Finite Group Databasebeta

← #29650103

Subgroups — #29650103

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455879C211yesmaximal, characteristic
2#21454894C211yesmaximal, characteristic, complemented
3#21444697C211yesmaximal, characteristic, complemented
4#21444683C211yesmaximal, characteristic, complemented
5#21444662C211yesmaximal, characteristic, complemented
6#21444648C211yesmaximal, characteristic, complemented
7#21444641C211yesmaximal, characteristic, complemented
8#21444629C211yesmaximal, characteristic, complemented
9C8×#11758201C211yesmaximal, characteristic, complemented
10C8×#11758199C211yesmaximal, characteristic, complemented
11#21444602C211yesmaximal, characteristic, complemented
12#21444253C211yesmaximal, characteristic, complemented
13#21444217C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#2988C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840086C411yescharacteristic
18#16840086C411yescharacteristic
19#16840057C411yescharacteristic
20#16840052C411yescharacteristic
21#16839962C411yescharacteristic
22#16839957C411yescharacteristic
23#16839907C411yescharacteristic
24#16839907C411yescharacteristic
25C4×#11758201C2211yescharacteristic
26C4×#11758201C2211yescharacteristic
27C4×#11758199C2211yescharacteristic
28C4×#11758199C2211yescharacteristic
29#16839841C2211yescharacteristic
30#16839841C2211yescharacteristic
31#16839832—21no—
32#16839832—21no—
33C8×D244C2211yescharacteristic
34C8×D244C2211yescharacteristic
35#16839819C2211yescharacteristic
36#16839815C2211yescharacteristic
37#16839815C2211yescharacteristic
38#16839727—21no—
39#16839727—21no—
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44Q8⋊#92418C2211yescharacteristic
45Q8⋊#92418C2211yescharacteristic
46D4⋊#92418C2211yescharacteristic
47D4⋊#92418C2211yescharacteristic
48#16839489C2211yescharacteristic
49#16839489C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839484C2211yescharacteristic
53#16839484C2211yescharacteristic
54#16839483C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C8×Q8×C61C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C8×D4×C61—21no—
60C8×D4×C61—21no—
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#431—21no—
64C61×#431C2211yescharacteristic
65C2×C4⋊C8×C61—21no—
66C2×C4⋊C8×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758201C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758199C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×#11758189—21no—
74C2×C8×D61—21no—
75C2×C8×D61—21no—
76#14519777C2×C411yescharacteristic
77#14519774C2×C411yescharacteristic
78#14519765—21no—
79#14519751—21no—
80#14519751C2×C411yescharacteristic
81#14519751C2×C411yescharacteristic
82C4×D244—21no—
83C4×D244C2311yescharacteristic
84C4×D244C2311yescharacteristic
85#14519710C2×C411yescharacteristic
86#14519710C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88#14519708C2×C411yescharacteristic
89C4⋊#92418—21no—
90C4⋊#92418C2×C411yescharacteristic
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519701C2×C411yescharacteristic
95#14519701C2×C411yescharacteristic
96#14519698C2×C411yescharacteristic
97#14519698C2×C411yescharacteristic
98#14519697C2×C411yescharacteristic
99#14519697C2×C411yescharacteristic
100#14519697C2×C411yescharacteristic
101#14519697C2×C411yescharacteristic
102C22⋊#92418—21no—
103C22⋊#92418—21no—
104C22⋊#92418C2×C411yescharacteristic
105C22⋊#92418C2×C411yescharacteristic
106#14519689—21no—
107#14519689—21no—
108#14519689—21no—
109#14519689—21no—
110#14519688—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61C2×C411yescharacteristic
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118C22×C8×C61—21no—
119C4×Q8×C61C2×C411yescharacteristic
120C4×Q8×C61C2311yescharacteristic
121C4×D4×C61—21no—
122C4×D4×C61—21no—
123C4×D4×C61C2×C411yescharacteristic
124C4×D4×C61C2311yescharacteristic
125#117×C61—21no—
126#117×C61C2×C411yescharacteristic
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C22×C411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—21no—
156C2×C22⋊D61—21no—
157#11758222—81no—
158#11758222—81no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244C22×C411yescharacteristic
162C2×D244C22×C411yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×Dic122—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—81no—
169C2×C8×C61—81no—
170C2×C8×C61—81no—
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C2×C8×C61C2×D411yescharacteristic
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61C22×C411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61#4111yescharacteristic
188C42×C61C2411yescharacteristic
189#11758201—22no—
190#11758201—22no—
191#11758199—22no—
192#11758199—22no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196#11758198—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61C22×C411yescharacteristic
199C4⋊Dic61C22×C411yescharacteristic
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208#11758189—81no—
209#11758189—81no—
210C8×D61—81no—
211C8×D61—81no—
212C23×C61—21no—
213C23×C61C4×D411yescharacteristic
214C22×D61—21no—
215C22×D61—21no—
216Q8×C61—21no—
217Q8×C61#13112yes—
218D4×C61—24no—
219D4×C61—21no—
220D4×C61#13112yes—
221C2×C4×C61—24no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—81no—
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C23×C411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C22⋊D61—81no—
240C22⋊D61—81no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243D244—21no—
244D244—21no—
245D244—21no—
246D244—21no—
247D244—81no—
248D244—81no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—41no—
253Dic122—81no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#17920—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—22no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61C2×C4×D411yescharacteristic
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C4×C61—21no—
283C4×C61—22no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61C2×#13111yescharacteristic
290C4×C61C2×#13111yescharacteristic
291C4×C61#57611yescharacteristic
292C4×C61#57711yescharacteristic
293Dic61—41no—
294Dic61—41no—
295#3106—611no—
296#2988D6111yescharacteristic, complemented
297#2981—611no—
298#1588—611no—
299#1586—611no—
300#1583—611no—
301#1581—611no—
302#1580—611no—
303SD16⋊C8—611no—
304C8×SD16—611no—
305C8×D8—611no—
306#1573—611no—
307#1488—611no—
308#1480—611no—
309#1454—611no—
310C2×C61—41no—
311C2×C61—42no—
312C2×C61#292911yescharacteristic
313C2×C61#294611yescharacteristic
314C2×C61#295711yescharacteristic
315D61—81no—
316D61—81no—
317#532—611no—
318C4×#41C2×D6111yescharacteristic
319#482—611no—
320#482—611no—
321#477—611no—
322#476—611no—
323#460—611no—
324#459—611no—
325#449—611no—
326#449—611no—
327C8×Q8C2×D6111yescharacteristic
328C8×Q8C2×D6111yescharacteristic
329C4×SD16—611no—
330C4×SD16—611no—
331C4×D8—611no—
332C4×D8—611no—
333#436—611no—
334#436—611no—
335#435—1221no—
336#435—1221no—
337C8×D4—21no—
338C8×D4—21no—
339C8×D4—611no—
340C8×D4—611no—
341C8×D4C2×D6111yescharacteristic
342C8×D4C2×D6111yescharacteristic
343#432—611no—
344#431—21no—
345#431—611no—
346#431—611no—
347#431C2×D6111yescharacteristic
348C2×C4⋊C8—21no—
349C2×C4⋊C8C2×D6111yescharacteristic
350#408—1221no—
351#408—1221no—
352#335—611no—
353#335—611no—
354#334—611no—
355#334—611no—
356Q8⋊C8—611no—
357Q8⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364#322—611no—
365#322—611no—
366#322—611no—
367C82—611no—
368C61#1792011yescharacteristic, complemented, Sylow
369C2×#41—1221no—
370C2×#41C4×D6111yescharacteristic
371C2×SD16—611no—
372C2×SD16—611no—
373C2×D8—611no—
374C2×D8—611no—
375C2×M16—1221no—
376C2×M16—1221no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—1221no—
381C22×C8—1221no—
382C4⋊Q8—611no—
383#127—611no—
384#124—1221no—
385#121—611no—
386#121—611no—
387#121—1221no—
388C4×Q8C4×D6111yescharacteristic
389C4×Q8C22×D6111yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—1221no—
395C4×D4C4×D6111yescharacteristic
396C4×D4C22×D6111yescharacteristic
397#117—21no—
398#117C4×D6111yescharacteristic
399C2×C42—21no—
400C2×C42C22×D6111yescharacteristic
401#107—611no—
402#107—611no—
403#106—611no—
404#106—611no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—611no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—1221no—
413C4⋊C8C22⋊D6111yescharacteristic
414C4⋊C8C22⋊D6111yescharacteristic
415C4⋊C8C22×D6111yescharacteristic
416C4⋊C8C22×D6111yescharacteristic
417#103—611no—
418#103—611no—
419#102—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—611no—
428C22⋊C8—611no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8C22⋊D6111yescharacteristic
436C22⋊C8C22⋊D6111yescharacteristic
437#97—1221no—
438C4×C8—21no—
439C4×C8—21no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8C22×D6111yescharacteristic
445C4×C8C22×D6111yescharacteristic
446#41—22no—
447#41—22no—
448#41—4881no—
449#41—4881no—
450C2×Q8—1221no—
451C2×Q8C2×C4×D6111yescharacteristic
452C2×D4—21no—
453C2×D4—611no—
454C2×D4—611no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4C2×C4×D6111yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4#1175822211yescharacteristic
467C22×C4C2×C22⋊D6111yescharacteristic
468SD16—1222no—
469SD16—1222no—
470D8—1222no—
471D8—1222no—
472M16—4881no—
473M16—4881no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—4881no—
488C2×C8—4881no—
489C2×C8C2×C22⋊D6111yescharacteristic
490C2×C8C2×C22⋊D6111yescharacteristic
491C2×C8C2×C22⋊D6111yescharacteristic
492C2×C8C2×C22⋊D6111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4C2×C4×D6111yescharacteristic
499C4⋊C4C2×C4×D6111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C22⋊C4—1221no—
506C22⋊C4—1221no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C2×C4×D6111yescharacteristic
511C42#1175822211yescharacteristic
512C42C2×C22⋊D6111yescharacteristic
513C42C23×D6111yescharacteristic
514C23—21no—
515C23—1221no—
516C23—1221no—
517C23C4×C22⋊D6111yescharacteristic
518Q8—21no—
519Q8—4881no—
520Q8#1451978312yes—
521D4—24no—
522D4—21no—
523D4—1221no—
524D4—1221no—
525D4—1221no—
526D4—1221no—
527D4—4881no—
528D4—4881no—
529D4—4881no—
530D4—4881no—
531D4#1451978312yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4C4×C22⋊D6111yescharacteristic
551C2×C4C4×C22⋊D6111yescharacteristic
552C2×C4C4×C22⋊D6111yescharacteristic
553C2×C4C22×C4×D6111yescharacteristic
554C2×C4C22×C22⋊D6111yescharacteristic
555C2×C4C2×#1175822211yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—1221no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—2441no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22C2×C4×C22⋊D6111yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—2441no—
591C4—2441no—
592C4C2×#1451978311yescharacteristic
593C4C2×#1451978311yescharacteristic
594C4#1684056511yescharacteristic
595C4#1684057011yescharacteristic
596C2—41no—
597C2—42no—
598C2—4881no—
599C2—4881no—
600C2#2145451311yescharacteristic
601C2#2145464711yescharacteristic
602C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2988C2
socleC22×C61C2×C4×D4
prime radical#21455879C2
cosocleC42×C61C24
hypercenter#2988D61
hypocenterC61#17920
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2988

Complements

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

NH ≅ G/Ntype
2. #21454894C2semidirect
3. #21444697C2semidirect
4. #21444683C2semidirect
5. #21444662C2semidirect
6. #21444648C2semidirect
7. #21444641C2semidirect
8. #21444629C2semidirect
9. C8×#11758201C2semidirect
10. C8×#11758199C2semidirect
11. #21444602C2semidirect
12. #21444253C2semidirect
13. #21444217C2semidirect
14. #21444119C2semidirect
15. C61×#2988C2semidirect
296. #2988D61semidirect
368. C61#17920semidirect

Maximal subgroups

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

subgroupindex
#214558792
#214548942
#214446972
#214446832
#214446622
#214446482
#214446412
#214446292
C8×#117582012
C8×#117581992
#214446022
#214442532
#214442172
#214441192
C61×#29882
#1792061