Finite Group Databasebeta

← #30597255

Subgroups — #30597255

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462496C211yesmaximal, characteristic
2#21462268C211yesmaximal, characteristic
3#21460719C214yesmaximal
4#21454451C211yesmaximal, characteristic
5C2×#14519856C412yes—
6#16840784—21no—
7#16840783C412yescomplemented
8#16840781—21no—
9#16840778C412yescomplemented
10#16840766—21no—
11#16840733C2212yes—
12C4×#11758213—21no—
13#16840708—21no—
14#16840706—21no—
15#16840704C412yes—
16#16840704C2212yes—
17C4×C4⋊#6923—21no—
18C4×C4⋊#6923—21no—
19C2×C42×D61C2211yescharacteristic
20#16839818—21no—
21#16839818—21no—
22#16839814—21no—
23#16839814—21no—
24#16839786C411yescharacteristic, complemented
25#16839725C2212yes—
26M16×Dic61C412yescomplemented
27C61×#423C411yescharacteristic, complemented
28C2×#11758213—22no—
29#14519856—44no—
30C2×C4⋊#6923—22no—
31C2×C4⋊#6923—22no—
32C2×C4⋊#6923—22no—
33C2×C22⋊#6923C2×C414yes—
34C2×C4×#6923—22no—
35C4⋊#92420—22no—
36C4⋊#92420—22no—
37#14519834—22no—
38C22⋊#92420C2×C414yes—
39#14519832—22no—
40C4×#92420—22no—
41(C2×#6923)⋊C4—22no—
42(C2×#6923)⋊C4—22no—
43C22×C4×D61C2×C411yescharacteristic
44C22×C4×D61C2×C411yescharacteristic
45C22×C4×D61C2311yescharacteristic
46C2×#11758194C2×C412yes—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C42×D61D411yescharacteristic
51C42×D61D411yescharacteristic
52C42×D61D411yescharacteristic
53C42×D61D411yescharacteristic
54C42×D61D411yescharacteristic
55C42×D61D411yescharacteristic
56C42×D61Q811yescharacteristic
57C42×D61Q811yescharacteristic
58C4⋊#92418—21no—
59C4⋊#92418—21no—
60#14519689—22no—
61#14519689—22no—
62#14519687—22no—
63C8×Dic61—22no—
64C2×M16×C61C2×C412yes—
65C2×C42×C61C2×C411yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C23×D61C22×C411yescharacteristic
69C22×#6923—24no—
70C22×C4×C61C4211yescharacteristic
71C22×C4×C61C4211yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61C4211yescharacteristic
74C22×Dic61C4211yescharacteristic
75C22×Dic61C22×C411yescharacteristic
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—42no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61C22⋊C411yescharacteristic
82C2×C4×D61C22⋊C411yescharacteristic
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61C4⋊C411yescharacteristic
86C2×C4×D61C4⋊C411yescharacteristic
87C2×C4×D61C4⋊C411yescharacteristic
88C2×C4×D61C4⋊C411yescharacteristic
89C2×C4×D61C2×D411yescharacteristic
90C2×C4×D61C2×D411yescharacteristic
91C2×C4×D61C2×D411yescharacteristic
92C2×C4×D61C2×Q811yescharacteristic
93C22⋊#6923—44no—
94C2×#92420—24no—
95C4⋊#6923—44no—
96C4⋊#6923—42no—
97C4⋊#6923—42no—
98C4⋊#6923—44no—
99C4×#6923—44no—
100#11758213—42no—
101#11758213—42no—
102M16×C61—42no—
103C2×C8×C61—22no—
104C42×C61C22⋊C411yescharacteristic
105C42×C61C22⋊C411yescharacteristic
106C42×C61C4⋊C411yescharacteristic
107C42×C61C4⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120#11758194—42no—
121C2×#92418—22no—
122C23×C61C2×C4211yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61C2×C22⋊C411yescharacteristic
128C22×D61C2×C4⋊C411yescharacteristic
129C2×#6923—44no—
130C2×#6923—44no—
131C2×#6923—44no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61#9511yescharacteristic
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C2×C4⋊C411yescharacteristic
142C2×Dic61—22no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61#9511yescharacteristic
146C2×Dic61#9511yescharacteristic
147C2×Dic61#9511yescharacteristic
148C2×Dic61#9511yescharacteristic
149C2×Dic61C2×C22⋊C411yescharacteristic
150C2×Dic61C2×C4⋊C411yescharacteristic
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—22no—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—22no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61#10012yes—
166C4×D61#10112yes—
167#92420—44no—
168C8×C61—42no—
169#92418—42no—
170#8105—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61C2×#9511yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—42no—
181C2×D61—42no—
182C2×D61C2×#10011yescharacteristic
183C2×D61C2×#10111yescharacteristic
184#6923—84no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61#34312yes—
189C4×C61#34412yes—
190C4×C61#41011yescharacteristic
191C4×C61#41011yescharacteristic
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—21no—
196Dic61—21no—
197Dic61#34312yes—
198#2920—611no—
199#2920—611no—
200#2285—611no—
201#1305—614no—
202C2×C61—41no—
203C2×C61#174011yescharacteristic
204C2×C61C2×#34311yescharacteristic
205C2×C61C2×#34411yescharacteristic
206D61—21no—
207D61—21no—
208D61—41no—
209C2×#117—612no—
210C22×C42—611no—
211#432—612no—
212#432—1221no—
213#432—1221no—
214#432—1221no—
215#431—612no—
216#431—1221no—
217#431—1221no—
218#431—1221no—
219#423—611no—
220#423—1221no—
221#423#692311yescharacteristic, complemented
222#407—612no—
223#407—612no—
224C4×M16—612no—
225C4×M16—1221no—
226#384—1221no—
227#382—1221no—
228#380—612no—
229#380—612no—
230C4×C4⋊C4—1221no—
231C4×C4⋊C4—1221no—
232C61#810511yescharacteristic, complemented, Sylow
233C23×C4—611no—
234C23×C4—611no—
235C23×C4—611no—
236C2×M16—612no—
237C2×M16—1222no—
238C2×M16C2×#692312yes—
239#117—2444no—
240C2×C4⋊C4—1222no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1222no—
243C2×C22⋊C4—614no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—1222no—
256C2×C42C2×#692311yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—1222no—
260C4⋊C8—1222no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263C22⋊C8—614no—
264C22⋊C8—1222no—
265C22⋊C8—1222no—
266C22⋊C8—1222no—
267#97—1222no—
268#97—1222no—
269C4×C8—1222no—
270C4×C8—1222no—
271#95—1222no—
272#95—1222no—
273C24—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1222no—
290C22×C4—1222no—
291C22×C4—1224no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2442no—
295C22×C4C4×#692311yescharacteristic
296C22×C4C4×#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298M16—42no—
299M16—2442no—
300M16—2442no—
301M16—2442no—
302C2×C8—22no—
303C2×C8—1224no—
304C2×C8—1222no—
305C4⋊C4—2444no—
306C4⋊C4—2442no—
307C4⋊C4—2442no—
308C4⋊C4—2444no—
309C22⋊C4—2444no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—611no—
322C42—2444no—
323C42C4⋊#692311yescharacteristic
324C42C4⋊#692311yescharacteristic
325C42C22⋊#692311yescharacteristic
326C42C22⋊#692311yescharacteristic
327C23—611no—
328C23—611no—
329C23—1221no—
330C23—1221no—
331C23—2441no—
332C23—2441no—
333C23C2×C4×#692311yescharacteristic
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—611no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1222no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2444no—
364C2×C4—2444no—
365C2×C4—2444no—
366C2×C4(C2×#6923)⋊C411yescharacteristic
367C2×C4(C2×#6923)⋊C411yescharacteristic
368C2×C4(C2×#6923)⋊C411yescharacteristic
369C2×C4(C2×#6923)⋊C411yescharacteristic
370C2×C4C2×C22⋊#692311yescharacteristic
371C2×C4C2×C4⋊#692311yescharacteristic
372C8—42no—
373C8—2444no—
374C8—2442no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—611no—
379C22—611no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—1221no—
385C22—2442no—
386C22—2442no—
387C22C2×(C2×#6923)⋊C411yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—612no—
392C4—1221no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—1221no—
397C4—4884no—
398C4#1684064112yes—
399C4#1684064512yes—
400C4#1684074211yescharacteristic
401C4#1684074311yescharacteristic
402C2—41no—
403C2—1221no—
404C2—1221no—
405C2—2441no—
406C2#2146151911yescharacteristic
407C2C2×#1684064111yescharacteristic
408C2C2×#1684064511yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#423C4
socleC22×C61C2×#95
prime radicalC23×D61C22×C4
cosocleC22×C4×D61C23
hypercenter#423#6923
hypocenterC61#8105
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
7. #16840783C4semidirect
9. #16840778C4semidirect
24. #16839786C4semidirect
26. M16×Dic61C4semidirect
27. C61×#423C4semidirect
221. #423#6923semidirect
232. C61#8105semidirect

Maximal subgroups

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

subgroupindex
#214624962
#214622682
#214607192
#214544512
#810561