Finite Group Databasebeta

← #30615343

Subgroups — #30615343

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461750C212yesmaximal, complemented
2#21461739C212yesmaximal, complemented
3#21461728C212yesmaximal
4#21461703C211yesmaximal, characteristic
5#21461701C211yesmaximal, characteristic
6#21461625C212yesmaximal, complemented
7#21461574C212yesmaximal
8#21461541C212yesmaximal, complemented
9#21454244C211yesmaximal, characteristic
10D61⋊#108C2212yes—
11#16840772C2212yes—
12#16840748C2212yes—
13#16840741C2212yes—
14#16840725C2214yes—
15#16840644C2214yes—
16#16840633C2214yes—
17#16840631C2212yes—
18#16840630C2212yes—
19#16840629C2214yes—
20C2×#14519783C2211yescharacteristic
21C2×#14519783C2211yescharacteristic
22C4×#11758222C2211yescharacteristic
23#16839719C411yescharacteristic, complemented
24#16839719C411yescharacteristic, complemented
25#16839719C2211yescharacteristic
26#16839719C2211yescharacteristic
27#16839717C411yescharacteristic, complemented
28#16839717C411yescharacteristic, complemented
29C4×#11758194C411yescharacteristic, complemented
30#16839714C411yescharacteristic, complemented
31#16839714C2211yescharacteristic
32#97×D61C411yescharacteristic, complemented
33#97×D61C2211yescharacteristic
34C2×#97×C61C411yescharacteristic, complemented
35D61⋊M16C2314yes—
36#14519856C2314yes—
37#14519848—22no—
38#14519847—22no—
39#14519846—22no—
40#14519845—22no—
41#14519838—22no—
42#14519837—22no—
43#14519836—22no—
44#14519835—22no—
45#14519831—24no—
46C8×#6923—24no—
47C2×#11758222C2311yescharacteristic
48#14519783—24no—
49#14519783—22no—
50#14519783—22no—
51C2×#11758194C2×C411yescharacteristic
52C2×#11758194C2×C411yescharacteristic
53C2×#11758189C2×C411yescharacteristic
54C2×#11758189C2×C411yescharacteristic
55C2×#11758189C2311yescharacteristic
56C2×#11758189C2311yescharacteristic
57C2×C8×D61C2×C411yescharacteristic
58C2×C8×D61C2×C411yescharacteristic
59C2×C8×D61C2311yescharacteristic
60C2×C8×D61C2311yescharacteristic
61C4×Dic122—21no—
62C4×D244—21no—
63C4×C22⋊D61—21no—
64C4×C22⋊D61—21no—
65#14519736C2×C411yescharacteristic
66#14519734C2×C411yescharacteristic
67#14519734C2311yescharacteristic
68C42×D61C2×C411yescharacteristic
69C42×D61C2311yescharacteristic
70#14519688C2×C411yescharacteristic
71#14519688C2×C411yescharacteristic
72#14519687C2×C411yescharacteristic
73#14519687C2×C411yescharacteristic
74#14519687C2×C411yescharacteristic
75#14519687C2×C411yescharacteristic
76C4×#92418C2×C411yescharacteristic
77C4×#92418C2×C411yescharacteristic
78C8×Dic61C2×C411yescharacteristic
79C8×Dic61C2×C411yescharacteristic
80C8×Dic61C2×C411yescharacteristic
81C8×Dic61C2×C411yescharacteristic
82C22×C8×C61C2×C411yescharacteristic
83C22×C8×C61C2×C411yescharacteristic
84C2×C42×C61C2×C411yescharacteristic
85#97×C61C2×C411yescharacteristic
86#97×C61C2×C411yescharacteristic
87#97×C61C2×C411yescharacteristic
88#97×C61C2×C411yescharacteristic
89C22×C4×C61—21no—
90C22×C4×C61C22×C411yescharacteristic
91C2×C22⋊D61#4111yescharacteristic
92C2×C22⋊D61#4111yescharacteristic
93#11758222—22no—
94#11758222—22no—
95C2×D244#4111yescharacteristic
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61C22×C411yescharacteristic
99C2×C4×D61C2411yescharacteristic
100C2×Dic122#4111yescharacteristic
101C22⋊#6923—24no—
102#11758217—24no—
103C4⋊#6923—24no—
104C4×#6923—24no—
105#11758213—24no—
106D61⋊C8—24no—
107C2×C8×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61—22no—
110C2×C8×C61C22×C411yescharacteristic
111C2×C8×C61C22×C411yescharacteristic
112C2×C8×C61C22×C411yescharacteristic
113C2×C8×C61C22×C411yescharacteristic
114C42×C61—21no—
115C42×C61C22×C411yescharacteristic
116C42×C61C22×C411yescharacteristic
117C22⋊Dic61—21no—
118#11758198—21no—
119#11758198—21no—
120C4⋊Dic61—21no—
121#11758196—21no—
122#11758196—21no—
123C4×Dic61—21no—
124C4×Dic61—21no—
125C4×Dic61C22×C411yescharacteristic
126C4×Dic61C22×C411yescharacteristic
127#11758194—22no—
128#11758194—22no—
129C2×#92418C22×C411yescharacteristic
130C2×#92418C22×C411yescharacteristic
131C2×#92418C22×C411yescharacteristic
132C2×#92418C22×C411yescharacteristic
133#11758189—22no—
134#11758189—22no—
135#11758189—22no—
136#11758189—22no—
137C8×D61—21no—
138C8×D61—21no—
139C8×D61—22no—
140C8×D61#4114yes—
141C8×D61#4112yes—
142C8×D61#4112yes—
143C23×C61#11711yescharacteristic
144C22×D61#11711yescharacteristic
145C22×D61C2×#4111yescharacteristic
146C2×#6923—44no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—81no—
152C2×C4×C61#11711yescharacteristic
153C2×C4×C61C23×C411yescharacteristic
154C22⋊D61—22no—
155C22⋊D61—22no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61#11711yescharacteristic
159C2×Dic61C2×#4111yescharacteristic
160D244—22no—
161C4×D61—21no—
162C4×D61—21no—
163C4×D61—81no—
164C4×D61—81no—
165C4×D61C2×#4112yes—
166C4×D61C2×#4112yes—
167Dic122—22no—
168#92420—44no—
169C8×C61—21no—
170C8×C61—21no—
171C8×C61#11711yescharacteristic
172C8×C61#11711yescharacteristic
173C8×C61#11712yes—
174#92418—21no—
175#92418—21no—
176#92418#11712yes—
177#92418#11712yes—
178#20788—611nomaximal, Sylow
179C22×C61—21no—
180C22×C61—41no—
181C22×C61C2×#11711yescharacteristic
182C2×D61—21no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61#52912yes—
186#6923—84no—
187C4×C61—21no—
188C4×C61—41no—
189C4×C61—41no—
190C4×C61C2×#11711yescharacteristic
191C4×C61C2×#11711yescharacteristic
192Dic61—21no—
193Dic61—41no—
194Dic61—41no—
195Dic61#52912yes—
196#2875—611no—
197#1841—612no—
198#1833—612no—
199#1827—612no—
200#1813—611no—
201#1812—611no—
202#1773—612no—
203#1757—612no—
204#1747—612no—
205C2×C61—21no—
206C2×C61—41no—
207C2×C61#228311yescharacteristic
208D61—22no—
209D61—41no—
210C2×#131—611no—
211C2×#131—611no—
212C4×#41—611no—
213C2×#108—612no—
214#427—612no—
215#413—612no—
216#410—612no—
217#405—611no—
218#405—611no—
219#405—611no—
220#405—611no—
221#405—611no—
222#405—611no—
223#405—614no—
224C4×M16—611no—
225C4×M16—611no—
226C4×M16—611no—
227C2×#97—611no—
228C2×#97—611no—
229C2×#97#692311yescharacteristic, complemented
230#344—614no—
231#339—614no—
232#338—612no—
233H(3,ℤ/4)—612no—
234H(3,ℤ/4)—614no—
235C61#2078811yescharacteristic, complemented, Sylow
236C2×#41—611no—
237#131—1224no—
238#131—1222no—
239#131—1222no—
240C2×M16—611no—
241C2×M16—611no—
242C2×M16—611no—
243C2×M16—611no—
244C2×M16—611no—
245C2×M16—611no—
246C2×M16—614no—
247C22×C8—611no—
248C22×C8—611no—
249C22×C8—611no—
250C22×C8—611no—
251C22×C8C2×#692311yescharacteristic
252C22×C8C2×#692311yescharacteristic
253C4×Q8—1221no—
254C4×D4—1221no—
255C4×D4—1221no—
256C4×D4—1221no—
257#117—611no—
258#117—611no—
259#117—611no—
260#117—614no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42C2×#692311yescharacteristic
264#108—1222no—
265#108—1222no—
266#107—1222no—
267#106—1222no—
268#101—1222no—
269#100—1222no—
270#99—1222no—
271#99—1222no—
272#97—611no—
273#97—611no—
274#97—611no—
275#97—611no—
276#97—611no—
277#97—611no—
278#97—1224no—
279#97C2×#692311yescharacteristic
280#97C2×#692311yescharacteristic
281#97C2×#692311yescharacteristic
282#97C2×#692311yescharacteristic
283C4×C8—611no—
284C4×C8—611no—
285C4×C8—611no—
286C4×C8—611no—
287C4×C8—611no—
288C4×C8—611no—
289C4×C8—1224no—
290#41—1222no—
291#41—1222no—
292C2×Q8—611no—
293C2×D4—611no—
294C2×D4—611no—
295C2×D4—611no—
296C22×C4—21no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4C22×#692311yescharacteristic
302M16—1222no—
303M16—1222no—
304M16—1222no—
305M16—1222no—
306M16—1222no—
307M16—1222no—
308M16—1224no—
309M16—1224no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—611no—
314C2×C8—611no—
315C2×C8—614no—
316C2×C8—612no—
317C2×C8—612no—
318C2×C8—611no—
319C2×C8—611no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—1222no—
323C2×C8—1224no—
324C2×C8C22×#692311yescharacteristic
325C2×C8C22×#692311yescharacteristic
326C2×C8C22×#692311yescharacteristic
327C2×C8C22×#692311yescharacteristic
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1224no—
331C4⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1224no—
336C42—21no—
337C42—611no—
338C42—611no—
339C42—1221no—
340C42—1221no—
341C42—1224no—
342C42C22×#692311yescharacteristic
343C42C22×#692311yescharacteristic
344C23—611no—
345C23—611no—
346C23#1451985611yescharacteristic
347Q8—1222no—
348D4—1222no—
349D4—1222no—
350D4—1222no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—81no—
356C2×C4—611no—
357C2×C4—612no—
358C2×C4—612no—
359C2×C4—611no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—4881no—
365C2×C4—4881no—
366C2×C4—2444no—
367C2×C4#1451985611yescharacteristic
368C2×C4C23×#692311yescharacteristic
369C8—21no—
370C8—21no—
371C8—612no—
372C8—612no—
373C8—1221no—
374C8—1221no—
375C8—2444no—
376C8#1451985611yescharacteristic
377C8#1451985611yescharacteristic
378C8#1451985612yes—
379C22—21no—
380C22—41no—
381C22—612no—
382C22—1221no—
383C22—2441no—
384C22—2441no—
385C22C2×#1451985611yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—612no—
390C4—1221no—
391C4—4884no—
392C4—2441no—
393C4—2441no—
394C4C2×#1451985611yescharacteristic
395C4C2×#1451985611yescharacteristic
396C2—21no—
397C2—41no—
398C2—1222no—
399C2—2441no—
400C2#2146226611yescharacteristic
subgroupG/H
centerC4C2×#14519856
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#97×C61C4
socleC2×C61#2283
prime radicalC2×#11758222C23
cosocleC2×C4×D61C24
hypercenterC2×#97#6923
hypocenterC61#20788
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ #97 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. #21461750C2semidirect
2. #21461739C2semidirect
6. #21461625C2semidirect
8. #21461541C2semidirect
23. #16839719C4semidirect
24. #16839719C4semidirect
27. #16839717C4semidirect
28. #16839717C4semidirect
29. C4×#11758194C4semidirect
30. #16839714C4semidirect
32. #97×D61C4semidirect
34. C2×#97×C61C4semidirect
229. C2×#97#6923semidirect
235. C61#20788semidirect

Maximal subgroups

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

subgroupindex
#214617502
#214617392
#214617282
#214617032
#214617012
#214616252
#214615742
#214615412
#214542442
#2078861