Finite Group Databasebeta

← #30597570

Subgroups — #30597570

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461605C211yesmaximal, characteristic, complemented
2C42×#92420C211yesmaximal, characteristic, complemented
3C2×#16840610C212yesmaximal
4#21460655C212yesmaximal, complemented
5#21448277C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×#14519832—21no—
8C2×C4×#92420—21no—
9C2×C4×#92420—21no—
10C2×C4×#92420C2212yes—
11#16840628—21no—
12#16840610C418yescomplemented
13C2×#14519739C2211yescharacteristic
14C2×#14519735—21no—
15#16839664C411yescharacteristic
16#16839663C411yescharacteristic
17#16839661C411yescharacteristic
18#16839654—21no—
19#16839652—21no—
20C4⋊C4×Dic61C2211yescharacteristic
21#16839609—21no—
22C42×Dic61C2211yescharacteristic
23C61×#389C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26C4⋊#92420—22no—
27C4⋊#92420C2×C414yes—
28#14519832—42no—
29C4×#92420—24no—
30C4×#92420—24no—
31C4×#92420—22no—
32C4×#92420C2×C414yes—
33C22×D244C2×C411yescharacteristic
34C22×C4×D61—21no—
35#14519739—22no—
36#14519739C2×C414yes—
37#14519735—42no—
38#14519735—42no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61C2311yescharacteristic
53#14519684—21no—
54#14519684—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59#95×C61—21no—
60C23×D61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×D244—22no—
72C2×D244—22no—
73C2×D244—21no—
74C2×D244C4212yes—
75C2×C4×D61—24no—
76C2×C4×D61—41no—
77C2×C4×D61—41no—
78C2×C4×D61—42no—
79C2×#92420—24no—
80C2×#92420—24no—
81C2×#92420—24no—
82C2×#92420—24no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61C4212yes—
89C42×C61—22no—
90#11758198—24no—
91#11758198—42no—
92#11758198—42no—
93#11758198—42no—
94#11758198—42no—
95C4⋊Dic61—22no—
96C4⋊Dic61—42no—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C4×Dic61—22no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C4×Dic61D812yes—
104C4×Dic61SD1612yes—
105C4×Dic61C22×C412yes—
106C4×Dic61#4112yes—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—22no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#10212yes—
126C2×C4×C61#10412yes—
127C2×C4×C61C2×C4211yescharacteristic
128C2×C4×C61#11711yescharacteristic
129C2×C4×C61#13112yes—
130C2×C4×C61#13112yes—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61#10212yes—
141C2×Dic61#10412yes—
142C2×Dic61C4×D412yes—
143C2×Dic61C4×D412yes—
144C2×Dic61C2×D811yescharacteristic
145C2×Dic61C2×SD1611yescharacteristic
146C2×Dic61#13512yes—
147D244—24no—
148D244—42no—
149C4×D61—44no—
150C4×D61—44no—
151#92420—28no—
152#92420—44no—
153#8177—611nomaximal, Sylow
154C22×C61C4×C22⋊C411yescharacteristic
155C22×C61#40811yescharacteristic
156C22×C61#40811yescharacteristic
157C22×C61C2×#10211yescharacteristic
158C22×C61#41611yescharacteristic
159C22×C61C2×#10411yescharacteristic
160C22×C61C2×#10411yescharacteristic
161C2×D61—42no—
162C2×D61—42no—
163C2×D61—42no—
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C4×C61—22no—
169C4×C61—22no—
170C4×C61—42no—
171C4×C61—81no—
172C4×C61#40512yes—
173C4×C61#43312yes—
174Dic61—22no—
175Dic61—22no—
176Dic61—22no—
177Dic61—81no—
178Dic61C4×D812yes—
179Dic61C4×SD1612yes—
180#2293—611no—
181#1767—611no—
182C42×C8—611no—
183C2×D4⋊C8—612no—
184#1279—612no—
185C2×C61#149211yescharacteristic
186C2×C61#149211yescharacteristic
187C2×C61#149411yescharacteristic
188C2×C61#149411yescharacteristic
189C2×C61#175011yescharacteristic
190C2×C61C4×#10411yescharacteristic
191C2×C61C4×#10211yescharacteristic
192D61—82no—
193C2×C4×D4—611no—
194C2×#117—1221no—
195C2×C4⋊C8—612no—
196C2×#97—1221no—
197C2×C4×C8—612no—
198C2×C4×C8—1221no—
199C2×C4×C8—1221no—
200#390—611no—
201#390—611no—
202#389—611no—
203#389#692311yescharacteristic
204#388—1221no—
205#388—1221no—
206C4×C4⋊C4—611no—
207C4×C22⋊C4—1221no—
208C43—611no—
209#336—1221no—
210D4⋊C8—618no—
211C61#817711yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C23×C4—1221no—
214C22×C8—1222no—
215C22×C8—1222no—
216C4×D4—614no—
217C4×D4—1222no—
218#117—2442no—
219#117—2442no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4C2×#692311yescharacteristic
224C2×C4⋊C4C2×#692311yescharacteristic
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—1221no—
237C2×C42C2×#692311yescharacteristic
238C4⋊C8—614no—
239C4⋊C8—1222no—
240#97—2442no—
241C4×C8—614no—
242C4×C8—1222no—
243C4×C8—1224no—
244C4×C8—1224no—
245#95—21no—
246#95—1221no—
247#95—1221no—
248C24—1221no—
249C2×D4—612no—
250C2×D4—1221no—
251C2×D4—1222no—
252C2×D4—1222no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1224no—
260C22×C4—1221no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4—2442no—
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22⋊#692311yescharacteristic
266C22×C4C22×#692311yescharacteristic
267C2×C8—1224no—
268C2×C8—1224no—
269C2×C8—1224no—
270C2×C8—1224no—
271C2×C8—2442no—
272C2×C8—2442no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—1222no—
277C4⋊C4—2442no—
278C4⋊C4C4×#692312yes—
279C22⋊C4—1224no—
280C22⋊C4—2442no—
281C22⋊C4—2442no—
282C22⋊C4—2442no—
283C22⋊C4—2442no—
284C42—22no—
285C42—612no—
286C42—612no—
287C42—612no—
288C42—612no—
289C42—1222no—
290C42—1222no—
291C42—1222no—
292C42—1222no—
293C42—2441no—
294C42—2441no—
295C23—1222no—
296C23—2441no—
297C23—2441no—
298C23—2441no—
299C23—2441no—
300C23—2441no—
301C23—2441no—
302C23C2×C22⋊#692311yescharacteristic
303D4—1224no—
304D4—2442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—612no—
318C2×C4—612no—
319C2×C4—612no—
320C2×C4—612no—
321C2×C4—612no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—2444no—
329C2×C4—2444no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4#1451983912yes—
334C2×C4#1451984212yes—
335C2×C4C2×C4×#692311yescharacteristic
336C2×C4#1451985611yescharacteristic
337C2×C4#1451986412yes—
338C2×C4#1451986512yes—
339C8—1228no—
340C8—2444no—
341C22—4881no—
342C22—4881no—
343C22—4881no—
344C22—4881no—
345C22—2442no—
346C22—2442no—
347C22—2442no—
348C22C4×C22⋊#692311yescharacteristic
349C22#1684073511yescharacteristic
350C22#1684073711yescharacteristic
351C22C2×#1451983911yescharacteristic
352C22#1684075211yescharacteristic
353C22D61⋊#10411yescharacteristic
354C22C2×#1451984211yescharacteristic
355C4—22no—
356C4—22no—
357C4—42no—
358C4—81no—
359C4—612no—
360C4—612no—
361C4—1222no—
362C4—1222no—
363C4—1222no—
364C4—4881no—
365C4#1684072712yes—
366C4#1684078712yes—
367C2—4882no—
368C2#2146116411yescharacteristic
369C2#2146116611yescharacteristic
370C2#2146117211yescharacteristic
371C2#2146117311yescharacteristic
372C2#2146154811yescharacteristic
373C2C4×#1451984211yescharacteristic
374C2C4×#1451983911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#8177
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #21461605C2semidirect
2. C42×#92420C2semidirect
4. #21460655C2semidirect
12. #16840610C4semidirect
211. C61#8177semidirect

Maximal subgroups

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

subgroupindex
#214616052
C42×#924202
C2×#168406102
#214606552
#214482772
#817761