Finite Group Databasebeta

← Q8×#14556551 #33245843

Subgroups — Q8×#14556551 #33245843

Order 18688.

3148 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D73C211yesmaximal, characteristic
2C22×Q8×Dic73C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
4#22612988C213yesmaximal, complemented
5#22612941C213yesmaximal, complemented
6#22612934C213yesmaximal, complemented
7Q8×#11924007C211yesmaximal, characteristic, complemented
8#22612827C213yesmaximal
9Q8×#11924005C211yesmaximal, characteristic, complemented
10#22612500C213yesmaximal, complemented
11#22612469C213yesmaximal, complemented
12#22612459C213yesmaximal, complemented
13C4×Q8×Dic73C211yesmaximal, characteristic, complemented
14C4×#14556551C213yesmaximal
15Q8×C22⋊C4×C73C211yesmaximal, characteristic, complemented
16C22×Q8×D73C2211yescharacteristic
17Q8×C22⋊D73C4116yescomplemented
18C2×#14556589C2213yes—
19C2×#14556570C2213yes—
20C2×#14556567C2213yes—
21C2×Q8×Dic73—28no—
22C2×Q8×Dic73C2213yes—
23C2×Q8×Dic73C2211yescharacteristic
24C2×Q8×Dic73C2213yes—
25C2×Q8×Dic73C2211yescharacteristic
26C2×Q8×Dic73C2211yescharacteristic
27C2×C4×Dic146C2213yes—
28C2×#14556556C2213yes—
29C4×Q8×D73—28no—
30C2×C4×C22⋊D73C2213yes—
31C2×#14556551C2213yes—
32C2×#14556551C2211yescharacteristic
33C22×C4⋊Dic73C2213yes—
34C2×C4⋊C4×D73C2213yes—
35C22×C4×Dic73C2213yes—
36C2×C42×D73C2213yes—
37#17988493C2213yes—
38#17988492C2213yes—
39#17988485C2213yes—
40#17988484C2216yes—
41#17988484C2216yes—
42#17988483C2213yes—
43#17988474C2216yes—
44#17988469C2216yes—
45#17988461C2216yes—
46#17988459C2216yes—
47#17988456C2213yes—
48#17988444C2213yes—
49C4⋊C4×Dic73C2213yes—
50C4⋊C4×Dic73C2213yes—
51C4×#11924007C2213yes—
52C4×C4⋊Dic73C2213yes—
53#17988438C2213yes—
54#17988438C2216yes—
55#17988438C2213yes—
56C22⋊C4×Dic73C2213yes—
57C22⋊C4×Dic73C2213yes—
58C4×#11924005C2213yes—
59#17988434C2213yes—
60#17988434C2213yes—
61C42×Dic73C2213yes—
62C23×Q8×C73C2211yescharacteristic
63C2×C4×Q8×C73C2211yescharacteristic
64C2×C4×Q8×C73C2211yescharacteristic
65#391×C73C2213yes—
66#391×C73C2213yes—
67#380×C73C2213yes—
68C4×C22⋊C4×C73C2213yes—
69C22×Dic146C2313yes—
70C2×Q8×D73—24no—
71C2×Q8×D73—24no—
72C2×Q8×D73C2×C418yescomplemented
73C22×C22⋊D73C2311yescharacteristic
74C23×Dic73C2313yes—
75C23×Dic73C2311yescharacteristic
76C22×C4×D73C2313yes—
77C22×C4×D73C2313yes—
78C22×C4×D73C2311yescharacteristic
79#14556589C2×C4124yescomplemented
80#14556570C2×C4124yescomplemented
81#14556567C2×C4124yescomplemented
82Q8×Dic73—212no—
83Q8×Dic73—212no—
84Q8×Dic73—24no—
85Q8×Dic73C2×C418yescomplemented
86Q8×Dic73D418yescomplemented
87C4×Dic146—212no—
88#14556556—212no—
89C4×C22⋊D73C2×C4124yes—
90#14556551—212no—
91#14556551Q818yesdirect product factor
92C2×C4⋊Dic73—212no—
93C2×C4⋊Dic73C2313yes—
94C2×C4⋊Dic73C2316yes—
95C2×C4⋊Dic73C2313yes—
96C2×C4⋊Dic73C2313yes—
97C2×#11924007C2313yes—
98C2×#11924007C2316yes—
99C2×#11924007C2316yes—
100C2×#11924007C2313yes—
101C2×#11924007C2316yes—
102C2×#11924007C2311yescharacteristic
103C4⋊C4×D73—212no—
104C2×C22⋊Dic73C2313yes—
105C2×#11924005C2313yes—
106C2×#11924005C2313yes—
107C2×#11924005C2311yescharacteristic
108C2×C4×Dic73—212no—
109C2×C4×Dic73C2313yes—
110C2×C4×Dic73C2313yes—
111C2×C4×Dic73C2313yes—
112C2×C4×Dic73C2313yes—
113C2×C4×Dic73C2313yes—
114C2×C4×Dic73C2313yes—
115C2×C4×Dic73C2313yes—
116C2×C4×Dic73C2313yes—
117C2×C4×Dic73C2313yes—
118C2×C4×Dic73C2313yes—
119C2×C4×Dic73C2311yescharacteristic
120C42×D73—212no—
121#14556498C2313yes—
122#14556498C2313yes—
123#14556498C2313yes—
124#14556498C2313yes—
125#14556498C2316yes—
126#14556498C2316yes—
127C22×Q8×C73—24no—
128C22×Q8×C73—24no—
129C22×Q8×C73C2×C418yescomplemented
130C22×Q8×C73C2313yes—
131C22×Q8×C73C2311yescharacteristic
132C23×C4×C73C2313yes—
133C4×Q8×C73—24no—
134C4×Q8×C73—24no—
135C2×C4⋊C4×C73C2313yes—
136C2×C4⋊C4×C73C2313yes—
137C2×C22⋊C4×C73C2313yes—
138C2×C22⋊C4×C73C2311yescharacteristic
139C2×C42×C73C2313yes—
140C2×C42×C73C2313yes—
141#95×C73C2313yes—
142#95×C73C2313yes—
143#95×C73C2316yes—
144C23×D73C2411yescharacteristic
145C2×Dic146—26no—
146C2×Dic146—26no—
147C2×Dic146C22×C4112yes—
148Q8×D73—232no—
149C2×C22⋊D73C22×C414yes—
150C2×C22⋊D73C2×Q814yes—
151C2×C22⋊D73#4114yes—
152C22×Dic73—22no—
153C22×Dic73—22no—
154C22×Dic73—26no—
155C22×Dic73—26no—
156C22×Dic73—43no—
157C22×Dic73C2×Q814yescomplemented
158C22×Dic73C2413yes—
159C22×Dic73C2413yes—
160C22×Dic73C2413yes—
161C22×Dic73C2413yes—
162C22×Dic73C2411yescharacteristic
163C22×Dic73C2411yescharacteristic
164C22×Dic73C2411yescharacteristic
165C2×C4×D73—26no—
166C2×C4×D73—26no—
167C2×C4×D73—22no—
168C2×C4×D73—22no—
169C2×C4×D73—26no—
170C2×C4×D73—26no—
171C2×C4×D73—43no—
172C2×C4×D73C22×C4112yes—
173C2×C4×D73C2×Q814yescomplemented
174C4⋊Dic73—26no—
175C4⋊Dic73—212no—
176C4⋊Dic73C22×C4112yes—
177C4⋊Dic73C2×D4112yes—
178#11924007—212no—
179#11924007—26no—
180#11924007—46no—
181#11924007C22×C4112yes—
182#11924007C22×C4124yes—
183#11924007C2×Q814yescomplemented
184C22⋊Dic73C22×C4112yes—
185#11924005—26no—
186#11924005C22×C4112yes—
187#11924005C2×Q814yescomplemented
188C4×Dic73—26no—
189C4×Dic73—26no—
190C4×Dic73—26no—
191C4×Dic73—26no—
192C4×Dic73—26no—
193C4×Dic73—26no—
194C4×Dic73—26no—
195C4×Dic73—43no—
196C4×Dic73C22×C4112yes—
197C4×Dic73C2×D4112yes—
198C4×Dic73C2×Q814yescomplemented
199C24×C73C2411yescharacteristic
200C2×Q8×C73—232no—
201C2×Q8×C73—26no—
202C2×Q8×C73—26no—
203C2×Q8×C73C22×C4112yes—
204C2×Q8×C73C22×C414yes—
205C2×Q8×C73C2×D414yes—
206C2×Q8×C73#4114yes—
207C22×C4×C73—26no—
208C22×C4×C73—26no—
209C22×C4×C73C22×C4112yes—
210C22×C4×C73C2413yes—
211C22×C4×C73C2413yes—
212C22×C4×C73C2413yes—
213C22×C4×C73C2411yescharacteristic
214C22×C4×C73C2411yescharacteristic
215C22×C4×C73C2413yes—
216C4⋊C4×C73—26no—
217C4⋊C4×C73—26no—
218C22⋊C4×C73—26no—
219C22⋊C4×C73C2×Q814yescomplemented
220C42×C73—26no—
221C42×C73—26no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73C23×C412yes—
227C23×C73C22×Q812yes—
228C23×C73C2×#4112yes—
229C23×C73C2511yescharacteristic
230C22×D73—21no—
231C22×D73—21no—
232C22×D73—21no—
233C22×D73—21no—
234C22×D73C23×C412yes—
235C22×D73C22×Q812yes—
236C22×D73C2×#4112yes—
237Q8×C73—224no—
238Q8×C73C4×D4116yescomplemented
239C2×C4×C73—21no—
240C2×C4×C73—23no—
241C2×C4×C73—21no—
242C2×C4×C73—23no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—224no—
246C2×C4×C73—23no—
247C2×C4×C73—23no—
248C2×C4×C73—23no—
249C2×C4×C73—23no—
250C2×C4×C73—23no—
251C2×C4×C73—23no—
252C2×C4×C73C23×C416yes—
253C2×C4×C73C23×C416yes—
254C2×C4×C73C22×D416yes—
255C2×C4×C73C22×Q812yes—
256C2×C4×C73C22×Q812yes—
257C2×C4×C73C2×#4116yes—
258C22⋊D73C4×Q8116yescomplemented
259C2×Dic73—21no—
260C2×Dic73—23no—
261C2×Dic73—23no—
262C2×Dic73—23no—
263C2×Dic73—23no—
264C2×Dic73—21no—
265C2×Dic73—23no—
266C2×Dic73—23no—
267C2×Dic73—28no—
268C2×Dic73—23no—
269C2×Dic73—23no—
270C2×Dic73—23no—
271C2×Dic73—412no—
272C2×Dic73C23×C416yes—
273C2×Dic73C23×C416yes—
274C2×Dic73C23×C412yes—
275C2×Dic73C22×D416yes—
276C2×Dic73C22×D412yes—
277C2×Dic73C22×Q812yes—
278C2×Dic73C22×Q812yes—
279C2×Dic73C22×Q812yes—
280C2×Dic73C2×#4112yes—
281C2×Dic732−1+412yes—
282C4×D73—224no—
283C4×D73—28no—
284C4×D73—412no—
285Dic146—224no—
286C22×C73—22no—
287C22×C73—22no—
288C22×C73—22no—
289C22×C73—22no—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73C2×C4×Q814yescomplemented
293C22×C73C24×C411yescharacteristic
294C22×C73C23×D411yescharacteristic
295C22×C73C23×Q811yescharacteristic
296C22×C73C22×#4111yescharacteristic
297C22×C73C22×#4111yescharacteristic
298C22×C73C2×2−1+411yescharacteristic
299C22×C73#58511yescharacteristic
300C2×D73—22no—
301C2×D73—22no—
302C2×D73—22no—
303C2×D73—22no—
304C2×D73—22no—
305C2×D73—22no—
306C2×D73C2×C4×Q814yescomplemented
307C4×C73—26no—
308C4×C73—22no—
309C4×C73—22no—
310C4×C73—43no—
311C4×C73—43no—
312C4×C73C2×C4×D4112yes—
313Dic73—26no—
314Dic73—26no—
315Dic73—22no—
316Dic73—26no—
317Dic73—43no—
318Dic73C2×C4×Q814yescomplemented
319Dic73D4×Q814yescomplemented
320C4×D4×Q8—731nomaximal, Sylow
321C2×C73—24no—
322C2×C73C22×C4×D411yescharacteristic
323C2×C73C22×C4×Q811yescharacteristic
324C2×C73C4×2−1+411yescharacteristic
325C2×C73C2×D4×Q811yescharacteristic
326C2×C73D4×#4111yescharacteristic
327C2×C73Q8×#4111yescharacteristic
328C2×C73#348211yescharacteristic
329D73—24no—
330C2×D4×Q8—731no—
331C22×C4×Q8—731no—
332C22×C4×Q8—731no—
333#2365—733no—
334#2360—733no—
335#2360—733no—
336Q8×C4⋊C4—731no—
337D4×C4⋊C4—733no—
338Q8×C22⋊C4—731no—
339Q8×C22⋊C4D7311yescharacteristic, complemented
340C4×C4⋊Q8—733no—
341C4×C22⋊Q8—733no—
342C4×C22⋊Q8—733no—
343C42×Q8—731no—
344C42×D4—733no—
345C73C4×D4×Q811yescharacteristic, complemented, Sylow
346C23×Q8—731no—
347C23×Q8C2×D7311yescharacteristic
348D4×Q8—7316no—
349C2×C4⋊Q8—733no—
350C2×C22⋊Q8—733no—
351C2×C22⋊Q8—733no—
352C2×C4×Q8—731no—
353C2×C4×Q8—731no—
354C2×C4×Q8—733no—
355C2×C4×Q8—731no—
356C2×C4×Q8—733no—
357C2×C4×Q8—733no—
358C2×C4×Q8—733no—
359C2×C4×Q8—1468no—
360C2×C4×Q8—1468no—
361C2×C4×Q8C2×D7311yescharacteristic
362C2×C4×Q8C2×D7311yescharacteristic
363C2×C4×D4—733no—
364C2×C4×D4—731no—
365C2×C4×D4—733no—
366C22×C4⋊C4—733no—
367C22×C4⋊C4—733no—
368C22×C42—733no—
369C22×C42—733no—
370#391—733no—
371#391—733no—
372#391C2×D7313yes—
373#391C2×D7313yes—
374#389—733no—
375#389—733no—
376#389—736no—
377#389—736no—
378#387—736no—
379#387—736no—
380#385—736no—
381#385—736no—
382#384—733no—
383#380—733no—
384#380C2×D7313yes—
385C4×C4⋊C4—733no—
386C4×C4⋊C4—733no—
387C4×C4⋊C4—733no—
388C4×C4⋊C4—733no—
389C4×C4⋊C4—733no—
390C4×C4⋊C4—736no—
391C4×C4⋊C4—733no—
392C4×C22⋊C4—733no—
393C4×C22⋊C4—733no—
394C4×C22⋊C4—733no—
395C4×C22⋊C4—733no—
396C4×C22⋊C4—733no—
397C4×C22⋊C4C2×D7313yes—
398C43—733no—
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—738no—
402C22×Q8—733no—
403C22×Q8—1464no—
404C22×Q8—1464no—
405C22×Q8C4×D7318yescomplemented
406C22×Q8C22×D7313yes—
407C22×Q8C22×D7311yescharacteristic
408C22×D4—731no—
409C23×C4—733no—
410C23×C4—733no—
411C23×C4—731no—
412C23×C4—733no—
413C23×C4—731no—
414C23×C4C22×D7313yes—
415C4⋊Q8—7324no—
416C22⋊Q8—7324no—
417C22⋊Q8—7324no—
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—738no—
421C4×Q8—738no—
422C4×Q8—14612no—
423C4×Q8—14612no—
424C4×Q8—14612no—
425C4×Q8—14612no—
426C4×Q8—1464no—
427C4×D4—7324no—
428C4×D4—738no—
429C4×D4—14612no—
430C2×C4⋊C4—736no—
431C2×C4⋊C4—733no—
432C2×C4⋊C4—733no—
433C2×C4⋊C4—731no—
434C2×C4⋊C4—733no—
435C2×C4⋊C4—736no—
436C2×C4⋊C4—733no—
437C2×C4⋊C4—736no—
438C2×C4⋊C4—736no—
439C2×C4⋊C4—733no—
440C2×C4⋊C4—14612no—
441C2×C4⋊C4—14612no—
442C2×C4⋊C4C22×D7313yes—
443C2×C4⋊C4C22×D7313yes—
444C2×C22⋊C4—733no—
445C2×C22⋊C4—733no—
446C2×C22⋊C4—731no—
447C2×C22⋊C4—733no—
448C2×C22⋊C4C22×D7313yes—
449C2×C22⋊C4C22×D7311yescharacteristic
450C2×C42—733no—
451C2×C42—733no—
452C2×C42—731no—
453C2×C42—733no—
454C2×C42—733no—
455C2×C42—733no—
456C2×C42—733no—
457C2×C42—733no—
458C2×C42—733no—
459C2×C42—733no—
460C2×C42—733no—
461C2×C42—14612no—
462C2×C42—14612no—
463C2×C42C22×D7313yes—
464C2×C42C22×D7313yes—
465#95—733no—
466#95—733no—
467#95—733no—
468#95—733no—
469#95—736no—
470#95—736no—
471#95C22×D7313yes—
472#95C22×D7313yes—
473#95C22×D7316yes—
474C24—731no—
475C24C23×D7311yescharacteristic
476C2×Q8—232no—
477C2×Q8—26no—
478C2×Q8—26no—
479C2×Q8—7312no—
480C2×Q8—14632no—
481C2×Q8—1466no—
482C2×Q8—1466no—
483C2×Q8C2×C4×D73112yes—
484C2×Q8C2×C4×D7314yes—
485C2×Q8D4×D7314yes—
486C2×Q8#1192402714yes—
487C2×D4—734no—
488C2×D4—734no—
489C2×D4—734no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—2923no—
493C22×C4—2923no—
494C22×C4—731no—
495C22×C4—731no—
496C22×C4—734no—
497C22×C4—731no—
498C22×C4—733no—
499C22×C4—733no—
500C22×C4—733no—
501C22×C4—7312no—
502C22×C4—734no—
503C22×C4—733no—
504C22×C4—1466no—
505C22×C4—1466no—
506C22×C4—1462no—
507C22×C4—1462no—
508C22×C4—1466no—
509C22×C4—1466no—
510C22×C4—1462no—
511C22×C4—1462no—
512C22×C4—1466no—
513C22×C4—1466no—
514C22×C4C2×C4×D73112yes—
515C22×C4C23×D7313yes—
516C22×C4C23×D7313yes—
517C22×C4C23×D7313yes—
518C22×C4C23×D7311yescharacteristic
519C22×C4C23×D7311yescharacteristic
520C22×C4C23×D7313yes—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—2926no—
524C4⋊C4—7312no—
525C4⋊C4—7324no—
526C4⋊C4—7312no—
527C4⋊C4—7312no—
528C4⋊C4—734no—
529C4⋊C4—14612no—
530C4⋊C4—1466no—
531C4⋊C4—14612no—
532C4⋊C4—1466no—
533C22⋊C4—26no—
534C22⋊C4—7312no—
535C22⋊C4—7312no—
536C22⋊C4—734no—
537C22⋊C4—1466no—
538C22⋊C4Q8×D7314yescomplemented
539C42—26no—
540C42—26no—
541C42—2923no—
542C42—7312no—
543C42—7312no—
544C42—734no—
545C42—1466no—
546C42—1466no—
547C42—1466no—
548C42—1466no—
549C42—1466no—
550C42—1466no—
551C42—1466no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—732no—
557C23—732no—
558C23—732no—
559C23—1461no—
560C23—1461no—
561C23—1461no—
562C23—1461no—
563C23C22×C4×D7312yes—
564C23C2×Q8×D7312yes—
565C23#41×D7312yes—
566C23C24×D7311yescharacteristic
567Q8—224no—
568Q8—14624no—
569Q8#14556551116yesdirect product factor
570D4—7316no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—224no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—29212no—
585C2×C4—29212no—
586C2×C4—732no—
587C2×C4—732no—
588C2×C4—732no—
589C2×C4—732no—
590C2×C4—732no—
591C2×C4—732no—
592C2×C4—736no—
593C2×C4—736no—
594C2×C4—736no—
595C2×C4—732no—
596C2×C4—1468no—
597C2×C4—1463no—
598C2×C4—1463no—
599C2×C4—1463no—
600C2×C4—1468no—
601C2×C4—1461no—
602C2×C4—1463no—
603C2×C4—1463no—
604C2×C4—1463no—
605C2×C4—1463no—
606C2×C4—1461no—
607C2×C4—1463no—
608C2×C4—1463no—
609C2×C4—14624no—
610C2×C4C22×C4×D7316yes—
611C2×C4C22×C4×D7316yes—
612C2×C4C2×D4×D7316yes—
613C2×C4C2×Q8×D7312yes—
614C2×C4C2×Q8×D7312yes—
615C2×C4C2×#1192402716yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—734no—
623C22—1462no—
624C22—1462no—
625C22—1462no—
626C22—1462no—
627C22—1462no—
628C22—1462no—
629C22C4×Q8×D7314yescomplemented
630C22C23×C4×D7311yescharacteristic
631C22C22×D4×D7311yescharacteristic
632C22C22×Q8×D7311yescharacteristic
633C22C2×#41×D7311yescharacteristic
634C22C22×#1192402711yescharacteristic
635C222−1+4×D7311yescharacteristic
636C22#1798942411yescharacteristic
637C4—22no—
638C4—26no—
639C4—22no—
640C4—43no—
641C4—43no—
642C4—2923no—
643C4—734no—
644C4—734no—
645C4—1466no—
646C4—1466no—
647C4—1462no—
648C4—1466no—
649C4C2×#14556551112yes—
650C2—24no—
651C2—1464no—
652C2C22×#1455655111yescharacteristic
653C2C2×C4×Q8×D7311yescharacteristic
654C2#2262314011yescharacteristic
655C2D4×Q8×D7311yescharacteristic
656C2#2262342011yescharacteristic
657C2Q8×#1192402711yescharacteristic
658C2#2262354711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingQ8×C22⋊C4×C73C2
socle, cosocleC23×C73C25
prime radicalC22×C22⋊D73C23
hypercenterQ8×C22⋊C4D73
hypocenterC73C4×D4×Q8
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic73C2semidirect
3. C2×C4×Q8×D73C2semidirect
4. #22612988C2semidirect
5. #22612941C2semidirect
6. #22612934C2semidirect
7. Q8×#11924007C2semidirect
9. Q8×#11924005C2semidirect
10. #22612500C2semidirect
11. #22612469C2semidirect
12. #22612459C2semidirect
13. C4×Q8×Dic73C2semidirect
15. Q8×C22⋊C4×C73C2semidirect
17. Q8×C22⋊D73C4semidirect
72. C2×Q8×D73C2×C4semidirect
79. #14556589C2×C4semidirect
80. #14556570C2×C4semidirect
81. #14556567C2×C4semidirect
85. Q8×Dic73C2×C4semidirect
86. Q8×Dic73D4semidirect
91. #14556551Q8direct (N × H)
129. C22×Q8×C73C2×C4semidirect
157. C22×Dic73C2×Q8semidirect
173. C2×C4×D73C2×Q8semidirect
183. #11924007C2×Q8semidirect
187. #11924005C2×Q8semidirect
198. C4×Dic73C2×Q8semidirect
219. C22⋊C4×C73C2×Q8semidirect
238. Q8×C73C4×D4semidirect
258. C22⋊D73C4×Q8semidirect
292. C22×C73C2×C4×Q8semidirect
306. C2×D73C2×C4×Q8semidirect
318. Dic73C2×C4×Q8semidirect
319. Dic73D4×Q8semidirect
339. Q8×C22⋊C4D73semidirect
345. C73C4×D4×Q8semidirect
405. C22×Q8C4×D73semidirect
538. C22⋊C4Q8×D73semidirect
569. Q8#14556551direct (N × H)
629. C22C4×Q8×D73semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D732
C22×Q8×Dic732
C2×C4×Q8×D732
#226129882
#226129412
#226129342
Q8×#119240072
#226128272
Q8×#119240052
#226125002
#226124692
#226124592
C4×Q8×Dic732
C4×#145565512
Q8×C22⋊C4×C732
C4×D4×Q873