Finite Group Databasebeta

← #30607290

Subgroups — #30607290

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#21462056C211yesmaximal, characteristic
2#21461703C211yesmaximal, characteristic
3#21460901C212yesmaximal, complemented
4#21460883C212yesmaximal, complemented
5#21454410C211yesmaximal, characteristic
6D61⋊M32C2212yes—
7D61⋊#108C2212yes—
8#16840748—21no—
9#16840659—21no—
10#16840658—21no—
11#16840631—21no—
12C2×#14519783C2211yescharacteristic
13#16840243—21no—
14#16839802—21no—
15#16839801—21no—
16#16839801—21no—
17#16839800C411yescharacteristic
18#16839797C411yescharacteristic
19#16839797C2211yescharacteristic
20#106×D61C411yescharacteristic
21#106×D61C2211yescharacteristic
22C2×#106×C61C411yescharacteristic
23D61⋊M16—22no—
24#14519852—22no—
25#14519851—22no—
26D61⋊C16—22no—
27#14519848—22no—
28#14519847—22no—
29#14519838—41no—
30#14519837—41no—
31C2×#11758222D411yescharacteristic
32#14519783—22no—
33#14519783—22no—
34C2×#11758194D411yescharacteristic
35C2×#11758189D411yescharacteristic
36C2×#11758189D411yescharacteristic
37C2×C8×D61C2×C411yescharacteristic
38C2×C8×D61C2311yescharacteristic
39#14519742—41no—
40#14519739—41no—
41C4×C22⋊D61—41no—
42C4×C22⋊D61—41no—
43#14519736—21no—
44#14519735—21no—
45#14519735—21no—
46C4⋊C4×D61—21no—
47C4⋊C4×D61—21no—
48#14519711—21no—
49#14519710—21no—
50#14519710—21no—
51#14519709C2×C411yescharacteristic
52#14519709C2×C411yescharacteristic
53#14519708—21no—
54#14519708—21no—
55C22×C8×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61—21no—
57#106×C61—21no—
58#106×C61C2×C411yescharacteristic
59#106×C61C2×C411yescharacteristic
60C22×C4×C61—41no—
61C22×C4×C61C22⋊C411yescharacteristic
62C2×C22⋊D61D811yescharacteristic
63C2×C22⋊D61SD1611yescharacteristic
64#11758222—22no—
65#11758222—22no—
66C2×D244SD1611yescharacteristic
67C2×C4×D61—41no—
68C2×C4×D61—41no—
69C2×C4×D61C22⋊C411yescharacteristic
70C2×C4×D61C2×D411yescharacteristic
71C2×Dic122D811yescharacteristic
72#11758217—42no—
73#11758213—42no—
74D61⋊C8—42no—
75C2×C8×C61—21no—
76C2×C8×C61—21no—
77C2×C8×C61C22⋊C411yescharacteristic
78C2×C8×C61C22×C411yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C22⋊Dic61—41no—
83#11758198—41no—
84#11758198—41no—
85C4⋊Dic61—21no—
86C4⋊Dic61—21no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—41no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92#11758194—22no—
93C2×#92418C22⋊C411yescharacteristic
94C2×#92418C2×D411yescharacteristic
95#11758189—22no—
96#11758189—22no—
97C8×D61—21no—
98C8×D61—21no—
99C8×D61#4112yes—
100C8×D61#4112yes—
101#11758187—42no—
102C23×C61#10211yescharacteristic
103C22×D61#10211yescharacteristic
104C22×D61C2×SD1611yescharacteristic
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—161no—
110C2×C4×C61#10211yescharacteristic
111C2×C4×C61C2×C22⋊C411yescharacteristic
112C22⋊D61—22no—
113C22⋊D61—22no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61#10211yescharacteristic
117C2×Dic61C2×D811yescharacteristic
118D244—22no—
119C4×D61—21no—
120C4×D61—21no—
121C4×D61—161no—
122C4×D61—161no—
123C4×D61#12312yes—
124C4×D61#13712yes—
125Dic122—22no—
126#92420—82no—
127C8×C61—21no—
128C8×C61#11711yescharacteristic
129C8×C61#11711yescharacteristic
130#92418—21no—
131#92418#12312yes—
132#12874—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—41no—
135C22×C61C2×#10211yescharacteristic
136C2×D61—21no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61#48312yes—
140C4×C61—21no—
141C4×C61—81no—
142C4×C61—81no—
143C4×C61#38111yescharacteristic
144C4×C61#41911yescharacteristic
145Dic61—21no—
146Dic61—81no—
147Dic61—81no—
148Dic61#48012yes—
149#2912—611no—
150#2115—611no—
151#1813—611no—
152#1389—612no—
153#1383—612no—
154C2×C61—21no—
155C2×C61—41no—
156C2×C61#182311yescharacteristic
157D61—22no—
158D61—41no—
159C2×#131—611no—
160#520—1221no—
161C2×M32—612no—
162C2×#108—612no—
163#428—1221no—
164#428—1221no—
165#428—1221no—
166#427—611no—
167#427—611no—
168#427—611no—
169C2×#106—611no—
170C2×#106—611no—
171C2×#106#692311yescharacteristic
172#413—1221no—
173#349—1221no—
174#349—1221no—
175#338—1221no—
176C61#1287411yescharacteristic, complemented, Sylow
177C2×#41—611no—
178#131—1222no—
179#131—1222no—
180C2×M16—611no—
181C2×M16—611no—
182C2×M16—611no—
183C2×M16—1222no—
184C22×C8—611no—
185C22×C8—611no—
186C22×C8C2×#692311yescharacteristic
187C4×Q8—2441no—
188C4×D4—2441no—
189C4×D4—2441no—
190C4×D4—2441no—
191#117—1221no—
192#117—1221no—
193#117—1221no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197M32—1222no—
198M32—1222no—
199C2×C16—1222no—
200#108—1222no—
201#108—1222no—
202#107—1221no—
203#107—1221no—
204#107—1221no—
205#106—21no—
206#106—611no—
207#106—611no—
208#106—1221no—
209#106—1221no—
210#106C2×#692311yescharacteristic
211#106C2×#692311yescharacteristic
212#101—2441no—
213#100—2441no—
214#41—1222no—
215#41—1222no—
216C2×Q8—611no—
217C2×D4—611no—
218C2×D4—611no—
219C2×D4—611no—
220C22×C4—41no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—2441no—
224C22×C4—2441no—
225C22×C4C22⋊#692311yescharacteristic
226M16—1222no—
227M16—1222no—
228M16—1222no—
229M16—2442no—
230M16—2442no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—611no—
234C2×C8—612no—
235C2×C8—612no—
236C2×C8—611no—
237C2×C8—1221no—
238C2×C8—1221no—
239C2×C8—2442no—
240C2×C8C22⋊#692311yescharacteristic
241C2×C8C22×#692311yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—41no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C42—2441no—
253C42—2441no—
254C42—2441no—
255C16—2442no—
256C23—611no—
257C23—611no—
258C23#1451983911yescharacteristic
259Q8—1222no—
260D4—1222no—
261D4—1222no—
262D4—1222no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—161no—
268C2×C4—611no—
269C2×C4—612no—
270C2×C4—612no—
271C2×C4—611no—
272C2×C4—1221no—
273C2×C4—1221no—
274C2×C4—9761no—
275C2×C4—9761no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4#1451983911yescharacteristic
279C2×C4C2×C22⋊#692311yescharacteristic
280C8—21no—
281C8—612no—
282C8—1221no—
283C8—4882no—
284C8#1451985611yescharacteristic
285C8#1451985611yescharacteristic
286C22—21no—
287C22—41no—
288C22—612no—
289C22—1221no—
290C22—2441no—
291C22—2441no—
292C22C2×#1451983911yescharacteristic
293C4—21no—
294C4—81no—
295C4—81no—
296C4—612no—
297C4—1221no—
298C4—4881no—
299C4—4881no—
300C4#1684070511yescharacteristic
301C4#1684075511yescharacteristic
302C2—21no—
303C2—41no—
304C2—1222no—
305C2—2441no—
306C2#2146172211yescharacteristic
subgroupG/H
centerC2#21461722
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC2×#106×C61C4
socleC2×C61#1823
prime radicalC2×#11758222D4
cosocleC2×C8×D61C23
hypercenterC2×#106#6923
hypocenterC61#12874
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #21460901C2semidirect
4. #21460883C2semidirect
176. C61#12874semidirect

Maximal subgroups

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

subgroupindex
#214620562
#214617032
#214609012
#214608832
#214544102
#1287461