Finite Group Databasebeta

← #29595213

Subgroups — #29595213

Order 15616.

452 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454535C211yesmaximal, characteristic
2#21447502C211yesmaximal, characteristic
3#21447482C211yesmaximal, characteristic
4#21445619C211yesmaximal, characteristic, complemented
5#21443949C211yesmaximal, characteristic, complemented
6#21443947C211yesmaximal, characteristic, complemented
7C61×#1757C211yesmaximal, characteristic, complemented
8C2×#14519783C411yescharacteristic, complemented
9#16840308C2211yescharacteristic
10#16839833—21no—
11#16839833—21no—
12#16839831—21no—
13#16839831—21no—
14#16839785C411yescharacteristic, complemented
15#16839746C2211yescharacteristic
16#16839736C2211yescharacteristic
17#16839730C411yescharacteristic, complemented
18#16839729C2211yescharacteristic
19#16839717—21no—
20C2×#14519687C411yescharacteristic, complemented
21#16839560C412yescomplemented
22#16839558C412yescomplemented
23#16839556C412yes—
24#16839554C412yes—
25#16839533—21no—
26C2×#131×C61C2211yescharacteristic
27C61×#413C2211yescharacteristic
28C61×#410C2211yescharacteristic
29C61×#405—21no—
30C61×#344—21no—
31C2×#11758222C2×C411yescharacteristic
32#14519783—41no—
33#14519783—41no—
34C2×#11758194—21no—
35C2×#11758194C2×C411yescharacteristic
36C2×#11758189—21no—
37C22×#92418C2×C411yescharacteristic
38C2×C8×D61—21no—
39#14519775C2×C411yescharacteristic
40#14519773C2×C411yescharacteristic
41#14519766C2×C411yescharacteristic
42#14519764C2×C411yescharacteristic
43#14519749—21no—
44#14519749—21no—
45C4×C22⋊D61—21no—
46C4×C22⋊D61—21no—
47#14519736—21no—
48C2×C4×Dic61C2×C411yescharacteristic
49#14519706—21no—
50#14519706—21no—
51#14519696C2×C412yes—
52#14519694—21no—
53#14519692—21no—
54#14519692C2×C412yes—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57#14519689—21no—
58#14519689—21no—
59#14519687—21no—
60#14519687—21no—
61#14519687—41no—
62C8×Dic61—41no—
63C2×#41×C61C2311yescharacteristic
64#131×C61—41no—
65#131×C61—41no—
66C2×M16×C61—21no—
67C2×M16×C61C2×C411yescharacteristic
68C2×M16×C61D411yescharacteristic
69C2×M16×C61D411yescharacteristic
70C22×C8×C61C2×C411yescharacteristic
71C22×C8×C61D411yescharacteristic
72C22×C8×C61D411yescharacteristic
73#117×C61—21no—
74#101×C61C2×C412yes—
75#100×C61—21no—
76#99×C61—21no—
77#99×C61C2×C412yes—
78#97×C61—41no—
79C4×C8×C61—41no—
80#41×C61—41no—
81#41×C61—41no—
82C2×Q8×C61C22×C411yescharacteristic
83C2×D4×C61C22×C411yescharacteristic
84C2×D4×C61#4111yescharacteristic
85C2×D4×C61#4111yescharacteristic
86C22×C4×C61C22×C411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C2×C22⋊D61—21no—
90C2×C22⋊D61—21no—
91C2×C22⋊D61—21no—
92C22×Dic61—21no—
93#11758222—41no—
94#11758222—41no—
95C2×D244C4211yescharacteristic
96C2×C4×D61—21no—
97C2×Dic122C4211yescharacteristic
98M16×C61—22no—
99M16×C61—41no—
100M16×C61—41no—
101M16×C61—41no—
102M16×C61—41no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—21no—
109C2×C8×C61—41no—
110C2×C8×C61C22⋊C411yescharacteristic
111C2×C8×C61C22⋊C411yescharacteristic
112C2×C8×C61C22⋊C411yescharacteristic
113C2×C8×C61C22⋊C411yescharacteristic
114C4⋊C4×C61—41no—
115C22⋊C4×C61—22no—
116C42×C61—41no—
117C22⋊Dic61—21no—
118C22⋊Dic61—21no—
119C22⋊Dic61—22no—
120#11758198—21no—
121#11758198—21no—
122C4⋊Dic61—41no—
123#11758196—21no—
124#11758196—21no—
125C4×Dic61—21no—
126C4×Dic61—41no—
127C4×Dic61C4211yescharacteristic
128C4×Dic61C4211yescharacteristic
129#11758194—22no—
130#11758194—41no—
131#11758194—41no—
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418—41no—
135C2×#92418—41no—
136#11758189—41no—
137#11758189—41no—
138C8×D61—42no—
139C23×C61#11711yescharacteristic
140C23×C61C4×D411yescharacteristic
141C23×C61C4×D411yescharacteristic
142C22×D61—21no—
143Q8×C61—41no—
144D4×C61—41no—
145D4×C61—41no—
146D4×C61—41no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—42no—
154C2×C4×C61C2×C4211yescharacteristic
155C2×C4×C61C2×C22⋊C411yescharacteristic
156C2×C4×C61C4×D411yescharacteristic
157C2×C4×C61C4×D411yescharacteristic
158C22⋊D61—42no—
159C22⋊D61—81no—
160C22⋊D61—81no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—42no—
165C2×Dic61—81no—
166D244—41no—
167C4×D61—41no—
168C4×D61—41no—
169Dic122—41no—
170C8×C61—21no—
171C8×C61—21no—
172C8×C61—21no—
173C8×C61—42no—
174C8×C61#9911yescharacteristic
175C8×C61#9911yescharacteristic
176#92418—42no—
177#92418—41no—
178#92418—41no—
179#12634—611nomaximal, Sylow
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61C4×C22⋊C411yescharacteristic
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—82no—
194C4×C61C2×#9911yescharacteristic
195C4×C61#41011yescharacteristic
196Dic61—41no—
197Dic61—41no—
198Dic61—41no—
199Dic61—82no—
200#2932—611no—
201#2132—611no—
202#2126—611no—
203#1757—611no—
204#1757D6111yescharacteristic, complemented
205#1395—611no—
206#1395—611no—
207C2×C61—21no—
208C2×C61—41no—
209C2×C61—41no—
210C2×C61—41no—
211C2×C61C4×#9911yescharacteristic
212D61—81no—
213C2×#131—611no—
214C2×#131C2×D6111yescharacteristic
215#532—611no—
216#435—1221no—
217#435—1221no—
218#435—1221no—
219#435—1221no—
220#423—611no—
221#413—611no—
222#413C2×D6111yescharacteristic
223#410—611no—
224#410C2×D6111yescharacteristic
225#408—611no—
226#408—611no—
227#405—21no—
228#405—1221no—
229C2×#97—611no—
230#356—612no—
231#355—612no—
232#354—612no—
233#353—612no—
234#344—21no—
235#344—1221no—
236C61#1263411yescharacteristic, complemented, Sylow
237C2×#41—611no—
238C2×#41C22×D6111yescharacteristic
239#131—41no—
240#131—41no—
241#131—2441no—
242#131—2441no—
243C2×M16—21no—
244C2×M16—611no—
245C2×M16—1221no—
246C2×M16—1221no—
247C2×M16C4×D6111yescharacteristic
248C2×M16D24411yescharacteristic
249C2×M16C22⋊D6111yescharacteristic
250C22×C8—611no—
251C22×C8—1221no—
252C22×C8C4×D6111yescharacteristic
253C22×C8D24411yescharacteristic
254C22×C8C22⋊D6111yescharacteristic
255C4⋊Q8—611no—
256#127—611no—
257#124—611no—
258#124—611no—
259#121—1221no—
260#121—1221no—
261C4×D4—1221no—
262C4×D4—1221no—
263#117—21no—
264#117—1221no—
265C2×C42—611no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268#101—612no—
269#101C4×D6112yes—
270#100—21no—
271#100—1221no—
272#99—21no—
273#99—612no—
274#99—1221no—
275#99C4×D6112yes—
276C22⋊C8—1221no—
277C22⋊C8—1221no—
278C22⋊C8—1221no—
279C22⋊C8—1221no—
280#97—41no—
281#97—1221no—
282#97—1221no—
283#97—2441no—
284C4×C8—41no—
285C4×C8—2441no—
286#41—41no—
287#41—41no—
288#41—2441no—
289#41—2441no—
290C2×Q8—611no—
291C2×Q8C2×C4×D6111yescharacteristic
292C2×D4—611no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4C2×C4×D6111yescharacteristic
297C2×D4#1175822211yescharacteristic
298C2×D4#1175822211yescharacteristic
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4C2×C4×D6111yescharacteristic
302C22×C4C2×D24411yescharacteristic
303C22×C4C2×C22⋊D6111yescharacteristic
304M16—22no—
305M16—41no—
306M16—41no—
307M16—41no—
308M16—41no—
309M16—1222no—
310M16—2441no—
311M16—2441no—
312M16—2441no—
313M16—2441no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—41no—
321C2×C8—1221no—
322C2×C8—1221no—
323C2×C8—2442no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8#1175819811yescharacteristic
327C2×C8#1175819811yescharacteristic
328C2×C8#1175819811yescharacteristic
329C2×C8#1175819811yescharacteristic
330C4⋊C4—41no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4—2441no—
334C22⋊C4—22no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1222no—
340C42—41no—
341C42—611no—
342C42—611no—
343C42—1221no—
344C42—2441no—
345C23—1221no—
346C23#1451973411yescharacteristic
347C23C4×C22⋊D6111yescharacteristic
348C23C4×D24411yescharacteristic
349Q8—41no—
350Q8—2441no—
351D4—41no—
352D4—41no—
353D4—41no—
354D4—4881no—
355D4—4881no—
356D4—2441no—
357D4—2442no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—4881no—
369C2×C4—2442no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4C42×D6111yescharacteristic
373C2×C4C2×#1175819811yescharacteristic
374C2×C4C4×C22⋊D6111yescharacteristic
375C2×C4C4×D24411yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8—42no—
380C8—2442no—
381C8—2441no—
382C8—2441no—
383C8#1451969111yescharacteristic
384C8#1451969111yescharacteristic
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22C4×#1175819811yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—82no—
399C4—4882no—
400C4—2441no—
401C4—2441no—
402C4—2441no—
403C4C2×#1451969111yescharacteristic
404C4#1683973511yescharacteristic
405C2—21no—
406C2—41no—
407C2—41no—
408C2—41no—
409C2—4881no—
410C2C4×#1451969111yescharacteristic
subgroupG/H
centerC4C2×#14519691
commutatorC2×C4×C61C2×C42
FrattiniC2×#41C22×D61
FittingC61×#1757C2
socleC2×C61C4×#99
prime radical#16840308C22
cosocleC2×#41×C61C23
hypercenter#1757D61
hypocenterC61#12634
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
4. #21445619C2semidirect
5. #21443949C2semidirect
6. #21443947C2semidirect
7. C61×#1757C2semidirect
8. C2×#14519783C4semidirect
14. #16839785C4semidirect
17. #16839730C4semidirect
20. C2×#14519687C4semidirect
21. #16839560C4semidirect
22. #16839558C4semidirect
204. #1757D61semidirect
236. C61#12634semidirect

Maximal subgroups

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

subgroupindex
#214545352
#214475022
#214474822
#214456192
#214439492
#214439472
C61×#17572
#1263461