Finite Group Databasebeta

← #30599163

Subgroups — #30599163

Order 15616.

430 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 102 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#21461759C211yesmaximal, characteristic, complemented
2D61⋊#335C211yesmaximal, characteristic, complemented
3#21461330C212yesmaximal
4#21460688C212yesmaximal, complemented
5#21454526C211yesmaximal, characteristic
6C2×#14519848—21no—
7C2×#14519847—21no—
8#16840767C2212yes—
9D61⋊(C4⋊C8)C2212yes—
10#16840626—21no—
11#16840625—21no—
12#16840621—22no—
13#16840620—22no—
14C2×#14519783—21no—
15#16840309C2211yescharacteristic
16#16839840C411yescharacteristic
17#16839839C411yescharacteristic
18#16839837—21no—
19C8×D244C411yescharacteristic
20C8×C22⋊D61—21no—
21#16839784C2211yescharacteristic
22#16839727—21no—
23C4×C8×D61C2211yescharacteristic
24C8×D4×C61C411yescharacteristic
25C2×#11758213—22no—
26C2×D61⋊C8—22no—
27#14519848—42no—
28#14519847—42no—
29#14519844—22no—
30#14519844—22no—
31#14519844—22no—
32C4⋊#92420—22no—
33C2×#11758222—21no—
34#14519783—42no—
35#14519783—42no—
36C2×#11758194—21no—
37C2×#11758189—21no—
38C2×#11758189—21no—
39C2×C8×D61—21no—
40C2×C8×D61D411yescharacteristic
41C2×C8×D61D411yescharacteristic
42#14519776D411yescharacteristic
43#14519773D411yescharacteristic
44#14519763—21no—
45#14519752Q811yescharacteristic
46#14519750—21no—
47#14519748Q811yescharacteristic
48C4×D244C2×C411yescharacteristic
49C4×C22⋊D61—21no—
50C42×D61C2311yescharacteristic
51C4⋊#92418C2×C411yescharacteristic
52#14519706—21no—
53C22⋊#92418—21no—
54#14519689—21no—
55#14519689—21no—
56C4×#92418C2×C411yescharacteristic
57C8×Dic61D411yescharacteristic
58C8×Dic61D411yescharacteristic
59C22×C8×C61—21no—
60C4×D4×C61C2×C411yescharacteristic
61C4⋊C8×C61C2×C411yescharacteristic
62C22⋊C8×C61—21no—
63C4×C8×C61C2×C411yescharacteristic
64C2×D4×C61C4⋊C411yescharacteristic
65C22×C4×C61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69#11758222—41no—
70#11758222—41no—
71#11758222—41no—
72#11758222—41no—
73C2×D244—21no—
74C2×D244C4⋊C411yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61C2×D411yescharacteristic
77C2×C4×D61C2×Q811yescharacteristic
78C2×C4×D61#4111yescharacteristic
79C2×Dic122—21no—
80C2×#92420—42no—
81C2×#92420—42no—
82#11758213—42no—
83#11758213—42no—
84D61⋊C8—82no—
85C2×C8×C61—21no—
86C2×C8×C61—42no—
87C2×C8×C61C22⋊C411yescharacteristic
88C2×C8×C61C22⋊C411yescharacteristic
89C4⋊C4×C61C4⋊C411yescharacteristic
90C22⋊C4×C61—21no—
91C42×C61C22×C411yescharacteristic
92C22⋊Dic61—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61C4⋊C411yescharacteristic
96#11758196—21no—
97C4×Dic61C2×D411yescharacteristic
98C4×Dic61C2×D411yescharacteristic
99C4×Dic61#4111yescharacteristic
100#11758194—42no—
101C2×#92418—21no—
102C2×#92418C22⋊C411yescharacteristic
103C2×#92418C22⋊C411yescharacteristic
104#11758189—41no—
105#11758189—41no—
106#11758189—42no—
107C8×D61—21no—
108C8×D61—21no—
109C8×D61—42no—
110C8×D61D812yes—
111C8×D61SD1612yes—
112C23×C61—21no—
113C22×D61—21no—
114C22×D61C22⋊Q811yescharacteristic
115D4×C61—41no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61C2×C22⋊C411yescharacteristic
120C2×C4×C61C2×C4⋊C411yescharacteristic
121C2×C4×C61#11711yescharacteristic
122C22⋊D61—41no—
123C22⋊D61—41no—
124C22⋊D61—41no—
125C22⋊D61—41no—
126C22⋊D61—41no—
127C22⋊D61—41no—
128C2×Dic61—21no—
129C2×Dic61#12111yescharacteristic
130C2×Dic61#12111yescharacteristic
131C2×Dic61C22⋊Q811yescharacteristic
132D244—41no—
133D244—41no—
134D244—41no—
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—41no—
138C4×D61—41no—
139C4×D61—41no—
140C4×D61C2×D811yescharacteristic
141C4×D61C2×SD1611yescharacteristic
142C4×D61AGL(1,ℤ/8)11yescharacteristic
143C4×D61#13711yescharacteristic
144Dic122—41no—
145Dic122—41no—
146#92420—82no—
147#92420—82no—
148C8×C61—21no—
149C8×C61—41no—
150C8×C61#10212yes—
151#92418—21no—
152#92418—41no—
153#92418#10212yes—
154#8684—611nomaximal, Sylow
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61#38011yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61#47411yescharacteristic
165C2×D61#47611yescharacteristic
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—41no—
169C4×C61C2×#10211yescharacteristic
170C4×C61#41711yescharacteristic
171Dic61—21no—
172Dic61—41no—
173Dic61#45911yescharacteristic
174Dic61#46111yescharacteristic
175Dic61#47211yescharacteristic
176Dic61#47311yescharacteristic
177#2931—611no—
178#1848—611no—
179C2×#335—611no—
180#1547—612no—
181#1292—612no—
182C2×C61—81no—
183C2×C61#180211yescharacteristic
184C2×C61#181311yescharacteristic
185C2×C61#181611yescharacteristic
186D61—21no—
187D61—21no—
188D61—81no—
189C2×#131—1221no—
190#532—611no—
191#436—611no—
192#436—611no—
193#436—1221no—
194C8×D4—611no—
195C8×D4—1221no—
196C8×D4#692311yescharacteristic
197C2×#108—1221no—
198C2×#108—1221no—
199#423—611no—
200#423—612no—
201C2×C4⋊C8—612no—
202#408—1221no—
203C2×C4×C8—611no—
204#335—1221no—
205#335—1221no—
206#332—1222no—
207#331—1222no—
208C61#868411yescharacteristic, complemented, Sylow
209C2×#41—1221no—
210#131—2442no—
211#131—2442no—
212C2×M16—1221no—
213C2×M16—1221no—
214C2×M16—1221no—
215C2×M16—1222no—
216C22×C8—21no—
217C22×C8—611no—
218C22×C8—611no—
219C22×C8—1221no—
220C22×C8—1222no—
221C4⋊Q8—611no—
222#127—611no—
223#124—1221no—
224#121—611no—
225#121—611no—
226#121—1221no—
227C4×D4—611no—
228C4×D4—1221no—
229C4×D4C2×#692311yescharacteristic
230C2×C42—611no—
231#108—2442no—
232#108—2442no—
233C4⋊C8—611no—
234C4⋊C8—1221no—
235C4⋊C8—1222no—
236C4⋊C8—1222no—
237C4⋊C8—1222no—
238C4⋊C8—1222no—
239C4⋊C8C2×#692311yescharacteristic
240C22⋊C8—21no—
241C22⋊C8—1221no—
242C22⋊C8—1221no—
243C22⋊C8—1221no—
244C4×C8—611no—
245C4×C8—611no—
246C4×C8—611no—
247C4×C8C2×#692311yescharacteristic
248#41—2441no—
249#41—2441no—
250#41—2441no—
251#41—2441no—
252C2×Q8—1221no—
253C2×D4—611no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4C4⋊#692311yescharacteristic
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—1221no—
264M16—2442no—
265M16—2441no—
266M16—2441no—
267M16—2442no—
268M16—2442no—
269M16—2442no—
270C2×C8—21no—
271C2×C8—42no—
272C2×C8—611no—
273C2×C8—612no—
274C2×C8—612no—
275C2×C8—611no—
276C2×C8—1221no—
277C2×C8—1221no—
278C2×C8—1221no—
279C2×C8—4882no—
280C2×C8—2442no—
281C2×C8—2442no—
282C2×C8—2442no—
283C2×C8C22⋊#692311yescharacteristic
284C2×C8C22⋊#692311yescharacteristic
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4C4⋊#692311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C42—611no—
293C42—611no—
294C42—611no—
295C42C22×#692311yescharacteristic
296C23—21no—
297C23—611no—
298C23—1221no—
299Q8—2441no—
300Q8—2441no—
301D4—41no—
302D4—2441no—
303D4—2441no—
304D4—2441no—
305D4—2441no—
306D4—2441no—
307D4—2441no—
308D4—2441no—
309D4—2441no—
310D4—2441no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4C2×C22⋊#692311yescharacteristic
328C2×C4C2×C4⋊#692311yescharacteristic
329C2×C4#1451985611yescharacteristic
330C8—21no—
331C8—41no—
332C8—612no—
333C8—1221no—
334C8—4882no—
335C8—4882no—
336C8—2441no—
337C8#1451983912yes—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—611no—
342C22—611no—
343C22—1221no—
344C22—1221no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22#1684070411yescharacteristic
349C4—21no—
350C4—21no—
351C4—41no—
352C4—611no—
353C4—611no—
354C4—611no—
355C4—611no—
356C4—1221no—
357C4—2441no—
358C4C2×#1451983911yescharacteristic
359C4#1684075311yescharacteristic
360C2—81no—
361C2—1221no—
362C2—1221no—
363C2—4881no—
364C2#2146168711yescharacteristic
365C2#2146170311yescharacteristic
366C2#2146170811yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC8×D4×C61C4
socleC22×C61#380
prime radical#16840309C22
cosocleC42×D61C23
hypercenterC8×D4#6923
hypocenterC61#8684
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #21461759C2semidirect
2. D61⋊#335C2semidirect
4. #21460688C2semidirect
208. C61#8684semidirect

Maximal subgroups

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

subgroupindex
#214617592
D61⋊#3352
#214613302
#214606882
#214545262
#868461