Finite Group Databasebeta

← #30597928

Subgroups — #30597928

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461613C211yesmaximal, characteristic, complemented
2#21461316C211yesmaximal, characteristic
3#21461198C211yesmaximal, characteristic
4#21461023C211yesmaximal, characteristic, complemented
5#21460715C211yesmaximal, characteristic, complemented
6#21460709C211yesmaximal, characteristic, complemented
7#21454528C211yesmaximal, characteristic
8#16840780C2211yescharacteristic
9#16840780C2211yescharacteristic
10D61⋊(C4⋊C8)C2211yescharacteristic
11C2×#14519831—21no—
12C4×C4⋊#6923C2211yescharacteristic
13(C2×#6923)⋊C8—21no—
14#16840621C412yescomplemented
15#16840620C412yescomplemented
16#16840614C412yes—
17#16840613C412yes—
18#16840603—21no—
19C8×#92420—21no—
20C2×#14519785—21no—
21#16840309C2211yescharacteristic
22#16839841C411yescharacteristic, complemented
23#16839838—21no—
24D4×#92418C411yescharacteristic, complemented
25#16839827C411yescharacteristic, complemented
26#16839825—21no—
27#16839784C2211yescharacteristic
28#16839727—21no—
29C4×C8×D61C2211yescharacteristic
30C61×#436C411yescharacteristic, complemented
31C2×D61⋊C8—21no—
32C2×C4⋊#6923—21no—
33C2×C4×#6923—21no—
34#14519844—21no—
35#14519844C2×C412yes—
36#14519844C2×C412yes—
37C4⋊#92420—21no—
38#14519834—21no—
39#14519834C2×C412yes—
40#14519831—42no—
41C4×#92420—21no—
42C4×#92420—21no—
43(C2×#6923)⋊C4C2×C412yes—
44C2×#11758222—21no—
45#14519785—42no—
46#14519785—42no—
47C2×#11758189—21no—
48C2×#11758189—21no—
49C22×#92418—21no—
50C2×C8×D61—21no—
51C2×C8×D61D411yescharacteristic
52C2×C8×D61D411yescharacteristic
53#14519776C2×C411yescharacteristic
54#14519773C2×C411yescharacteristic
55#14519763—21no—
56#14519752C2×C411yescharacteristic
57#14519750—21no—
58#14519748C2×C411yescharacteristic
59C4×D244C2×C411yescharacteristic
60C4×C22⋊D61—21no—
61C42×D61C2311yescharacteristic
62C4⋊#92418C2×C411yescharacteristic
63#14519706—21no—
64C22⋊#92418—21no—
65#14519689—21no—
66#14519689—21no—
67C4×#92418C2×C411yescharacteristic
68C8×Dic61D411yescharacteristic
69C8×Dic61D411yescharacteristic
70C2×M16×C61—21no—
71C4×D4×C61C2×C411yescharacteristic
72C4⋊C8×C61C2×C411yescharacteristic
73C22⋊C8×C61—21no—
74C4×C8×C61C2×C411yescharacteristic
75C22×#6923—22no—
76C2×D4×C61C4211yescharacteristic
77C22×C4×C61—21no—
78C2×C22⋊D61—21no—
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81#11758222—41no—
82#11758222—41no—
83#11758222—41no—
84#11758222—41no—
85C2×D244—21no—
86C2×D244C4211yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61C22×C411yescharacteristic
89C2×C4×D61C2×D411yescharacteristic
90C2×C4×D61#4111yescharacteristic
91C2×Dic122—21no—
92C2×#92420—22no—
93C2×#92420—22no—
94C2×#92420—22no—
95C4⋊#6923—42no—
96C4×#6923—41no—
97C4×#6923—41no—
98D61⋊C8—41no—
99D61⋊C8—41no—
100M16×C61—42no—
101C2×C8×C61—21no—
102C2×C8×C61C22⋊C411yescharacteristic
103C2×C8×C61C22⋊C411yescharacteristic
104C4⋊C4×C61C4211yescharacteristic
105C22⋊C4×C61—21no—
106C42×C61C22×C411yescharacteristic
107C22⋊Dic61—21no—
108#11758198—21no—
109#11758198—21no—
110C4⋊Dic61C4211yescharacteristic
111#11758196—21no—
112C4×Dic61C22×C411yescharacteristic
113C4×Dic61C2×D411yescharacteristic
114C4×Dic61#4111yescharacteristic
115C2×#92418—21no—
116C2×#92418—42no—
117C2×#92418C22⋊C411yescharacteristic
118C2×#92418C22⋊C411yescharacteristic
119#11758189—41no—
120#11758189—41no—
121#11758189—42no—
122C8×D61—21no—
123C8×D61—21no—
124C8×D61—42no—
125C8×D61D812yes—
126C8×D61SD1612yes—
127C23×C61—21no—
128C22×D61—21no—
129C22×D61C4×D411yescharacteristic
130C2×#6923—42no—
131C2×#6923—42no—
132C2×#6923—42no—
133D4×C61—41no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61C2×C4211yescharacteristic
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61#11711yescharacteristic
140C22⋊D61—41no—
141C22⋊D61—41no—
142C22⋊D61—41no—
143C22⋊D61—41no—
144C22⋊D61—42no—
145C2×Dic61—21no—
146C2×Dic61C4×D411yescharacteristic
147C2×Dic61C4×D411yescharacteristic
148C2×Dic61C4×D411yescharacteristic
149D244—41no—
150D244—41no—
151D244—41no—
152C4×D61—22no—
153C4×D61—41no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61C2×D811yescharacteristic
157C4×D61C2×SD1611yescharacteristic
158C4×D61#13511yescharacteristic
159C4×D61#13511yescharacteristic
160Dic122—41no—
161Dic122—41no—
162#92420—42no—
163#92420—42no—
164#92420—42no—
165C8×C61—21no—
166C8×C61—41no—
167C8×C61#10212yes—
168#92418—21no—
169#92418—41no—
170#92418#10212yes—
171#8255—611nomaximal, Sylow
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61C4×C22⋊C411yescharacteristic
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61C4×D811yescharacteristic
182C2×D61C4×SD1611yescharacteristic
183#6923—82no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61C2×#10211yescharacteristic
188C4×C61#41611yescharacteristic
189Dic61—21no—
190Dic61—41no—
191Dic61C4×D811yescharacteristic
192Dic61C4×SD1611yescharacteristic
193Dic61#44412yes—
194#2931—611no—
195#1770—611no—
196#1540—611no—
197#1502—611no—
198#1450—611no—
199#1303—611no—
200#1301—611no—
201C2×C61—81no—
202C2×C61#175711yescharacteristic
203C2×C61C4×#10211yescharacteristic
204C2×C61#176511yescharacteristic
205D61—21no—
206D61—21no—
207D61—81no—
208C2×#131—1221no—
209#532—611no—
210#436—611no—
211#436—1221no—
212#436#692311yescharacteristic, complemented
213C8×D4—611no—
214C8×D4—611no—
215C8×D4—1221no—
216#431—611no—
217#431—611no—
218#423—611no—
219C2×C4⋊C8—611no—
220#408—1221no—
221C2×#97—1221no—
222C2×C4×C8—611no—
223C4×C4⋊C4—611no—
224#336—1221no—
225#332—612no—
226#331—612no—
227#327—612no—
228#327—612no—
229#322—1221no—
230C82—1221no—
231C61#825511yescharacteristic, complemented, Sylow
232C2×#41—1221no—
233#131—2442no—
234#131—2442no—
235C2×M16—21no—
236C2×M16—1221no—
237C2×M16—1221no—
238C22×C8—611no—
239C22×C8—611no—
240C22×C8—1221no—
241C22×C8—1221no—
242C22×C8—1221no—
243C4⋊Q8—611no—
244#127—611no—
245#124—1221no—
246#121—611no—
247#121—611no—
248#121—1221no—
249C4×D4—611no—
250C4×D4—1221no—
251C4×D4C2×#692311yescharacteristic
252C2×C4⋊C4—1221no—
253C2×C42—611no—
254C2×C42—1221no—
255C4⋊C8—612no—
256C4⋊C8—612no—
257C4⋊C8—611no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261C4⋊C8C2×#692311yescharacteristic
262C22⋊C8—21no—
263C22⋊C8—612no—
264C22⋊C8—1221no—
265C22⋊C8—1221no—
266C22⋊C8—1221no—
267C22⋊C8—1221no—
268#97—2442no—
269C4×C8—611no—
270C4×C8—611no—
271C4×C8—611no—
272C4×C8—1221no—
273C4×C8—1221no—
274C4×C8C2×#692311yescharacteristic
275#95—612no—
276#41—2441no—
277#41—2441no—
278#41—2441no—
279#41—2441no—
280C2×Q8—1221no—
281C2×D4—611no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4C4×#692311yescharacteristic
287C22×C4—21no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1222no—
293M16—42no—
294M16—2441no—
295M16—2441no—
296M16—2442no—
297C2×C8—21no—
298C2×C8—611no—
299C2×C8—612no—
300C2×C8—612no—
301C2×C8—611no—
302C2×C8—1221no—
303C2×C8—1221no—
304C2×C8—1222no—
305C2×C8—1222no—
306C2×C8—1222no—
307C2×C8—1221no—
308C2×C8—2442no—
309C2×C8—2442no—
310C2×C8—2441no—
311C2×C8—2441no—
312C2×C8C22⋊#692311yescharacteristic
313C2×C8C22⋊#692311yescharacteristic
314C4⋊C4—611no—
315C4⋊C4—1221no—
316C4⋊C4—2442no—
317C4⋊C4C4×#692311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C42—611no—
323C42—611no—
324C42—611no—
325C42—2441no—
326C42—2441no—
327C42C22×#692311yescharacteristic
328C23—21no—
329C23—611no—
330C23—1221no—
331Q8—2441no—
332Q8—2441no—
333D4—41no—
334D4—2441no—
335D4—2441no—
336D4—2441no—
337D4—2442no—
338D4—2441no—
339D4—2441no—
340D4—2441no—
341D4—2441no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—1222no—
353C2×C4—1221no—
354C2×C4—2441no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2442no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4C2×C4×#692311yescharacteristic
361C2×C4C2×C22⋊#692311yescharacteristic
362C2×C4#1451985611yescharacteristic
363C8—21no—
364C8—41no—
365C8—612no—
366C8—1221no—
367C8—2442no—
368C8—2442no—
369C8—2442no—
370C8—2441no—
371C8#1451983912yes—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—611no—
376C22—611no—
377C22—1221no—
378C22—1221no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22C4×C22⋊#692311yescharacteristic
383C4—21no—
384C4—21no—
385C4—41no—
386C4—611no—
387C4—611no—
388C4—612no—
389C4—1221no—
390C4—4882no—
391C4—2441no—
392C4C2×#1451983911yescharacteristic
393C4#1684075211yescharacteristic
394C2—81no—
395C2—1221no—
396C2—1221no—
397C2—4881no—
398C2#2146157511yescharacteristic
399C2C4×#1451983911yescharacteristic
400C2#2146159711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C4×C22⋊C4
prime radical#16840309C22
cosocleC42×D61C23
hypercenter#436#6923
hypocenterC61#8255
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #21461613C2semidirect
4. #21461023C2semidirect
5. #21460715C2semidirect
6. #21460709C2semidirect
14. #16840621C4semidirect
15. #16840620C4semidirect
22. #16839841C4semidirect
24. D4×#92418C4semidirect
25. #16839827C4semidirect
30. C61×#436C4semidirect
212. #436#6923semidirect
231. C61#8255semidirect

Maximal subgroups

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

subgroupindex
#214616132
#214613162
#214611982
#214610232
#214607152
#214607092
#214545282
#825561