Finite Group Databasebeta

← #29711100

Subgroups — #29711100

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758201C211yesmaximal, characteristic, complemented
2C2×#16839901C212yesmaximal, complemented
3C2×#16839912C211yesmaximal, characteristic, complemented
4#21449175C211yesmaximal, characteristic
5#21446902C212yesmaximal, complemented
6#21446820C212yesmaximal, complemented
7#21446243C211yesmaximal, characteristic, complemented
8#21446174C212yesmaximal, complemented
9#21446112C211yesmaximal, characteristic, complemented
10#21445754C211yesmaximal, characteristic, complemented
11C2×D4×Q8×C61C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic
13C22×#11758201—28no—
14C22×#11758201—24no—
15C22×#11758201C2212yes—
16C22×#11758201C2212yes—
17C22×#11758201C2212yes—
18C23×#92418C2211yescharacteristic
19C2×#14519751C2212yes—
20C2×#14519745—21no—
21#16839912—24no—
22#16839901—28no—
23C2×#14519701C2212yescomplemented
24C2×#14519701C2212yescomplemented
25C2×#14519701C2212yescomplemented
26C2×#14519697C2212yes—
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2212yescomplemented
29#16839679—21no—
30#16839671—21no—
31#16839664C2212yes—
32#16839622C2211yescharacteristic
33#16839617—21no—
34#16839524C2212yescomplemented
35#16839517C2212yescomplemented
36C23×Q8×C61C2211yescharacteristic
37C23×Q8×C61C2211yescharacteristic, complemented
38D4×Q8×C61—24no—
39D4×Q8×C61—24no—
40C2×C4⋊Q8×C61—21no—
41C2×C4⋊Q8×C61C2211yescharacteristic, complemented
42C2×C22⋊Q8×C61—21no—
43C2×C22⋊Q8×C61—21no—
44C2×C22⋊Q8×C61C2211yescharacteristic
45C2×C22⋊Q8×C61C2211yescharacteristic, complemented
46C2×C4×Q8×C61C2211yescharacteristic, complemented
47C2×C4×D4×C61—21no—
48C2×C4×D4×C61C2211yescharacteristic
49C24×D61—21no—
50C22×D244—22no—
51C22×D244—24no—
52C22×D244—22no—
53C22×D244—21no—
54C22×D244—42no—
55C22×D244C2312yes—
56C22×C22⋊D61—22no—
57C2×#11758201—232no—
58C2×#11758201—24no—
59C2×#11758201—24no—
60C2×#11758201—24no—
61C2×#11758201—24no—
62C2×#11758201—24no—
63C2×#11758201—24no—
64C2×#11758201—24no—
65C2×#11758201—42no—
66C2×#11758201D418yescomplemented
67C22×#92418—22no—
68C22×#92418—24no—
69C22×#92418C2312yes—
70C22×#92418C2312yes—
71#14519751—24no—
72#14519751—42no—
73#14519745—44no—
74C2×C4⋊Dic61C2312yes—
75C2×C22⋊Dic61—21no—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198—22no—
79#14519701—24no—
80#14519701—24no—
81#14519701—42no—
82#14519697—24no—
83C22⋊#92418—22no—
84C22⋊#92418—24no—
85#14519684—21no—
86C22×Q8×C61—22no—
87C22×Q8×C61—22no—
88C22×Q8×C61—21no—
89C22×Q8×C61—21no—
90C22×Q8×C61—22no—
91C22×Q8×C61—24no—
92C22×Q8×C61—24no—
93C22×Q8×C61—42no—
94C22×Q8×C61—42no—
95C22×Q8×C61D414yescomplemented
96C22×Q8×C61C2311yescharacteristic
97C22×Q8×C61C2311yescharacteristic
98C22×Q8×C61C2311yescharacteristic
99C22×D4×C61D411yescharacteristic
100C23×C4×C61—21no—
101C23×C4×C61—21no—
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C4⋊Q8×C61—28no—
105C4⋊Q8×C61—22no—
106C4⋊Q8×C61—22no—
107C22⋊Q8×C61—28no—
108C22⋊Q8×C61—28no—
109C22⋊Q8×C61—22no—
110C22⋊Q8×C61—22no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61D414yescomplemented
113C4×Q8×C61—22no—
114C4×Q8×C61—22no—
115C4×D4×C61—28no—
116C4×D4×C61—22no—
117C4×D4×C61—22no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61D411yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C42×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C24×C61C2×D411yescharacteristic
132C24×C61C2×D411yescharacteristic
133C23×D61—22no—
134C23×D61—44no—
135C23×D61—42no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61—82no—
139C2×Q8×C61—24no—
140C2×Q8×C61—24no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—22no—
145C2×Q8×C61—28no—
146C2×Q8×C61—22no—
147C2×Q8×C61—22no—
148C2×Q8×C61—22no—
149C2×Q8×C61—22no—
150C2×Q8×C61—44no—
151C2×Q8×C61—44no—
152C2×Q8×C61—44no—
153C2×Q8×C61—48no—
154C2×Q8×C61—48no—
155C2×Q8×C61—44no—
156C2×Q8×C61—44no—
157C2×Q8×C61C2×D412yes—
158C2×Q8×C61C2×D412yes—
159C2×Q8×C61C2×D414yes—
160C2×Q8×C61C2×D412yes—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61SD1614yescomplemented
164C22×C4×C61—21no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—24no—
168C22×C4×C61—24no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—44no—
177C22×C4×C61—44no—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2×D412yes—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2411yescharacteristic
185C2×C22⋊D61—44no—
186C2×C22⋊D61—44no—
187C2×C22⋊D61—82no—
188C22×Dic61—22no—
189C2×D244—28no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—48no—
196C2×D244—44no—
197C2×D244—44no—
198C2×D244—42no—
199C2×D244C2×D414yes—
200C4⋊C4×C61—24no—
201C4⋊C4×C61—24no—
202C4⋊C4×C61—24no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—24no—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C2×D412yes—
208C22⋊C4×C61—24no—
209C22⋊C4×C61—24no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C42×C61—24no—
213C42×C61—21no—
214C42×C61—21no—
215C22⋊Dic61—42no—
216#11758201—216no—
217#11758201—216no—
218#11758201—48no—
219#11758198—44no—
220#11758198—44no—
221#11758198—82no—
222C4⋊Dic61—22no—
223C4⋊Dic61—22no—
224C2×#92418—28no—
225C2×#92418—22no—
226C2×#92418—22no—
227C2×#92418—22no—
228C2×#92418—22no—
229C2×#92418—22no—
230C2×#92418C2×D414yes—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—21no—
234C23×C61—22no—
235C23×C61—21no—
236C23×C61—22no—
237C23×C61#12012yes—
238C23×C61C2×SD1612yes—
239C23×C61C2×SD1612yescomplemented
240C23×C61#13712yes—
241C23×C61C22×D411yescharacteristic
242C22×D61—24no—
243C22×D61—48no—
244C22×D61—42no—
245C22×D61—42no—
246C22×D61—42no—
247C22×D61—42no—
248C22×D61—42no—
249C22×D61—42no—
250C22×D61—88no—
251C22×D61—88no—
252C22×D61—84no—
253C22×D61—84no—
254Q8×C61—22no—
255Q8×C61—24no—
256Q8×C61—22no—
257Q8×C61—22no—
258Q8×C61—24no—
259Q8×C61—48no—
260Q8×C61—48no—
261Q8×C61—41no—
262Q8×C61—41no—
263Q8×C61—42no—
264Q8×C61#12014yescomplemented
265D4×C61—28no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—24no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—21no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—21no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—48no—
282C2×C4×C61—48no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—42no—
289C2×C4×C61#12012yes—
290C2×C4×C61C2×SD1612yescomplemented
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C22×D412yes—
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61H(5,𝔽2)12yes—
295C22⋊D61—88no—
296C2×Dic61—42no—
297C2×Dic61—42no—
298C2×Dic61—42no—
299D244—24no—
300D244—24no—
301D244—48no—
302D244—42no—
303D244—42no—
304#92418—24no—
305#92418—42no—
306#23855—611nomaximal, Sylow
307C22×C61—22no—
308C22×C61—22no—
309C22×C61—24no—
310C22×C61—24no—
311C22×C61—22no—
312C22×C61—24no—
313C22×C61—41no—
314C22×C61—41no—
315C22×C61—42no—
316C22×C61#44814yescomplemented
317C22×C61C2×#12011yescharacteristic
318C22×C61D4212yes—
319C22×C61C22×SD1611yescharacteristic
320C22×C61C2×#13711yescharacteristic
321C22×C61#57712yes—
322C2×D61—44no—
323C2×D61—44no—
324C2×D61—44no—
325C2×D61—816no—
326C2×D61—82no—
327C2×D61—82no—
328C2×D61—82no—
329C2×D61—82no—
330C4×C61—22no—
331C4×C61—24no—
332C4×C61—22no—
333C4×C61—41no—
334C4×C61—42no—
335C4×C61—42no—
336C4×C61—41no—
337C4×C61—42no—
338C4×C61C2×#12011yescharacteristic
339C4×C61#53411yescharacteristic
340C4×C61D4212yes—
341Dic61—82no—
342C23×SD16—611no—
343C2×D4×Q8D6111yescharacteristic, complemented
344C2×#448—612no—
345C2×#450—611no—
346#2408—611no—
347#2013—612no—
348#2000—612no—
349#1892—611no—
350#1880—612no—
351#1869—611no—
352#1787—611no—
353C2×C61—24no—
354C2×C61—42no—
355C2×C61#240311yescharacteristic
356C2×C61C2×#44811yescharacteristic
357C2×C61#301011yescharacteristic
358C2×C61#326612yes—
359C2×C61D4×SD1612yes—
360D61—84no—
361C23×Q8C2×D6111yescharacteristic
362C23×Q8C2×D6111yescharacteristic, complemented
363C23×D4—611no—
364C22×SD16—612no—
365C22×SD16—612no—
366C22×SD16—612no—
367C22×SD16—1228no—
368C22×SD16—1224no—
369C23×C8—611no—
370D4×Q8—24no—
371D4×Q8—24no—
372C2×C4⋊Q8—21no—
373C2×C4⋊Q8C2×D6111yescharacteristic, complemented
374C2×C22⋊Q8—21no—
375C2×C22⋊Q8—21no—
376C2×C22⋊Q8C2×D6111yescharacteristic
377C2×C22⋊Q8C2×D6111yescharacteristic, complemented
378C2×#121—612no—
379C2×#120—1221no—
380C2×C4×Q8C2×D6111yescharacteristic, complemented
381C2×C4×D4—21no—
382C2×C4×D4C2×D6111yescharacteristic
383#450—1224no—
384#448—1228no—
385C2×#103—612no—
386C2×#103—612no—
387C2×#103—612no—
388C2×#102—612no—
389C2×C22⋊C8—611no—
390C2×C22⋊C8—612no—
391#394—1221no—
392#392—1221no—
393#390—612no—
394#380—611no—
395#379—1221no—
396#340—612no—
397#336—612no—
398C61#2385511yescharacteristic, complemented, Sylow
399C25—1221no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8—22no—
405C22×Q8—24no—
406C22×Q8—24no—
407C22×Q8—42no—
408C22×Q8—42no—
409C22×Q8C22⋊D6114yescomplemented
410C22×Q8C22×D6111yescharacteristic
411C22×Q8C22×D6111yescharacteristic
412C22×Q8C22×D6111yescharacteristic
413C22×D4—612no—
414C22×D4—1224no—
415C22×D4—1222no—
416C22×D4—1222no—
417C22×D4—1222no—
418C22×D4—1221no—
419C22×D4—2442no—
420C22×D4C22⋊D6111yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4C22×D6111yescharacteristic
424C23×C4C22×D6111yescharacteristic
425C2×SD16—618no—
426C2×SD16—1224no—
427C2×SD16—1224no—
428C2×SD16—12232no—
429C2×SD16—1224no—
430C2×SD16—1224no—
431C2×SD16—1224no—
432C2×SD16—1224no—
433C2×SD16—1224no—
434C2×SD16—2442no—
435C22×C8—612no—
436C22×C8—612no—
437C22×C8—1224no—
438C22×C8—1222no—
439C4⋊Q8—28no—
440C4⋊Q8—22no—
441C4⋊Q8—22no—
442C22⋊Q8—28no—
443C22⋊Q8—28no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8C22⋊D6114yescomplemented
448#121—1224no—
449#121—2442no—
450#120—2444no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×D4—28no—
454C4×D4—22no—
455C4×D4—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—612no—
462C2×C4⋊C4C22⋊D6111yescharacteristic
463C2×C4⋊C4C22×D6111yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1222no—
467C2×C22⋊C4—1221no—
468C2×C22⋊C4—1222no—
469C2×C22⋊C4—1222no—
470C2×C22⋊C4C22⋊D6111yescharacteristic
471C2×C22⋊C4C22⋊D6111yescharacteristic
472C2×C42—21no—
473C2×C42C22×D6111yescharacteristic
474#103—1224no—
475#103—1224no—
476#103—2442no—
477#102—1224no—
478C22⋊C8—1224no—
479C22⋊C8—1222no—
480#95—1221no—
481C24—1222no—
482C24—4882no—
483C24—2444no—
484C24—2442no—
485C24—2442no—
486C24—2442no—
487C24C2×C22⋊D6111yescharacteristic
488C24C2×C22⋊D6111yescharacteristic
489C2×Q8—24no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—22no—
494C2×Q8—24no—
495C2×Q8—28no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—48no—
504C2×Q8—48no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8D4×D6114yes—
508C2×Q8C2×C22⋊D6112yes—
509C2×Q8C2×C22⋊D6112yes—
510C2×Q8C2×C22⋊D6112yes—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—614no—
514C2×D4—1228no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1222no—
519C2×D4—1222no—
520C2×D4—4882no—
521C2×D4—2448no—
522C2×D4—2444no—
523C2×D4—2444no—
524C2×D4—2444no—
525C2×D4—2444no—
526C2×D4—2442no—
527C2×D4#1175820114yescomplemented
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—1222no—
543C22×C4C2×C22⋊D6111yescharacteristic
544C22×C4C2×C22⋊D6111yescharacteristic
545C22×C4C2×C22⋊D6112yes—
546C22×C4C2×C22⋊D6112yes—
547C22×C4C2×C22⋊D6111yescharacteristic
548C22×C4C2×C22⋊D6111yescharacteristic
549C22×C4C23×D6111yescharacteristic
550SD16—12216no—
551SD16—12216no—
552SD16—2448no—
553C2×C8—614no—
554C2×C8—1228no—
555C2×C8—1222no—
556C2×C8—1222no—
557C2×C8—1222no—
558C2×C8—1222no—
559C2×C8—1222no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—24no—
566C4⋊C4—22no—
567C4⋊C4—1222no—
568C4⋊C4—1222no—
569C4⋊C4C2×C22⋊D6112yes—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—4882no—
575C22⋊C4—2444no—
576C22⋊C4—2442no—
577C22⋊C4—2444no—
578C42—24no—
579C42—21no—
580C42—21no—
581C23—22no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—22no—
587C23—1224no—
588C23—4884no—
589C23—4888no—
590C23—4888no—
591C23—4884no—
592C23—2448no—
593C23—2442no—
594C23—2442no—
595C23—2442no—
596C23—2442no—
597C23—2442no—
598C23—2442no—
599C23#1451974612yes—
600C23C2×#1175820112yes—
601C23C2×#1175820112yescomplemented
602C23#1451980812yes—
603C23C22×C22⋊D6111yescharacteristic
604Q8—22no—
605Q8—24no—
606Q8—22no—
607Q8—22no—
608Q8—24no—
609Q8—48no—
610Q8—48no—
611Q8—41no—
612Q8—41no—
613Q8—42no—
614Q8#1451974514yescomplemented
615D4—28no—
616D4—1224no—
617D4—1224no—
618D4—4888no—
619D4—2448no—
620D4—2442no—
621D4—2442no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—48no—
638C2×C4—48no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—2442no—
646C2×C4—2442no—
647C2×C4—2442no—
648C2×C4#1451974612yes—
649C2×C4C2×#1175820112yescomplemented
650C2×C4C2×D4×D6112yes—
651C2×C4C22×C22⋊D6111yescharacteristic
652C2×C4C22×C22⋊D6111yescharacteristic
653C2×C4#1451982212yes—
654C8—1224no—
655C8—2442no—
656C22—22no—
657C22—24no—
658C22—22no—
659C22—24no—
660C22—24no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—48816no—
666C22—4882no—
667C22—4882no—
668C22—4882no—
669C22—4882no—
670C22—2444no—
671C22—2444no—
672C22—2444no—
673C22#1683990114yescomplemented
674C22C2×#1451974611yescharacteristic
675C22D4×C22⋊D6112yes—
676C22C22×#1175820111yescharacteristic
677C22C2×#1451980811yescharacteristic
678C22#1684057012yes—
679C4—22no—
680C4—22no—
681C4—24no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—42no—
687C4—4882no—
688C4C2×#1451974511yescharacteristic
689C4#1684032111yescharacteristic
690C4D4×C22⋊D6112yes—
691C2—24no—
692C2—42no—
693C2—4884no—
694C2#2144912911yescharacteristic
695C2C2×#1683990111yescharacteristic
696C2#2145510511yescharacteristic
697C2#2145733012yes—
698C2D4×#1175820112yes—
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×D4×Q8×C61C2
socleC23×C61C22×D4
prime radical#21449175C2
hypercenterC2×D4×Q8D61
hypocenterC61#23855
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C23×#11758201C2semidirect
2. C2×#16839901C2semidirect
3. C2×#16839912C2semidirect
5. #21446902C2semidirect
6. #21446820C2semidirect
7. #21446243C2semidirect
8. #21446174C2semidirect
9. #21446112C2semidirect
10. #21445754C2semidirect
11. C2×D4×Q8×C61C2semidirect
23. C2×#14519701C22semidirect
24. C2×#14519701C22semidirect
25. C2×#14519701C22semidirect
28. C2×C22⋊#92418C22semidirect
34. #16839524C22semidirect
35. #16839517C22semidirect
37. C23×Q8×C61C22semidirect
41. C2×C4⋊Q8×C61C22semidirect
45. C2×C22⋊Q8×C61C22semidirect
46. C2×C4×Q8×C61C22semidirect
66. C2×#11758201D4semidirect
95. C22×Q8×C61D4semidirect
112. C22⋊Q8×C61D4semidirect
163. C2×D4×C61SD16semidirect
239. C23×C61C2×SD16semidirect
264. Q8×C61#120semidirect
290. C2×C4×C61C2×SD16semidirect
316. C22×C61#448semidirect
343. C2×D4×Q8D61semidirect
362. C23×Q8C2×D61semidirect
373. C2×C4⋊Q8C2×D61semidirect
377. C2×C22⋊Q8C2×D61semidirect
380. C2×C4×Q8C2×D61semidirect
398. C61#23855semidirect
409. C22×Q8C22⋊D61semidirect
447. C22⋊Q8C22⋊D61semidirect
527. C2×D4#11758201semidirect
601. C23C2×#11758201semidirect
614. Q8#14519745semidirect
649. C2×C4C2×#11758201semidirect
673. C22#16839901semidirect

Maximal subgroups

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

subgroupindex
C23×#117582012
C2×#168399012
C2×#168399122
#214491752
#214469022
#214468202
#214462432
#214461742
#214461122
#214457542
C2×D4×Q8×C612
#2385561