—
293#117×C67C2318yes—
294#117×C67C2314yes—
295#117×C67C2314yes—
296C2×C4⋊C4×C67C2311yescharacteristic
297C2×C4⋊C4×C67C2311yescharacteristic
298C2×C4⋊C4×C67C2312yes—
299C2×C4⋊C4×C67C2312yes—
300C2×C22⋊C4×C67C2312yes—
301C2×C22⋊C4×C67C2312yes—
302C2×C22⋊C4×C67C2312yes—
303C2×C42×C67C2311yescharacteristic
304C2×C42×C67C2312yes—
305C2×C42×C67C2311yescharacteristic
306C2×C42×C67C2311yescharacteristic
307C2×C42×C67C2311yescharacteristic
308C2×C42×C67C2312yes—
309C2×C42×C67C2312yes—
310C2×C42×C67C2314yes—
311C2×C42×C67C2314yes—
312C2×C42×C67C2312yes—
313C2×C42×C67C2312yes—
314C2×C42×C67C2314yes—
315C2×C42×C67C2314yes—
316C2×C42×C67C2312yes—
317C2×C42×C67C2312yes—
318C23×D67C2418yes—
319#11761628—216no—
320#11761628—48no—
321#11761628—48no—
322#11761627—232no—
323C2×Dic134—48no—
324C2×Dic134C2414yes—
325C2×Dic134C2414yes—
326C2×Dic134C2414yes—
327C2×Dic134C2418yes—
328C2×D268—48no—
329C2×D268C2414yes—
330C2×D268C2414yes—
331C2×D268C2414yes—
332C2×D268C2418yes—
333C2×C22⋊D67—232no—
334C2×C22⋊D67C24116yes—
335C2×C22⋊D67C2418yes—
336C2×C22⋊D67C2418yes—
337C2×C22⋊D67C2418yes—
338D4×D67—232no—
339C22×Dic67C2418yes—
340C22×Dic67C2418yes—
341C22×Dic67C2418yes—
342C2×C4×D67—416no—
343C2×C4×D67C2418yes—
344C2×C4×D67C2418yes—
345C2×C4×D67C2418yes—
346C2×C4×D67C24116yes—
347C4⋊Dic67C2414yes—
348C4⋊Dic67C2414yes—
349C4⋊Dic67C2414yes—
350C4⋊Dic67C2418yes—
351C4⋊Dic67C2418yes—
352C4⋊Dic67C2414yes—
353C4⋊Dic67C2414yes—
354C4⋊Dic67C2414yes—
355Dic67⋊C4C24116yes—
356Dic67⋊C4C2418yes—
357Dic67⋊C4C2418yes—
358Dic67⋊C4C2418yes—
359Dic67⋊C4C2418yes—
360Dic67⋊C4C24116yes—
361Dic67⋊C4C24116yes—
362Dic67⋊C4C24116yes—
363Dic67⋊C4C2418yes—
364Dic67⋊C4C2418yes—
365C22⋊Dic67C24116yes—
366C22⋊Dic67C2418yes—
367C22⋊Dic67C2418yes—
368C22⋊Dic67C2418yes—
369(C2×D67)⋊C4C2418yes—
370(C2×D67)⋊C4C24116yes—
371(C2×D67)⋊C4C2418yes—
372(C2×D67)⋊C4C2418yes—
373(C2×D67)⋊C4C2418yes—
374(C2×D67)⋊C4C2418yes—
375(C2×D67)⋊C4C24116yes—
376(C2×D67)⋊C4C24116yes—
377(C2×D67)⋊C4C24116yes—
378(C2×D67)⋊C4C2418yes—
379C4×Dic67C2418yes—
380C4×Dic67C2418yes—
381C4×Dic67C2418yes—
382C4×Dic67C24116yes—
383C24×C67C2411yescharacteristic
384C24×C67C2412yes—
385#41×C67—216no—
386#41×C67—216no—
387C2×Q8×C67—24no—
388C2×Q8×C67C2414yes—
389C2×D4×C67—28no—
390C2×D4×C67#4118yescomplemented
391C2×D4×C67C2418yes—
392C2×D4×C67C2414yes—
393C22×C4×C67—28no—
394C22×C4×C67—24no—
395C22×C4×C67—44no—
396C22×C4×C67—44no—
397C22×C4×C67—42no—
398C22×C4×C67—42no—
399C22×C4×C67C2411yescharacteristic
400C22×C4×C67C2411yescharacteristic
401C22×C4×C67C2411yescharacteristic
402C22×C4×C67C2412yes—
403C22×C4×C67C2414yes—
404C22×C4×C67C2414yes—
405C22×C4×C67C2412yes—
406C22×C4×C67C2412yes—
407C22×C4×C67C2414yes—
408C22×C4×C67C2414yes—
409C22×C4×C67C2412yes—
410C22×C4×C67C2412yes—
411C22×C4×C67C2411yescharacteristic
412C22×C4×C67C2412yes—
413C22×C4×C67C2411yescharacteristic
414C22×C4×C67C2412yes—
415C22×C4×C67C2414yes—
416C22×C4×C67C2414yes—
417C22×C4×C67C2412yes—
418C22×C4×C67C2412yes—
419C22×C4×C67C2411yescharacteristic
420C4⋊C4×C67C2414yes—
421C4⋊C4×C67C2414yes—
422C4⋊C4×C67C2418yes—
423C4⋊C4×C67C2418yes—
424C22⋊C4×C67C2418yes—
425C22⋊C4×C67C2418yes—
426C22⋊C4×C67C2418yes—
427C42×C67C2411yescharacteristic
428C42×C67C2411yescharacteristic
429C42×C67C2411yescharacteristic
430C42×C67C2411yescharacteristic
431C42×C67C2414yes—
432C42×C67C2412yes—
433C42×C67C2414yes—
434C42×C67C2412yes—
435C42×C67C2412yes—
436C42×C67C2412yes—
437C42×C67C2414yes—
438C42×C67C2414yes—
439C42×C67C2412yes—
440C42×C67C2414yes—
441C42×C67C2412yes—
442C42×C67C2414yes—
443C23×C67—22no—
444C23×C67—42no—
445C23×C67—42no—
446C23×C67—41no—
447C23×C67—41no—
448C23×C67C2×#4118yes—
449C23×C67C2512yes—
450C23×C67C2514yes—
451C23×C67C2511yescharacteristic
452C22×D67—216no—
453C22×D67—48no—
454C22×D67—48no—
455C22×D67C2518yes—
456Q8×C67—28no—
457D4×C67—216no—
458D4×C67C2×#41116yes—
459C2×C4×C67—22no—
460C2×C4×C67—24no—
461C2×C4×C67—28no—
462C2×C4×C67—28no—
463C2×C4×C67—24no—
464C2×C4×C67—24no—
465C2×C4×C67—22no—
466C2×C4×C67—22no—
467C2×C4×C67—28no—
468C2×C4×C67—28no—
469C2×C4×C67—24no—
470C2×C4×C67—24no—
471C2×C4×C67—42no—
472C2×C4×C67—41no—
473C2×C4×C67—44no—
474C2×C4×C67—42no—
475C2×C4×C67—42no—
476C2×C4×C67—41no—
477C2×C4×C67—44no—
478C2×C4×C67—42no—
479C2×C4×C67C2×#4114yes—
480C2×C4×C67C2511yescharacteristic
481C2×C4×C67C2511yescharacteristic
482C2×C4×C67C2511yescharacteristic
483C2×C4×C67C2511yescharacteristic
484C2×C4×C67C2512yes—
485C2×C4×C67C2514yes—
486C2×C4×C67C2514yes—
487C2×C4×C67C2512yes—
488C2×C4×C67C2514yes—
489C2×C4×C67C2512yes—
490C2×C4×C67C2511yescharacteristic
491C2×C4×C67C2511yescharacteristic
492C22⋊D67—232no—
493C22⋊D67—216no—
494C22⋊D67—48no—
495C22⋊D67—48no—
496C2×Dic67—216no—
497C2×Dic67—48no—
498C2×Dic67—48no—
499C2×Dic67C2518yes—
500C2×Dic67C2518yes—
501C2×Dic67C2518yes—
502D268—28no—
503D268—28no—
504D268—48no—
505D268—44no—
506C4×D67—216no—
507C4×D67—216no—
508C4×D67—416no—
509C4×D67—48no—
510Dic134—28no—
511Dic134—28no—
512Dic134—48no—
513Dic134—44no—
514C22×C67—24no—
515C22×C67—24no—
516C22×C67—21no—
517C22×C67—21no—
518C22×C67—22no—
519C22×C67—22no—
520C22×C67—22no—
521C22×C67—48no—
522C22×C67—44no—
523C22×C67C22×#4118yes—
524C22×C67C22×#4112yes—
525C22×C67C2611yescharacteristic
526C2×D67—28no—
527C2×D67—28no—
528C2×D67—28no—
529C2×D67—816no—
530C4×C67—21no—
531C4×C67—21no—
532C4×C67—24no—
533C4×C67—24no—
534C4×C67—22no—
535C4×C67—24no—
536C4×C67—22no—
537C4×C67—21no—
538C4×C67—21no—
539C4×C67C22×#4114yes—
540C4×C67#58512yes—
541C4×C67#58512yes—
542Dic67—28no—
543Dic67—28no—
544Dic67—28no—
545#62781—671nomaximal, Sylow
546C2×C67—28no—
547C2×C67—22no—
548C2×C67—42no—
549C2×C67C23×#4111yescharacteristic
550C2×C67C2×#58511yescharacteristic
551C2×C67C2×#58511yescharacteristic
552D67—48no—
553#3521—678no—
554#3515—674no—
555#3514—674no—
556#3507—672no—
557#3505—674no—
558#3501—671no—
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×#41D6711yescharacteristic, complemented
572C67#6278111yescharacteristic, complemented, Sylow
573C2×H(5,𝔽2)—672no—
574C22×#41C2×D6711yescharacteristic
575#559—674no—
576#557—674no—
577#556—678no—
578#556—674no—
579#556—678no—
580#555—678no—
581#554—674no—
582#554—674no—
583#554—678no—
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×Q8—674no—
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#544—672no—
606#543—674no—
607#542—678no—
608#541—678no—
609#539—6716no—
610#539—678no—
611#539—678no—
612#538—6716no—
613#538—678no—
614#537—672no—
615#536—674no—
616#534—678no—
617#534—674no—
618#533—678no—
619#533—672no—
620#533—672no—
621#533—672no—
622#532—672no—
623#532—672no—
624#532—672no—
625#529—678no—
626#529—6716no—
627#529—674no—
628#529—678no—
629#529—678no—
630#529—678no—
631#529—678no—
632#529—678no—
633#529—678no—
634#529—678no—
635#529—674no—
636#529—674no—
637#529—674no—
638#529—674no—
639#529—674no—
640C2×#126—678no—
641C2×#125—674no—
642C2×#124—674no—
643#525—674no—
644#525—674no—
645#525—674no—
646#525—6716no—
647C2×#123—678no—
648C2×C22⋊Q8—674no—
649C2×#121—674no—
650#520—678no—
651#520—674no—
652#518—672no—
653#518—678no—
654#518—678no—
655C4×#41—678no—
656C4×#41—674no—
657C4×#41—674no—
658C4×#41—674no—
659C4×#41C2×D6714yescomplemented
660C4×#41C2×D6714yescomplemented
661C4×#41C2×D6714yescomplemented
662C4×#41C2×D6714yescomplemented
663C2×C4×Q8—674no—
664C2×C4×Q8C2×D6711yescharacteristic, complemented
665C2×C4×Q8C2×D6711yescharacteristic, complemented
666C2×C4×D4—678no—
667C2×C4×D4—678no—
668C2×C4×D4—674no—
669C2×C4×D4C2×D6711yescharacteristic
670C2×C4×D4C2×D6711yescharacteristic
671C2×C4×D4C2×D6712yescomplemented
672C2×C4×D4C2×D6712yescomplemented
673C2×#117—678no—
674C2×#117C2×D6712yescomplemented
675C2×#117C2×D6711yescharacteristic, complemented
676C22×C42C2×D6712yescomplemented
677C22×C42C2×D6711yescharacteristic, complemented
678H(5,𝔽2)—13416no—
679C2×#41—28no—
680C2×#41—678no—
681C2×#41—674no—
682C2×#41—674no—
683C2×#41—674no—
684C2×#41C22×D6714yes—
685C2×#41C22×D6714yes—
686C22×Q8—674no—
687C22×Q8C22×D6711yescharacteristic
688C22×D4—678no—
689C22×D4—678no—
690C22×D4—674no—
691C22×D4C22×D6712yes—
692C22×D4C22×D6711yescharacteristic
693C23×C4—678no—
694C23×C4C22×D6712yes—
695C23×C4C22×D6711yescharacteristic
696C23×C4C22×D6712yes—
697C23×C4C22×D6712yes—
698C23×C4C22×D6711yescharacteristic
699C23×C4C22×D6711yescharacteristic
700C4⋊Q8—678no—
701C4⋊Q8—678no—
702C4⋊Q8—672no—
703C4⋊Q8—672no—
704C4⋊Q8—672no—
705#127—672no—
706#126—6716no—
707#126—6716no—
708#126—6716no—
709#126—678no—
710#126—6716no—
711#126—6716no—
712#126—6716no—
713#126—678no—
714#125—6716no—
715#125—678no—
716#125—6716no—
717#125—674no—
718#125—678no—
719#125—678no—
720#125—678no—
721#125—674no—
722#125—674no—
723#124—678no—
724#124—6716no—
725#124—674no—
726#124—678no—
727#124—678no—
728#124—678no—
729#124—674no—
730#124—674no—
731#123—6716no—
732#123—678no—
733#123—6716no—
734#123—6716no—
735#123—6716no—
736#123—678no—
737#123—678no—
738#123—6716no—
739#123—6716no—
740#123—6716no—
741#123—6716no—
742C22⋊Q8—678no—
743C22⋊Q8—678no—
744C22⋊Q8—674no—
745C22⋊Q8—678no—
746C22⋊Q8—678no—
747C22⋊Q8—678no—
748C22⋊Q8—674no—
749C22⋊Q8—674no—
750C22⋊Q8—674no—
751C22⋊Q8—674no—
752C22⋊Q8—674no—
753C22⋊Q8—6716no—
754C22⋊Q8—678no—
755C22⋊Q8—6716no—
756C22⋊Q8—6716no—
757C22⋊Q8—6716no—
758#121—6716no—
759#121—6716no—
760#121—674no—
761#121—678no—
762#121—678no—
763#121—678no—
764#121—674no—
765#121—674no—
766#121—674no—
767#121—674no—
768#121—674no—
769#121—678no—
770#121—6716no—
771#120—678no—
772#120—6716no—
773#120—6716no—
774C4×Q8—678no—
775C4×Q8—674no—
776C4×Q8—678no—
777C4×Q8—678no—
778C4×Q8—678no—
779C4×Q8—674no—
780C4×Q8—674no—
781C4×Q8—674no—
782C4×Q8—674no—
783C4×Q8—674no—
784C4×Q8C22×D6714yes—
785C4×Q8C22×D6714yes—
786C4×Q8C22×D6714yes—
787C4×Q8C22×D6714yes—
788C4×D4—678no—
789C4×D4—678no—
790C4×D4—6716no—
791C4×D4—678no—
792C4×D4—6716no—
793C4×D4—6716no—
794C4×D4—678no—
795C4×D4—678no—
796C4×D4—678no—
797C4×D4—678no—
798C4×D4—678no—
799C4×D4—678no—
800C4×D4—6716no—
801C4×D4—6716no—
802C4×D4—674no—
803C4×D4—674no—
804C4×D4—678no—
805C4×D4—678no—
806C4×D4—678no—
807C4×D4—674no—
808C4×D4—674no—
809C4×D4—674no—
810C4×D4—674no—
811C4×D4C22×D6714yes—
812C4×D4C22×D6714yes—
813C4×D4C22×D6714yes—
814C4×D4C22×D6714yes—
815C4×D4C22×D6718yes—
816C4×D4C22×D6718yes—
817C4×D4C22×D6718yes—
818C4×D4C22×D6718yes—
819#117—674no—
820#117—674no—
821#117—674no—
822#117—678no—
823#117—6716no—
824#117—678no—
825#117—6716no—
826#117—6716no—
827#117—6716no—
828#117—678no—
829#117—678no—
830#117C22×D6718yes—
831#117C22×D6718yes—
832#117C22×D6714yes—
833#117C22×D6714yes—
834C2×C4⋊C4—678no—
835C2×C4⋊C4—678no—
836C2×C4⋊C4—678no—
837C2×C4⋊C4—674no—
838C2×C4⋊C4—674no—
839C2×C4⋊C4—678no—
840C2×C4⋊C4—678no—
841C2×C4⋊C4C22×D6711yescharacteristic
842C2×C4⋊C4C22×D6711yescharacteristic
843C2×C4⋊C4C22×D6712yes—
844C2×C4⋊C4C22×D6712yes—
845C2×C22⋊C4—678no—
846C2×C22⋊C4—678no—
847C2×C22⋊C4—678no—
848C2×C22⋊C4—678no—
849C2×C22⋊C4—678no—
850C2×C22⋊C4—6716no—
851C2×C22⋊C4C22×D6712yes—
852C2×C22⋊C4C22×D6712yes—
853C2×C22⋊C4C22×D6712yes—
854C2×C42—678no—
855C2×C42—678no—
856C2×C42C22×D6714yes—
857C2×C42C22×D6711yescharacteristic
858C2×C42C22×D6712yes—
859C2×C42C22×D6714yes—
860C2×C42C22×D6711yescharacteristic
861C2×C42C22×D6711yescharacteristic
862C2×C42C22×D6712yes—
863C2×C42C22×D6712yes—
864C2×C42C22×D6712yes—
865C2×C42C22×D6712yes—
866C2×C42C22×D6714yes—
867C2×C42C22×D6714yes—
868C2×C42C22×D6712yes—
869C2×C42C22×D6712yes—
870C2×C42C22×D6711yescharacteristic
871C24—678no—
872C24C23×D6711yescharacteristic
873C24C23×D6712yes—
874#41—216no—
875#41—216no—
876#41—2688no—
877#41—2688no—
878#41—13432no—
879#41—13416no—
880C2×Q8—24no—
881C2×Q8—2688no—
882C2×Q8—674no—
883C2×Q8—678no—
884C2×Q8—674no—
885C2×Q8—674no—
886C2×Q8C23×D6714yes—
887C2×D4—28no—
888C2×D4—2688no—
889C2×D4—678no—
890C2×D4—678no—
891C2×D4—678no—
892C2×D4—6716no—
893C2×D4—674no—
894C2×D4—678no—
895C2×D4—674no—
896C2×D4—674no—
897C2×D4—13432no—
898C2×D4—13432no—
899C2×D4#1176162818yescomplemented
900C2×D4C23×D6718yes—
901C2×D4C23×D6714yes—
902C22×C4—28no—
903C22×C4—24no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—26816no—
909C22×C4—678no—
910C22×C4—678no—
911C22×C4—678no—
912C22×C4—6716no—
913C22×C4—678no—
914C22×C4—678no—
915C22×C4—678no—
916C22×C4C23×D6711yescharacteristic
917C22×C4C23×D6711yescharacteristic
918C22×C4C23×D6714yes—
919C22×C4C23×D6714yes—
920C22×C4C23×D6714yes—
921C22×C4C23×D6712yes—
922C22×C4C23×D6712yes—
923C22×C4C23×D6712yes—
924C22×C4C23×D6712yes—
925C22×C4C23×D6714yes—
926C22×C4C23×D6711yescharacteristic
927C22×C4C23×D6712yes—
928C22×C4C23×D6714yes—
929C22×C4C23×D6714yes—
930C22×C4C23×D6711yescharacteristic
931C22×C4C23×D6712yes—
932C22×C4C23×D6711yescharacteristic
933C22×C4C23×D6712yes—
934C22×C4C23×D6712yes—
935C22×C4C23×D6712yes—
936C22×C4C23×D6711yescharacteristic
937C4⋊C4—678no—
938C4⋊C4—678no—
939C4⋊C4—674no—
940C4⋊C4—674no—
941C4⋊C4—6716no—
942C4⋊C4—678no—
943C4⋊C4—674no—
944C4⋊C4—678no—
945C4⋊C4—6716no—
946C4⋊C4—6716no—
947C4⋊C4—678no—
948C4⋊C4—678no—
949C4⋊C4—6716no—
950C4⋊C4—674no—
951C4⋊C4—678no—
952C4⋊C4—674no—
953C4⋊C4—674no—
954C4⋊C4—678no—
955C4⋊C4C23×D6714yes—
956C4⋊C4C23×D6714yes—
957C4⋊C4C23×D6718yes—
958C4⋊C4C23×D6718yes—
959C22⋊C4—678no—
960C22⋊C4—6716no—
961C22⋊C4—678no—
962C22⋊C4—678no—
963C22⋊C4—678no—
964C22⋊C4—678no—
965C22⋊C4—678no—
966C22⋊C4—678no—
967C22⋊C4—6716no—
968C22⋊C4—678no—
969C22⋊C4—6716no—
970C22⋊C4—6716no—
971C22⋊C4—6716no—
972C22⋊C4—678no—
973C22⋊C4C23×D6718yes—
974C22⋊C4C23×D6718yes—
975C22⋊C4C23×D6718yes—
976C42—678no—
977C42—6716no—
978C42—678no—
979C42—678no—
980C42C23×D6711yescharacteristic
981C42C23×D6711yescharacteristic
982C42C23×D6714yes—
983C42C23×D6712yes—
984C42C23×D6712yes—
985C42C23×D6714yes—
986C42C23×D6714yes—
987C42C23×D6712yes—
988C42C23×D6714yes—
989C42C23×D6712yes—
990C42C23×D6712yes—
991C42C23×D6714yes—
992C42C23×D6712yes—
993C42C23×D6711yescharacteristic
994C42C23×D6711yescharacteristic
995C42C23×D6714yes—
996C23—22no—
997C23—42no—
998C23—42no—
999C23—41no—
1000C23—41no—
1001C23—2688no—
1002C23—2688no—
1003C23—678no—
1004C23—13416no—
1005C23C2×#1176162818yes—
1006C23C24×D6712yes—
1007C23C24×D6711yescharacteristic
1008C23C24×D6714yes—
1009Q8—28no—
1010Q8—2688no—
1011Q8—2684no—
1012Q8—1348no—
1013Q8—1348no—
1014D4—216no—
1015D4—2688no—
1016D4—2684no—
1017D4—2688no—
1018D4—2688no—
1019D4—13416no—
1020D4—13432no—
1021D4—1348no—
1022D4—1348no—
1023D4C2×#11761628116yes—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—28no—
1033C2×C4—28no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—44no—
1037C2×C4—42no—
1038C2×C4—44no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—41no—
1042C2×C4—42no—
1043C2×C4—41no—
1044C2×C4—26816no—
1045C2×C4—2688no—
1046C2×C4—2688no—
1047C2×C4—2688no—
1048C2×C4—678no—
1049C2×C4—678no—
1050C2×C4—678no—
1051C2×C4—13416no—
1052C2×C4—13416no—
1053C2×C4—13416no—
1054C2×C4C2×#1176162814yes—
1055C2×C4C24×D6712yes—
1056C2×C4C24×D6714yes—
1057C2×C4C24×D6711yescharacteristic
1058C2×C4C24×D6711yescharacteristic
1059C2×C4C24×D6711yescharacteristic
1060C2×C4C24×D6711yescharacteristic
1061C2×C4C24×D6714yes—
1062C2×C4C24×D6712yes—
1063C2×C4C24×D6714yes—
1064C2×C4C24×D6712yes—
1065C2×C4C24×D6711yescharacteristic
1066C2×C4C24×D6711yescharacteristic
1067C22—21no—
1068C22—21no—
1069C22—24no—
1070C22—24no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—48no—
1075C22—44no—
1076C22—53616no—
1077C22—1348no—
1078C22—1348no—
1079C22—1348no—
1080C22C22×#1176162812yes—
1081C22C22×#1176162818yes—
1082C22C25×D6711yescharacteristic
1083C4—21no—
1084C4—21no—
1085C4—24no—
1086C4—21no—
1087C4—21no—
1088C4—24no—
1089C4—22no—
1090C4—24no—
1091C4—22no—
1092C4—1348no—
1093C4—1348no—
1094C4—1348no—
1095C4C22×#1176162814yes—
1096C4#1686423212yes—
1097C4#1686423212yes—
1098C2—22no—
1099C2—28no—
1100C2—42no—
1101C2—2688no—
1102C2C23×#1176162811yescharacteristic
1103C2C2×#1686423211yescharacteristic
1104C2C2×#1686423211yescharacteristic
subgroupG/H
centerC2×C4C24×D67
commutator, socle, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×C4×#41×C67C2
hypercenterC2×C4×#41D67
hypocenterC67#62781
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22574277C2semidirect
2. #22574187C2semidirect
3. #22574170C2semidirect
4. #22574074C2semidirect
5. #22574048C2semidirect
6. #22574012C2semidirect
7. #22573973C2semidirect
8. #22573929C2semidirect
9. #22573907C2semidirect
10. #22573853C2semidirect
11. #22573824C2semidirect
12. #22573819C2semidirect
13. #22573771C2semidirect
14. #22573642C2semidirect
15. #22573618C2semidirect
16. #22573505C2semidirect
17. C2×#16863930C2semidirect
18. C4×#14524088C2semidirect
19. C2×C4×#41×C67C2semidirect
21. #16864131C22semidirect
22. #16864124C22semidirect
23. #16864119C22semidirect
24. #16864118C22semidirect
25. #16864114C22semidirect
26. #16864109C22semidirect
27. #16864106C22semidirect
28. #16864105C22semidirect
29. #16864103C22semidirect
30. #16864095C22semidirect
31. #16864092C22semidirect
32. #16864090C22semidirect
33. #16864087C22semidirect
34. #16864086C22semidirect
35. #16864085C22semidirect
36. #16864079C22semidirect
37. #16864079C22semidirect
38. #16864075C22semidirect
39. #16864070C22semidirect
40. #16864070C22semidirect
41. D4×Dic134C22semidirect
42. #16864055C22semidirect
43. #16864050C22semidirect
44. #16864045C22semidirect
45. #16864045C22semidirect
46. #16864042C22semidirect
47. #16864041C22semidirect
48. #16864034C22semidirect
49. #16864034C22semidirect
50. D4×D268C22semidirect
51. #16864027C22semidirect
52. #16864022C22semidirect
53. #16864018C22semidirect
54. #16864004C22semidirect
55. #16863993C22semidirect
56. #16863993C22semidirect
57. #16863988C22semidirect
58. #16863984C22semidirect
59. #16863979C22semidirect
61. #16863970C22semidirect
63. #16863955C22semidirect
64. #16863953C22semidirect
65. #16863953C22semidirect
66. #16863953C22semidirect
67. #16863950C22semidirect
69. #16863946C22semidirect
70. #16863946C22semidirect
71. #16863933C22semidirect
72. #16863930C22semidirect
73. #16863930C22semidirect
74. #16863930C22semidirect
75. #16863930C22semidirect
76. #16863930C22semidirect
77. #16863930C22semidirect
78. #16863930C22semidirect
79. #16863930C22semidirect
80. #16863930C22semidirect
81. #16863930C22semidirect
82. #16863930C22semidirect
83. #16863930C22semidirect
84. #16863930C22semidirect
85. #16863926C22semidirect
86. C2×#14524037C22semidirect
87. C2×#14524035C22semidirect
88. C2×#14524031C22semidirect
89. #16863907C22semidirect
90. #16863907C22semidirect
91. #16863907C22semidirect
92. #16863905C22semidirect
93. C2×#14524026C22semidirect
94. C2×#14524022C22semidirect
96. #16863877C22semidirect
97. #16863875C22semidirect
99. #16863869C22semidirect
100. #16863868C22semidirect
101. C4×#11761628C22semidirect
102. C4×#11761628C22semidirect
103. C4×#11761628C22semidirect
104. C4×#11761627C22semidirect
105. C2×C4×Dic134C22semidirect
106. C2×C4×D268C22semidirect
107. C2×C4×C22⋊D67C22semidirect
108. C4×D4×D67C22semidirect
109. C2×#14524000C22semidirect
111. C4×#41×C67C22semidirect
112. C4×#41×C67C22semidirect
113. C4×#41×C67C22semidirect
114. C4×#41×C67C22semidirect
115. C2×C4×Q8×C67C22semidirect
116. C2×C4×Q8×C67C22semidirect
119. C2×C4×D4×C67C22semidirect
120. C2×C4×D4×C67C22semidirect
121. C2×#117×C67C22semidirect
122. C2×#117×C67C22semidirect
123. C22×C42×C67C22semidirect
124. C22×C42×C67C22semidirect
390. C2×D4×C67#41semidirect
571. C2×C4×#41D67semidirect
572. C67#62781semidirect
659. C4×#41C2×D67semidirect
660. C4×#41C2×D67semidirect
661. C4×#41C2×D67semidirect
662. C4×#41C2×D67semidirect
664. C2×C4×Q8C2×D67semidirect
665. C2×C4×Q8C2×D67semidirect
671. C2×C4×D4C2×D67semidirect
672. C2×C4×D4C2×D67semidirect
674. C2×#117C2×D67semidirect
675. C2×#117C2×D67semidirect
676. C22×C42C2×D67semidirect
677. C22×C42C2×D67semidirect
899. C2×D4#11761628semidirect

Maximal subgroups

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

subgroupindex
#225742772
#225741872
#225741702
#225740742
#225740482
#225740122
#225739732
#225739292
#225739072
#225738532
#225738242
#225738192
#225737712
#225736422
#225736182
#225735052
C2×#168639302
C4×#145240882
C2×C4×#41×C672
#6278167