Finite Group Databasebeta

← #30607180

Subgroups — #30607180

Order 15616.

376 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462161C211yesmaximal, characteristic
2D61⋊#362C211yesmaximal, characteristic
3#21462129C211yesmaximal, characteristic
4#21461739C211yesmaximal, characteristic
5#21460901C211yesmaximal, characteristic
6#21460886C211yesmaximal, characteristic
7#21454684C211yesmaximal, characteristic
8D61⋊M32C2211yescharacteristic
9D61⋊M32C2211yescharacteristic
10D61⋊#108C2211yescharacteristic
11#16840772C2211yescharacteristic
12#16840685—21no—
13#16840684—21no—
14#16840681—22no—
15#16840675—22no—
16#16840644—21no—
17#16840629—21no—
18C2×Q16×D61C2211yescharacteristic
19#16840238—21no—
20#16839870C411yescharacteristic, complemented
21#16839869C411yescharacteristic, complemented
22#16839868C411yescharacteristic, complemented
23C4×#11758202—21no—
24#16839854—21no—
25#16839797C2211yescharacteristic
26#16839769—21no—
27#16839719C2211yescharacteristic
28C61×#441C411yescharacteristic, complemented
29D61⋊M16—21no—
30#14519856—21no—
31#14519852—21no—
32#14519852—21no—
33#14519851—21no—
34#14519851—21no—
35D61⋊C16—21no—
36D61⋊C16—21no—
37#14519848—21no—
38#14519847—21no—
39#14519846—21no—
40#14519845—21no—
41C2×Q8×D61—21no—
42C2×Dic244C2×C411yescharacteristic
43C2×#11758202—21no—
44Q16×D61—21no—
45Q16×D61—21no—
46Q16×D61D412yes—
47Q16×D61Q812yes—
48C2×#11758189D411yescharacteristic
49C2×C8×D61C2311yescharacteristic
50Q8×Dic61—21no—
51C4×Dic122—21no—
52C4×Dic122—41no—
53#14519742—21no—
54#14519742—41no—
55#14519735—21no—
56#14519735—41no—
57#14519734—41no—
58#14519734D411yescharacteristic
59#14519710—21no—
60#14519709C2×C411yescharacteristic
61#14519702—21no—
62#14519701—21no—
63#14519700—21no—
64#14519687C2×C411yescharacteristic
65C4×#92418D411yescharacteristic
66C8×Dic61D411yescharacteristic
67C2×Q16×C61C2×C411yescharacteristic
68C4×Q8×C61—21no—
69#106×C61C2×C411yescharacteristic
70#103×C61—21no—
71#97×C61C2×C411yescharacteristic
72C2×Q8×C61—21no—
73Q8×D61—22no—
74Q8×D61—22no—
75Q8×D61—41no—
76Q8×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61C2×D411yescharacteristic
79C2×Dic122—21no—
80C2×Dic122—41no—
81C22⋊#6923—41no—
82#11758217—41no—
83C4⋊#6923—41no—
84C4×#6923—41no—
85#11758213—41no—
86D61⋊C8—41no—
87Q16×C61—21no—
88Q16×C61C4⋊C412yes—
89C2×C8×C61C22⋊C411yescharacteristic
90C2×C8×C61C22×C411yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C42×C61—41no—
94C42×C61C22⋊C411yescharacteristic
95#11758202—22no—
96#11758202—22no—
97#11758198—21no—
98#11758198—41no—
99C4⋊Dic61—21no—
100C4⋊Dic61—41no—
101#11758196—21no—
102#11758196—41no—
103#11758196—41no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C4×Dic61C22⋊C411yescharacteristic
109C2×#92418C22⋊C411yescharacteristic
110C2×#92418C2×D411yescharacteristic
111Dic244—21no—
112Dic244C4⋊C412yes—
113#11758189—21no—
114#11758189—21no—
115C8×D61C2×D411yescharacteristic
116C8×D61C2×Q811yescharacteristic
117C8×D61#4111yescharacteristic
118C8×D61#4111yescharacteristic
119#11758187—41no—
120#11758187—41no—
121C22×D61AGL(1,ℤ/8)11yescharacteristic
122C2×#6923—81no—
123Q8×C61—22no—
124Q8×C61—41no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61C2×C22⋊C411yescharacteristic
129C2×Dic61—21no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61AGL(1,ℤ/8)11yescharacteristic
133C4×D61—42no—
134C4×D61—42no—
135C4×D61#12111yescharacteristic
136C4×D61C22⋊Q811yescharacteristic
137C4×D61#13511yescharacteristic
138C4×D61#13511yescharacteristic
139Dic122—22no—
140Dic122—41no—
141Dic122—42no—
142Dic122—42no—
143#92420—81no—
144C8×C61—21no—
145C8×C61C2×C4⋊C411yescharacteristic
146C8×C61#11711yescharacteristic
147#92418—21no—
148#92418#12111yescharacteristic
149#92418C22⋊Q811yescharacteristic
150#12827—611nomaximal, Sylow
151C22×C61#41811yescharacteristic
152C2×D61—41no—
153C2×D61#46311yescharacteristic
154C2×D61#47811yescharacteristic
155#6923—161no—
156C4×C61—41no—
157C4×C61—42no—
158C4×C61—81no—
159C4×C61#38011yescharacteristic
160C4×C61#41611yescharacteristic
161Dic61—41no—
162Dic61—42no—
163Dic61—81no—
164Dic61#46311yescharacteristic
165Dic61#47811yescharacteristic
166#2950—611no—
167#2153—611no—
168C2×#362—611no—
169#2141—611no—
170#1833—611no—
171#1389—611no—
172#1384—611no—
173C2×C61—21no—
174C2×C61#180411yescharacteristic
175D61—21no—
176D61—21no—
177C22×Q16—611no—
178#519—1221no—
179C2×M32—611no—
180C2×M32—611no—
181#441—611no—
182#441—611no—
183#441—611no—
184#441#692311yescharacteristic, complemented
185C4×Q16—1221no—
186C4×Q16—1221no—
187C2×#108—611no—
188#427—611no—
189#427—611no—
190#419—1221no—
191#405—611no—
192#364—1221no—
193#364—1221no—
194#362—1222no—
195#358—1222no—
196#344—1221no—
197H(3,ℤ/4)—1221no—
198C61#1282711yescharacteristic, complemented, Sylow
199C22×Q8—1221no—
200C2×Q16—612no—
201C2×Q16—612no—
202C2×Q16—611no—
203C2×Q16—1221no—
204C2×Q16—1221no—
205C2×Q16—1221no—
206C2×Q16C2×#692311yescharacteristic
207C2×M16—611no—
208C2×M16—1221no—
209C22×C8—611no—
210C4×Q8—21no—
211C4×Q8—1221no—
212C4×Q8—1221no—
213C4×Q8—1221no—
214C4×Q8—2441no—
215C4×Q8—2441no—
216#117—611no—
217#117—1221no—
218#117—1221no—
219#117—2441no—
220#117—2441no—
221M32—1221no—
222M32—1221no—
223M32—1221no—
224M32—1221no—
225C2×C16—1221no—
226C2×C16—1221no—
227#108—1221no—
228#108—1221no—
229#107—1221no—
230#107—1221no—
231#106—611no—
232#106—1221no—
233#106C2×#692311yescharacteristic
234#103—21no—
235#103—1221no—
236#103—1221no—
237#103—1221no—
238#97—611no—
239#97C2×#692311yescharacteristic
240C4×C8—611no—
241C4×C8—611no—
242C2×Q8—21no—
243C2×Q8—1222no—
244C2×Q8—1222no—
245C2×Q8—1221no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C22×C4—611no—
250C22×C4—2441no—
251Q16—21no—
252Q16—612no—
253Q16—1222no—
254Q16—1222no—
255Q16—1221no—
256Q16C4⋊#692312yes—
257M16—1221no—
258M16—1221no—
259M16—2441no—
260M16—2441no—
261C2×C8—611no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—2441no—
268C2×C8C22⋊#692311yescharacteristic
269C2×C8C22×#692311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C22⋊C4—1221no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C42—41no—
282C42—611no—
283C42—2441no—
284C42—2441no—
285C42—2441no—
286C42—2441no—
287C42—2441no—
288C42C22⋊#692311yescharacteristic
289C16—2441no—
290C16—2441no—
291C23—611no—
292Q8—22no—
293Q8—41no—
294Q8—1222no—
295Q8—2442no—
296Q8—2442no—
297Q8—2441no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—1221no—
307C2×C4—4881no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4C2×C22⋊#692311yescharacteristic
313C8—21no—
314C8—611no—
315C8—611no—
316C8—1221no—
317C8—4881no—
318C8C2×C4⋊#692311yescharacteristic
319C8#1451985611yescharacteristic
320C22—611no—
321C22—611no—
322C22—2441no—
323C22#1684075411yescharacteristic
324C4—41no—
325C4—42no—
326C4—81no—
327C4—611no—
328C4—611no—
329C4—9761no—
330C4—4881no—
331C4—2441no—
332C4—2442no—
333C4#1684070411yescharacteristic
334C4#1684075211yescharacteristic
335C2—21no—
336C2—1221no—
337C2—1221no—
338C2#2146168911yescharacteristic
subgroupG/H
centerC2#21461689
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#441C4
socleC2×C61#1804
prime radicalC22×D61AGL(1,ℤ/8)
cosocleC2×C8×D61C23
hypercenter#441#6923
hypocenterC61#12827
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #441

Complements

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

NH ≅ G/Ntype
20. #16839870C4semidirect
21. #16839869C4semidirect
22. #16839868C4semidirect
28. C61×#441C4semidirect
184. #441#6923semidirect
198. C61#12827semidirect

Maximal subgroups

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

subgroupindex
#214621612
D61⋊#3622
#214621292
#214617392
#214609012
#214608862
#214546842
#1282761