Finite Group Databasebeta

← #30607191

Subgroups — #30607191

Order 15616.

358 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 96 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#21462166C211yesmaximal, characteristic, complemented
2C2×#16840687C211yesmaximal, characteristic, complemented
3#21461707C211yesmaximal, characteristic
4#21461705C211yesmaximal, characteristic
5#21460897C211yesmaximal, characteristic, complemented
6#21460891C211yesmaximal, characteristic, complemented
7#21458920C211yesmaximal, characteristic
8D61⋊#108C2211yescharacteristic
9C2×#14519847C2211yescharacteristic
10#16840772C2211yescharacteristic
11C2×#14519845C2211yescharacteristic
12#16840759—21no—
13#16840753—21no—
14#16840687—21no—
15#16840687—21no—
16#16840687—21no—
17#16840686—21no—
18#16840645—21no—
19#16840641—21no—
20#131×D61C2211yescharacteristic
21#16840180—21no—
22#16840180C411yescharacteristic, complemented
23#16840179C411yescharacteristic, complemented
24#16840178—21no—
25#16840178C411yescharacteristic, complemented
26C2×#14519716—21no—
27C2×#14519716C2211yescharacteristic
28M32×D61—21no—
29M32×D61C2211yescharacteristic
30C61×#504C411yescharacteristic, complemented
31C2×#11758213—21no—
32D61⋊M16—21no—
33#14519856—21no—
34C2×C4⋊#6923—21no—
35#14519848—21no—
36#14519847—21no—
37#14519847—21no—
38#14519847—21no—
39#14519846—21no—
40#14519845—21no—
41#14519845—21no—
42#14519845—21no—
43#14519842—41no—
44#14519841—41no—
45#14519840—41no—
46#14519839—41no—
47#41×D61D411yescharacteristic
48#14519785—21no—
49#14519785Q811yescharacteristic
50#14519784Q811yescharacteristic
51#14519783—21no—
52#14519783C2×C411yescharacteristic
53M16×D61—21no—
54M16×D61D411yescharacteristic
55C2×C8×D61—21no—
56C2×C8×D61C2311yescharacteristic
57#14519717—21no—
58#14519717C2×C411yescharacteristic
59#14519716—21no—
60#14519716—21no—
61#14519716—21no—
62#14519716D411yescharacteristic
63#14519716D411yescharacteristic
64#14519716D411yescharacteristic
65#14519716D411yescharacteristic
66C2×#11758185—21no—
67C2×#11758185C2×C411yescharacteristic
68C16×D61—21no—
69C16×D61—21no—
70C16×D61—21no—
71#131×C61C2×C411yescharacteristic
72M32×C61—21no—
73M32×C61C2×C411yescharacteristic
74C2×C16×C61—21no—
75C2×C16×C61C2×C411yescharacteristic
76C22×#6923—41no—
77#41×C61C4⋊C411yescharacteristic
78#11758226SD1611yescharacteristic
79Q8×D61SD1611yescharacteristic
80#11758224—21no—
81#11758224SD1611yescharacteristic
82D4×D61—21no—
83D4×D61SD1611yescharacteristic
84#11758222—21no—
85#11758222C4⋊C411yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61C2×D411yescharacteristic
88C22⋊#6923—41no—
89#11758217—41no—
90C2×#92420—41no—
91C4⋊#6923—41no—
92C4⋊#6923—41no—
93C4⋊#6923—41no—
94C4×#6923—41no—
95#11758213—41no—
96#11758213—41no—
97#11758213—41no—
98D61⋊C8—41no—
99M16×C61—21no—
100M16×C61C4⋊C411yescharacteristic
101C2×C8×C61—21no—
102C2×C8×C61C22×C411yescharacteristic
103#11758194—21no—
104#11758194C4⋊C411yescharacteristic
105C2×#92418—21no—
106C2×#92418C2×Q811yescharacteristic
107#11758189—21no—
108#11758189—21no—
109#11758189—21no—
110C8×D61—21no—
111C8×D61—21no—
112C8×D61—21no—
113C8×D61C2×D411yescharacteristic
114C8×D61C2×D411yescharacteristic
115C8×D61#4111yescharacteristic
116C8×D61#4111yescharacteristic
117C16×C61—21no—
118C16×C61C22⋊C411yescharacteristic
119C16×C61C22⋊C411yescharacteristic
120#11758185—21no—
121#11758185C22⋊C411yescharacteristic
122#11758185C22⋊C411yescharacteristic
123C22×D61—21no—
124C22×D61#13511yescharacteristic
125C2×#6923—81no—
126C2×#6923—81no—
127C2×#6923—161no—
128Q8×C61#10611yescharacteristic
129D4×C61—21no—
130D4×C61#10611yescharacteristic
131C2×C4×C61—21no—
132C2×C4×C61C2×C4⋊C411yescharacteristic
133C22⋊D61—21no—
134C22⋊D61—21no—
135C22⋊D61—21no—
136C2×Dic61—21no—
137C2×Dic61#13511yescharacteristic
138D244—21no—
139D244#10611yescharacteristic
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61#12111yescharacteristic
144C4×D61#12111yescharacteristic
145C4×D61C2×SD1611yescharacteristic
146C4×D61C2×SD1611yescharacteristic
147Dic122—21no—
148Dic122#10611yescharacteristic
149#92420—81no—
150#92420—81no—
151C8×C61—21no—
152C8×C61C2×C22⋊C411yescharacteristic
153C8×C61#11711yescharacteristic
154#92418—21no—
155#92418C22⋊Q811yescharacteristic
156#92418C22⋊Q811yescharacteristic
157#12833—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61#42711yescharacteristic
160C2×D61—21no—
161C2×D61—41no—
162C2×D61—81no—
163C2×D61#46511yescharacteristic
164C2×D61#46511yescharacteristic
165#6923—161no—
166#6923—161no—
167C4×C61—21no—
168C4×C61#38011yescharacteristic
169C4×C61C2×#10611yescharacteristic
170Dic61—21no—
171Dic61#46511yescharacteristic
172Dic61#46511yescharacteristic
173#3407—611no—
174#2155—611no—
175C2×#365—611no—
176#1815—611no—
177#1814—611no—
178#1388—611no—
179#1386—611no—
180C2×C61—21no—
181C2×C61—41no—
182C2×C61#180711yescharacteristic
183D61—21no—
184D61—21no—
185D61—41no—
186C2×#131—611no—
187#504—611no—
188#504—611no—
189#504—611no—
190#504—1221no—
191#504—1221no—
192#504#692311yescharacteristic, complemented
193C2×M32—611no—
194C2×M32—611no—
195C2×M32—1221no—
196C2×M32—1221no—
197C2×#108—611no—
198C2×#108—611no—
199#427—611no—
200C2×#106—611no—
201#421—1221no—
202#417—1221no—
203#365—1221no—
204#365—1221no—
205#365—1221no—
206#365—1221no—
207#344—1221no—
208#343—1221no—
209C61#1283311yescharacteristic, complemented, Sylow
210C2×#41—611no—
211#131—611no—
212#131—611no—
213#131—611no—
214#131—1221no—
215#131—1221no—
216#131C2×#692311yescharacteristic
217C2×M16—611no—
218C2×M16—1221no—
219C2×M16—1221no—
220C2×M16—1221no—
221C22×C8—611no—
222C22×C8—1221no—
223#117—1221no—
224C2×C4⋊C4—1221no—
225M32—21no—
226M32—611no—
227M32—611no—
228M32—611no—
229M32—611no—
230M32—611no—
231M32—1221no—
232M32—1221no—
233M32—1221no—
234M32—1221no—
235M32C2×#692311yescharacteristic
236C2×C16—21no—
237C2×C16—611no—
238C2×C16—1221no—
239C2×C16—1221no—
240C2×C16—1221no—
241C2×C16—1221no—
242C2×C16C2×#692311yescharacteristic
243#108—1221no—
244#108—1221no—
245#108—1221no—
246#108—1221no—
247#107—1221no—
248#106—1221no—
249#106—1221no—
250#106—1221no—
251#104—2441no—
252#104—2441no—
253#103—2441no—
254#102—2441no—
255#41—611no—
256#41—611no—
257#41—611no—
258#41—1221no—
259#41—1221no—
260#41C4⋊#692311yescharacteristic
261C2×Q8—611no—
262C2×D4—611no—
263C2×D4—1221no—
264C22×C4—611no—
265C22×C4—1221no—
266C22×C4—2441no—
267M16—21no—
268M16—611no—
269M16—1221no—
270M16—1221no—
271M16—1221no—
272M16—1221no—
273M16—2441no—
274M16—2441no—
275M16—2441no—
276M16—2441no—
277M16C4⋊#692311yescharacteristic
278C2×C8—21no—
279C2×C8—611no—
280C2×C8—611no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—1221no—
285C2×C8—1221no—
286C2×C8—1221no—
287C2×C8—1221no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8C22×#692311yescharacteristic
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C4⋊C4—2441no—
294C22⋊C4—2441no—
295C42—2441no—
296C16—21no—
297C16—611no—
298C16—611no—
299C16—1221no—
300C16C22⋊#692311yescharacteristic
301C16C22⋊#692311yescharacteristic
302C23—611no—
303C23—1221no—
304Q8—611no—
305Q8—1221no—
306Q8#1451984511yescharacteristic
307D4—21no—
308D4—611no—
309D4—1221no—
310D4—1221no—
311D4—1221no—
312D4—1221no—
313D4#1451984511yescharacteristic
314C2×C4—21no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—9761no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4C2×C4⋊#692311yescharacteristic
328C8—21no—
329C8—611no—
330C8—611no—
331C8—1221no—
332C8—4881no—
333C8—4881no—
334C8C2×C22⋊#692311yescharacteristic
335C8#1451985611yescharacteristic
336C22—21no—
337C22—611no—
338C22—611no—
339C22—1221no—
340C22—4881no—
341C22—2441no—
342C22#1684077211yescharacteristic
343C4—21no—
344C4—611no—
345C4—611no—
346C4—1221no—
347C4—9761no—
348C4—9761no—
349C4#1684070411yescharacteristic
350C4C2×#1451984511yescharacteristic
351C2—21no—
352C2—41no—
353C2—1221no—
354C2—1221no—
355C2—2441no—
356C2#2146169511yescharacteristic
subgroupG/H
centerC2#21461695
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#504C4
socleC2×C61#1807
prime radical#41×D61D4
cosocleC2×C8×D61C23
hypercenter#504#6923
hypocenterC61#12833
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504

Complements

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

NH ≅ G/Ntype
1. #21462166C2semidirect
2. C2×#16840687C2semidirect
5. #21460897C2semidirect
6. #21460891C2semidirect
22. #16840180C4semidirect
23. #16840179C4semidirect
25. #16840178C4semidirect
30. C61×#504C4semidirect
192. #504#6923semidirect
209. C61#12833semidirect

Maximal subgroups

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

subgroupindex
#214621662
C2×#168406872
#214617072
#214617052
#214608972
#214608912
#214589202
#1283361