Finite Group Databasebeta

← Q8×#14519737 #29839872

Subgroups — Q8×#14519737 #29839872

Order 15616.

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⋊D61C211yesmaximal, characteristic
2C22×Q8×Dic61C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
4#21448876C213yesmaximal, complemented
5#21448829C213yesmaximal, complemented
6#21448822C213yesmaximal, complemented
7Q8×#11758196C211yesmaximal, characteristic, complemented
8#21448715C213yesmaximal
9Q8×#11758198C211yesmaximal, characteristic, complemented
10#21448388C213yesmaximal, complemented
11#21448357C213yesmaximal, complemented
12#21448347C213yesmaximal, complemented
13C4×Q8×Dic61C211yesmaximal, characteristic, complemented
14C4×#14519737C213yesmaximal
15Q8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17Q8×C22⋊D61C4116yescomplemented
18C2×#14519775C2213yes—
19C2×#14519756C2213yes—
20C2×#14519753C2213yes—
21C2×Q8×Dic61—28no—
22C2×Q8×Dic61C2211yescharacteristic
23C2×Q8×Dic61C2213yes—
24C2×Q8×Dic61C2213yes—
25C2×Q8×Dic61C2211yescharacteristic
26C2×Q8×Dic61C2211yescharacteristic
27C2×C4×Dic122C2213yes—
28C2×#14519742C2213yes—
29C4×Q8×D61—28no—
30C2×C4×C22⋊D61C2213yes—
31C2×#14519737C2213yes—
32C2×#14519737C2211yescharacteristic
33C22×C4⋊Dic61C2213yes—
34C2×C4⋊C4×D61C2213yes—
35C22×C4×Dic61C2213yes—
36C2×C42×D61C2213yes—
37#16839668C2213yes—
38#16839667C2213yes—
39#16839660C2213yes—
40#16839659C2216yes—
41#16839659C2216yes—
42#16839658C2213yes—
43#16839649C2216yes—
44#16839644C2216yes—
45#16839636C2216yes—
46#16839634C2216yes—
47#16839631C2213yes—
48#16839619C2213yes—
49C4⋊C4×Dic61C2213yes—
50C4⋊C4×Dic61C2213yes—
51C4×#11758196C2213yes—
52C4×C4⋊Dic61C2213yes—
53#16839613C2216yes—
54#16839613C2213yes—
55#16839613C2213yes—
56C22⋊C4×Dic61C2213yes—
57C22⋊C4×Dic61C2213yes—
58C4×#11758198C2213yes—
59#16839609C2213yes—
60#16839609C2213yes—
61C42×Dic61C2213yes—
62C23×Q8×C61C2211yescharacteristic
63C2×C4×Q8×C61C2211yescharacteristic
64C2×C4×Q8×C61C2211yescharacteristic
65C61×#391C2213yes—
66C61×#391C2213yes—
67C61×#380C2213yes—
68C4×C22⋊C4×C61C2213yes—
69C22×Dic122C2313yes—
70C2×Q8×D61—24no—
71C2×Q8×D61—24no—
72C2×Q8×D61C2×C418yescomplemented
73C22×C22⋊D61C2311yescharacteristic
74C23×Dic61C2313yes—
75C23×Dic61C2311yescharacteristic
76C22×C4×D61C2313yes—
77C22×C4×D61C2313yes—
78C22×C4×D61C2311yescharacteristic
79#14519775C2×C4124yescomplemented
80#14519756C2×C4124yescomplemented
81#14519753C2×C4124yescomplemented
82Q8×Dic61—24no—
83Q8×Dic61—212no—
84Q8×Dic61—212no—
85Q8×Dic61C2×C418yescomplemented
86Q8×Dic61D418yescomplemented
87C4×Dic122—212no—
88#14519742—212no—
89C4×C22⋊D61C2×C4124yes—
90#14519737—212no—
91#14519737Q818yesdirect product factor
92C2×C4⋊Dic61—212no—
93C2×C4⋊Dic61C2313yes—
94C2×C4⋊Dic61C2316yes—
95C2×C4⋊Dic61C2313yes—
96C2×C4⋊Dic61C2313yes—
97C2×#11758196C2316yes—
98C2×#11758196C2313yes—
99C2×#11758196C2316yes—
100C2×#11758196C2313yes—
101C2×#11758196C2316yes—
102C2×#11758196C2311yescharacteristic
103C4⋊C4×D61—212no—
104C2×C22⋊Dic61C2313yes—
105C2×#11758198C2313yes—
106C2×#11758198C2313yes—
107C2×#11758198C2311yescharacteristic
108C2×C4×Dic61—212no—
109C2×C4×Dic61C2313yes—
110C2×C4×Dic61C2313yes—
111C2×C4×Dic61C2313yes—
112C2×C4×Dic61C2313yes—
113C2×C4×Dic61C2313yes—
114C2×C4×Dic61C2313yes—
115C2×C4×Dic61C2313yes—
116C2×C4×Dic61C2313yes—
117C2×C4×Dic61C2313yes—
118C2×C4×Dic61C2313yes—
119C2×C4×Dic61C2311yescharacteristic
120C42×D61—212no—
121#14519684C2313yes—
122#14519684C2313yes—
123#14519684C2313yes—
124#14519684C2313yes—
125#14519684C2316yes—
126#14519684C2316yes—
127C22×Q8×C61—24no—
128C22×Q8×C61—24no—
129C22×Q8×C61C2×C418yescomplemented
130C22×Q8×C61C2313yes—
131C22×Q8×C61C2311yescharacteristic
132C23×C4×C61C2313yes—
133C4×Q8×C61—24no—
134C4×Q8×C61—24no—
135C2×C4⋊C4×C61C2313yes—
136C2×C4⋊C4×C61C2313yes—
137C2×C22⋊C4×C61C2313yes—
138C2×C22⋊C4×C61C2311yescharacteristic
139C2×C42×C61C2313yes—
140C2×C42×C61C2313yes—
141#95×C61C2313yes—
142#95×C61C2313yes—
143#95×C61C2316yes—
144C24×C61C2411yescharacteristic
145C23×D61C2411yescharacteristic
146C2×Q8×C61—232no—
147C2×Q8×C61—26no—
148C2×Q8×C61—26no—
149C2×Q8×C61C22×C4112yes—
150C2×Q8×C61C22×C414yes—
151C2×Q8×C61C2×D414yes—
152C2×Q8×C61#4114yes—
153C22×C4×C61—26no—
154C22×C4×C61—26no—
155C22×C4×C61C22×C4112yes—
156C22×C4×C61C2413yes—
157C22×C4×C61C2413yes—
158C22×C4×C61C2413yes—
159C22×C4×C61C2411yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C22×C4×C61C2413yes—
162C2×C22⋊D61C22×C414yes—
163C2×C22⋊D61C2×Q814yes—
164C2×C22⋊D61#4114yes—
165C22×Dic61—22no—
166C22×Dic61—22no—
167C22×Dic61—26no—
168C22×Dic61—26no—
169C22×Dic61—43no—
170C22×Dic61C2×Q814yescomplemented
171C22×Dic61C2413yes—
172C22×Dic61C2413yes—
173C22×Dic61C2413yes—
174C22×Dic61C2413yes—
175C22×Dic61C2411yescharacteristic
176C22×Dic61C2411yescharacteristic
177C22×Dic61C2411yescharacteristic
178Q8×D61—232no—
179C2×C4×D61—26no—
180C2×C4×D61—26no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—26no—
184C2×C4×D61—26no—
185C2×C4×D61—43no—
186C2×C4×D61C22×C4112yes—
187C2×C4×D61C2×Q814yescomplemented
188C2×Dic122—26no—
189C2×Dic122—26no—
190C2×Dic122C22×C4112yes—
191C4⋊C4×C61—26no—
192C4⋊C4×C61—26no—
193C22⋊C4×C61—26no—
194C22⋊C4×C61C2×Q814yescomplemented
195C42×C61—26no—
196C42×C61—26no—
197C22⋊Dic61C22×C4112yes—
198#11758198—26no—
199#11758198C22×C4112yes—
200#11758198C2×Q814yescomplemented
201C4⋊Dic61—26no—
202C4⋊Dic61—212no—
203C4⋊Dic61C22×C4112yes—
204C4⋊Dic61C2×D4112yes—
205#11758196—212no—
206#11758196—26no—
207#11758196—46no—
208#11758196C22×C4112yes—
209#11758196C22×C4124yes—
210#11758196C2×Q814yescomplemented
211C4×Dic61—26no—
212C4×Dic61—26no—
213C4×Dic61—26no—
214C4×Dic61—26no—
215C4×Dic61—26no—
216C4×Dic61—26no—
217C4×Dic61—26no—
218C4×Dic61—43no—
219C4×Dic61C22×C4112yes—
220C4×Dic61C2×D4112yes—
221C4×Dic61C2×Q814yescomplemented
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61C23×C412yes—
227C23×C61C22×Q812yes—
228C23×C61C2×#4112yes—
229C23×C61C2511yescharacteristic
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61C23×C412yes—
235C22×D61C22×Q812yes—
236C22×D61C2×#4112yes—
237Q8×C61—224no—
238Q8×C61C4×D4116yescomplemented
239C2×C4×C61—21no—
240C2×C4×C61—23no—
241C2×C4×C61—21no—
242C2×C4×C61—23no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—224no—
246C2×C4×C61—23no—
247C2×C4×C61—23no—
248C2×C4×C61—23no—
249C2×C4×C61—23no—
250C2×C4×C61—23no—
251C2×C4×C61—23no—
252C2×C4×C61C23×C416yes—
253C2×C4×C61C23×C416yes—
254C2×C4×C61C22×D416yes—
255C2×C4×C61C22×Q812yes—
256C2×C4×C61C22×Q812yes—
257C2×C4×C61C2×#4116yes—
258C22⋊D61C4×Q8116yescomplemented
259C2×Dic61—21no—
260C2×Dic61—23no—
261C2×Dic61—23no—
262C2×Dic61—23no—
263C2×Dic61—23no—
264C2×Dic61—21no—
265C2×Dic61—23no—
266C2×Dic61—23no—
267C2×Dic61—28no—
268C2×Dic61—23no—
269C2×Dic61—23no—
270C2×Dic61—23no—
271C2×Dic61—412no—
272C2×Dic61C23×C416yes—
273C2×Dic61C23×C416yes—
274C2×Dic61C23×C412yes—
275C2×Dic61C22×D416yes—
276C2×Dic61C22×D412yes—
277C2×Dic61C22×Q812yes—
278C2×Dic61C22×Q812yes—
279C2×Dic61C22×Q812yes—
280C2×Dic61C2×#4112yes—
281C2×Dic612−1+412yes—
282C4×D61—224no—
283C4×D61—28no—
284C4×D61—412no—
285Dic122—224no—
286C4×D4×Q8—611nomaximal, Sylow
287C22×C61—22no—
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61C2×C4×Q814yescomplemented
294C22×C61C24×C411yescharacteristic
295C22×C61C23×D411yescharacteristic
296C22×C61C23×Q811yescharacteristic
297C22×C61C22×#4111yescharacteristic
298C22×C61C22×#4111yescharacteristic
299C22×C61C2×2−1+411yescharacteristic
300C22×C61#58511yescharacteristic
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—22no—
307C2×D61C2×C4×Q814yescomplemented
308C4×C61—26no—
309C4×C61—22no—
310C4×C61—22no—
311C4×C61—43no—
312C4×C61—43no—
313C4×C61C2×C4×D4112yes—
314Dic61—26no—
315Dic61—26no—
316Dic61—22no—
317Dic61—26no—
318Dic61—43no—
319Dic61C2×C4×Q814yescomplemented
320Dic61D4×Q814yescomplemented
321C2×D4×Q8—611no—
322C22×C4×Q8—611no—
323C22×C4×Q8—611no—
324#2365—613no—
325#2360—613no—
326#2360—613no—
327Q8×C4⋊C4—611no—
328D4×C4⋊C4—613no—
329Q8×C22⋊C4—611no—
330Q8×C22⋊C4D6111yescharacteristic, complemented
331C4×C4⋊Q8—613no—
332C4×C22⋊Q8—613no—
333C4×C22⋊Q8—613no—
334C42×Q8—611no—
335C42×D4—613no—
336C2×C61—24no—
337C2×C61C22×C4×D411yescharacteristic
338C2×C61C22×C4×Q811yescharacteristic
339C2×C61C4×2−1+411yescharacteristic
340C2×C61C2×D4×Q811yescharacteristic
341C2×C61D4×#4111yescharacteristic
342C2×C61Q8×#4111yescharacteristic
343C2×C61#348211yescharacteristic
344D61—24no—
345C23×Q8—611no—
346C23×Q8C2×D6111yescharacteristic
347D4×Q8—6116no—
348C2×C4⋊Q8—613no—
349C2×C22⋊Q8—613no—
350C2×C22⋊Q8—613no—
351C2×C4×Q8—611no—
352C2×C4×Q8—611no—
353C2×C4×Q8—613no—
354C2×C4×Q8—611no—
355C2×C4×Q8—613no—
356C2×C4×Q8—613no—
357C2×C4×Q8—613no—
358C2×C4×Q8—1228no—
359C2×C4×Q8—1228no—
360C2×C4×Q8C2×D6111yescharacteristic
361C2×C4×Q8C2×D6111yescharacteristic
362C2×C4×D4—613no—
363C2×C4×D4—611no—
364C2×C4×D4—613no—
365C22×C4⋊C4—613no—
366C22×C4⋊C4—613no—
367C22×C42—613no—
368C22×C42—613no—
369#391—613no—
370#391—613no—
371#391C2×D6113yes—
372#391C2×D6113yes—
373#389—613no—
374#389—613no—
375#389—616no—
376#389—616no—
377#387—616no—
378#387—616no—
379#385—616no—
380#385—616no—
381#384—613no—
382#380—613no—
383#380C2×D6113yes—
384C4×C4⋊C4—613no—
385C4×C4⋊C4—613no—
386C4×C4⋊C4—613no—
387C4×C4⋊C4—613no—
388C4×C4⋊C4—613no—
389C4×C4⋊C4—616no—
390C4×C4⋊C4—613no—
391C4×C22⋊C4—613no—
392C4×C22⋊C4—613no—
393C4×C22⋊C4—613no—
394C4×C22⋊C4—613no—
395C4×C22⋊C4—613no—
396C4×C22⋊C4C2×D6113yes—
397C43—613no—
398C61C4×D4×Q811yescharacteristic, complemented, Sylow
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—618no—
402C22×Q8—613no—
403C22×Q8—1224no—
404C22×Q8—1224no—
405C22×Q8C4×D6118yescomplemented
406C22×Q8C22×D6113yes—
407C22×Q8C22×D6111yescharacteristic
408C22×D4—611no—
409C23×C4—611no—
410C23×C4—613no—
411C23×C4—611no—
412C23×C4—613no—
413C23×C4—613no—
414C23×C4C22×D6113yes—
415C4⋊Q8—6124no—
416C22⋊Q8—6124no—
417C22⋊Q8—6124no—
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—618no—
421C4×Q8—618no—
422C4×Q8—12212no—
423C4×Q8—12212no—
424C4×Q8—12212no—
425C4×Q8—12212no—
426C4×Q8—1224no—
427C4×D4—6124no—
428C4×D4—618no—
429C4×D4—12212no—
430C2×C4⋊C4—613no—
431C2×C4⋊C4—613no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—613no—
434C2×C4⋊C4—616no—
435C2×C4⋊C4—613no—
436C2×C4⋊C4—616no—
437C2×C4⋊C4—616no—
438C2×C4⋊C4—613no—
439C2×C4⋊C4—616no—
440C2×C4⋊C4—12212no—
441C2×C4⋊C4—12212no—
442C2×C4⋊C4C22×D6113yes—
443C2×C4⋊C4C22×D6113yes—
444C2×C22⋊C4—613no—
445C2×C22⋊C4—613no—
446C2×C22⋊C4—611no—
447C2×C22⋊C4—613no—
448C2×C22⋊C4C22×D6113yes—
449C2×C22⋊C4C22×D6111yescharacteristic
450C2×C42—613no—
451C2×C42—611no—
452C2×C42—613no—
453C2×C42—613no—
454C2×C42—613no—
455C2×C42—613no—
456C2×C42—613no—
457C2×C42—613no—
458C2×C42—613no—
459C2×C42—613no—
460C2×C42—613no—
461C2×C42—12212no—
462C2×C42—12212no—
463C2×C42C22×D6113yes—
464C2×C42C22×D6113yes—
465#95—613no—
466#95—613no—
467#95—613no—
468#95—613no—
469#95—616no—
470#95—616no—
471#95C22×D6113yes—
472#95C22×D6113yes—
473#95C22×D6116yes—
474C24—611no—
475C24C23×D6111yescharacteristic
476C2×Q8—232no—
477C2×Q8—26no—
478C2×Q8—26no—
479C2×Q8—6112no—
480C2×Q8—12232no—
481C2×Q8—1226no—
482C2×Q8—1226no—
483C2×Q8C2×C4×D61112yes—
484C2×Q8C2×C4×D6114yes—
485C2×Q8D4×D6114yes—
486C2×Q8#1175822414yes—
487C2×D4—614no—
488C2×D4—614no—
489C2×D4—614no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—614no—
495C22×C4—611no—
496C22×C4—613no—
497C22×C4—613no—
498C22×C4—613no—
499C22×C4—6112no—
500C22×C4—614no—
501C22×C4—613no—
502C22×C4—1222no—
503C22×C4—1222no—
504C22×C4—1226no—
505C22×C4—1226no—
506C22×C4—1222no—
507C22×C4—1222no—
508C22×C4—1226no—
509C22×C4—1226no—
510C22×C4—1226no—
511C22×C4—1226no—
512C22×C4—2443no—
513C22×C4—2443no—
514C22×C4C2×C4×D61112yes—
515C22×C4C23×D6113yes—
516C22×C4C23×D6113yes—
517C22×C4C23×D6113yes—
518C22×C4C23×D6111yescharacteristic
519C22×C4C23×D6111yescharacteristic
520C22×C4C23×D6113yes—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—6112no—
524C4⋊C4—6124no—
525C4⋊C4—6112no—
526C4⋊C4—6112no—
527C4⋊C4—614no—
528C4⋊C4—12212no—
529C4⋊C4—12212no—
530C4⋊C4—1226no—
531C4⋊C4—1226no—
532C4⋊C4—2446no—
533C22⋊C4—26no—
534C22⋊C4—6112no—
535C22⋊C4—6112no—
536C22⋊C4—614no—
537C22⋊C4—1226no—
538C22⋊C4Q8×D6114yescomplemented
539C42—26no—
540C42—26no—
541C42—6112no—
542C42—6112no—
543C42—614no—
544C42—1226no—
545C42—1226no—
546C42—1226no—
547C42—1226no—
548C42—1226no—
549C42—1226no—
550C42—1226no—
551C42—2443no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—612no—
557C23—612no—
558C23—612no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23C22×C4×D6112yes—
564C23C2×Q8×D6112yes—
565C23#41×D6112yes—
566C23C24×D6111yescharacteristic
567Q8—224no—
568Q8—12224no—
569Q8#14519737116yesdirect product factor
570D4—6116no—
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—612no—
585C2×C4—612no—
586C2×C4—612no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—612no—
590C2×C4—616no—
591C2×C4—616no—
592C2×C4—616no—
593C2×C4—612no—
594C2×C4—1228no—
595C2×C4—1228no—
596C2×C4—1221no—
597C2×C4—1223no—
598C2×C4—1223no—
599C2×C4—1223no—
600C2×C4—1223no—
601C2×C4—1221no—
602C2×C4—1223no—
603C2×C4—1223no—
604C2×C4—12224no—
605C2×C4—1223no—
606C2×C4—1223no—
607C2×C4—1223no—
608C2×C4—24412no—
609C2×C4—24412no—
610C2×C4C22×C4×D6116yes—
611C2×C4C22×C4×D6116yes—
612C2×C4C2×D4×D6116yes—
613C2×C4C2×Q8×D6112yes—
614C2×C4C2×Q8×D6112yes—
615C2×C4C2×#1175822416yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—614no—
623C22—1222no—
624C22—1222no—
625C22—1222no—
626C22—1222no—
627C22—1222no—
628C22—1222no—
629C22C4×Q8×D6114yescomplemented
630C22C23×C4×D6111yescharacteristic
631C22C22×D4×D6111yescharacteristic
632C22C22×Q8×D6111yescharacteristic
633C22C2×#41×D6111yescharacteristic
634C22C22×#1175822411yescharacteristic
635C222−1+4×D6111yescharacteristic
636C22#1684059911yescharacteristic
637C4—26no—
638C4—22no—
639C4—22no—
640C4—43no—
641C4—43no—
642C4—614no—
643C4—614no—
644C4—1226no—
645C4—1226no—
646C4—1222no—
647C4—1226no—
648C4—2443no—
649C4C2×#14519737112yes—
650C2—24no—
651C2—1224no—
652C2C22×#1451973711yescharacteristic
653C2C2×C4×Q8×D6111yescharacteristic
654C2#2145902811yescharacteristic
655C2D4×Q8×D6111yescharacteristic
656C2#2145930811yescharacteristic
657C2Q8×#1175822411yescharacteristic
658C2#2145943511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingQ8×C22⋊C4×C61C2
socle, cosocleC23×C61C25
prime radicalC22×C22⋊D61C23
hypercenterQ8×C22⋊C4D61
hypocenterC61C4×D4×Q8
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic61C2semidirect
3. C2×C4×Q8×D61C2semidirect
4. #21448876C2semidirect
5. #21448829C2semidirect
6. #21448822C2semidirect
7. Q8×#11758196C2semidirect
9. Q8×#11758198C2semidirect
10. #21448388C2semidirect
11. #21448357C2semidirect
12. #21448347C2semidirect
13. C4×Q8×Dic61C2semidirect
15. Q8×C22⋊C4×C61C2semidirect
17. Q8×C22⋊D61C4semidirect
72. C2×Q8×D61C2×C4semidirect
79. #14519775C2×C4semidirect
80. #14519756C2×C4semidirect
81. #14519753C2×C4semidirect
85. Q8×Dic61C2×C4semidirect
86. Q8×Dic61D4semidirect
91. #14519737Q8direct (N × H)
129. C22×Q8×C61C2×C4semidirect
170. C22×Dic61C2×Q8semidirect
187. C2×C4×D61C2×Q8semidirect
194. C22⋊C4×C61C2×Q8semidirect
200. #11758198C2×Q8semidirect
210. #11758196C2×Q8semidirect
221. C4×Dic61C2×Q8semidirect
238. Q8×C61C4×D4semidirect
258. C22⋊D61C4×Q8semidirect
293. C22×C61C2×C4×Q8semidirect
307. C2×D61C2×C4×Q8semidirect
319. Dic61C2×C4×Q8semidirect
320. Dic61D4×Q8semidirect
330. Q8×C22⋊C4D61semidirect
398. C61C4×D4×Q8semidirect
405. C22×Q8C4×D61semidirect
538. C22⋊C4Q8×D61semidirect
569. Q8#14519737direct (N × H)
629. C22C4×Q8×D61semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D612
C22×Q8×Dic612
C2×C4×Q8×D612
#214488762
#214488292
#214488222
Q8×#117581962
#214487152
Q8×#117581982
#214483882
#214483572
#214483472
C4×Q8×Dic612
C4×#145197372
Q8×C22⋊C4×C612
C4×D4×Q861