Finite Group Databasebeta

← #29710910

Subgroups — #29710910

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454757C211yesmaximal, characteristic, complemented
2#21454720C211yesmaximal, characteristic
3#21447402C211yesmaximal, characteristic, complemented
4#21447396C211yesmaximal, characteristic, complemented
5#21447274C211yesmaximal, characteristic, complemented
6#21447272C211yesmaximal, characteristic, complemented
7#21447124C211yesmaximal, characteristic
8#21447104C211yesmaximal, characteristic
9#21446994C211yesmaximal, characteristic, complemented
10#21446993C211yesmaximal, characteristic, complemented
11#21445665C211yesmaximal, characteristic, complemented
12#21445661C211yesmaximal, characteristic, complemented
13#21445620C211yesmaximal, characteristic, complemented
14#21445574C211yesmaximal, characteristic, complemented
15C61×#1757C211yesmaximal, characteristic, complemented
16#16840560C2211yescharacteristic
17C2×#14519783C2211yescharacteristic
18#16840315C2211yescharacteristic
19#16839892—22no—
20#16839890—22no—
21#16839882—22no—
22#16839877—22no—
23#16839810C2211yescharacteristic
24#16839790C2211yescharacteristic
25#16839789C2211yescharacteristic
26#16839785C2211yescharacteristic
27#16839779C2211yescharacteristic
28#16839778C2211yescharacteristic
29C2×#14519704C2211yescharacteristic
30C2×#14519703C2211yescharacteristic
31#16839758C2211yescharacteristic
32#16839756C2211yescharacteristic
33#16839744C2211yescharacteristic
34#16839735C2211yescharacteristic
35#16839717C2211yescharacteristic
36#16839717C2211yescharacteristic
37C2×#14519687C2211yescharacteristic
38#16839534C2211yescharacteristic
39#16839532C2211yescharacteristic
40#16839526C2211yescharacteristic
41#16839526C2211yescharacteristic
42#16839523C2211yescharacteristic
43#16839521C2211yescharacteristic
44#16839520C2211yescharacteristic
45#16839519C2211yescharacteristic
46#16839518C2211yescharacteristic
47#16839518C2211yescharacteristic
48C2×#131×C61C2211yescharacteristic
49C61×#413C2211yescharacteristic
50C61×#410C2211yescharacteristic
51C61×#405C2211yescharacteristic
52C61×#405C2211yescharacteristic
53C61×#344C2211yescharacteristic
54C61×#344C2211yescharacteristic
55C2×#11758222C2311yescharacteristic
56#14519808—21no—
57#14519807—21no—
58#14519803—21no—
59#14519802—21no—
60#14519797—22no—
61#14519783—21no—
62#14519783—21no—
63#14519783—21no—
64#14519783—21no—
65C2×#11758194C2311yescharacteristic
66C2×#11758194C2311yescharacteristic
67C2×#11758194C2311yescharacteristic
68C2×#11758189—21no—
69C22×#92418C2311yescharacteristic
70C2×C8×D61—21no—
71#14519776—21no—
72#14519768—21no—
73#14519754—22no—
74C4×Dic122—22no—
75#14519736C2311yescharacteristic
76#14519736C2311yescharacteristic
77C2×C4×Dic61C2311yescharacteristic
78#14519712—22no—
79C4⋊#92418—22no—
80#14519706—22no—
81#14519706—22no—
82#14519704—22no—
83#14519704—21no—
84#14519704—21no—
85#14519703—22no—
86#14519703—21no—
87#14519703—21no—
88#14519701—21no—
89#14519700—21no—
90#14519698—21no—
91#14519697—21no—
92#14519695—21no—
93#14519693—21no—
94#14519691—22no—
95#14519687—21no—
96#14519687—21no—
97#14519687—21no—
98#14519687D412yes—
99C8×Dic61—21no—
100C8×Dic61D412yes—
101C2×#41×C61C2311yescharacteristic
102#131×C61—21no—
103#131×C61—21no—
104#131×C61—21no—
105#131×C61—21no—
106C2×M16×C61—21no—
107C2×M16×C61C2311yescharacteristic
108C2×M16×C61C2311yescharacteristic
109C2×M16×C61C2311yescharacteristic
110C22×C8×C61—21no—
111C22×C8×C61C2311yescharacteristic
112#117×C61C2311yescharacteristic
113#117×C61C2311yescharacteristic
114#101×C61—21no—
115#100×C61—21no—
116#99×C61—22no—
117#97×C61—21no—
118#97×C61—21no—
119C4×C8×C61—21no—
120C4×C8×C61—21no—
121#41×C61—21no—
122#41×C61—21no—
123#41×C61—21no—
124#41×C61—21no—
125C2×Q8×C61#4111yescharacteristic
126C2×D4×C61—21no—
127C2×D4×C61#4111yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61C2411yescharacteristic
130C2×C22⋊D61—21no—
131C22×Dic61—21no—
132#11758222—21no—
133#11758222—21no—
134#11758222—21no—
135#11758222—21no—
136C2×D244#4111yescharacteristic
137C2×C4×D61—21no—
138C2×Dic122—22no—
139C2×Dic122#4111yescharacteristic
140M16×C61—21no—
141M16×C61—21no—
142M16×C61—21no—
143M16×C61—21no—
144M16×C61—21no—
145M16×C61—21no—
146M16×C61—41no—
147M16×C61—41no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—41no—
152C2×C8×C61—41no—
153C2×C8×C61C2×D411yescharacteristic
154C2×C8×C61C2×D411yescharacteristic
155C2×C8×C61#4111yescharacteristic
156C2×C8×C61#4111yescharacteristic
157C2×C8×C61#4111yescharacteristic
158C2×C8×C61#4111yescharacteristic
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C22⋊C4×C61—21no—
162C22⋊C4×C61#4112yes—
163C42×C61—21no—
164C42×C61—21no—
165C22⋊Dic61—21no—
166C22⋊Dic61—21no—
167#11758202—22no—
168#11758201—22no—
169#11758200—22no—
170#11758199—22no—
171C4⋊Dic61—22no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174#11758196—22no—
175#11758196—22no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61C2×D412yes—
179C4×Dic61#4111yescharacteristic
180C4×Dic61#4111yescharacteristic
181#11758194—21no—
182#11758194—21no—
183#11758194—21no—
184#11758194—21no—
185#11758194—21no—
186#11758194—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418C2×D412yes—
193#11758189—41no—
194#11758189—41no—
195C8×D61—41no—
196C8×D61—41no—
197C23×C61—21no—
198C23×C61C2×#4111yescharacteristic
199C22×D61—21no—
200Q8×C61—21no—
201Q8×C61—21no—
202D4×C61—21no—
203D4×C61—21no—
204D4×C61—41no—
205D4×C61—41no—
206C2×C4×C61—22no—
207C2×C4×C61—21no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C2×#4111yescharacteristic
213C2×C4×C61C2×#4111yescharacteristic
214C2×C4×C61C2×#4111yescharacteristic
215C2×C4×C61C2×#4111yescharacteristic
216C2×C4×C61C2×#4111yescharacteristic
217C22⋊D61—41no—
218C22⋊D61—41no—
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—22no—
222C2×Dic61—21no—
223C2×Dic61—41no—
224C2×Dic61—81no—
225D244—21no—
226D244—21no—
227C4×D61—41no—
228C4×D61—41no—
229Dic122—21no—
230Dic122—21no—
231Dic122—82no—
232C8×C61—41no—
233C8×C61—41no—
234C8×C61—41no—
235C8×C61#12411yescharacteristic
236C8×C61#12411yescharacteristic
237C8×C61#12411yescharacteristic
238C8×C61#12411yescharacteristic
239#92418—22no—
240#92418—41no—
241#92418—41no—
242#92418—41no—
243#23834—611nomaximal, Sylow
244C22×C61—41no—
245C22×C61—41no—
246C22×C61—81no—
247C22×C61#52511yescharacteristic
248C22×C61#52911yescharacteristic
249C22×C61#52911yescharacteristic
250C2×D61—41no—
251C2×D61—81no—
252C4×C61—42no—
253C4×C61—41no—
254C4×C61—81no—
255C4×C61#52511yescharacteristic
256C4×C61C2×#12411yescharacteristic
257C4×C61#52911yescharacteristic
258C4×C61#52911yescharacteristic
259Dic61—41no—
260Dic61—42no—
261Dic61—41no—
262Dic61—41no—
263Dic61—81no—
264#2961—611no—
265#2955—611no—
266#2103—611no—
267#2102—611no—
268#2080—611no—
269#2080—611no—
270#2053—611no—
271#2050—611no—
272#2031—611no—
273#2031—611no—
274#1765—611no—
275#1765—611no—
276#1757—611no—
277#1757D6111yescharacteristic, complemented
278#1747—611no—
279C2×C61—21no—
280C2×C61—21no—
281C2×C61—21no—
282C2×C61—81no—
283C2×C61#239811yescharacteristic
284D61—81no—
285#575—611no—
286C2×#131—611no—
287C2×#131C2×D6111yescharacteristic
288#533—611no—
289#446—1222no—
290#446—1222no—
291#444—1222no—
292#443—1222no—
293#430—611no—
294#424—611no—
295#424—611no—
296#423—611no—
297#421—611no—
298#421—611no—
299C2×#104—611no—
300C2×#104—611no—
301#416—611no—
302#416—611no—
303#413—611no—
304#413C2×D6111yescharacteristic
305#410—611no—
306#410C2×D6111yescharacteristic
307#405—611no—
308#405—611no—
309#405C2×D6111yescharacteristic
310#405C2×D6111yescharacteristic
311C2×#97—611no—
312#344—611no—
313#344—611no—
314#344C2×D6111yescharacteristic
315#344C2×D6111yescharacteristic
316#341—611no—
317#341—611no—
318#339—611no—
319#339—611no—
320#338—611no—
321H(3,ℤ/4)—611no—
322H(3,ℤ/4)—611no—
323H(3,ℤ/4)—611no—
324C61#2383411yescharacteristic, complemented, Sylow
325C2×#41—611no—
326C2×#41C22×D6111yescharacteristic
327#137—1221no—
328#137—1221no—
329AGL(1,ℤ/8)—1221no—
330AGL(1,ℤ/8)—1221no—
331#135—1222no—
332#131—21no—
333#131—21no—
334#131—21no—
335#131—21no—
336#131—1221no—
337#131—1221no—
338#131—1221no—
339#131—1221no—
340C2×M16—21no—
341C2×M16—611no—
342C2×M16—611no—
343C2×M16—611no—
344C2×M16—1221no—
345C2×M16C22×D6111yescharacteristic
346C2×M16C22×D6111yescharacteristic
347C2×M16C22×D6111yescharacteristic
348C22×C8—21no—
349C22×C8—611no—
350C22×C8—1221no—
351C22×C8C22×D6111yescharacteristic
352C4⋊Q8—1221no—
353#125—1221no—
354C22⋊Q8—1222no—
355C4×Q8—1222no—
356#117—611no—
357#117—611no—
358#117C22×D6111yescharacteristic
359#117C22×D6111yescharacteristic
360C2×C42—611no—
361#108—1222no—
362C4⋊C8—1222no—
363C4⋊C8—1222no—
364C4⋊C8—1222no—
365#104—1221no—
366#104—1221no—
367#104—1222no—
368#104—1221no—
369#104—1221no—
370#104—1222no—
371#103—1221no—
372#103—1221no—
373#102—1221no—
374#102—1221no—
375#101—21no—
376#101—1221no—
377#100—21no—
378#100—1221no—
379#99—22no—
380#99—1222no—
381#97—21no—
382#97—21no—
383#97—612no—
384#97—1221no—
385#97—1221no—
386#97—1221no—
387C4×C8—21no—
388C4×C8—21no—
389C4×C8—612no—
390C4×C8—1221no—
391#41—21no—
392#41—21no—
393#41—21no—
394#41—21no—
395#41—1221no—
396#41—1221no—
397#41—1221no—
398#41—1221no—
399C2×Q8—611no—
400C2×Q8—1222no—
401C2×Q8#1175822211yescharacteristic
402C2×D4—21no—
403C2×D4—611no—
404C2×D4—1221no—
405C2×D4#1175822211yescharacteristic
406C22×C4—21no—
407C22×C4—1221no—
408C22×C4—1221no—
409C22×C4C23×D6111yescharacteristic
410Q16—1222no—
411SD16—1222no—
412SD16—1222no—
413D8—1222no—
414M16—21no—
415M16—21no—
416M16—21no—
417M16—21no—
418M16—21no—
419M16—21no—
420M16—41no—
421M16—41no—
422M16—1221no—
423M16—1221no—
424M16—1221no—
425M16—1221no—
426M16—1221no—
427M16—1221no—
428M16—2441no—
429M16—2441no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—41no—
434C2×C8—41no—
435C2×C8—612no—
436C2×C8—1221no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8—2441no—
442C2×C8—2441no—
443C2×C8#1175822211yescharacteristic
444C2×C8#1175822211yescharacteristic
445C2×C8D4×D6111yescharacteristic
446C2×C8D4×D6111yescharacteristic
447C2×C8#1175822411yescharacteristic
448C2×C8#1175822411yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—1222no—
452C4⋊C4—1222no—
453C4⋊C4—1222no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C22⋊C4—21no—
457C22⋊C4—1221no—
458C22⋊C4—1221no—
459C22⋊C4#1175822212yes—
460C42—21no—
461C42—21no—
462C42—612no—
463C42—611no—
464C42—611no—
465C42—1221no—
466C42—1221no—
467C23—21no—
468C23—1221no—
469C23C2×#1175822211yescharacteristic
470Q8—21no—
471Q8—21no—
472Q8—1221no—
473Q8—1221no—
474Q8—4882no—
475D4—21no—
476D4—21no—
477D4—41no—
478D4—41no—
479D4—1221no—
480D4—1221no—
481D4—2441no—
482D4—2441no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—1221no—
489C2×C4—1221no—
490C2×C4—1222no—
491C2×C4—1221no—
492C2×C4—4881no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4C2×D4×D6111yescharacteristic
497C2×C4#41×D6111yescharacteristic
498C2×C4#41×D6111yescharacteristic
499C2×C4C2×#1175822411yescharacteristic
500C2×C4C2×#1175822211yescharacteristic
501C2×C4C2×#1175822211yescharacteristic
502C8—41no—
503C8—41no—
504C8—41no—
505C8—1222no—
506C8—2441no—
507C8—2441no—
508C8—2441no—
509C8#1451976311yescharacteristic
510C8#1451976311yescharacteristic
511C8#1451976311yescharacteristic
512C8#1451976311yescharacteristic
513C22—41no—
514C22—41no—
515C22—81no—
516C22—4881no—
517C22—2441no—
518C22#1684027111yescharacteristic
519C22#1684029411yescharacteristic
520C22#1684029611yescharacteristic
521C4—42no—
522C4—41no—
523C4—81no—
524C4—4881no—
525C4—2441no—
526C4—2441no—
527C4—2442no—
528C4—2441no—
529C4#1684027111yescharacteristic
530C4C2×#1451976311yescharacteristic
531C4#1684029011yescharacteristic
532C4#1684029211yescharacteristic
533C2—21no—
534C2—21no—
535C2—21no—
536C2—81no—
537C2—4881no—
538C2#2144910611yescharacteristic
subgroupG/H
centerC4C2×#14519763
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1757C2
socleC2×C61#2398
prime radical#16840560C22
hypercenter#1757D61
hypocenterC61#23834
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C8 ◁ #1757

Complements

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

NH ≅ G/Ntype
1. #21454757C2semidirect
3. #21447402C2semidirect
4. #21447396C2semidirect
5. #21447274C2semidirect
6. #21447272C2semidirect
9. #21446994C2semidirect
10. #21446993C2semidirect
11. #21445665C2semidirect
12. #21445661C2semidirect
13. #21445620C2semidirect
14. #21445574C2semidirect
15. C61×#1757C2semidirect
277. #1757D61semidirect
324. C61#23834semidirect

Maximal subgroups

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

subgroupindex
#214547572
#214547202
#214474022
#214473962
#214472742
#214472722
#214471242
#214471042
#214469942
#214469932
#214456652
#214456612
#214456202
#214455742
C61×#17572
#2383461