Finite Group Databasebeta

← #29663995

Subgroups — #29663995

Order 15616.

638 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
1C2×#16840113C211yesmaximal, characteristic, complemented
2#21455635C211yesmaximal, characteristic
3#21455635C211yesmaximal, characteristic
4C8×#11758222C211yesmaximal, characteristic
5#21445278C214yesmaximal, complemented
6#21445271C214yesmaximal, complemented
7#21444505C211yesmaximal, characteristic, complemented
8#21444501C211yesmaximal, characteristic, complemented
9C61×#1567C211yesmaximal, characteristic, complemented
10C2×#14519777C2211yescharacteristic
11C2×#14519777C2211yescharacteristic
12C4×#11758222C2211yescharacteristic
13#16840113—21no—
14#16840113—21no—
15#16840113C2214yes—
16#16840058—21no—
17#16840058C2212yes—
18#16840053—21no—
19#16840053C2212yes—
20#16840048—21no—
21#16840048C2212yes—
22#16840043—21no—
23#16840043C2212yes—
24C8×Dic122C2212yes—
25C8×D244C2212yes—
26C8×C22⋊D61—22no—
27#16839815C2211yescharacteristic
28#16839813—21no—
29#16839804—21no—
30#16839804—21no—
31#16839764—21no—
32#16839764—21no—
33C2×#14519702—22no—
34C4×C8×D61—21no—
35#16839510C2214yes—
36#16839507C2214yes—
37C61×#423C2211yescharacteristic
38C61×#423C2211yescharacteristic
39C2×C4×C8×C61C2211yescharacteristic
40C61×#335C2214yes—
41C2×#11758222D411yescharacteristic
42C22×Dic122—21no—
43C22×Dic122—21no—
44C2×C8×D61—22no—
45#14519777—21no—
46#14519777—21no—
47#14519777—21no—
48#14519777—21no—
49#14519777—21no—
50#14519777—21no—
51#14519777C2312yes—
52#14519777C2312yes—
53C4×Dic122D411yescharacteristic
54C4×Dic122C2311yescharacteristic
55C4×D244D411yescharacteristic
56C4×D244C2311yescharacteristic
57C4×C22⋊D61—21no—
58C4×C22⋊D61—21no—
59#14519736D411yescharacteristic
60#14519734—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C42×D61—21no—
66#14519711—22no—
67#14519711—22no—
68#14519709—22no—
69#14519709—22no—
70C4⋊#92418C2312yes—
71#14519706—22no—
72#14519702—22no—
73#14519702—22no—
74#14519702—24no—
75#14519702—24no—
76#14519699—22no—
77#14519699—22no—
78C22⋊#92418—21no—
79#14519689—22no—
80C4×#92418—21no—
81C8×Dic61—22no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C22×C8×C61D412yes—
85C2×C42×C61C2311yescharacteristic
86C4⋊C8×C61—21no—
87C4⋊C8×C61—21no—
88C4⋊C8×C61C2312yes—
89C4⋊C8×C61C2312yes—
90C4×C8×C61D411yescharacteristic
91C4×C8×C61D411yescharacteristic
92C4×C8×C61C2312yes—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C2×C22⋊D61—21no—
97C22×Dic61—41no—
98C22×Dic61—41no—
99#11758222—22no—
100#11758222Q1614yes—
101C2×D244C2×D411yescharacteristic
102C2×C4×D61—21no—
103C2×C4×D61—21no—
104C2×C4×D61—21no—
105C2×Dic122—22no—
106C2×Dic122—22no—
107C2×Dic122—44no—
108C2×Dic122—41no—
109C2×Dic122—41no—
110C2×Dic122—82no—
111C2×Dic122C2×D411yescharacteristic
112M16×C61—42no—
113M16×C61—42no—
114C2×C8×C61—22no—
115C2×C8×C61—22no—
116C2×C8×C61—42no—
117C2×C8×C61C2×D412yes—
118C2×C8×C61C2×D412yes—
119C42×C61C2×D411yescharacteristic
120C42×C61C2×D411yescharacteristic
121C42×C61#4111yescharacteristic
122C42×C61C2411yescharacteristic
123C22⋊Dic61—21no—
124#11758198—21no—
125#11758198—21no—
126C4⋊Dic61—22no—
127C4⋊Dic61—22no—
128C4⋊Dic61—22no—
129C4⋊Dic61—22no—
130C4⋊Dic61—41no—
131C4⋊Dic61—41no—
132C4⋊Dic61—41no—
133C4⋊Dic61—41no—
134C4⋊Dic61C2×D411yescharacteristic
135C4⋊Dic61C2×D411yescharacteristic
136#11758196—21no—
137#11758196—21no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140C4×Dic61—21no—
141C2×#92418—22no—
142C8×D61—44no—
143C23×C61#12111yescharacteristic
144C22×D61—21no—
145C2×C4×C61—22no—
146C2×C4×C61—22no—
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61C2×Q1612yes—
151C2×C4×C61#13512yes—
152C2×C4×C61C22×D411yescharacteristic
153C2×C4×C61C22×D411yescharacteristic
154C2×C4×C61C2×#4111yescharacteristic
155C22⋊D61—24no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—42no—
160C2×Dic61—42no—
161C2×Dic61—82no—
162C2×Dic61—82no—
163D244—21no—
164D244C2×Q1612yes—
165C4×D61—24no—
166C4×D61—42no—
167C4×D61—42no—
168Dic122—21no—
169Dic122—44no—
170Dic122—82no—
171Dic122—82no—
172Dic122—82no—
173Dic122C2×Q1612yes—
174C8×C61—22no—
175C8×C61—22no—
176C8×C61—42no—
177C8×C61—42no—
178#92418—42no—
179#19277—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61#46712yes—
183C22×C61C2×#12111yescharacteristic
184C2×D61—22no—
185C2×D61—41no—
186C2×D61—41no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61#46712yes—
190C4×C61#47112yes—
191C4×C61C22×Q1611yescharacteristic
192C4×C61C2×#13511yescharacteristic
193C4×C61#57512yes—
194Dic61—22no—
195Dic61—41no—
196Dic61—41no—
197Dic61—82no—
198Dic61—82no—
199C2×#487—611no—
200#3079—611no—
201#3079—611no—
202C8×#41—611no—
203#1684—614no—
204#1683—614no—
205#1567D6111yescharacteristic, complemented
206#1549—611no—
207#1548—611no—
208C2×C61—22no—
209C2×C61#304011yescharacteristic
210C2×C61C2×#46711yescharacteristic
211C2×C61C2×#47111yescharacteristic
212D61—42no—
213C2×C4⋊Q8—611no—
214C2×C4⋊Q8—611no—
215C4×#41—611no—
216#487—614no—
217#487—1221no—
218#487—1221no—
219#477—612no—
220#477—1221no—
221#476—612no—
222#476—1221no—
223#475—612no—
224#475—1221no—
225#474—612no—
226#474—1221no—
227C8×Q8—612no—
228C8×D4—612no—
229C8×D4—1222no—
230#431—611no—
231#431—1221no—
232#428—1221no—
233#428—1221no—
234#423C2×D6111yescharacteristic
235#423C2×D6111yescharacteristic
236#417—1221no—
237#417—1221no—
238C2×#103—1222no—
239C2×C4×C8—1221no—
240C2×C4×C8C2×D6111yescharacteristic
241#335C2×D6114yes—
242#333—614no—
243#332—614no—
244C61#1927711yescharacteristic, complemented, Sylow
245C2×#41—611no—
246C22×Q8—1221no—
247C22×Q8—1221no—
248C2×M16—21no—
249C2×M16—21no—
250C22×C8—1222no—
251C22×C8D24412yes—
252C4⋊Q8—612no—
253C4⋊Q8—612no—
254C4⋊Q8—1221no—
255C4⋊Q8—1221no—
256C4⋊Q8—1221no—
257C4⋊Q8—1221no—
258C4⋊Q8—1221no—
259C4⋊Q8—1221no—
260C4×Q8—611no—
261C4×Q8—611no—
262C4×D4—611no—
263C4×D4—611no—
264C4×D4—1221no—
265C4×D4—1221no—
266#117—611no—
267#117—1221no—
268C2×C4⋊C4—1221no—
269C2×C4⋊C4—1221no—
270C2×C4⋊C4—1221no—
271C2×C4⋊C4—1221no—
272C2×C42—1221no—
273C2×C42C22×D6111yescharacteristic
274#107—1222no—
275#107—1222no—
276#106—1222no—
277#106—1222no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—612no—
281C4⋊C8—1222no—
282C4⋊C8C22×D6112yes—
283C4⋊C8C22×D6112yes—
284#103—1222no—
285#103—1222no—
286#103—1224no—
287#103—1224no—
288#102—1222no—
289#102—1222no—
290C22⋊C8—1221no—
291C22⋊C8—1222no—
292C4×C8—1222no—
293C4×C8—1221no—
294C4×C8D24411yescharacteristic
295C4×C8D24411yescharacteristic
296C4×C8C22×D6112yes—
297#41—614no—
298#41—1222no—
299C2×Q8—611no—
300C2×Q8—1222no—
301C2×Q8—1222no—
302C2×Q8—4882no—
303C2×Q8—2444no—
304C2×Q8—2441no—
305C2×Q8—2441no—
306C2×D4—611no—
307C2×D4—1221no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—2441no—
312C22×C4—2441no—
313C22×C4C2×D24411yescharacteristic
314C22×C4D4×D6111yescharacteristic
315C22×C4#1175822611yescharacteristic
316M16—42no—
317M16—42no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—42no—
321C2×C8—1222no—
322C2×C8—2444no—
323C2×C8C2×D24412yes—
324C2×C8C2×D24412yes—
325C4⋊C4—611no—
326C4⋊C4—611no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1222no—
330C4⋊C4—1222no—
331C4⋊C4—1222no—
332C4⋊C4—1222no—
333C4⋊C4—2441no—
334C4⋊C4—2441no—
335C4⋊C4—2441no—
336C4⋊C4—2441no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C42—1221no—
341C42—1221no—
342C42—1221no—
343C42C2×D24411yescharacteristic
344C42D4×D6111yescharacteristic
345C42#1175822611yescharacteristic
346C42C23×D6111yescharacteristic
347C23—1221no—
348C23#1451975211yescharacteristic
349Q8—612no—
350Q8—1221no—
351Q8—4882no—
352Q8—4882no—
353Q8—4882no—
354Q8—2444no—
355D4—612no—
356D4—1224no—
357D4—1221no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—1221no—
361C2×C4—1224no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—4882no—
365C2×C4—4882no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4#1451975211yescharacteristic
371C2×C4#1451975211yescharacteristic
372C2×C4#1451975211yescharacteristic
373C2×C4Q16×D6112yes—
374C2×C4#1451979612yes—
375C2×C4C2×D4×D6111yescharacteristic
376C2×C4C22×D24411yescharacteristic
377C2×C4C2×#1175822611yescharacteristic
378C8—22no—
379C8—22no—
380C8—42no—
381C8—42no—
382C8—2442no—
383C22—21no—
384C22—21no—
385C22—1222no—
386C22—2441no—
387C22—2441no—
388C22#1684000412yes—
389C22C2×#1451975211yescharacteristic
390C4—21no—
391C4—21no—
392C4—1222no—
393C4—4882no—
394C4—4882no—
395C4—2441no—
396C4—2441no—
397C4#1684000412yes—
398C4#1684002612yes—
399C4C2×Q16×D6111yescharacteristic
400C4C2×#1451979611yescharacteristic
401C4#1684056212yes—
402C2—22no—
403C2—2442no—
404C2#2145531411yescharacteristic
405C2C2×#1684000411yescharacteristic
406C2C2×#1684002611yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1567C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#1567D61
hypocenterC61#19277
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
1. C2×#16840113C2semidirect
5. #21445278C2semidirect
6. #21445271C2semidirect
7. #21444505C2semidirect
8. #21444501C2semidirect
9. C61×#1567C2semidirect
205. #1567D61semidirect
244. C61#19277semidirect

Maximal subgroups

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

subgroupindex
C2×#168401132
#214556352
C8×#117582222
#214452782
#214452712
#214445052
#214445012
C61×#15672
#1927761