Finite Group Databasebeta

← #30624273

Subgroups — #30624273

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462788C211yesmaximal, characteristic, complemented
2#21462786C211yesmaximal, characteristic, complemented
3#21462210C214yesmaximal, complemented
4#21462207C214yesmaximal, complemented
5#21462162C211yesmaximal, characteristic, complemented
6C2×#16840661C211yesmaximal, characteristic, complemented
7C2×#16840660C211yesmaximal, characteristic, complemented
8#21462028C211yesmaximal, characteristic, complemented
9#21454718C211yesmaximal, characteristic
10#16840821—22no—
11#16840821C2214yescomplemented
12#16840820—22no—
13#16840820C2214yescomplemented
14D61⋊M32—22no—
15C2×#14519851—22no—
16C2×#14519851C2211yescharacteristic
17C2×#14519851C2211yescharacteristic
18C2×#14519851C2211yescharacteristic
19C22×#11758187C2211yescharacteristic
20#16840685C2214yescomplemented
21#16840661C2212yescomplemented
22#16840661C2212yescomplemented
23#16840660C2212yescomplemented
24#16840660C2212yescomplemented
25#16840650C2212yescomplemented
26C4×#11758187C2212yescomplemented
27#16840560C411yescharacteristic
28C2×#14519785C2211yescharacteristic
29C2×#14519784C2211yescharacteristic
30#16839881C414yes—
31#16839876C2214yes—
32#16839810C411yescharacteristic
33#16839780C411yescharacteristic
34#16839718C2211yescharacteristic
35C61×#421C411yescharacteristic
36#14519852—24no—
37#14519851—21no—
38#14519851—21no—
39#14519851—24no—
40#14519851D412yes—
41#14519851D412yes—
42#14519851C2312yes—
43#14519851C2312yes—
44D61⋊C16—24no—
45C2×#11758187—21no—
46C2×#11758187—21no—
47C2×#11758187—21no—
48C2×#11758187—21no—
49C2×#11758187—24no—
50C2×#11758187C2311yescharacteristic
51C2×#11758187C2311yescharacteristic
52C2×#11758187C2312yes—
53C2×#11758222C2×C411yescharacteristic
54#14519808C812yes—
55#14519807C812yes—
56#14519803C812yes—
57#14519802C812yes—
58#14519797C2×C414yes—
59#14519785—21no—
60#14519785—21no—
61#14519785C2×C412yes—
62#14519785C2312yes—
63#14519784—21no—
64#14519784—21no—
65#14519784C2×C412yes—
66#14519784C2312yes—
67C2×#11758194—21no—
68C2×#11758194C2×C411yescharacteristic
69C2×#11758194C2×C411yescharacteristic
70C2×#11758189—21no—
71C22×#92418—21no—
72C22×#92418C2311yescharacteristic
73C2×C8×D61—21no—
74#14519712C2×C414yes—
75#14519705C2×C414yes—
76#14519688C2×C412yes—
77C4×#92418C2312yes—
78C2×#41×C61C2×C411yescharacteristic
79C2×M16×C61C2×C411yescharacteristic
80#117×C61C2×C411yescharacteristic
81#104×C61C2×C414yes—
82#41×C61—21no—
83#41×C61—21no—
84#41×C61C2×C812yes—
85#41×C61C22×C412yes—
86C2×Q8×C61C2×C811yescharacteristic
87C2×D4×C61—21no—
88C2×D4×C61C2×C811yescharacteristic
89C22×C4×C61—21no—
90C22×C4×C61C22×C411yescharacteristic
91C2×C22⋊D61—21no—
92#11758222—21no—
93#11758222—21no—
94#11758222C2×C812yes—
95#11758222C22×C412yes—
96C2×D244C2×C811yescharacteristic
97C2×C4×D61—21no—
98C2×Dic122C2×C811yescharacteristic
99M16×C61—21no—
100M16×C61C22×C412yes—
101C2×C8×C61—21no—
102C4⋊C4×C61—21no—
103C22⋊C4×C61—21no—
104C42×C61C22×C412yes—
105#11758202C2×C814yes—
106#11758201C2×C814yes—
107#11758200C2×C814yes—
108#11758199C2×C814yes—
109#11758194—21no—
110#11758194—22no—
111#11758194—22no—
112#11758194C2×C812yes—
113#11758194C2×C812yes—
114#11758194C22×C412yes—
115C2×#92418—21no—
116C2×#92418—22no—
117C2×#92418—22no—
118C2×#92418C22×C411yescharacteristic
119C2×#92418C22×C412yes—
120C2×#92418C2×D411yescharacteristic
121C2×#92418C2×D411yescharacteristic
122C2×#92418#4111yescharacteristic
123C2×#92418#4111yescharacteristic
124C2×#92418C2411yescharacteristic
125#11758189—22no—
126#11758189—22no—
127C8×D61—22no—
128C8×D61—22no—
129#11758187—22no—
130#11758187—22no—
131#11758187—21no—
132#11758187—21no—
133#11758187C2×D414yes—
134C23×C61—21no—
135C23×C61#13111yescharacteristic
136C22×D61—21no—
137Q8×C61—21no—
138Q8×C61C22×C812yes—
139D4×C61—22no—
140D4×C61—22no—
141D4×C61—21no—
142D4×C61C22×C812yes—
143C2×C4×C61—21no—
144C2×C4×C61—22no—
145C2×C4×C61—22no—
146C2×C4×C61—22no—
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61C4×D411yescharacteristic
149C2×C4×C61C22×C811yescharacteristic
150C2×C4×C61C22×C811yescharacteristic
151C2×C4×C61#13111yescharacteristic
152C2×C4×C61C23×C411yescharacteristic
153C22⋊D61—22no—
154C22⋊D61—22no—
155C2×Dic61—21no—
156D244—21no—
157D244C22×C812yes—
158C4×D61—22no—
159C4×D61—22no—
160Dic122—21no—
161Dic122C22×C812yes—
162C8×C61—22no—
163#92418—22no—
164#92418C4×D411yescharacteristic
165#92418C4×D411yescharacteristic
166#92418C22×C814yes—
167#92418C22×D411yescharacteristic
168#92418C2×#4111yescharacteristic
169#33442—611nomaximal, Sylow
170C22×C61—22no—
171C22×C61—41no—
172C22×C61—81no—
173C22×C61C8×D411yescharacteristic
174C22×C61C8×D411yescharacteristic
175C22×C61C2×#13111yescharacteristic
176C2×D61—22no—
177C2×D61—81no—
178C4×C61—22no—
179C4×C61—42no—
180C4×C61C8×D411yescharacteristic
181C4×C61C8×D411yescharacteristic
182C4×C61C2×C4×D411yescharacteristic
183C4×C61C23×C811yescharacteristic
184Dic61—22no—
185#3407—611no—
186#3407—611no—
187#2955—611no—
188#2171—614no—
189#2170—614no—
190#2153—611no—
191C2×#350—611no—
192C2×#350—611no—
193#2108—611no—
194C2×C61—21no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—42no—
198C2×C61C2×C8×D411yescharacteristic
199D61—42no—
200#575—611no—
201C2×#131—611no—
202C2×#131—611no—
203#504—614no—
204#504—614no—
205#504—1222no—
206#504—1222no—
207C2×M32—611no—
208C2×M32—611no—
209C2×M32—611no—
210C2×M32—1222no—
211C2×M32—1222no—
212C22×C16—611no—
213#444—614no—
214#443—614no—
215#430—611no—
216#421—611no—
217#421#692311yescharacteristic
218#405—611no—
219#364—614no—
220#350—612no—
221#350—612no—
222#350—612no—
223#350—612no—
224#346—612no—
225C4×C16—612no—
226C61#3344211yescharacteristic, complemented, Sylow
227C2×#41—611no—
228C2×#41C2×#692311yescharacteristic
229#137—612no—
230#137—612no—
231AGL(1,ℤ/8)—612no—
232AGL(1,ℤ/8)—612no—
233#135—614no—
234#131—612no—
235#131—612no—
236#131—612no—
237#131—612no—
238#131—1221no—
239#131—1221no—
240#131—1221no—
241#131—1221no—
242C2×M16—611no—
243C2×M16—611no—
244C2×M16—1221no—
245C2×M16—1221no—
246C2×M16C2×#692311yescharacteristic
247C22×C8—611no—
248C22×C8—1221no—
249C22×C8—1221no—
250#117C2×#692311yescharacteristic
251M32—612no—
252M32—612no—
253M32—612no—
254M32—612no—
255M32—1224no—
256M32—1224no—
257M32—1221no—
258M32—1221no—
259C2×C16—612no—
260C2×C16—611no—
261C2×C16—611no—
262C2×C16—1224no—
263C2×C16—1224no—
264C2×C16—1221no—
265C2×C16—1221no—
266C2×C16—1221no—
267C2×C16—1221no—
268#108—614no—
269#104—614no—
270#104C2×#692314yes—
271#97—612no—
272C4×C8—612no—
273#41—21no—
274#41—21no—
275#41—612no—
276#41—612no—
277#41—1221no—
278#41—1221no—
279#41D61⋊C812yes—
280#41C22×#692312yes—
281C2×Q8—611no—
282C2×Q8D61⋊C811yescharacteristic
283C2×D4—21no—
284C2×D4—611no—
285C2×D4—1221no—
286C2×D4D61⋊C811yescharacteristic
287C22×C4—21no—
288C22×C4—1221no—
289C22×C4C22×#692311yescharacteristic
290Q16—614no—
291SD16—614no—
292SD16—614no—
293D8—614no—
294M16—21no—
295M16—612no—
296M16—612no—
297M16—612no—
298M16—1222no—
299M16—1222no—
300M16—1222no—
301M16—1222no—
302M16—1221no—
303M16C22×#692312yes—
304C2×C8—21no—
305C2×C8—611no—
306C2×C8—611no—
307C2×C8—611no—
308C2×C8—611no—
309C2×C8—611no—
310C2×C8—612no—
311C2×C8—611no—
312C2×C8—1222no—
313C2×C8—1222no—
314C2×C8—1222no—
315C2×C8—1222no—
316C2×C8—1221no—
317C4⋊C4—21no—
318C22⋊C4—21no—
319C42C22×#692312yes—
320C16—614no—
321C16—1221no—
322C16—1221no—
323C16—1222no—
324C16—1222no—
325C23—21no—
326C23—1221no—
327C23#1451986411yescharacteristic
328Q8—21no—
329Q8—612no—
330Q8—1221no—
331Q8C2×D61⋊C812yes—
332D4—22no—
333D4—22no—
334D4—21no—
335D4—612no—
336D4—1222no—
337D4—1222no—
338D4—1221no—
339D4C2×D61⋊C812yes—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—1221no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4D4×#692311yescharacteristic
348C2×C4D4×#692311yescharacteristic
349C2×C4C2×D61⋊C811yescharacteristic
350C2×C4C2×D61⋊C811yescharacteristic
351C2×C4#1451986411yescharacteristic
352C2×C4C23×#692311yescharacteristic
353C8—22no—
354C8—611no—
355C8—611no—
356C8—611no—
357C8—611no—
358C8—614no—
359C8—1222no—
360C22—22no—
361C22—41no—
362C22—81no—
363C22—1222no—
364C22—4881no—
365C22#1684078911yescharacteristic
366C22#1684078911yescharacteristic
367C22C2×#1451986411yescharacteristic
368C4—22no—
369C4—42no—
370C4—1222no—
371C4#1684078911yescharacteristic
372C4#1684078911yescharacteristic
373C4C2×D4×#692311yescharacteristic
374C4C22×D61⋊C811yescharacteristic
375C2—21no—
376C2—21no—
377C2—21no—
378C2—42no—
379C2—2442no—
380C2C2×#1684078911yescharacteristic
subgroupG/H
centerC4C2×D4×#6923
commutatorC4×C61C23×C8
FrattiniC2×C4C23×#6923
FittingC61×#421C4
socleC2×C61C2×C8×D4
prime radical#16840560C4
cosocleC2×#92418C24
hypercenter#421#6923
hypocenterC61#33442
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #21462788C2semidirect
2. #21462786C2semidirect
3. #21462210C2semidirect
4. #21462207C2semidirect
5. #21462162C2semidirect
6. C2×#16840661C2semidirect
7. C2×#16840660C2semidirect
8. #21462028C2semidirect
11. #16840821C22semidirect
13. #16840820C22semidirect
20. #16840685C22semidirect
21. #16840661C22semidirect
22. #16840661C22semidirect
23. #16840660C22semidirect
24. #16840660C22semidirect
25. #16840650C22semidirect
26. C4×#11758187C22semidirect
226. C61#33442semidirect

Maximal subgroups

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

subgroupindex
#214627882
#214627862
#214622102
#214622072
#214621622
C2×#168406612
C2×#168406602
#214620282
#214547182
#3344261