Finite Group Databasebeta

← #30604754

Subgroups — #30604754

Order 15616.

536 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461524C211yesmaximal, characteristic, complemented
2#21461052C211yesmaximal, characteristic, complemented
3#21460804C212yesmaximal, complemented
4#21460802C212yesmaximal, complemented
5#21449059C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7#16840778—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×C4×D244—21no—
13C2×C4×D244C411yescharacteristic
14C2×#14519734C2211yescharacteristic
15#16839694C2211yescharacteristic
16#16839689C411yescharacteristic
17#16839684—21no—
18#16839680C2211yescharacteristic
19#16839679—21no—
20#16839672C411yescharacteristic
21C4×#11758198—21no—
22C4×C4⋊C4×C61C411yescharacteristic
23C2×#11758213—41no—
24D61⋊M16—24no—
25D61⋊M16—42no—
26C2×#11758217—22no—
27C2×D61⋊C8—41no—
28C4⋊#92420—41no—
29C22⋊#92420—22no—
30C4×#92420—41no—
31C22×D244—21no—
32C22×D244C2×C411yescharacteristic
33C22×C4×D61—21no—
34C22×C4×D61D411yescharacteristic
35C4×D244—41no—
36C4×D244—41no—
37C4×D244—42no—
38C4×D244—42no—
39#14519734—41no—
40#14519734—41no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C2×#11758196C2311yescharacteristic
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198C2×C411yescharacteristic
51C2×#11758198D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61—21no—
56C2×C42×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58#95×C61C2×C411yescharacteristic
59#95×C61C2×C411yescharacteristic
60C23×D61—21no—
61C23×D61C22⋊C411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×D244—42no—
72C2×D244—41no—
73C2×D244—42no—
74C2×D244—42no—
75C2×D244—42no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—22no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61D812yes—
84C2×C4×D61SD1612yes—
85#11758217—24no—
86#11758217—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89#11758213—44no—
90D61⋊C8—44no—
91C4⋊C4×C61—42no—
92C42×C61—21no—
93C42×C61—21no—
94C42×C61—42no—
95#11758198—41no—
96#11758198—41no—
97#11758198—42no—
98#11758198—42no—
99#11758198—42no—
100#11758198—42no—
101#11758198—41no—
102#11758198—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—22no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61#10212yes—
123C2×C4×C61—22no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#9911yescharacteristic
134C2×C4×C61#9911yescharacteristic
135C2×C4×C61#10212yes—
136C2×C4×C61#10412yes—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61C2×D811yescharacteristic
147C2×Dic61C2×SD1611yescharacteristic
148D244—42no—
149D244—48no—
150D244—42no—
151C4×D61—22no—
152C4×D61—22no—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—82no—
156C4×D61—82no—
157#92420—44no—
158#92420—82no—
159#11697—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61C2×#9911yescharacteristic
163C22×C61C2×#10211yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—42no—
169C2×D61—42no—
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—42no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61—81no—
181C4×C61#32712yes—
182C4×C61#32712yes—
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—41no—
187Dic61—81no—
188#2392—611no—
189#1742—611no—
190#1458—611no—
191#1346—612no—
192#1345—612no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61C2×#32711yescharacteristic
196C2×C61#212011yescharacteristic
197C2×C61#213211yescharacteristic
198D61—42no—
199D61—82no—
200C22×M16—1221no—
201C2×C4×D4—611no—
202C2×C4×D4—1221no—
203C2×#117—611no—
204#431—1221no—
205#398—611no—
206#397—611no—
207#396—1221no—
208#394—611no—
209#394—1221no—
210#392—611no—
211C4×C4⋊C4#692311yescharacteristic
212C4×C22⋊C4—1221no—
213#343—612no—
214#343—1221no—
215#324—612no—
216#323—1221no—
217C61#1169711yescharacteristic, complemented, Sylow
218C22×D4—611no—
219C22×D4—1221no—
220C23×C4—611no—
221C23×C4—1221no—
222C2×M16—1222no—
223C2×M16—1224no—
224C2×M16—2442no—
225C2×M16—2441no—
226C22×C8—2441no—
227C4×D4—2441no—
228C4×D4—2441no—
229C4×D4—2442no—
230C4×D4—2442no—
231#117—2441no—
232#117—2441no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42—21no—
246C2×C42—611no—
247C2×C42C2×#692311yescharacteristic
248C4⋊C8—2441no—
249C22⋊C8—1222no—
250C4×C8—2441no—
251#95—1221no—
252#95—1221no—
253#95C2×#692311yescharacteristic
254#95C2×#692311yescharacteristic
255C24—611no—
256C24—1221no—
257C2×D4—2441no—
258C2×D4—2442no—
259C2×D4—2442no—
260C2×D4—2442no—
261C2×D4—2442no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—611no—
265C22×C4—612no—
266C22×C4—612no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1222no—
272C22×C4—1221no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4—2442no—
276C22×C4—2442no—
277C22×C4C22⋊#692311yescharacteristic
278C22×C4C22⋊#692311yescharacteristic
279C22×C4C22×#692311yescharacteristic
280M16—1224no—
281M16—2442no—
282M16—2444no—
283C2×C8—2442no—
284C2×C8—2444no—
285C2×C8—2442no—
286C4⋊C4—42no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2442no—
295C22⋊C4—2442no—
296C22⋊C4—2441no—
297C22⋊C4—2441no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C42—21no—
301C42—21no—
302C42—42no—
303C42—1221no—
304C42—1221no—
305C23—612no—
306C23—1222no—
307C23—1221no—
308C23—1221no—
309C23—2441no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23C2×C22⋊#692311yescharacteristic
318D4—2442no—
319D4—2448no—
320D4—2442no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—4882no—
342C2×C4—4882no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4#1451983611yescharacteristic
349C2×C4#1451983611yescharacteristic
350C2×C4#1451983912yes—
351C2×C4#1451984212yes—
352C8—4882no—
353C8—2444no—
354C22—21no—
355C22—21no—
356C22—1222no—
357C22—4881no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—2442no—
363C22—2442no—
364C22—2442no—
365C22—2442no—
366C22—2441no—
367C22—2441no—
368C22C2×#1451983611yescharacteristic
369C22C2×#1451983911yescharacteristic
370C22C2×#1451984211yescharacteristic
371C4—42no—
372C4—41no—
373C4—41no—
374C4—81no—
375C4—1221no—
376C4—1221no—
377C4—4881no—
378C4—2441no—
379C4—2441no—
380C4#1684061412yes—
381C4#1684061412yes—
382C2—21no—
383C2—21no—
384C2—4882no—
385C2—2442no—
386C2C2×#1684061411yescharacteristic
387C2#2146207211yescharacteristic
388C2#2146211211yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radical#16839672C4
cosocleC2×#11758196C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#11697
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461524C2semidirect
2. #21461052C2semidirect
3. #21460804C2semidirect
4. #21460802C2semidirect
217. C61#11697semidirect

Maximal subgroups

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

subgroupindex
#214615242
#214610522
#214608042
#214608022
#214490592
#1169761