Finite Group Databasebeta

← #29596933

Subgroups — #29596933

Order 15616.

466 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458921C211yesmaximal, characteristic, complemented
2#21454535C211yesmaximal, characteristic
3#21447447C211yesmaximal, characteristic, complemented
4#21447439C211yesmaximal, characteristic, complemented
5#21443898C211yesmaximal, characteristic, complemented
6#21443898C211yesmaximal, characteristic, complemented
7C61×#2117C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9#16840308C411yescharacteristic
10#16840180—22no—
11#16840178—22no—
12C2×#14519717C2211yescharacteristic
13C2×#14519717C2211yescharacteristic
14M32×D61—22no—
15#16839833—22no—
16#16839831—22no—
17#16839785C411yescharacteristic
18#16839730C411yescharacteristic
19#16839729C411yescharacteristic
20C2×#14519687C2211yescharacteristic
21#16839546—22no—
22#16839543—22no—
23C2×#131×C61C2211yescharacteristic
24C2×M32×C61C2211yescharacteristic
25C2×M32×C61C2211yescharacteristic
26C61×#350—22no—
27C2×#11758222C2×C411yescharacteristic
28#14519783—21no—
29#14519783—21no—
30#14519783—21no—
31#14519783—21no—
32C2×#11758194C2×C411yescharacteristic
33C2×#11758189D412yes—
34C22×#92418C2×C411yescharacteristic
35C2×C8×D61D412yes—
36#14519775C811yescharacteristic
37#14519773C811yescharacteristic
38#14519766C811yescharacteristic
39#14519764C811yescharacteristic
40#14519749—22no—
41C4×C22⋊D61—22no—
42C2×C4×Dic61C2×C411yescharacteristic
43#14519717—21no—
44#14519717—21no—
45#14519717—21no—
46#14519717—21no—
47#14519716—24no—
48C2×#11758185—21no—
49C2×#11758185D412yescomplemented
50C16×D61—24no—
51#14519706—22no—
52C22⋊#92418—22no—
53#14519689—22no—
54#14519687—21no—
55#14519687—21no—
56C2×#41×C61C2×C411yescharacteristic
57#131×C61—21no—
58#131×C61—21no—
59#131×C61—21no—
60#131×C61—21no—
61C2×M16×C61—21no—
62C2×M16×C61C2×C411yescharacteristic
63C22×C8×C61—21no—
64C22×C8×C61C2311yescharacteristic
65M32×C61—21no—
66M32×C61—21no—
67M32×C61—21no—
68M32×C61—21no—
69C2×C16×C61—21no—
70C2×C16×C61D412yescomplemented
71#41×C61—21no—
72#41×C61—21no—
73#41×C61—21no—
74#41×C61—21no—
75C2×Q8×C61C2×C811yescharacteristic
76C2×D4×C61—21no—
77C2×D4×C61C2×C811yescharacteristic
78C22×C4×C61—21no—
79C22×C4×C61C22×C411yescharacteristic
80C2×C22⋊D61—22no—
81C2×C22⋊D61M1612yes—
82C22×Dic61—21no—
83#11758222—21no—
84#11758222—21no—
85#11758222—21no—
86#11758222—21no—
87C2×D244C2×C811yescharacteristic
88C2×C4×D61C22⋊C412yes—
89C2×Dic122C2×C811yescharacteristic
90M16×C61—21no—
91M16×C61—21no—
92M16×C61—41no—
93M16×C61—41no—
94C2×C8×C61—21no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61#4111yescharacteristic
102C2×C8×C61#4111yescharacteristic
103C22⋊Dic61—22no—
104#11758198—22no—
105#11758196—22no—
106C4×Dic61—21no—
107C4×Dic61C2×C811yescharacteristic
108C4×Dic61C2×C811yescharacteristic
109#11758194—21no—
110#11758194—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418C22⋊C412yes—
115#11758189—22no—
116#11758189—22no—
117C8×D61—22no—
118C8×D61—22no—
119C16×C61—22no—
120C16×C61—41no—
121#11758185—22no—
122#11758185—41no—
123C23×C61—21no—
124C23×C61C2×M1611yescharacteristic
125C22×D61C22⋊C812yes—
126Q8×C61—21no—
127Q8×C61—21no—
128D4×C61—21no—
129D4×C61—21no—
130D4×C61—41no—
131D4×C61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61C2×C22⋊C411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61C22×C811yescharacteristic
139C2×C4×C61#13111yescharacteristic
140C2×C4×C61#13111yescharacteristic
141C22⋊D61—22no—
142C22⋊D61—22no—
143C22⋊D61—82no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—81no—
147C2×Dic61C22⋊C812yes—
148D244—21no—
149D244—21no—
150C4×D61—22no—
151C4×D61—22no—
152Dic122—21no—
153Dic122—21no—
154C8×C61—41no—
155C8×C61#12011yescharacteristic
156C8×C61#12111yescharacteristic
157C8×C61#12111yescharacteristic
158C8×C61#12311yescharacteristic
159#92418—22no—
160#92418—41no—
161#12988—611nomaximal, Sylow
162C22×C61—41no—
163C22×C61—42no—
164C22×C61—41no—
165C22×C61C2×C22⋊C811yescharacteristic
166C22×C61#43511yescharacteristic
167C22×C61#43511yescharacteristic
168C2×D61—22no—
169C2×D61—42no—
170C4×C61—41no—
171C4×C61#38611yescharacteristic
172C4×C61#40811yescharacteristic
173C4×C61C8×D411yescharacteristic
174C4×C61C8×D411yescharacteristic
175Dic61—22no—
176Dic61—41no—
177Dic61—41no—
178#3407—611no—
179#2932—611no—
180#2117—611no—
181#2117D6111yescharacteristic, complemented
182#2115—611no—
183#1375—611no—
184#1375—611no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—81no—
189C2×C61#186911yescharacteristic
190D61—42no—
191C2×#131—611no—
192C2×#131C2×D6111yescharacteristic
193#532—611no—
194#504—1222no—
195#504—1222no—
196C2×M32—611no—
197C2×M32—611no—
198C2×M32—1222no—
199C2×M32C2×D6111yescharacteristic
200C2×M32C2×D6111yescharacteristic
201#435—1222no—
202#435—1222no—
203#423—611no—
204#408—611no—
205#408—611no—
206C2×#97—611no—
207#350—22no—
208#350—1222no—
209#349—1222no—
210C61#1298811yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×#41C4×D6111yescharacteristic
213#131—21no—
214#131—21no—
215#131—21no—
216#131—21no—
217#131—1221no—
218#131—1221no—
219#131—1221no—
220#131—1221no—
221C2×M16—21no—
222C2×M16—611no—
223C2×M16—612no—
224C2×M16C4×D6111yescharacteristic
225C22×C8—21no—
226C22×C8—612no—
227C22×C8—611no—
228C22×C8C22×D6111yescharacteristic
229C4⋊Q8—611no—
230#127—611no—
231#124—611no—
232#124—611no—
233#121—1222no—
234C4×D4—1222no—
235C2×C42—611no—
236M32—21no—
237M32—21no—
238M32—21no—
239M32—21no—
240M32—1224no—
241M32—1221no—
242M32—1221no—
243M32—1221no—
244M32—1221no—
245C2×C16—21no—
246C2×C16—612no—
247C2×C16—1224no—
248C2×C16—1221no—
249C2×C16C22⋊D6112yescomplemented
250C4⋊C8—1222no—
251C22⋊C8—1222no—
252C22⋊C8—1222no—
253#97—1221no—
254#97—1221no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41—1221no—
260#41—1221no—
261#41—1221no—
262#41—1221no—
263C2×Q8—611no—
264C2×Q8C8×D6111yescharacteristic
265C2×D4—21no—
266C2×D4—612no—
267C2×D4—611no—
268C2×D4—1222no—
269C2×D4C8×D6111yescharacteristic
270C22×C4—21no—
271C22×C4—612no—
272C22×C4—1221no—
273C22×C4C2×C4×D6111yescharacteristic
274M16—21no—
275M16—21no—
276M16—41no—
277M16—41no—
278M16—1221no—
279M16—1221no—
280M16—1222no—
281M16—1222no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—612no—
286C2×C8—1222no—
287C2×C8—1222no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8#1175822211yescharacteristic
292C2×C8D4×D6111yescharacteristic
293C2×C8D4×D6111yescharacteristic
294C2×C8D4×D6111yescharacteristic
295C2×C8#1175822411yescharacteristic
296C2×C8C2×C22⋊D6111yescharacteristic
297C4⋊C4—1222no—
298C22⋊C4—1222no—
299C22⋊C4—1222no—
300C42—611no—
301C42—611no—
302C42—1221no—
303C16—22no—
304C16—41no—
305C16—1222no—
306C16—2441no—
307C23—21no—
308C23—612no—
309C23M16×D6111yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—1221no—
313Q8—1221no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—41no—
318D4—1222no—
319D4—1222no—
320D4—1221no—
321D4—1221no—
322D4—4882no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—612no—
327C2×C4—1222no—
328C2×C4—1222no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—4881no—
332C2×C4C22⋊C4×D6111yescharacteristic
333C2×C4#1451973711yescharacteristic
334C2×C4C4×C22⋊D6111yescharacteristic
335C2×C4C2×C8×D6111yescharacteristic
336C2×C4#1451978311yescharacteristic
337C2×C4#1451978511yescharacteristic
338C8—41no—
339C8—1222no—
340C8—2441no—
341C8#1451974511yescharacteristic
342C8#1451974811yescharacteristic
343C8#1451975011yescharacteristic
344C8#1451975911yescharacteristic
345C22—41no—
346C22—42no—
347C22—41no—
348C22—1222no—
349C22—2442no—
350C22C22⋊C8×D6111yescharacteristic
351C22#1683983111yescharacteristic
352C22#1683983611yescharacteristic
353C4—41no—
354C4—1222no—
355C4—2441no—
356C4—2441no—
357C4#1683963811yescharacteristic
358C4#1683972711yescharacteristic
359C4#1683982511yescharacteristic
360C4C8×C22⋊D6111yescharacteristic
361C2—21no—
362C2—21no—
363C2—21no—
364C2—81no—
365C2—2442no—
366C2#2144610811yescharacteristic
subgroupG/H
centerC4#16839638
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#2117C2
socleC2×C61#1869
prime radical#16840308C4
cosocleC22×C8×C61C23
hypercenter#2117D61
hypocenterC61#12988
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. #21458921C2semidirect
3. #21447447C2semidirect
4. #21447439C2semidirect
5. #21443898C2semidirect
6. #21443898C2semidirect
7. C61×#2117C2semidirect
49. C2×#11758185D4semidirect
70. C2×C16×C61D4semidirect
181. #2117D61semidirect
210. C61#12988semidirect
249. C2×C16C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214589212
#214545352
#214474472
#214474392
#214438982
C61×#21172
#1298861