Finite Group Databasebeta

← #30607573

Subgroups — #30607573

Order 15616.

462 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462595C211yesmaximal, characteristic, complemented
2#21462140C211yesmaximal, characteristic, complemented
3#21462134C211yesmaximal, characteristic, complemented
4#21461976C211yesmaximal, characteristic, complemented
5#21460881C211yesmaximal, characteristic, complemented
6#21460872C211yesmaximal, characteristic, complemented
7C2×#16840191C211yesmaximal, characteristic
8#16840840—21no—
9D61⋊M32C2211yescharacteristic
10#16840809—22no—
11#16840804—22no—
12D61⋊#108C2211yescharacteristic
13#16840772C2211yescharacteristic
14#16840760—21no—
15#16840760—21no—
16#16840742—21no—
17#16840725C2211yescharacteristic
18#16840678—22no—
19#16840676—22no—
20C2×#14519796C2211yescharacteristic
21C2×#14519796C2211yescharacteristic
22#16840191—22no—
23#16840191—22no—
24C2×Dic488C411yescharacteristic, complemented
25C2×#14519721C411yescharacteristic, complemented
26C2×#14519721C411yescharacteristic, complemented
27C2×C16×D61C2211yescharacteristic
28C2×D16×C61C411yescharacteristic, complemented
29#14519864—24no—
30#14519864—42no—
31D61⋊M16—21no—
32D61⋊M16D411yescharacteristic
33C2×#11758217—42no—
34#14519856—21no—
35#14519856D411yescharacteristic
36#14519852—21no—
37#14519851—21no—
38D61⋊C16—21no—
39#14519848D412yes—
40#14519847—21no—
41#14519846—21no—
42#14519845—21no—
43#14519841—24no—
44#14519841—42no—
45#14519835—42no—
46#14519831—21no—
47C8×#6923—21no—
48C2×#11758224—21no—
49C2×#11758224—21no—
50#14519796—21no—
51#14519796—21no—
52#14519796—21no—
53#14519796—21no—
54#14519796—21no—
55#14519796—21no—
56#14519796D412yes—
57#14519796D412yes—
58C2×Dic244C2×C411yescharacteristic
59C2×Dic244C2×C411yescharacteristic
60C2×#11758200—21no—
61C2×#11758200—21no—
62C2×C8×D61C2311yescharacteristic
63Dic488—22no—
64#14519721—22no—
65#14519721—22no—
66C2×#11758185C2×C411yescharacteristic
67C16×D61—21no—
68C16×D61—21no—
69C2×D8×C61C2×C411yescharacteristic
70C2×D8×C61C2×C411yescharacteristic
71D16×C61—22no—
72C2×C16×C61C2×C411yescharacteristic
73C2×D4×C61—21no—
74C2×D4×C61—21no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79#11758224—22no—
80#11758224—22no—
81#11758224—41no—
82#11758224—41no—
83#11758224—41no—
84#11758224—41no—
85#11758224—41no—
86#11758224—41no—
87C2×C4×D61C2×D411yescharacteristic
88C2×Dic122—21no—
89C2×Dic122—21no—
90C22⋊#6923—21no—
91C22⋊#6923—41no—
92#11758217—21no—
93#11758217—44no—
94#11758217—41no—
95C2×#92420—44no—
96C4⋊#6923—21no—
97C4⋊#6923—41no—
98C4×#6923—21no—
99C4×#6923—41no—
100#11758213—22no—
101#11758213D812yes—
102D61⋊C8—21no—
103D61⋊C8—41no—
104D8×C61—21no—
105D8×C61—21no—
106D8×C61—21no—
107D8×C61C22⋊C412yes—
108C2×C8×C61C22×C411yescharacteristic
109#11758200—22no—
110#11758200—22no—
111#11758200—41no—
112#11758200—41no—
113C2×#92418#4111yescharacteristic
114Dic244—21no—
115Dic244—21no—
116Dic244—21no—
117Dic244C22⋊C412yes—
118C8×D61C2×D411yescharacteristic
119C8×D61C2×D411yescharacteristic
120C8×D61C2×D411yescharacteristic
121C8×D61#4111yescharacteristic
122#11758187—41no—
123C16×C61—21no—
124#11758185—21no—
125C23×C61—41no—
126C23×C61—41no—
127C22×D61AGL(1,ℤ/8)11yescharacteristic
128C2×#6923—41no—
129C2×#6923—81no—
130D4×C61—22no—
131D4×C61—41no—
132D4×C61—41no—
133D4×C61—41no—
134C2×C4×C61C4×D411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145C2×Dic61AGL(1,ℤ/8)11yescharacteristic
146C4×D61#12011yescharacteristic
147C4×D61#12111yescharacteristic
148C4×D61C2×D811yescharacteristic
149C4×D61#13511yescharacteristic
150Dic122—22no—
151Dic122—41no—
152Dic122—41no—
153Dic122—41no—
154#92420—22no—
155#92420—42no—
156C8×C61C2×C22⋊C411yescharacteristic
157C8×C61C4×D411yescharacteristic
158#92418#12111yescharacteristic
159#92418#12311yescharacteristic
160#13016—611nomaximal, Sylow
161C22×C61—42no—
162C22×C61—81no—
163C22×C61—161no—
164C22×C61—161no—
165C22×C61#44211yescharacteristic
166C2×D61—41no—
167C2×D61#44911yescharacteristic
168C2×D61#45911yescharacteristic
169#6923—81no—
170#6923—161no—
171C4×C61#38611yescharacteristic
172C4×C61C4×D811yescharacteristic
173Dic61—42no—
174Dic61—81no—
175Dic61#44711yescharacteristic
176Dic61#46311yescharacteristic
177C2×#508—611no—
178#2957—611no—
179#2145—611no—
180#2143—611no—
181#1976—611no—
182#1382—611no—
183#1379—611no—
184C2×C61—21no—
185C2×C61—82no—
186C2×C61—161no—
187C2×C61#187911yescharacteristic
188D61—21no—
189D61—21no—
190C2×#135—611no—
191C2×#135—611no—
192#568—1221no—
193#508—1222no—
194#508—1222no—
195C2×Q32—611no—
196C2×SD32—611no—
197C2×SD32—611no—
198C2×D16#692311yescharacteristic, complemented
199C2×M32—611no—
200C22×C16—611no—
201#444—1222no—
202#443—1222no—
203C2×#108—611no—
204#427—611no—
205#421—1221no—
206#421—1221no—
207#410—1221no—
208#405—611no—
209#360—1222no—
210#359—1222no—
211C61#1301611yescharacteristic, complemented, Sylow
212C2×#41—1221no—
213C2×#41—1221no—
214#135—612no—
215#135—612no—
216#135—1221no—
217#135—1221no—
218#135—1221no—
219#135—1221no—
220#135—1221no—
221#135—1221no—
222C2×Q16—611no—
223C2×Q16—611no—
224C2×SD16—1221no—
225C2×SD16—1221no—
226C2×D8C2×#692311yescharacteristic
227C2×D8C2×#692311yescharacteristic
228#131—1224no—
229#131—2442no—
230C2×M16—611no—
231C2×M16—1221no—
232C2×M16—2442no—
233C22×C8—611no—
234#117—611no—
235#117—1221no—
236Q32—1222no—
237SD32—1222no—
238SD32—1222no—
239D16—22no—
240M32—1221no—
241M32—1221no—
242C2×C16—611no—
243C2×C16—1221no—
244C2×C16—1221no—
245C2×C16—1221no—
246C2×C16C2×#692311yescharacteristic
247#108—612no—
248#108—1221no—
249#107—1221no—
250#106—1221no—
251#104—1224no—
252#104—2442no—
253#99—2442no—
254#97—1221no—
255C4×C8—1221no—
256#41—1222no—
257#41—1222no—
258#41—2441no—
259#41—2441no—
260#41—2441no—
261#41—2441no—
262#41—2441no—
263#41—2441no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—2441no—
269C2×D4—2441no—
270C22×C4—611no—
271C22×C4—2441no—
272C22×C4—2441no—
273Q16—612no—
274Q16—1221no—
275Q16—1221no—
276Q16—1221no—
277SD16—1222no—
278SD16—1222no—
279SD16—2441no—
280SD16—2441no—
281D8—21no—
282D8—21no—
283D8—21no—
284D8C22⋊#692312yes—
285M16—612no—
286M16—1221no—
287M16—1222no—
288M16—2444no—
289M16—2441no—
290C2×C8—611no—
291C2×C8—611no—
292C2×C8—611no—
293C2×C8—611no—
294C2×C8—611no—
295C2×C8—1221no—
296C2×C8—2444no—
297C2×C8—2441no—
298C2×C8C22×#692311yescharacteristic
299C4⋊C4—1221no—
300C4⋊C4—2441no—
301C22⋊C4—1221no—
302C22⋊C4—2441no—
303C42—1221no—
304C42—2441no—
305C16—21no—
306C16—1221no—
307C16—2441no—
308C23—41no—
309C23—41no—
310C23—611no—
311Q8—1222no—
312Q8—2441no—
313Q8—2441no—
314Q8—2441no—
315D4—22no—
316D4—41no—
317D4—41no—
318D4—41no—
319D4—4881no—
320D4—4881no—
321D4—2442no—
322D4—2442no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4D4×#692311yescharacteristic
337C8—611no—
338C8—611no—
339C8—1222no—
340C8—2442no—
341C8C2×C22⋊#692311yescharacteristic
342C8D4×#692311yescharacteristic
343C22—42no—
344C22—81no—
345C22—161no—
346C22—161no—
347C22—611no—
348C22—611no—
349C22—2441no—
350C22#1684080311yescharacteristic
351C4—611no—
352C4—611no—
353C4—9761no—
354C4—4881no—
355C4—4881no—
356C4—2442no—
357C4#1684071011yescharacteristic
358C4D8×#692311yescharacteristic
359C2—21no—
360C2—82no—
361C2—161no—
362C2—1221no—
363C2—1221no—
364C2#2146181411yescharacteristic
subgroupG/H
centerC2#21461814
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×D16×C61C4
socleC2×C61#1879
prime radicalC2×#16840191C2
cosocleC2×C8×D61C23
hypercenterC2×D16#6923
hypocenterC61#13016
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #21462595C2semidirect
2. #21462140C2semidirect
3. #21462134C2semidirect
4. #21461976C2semidirect
5. #21460881C2semidirect
6. #21460872C2semidirect
24. C2×Dic488C4semidirect
25. C2×#14519721C4semidirect
26. C2×#14519721C4semidirect
28. C2×D16×C61C4semidirect
198. C2×D16#6923semidirect
211. C61#13016semidirect

Maximal subgroups

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

subgroupindex
#214625952
#214621402
#214621342
#214619762
#214608812
#214608722
C2×#168401912
#1301661