Finite Group Databasebeta

← Q8×#6771 #14484675

Subgroups — Q8×#6771 #14484675

Order 1920.

2136 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×D15C211yesmaximal, characteristic, complemented
2C4×C5×D3×Q8C211yesmaximal, characteristic, complemented
3C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
4Q8×#1204C211yesmaximal, characteristic, complemented
5Q8×#1203C211yesmaximal, characteristic, complemented
6Q8×#1202C211yesmaximal, characteristic, complemented
7Q8×#1201C211yesmaximal, characteristic, complemented
8#11753825C213yesmaximal, complemented
9#11753715C213yesmaximal, complemented
10#11753712C213yesmaximal, complemented
11#11753705C213yesmaximal, complemented
12C4×#6771C213yesmaximal
13#11752513C213yesmaximal, complemented
14#11752500C213yesmaximal, complemented
15#11752497C213yesmaximal, complemented
16Q8×#709—31nomaximal, Hall
17C2×Q8×D15C2211yescharacteristic
18C2×C5×D3×Q8C2211yescharacteristic
19C2×C3×Q8×D5C2211yescharacteristic
20C2×#6771C2211yescharacteristic
21C3×C4×C5×Q8C2211yescharacteristic
22Q8×Dic15C2211yescharacteristic
23C4⋊C4×D15C2213yes—
24#91776C2213yes—
25C42×D15C2213yes—
26C4×Dic30C2213yes—
27C5×Q8×Dic3C2211yescharacteristic
28C5×D3×C4⋊C4C2213yes—
29C5×#887C2213yes—
30C42×C5×D3C2213yes—
31C4×C5×Dic6C2213yes—
32C3×Q8×Dic5C2211yescharacteristic
33C3×D5×C4⋊C4C2213yes—
34C3×#4033C2213yes—
35C3×C42×D5C2213yes—
36C3×C4×Dic10C2213yes—
37#91470C2213yes—
38#91469C2213yes—
39#91468C2213yes—
40C4×#1204C2216yes—
41C4×#1204C2213yes—
42C4×#1204C2213yes—
43C4×#1203C2213yes—
44C4×#1203C2213yes—
45C4×#1202C2213yes—
46C4×#1202C2213yes—
47C4×#1201C2213yes—
48C4×#1201C2213yes—
49#91390C2213yes—
50#91389C2213yes—
51#91386C2213yes—
52#91385C2213yes—
53#91383C2213yes—
54#91382C2216yes—
55#91379C2216yes—
56#91378C2216yes—
57#91377C2216yes—
58#91376C2213yes—
59#91371C2213yes—
60#91369C2213yes—
61#91365C2213yes—
62#91360C2213yes—
63#91359C2213yes—
64#91357C2213yes—
65#91352C2216yes—
66#91349C2216yes—
67Q8×#235—51nomaximal, Hall
68C2×C4×C5×Q8—31no—
69Q8×C22⋊D5—31no—
70Q8×C22⋊D5—31no—
71#65913—33no—
72#65912—33no—
73#65912—33no—
74Q8×D20—31no—
75C4×Q8×D5—31no—
76C4×Q8×D5D311yescharacteristic, complemented
77#65901—33no—
78Q8×Dic10—31no—
79#65845—33no—
80#65845—33no—
81C4×#709—33no—
82#65804—33no—
83C2×C3×C5×Q8C2311yescharacteristic
84Q8×D15—24no—
85C2×C4×D15C2313yes—
86C2×C4×D15C2313yes—
87C2×C4×D15C2311yescharacteristic
88C2×Dic30C2313yes—
89C5×D3×Q8—24no—
90C2×C4×C5×D3C2313yes—
91C2×C4×C5×D3C2313yes—
92C2×C4×C5×D3C2311yescharacteristic
93C2×C5×Dic6C2313yes—
94C3×Q8×D5—24no—
95C2×C3×C4×D5C2313yes—
96C2×C3×C4×D5C2313yes—
97C2×C3×C4×D5C2311yescharacteristic
98C2×C3×Dic10C2313yes—
99C2×#1204C2316yes—
100C2×#1204C2311yescharacteristic
101C2×#1203C2311yescharacteristic
102C2×#1202C2311yescharacteristic
103C2×#1201C2311yescharacteristic
104#6771Q818yesdirect product factor
105C3×C5×C4⋊C4C2313yes—
106C3×C42×C5C2313yes—
107C4⋊Dic15C2313yes—
108#6712C2316yes—
109C4×Dic15C2313yes—
110C4×Dic15C2313yes—
111C4×Dic15C2313yes—
112C5×C4⋊Dic3C2313yes—
113C5×Dic3⋊C4C2316yes—
114C4×C5×Dic3C2313yes—
115C4×C5×Dic3C2313yes—
116C4×C5×Dic3C2313yes—
117C3×C4⋊Dic5C2313yes—
118C3×#683C2316yes—
119C3×C4×Dic5C2313yes—
120C3×C4×Dic5C2313yes—
121C3×C4×Dic5C2313yes—
122Dic3⋊Dic5C2313yes—
123Dic3⋊Dic5C2313yes—
124Dic3⋊Dic5C2316yes—
125#6669C2313yes—
126#6669C2313yes—
127#6669C2316yes—
128#6668C2313yes—
129#6668C2313yes—
130#6668C2316yes—
131#6667C2313yes—
132#6667C2313yes—
133(C2×D3)⋊Dic5C2313yes—
134(C2×D3)⋊Dic5C2313yes—
135#6665C2313yes—
136#6665C2313yes—
137C2×C3×C4×Q8—51no—
138Q8×#67—51no—
139Q8×#67—51no—
140#5579—53no—
141#5578—53no—
142#5578—53no—
143Q8×D12—51no—
144C4×D3×Q8—51no—
145C4×D3×Q8D511yescharacteristic, complemented
146#5567—53no—
147Q8×Dic6—51no—
148#5511—53no—
149#5511—53no—
150C4×#235—53no—
151#5470—53no—
152C22×C5×Q8—31no—
153C2×Q8×D5—31no—
154C2×Q8×D5C2×D311yescharacteristic
155C2×#709—31no—
156C4×C5×Q8—31no—
157C4×C5×Q8—33no—
158C4×C5×Q8—33no—
159C4×C5×Q8C2×D311yescharacteristic
160C2×C5×C4⋊C4—33no—
161C2×C42×C5—33no—
162#4092—33no—
163#4092—33no—
164Q8×Dic5—31no—
165Q8×Dic5C2×D311yescharacteristic
166#4090—33no—
167#4090—33no—
168C4×C22⋊D5—33no—
169C4×C22⋊D5—33no—
170C4×C22⋊D5—33no—
171C4×C22⋊D5—33no—
172#4072—33no—
173#4070—33no—
174#4070—33no—
175#4070—36no—
176#4043—33no—
177#4043—33no—
178#4042—36no—
179#4042—36no—
180D5×C4⋊C4—33no—
181D5×C4⋊C4C2×D313yes—
182#4035—36no—
183#4035—36no—
184#4034—33no—
185#4034—33no—
186#4033—33no—
187#4033C2×D313yes—
188C4×D20—33no—
189C4×D20—33no—
190#4018—33no—
191#4018—33no—
192C42×D5—33no—
193C42×D5C2×D313yes—
194#4016—36no—
195#4015—33no—
196#4015—33no—
197C4×Dic10—33no—
198C4×Dic10—36no—
199C4×Dic10—33no—
200C4×Dic10—33no—
201C4×Dic10C2×D313yes—
202Q8×#41—151noSylow
203C22×D15C2411yescharacteristic
204C22×C5×D3C2411yescharacteristic
205C22×C3×D5C2411yescharacteristic
206C3×C5×Q8#4114yescomplemented
207C2×C3×C4×C5C2413yes—
208C2×C3×C4×C5C2411yescharacteristic
209C2×C3×C4×C5C2413yes—
210C2×Dic15C2413yes—
211C2×Dic15C2413yes—
212C2×Dic15C2411yescharacteristic
213C4×D15—26no—
214C4×D15—43no—
215C4×D15C2×Q814yescomplemented
216Dic30—26no—
217C2×C5×Dic3C2413yes—
218C2×C5×Dic3C2413yes—
219C2×C5×Dic3C2411yescharacteristic
220C4×C5×D3—26no—
221C4×C5×D3—43no—
222C4×C5×D3C2×Q814yescomplemented
223C5×Dic6—26no—
224C2×C3×Dic5C2413yes—
225C2×C3×Dic5C2413yes—
226C2×C3×Dic5C2411yescharacteristic
227C3×C4×D5—26no—
228C3×C4×D5—43no—
229C3×C4×D5C2×Q814yescomplemented
230C3×Dic10—26no—
231#1204—46no—
232#1204C2×Q814yescomplemented
233#1203C2×Q814yescomplemented
234#1202C2×Q814yescomplemented
235#1201C2×Q814yescomplemented
236C22×C3×Q8—51no—
237C2×D3×Q8—51no—
238C2×D3×Q8C2×D511yescharacteristic
239C2×#235—51no—
240C3×C4×Q8—51no—
241C3×C4×Q8—53no—
242C3×C4×Q8—53no—
243C3×C4×Q8C2×D511yescharacteristic
244C2×C3×C4⋊C4—53no—
245C2×C3×C42—53no—
246#946—53no—
247#946—53no—
248Q8×Dic3—51no—
249Q8×Dic3C2×D511yescharacteristic
250#944—53no—
251#944—53no—
252C4×#67—53no—
253C4×#67—53no—
254C4×#67—53no—
255C4×#67—53no—
256#926—53no—
257#924—53no—
258#924—53no—
259#924—56no—
260#897—53no—
261#897—53no—
262#896—56no—
263#896—56no—
264D3×C4⋊C4—53no—
265D3×C4⋊C4C2×D513yes—
266#889—56no—
267#889—56no—
268#888—53no—
269#888—53no—
270#887—53no—
271#887C2×D513yes—
272C4×D12—53no—
273C4×D12—53no—
274#872—53no—
275#872—53no—
276C42×D3—53no—
277C42×D3C2×D513yes—
278#870—56no—
279#869—53no—
280#869—53no—
281C4×Dic6—53no—
282C4×Dic6—56no—
283C4×Dic6—53no—
284C4×Dic6—53no—
285C4×Dic6C2×D513yes—
286C2×C5×Q8—33no—
287C2×C5×Q8—64no—
288C2×C5×Q8C22×D311yescharacteristic
289C22×C4×C5—31no—
290C22×C4×C5—33no—
291C22×C4×C5—33no—
292C2×C22⋊D5—31no—
293C2×C22⋊D5—31no—
294Q8×D5—24no—
295Q8×D5—64no—
296#709—38no—
297C2×D20—31no—
298C2×C4×D5—31no—
299C2×C4×D5—33no—
300C2×C4×D5—33no—
301C2×C4×D5C22×D313yes—
302C2×C4×D5C22×D313yes—
303C2×C4×D5C22×D311yescharacteristic
304C2×Dic10—31no—
305C2×Dic10—33no—
306C2×Dic10—36no—
307C2×Dic10C22×D313yes—
308C5×C4⋊C4—36no—
309C5×C4⋊C4—33no—
310C5×C4⋊C4C22×D313yes—
311C42×C5—33no—
312C42×C5—33no—
313C42×C5—33no—
314C42×C5C22×D313yes—
315C22⋊Dic5—33no—
316C22⋊Dic5—33no—
317#685—33no—
318#685—33no—
319#685—33no—
320#685—33no—
321C4⋊Dic5—33no—
322C4⋊Dic5—33no—
323C4⋊Dic5—33no—
324C4⋊Dic5—36no—
325C4⋊Dic5C22×D313yes—
326#683—36no—
327#683—36no—
328#683—33no—
329#683—33no—
330#683—36no—
331#683—33no—
332#683—33no—
333#683C22×D316yes—
334C4×Dic5—33no—
335C4×Dic5—33no—
336C4×Dic5—33no—
337C4×Dic5C22×D313yes—
338C4×Dic5C22×D313yes—
339C4×Dic5C22×D313yes—
340Q82—151no—
341#557—153no—
342#554—153no—
343#554—153no—
344#554—153no—
345D4×Q8—151no—
346D4×Q8—151no—
347D4×Q8—151no—
348#533—153no—
349#533—153no—
350#533—153no—
351C4×#41—153no—
352C2×C4×Q8—31no—
353C2×C4×Q8—51no—
354C2×C4×Q8—151no—
355C22×C3×C5C2511yescharacteristic
356C2×D15—21no—
357C2×D15—21no—
358C2×D15C22×Q812yes—
359C2×C5×D3—21no—
360C2×C5×D3—21no—
361C2×C5×D3C22×Q812yes—
362C2×C3×D5—21no—
363C2×C3×D5—21no—
364C2×C3×D5C22×Q812yes—
365C3×C4×C5—23no—
366C3×C4×C5C22×Q812yes—
367C3×C4×C5C2×#4116yes—
368Dic15—23no—
369Dic15—23no—
370Dic15C22×Q812yes—
371C3×Dic5—23no—
372C3×Dic5—23no—
373C3×Dic5C22×Q812yes—
374C5×Dic3—23no—
375C5×Dic3—23no—
376C5×Dic3C22×Q812yes—
377C2×C3×Q8—53no—
378C2×C3×Q8—104no—
379C2×C3×Q8C22×D511yescharacteristic
380C22×C3×C4—51no—
381C22×C3×C4—53no—
382C22×C3×C4—53no—
383C2×#67—51no—
384C2×#67—51no—
385D3×Q8—24no—
386D3×Q8—104no—
387#235—58no—
388C2×D12—51no—
389C2×C4×D3—51no—
390C2×C4×D3—53no—
391C2×C4×D3—53no—
392C2×C4×D3C22×D513yes—
393C2×C4×D3C22×D513yes—
394C2×C4×D3C22×D511yescharacteristic
395C2×Dic6—51no—
396C2×Dic6—53no—
397C2×Dic6—56no—
398C2×Dic6C22×D513yes—
399C3×C4⋊C4—56no—
400C3×C4⋊C4—53no—
401C3×C4⋊C4C22×D513yes—
402C3×C42—53no—
403C3×C42—53no—
404C3×C42—53no—
405C3×C42C22×D513yes—
406#217—53no—
407#217—53no—
408(C2×D3)⋊C4—53no—
409(C2×D3)⋊C4—53no—
410(C2×D3)⋊C4—53no—
411(C2×D3)⋊C4—53no—
412C4⋊Dic3—53no—
413C4⋊Dic3—53no—
414C4⋊Dic3—53no—
415C4⋊Dic3—56no—
416C4⋊Dic3C22×D513yes—
417Dic3⋊C4—56no—
418Dic3⋊C4—56no—
419Dic3⋊C4—53no—
420Dic3⋊C4—53no—
421Dic3⋊C4—56no—
422Dic3⋊C4—53no—
423Dic3⋊C4—53no—
424Dic3⋊C4C22×D516yes—
425C4×Dic3—53no—
426C4×Dic3—53no—
427C4×Dic3—53no—
428C4×Dic3C22×D513yes—
429C4×Dic3C22×D513yes—
430C4×Dic3C22×D513yes—
431C23×C5—31no—
432C22×D5—31no—
433C22×D5C23×D311yescharacteristic
434C5×Q8—66no—
435C5×Q8#23514yescomplemented
436C2×C4×C5—31no—
437C2×C4×C5—34no—
438C2×C4×C5—33no—
439C2×C4×C5—33no—
440C2×C4×C5—66no—
441C2×C4×C5—123no—
442C2×C4×C5C23×D313yes—
443C2×C4×C5C23×D313yes—
444C2×C4×C5C23×D311yescharacteristic
445C22⋊D5—34no—
446C22⋊D5—34no—
447C2×Dic5—31no—
448C2×Dic5—33no—
449C2×Dic5—33no—
450C2×Dic5C23×D313yes—
451C2×Dic5C23×D313yes—
452C2×Dic5C23×D311yescharacteristic
453D20—34no—
454C4×D5—26no—
455C4×D5—34no—
456C4×D5—43no—
457C4×D5—66no—
458C4×D5—123no—
459C4×D5D3×Q814yescomplemented
460Dic10—26no—
461Dic10—34no—
462Dic10—66no—
463Dic10—126no—
464C2×#41—151no—
465C22×Q8—31no—
466C22×Q8—51no—
467C22×Q8—151no—
468C4⋊Q8—153no—
469C4⋊Q8—153no—
470C4⋊Q8—153no—
471C4⋊Q8—153no—
472C4⋊Q8—153no—
473C4⋊Q8—153no—
474#125—156no—
475#125—156no—
476#125—156no—
477C22⋊Q8—156no—
478C22⋊Q8—153no—
479C22⋊Q8—156no—
480C22⋊Q8—153no—
481C22⋊Q8—153no—
482C22⋊Q8—156no—
483C22⋊Q8—153no—
484C22⋊Q8—153no—
485C22⋊Q8—153no—
486C4×Q8—31no—
487C4×Q8—33no—
488C4×Q8—33no—
489C4×Q8—51no—
490C4×Q8—53no—
491C4×Q8—53no—
492C4×Q8—153no—
493C4×Q8—153no—
494C4×Q8—156no—
495C4×Q8—151no—
496C4×Q8—153no—
497C4×Q8—153no—
498C4×Q8D3×D511yescharacteristic
499C4×D4—153no—
500C4×D4—153no—
501C4×D4—153no—
502C4×D4—153no—
503C4×D4—153no—
504C4×D4—153no—
505#117—153no—
506#117—153no—
507#117—153no—
508C2×C4⋊C4—33no—
509C2×C4⋊C4—53no—
510C2×C4⋊C4—153no—
511C2×C42—33no—
512C2×C42—53no—
513C2×C42—153no—
514C2×C3×C5C23×Q811yescharacteristic
515C2×C3×C5C22×#4111yescharacteristic
516C2×C3×C5#58511yescharacteristic
517D15—22no—
518C3×D5—22no—
519C5×D3—22no—
520C23×C3—51no—
521C22×D3—51no—
522C22×D3C23×D511yescharacteristic
523C3×Q8—106no—
524C3×Q8#70914yescomplemented
525C2×C3×C4—51no—
526C2×C3×C4—54no—
527C2×C3×C4—53no—
528C2×C3×C4—53no—
529C2×C3×C4—106no—
530C2×C3×C4—203no—
531C2×C3×C4C23×D513yes—
532C2×C3×C4C23×D513yes—
533C2×C3×C4C23×D511yescharacteristic
534#67—54no—
535#67—54no—
536C2×Dic3—51no—
537C2×Dic3—53no—
538C2×Dic3—53no—
539C2×Dic3C23×D513yes—
540C2×Dic3C23×D513yes—
541C2×Dic3C23×D511yescharacteristic
542D12—54no—
543C4×D3—26no—
544C4×D3—43no—
545C4×D3—54no—
546C4×D3—106no—
547C4×D3—203no—
548C4×D3Q8×D514yescomplemented
549Dic6—26no—
550Dic6—54no—
551Dic6—106no—
552Dic6—206no—
553C22×C5—32no—
554C22×C5—61no—
555C22×C5—61no—
556C22×C5C24×D311yescharacteristic
557C2×D5—21no—
558C2×D5—21no—
559C2×D5—32no—
560C2×D5—61no—
561C2×D5—61no—
562C2×D5C2×D3×Q812yes—
563C4×C5—23no—
564C4×C5—32no—
565C4×C5—63no—
566C4×C5—63no—
567C4×C5C2×#23516yes—
568C4×C5C2×D3×Q812yes—
569Dic5—23no—
570Dic5—23no—
571Dic5—32no—
572Dic5—63no—
573Dic5—63no—
574Dic5C2×D3×Q812yes—
575#41—158no—
576C2×Q8—33no—
577C2×Q8—53no—
578C2×Q8—64no—
579C2×Q8—104no—
580C2×Q8—151no—
581C2×Q8—156no—
582C2×Q8—153no—
583C2×Q8—304no—
584C2×Q8C2×D3×D511yescharacteristic
585C2×D4—151no—
586C2×D4—151no—
587C2×D4—151no—
588C22×C4—31no—
589C22×C4—33no—
590C22×C4—33no—
591C22×C4—51no—
592C22×C4—53no—
593C22×C4—53no—
594C22×C4—151no—
595C22×C4—153no—
596C22×C4—153no—
597C4⋊C4—36no—
598C4⋊C4—33no—
599C4⋊C4—56no—
600C4⋊C4—53no—
601C4⋊C4—153no—
602C4⋊C4—153no—
603C4⋊C4—153no—
604C4⋊C4—153no—
605C4⋊C4—153no—
606C4⋊C4—153no—
607C4⋊C4—156no—
608C4⋊C4—156no—
609C4⋊C4—156no—
610C4⋊C4—156no—
611C4⋊C4—153no—
612C4⋊C4C2×D3×D513yes—
613C22⋊C4—153no—
614C22⋊C4—153no—
615C22⋊C4—153no—
616C22⋊C4—153no—
617C22⋊C4—153no—
618C22⋊C4—153no—
619C42—33no—
620C42—33no—
621C42—33no—
622C42—53no—
623C42—53no—
624C42—53no—
625C42—153no—
626C42—153no—
627C42—153no—
628C42C2×D3×D513yes—
629C3×C5Q8×#4111yescharacteristic, complemented, Hall
630C22×C3—52no—
631C22×C3—101no—
632C22×C3—101no—
633C22×C3C24×D511yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—52no—
637C2×D3—101no—
638C2×D3—101no—
639C2×D3C2×Q8×D512yes—
640C3×C4—23no—
641C3×C4—52no—
642C3×C4—103no—
643C3×C4—103no—
644C3×C4C2×#70916yes—
645C3×C4C2×Q8×D512yes—
646Dic3—23no—
647Dic3—23no—
648Dic3—52no—
649Dic3—103no—
650Dic3—103no—
651Dic3C2×Q8×D512yes—
652C2×C5—62no—
653C2×C5C22×#23511yescharacteristic
654C2×C5C22×D3×Q811yescharacteristic
655C2×C5#596411yescharacteristic
656D5—22no—
657D5—62no—
658C23—31no—
659C23—51no—
660C23—151no—
661Q8—66no—
662Q8—106no—
663Q8—154no—
664Q8—306no—
665Q8—606no—
666Q8#677114yesdirect product factor
667D4—154no—
668D4—154no—
669D4—154no—
670C2×C4—31no—
671C2×C4—34no—
672C2×C4—33no—
673C2×C4—33no—
674C2×C4—51no—
675C2×C4—54no—
676C2×C4—53no—
677C2×C4—53no—
678C2×C4—66no—
679C2×C4—106no—
680C2×C4—123no—
681C2×C4—151no—
682C2×C4—154no—
683C2×C4—153no—
684C2×C4—153no—
685C2×C4—203no—
686C2×C4—306no—
687C2×C4—603no—
688C2×C4C22×D3×D513yes—
689C2×C4C22×D3×D513yes—
690C2×C4C22×D3×D511yescharacteristic
691C2×C3—102no—
692C2×C3C22×#70911yescharacteristic
693C2×C3C22×Q8×D511yescharacteristic
694C2×C3#6628311yescharacteristic
695D3—22no—
696D3—102no—
697C5Q8×#23511yescharacteristic, complemented, Sylow
698C22—32no—
699C22—52no—
700C22—61no—
701C22—61no—
702C22—101no—
703C22—101no—
704C22—152no—
705C22—301no—
706C22—301no—
707C22C23×D3×D511yescharacteristic
708C4—23no—
709C4—32no—
710C4—52no—
711C4—63no—
712C4—63no—
713C4—103no—
714C4—103no—
715C4—152no—
716C4—303no—
717C4—303no—
718C4C2×#677116yes—
719C4D3×Q8×D512yes—
720C3Q8×#70911yescharacteristic, complemented, Sylow
721C2—62no—
722C2—102no—
723C2—302no—
724C2C22×#677111yescharacteristic
725C2C2×D3×Q8×D511yescharacteristic
726C2#1175705811yescharacteristic
subgroupG/H
centerC2×C4C22×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC3×C4×C5×Q8C22
prime radicalC2×#6771C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5Q8×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×D15C2semidirect
2. C4×C5×D3×Q8C2semidirect
3. C3×C4×Q8×D5C2semidirect
4. Q8×#1204C2semidirect
5. Q8×#1203C2semidirect
6. Q8×#1202C2semidirect
7. Q8×#1201C2semidirect
8. #11753825C2semidirect
9. #11753715C2semidirect
10. #11753712C2semidirect
11. #11753705C2semidirect
13. #11752513C2semidirect
14. #11752500C2semidirect
15. #11752497C2semidirect
76. C4×Q8×D5D3semidirect
104. #6771Q8direct (N × H)
145. C4×D3×Q8D5semidirect
206. C3×C5×Q8#41semidirect
215. C4×D15C2×Q8semidirect
222. C4×C5×D3C2×Q8semidirect
229. C3×C4×D5C2×Q8semidirect
232. #1204C2×Q8semidirect
233. #1203C2×Q8semidirect
234. #1202C2×Q8semidirect
235. #1201C2×Q8semidirect
435. C5×Q8#235semidirect
459. C4×D5D3×Q8semidirect
524. C3×Q8#709semidirect
548. C4×D3Q8×D5semidirect
629. C3×C5Q8×#41semidirect
666. Q8#6771direct (N × H)
697. C5Q8×#235semidirect
720. C3Q8×#709semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D152
C4×C5×D3×Q82
C3×C4×Q8×D52
Q8×#12042
Q8×#12032
Q8×#12022
Q8×#12012
#117538252
#117537152
#117537122
#117537052
C4×#67712
#117525132
#117525002
#117524972
Q8×#7093
Q8×#2355