Finite Group Databasebeta

← #30616896

Subgroups — #30616896

Order 15616.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840841C211yesmaximal, characteristic, complemented
2C2×#16840807C211yesmaximal, characteristic, complemented
3C2×#16840804C211yesmaximal, characteristic, complemented
4#21462537C211yesmaximal, characteristic, complemented
5#21461811C211yesmaximal, characteristic, complemented
6#21461810C211yesmaximal, characteristic, complemented
7#21461802C211yesmaximal, characteristic, complemented
8#21461787C211yesmaximal, characteristic, complemented
9#21461786C211yesmaximal, characteristic, complemented
10#21461771C211yesmaximal, characteristic, complemented
11#21461661C211yesmaximal, characteristic, complemented
12#21461598C211yesmaximal, characteristic, complemented
13#21461596C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic, complemented
15#21455034C211yesmaximal, characteristic
16#16840841—24no—
17#16840841—24no—
18C2×#14519865C2211yescharacteristic
19C2×#14519865C2211yescharacteristic
20C2×#14519864—21no—
21C2×#14519864—21no—
22C2×#14519864C2211yescharacteristic
23C2×#14519864C2211yescharacteristic
24C2×#14519864C2211yescharacteristic, complemented
25C22×#11758213—21no—
26C22×#11758213C2211yescharacteristic
27C2×D61⋊M16—21no—
28C2×D61⋊M16C2211yescharacteristic
29#16840807—24no—
30#16840804—24no—
31#16840797—21no—
32#16840795—21no—
33#16840793—21no—
34#16840791—21no—
35C2×#14519848C2211yescharacteristic, complemented
36C2×#14519848C2211yescharacteristic, complemented
37#16840769C2211yescharacteristic, complemented
38C2×#14519842C2211yescharacteristic
39C2×#14519842C2211yescharacteristic
40C2×#14519841C2211yescharacteristic
41C2×#14519841C2211yescharacteristic
42C2×#14519841C2211yescharacteristic, complemented
43C2×#14519841C2211yescharacteristic, complemented
44#16840736C2211yescharacteristic, complemented
45#16840733C2211yescharacteristic
46#16840727C2211yescharacteristic, complemented
47C2×#14519831C2211yescharacteristic, complemented
48C2×C8×#6923C2211yescharacteristic, complemented
49C4×C22⋊#6923C2211yescharacteristic
50#16840638C2211yescharacteristic, complemented
51#16840638C2211yescharacteristic, complemented
52#16840632C2211yescharacteristic, complemented
53#16840632C2211yescharacteristic, complemented
54(C2×#6923)⋊C8C2211yescharacteristic, complemented
55(C2×#6923)⋊C8C2211yescharacteristic, complemented
56C2×#41×D61C2211yescharacteristic
57C2×#14519798C2211yescharacteristic
58C2×#14519796C2211yescharacteristic
59#16840272C2211yescharacteristic
60#16839926C411yescharacteristic, complemented
61#16839924C411yescharacteristic, complemented
62#16839919C411yescharacteristic, complemented
63#16839914C411yescharacteristic, complemented
64#16839905C411yescharacteristic, complemented
65#16839899C411yescharacteristic, complemented
66#16839894C411yescharacteristic, complemented
67#16839757C2211yescharacteristic
68#16839755C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#449C411yescharacteristic, complemented
71#14519865—22no—
72#14519865—22no—
73#14519865—22no—
74#14519865D414yescomplemented
75#14519864—28no—
76#14519864—28no—
77#14519864—22no—
78#14519864—22no—
79#14519864—22no—
80#14519864—22no—
81#14519864—22no—
82#14519864D414yescomplemented
83C2×#11758213—28no—
84C2×#11758213—21no—
85C2×#11758213—21no—
86C2×#11758213—21no—
87C2×#11758213—22no—
88C2×#11758213—22no—
89C2×#11758213D411yescharacteristic
90C2×#11758213D411yescharacteristic
91C2×#11758213C2311yescharacteristic
92C2×#11758213C2311yescharacteristic
93C2×#11758213C2311yescharacteristic
94C2×#11758213C2311yescharacteristic
95D61⋊M16—28no—
96D61⋊M16—22no—
97D61⋊M16—22no—
98C2×#11758217—21no—
99C2×#11758217—21no—
100C2×#11758217—21no—
101C2×#11758217D411yescharacteristic
102C2×#11758217D411yescharacteristic
103C2×D61⋊C8—21no—
104C2×D61⋊C8—21no—
105C2×D61⋊C8C2311yescharacteristic
106C2×D61⋊C8C2311yescharacteristic
107C22×#92420—21no—
108C22×#92420—21no—
109C22×#92420—21no—
110C22×#92420—21no—
111C2×C22⋊#6923—21no—
112C2×C4×#6923C2311yescharacteristic
113C2×C4×#6923C2311yescharacteristic
114#14519848—22no—
115#14519848—22no—
116#14519844—21no—
117C4⋊#92420—21no—
118#14519842—22no—
119#14519842—22no—
120#14519841—22no—
121#14519841—22no—
122#14519841—22no—
123#14519841—22no—
124#14519834—21no—
125C22⋊#92420—21no—
126C22⋊#92420—21no—
127C22⋊#92420—21no—
128#14519832—21no—
129#14519831—22no—
130C4×#92420—21no—
131C8×#6923—22no—
132(C2×#6923)⋊C4—21no—
133C2×#11758226C2311yescharacteristic
134C2×#11758222—21no—
135C2×#11758222C2×C411yescharacteristic
136C2×#11758224—21no—
137C2×#11758224C2311yescharacteristic
138C2×#11758224C2311yescharacteristic
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142#41×D61—22no—
143C2×Q8×D61C2×C411yescharacteristic
144C2×D4×D61—21no—
145C2×D4×D61C2×C411yescharacteristic
146C22×C4×D61—21no—
147C22×C4×D61C2311yescharacteristic
148#14519798—22no—
149#14519798—22no—
150#14519796—22no—
151#14519796—22no—
152C2×Dic244C2×C411yescharacteristic
153C2×#11758202C2×C411yescharacteristic
154C2×#11758190C2×C411yescharacteristic
155C2×#11758200C2×C411yescharacteristic
156C2×#11758200C2×C411yescharacteristic
157C2×#11758199C2×C411yescharacteristic
158C2×C8×D61C2311yescharacteristic
159C2×C8×D61C2311yescharacteristic
160#14519759—21no—
161#14519757C2×C411yescharacteristic
162#14519756C2×C411yescharacteristic
163#14519748C2×C411yescharacteristic
164#14519745—21no—
165D4×Dic61—21no—
166#14519737—21no—
167#14519735C2311yescharacteristic
168#14519702C2×C411yescharacteristic
169#14519701C2×C411yescharacteristic
170#14519700C2×C411yescharacteristic
171#14519699C2×C411yescharacteristic
172#14519698C2×C411yescharacteristic
173#14519697C2×C411yescharacteristic
174C22⋊#92418C2×C411yescharacteristic
175#14519689C2×C411yescharacteristic
176#14519689C2×C411yescharacteristic
177C2×#41×C61C2×C411yescharacteristic
178C2×SD16×C61C2×C411yescharacteristic
179C2×D8×C61C2×C411yescharacteristic
180#121×C61C2×C411yescharacteristic
181#103×C61C2×C411yescharacteristic
182#102×C61C2×C411yescharacteristic
183C22⋊C8×C61C2×C411yescharacteristic
184C23×D61—21no—
185C23×D61#4111yescharacteristic
186C22×#6923—21no—
187C22×#6923—21no—
188#41×C61—22no—
189#41×C61—22no—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61C22×C411yescharacteristic
194C2×D4×C61C22×C411yescharacteristic
195C22×C4×C61—21no—
196C22×C4×C61C22×C411yescharacteristic
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61C2×D411yescharacteristic
205#11758226—21no—
206#11758226—21no—
207#11758226C2×D412yes—
208#11758226#4112yes—
209Q8×D61—22no—
210Q8×D61—22no—
211#11758224—24no—
212#11758224—24no—
213#11758224—21no—
214#11758224—21no—
215#11758224—21no—
216#11758224—21no—
217#11758224—21no—
218#11758224—21no—
219#11758224C2×D412yes—
220#11758224#4112yes—
221D4×D61—24no—
222D4×D61—24no—
223D4×D61—22no—
224D4×D61—22no—
225#11758222—24no—
226#11758222—24no—
227#11758222—22no—
228#11758222—22no—
229C2×D244—21no—
230C2×D244C22×C411yescharacteristic
231C2×C4×D61—24no—
232C2×C4×D61—24no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61C22×C411yescharacteristic
241C2×C4×D61C2×D411yescharacteristic
242C2×C4×D61#4111yescharacteristic
243C2×C4×D61C2411yescharacteristic
244C2×Dic122—21no—
245C2×Dic122C22×C411yescharacteristic
246C2×Dic122C22×C411yescharacteristic
247C22⋊#6923—42no—
248#11758217—24no—
249#11758217—24no—
250#11758217—22no—
251#11758217—22no—
252#11758217—42no—
253C2×#92420—24no—
254C2×#92420—24no—
255C2×#92420—21no—
256C2×#92420—21no—
257C2×#92420—24no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—42no—
261C2×#92420C2×D411yescharacteristic
262C2×#92420C2×D411yescharacteristic
263C2×#92420C2×D411yescharacteristic
264C2×#92420C2×D411yescharacteristic
265C4×#6923—21no—
266C4×#6923—21no—
267C4×#6923—21no—
268C4×#6923—21no—
269#11758213—24no—
270#11758213—24no—
271#11758213—21no—
272#11758213—21no—
273#11758213—22no—
274#11758213—22no—
275#11758213—24no—
276#11758213—21no—
277#11758213—21no—
278#11758213—21no—
279#11758213—21no—
280#11758213C2×D412yes—
281#11758213C2×D412yes—
282D61⋊C8—24no—
283D61⋊C8—21no—
284D61⋊C8—21no—
285D61⋊C8—24no—
286D61⋊C8C2×D412yes—
287D61⋊C8C2×D412yes—
288SD16×C61—22no—
289D8×C61—22no—
290C2×C8×C61C22×C411yescharacteristic
291C2×C8×C61C22×C411yescharacteristic
292C4⋊C4×C61C22×C411yescharacteristic
293C22⋊C4×C61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296#11758202—22no—
297#11758200—22no—
298#11758200—22no—
299#11758199—22no—
300#11758198—21no—
301#11758198—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61C22×C411yescharacteristic
304#11758196—21no—
305C4×Dic61—21no—
306C2×#92418C22×C411yescharacteristic
307C2×#92418C22×C411yescharacteristic
308Dic244—22no—
309#11758190—22no—
310C8×D61—21no—
311C8×D61—21no—
312C8×D61—21no—
313C8×D61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61C4×D411yescharacteristic
317C22×D61—21no—
318C22×D61—24no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—81no—
324C22×D61—81no—
325C22×D61C4×D411yescharacteristic
326C22×D61C2×#4111yescharacteristic
327C2×#6923—22no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333Q8×C61—21no—
334Q8×C61C4×D412yes—
335D4×C61—24no—
336D4×C61—21no—
337D4×C61—21no—
338D4×C61—21no—
339D4×C61—81no—
340D4×C61C4×D412yes—
341C2×C4×C61—24no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61C4×D411yescharacteristic
347C2×C4×C61C23×C411yescharacteristic
348C22⋊D61—24no—
349C22⋊D61—24no—
350C22⋊D61—22no—
351C22⋊D61—22no—
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—81no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—22no—
358C2×Dic61—21no—
359C2×Dic61—22no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61C4×D411yescharacteristic
365C2×Dic61C22×D411yescharacteristic
366D244—22no—
367D244—22no—
368D244—21no—
369D244C4×D412yes—
370C4×D61—24no—
371C4×D61—24no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—22no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—22no—
380C4×D61C22×D411yescharacteristic
381C4×D61C22×D411yescharacteristic
382C4×D61C2×#4111yescharacteristic
383C4×D61C2×#4111yescharacteristic
384Dic122—24no—
385Dic122—21no—
386Dic122—21no—
387Dic122—21no—
388Dic122C4×D412yes—
389#92420—21no—
390#92420—21no—
391#92420—22no—
392#92420—22no—
393#92420—41no—
394#92420—41no—
395#92420#12012yes—
396#92420#12012yes—
397C8×C61—21no—
398C8×C61—21no—
399#92418—21no—
400#92418—21no—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—22no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61C2×C4×D411yescharacteristic
412C2×D61—21no—
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—22no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—81no—
421C2×D61—81no—
422C2×D61—84no—
423C2×D61#52511yescharacteristic
424C2×D61#52511yescharacteristic
425#6923—42no—
426#6923—81no—
427C4×C61—22no—
428C4×C61—21no—
429C4×C61—41no—
430C4×C61C2×C4×D411yescharacteristic
431C4×C61C2×C4×D411yescharacteristic
432Dic61—21no—
433Dic61—22no—
434Dic61—41no—
435Dic61—41no—
436Dic61C2×#12011yescharacteristic
437Dic61#52511yescharacteristic
438C2×#568—611no—
439#3002—611no—
440C2×#444—611no—
441C2×#443—611no—
442#2930—611no—
443#1876—611no—
444#1876—611no—
445#1871—611no—
446#1866—611no—
447#1866—611no—
448#1855—611no—
449#1789—611no—
450#1765—611no—
451#1764—611no—
452#1753—611no—
453C2×C61—41no—
454C2×C61—42no—
455C2×C61—81no—
456C2×C61C4×#12011yescharacteristic
457C2×C61#295611yescharacteristic
458C2×C61#295711yescharacteristic
459D61—21no—
460D61—21no—
461D61—41no—
462D61—42no—
463C22×#41—611no—
464C2×#135—611no—
465C2×#135—611no—
466#568—1224no—
467#568—1224no—
468C2×#131—611no—
469C2×#131—611no—
470C2×#131—611no—
471C2×#131—611no—
472C2×#131—611no—
473C2×#131—1221no—
474C2×#131—1221no—
475C22×M16—611no—
476C22×M16—611no—
477C22×M16—1221no—
478C22×M16—1221no—
479#525—611no—
480#452—611no—
481#452—611no—
482#451—611no—
483#450—611no—
484#449—611no—
485#449#692311yescharacteristic, complemented
486#448—611no—
487#447—611no—
488#444—1224no—
489#443—1224no—
490#436—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494C2×#108—611no—
495C2×#108—611no—
496#424—611no—
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104—611no—
503#416—611no—
504#416—611no—
505#408—611no—
506#407—611no—
507C2×C22⋊C8—611no—
508#405—611no—
509C2×#97—611no—
510C2×C4×C8—611no—
511C4×C22⋊C4—611no—
512#341—611no—
513#341—611no—
514#339—611no—
515#339—611no—
516#336—611no—
517#336—611no—
518C61#2146811yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—611no—
523C2×#41—1221no—
524C2×#41—1221no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1222no—
529C2×#41C2×#692311yescharacteristic
530C22×Q8—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C23×C4—611no—
534C23×C4—1221no—
535#135—1222no—
536#135—1222no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16—611no—
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16—611no—
544C2×SD16C2×#692311yescharacteristic
545C2×D8—611no—
546C2×D8C2×#692311yescharacteristic
547#131—614no—
548#131—614no—
549#131—1222no—
550#131—1222no—
551#131—1222no—
552#131—1222no—
553#131—1222no—
554#131—1222no—
555#131—1222no—
556#131—1222no—
557#131—1228no—
558#131—1228no—
559C2×M16—611no—
560C2×M16—611no—
561C2×M16—611no—
562C2×M16—611no—
563C2×M16—611no—
564C2×M16—611no—
565C2×M16—611no—
566C2×M16—611no—
567C2×M16—1221no—
568C2×M16—1221no—
569C2×M16—1222no—
570C2×M16—1222no—
571C2×M16—1221no—
572C2×M16—1221no—
573C2×M16—1221no—
574C2×M16—1222no—
575C2×M16—1222no—
576C2×M16—1221no—
577C2×M16—1228no—
578C2×M16—1228no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—611no—
583C22×C8—1221no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C22×C8—1221no—
588C22×C8—1221no—
589#123—1221no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592#121—611no—
593#121C2×#692311yescharacteristic
594#120—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117—611no—
598C2×C22⋊C4—1221no—
599C2×C42—611no—
600C2×C42—611no—
601#108—1222no—
602#108—1222no—
603C4⋊C8—1221no—
604C4⋊C8—1221no—
605#104—1222no—
606#104—1222no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103—611no—
614#103C2×#692311yescharacteristic
615#102—611no—
616#102—611no—
617#102—611no—
618#102C2×#692311yescharacteristic
619C22⋊C8—611no—
620C22⋊C8—611no—
621C22⋊C8—611no—
622C22⋊C8—1221no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8C2×#692311yescharacteristic
627#97—1222no—
628#97—1221no—
629C4×C8—1222no—
630C4×C8—1221no—
631#95—1221no—
632C24—611no—
633C24—1221no—
634#41—22no—
635#41—22no—
636#41—612no—
637#41—612no—
638#41—612no—
639#41—612no—
640#41—1222no—
641#41—1222no—
642#41—1224no—
643#41—1224no—
644#41—1221no—
645#41—1221no—
646#41—1221no—
647#41—1221no—
648#41—1221no—
649#41—1221no—
650#41—1221no—
651#41—1221no—
652#41—1224no—
653#41—1224no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—1221no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8C22×#692311yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—611no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1222no—
666C2×D4—1224no—
667C2×D4—1224no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1222no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4C22×#692311yescharacteristic
674C2×D4C22×#692311yescharacteristic
675C22×C4—21no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1224no—
688C22×C4—1224no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4C22×#692311yescharacteristic
695Q16—1222no—
696Q16—1222no—
697SD16—22no—
698SD16—1222no—
699SD16—1222no—
700SD16—1222no—
701D8—22no—
702D8—1222no—
703M16—612no—
704M16—612no—
705M16—1222no—
706M16—1222no—
707M16—1222no—
708M16—1222no—
709M16—1224no—
710M16—1224no—
711M16—1221no—
712M16—1221no—
713M16—1224no—
714M16—1224no—
715M16—1224no—
716M16—1221no—
717M16—1221no—
718M16—1221no—
719M16—1221no—
720M16—2442no—
721C2×C8—611no—
722C2×C8—612no—
723C2×C8—611no—
724C2×C8—612no—
725C2×C8—611no—
726C2×C8—611no—
727C2×C8—611no—
728C2×C8—611no—
729C2×C8—1221no—
730C2×C8—1221no—
731C2×C8—1221no—
732C2×C8—1221no—
733C2×C8—1224no—
734C2×C8—1224no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1224no—
740C2×C8—1224no—
741C2×C8—1224no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—2442no—
745C2×C8C22×#692311yescharacteristic
746C2×C8C22×#692311yescharacteristic
747C4⋊C4—611no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4C22×#692311yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—2442no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C23—21no—
763C23—21no—
764C23—611no—
765C23—611no—
766C23—1221no—
767C23—1221no—
768C23—1224no—
769C23—1221no—
770C23—4881no—
771C23—4881no—
772C23—2441no—
773C23—2441no—
774C23D4×#692311yescharacteristic
775Q8—21no—
776Q8—612no—
777Q8—1224no—
778Q8—1221no—
779Q8—1221no—
780Q8—1221no—
781Q8D4×#692312yes—
782D4—24no—
783D4—21no—
784D4—21no—
785D4—21no—
786D4—81no—
787D4—612no—
788D4—1222no—
789D4—1222no—
790D4—1222no—
791D4—1222no—
792D4—1224no—
793D4—1224no—
794D4—1221no—
795D4—4881no—
796D4—2441no—
797D4—2441no—
798D4D4×#692312yes—
799C2×C4—24no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—1222no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1222no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1224no—
817C2×C4—1224no—
818C2×C4—1221no—
819C2×C4—1222no—
820C2×C4—1221no—
821C2×C4—1222no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1222no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4D4×#692311yescharacteristic
836C2×C4C23×#692311yescharacteristic
837C8—21no—
838C8—21no—
839C8—612no—
840C8—612no—
841C8—1221no—
842C8—1221no—
843C8—1222no—
844C8—1222no—
845C8—1221no—
846C8—1221no—
847C8—2441no—
848C8—2441no—
849C22—21no—
850C22—22no—
851C22—21no—
852C22—21no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—611no—
859C22—611no—
860C22—1221no—
861C22—1221no—
862C22—1221no—
863C22—1222no—
864C22—1221no—
865C22—1221no—
866C22—4881no—
867C22—4881no—
868C22—4884no—
869C22—2441no—
870C22—2441no—
871C22C2×D4×#692311yescharacteristic
872C4—21no—
873C4—22no—
874C4—41no—
875C4—611no—
876C4—611no—
877C4—1221no—
878C4—1222no—
879C4—4881no—
880C4—2442no—
881C4—2441no—
882C4—2441no—
883C4C2×D4×#692311yescharacteristic
884C4C2×D4×#692311yescharacteristic
885C2—41no—
886C2—42no—
887C2—81no—
888C2—1221no—
889C2—1221no—
890C2—2441no—
891C2—2442no—
892C2#120×#692311yescharacteristic
893C2#2146259311yescharacteristic
894C2#2146259611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#21455034C2
cosocleC2×C4×D61C24
hypercenter#449#6923
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#16840841C2semidirect
2. C2×#16840807C2semidirect
3. C2×#16840804C2semidirect
4. #21462537C2semidirect
5. #21461811C2semidirect
6. #21461810C2semidirect
7. #21461802C2semidirect
8. #21461787C2semidirect
9. #21461786C2semidirect
10. #21461771C2semidirect
11. #21461661C2semidirect
12. #21461598C2semidirect
13. #21461596C2semidirect
14. #21461562C2semidirect
24. C2×#14519864C22semidirect
35. C2×#14519848C22semidirect
36. C2×#14519848C22semidirect
37. #16840769C22semidirect
42. C2×#14519841C22semidirect
43. C2×#14519841C22semidirect
44. #16840736C22semidirect
46. #16840727C22semidirect
47. C2×#14519831C22semidirect
48. C2×C8×#6923C22semidirect
50. #16840638C22semidirect
51. #16840638C22semidirect
52. #16840632C22semidirect
53. #16840632C22semidirect
54. (C2×#6923)⋊C8C22semidirect
55. (C2×#6923)⋊C8C22semidirect
60. #16839926C4semidirect
61. #16839924C4semidirect
62. #16839919C4semidirect
63. #16839914C4semidirect
64. #16839905C4semidirect
65. #16839899C4semidirect
66. #16839894C4semidirect
70. C61×#449C4semidirect
74. #14519865D4semidirect
82. #14519864D4semidirect
485. #449#6923semidirect
518. C61#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#168408412
C2×#168408072
C2×#168408042
#214625372
#214618112
#214618102
#214618022
#214617872
#214617862
#214617712
#214616612
#214615982
#214615962
#214615622
#214550342
#2146861