Finite Group Databasebeta

← #29685872

Subgroups — #29685872

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×#16840527C211yesmaximal, characteristic, complemented
2#21455033C211yesmaximal, characteristic
3C2×#16839877C211yesmaximal, characteristic, complemented
4#21454520C211yesmaximal, characteristic, complemented
5#21446148C211yesmaximal, characteristic, complemented
6#21446143C211yesmaximal, characteristic, complemented
7#21446118C211yesmaximal, characteristic, complemented
8#21446092C211yesmaximal, characteristic, complemented
9#21446091C211yesmaximal, characteristic, complemented
10#21446022C211yesmaximal, characteristic, complemented
11#21445761C211yesmaximal, characteristic, complemented
12#21445663C211yesmaximal, characteristic, complemented
13#21445654C211yesmaximal, characteristic, complemented
14#21445604C211yesmaximal, characteristic, complemented
15C2×C61×#444C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18#16840527—24no—
19#16840527—24no—
20C2×#14519785—21no—
21C2×#14519785C2211yescharacteristic
22C2×#14519784C2211yescharacteristic
23C2×#14519783—21no—
24C2×#14519783C2211yescharacteristic
25C22×#11758189—21no—
26C22×#11758189C2211yescharacteristic
27C2×M16×D61—21no—
28C2×M16×D61C2211yescharacteristic
29#16840269C2211yescharacteristic
30#16839923C411yescharacteristic, complemented
31#16839921C411yescharacteristic, complemented
32#16839916C411yescharacteristic, complemented
33#16839911C411yescharacteristic, complemented
34#16839906C411yescharacteristic, complemented
35#16839904C411yescharacteristic, complemented
36#16839899C411yescharacteristic, complemented
37#16839894C411yescharacteristic, complemented
38#16839877—24no—
39#16839838—21no—
40#16839838—21no—
41#16839833—21no—
42#16839833—21no—
43C2×#14519712C2211yescharacteristic, complemented
44#16839790C2211yescharacteristic, complemented
45C2×#14519705C2211yescharacteristic
46C2×#14519704C2211yescharacteristic
47C2×#14519704C2211yescharacteristic, complemented
48C2×#14519703C2211yescharacteristic
49#16839759C2211yescharacteristic
50#16839758C2211yescharacteristic
51#16839729C2211yescharacteristic, complemented
52#16839725C2211yescharacteristic
53C2×#14519689C2211yescharacteristic
54#16839717C2211yescharacteristic, complemented
55C2×C8×Dic61C2211yescharacteristic, complemented
56C4×#11758198C2211yescharacteristic
57#16839527C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839523C2211yescharacteristic, complemented
60#16839522C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62#16839516C2211yescharacteristic, complemented
63C2×#135×C61C2211yescharacteristic
64C2×#131×C61C2211yescharacteristic
65C2×#131×C61C2211yescharacteristic, complemented
66C61×#444—24no—
67C2×#108×C61C2211yescharacteristic, complemented
68C2×#104×C61C2211yescharacteristic
69C2×#104×C61C2211yescharacteristic, complemented
70C2×#97×C61C2211yescharacteristic, complemented
71C2×#11758226C2×C411yescharacteristic
72C2×#11758222—21no—
73C2×#11758222C2311yescharacteristic
74C2×#11758224—21no—
75C2×#11758224C2×C411yescharacteristic
76#41×D61—22no—
77#41×D61—22no—
78#41×D61—22no—
79#41×D61—22no—
80C2×Q8×D61C2×C411yescharacteristic
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85#14519797—22no—
86#14519797—22no—
87C2×#11758202C2×C411yescharacteristic
88C2×#11758200C2×C411yescharacteristic
89C2×#11758201C2×C411yescharacteristic
90C2×#11758199C2×C411yescharacteristic
91#14519785—28no—
92#14519785—22no—
93#14519785—22no—
94#14519784—22no—
95#14519784—22no—
96#14519783—28no—
97#14519783—22no—
98#14519783D414yescomplemented
99C2×#11758194—21no—
100C2×#11758194C2311yescharacteristic
101C2×#11758194C2311yescharacteristic
102C2×#11758189—28no—
103C2×#11758189—21no—
104C2×#11758189—21no—
105C2×#11758189—22no—
106C2×#11758189—22no—
107C2×#11758189—21no—
108C2×#11758189D411yescharacteristic
109C2×#11758189D411yescharacteristic
110C2×#11758189D411yescharacteristic
111C2×#11758189D411yescharacteristic
112M16×D61—28no—
113M16×D61—22no—
114M16×D61—22no—
115C22×#92418—21no—
116C22×#92418C2311yescharacteristic
117C22×#92418C2311yescharacteristic
118C2×C8×D61—21no—
119C2×C8×D61—21no—
120C2×C8×D61—21no—
121#14519758—21no—
122#14519753C2×C411yescharacteristic
123#14519753C2×C411yescharacteristic
124#14519748C2×C411yescharacteristic
125#14519748C2×C411yescharacteristic
126#14519745—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129#14519736C2311yescharacteristic
130C2×#11758198—21no—
131C2×C4×Dic61C2311yescharacteristic
132#14519712—22no—
133#14519706—21no—
134#14519706—21no—
135#14519705—22no—
136#14519704—22no—
137#14519704—22no—
138#14519703—22no—
139#14519702C2×C411yescharacteristic
140#14519702C2×C411yescharacteristic
141#14519701C2×C411yescharacteristic
142#14519701C2×C411yescharacteristic
143#14519699C2×C411yescharacteristic
144#14519699C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic
146#14519698C2×C411yescharacteristic
147C22⋊#92418—21no—
148C22⋊#92418—21no—
149#14519689—21no—
150#14519689—21no—
151#14519689C2×C411yescharacteristic
152#14519689C2×C411yescharacteristic
153#14519689C2×C411yescharacteristic
154#14519689C2×C411yescharacteristic
155#14519687—21no—
156C8×Dic61—22no—
157C8×Dic61—21no—
158#14519684—21no—
159C2×#41×C61C2311yescharacteristic
160C2×#41×C61C2311yescharacteristic
161#135×C61—22no—
162#135×C61—22no—
163C2×Q16×C61C2×C411yescharacteristic
164C2×SD16×C61C2×C411yescharacteristic
165C2×SD16×C61C2×C411yescharacteristic
166C2×D8×C61C2×C411yescharacteristic
167#131×C61—22no—
168#131×C61—22no—
169#131×C61—22no—
170#131×C61D414yescomplemented
171C2×M16×C61—21no—
172C2×M16×C61—21no—
173C2×M16×C61C2311yescharacteristic
174C2×M16×C61C2311yescharacteristic
175C22×C8×C61—21no—
176C22×C8×C61—21no—
177C22×C8×C61C2311yescharacteristic
178C22×C8×C61C2311yescharacteristic
179C2×C42×C61C2311yescharacteristic
180#108×C61—22no—
181#104×C61—22no—
182#104×C61—22no—
183#97×C61—22no—
184C23×D61—21no—
185C23×D61#4111yescharacteristic
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—21no—
189#41×C61—21no—
190#41×C61—21no—
191#41×C61—21no—
192#41×C61C2×D412yes—
193#41×C61#4112yes—
194C2×Q8×C61C22×C411yescharacteristic
195C2×Q8×C61C22×C411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61C22×C411yescharacteristic
199C2×D4×C61C22×C411yescharacteristic
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61#4111yescharacteristic
212#11758226—22no—
213#11758226—22no—
214Q8×D61—22no—
215Q8×D61—22no—
216#11758224—24no—
217#11758224—24no—
218#11758224—22no—
219#11758224—22no—
220D4×D61—24no—
221D4×D61—24no—
222D4×D61—22no—
223D4×D61—22no—
224#11758222—24no—
225#11758222—24no—
226#11758222—21no—
227#11758222—21no—
228#11758222C2×D412yes—
229#11758222#4112yes—
230C2×D244—21no—
231C2×D244C22×C411yescharacteristic
232C2×C4×D61—24no—
233C2×C4×D61—24no—
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×D61—21no—
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×Dic122—21no—
246C2×Dic122C22×C411yescharacteristic
247Q16×C61—22no—
248SD16×C61—22no—
249SD16×C61—22no—
250D8×C61—22no—
251M16×C61—21no—
252M16×C61—24no—
253M16×C61—21no—
254M16×C61—21no—
255M16×C61—42no—
256M16×C61C2×D412yes—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—24no—
261C2×C8×C61—21no—
262C2×C8×C61—42no—
263C2×C8×C61C22×C411yescharacteristic
264C2×C8×C61C22×C411yescharacteristic
265C2×C8×C61C2×D411yescharacteristic
266C2×C8×C61C2×D411yescharacteristic
267C2×C8×C61C2×D412yes—
268C2×C8×C61C2×D412yes—
269C42×C61—21no—
270C42×C61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274#11758202—22no—
275#11758201—22no—
276#11758200—22no—
277#11758199—22no—
278#11758198—21no—
279#11758198—21no—
280#11758198—42no—
281C4⋊Dic61C22×C411yescharacteristic
282C4⋊Dic61C22×C411yescharacteristic
283#11758196—21no—
284#11758196—21no—
285C4×Dic61—21no—
286C4×Dic61—21no—
287C4×Dic61—21no—
288#11758194—24no—
289#11758194—21no—
290#11758194—21no—
291#11758194—21no—
292#11758194C2×D412yes—
293C2×#92418—24no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418C22×C411yescharacteristic
301C2×#92418C22×C411yescharacteristic
302C2×#92418C2×D411yescharacteristic
303C2×#92418C2×D411yescharacteristic
304#11758189—24no—
305#11758189—24no—
306#11758189—22no—
307#11758189—22no—
308#11758189—24no—
309#11758189—22no—
310#11758189—22no—
311C8×D61—24no—
312C8×D61—24no—
313C8×D61—24no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61C2×#4111yescharacteristic
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×D61C4×D411yescharacteristic
327Q8×C61—21no—
328Q8×C61—21no—
329Q8×C61—21no—
330Q8×C61C4×D412yes—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—21no—
334D4×C61—21no—
335D4×C61—21no—
336D4×C61—41no—
337D4×C61—41no—
338D4×C61C4×D412yes—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61C23×C411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C2×C4×C61C2×#4111yescharacteristic
354C22⋊D61—24no—
355C22⋊D61—24no—
356C22⋊D61—22no—
357C22⋊D61—22no—
358C22⋊D61—81no—
359C22⋊D61—81no—
360C2×Dic61—24no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—22no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61C4×D411yescharacteristic
370C2×Dic61C4×D411yescharacteristic
371D244—24no—
372D244—21no—
373D244C4×D412yes—
374C4×D61—24no—
375C4×D61—24no—
376C4×D61—21no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—22no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—22no—
385C4×D61—21no—
386Dic122—24no—
387Dic122—21no—
388Dic122C4×D412yes—
389C8×C61—21no—
390C8×C61—21no—
391C8×C61—22no—
392C8×C61—41no—
393C8×C61#12012yes—
394C8×C61#12012yes—
395#92418—21no—
396#92418—21no—
397#92418—22no—
398#92418—21no—
399#92418—21no—
400#92418—41no—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—22no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61C2×C4×D411yescharacteristic
411C22×C61#52511yescharacteristic
412C22×C61#52511yescharacteristic
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—22no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—41no—
427C4×C61—81no—
428C4×C61C2×C4×D411yescharacteristic
429C4×C61C2×C4×D411yescharacteristic
430C4×C61C2×#12011yescharacteristic
431C4×C61#52511yescharacteristic
432Dic61—21no—
433Dic61—22no—
434Dic61—21no—
435Dic61—42no—
436Dic61—41no—
437Dic61—41no—
438C2×#568—611no—
439#3002—611no—
440C2×#444D6111yescharacteristic, complemented
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—21no—
454C2×C61—21no—
455C2×C61—42no—
456C2×C61—81no—
457C2×C61C4×#12011yescharacteristic
458C2×C61#295611yescharacteristic
459C2×C61#295711yescharacteristic
460D61—41no—
461D61—41no—
462D61—42no—
463C22×#41—611no—
464C2×#135—611no—
465C2×#135C2×D6111yescharacteristic
466#568—1224no—
467#568—1224no—
468C2×#131—611no—
469C2×#131—611no—
470C2×#131—611no—
471C2×#131—1221no—
472C2×#131—1221no—
473C2×#131C2×D6111yescharacteristic
474C2×#131C2×D6111yescharacteristic, complemented
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—611no—
486#448—611no—
487#447—611no—
488#444—24no—
489#443—1224no—
490#436—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494C2×#108—611no—
495C2×#108C2×D6111yescharacteristic, complemented
496#424—611no—
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104C2×D6111yescharacteristic
502C2×#104C2×D6111yescharacteristic, complemented
503#416—611no—
504#416—611no—
505#408—611no—
506#407—611no—
507C2×C22⋊C8—611no—
508#405—611no—
509C2×#97C2×D6111yescharacteristic, complemented
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—1221no—
523C2×#41—1221no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41C22×D6111yescharacteristic
529C2×#41C22×D6111yescharacteristic
530C22×Q8—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C23×C4—611no—
534C23×C4—1221no—
535#135—22no—
536#135—22no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16C4×D6111yescharacteristic
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16C4×D6111yescharacteristic
544C2×SD16C4×D6111yescharacteristic
545C2×D8—611no—
546C2×D8C4×D6111yescharacteristic
547#131—22no—
548#131—22no—
549#131—22no—
550#131—614no—
551#131—1228no—
552#131—1222no—
553#131—1228no—
554#131—1222no—
555#131—1222no—
556#131—1222no—
557#131—1222no—
558#131C22⋊D6114yescomplemented
559C2×M16—21no—
560C2×M16—21no—
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—1228no—
570C2×M16—1221no—
571C2×M16—1222no—
572C2×M16—1228no—
573C2×M16—1222no—
574C2×M16—1222no—
575C2×M16—1221no—
576C2×M16—1222no—
577C2×M16C22×D6111yescharacteristic
578C2×M16C22×D6111yescharacteristic
579C22×C8—21no—
580C22×C8—21no—
581C22×C8—611no—
582C22×C8—611no—
583C22×C8—1221no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C22×C8C22×D6111yescharacteristic
588C22×C8C22×D6111yescharacteristic
589#123—1221no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592#121—611no—
593#121—611no—
594#120—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117—611no—
598C2×C22⋊C4—1221no—
599C2×C42—611no—
600C2×C42C22×D6111yescharacteristic
601#108—22no—
602#108—1222no—
603C4⋊C8—1221no—
604C4⋊C8—1221no—
605#104—22no—
606#104—22no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103—611no—
614#103—611no—
615#102—611no—
616#102—611no—
617#102—611no—
618#102—611no—
619C22⋊C8—611no—
620C22⋊C8—611no—
621C22⋊C8—611no—
622C22⋊C8—611no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8—1221no—
627#97—22no—
628#97—1221no—
629C4×C8—1222no—
630C4×C8—1221no—
631#95—1221no—
632C24—611no—
633C24—1221no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—612no—
641#41—612no—
642#41—1224no—
643#41—1224no—
644#41—1222no—
645#41—1224no—
646#41—1224no—
647#41—1222no—
648#41—1222no—
649#41—1222no—
650#41—1221no—
651#41—1221no—
652#41#1175822212yes—
653#41C2×C22⋊D6112yes—
654C2×Q8—611no—
655C2×Q8—1221no—
656C2×Q8—1222no—
657C2×Q8—1222no—
658C2×Q8C2×C4×D6111yescharacteristic
659C2×Q8C2×C4×D6111yescharacteristic
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×D4C2×C4×D6111yescharacteristic
674C2×D4C2×C4×D6111yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1224no—
686C22×C4—1224no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4C23×D6111yescharacteristic
695Q16—22no—
696Q16—1222no—
697SD16—22no—
698SD16—22no—
699SD16—1222no—
700SD16—1222no—
701D8—22no—
702D8—1222no—
703M16—21no—
704M16—24no—
705M16—21no—
706M16—21no—
707M16—42no—
708M16—612no—
709M16—1224no—
710M16—1224no—
711M16—1224no—
712M16—1221no—
713M16—1222no—
714M16—1222no—
715M16—1222no—
716M16—1222no—
717M16—1224no—
718M16—1221no—
719M16—1221no—
720M16C2×C22⋊D6112yes—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—24no—
725C2×C8—21no—
726C2×C8—42no—
727C2×C8—611no—
728C2×C8—611no—
729C2×C8—611no—
730C2×C8—611no—
731C2×C8—1224no—
732C2×C8—1224no—
733C2×C8—1224no—
734C2×C8—1221no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1224no—
740C2×C8—1221no—
741C2×C8C2×C4×D6111yescharacteristic
742C2×C8C2×C4×D6111yescharacteristic
743C2×C8D4×D6112yes—
744C2×C8D4×D6111yescharacteristic
745C2×C8D4×D6111yescharacteristic
746C2×C8C2×C22⋊D6112yes—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—2442no—
757C42—21no—
758C42—21no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C23—21no—
763C23—21no—
764C23—611no—
765C23—611no—
766C23—1224no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23—4881no—
771C23—4881no—
772C23—2441no—
773C23—2441no—
774C23#41×D6111yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—612no—
779Q8—1224no—
780Q8—1221no—
781Q8C4×C22⋊D6112yes—
782D4—22no—
783D4—22no—
784D4—21no—
785D4—21no—
786D4—21no—
787D4—41no—
788D4—41no—
789D4—612no—
790D4—1224no—
791D4—1224no—
792D4—1224no—
793D4—1222no—
794D4—1222no—
795D4—1221no—
796D4—4881no—
797D4—4881no—
798D4C4×C22⋊D6112yes—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—1224no—
811C2×C4—1224no—
812C2×C4—1224no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1222no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22×C4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C22×C22⋊D6111yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4C2×#1175822211yescharacteristic
837C8—21no—
838C8—21no—
839C8—22no—
840C8—41no—
841C8—1221no—
842C8—1221no—
843C8—1221no—
844C8—1221no—
845C8—1222no—
846C8—2441no—
847C8#1451974512yes—
848C8#1451974512yes—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—1221no—
858C22—1222no—
859C22—1221no—
860C22—1221no—
861C22—1221no—
862C22—1221no—
863C22—1221no—
864C22—4881no—
865C22—4881no—
866C22—4884no—
867C22—2441no—
868C22—2441no—
869C22C4×D4×D6111yescharacteristic
870C22#1684026911yescharacteristic
871C22#1684027111yescharacteristic
872C4—22no—
873C4—41no—
874C4—81no—
875C4—1221no—
876C4—1221no—
877C4—1222no—
878C4—2442no—
879C4—2441no—
880C4—2441no—
881C4C4×D4×D6111yescharacteristic
882C4C2×C4×C22⋊D6111yescharacteristic
883C4C2×#1451974511yescharacteristic
884C4#1684027111yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—81no—
889C2—2441no—
890C2—2441no—
891C2—2442no—
892C2C4×#1451974511yescharacteristic
893C2#2145472711yescharacteristic
894C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#444C2
socleC22×C61C2×C4×D4
prime radical#21455033C2
cosocleC22×C4×C61C24
hypercenterC2×#444D61
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
1. C2×#16840527C2semidirect
3. C2×#16839877C2semidirect
4. #21454520C2semidirect
5. #21446148C2semidirect
6. #21446143C2semidirect
7. #21446118C2semidirect
8. #21446092C2semidirect
9. #21446091C2semidirect
10. #21446022C2semidirect
11. #21445761C2semidirect
12. #21445663C2semidirect
13. #21445654C2semidirect
14. #21445604C2semidirect
15. C2×C61×#444C2semidirect
30. #16839923C4semidirect
31. #16839921C4semidirect
32. #16839916C4semidirect
33. #16839911C4semidirect
34. #16839906C4semidirect
35. #16839904C4semidirect
36. #16839899C4semidirect
37. #16839894C4semidirect
43. C2×#14519712C22semidirect
44. #16839790C22semidirect
47. C2×#14519704C22semidirect
51. #16839729C22semidirect
54. #16839717C22semidirect
55. C2×C8×Dic61C22semidirect
57. #16839527C22semidirect
58. #16839526C22semidirect
59. #16839523C22semidirect
60. #16839522C22semidirect
61. #16839517C22semidirect
62. #16839516C22semidirect
65. C2×#131×C61C22semidirect
67. C2×#108×C61C22semidirect
69. C2×#104×C61C22semidirect
70. C2×#97×C61C22semidirect
98. #14519783D4semidirect
170. #131×C61D4semidirect
440. C2×#444D61semidirect
474. C2×#131C2×D61semidirect
495. C2×#108C2×D61semidirect
502. C2×#104C2×D61semidirect
509. C2×#97C2×D61semidirect
518. C61#21468semidirect
558. #131C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
#214550332
C2×#168398772
#214545202
#214461482
#214461432
#214461182
#214460922
#214460912
#214460222
#214457612
#214456632
#214456542
#214456042
C2×C61×#4442
#2146861