Finite Group Databasebeta

← #29570183

Subgroups — #29570183

Order 15616.

520 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454451C211yesmaximal, characteristic
2#21454450C211yesmaximal, characteristic
3#21454447C211yesmaximal, characteristic
4#21443710C211yesmaximal, characteristic, complemented
5#21443709C211yesmaximal, characteristic, complemented
6#21443708C211yesmaximal, characteristic, complemented
7C61×#1299C211yesmaximal, characteristic, complemented
8C2×C42×D61C2211yescharacteristic
9#16839818—21no—
10#16839818—21no—
11#16839818C412yes—
12#16839817C412yes—
13#16839817C412yes—
14#16839816—21no—
15#16839815C2211yescharacteristic
16#16839814—21no—
17#16839814—21no—
18#16839813—21no—
19#16839813—21no—
20#16839813—21no—
21#16839786C2211yescharacteristic
22#16839785—21no—
23#16839784C412yes—
24#16839725—21no—
25#16839725C412yes—
26#16839724—21no—
27C4×#11758194C2211yescharacteristic
28M16×Dic61C412yes—
29C4×#11758189—21no—
30C61×#431C2211yescharacteristic
31C61×#423C2211yescharacteristic
32C4×M16×C61C2211yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61Q811yescharacteristic
36C2×#11758194—21no—
37C2×#11758194C2×C412yes—
38C2×#11758189—22no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61Q811yescharacteristic
42C42×D61C2×C411yescharacteristic
43C42×D61C2×C411yescharacteristic
44C42×D61C2×C411yescharacteristic
45C42×D61C2×C411yescharacteristic
46C42×D61D411yescharacteristic
47C42×D61D411yescharacteristic
48C42×D61D411yescharacteristic
49C42×D61D411yescharacteristic
50C4⋊#92418—21no—
51C4⋊#92418—21no—
52C4⋊#92418C2×C412yes—
53#14519706—22no—
54#14519706—22no—
55#14519706—22no—
56C22⋊#92418—21no—
57#14519689—22no—
58#14519689—22no—
59#14519689—22no—
60#14519689—22no—
61#14519689—22no—
62#14519688C2×C412yes—
63#14519687—22no—
64#14519687—22no—
65C4×#92418—21no—
66C4×#92418—21no—
67C8×Dic61—22no—
68C2×M16×C61—21no—
69C2×M16×C61C2×C412yes—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61C2×C412yes—
74C22⋊C8×C61—21no—
75#97×C61C2×C412yes—
76C4×C8×C61—21no—
77C4×C8×C61—21no—
78C23×D61C4⋊C411yescharacteristic
79C22×C4×C61C22×C411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×Q811yescharacteristic
82C22×Dic61C4⋊C411yescharacteristic
83C22×Dic61C4⋊C411yescharacteristic
84C22×Dic61C4⋊C411yescharacteristic
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×C4×D61C4211yescharacteristic
90C2×C4×D61C4211yescharacteristic
91C2×C4×D61C22⋊C411yescharacteristic
92C2×C4×D61C22⋊C411yescharacteristic
93C2×C4×D61C22⋊C411yescharacteristic
94C2×C4×D61C22⋊C411yescharacteristic
95C2×C4×D61C22⋊C411yescharacteristic
96C2×C4×D61C22⋊C411yescharacteristic
97C2×C4×D61C4⋊C411yescharacteristic
98C2×C4×D61C4⋊C411yescharacteristic
99C2×C4×D61C4⋊C411yescharacteristic
100C2×C4×D61C4⋊C411yescharacteristic
101M16×C61—42no—
102M16×C61—42no—
103C2×C8×C61—22no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C42×C61C22×C411yescharacteristic
107C42×C61C22×C411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C4×Dic61C4211yescharacteristic
111C4×Dic61C4211yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C22⋊C411yescharacteristic
115C4×Dic61C22⋊C411yescharacteristic
116C4×Dic61C22⋊C411yescharacteristic
117C4×Dic61C22⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C4×Dic61C4⋊C411yescharacteristic
121C4×Dic61C4⋊C411yescharacteristic
122#11758194—42no—
123#11758194—42no—
124C2×#92418—22no—
125C2×#92418—22no—
126C2×#92418—22no—
127#11758189—44no—
128C23×C61C2×C4⋊C411yescharacteristic
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C22×D61#9511yescharacteristic
133C22×D61#9511yescharacteristic
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61C2×C4211yescharacteristic
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C2×C22⋊C411yescharacteristic
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C2×C4⋊C411yescharacteristic
143C2×C4×C61C2×C4⋊C411yescharacteristic
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#9511yescharacteristic
148C2×Dic61#9511yescharacteristic
149C2×Dic61#9511yescharacteristic
150C2×Dic61#9511yescharacteristic
151C2×Dic61#9511yescharacteristic
152C2×Dic61#9511yescharacteristic
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—41no—
162C4×D61—41no—
163C4×D61—41no—
164C4×D61—41no—
165C4×D61—41no—
166C4×D61—41no—
167C8×C61—42no—
168C8×C61—42no—
169C8×C61—42no—
170#92418—42no—
171#92418—42no—
172#92418—42no—
173#8062—611nomaximal, Sylow
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61C2×#9511yescharacteristic
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—44no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61#41311yescharacteristic
189C4×C61#41311yescharacteristic
190C4×C61#42112yes—
191C4×C61#43012yes—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—21no—
196Dic61—21no—
197Dic61—21no—
198#2920—611no—
199#2920—611no—
200#2920—611no—
201#1299—611no—
202#1299—611no—
203#1299—611no—
204#1299D6111yescharacteristic, complemented
205C2×C61—41no—
206C2×C61#173311yescharacteristic
207C2×C61#173811yescharacteristic
208C2×C61#174211yescharacteristic
209D61—41no—
210D61—41no—
211C22×C42—611no—
212#432—612no—
213#432—612no—
214#432—612no—
215#432—1221no—
216#432—1221no—
217#432—1221no—
218#431—611no—
219#431—1221no—
220#431—1221no—
221#431—1221no—
222#431—1221no—
223#431—1221no—
224#431C2×D6111yescharacteristic
225#423—612no—
226#423—611no—
227#423—1221no—
228#423C2×D6111yescharacteristic
229#407—612no—
230#407—1221no—
231#407—1221no—
232C4×M16—611no—
233C4×M16—612no—
234C4×M16—1221no—
235C4×M16C2×D6111yescharacteristic
236C61#806211yescharacteristic, complemented, Sylow
237C23×C4—611no—
238C23×C4—611no—
239C23×C4—611no—
240C2×M16—21no—
241C2×M16—612no—
242C2×M16—1222no—
243C2×M16—1221no—
244C2×M16C4×D6112yes—
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—611no—
256C2×C42C22×D6111yescharacteristic
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—612no—
260C4⋊C8—1222no—
261C4⋊C8—1222no—
262C4⋊C8—1222no—
263C4⋊C8—1221no—
264C4⋊C8—1221no—
265C4⋊C8C4×D6112yes—
266C22⋊C8—21no—
267C22⋊C8—1222no—
268C22⋊C8—1222no—
269C22⋊C8—1222no—
270C22⋊C8—1222no—
271C22⋊C8—1222no—
272C22⋊C8—1221no—
273#97—612no—
274#97—1222no—
275#97—1222no—
276#97C4×D6112yes—
277C4×C8—21no—
278C4×C8—21no—
279C4×C8—1222no—
280C4×C8—1221no—
281C4×C8—1221no—
282C24—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—2441no—
299C22×C4—2441no—
300C22×C4—2442no—
301C22×C4—2442no—
302C22×C4C2×C4×D6111yescharacteristic
303C22×C4D4×D6111yescharacteristic
304C22×C4Q8×D6111yescharacteristic
305M16—42no—
306M16—42no—
307M16—2444no—
308M16—2442no—
309M16—2442no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—1222no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—611no—
322C42—611no—
323C42—611no—
324C42—611no—
325C42—611no—
326C42—611no—
327C42—611no—
328C42C2×C4×D6111yescharacteristic
329C42C2×C4×D6111yescharacteristic
330C42D4×D6111yescharacteristic
331C42D4×D6111yescharacteristic
332C23—611no—
333C23—611no—
334C23—2441no—
335C23—2441no—
336C23—2441no—
337C23C4⋊C4×D6111yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4C42×D6111yescharacteristic
366C2×C4C22⋊C4×D6111yescharacteristic
367C2×C4C22⋊C4×D6111yescharacteristic
368C2×C4C22⋊C4×D6111yescharacteristic
369C2×C4C4⋊C4×D6111yescharacteristic
370C2×C4C4⋊C4×D6111yescharacteristic
371C8—42no—
372C8—42no—
373C8—42no—
374C8—2442no—
375C8—2442no—
376C8—2442no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—1221no—
381C22—1221no—
382C22—1221no—
383C22—1221no—
384C22—1221no—
385C22—1221no—
386C22—2444no—
387C22#95×D6111yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—1221no—
392C4—1221no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—1221no—
397C4#1683974311yescharacteristic
398C4#1683974511yescharacteristic
399C4#1683977712yes—
400C4#1683980912yes—
401C2—41no—
402C2—2441no—
403C2—2441no—
404C2#2144552711yescharacteristic
405C2#2144554411yescharacteristic
406C2#2144555611yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC61×#1299C2
socleC22×C61C2×#95
prime radicalC23×D61C4⋊C4
cosocleC2×C42×C61C23
hypercenter#1299D61
hypocenterC61#8062
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
4. #21443710C2semidirect
5. #21443709C2semidirect
6. #21443708C2semidirect
7. C61×#1299C2semidirect
204. #1299D61semidirect
236. C61#8062semidirect

Maximal subgroups

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

subgroupindex
#214544512
#214544502
#214544472
#214437102
#214437092
#214437082
C61×#12992
#806261