Finite Group Databasebeta

← #30594549

Subgroups — #30594549

Order 15616.

464 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D61⋊#324C211yesmaximal, characteristic
2#21461004C211yesmaximal, characteristic
3#343×D61C211yesmaximal, characteristic
4C22×C4⋊#6923C411yescharacteristic
5D61⋊(C22⋊C8)—21no—
6C2×(C2×#6923)⋊C4—21no—
7C2×(C2×#6923)⋊C4—21no—
8C2×(C2×#6923)⋊C4C411yescharacteristic
9#16840608C412yescomplemented
10#16840607—21no—
11C2×M16×D61—21no—
12C2×C4⋊C4×D61C2211yescharacteristic
13#16839531C411yescharacteristic, complemented
14#16839530—21no—
15C61×#343C411yescharacteristic, complemented
16C23×#6923—21no—
17C23×#6923—21no—
18C2×D61⋊C8—41no—
19C2×C4⋊#6923—41no—
20C2×C4⋊#6923—42no—
21#14519834—41no—
22C22⋊#92420—22no—
23(C2×#6923)⋊C4—41no—
24(C2×#6923)⋊C4—42no—
25(C2×#6923)⋊C4—41no—
26(C2×#6923)⋊C4—41no—
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×#11758194—21no—
31C2×#11758189—41no—
32M16×D61—22no—
33M16×D61—22no—
34M16×D61—41no—
35M16×D61—41no—
36C2×C8×D61—41no—
37C2×C4⋊Dic61D411yescharacteristic
38C2×#11758196C2×C411yescharacteristic
39C2×#11758196Q811yescharacteristic
40C4⋊C4×D61—41no—
41C4⋊C4×D61—41no—
42C2×M16×C61—21no—
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C23×D61C22⋊C411yescharacteristic
45C22×#6923—22no—
46C22×#6923—22no—
47C22×#6923—41no—
48C22×#6923—41no—
49C22×#6923—41no—
50C22×#6923—41no—
51C22×#6923—41no—
52C22×#6923—41no—
53C22×#6923—41no—
54C22×#6923—41no—
55C22×#6923—41no—
56C22×#6923—41no—
57C22×#6923—41no—
58C22×#6923—41no—
59C22×C4×C61C4211yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C4⋊C411yescharacteristic
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C4⋊C411yescharacteristic
64C22×Dic61C4⋊C411yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61D811yescharacteristic
78C2×C4×D61SD1611yescharacteristic
79C2×C4×D61SD1611yescharacteristic
80C2×C4×D61Q1611yescharacteristic
81C2×#92420—42no—
82C4⋊#6923—42no—
83C4⋊#6923—42no—
84D61⋊C8—81no—
85D61⋊C8—81no—
86M16×C61—22no—
87M16×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊Dic61—41no—
91#11758196—41no—
92#11758196—41no—
93#11758194—22no—
94#11758194—41no—
95C2×#92418—41no—
96#11758189—42no—
97#11758189—42no—
98C8×D61—42no—
99C8×D61—42no—
100C23×C61#9511yescharacteristic
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61#9911yescharacteristic
106C22×D61#9911yescharacteristic
107C22×D61#10211yescharacteristic
108C22×D61#10311yescharacteristic
109C22×D61#10411yescharacteristic
110C22×D61#10411yescharacteristic
111C2×#6923—42no—
112C2×#6923—42no—
113C2×#6923—42no—
114C2×#6923—42no—
115C2×#6923—42no—
116C2×#6923—42no—
117C2×#6923—81no—
118C2×#6923—81no—
119C2×#6923—81no—
120C2×#6923—81no—
121C2×#6923—81no—
122C2×#6923—81no—
123C2×#6923—81no—
124C2×#6923—81no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61#10211yescharacteristic
132C2×C4×C61#10311yescharacteristic
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61#10611yescharacteristic
140C2×Dic61#10711yescharacteristic
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—42no—
150C4×D61—41no—
151C4×D61—41no—
152C4×D61—41no—
153C4×D61—41no—
154C4×D61—81no—
155#92420—82no—
156C8×C61—42no—
157#92418—42no—
158#7251—611nomaximal, Sylow
159C22×C61—21no—
160C22×C61—21no—
161C22×C61#33911yescharacteristic
162C22×C61#34011yescharacteristic
163C22×C61#34211yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61#32711yescharacteristic
175C2×D61#32711yescharacteristic
176C2×D61#32811yescharacteristic
177C2×D61#32811yescharacteristic
178C2×D61AΣL(1,𝔽16)11yescharacteristic
179C2×D61#35211yescharacteristic
180C2×D61#35511yescharacteristic
181C2×D61#35611yescharacteristic
182#6923—82no—
183#6923—82no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61—41no—
188Dic61—21no—
189Dic61—21no—
190Dic61—41no—
191Dic61—41no—
192C2×#343—611no—
193C2×#324—611no—
194#1441—611no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#129411yescharacteristic
198C2×C61#139011yescharacteristic
199C2×C61#139411yescharacteristic
200D61—21no—
201D61—21no—
202D61#134511yescharacteristic
203D61#134611yescharacteristic
204D61#135311yescharacteristic
205D61#135411yescharacteristic
206C22×M16—1221no—
207C22×C4⋊C4—611no—
208C22×C4⋊C4—611no—
209C2×C22⋊C8—1221no—
210C2×#95—611no—
211C2×#95—1221no—
212C2×#95—1221no—
213#343—611no—
214#343—1221no—
215#343#692311yescharacteristic, complemented
216#324—612no—
217#324—1221no—
218C61#725111yescharacteristic, complemented, Sylow
219C23×C4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C23×C4—1221no—
223C23×C4—1221no—
224C2×M16—21no—
225C2×M16—1222no—
226C2×M16—1222no—
227C2×M16—1221no—
228C2×M16—2441no—
229C2×M16—2441no—
230C2×M16—2441no—
231C22×C8—2441no—
232C22×C8—2441no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—2441no—
237C2×C4⋊C4—2441no—
238C2×C4⋊C4—2441no—
239C2×C4⋊C4—2442no—
240C2×C4⋊C4C2×#692311yescharacteristic
241C22⋊C8—1222no—
242C22⋊C8—2441no—
243#95—2441no—
244#95—2441no—
245#95—2441no—
246#95—2442no—
247C24—611no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4C4×#692311yescharacteristic
282C22×C4C4⋊#692311yescharacteristic
283C22×C4C22⋊#692311yescharacteristic
284M16—22no—
285M16—41no—
286M16—1222no—
287M16—2442no—
288M16—2442no—
289M16—2441no—
290C2×C8—41no—
291C2×C8—4881no—
292C2×C8—4881no—
293C2×C8—2442no—
294C2×C8—2442no—
295C2×C8—2442no—
296C2×C8—2441no—
297C4⋊C4—41no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4—2442no—
302C4⋊C4—2442no—
303C23—611no—
304C23—611no—
305C23—611no—
306C23—611no—
307C23—611no—
308C23—611no—
309C23—1221no—
310C23—1221no—
311C23—1221no—
312C23—1221no—
313C23(C2×#6923)⋊C411yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—4881no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4#1451983911yescharacteristic
357C2×C4#1451984011yescharacteristic
358C8—42no—
359C8—4882no—
360C8—2442no—
361C22—21no—
362C22—21no—
363C22—611no—
364C22—611no—
365C22—611no—
366C22—611no—
367C22—611no—
368C22—611no—
369C22—611no—
370C22—611no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1221no—
376C22—1221no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—1221no—
381C22#1684063311yescharacteristic
382C22#1684063511yescharacteristic
383C22#1684063911yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—1221no—
389C4—1221no—
390C4—4882no—
391C4—4882no—
392C4—2441no—
393C4—2441no—
394C2—21no—
395C2—21no—
396C2—611no—
397C2—611no—
398C2—611no—
399C2—611no—
400C2—1221no—
401C2—1221no—
402C2#2146069311yescharacteristic
403C2#2146090511yescharacteristic
404C2#2146091511yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#343C4
socleC22×C61#342
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×D61C22
hypercenter#343#6923
hypocenterC61#7251
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
9. #16840608C4semidirect
13. #16839531C4semidirect
15. C61×#343C4semidirect
215. #343#6923semidirect
218. C61#7251semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3242
#214610042
#343×D612
#725161