Finite Group Databasebeta

← #29574892

Subgroups — #29574892

Order 15616.

430 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455609C211yesmaximal, characteristic
2#21454484C211yesmaximal, characteristic
3#21444275C211yesmaximal, characteristic, complemented
4#21444221C211yesmaximal, characteristic, complemented
5#21444202C211yesmaximal, characteristic
6#21443716C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9C4×#11758222C2211yescharacteristic
10#16840070—21no—
11#16840063—21no—
12#16840058C411yescharacteristic
13#16840053C411yescharacteristic
14#16840048C411yescharacteristic
15#16840043C411yescharacteristic
16#16839822—22no—
17#16839818—21no—
18#16839815C2211yescharacteristic
19#16839814—21no—
20#16839800—21no—
21#16839786C2211yescharacteristic
22#16839759—21no—
23#16839728—21no—
24#16839717—21no—
25#16839494—21no—
26#16839494—22no—
27#16839492—21no—
28#16839492—21no—
29#16839491—21no—
30C2×C4⋊C8×C61C2211yescharacteristic
31C2×C4⋊C8×C61C2211yescharacteristic
32C2×C4×C8×C61C2211yescharacteristic
33C2×#11758222D411yescharacteristic
34C2×#11758194—21no—
35#14519777C2×C411yescharacteristic
36#14519777C2×C411yescharacteristic
37#14519769—21no—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C4×Dic122C2×C411yescharacteristic
43C4×Dic122D411yescharacteristic
44C4×D244C2×C411yescharacteristic
45C4×D244D411yescharacteristic
46C4×C22⋊D61—21no—
47C4×C22⋊D61—21no—
48#14519736—21no—
49#14519736D411yescharacteristic
50#14519734—21no—
51C42×D61—21no—
52#14519711—21no—
53#14519711—21no—
54#14519709—21no—
55#14519709—21no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418D412yes—
59#14519702—21no—
60#14519702—21no—
61#14519699—21no—
62#14519699—21no—
63C22⋊#92418—21no—
64#14519689—22no—
65#14519689—22no—
66#14519687—22no—
67C4×#92418—21no—
68C8×Dic61—22no—
69C22×C8×C61—21no—
70C22×C8×C61—21no—
71C22×C8×C61—21no—
72C2×C42×C61C2311yescharacteristic
73C4⋊C8×C61—21no—
74C4⋊C8×C61—21no—
75C4⋊C8×C61C2×C411yescharacteristic
76C4⋊C8×C61C2×C411yescharacteristic
77C4⋊C8×C61D411yescharacteristic
78C4⋊C8×C61D411yescharacteristic
79C4×C8×C61—21no—
80C4×C8×C61—21no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×C4×C61#4111yescharacteristic
84C2×C22⋊D61—21no—
85#11758222—21no—
86#11758222—21no—
87#11758222—21no—
88#11758222—21no—
89C2×D244C22⋊C411yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×Dic122—21no—
94C2×Dic122—21no—
95C2×Dic122C22⋊C411yescharacteristic
96C2×C8×C61—22no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—21no—
101C2×C8×C61—41no—
102C2×C8×C61—41no—
103C2×C8×C61—41no—
104C2×C8×C61—41no—
105C2×C8×C61—41no—
106C2×C8×C61—41no—
107C42×C61C22×C411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C22⋊Dic61—21no—
112C22⋊Dic61—41no—
113#11758198—21no—
114#11758198—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61C22⋊C411yescharacteristic
120C4⋊Dic61C22⋊C411yescharacteristic
121#11758196—21no—
122#11758196—21no—
123#11758196—41no—
124#11758196—41no—
125C4×Dic61—21no—
126C4×Dic61—21no—
127C4×Dic61—21no—
128C4×Dic61—41no—
129#11758194—41no—
130#11758194—41no—
131C2×#92418—22no—
132C2×#92418—41no—
133C23×C61#12311yescharacteristic
134C22×D61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—41no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#13511yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61#13711yescharacteristic
147C2×C4×C61#13711yescharacteristic
148C22⋊D61—41no—
149C22⋊D61—41no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155D244—21no—
156D244—21no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—81no—
162Dic122—21no—
163Dic122—21no—
164Dic122—42no—
165Dic122—41no—
166Dic122—41no—
167C8×C61—42no—
168C8×C61—41no—
169C8×C61—41no—
170C8×C61—41no—
171C8×C61—41no—
172#92418—42no—
173#92418—81no—
174#8994—611nomaximal, Sylow
175C22×C61—21no—
176C22×C61—21no—
177C22×C61#38611yescharacteristic
178C22×C61#48511yescharacteristic
179C22×C61#48511yescharacteristic
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61#41611yescharacteristic
187C4×C61#41911yescharacteristic
188C4×C61#44311yescharacteristic
189C4×C61#44411yescharacteristic
190C4×C61#45211yescharacteristic
191C4×C61#45211yescharacteristic
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195Dic61—81no—
196Dic61—81no—
197#3076—611no—
198#2925—611no—
199#1493—611no—
200#1481—611no—
201#1476—611no—
202#1301—611no—
203#1277D6111yescharacteristic, complemented
204C2×C61—21no—
205C2×C61—21no—
206C2×C61#187311yescharacteristic
207C2×C61#187611yescharacteristic
208C2×C61#188111yescharacteristic
209D61—81no—
210#533—611no—
211C4×#41—611no—
212#479—1221no—
213#478—1221no—
214#477—611no—
215#476—611no—
216#475—611no—
217#474—611no—
218#433—1222no—
219#432—1221no—
220#431—611no—
221#431—1221no—
222#427—1221no—
223#423—611no—
224C2×C4⋊C8C2×D6111yescharacteristic
225C2×C4⋊C8C2×D6111yescharacteristic
226#416—1221no—
227#408—1221no—
228#405—1221no—
229C2×C4×C8C2×D6111yescharacteristic
230Q8⋊C8—1222no—
231Q8⋊C8—1221no—
232Q8⋊C8—1221no—
233Q8⋊C8—1221no—
234D4⋊C8—1221no—
235C61#899411yescharacteristic, complemented, Sylow
236C2×#41—611no—
237C2×M16—1221no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C4⋊Q8—611no—
242C4⋊Q8—611no—
243#125—1221no—
244C22⋊Q8—1221no—
245C22⋊Q8—1221no—
246C4×Q8—611no—
247C4×Q8—611no—
248C4×Q8—1221no—
249C4×Q8—1221no—
250C4×D4—611no—
251C4×D4—611no—
252C4×D4—1221no—
253C4×D4—1221no—
254#117—611no—
255#117—1221no—
256#117—1221no—
257C2×C42—1221no—
258C2×C42C22×D6111yescharacteristic
259#107—1221no—
260#107—1221no—
261#106—1221no—
262#106—1221no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—612no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8C4×D6111yescharacteristic
269C4⋊C8C4×D6111yescharacteristic
270C4⋊C8D24411yescharacteristic
271C4⋊C8D24411yescharacteristic
272#103—1221no—
273#103—1221no—
274#102—1221no—
275#102—1221no—
276C22⋊C8—1222no—
277C22⋊C8—1222no—
278C22⋊C8—1221no—
279#97—1222no—
280C4×C8—21no—
281C4×C8—21no—
282C4×C8—1222no—
283C4×C8—1221no—
284#41—1221no—
285#41—1221no—
286#41—1221no—
287#41—1221no—
288C2×Q8—611no—
289C2×Q8—1221no—
290C2×Q8—1221no—
291C2×D4—611no—
292C2×D4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—1221no—
296C22×C4#1175822211yescharacteristic
297C22×C4D4×D6111yescharacteristic
298C22×C4#1175822611yescharacteristic
299M16—2441no—
300M16—2441no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—1222no—
313C2×C8—2441no—
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C4⋊C4—1221no—
322C4⋊C4—2441no—
323C4⋊C4—2441no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—2441no—
328C42—1221no—
329C42—1221no—
330C42—1221no—
331C42—2441no—
332C42C2×C4×D6111yescharacteristic
333C42C2×D24411yescharacteristic
334C42D4×D6111yescharacteristic
335C42D4×D6111yescharacteristic
336C23—1221no—
337C23#1451976211yescharacteristic
338Q8—1221no—
339Q8—1221no—
340Q8—2442no—
341Q8—2441no—
342Q8—2441no—
343D4—1221no—
344D4—1221no—
345D4—2441no—
346D4—2441no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—4881no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4C22⋊C4×D6111yescharacteristic
361C2×C4#1451973911yescharacteristic
362C2×C4C4×D24411yescharacteristic
363C2×C4#1451974711yescharacteristic
364C2×C4#1451975011yescharacteristic
365C2×C4#1451975211yescharacteristic
366C2×C4#1451979611yescharacteristic
367C2×C4#1451979811yescharacteristic
368C2×C4#1451980611yescharacteristic
369C2×C4#1451980911yescharacteristic
370C8—42no—
371C8—41no—
372C8—41no—
373C8—41no—
374C8—41no—
375C8—4881no—
376C8—2442no—
377C22—21no—
378C22—21no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22#1683964011yescharacteristic
383C22#1684010511yescharacteristic
384C22#1684010611yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—4881no—
389C4—4881no—
390C4—2441no—
391C4—2441no—
392C4—2441no—
393C4#1683975511yescharacteristic
394C4#1683976911yescharacteristic
395C4#1683988011yescharacteristic
396C4#1683988511yescharacteristic
397C4#1683992511yescharacteristic
398C4#1683992711yescharacteristic
399C2—21no—
400C2—21no—
401C2—4881no—
402C2#2144613011yescharacteristic
403C2#2144614511yescharacteristic
404C2#2144618211yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC22×C61#386
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#8994
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
3. #21444275C2semidirect
4. #21444221C2semidirect
6. #21443716C2semidirect
7. C61×#1277C2semidirect
203. #1277D61semidirect
235. C61#8994semidirect

Maximal subgroups

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

subgroupindex
#214556092
#214544842
#214442752
#214442212
#214442022
#214437162
C61×#12772
#899461