Finite Group Databasebeta

← #29595167

Subgroups — #29595167

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454511C211yesmaximal, characteristic
2#21447461C211yesmaximal, characteristic
3#21447458C211yesmaximal, characteristic
4#21445619C211yesmaximal, characteristic, complemented
5#21443941C211yesmaximal, characteristic, complemented
6#21443939C211yesmaximal, characteristic, complemented
7C61×#1757C211yesmaximal, characteristic, complemented
8C22×C8×D61C411yescharacteristic, complemented
9#16840269C2211yescharacteristic
10#16839831—21no—
11#16839831—21no—
12C8×C22⋊D61—21no—
13C8×C22⋊D61—21no—
14#16839790C411yescharacteristic, complemented
15#16839746C2211yescharacteristic
16#16839736C2211yescharacteristic
17#16839729C2211yescharacteristic
18#16839725C411yescharacteristic, complemented
19#16839717—21no—
20#16839717C411yescharacteristic, complemented
21#16839553C412yescomplemented
22#16839551C412yescomplemented
23#16839550C412yescomplemented
24#16839548C412yescomplemented
25#16839533—21no—
26C2×#131×C61C2211yescharacteristic
27C61×#413C2211yescharacteristic
28C61×#410C2211yescharacteristic
29C61×#405—21no—
30C61×#344—21no—
31C22×C4×D61C2×C411yescharacteristic
32C2×#11758194—21no—
33C2×#11758194C2×C411yescharacteristic
34C22×#92418C2×C411yescharacteristic
35C2×C8×D61—21no—
36C2×C8×D61—21no—
37C2×C8×D61—41no—
38C2×C8×D61—41no—
39#14519758C2×C411yescharacteristic
40#14519758C2×C411yescharacteristic
41#14519753—21no—
42#14519748—21no—
43#14519745C2×C411yescharacteristic
44#14519745C2×C411yescharacteristic
45C4×C22⋊D61—21no—
46C4×C22⋊D61—21no—
47#14519736—21no—
48#14519736C2×C411yescharacteristic
49#14519706—21no—
50#14519706—21no—
51#14519696—21no—
52#14519694C2×C412yes—
53#14519692—21no—
54#14519692C2×C412yes—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57#14519689—21no—
58#14519689—21no—
59#14519687—21no—
60#14519687—41no—
61C8×Dic61—21no—
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×C61—21no—
75#100×C61C2×C412yes—
76#99×C61—21no—
77#99×C61C2×C412yes—
78#97×C61—41no—
79C4×C8×C61—41no—
80C23×D61C4211yescharacteristic
81#41×C61—41no—
82#41×C61—41no—
83C2×Q8×C61#4111yescharacteristic
84C2×D4×C61C22×C411yescharacteristic
85C2×D4×C61C22×C411yescharacteristic
86C2×D4×C61#4111yescharacteristic
87C22×C4×C61C22×C411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C2×C22⋊D61—21no—
91C2×C22⋊D61—21no—
92C22×Dic61C4211yescharacteristic
93C2×C4×D61—21no—
94C2×C4×D61—21no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97M16×C61—22no—
98M16×C61—41no—
99M16×C61—41no—
100M16×C61—41no—
101M16×C61—41no—
102C2×C8×C61—21no—
103C2×C8×C61—21no—
104C2×C8×C61—21no—
105C2×C8×C61—21no—
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—41no—
109C2×C8×C61C22⋊C411yescharacteristic
110C2×C8×C61C22⋊C411yescharacteristic
111C2×C8×C61C22⋊C411yescharacteristic
112C2×C8×C61C22⋊C411yescharacteristic
113C4⋊C4×C61—41no—
114C22⋊C4×C61—22no—
115C42×C61—41no—
116C22⋊Dic61—21no—
117C22⋊Dic61—21no—
118C22⋊Dic61—22no—
119C22⋊Dic61C4211yescharacteristic
120C22⋊Dic61C4211yescharacteristic
121#11758198—21no—
122#11758198—21no—
123C4⋊Dic61—21no—
124C4⋊Dic61—41no—
125#11758196—21no—
126#11758196—21no—
127C4×Dic61—21no—
128C4×Dic61—41no—
129#11758194—22no—
130#11758194—41no—
131#11758194—41no—
132C2×#92418—21no—
133C2×#92418—21no—
134C2×#92418—41no—
135C2×#92418—41no—
136C8×D61—42no—
137C8×D61—41no—
138C8×D61—41no—
139C23×C61C2×C4211yescharacteristic
140C23×C61C4×D411yescharacteristic
141C23×C61C4×D411yescharacteristic
142C22×D61—21no—
143C22×D61—42no—
144C22×D61—41no—
145Q8×C61—41no—
146D4×C61—41no—
147D4×C61—41no—
148D4×C61—41no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—42no—
156C2×C4×C61C2×C22⋊C411yescharacteristic
157C2×C4×C61#11711yescharacteristic
158C2×C4×C61C4×D411yescharacteristic
159C2×C4×C61C4×D411yescharacteristic
160C22⋊D61—42no—
161C22⋊D61—42no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—41no—
166C2×Dic61—42no—
167C4×D61—42no—
168C4×D61—41no—
169C4×D61—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#12623—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—22no—
188C2×D61—41no—
189C2×D61—42no—
190C2×D61—41no—
191C2×D61—42no—
192C4×C61—21no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—82no—
196C4×C61C2×#9911yescharacteristic
197C4×C61#41011yescharacteristic
198Dic61—41no—
199Dic61—41no—
200Dic61—41no—
201Dic61—82no—
202#2929—611no—
203#2120—611no—
204#2120—611no—
205#1757—611no—
206#1757D6111yescharacteristic, complemented
207#1392—611no—
208#1391—611no—
209C2×C61—21no—
210C2×C61—41no—
211C2×C61—41no—
212C2×C61—41no—
213C2×C61C4×#9911yescharacteristic
214D61—42no—
215C2×#131C2×D6111yescharacteristic
216C23×C8—611no—
217#525—611no—
218#435—1221no—
219#435—1221no—
220C8×D4—1221no—
221C8×D4—1221no—
222#424—611no—
223#413—611no—
224#413C2×D6111yescharacteristic
225#410—611no—
226#410C2×D6111yescharacteristic
227#408—611no—
228#407—611no—
229#405—21no—
230#405—611no—
231#405—1221no—
232#352—612no—
233#352—612no—
234AΣL(1,𝔽16)—612no—
235AΣL(1,𝔽16)—612no—
236#344—21no—
237#344—1221no—
238C61#1262311yescharacteristic, complemented, Sylow
239C2×#41C22×D6111yescharacteristic
240C23×C4—611no—
241#131—41no—
242#131—41no—
243C2×M16—21no—
244C2×M16—611no—
245C2×M16—1221no—
246C2×M16C4×D6111yescharacteristic
247C2×M16D24411yescharacteristic
248C2×M16C22⋊D6111yescharacteristic
249C22×C8—611no—
250C22×C8—1221no—
251C22×C8—1221no—
252C22×C8—2441no—
253C22×C8—2441no—
254C22×C8C4×D6111yescharacteristic
255C22×C8D24411yescharacteristic
256C22×C8C22⋊D6111yescharacteristic
257#123—611no—
258#123—611no—
259C22⋊Q8—1221no—
260#121—1221no—
261#120—611no—
262#120—611no—
263C4×D4—1221no—
264C4×D4—1221no—
265#117—21no—
266#117—611no—
267#117—1221no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270#101—21no—
271#101—1221no—
272#100—612no—
273#100C4×D6112yes—
274#99—21no—
275#99—612no—
276#99—1221no—
277#99C4×D6112yes—
278C22⋊C8—1221no—
279C22⋊C8—1221no—
280C22⋊C8—1221no—
281C22⋊C8—1221no—
282#97—41no—
283#97—1221no—
284#97—2441no—
285C4×C8—41no—
286C4×C8—1221no—
287C4×C8—2441no—
288C24—611no—
289#41—41no—
290#41—41no—
291C2×Q8#1175822211yescharacteristic
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4C2×C4×D6111yescharacteristic
295C2×D4C2×C4×D6111yescharacteristic
296C2×D4#1175822211yescharacteristic
297C22×C4—611no—
298C22×C4—1221no—
299C22×C4—1221no—
300C22×C4—2441no—
301C22×C4—2441no—
302C22×C4C2×C4×D6111yescharacteristic
303C22×C4C2×D24411yescharacteristic
304C22×C4C2×C22⋊D6111yescharacteristic
305M16—22no—
306M16—41no—
307M16—41no—
308M16—41no—
309M16—41no—
310M16—1222no—
311M16—2441no—
312M16—2441no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—2442no—
323C2×C8—2441no—
324C2×C8—2441no—
325C2×C8—2441no—
326C2×C8—2441no—
327C2×C8#1175819811yescharacteristic
328C2×C8#1175819811yescharacteristic
329C2×C8#1175819811yescharacteristic
330C2×C8#1175819811yescharacteristic
331C4⋊C4—41no—
332C4⋊C4—1221no—
333C4⋊C4—1221no—
334C4⋊C4—1221no—
335C4⋊C4—2441no—
336C22⋊C4—22no—
337C22⋊C4—611no—
338C22⋊C4—611no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C22⋊C4—1221no—
343C22⋊C4—1222no—
344C42—41no—
345C42—1221no—
346C42—2441no—
347C23—1221no—
348C23—2441no—
349C23—2442no—
350C23C42×D6111yescharacteristic
351C23C4×C22⋊D6111yescharacteristic
352C23C4×D24411yescharacteristic
353Q8—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—2442no—
358D4—2442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—42no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4C2×#1175819811yescharacteristic
375C2×C4#1451973411yescharacteristic
376C2×C4C4×C22⋊D6111yescharacteristic
377C2×C4C4×D24411yescharacteristic
378C8—21no—
379C8—21no—
380C8—21no—
381C8—42no—
382C8—2442no—
383C8—2441no—
384C8—2441no—
385C8#1451969111yescharacteristic
386C8#1451969111yescharacteristic
387C22—21no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—1222no—
394C22—2441no—
395C22—2442no—
396C22—2442no—
397C22—2441no—
398C22C4×#1175819811yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—82no—
403C4—4882no—
404C4—2441no—
405C4—2441no—
406C4—2441no—
407C4C2×#1451969111yescharacteristic
408C4#1683973511yescharacteristic
409C2—21no—
410C2—41no—
411C2—41no—
412C2—41no—
413C2—2442no—
414C2C4×#1451969111yescharacteristic
subgroupG/H
centerC8#14519691
commutatorC23×C61C2×C42
FrattiniC2×#41C22×D61
FittingC61×#1757C2
socleC2×C61C4×#99
prime radical#16840269C22
cosocleC2×#41×C61C23
hypercenter#1757D61
hypocenterC61#12623
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C2×C8 ◁ C2×#131 ◁ #1757

Complements

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

NH ≅ G/Ntype
4. #21445619C2semidirect
5. #21443941C2semidirect
6. #21443939C2semidirect
7. C61×#1757C2semidirect
8. C22×C8×D61C4semidirect
14. #16839790C4semidirect
18. #16839725C4semidirect
20. #16839717C4semidirect
21. #16839553C4semidirect
22. #16839551C4semidirect
23. #16839550C4semidirect
24. #16839548C4semidirect
206. #1757D61semidirect
238. C61#12623semidirect

Maximal subgroups

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

subgroupindex
#214545112
#214474612
#214474582
#214456192
#214439412
#214439392
C61×#17572
#1262361