Finite Group Databasebeta

← #30607600

Subgroups — #30607600

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#21462580C211yesmaximal, characteristic, complemented
2#21462140C211yesmaximal, characteristic
3#21462129C211yesmaximal, characteristic, complemented
4#21461976C211yesmaximal, characteristic
5#21460887C211yesmaximal, characteristic, complemented
6#21460868C211yesmaximal, characteristic, complemented
7C2×#16840201C211yesmaximal, characteristic
8#16840830—21no—
9D61⋊M32C2211yescharacteristic
10#16840802—22no—
11Q16×#6923—22no—
12#16840772C2211yescharacteristic
13#16840772C2211yescharacteristic
14#16840760—21no—
15#16840755—21no—
16#16840742—21no—
17#16840725C2211yescharacteristic
18#16840678—22no—
19#16840675—22no—
20C2×#14519796C2211yescharacteristic
21C2×Q16×D61C2211yescharacteristic
22#16840201—22no—
23#16840201—22no—
24C2×Dic488C411yescharacteristic, complemented
25C2×#14519723C411yescharacteristic, complemented
26C2×#14519721C411yescharacteristic, complemented
27C2×#14519716C2211yescharacteristic
28C2×SD32×C61C411yescharacteristic, complemented
29D61⋊M16D411yescharacteristic
30Q8×#6923—24no—
31Q8×#6923—42no—
32#14519856—21no—
33#14519856—21no—
34#14519856—42no—
35#14519856D411yescharacteristic
36#14519852—21no—
37#14519851—21no—
38D61⋊C16—21no—
39#14519846—21no—
40#14519846—21no—
41#14519845—21no—
42#14519845D412yes—
43#14519841—42no—
44#14519840—24no—
45#14519835—42no—
46#14519831—21no—
47C8×#6923—21no—
48C2×#11758224—21no—
49C2×Q8×D61—21no—
50#14519796—21no—
51#14519796—21no—
52#14519796—21no—
53#14519796—21no—
54C2×Dic244C2×C411yescharacteristic
55C2×Dic244C2×C411yescharacteristic
56C2×#11758202—21no—
57Q16×D61—21no—
58Q16×D61—21no—
59Q16×D61D412yes—
60Q16×D61D412yes—
61C2×#11758200—21no—
62C2×C8×D61C2311yescharacteristic
63Dic488—22no—
64#14519723—22no—
65#14519721—22no—
66#14519716—21no—
67#14519716—21no—
68C2×#11758185C2×C411yescharacteristic
69C2×Q16×C61C2×C411yescharacteristic
70C2×D8×C61C2×C411yescharacteristic
71SD32×C61—22no—
72C2×C16×C61C2×C411yescharacteristic
73C2×Q8×C61—21no—
74C2×D4×C61—21no—
75C2×C22⋊D61—41no—
76C22×Dic61—41no—
77Q8×D61—22no—
78Q8×D61—22no—
79Q8×D61—41no—
80Q8×D61—41no—
81#11758224—41no—
82#11758224—41no—
83#11758224—41no—
84#11758224—41no—
85C2×C4×D61—41no—
86C2×C4×D61C2×D411yescharacteristic
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122—41no—
90C22⋊#6923—41no—
91C22⋊#6923—41no—
92C22⋊#6923D812yes—
93#11758217—21no—
94C4⋊#6923—22no—
95C4⋊#6923—21no—
96C4⋊#6923—44no—
97C4⋊#6923—41no—
98C4×#6923—21no—
99C4×#6923—44no—
100C4×#6923—41no—
101C4×#6923—41no—
102#11758213—21no—
103D61⋊C8—21no—
104Q16×C61—21no—
105Q16×C61C22⋊C412yes—
106D8×C61—21no—
107D8×C61—21no—
108C2×C8×C61C22×C411yescharacteristic
109#11758202—22no—
110#11758202—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—
126C22×D61C2×D811yescharacteristic
127C2×#6923—22no—
128C2×#6923—42no—
129C2×#6923—81no—
130Q8×C61—22no—
131Q8×C61—41no—
132D4×C61—41no—
133D4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61C4×D411yescharacteristic
136C22⋊D61—81no—
137C22⋊D61—81no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61#13511yescharacteristic
143C4×D61—42no—
144C4×D61—42no—
145C4×D61#12011yescharacteristic
146C4×D61#12111yescharacteristic
147C4×D61AGL(1,ℤ/8)11yescharacteristic
148C4×D61AGL(1,ℤ/8)11yescharacteristic
149Dic122—22no—
150Dic122—41no—
151Dic122—42no—
152Dic122—42no—
153Dic122—41no—
154Dic122—41no—
155#92420—41no—
156C8×C61C2×C22⋊C411yescharacteristic
157C8×C61C4×D411yescharacteristic
158#92418#12111yescharacteristic
159#92418#12311yescharacteristic
160#13034—611nomaximal, Sylow
161C22×C61—81no—
162C22×C61—161no—
163C22×C61C4×D811yescharacteristic
164C2×D61—41no—
165C2×D61#44711yescharacteristic
166C2×D61#45911yescharacteristic
167#6923—42no—
168#6923—82no—
169#6923—161no—
170C4×C61—42no—
171C4×C61#38611yescharacteristic
172C4×C61#44211yescharacteristic
173Dic61—42no—
174Dic61—81no—
175Dic61#44911yescharacteristic
176Dic61#46311yescharacteristic
177C2×#510—611no—
178#2950—611no—
179#2145—611no—
180#2141—611no—
181#1976—611no—
182#1384—611no—
183#1378—611no—
184C2×C61—21no—
185C2×C61—161no—
186C2×C61#187911yescharacteristic
187D61—21no—
188D61—21no—
189C2×#135—611no—
190C22×Q16—611no—
191#519—1221no—
192#510—1222no—
193#510—1222no—
194C2×Q32—611no—
195C2×Q32—611no—
196C2×SD32—611no—
197C2×SD32#692311yescharacteristic, complemented
198C2×M32—611no—
199C2×M32—611no—
200#441—1222no—
201C4×Q16—1222no—
202#427—611no—
203#427—611no—
204#421—1221no—
205#419—1221no—
206#410—1221no—
207#405—611no—
208#360—1222no—
209#358—1222no—
210C61#1303411yescharacteristic, complemented, Sylow
211C2×#41—1221no—
212C22×Q8—1221no—
213#135—1221no—
214#135—1221no—
215#135—1221no—
216#135—1221no—
217C2×Q16—612no—
218C2×Q16—612no—
219C2×Q16—611no—
220C2×Q16—611no—
221C2×Q16—1221no—
222C2×Q16—1221no—
223C2×Q16—1221no—
224C2×Q16C2×#692311yescharacteristic
225C2×SD16—1221no—
226C2×D8C2×#692311yescharacteristic
227C2×M16—611no—
228C22×C8—611no—
229C4×Q8—1224no—
230C4×Q8—2442no—
231#117—611no—
232#117—1221no—
233#117—1221no—
234#117—2442no—
235Q32—1222no—
236Q32—1222no—
237SD32—22no—
238SD32—1222no—
239M32—1221no—
240M32—1221no—
241M32—1221no—
242M32—1221no—
243C2×C16—611no—
244C2×C16—1221no—
245C2×C16C2×#692311yescharacteristic
246#107—1221no—
247#107—1221no—
248#106—612no—
249#106—1221no—
250#104—2442no—
251#103—1224no—
252#99—2442no—
253#97—1221no—
254C4×C8—1221no—
255#41—2441no—
256#41—2441no—
257#41—2441no—
258#41—2441no—
259C2×Q8—21no—
260C2×Q8—1222no—
261C2×Q8—1222no—
262C2×Q8—1221no—
263C2×Q8—1221no—
264C2×Q8—2441no—
265C2×Q8—2441no—
266C2×Q8—2441no—
267C2×D4—21no—
268C2×D4—2441no—
269C22×C4—611no—
270C22×C4—2441no—
271C22×C4—2441no—
272Q16—21no—
273Q16—612no—
274Q16—1222no—
275Q16—1222no—
276Q16—1221no—
277Q16—1221no—
278Q16—1221no—
279Q16C22⋊#692312yes—
280SD16—2441no—
281SD16—2441no—
282D8—21no—
283D8—21no—
284M16—1221no—
285M16—1221no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8—611no—
291C2×C8—1221no—
292C2×C8C22×#692311yescharacteristic
293C4⋊C4—1221no—
294C4⋊C4—1222no—
295C4⋊C4—2441no—
296C4⋊C4—2444no—
297C22⋊C4—612no—
298C22⋊C4—2441no—
299C22⋊C4—2441no—
300C42—1221no—
301C42—2441no—
302C42—2441no—
303C42—2444no—
304C16—21no—
305C16—1221no—
306C16—2441no—
307C23—41no—
308C23—611no—
309Q8—22no—
310Q8—41no—
311Q8—1222no—
312Q8—2442no—
313Q8—2442no—
314Q8—2441no—
315Q8—2441no—
316Q8—2441no—
317D4—41no—
318D4—41no—
319D4—4881no—
320D4—4881no—
321C2×C4—41no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—1222no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4D4×#692311yescharacteristic
337C8—611no—
338C8—611no—
339C8—2441no—
340C8C2×C22⋊#692311yescharacteristic
341C8D4×#692311yescharacteristic
342C22—81no—
343C22—161no—
344C22—611no—
345C22—611no—
346C22—2441no—
347C22D8×#692311yescharacteristic
348C4—42no—
349C4—611no—
350C4—611no—
351C4—9761no—
352C4—4882no—
353C4—4881no—
354C4—2442no—
355C4—2442no—
356C4#1684071011yescharacteristic
357C4#1684080311yescharacteristic
358C2—21no—
359C2—161no—
360C2—1221no—
361C2—1221no—
362C2#2146181411yescharacteristic
subgroupG/H
centerC2#21461814
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×SD32×C61C4
socleC2×C61#1879
prime radicalC2×#14519796C22
cosocleC2×C8×D61C23
hypercenterC2×SD32#6923
hypocenterC61#13034
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #21462580C2semidirect
3. #21462129C2semidirect
5. #21460887C2semidirect
6. #21460868C2semidirect
24. C2×Dic488C4semidirect
25. C2×#14519723C4semidirect
26. C2×#14519721C4semidirect
28. C2×SD32×C61C4semidirect
197. C2×SD32#6923semidirect
210. C61#13034semidirect

Maximal subgroups

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

subgroupindex
#214625802
#214621402
#214621292
#214619762
#214608872
#214608682
C2×#168402012
#1303461