Finite Group Databasebeta

← #29576426

Subgroups — #29576426

Order 15616.

534 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839963C211yesmaximal, characteristic
2#21454770C211yesmaximal, characteristic, complemented
3#21446658C211yesmaximal, characteristic
4#21444488C211yesmaximal, characteristic
5#21444247C211yesmaximal, characteristic, complemented
6#21443669C211yesmaximal, characteristic, complemented
7C61×#1292C211yesmaximal, characteristic, complemented
8C22×#11758190C412yes—
9C2×#14519774C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16839963—21no—
12#16839963—21no—
13#16839963—21no—
14#16839963—21no—
15#16839891—22no—
16#16839889—21no—
17#16839886—21no—
18#16839815C2211yescharacteristic
19#16839785—21no—
20C2×#14519699C412yes—
21C2×#14519693—21no—
22C2×#14519693—21no—
23C4×#11758194C2211yescharacteristic
24M16×Dic61—21no—
25#16839505—22no—
26#16839492—21no—
27#16839492—21no—
28C61×#423C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C2×C4⋊C8×C61C2211yescharacteristic
31C22×Dic122C2×C411yescharacteristic
32C22×D244—21no—
33C22×D244—21no—
34C22×D244C2×C412yes—
35C2×#11758190—22no—
36C2×#11758190—22no—
37C2×#11758190—44no—
38C2×#11758194D411yescharacteristic
39C2×#11758194D411yescharacteristic
40#14519774—21no—
41#14519774—21no—
42#14519774—21no—
43#14519774—21no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×Dic122D411yescharacteristic
47C4×Dic122D411yescharacteristic
48C4×Dic122D411yescharacteristic
49C4×Dic122D411yescharacteristic
50C2×C4⋊Dic61C2×C411yescharacteristic
51C2×#11758196—21no—
52C2×C4×Dic61—21no—
53C4⋊#92418—21no—
54#14519706—22no—
55#14519706—22no—
56#14519699—22no—
57#14519699—22no—
58#14519693—42no—
59#14519693—42no—
60C22⋊#92418—21no—
61#14519688—21no—
62#14519687—22no—
63C4×#92418—21no—
64C4×#92418—21no—
65C8×Dic61—22no—
66C2×M16×C61—21no—
67C2×M16×C61—21no—
68C22×C8×C61C2×C412yes—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61—21no—
73C4⋊C8×C61—21no—
74C4⋊C8×C61—21no—
75C4⋊C8×C61D412yes—
76C23×D61—22no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61#4111yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—42no—
85C2×D244—42no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—82no—
95C2×Dic122—22no—
96C2×Dic122—21no—
97C2×Dic122—41no—
98C2×Dic122C22⋊C411yescharacteristic
99C2×Dic122C22⋊C411yescharacteristic
100M16×C61—41no—
101M16×C61—41no—
102M16×C61—41no—
103M16×C61—41no—
104C2×C8×C61—22no—
105C2×C8×C61—22no—
106C2×C8×C61—42no—
107C2×C8×C61—41no—
108C42×C61C2×D411yescharacteristic
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C4⋊Dic61—21no—
113C4⋊Dic61C22⋊C411yescharacteristic
114C4⋊Dic61C22⋊C411yescharacteristic
115#11758196—21no—
116#11758196—21no—
117#11758196—21no—
118#11758196—21no—
119C4×Dic61—21no—
120C4×Dic61—21no—
121C4×Dic61—21no—
122C4×Dic61—21no—
123#11758194—21no—
124#11758194—21no—
125#11758194—21no—
126#11758194SD1612yescomplemented
127C2×#92418—21no—
128C2×#92418—21no—
129C2×#92418—41no—
130#11758190—44no—
131#11758190—44no—
132C23×C61C4×D411yescharacteristic
133C22×D61—42no—
134C22×D61—42no—
135C22×D61—42no—
136C22×D61—82no—
137C22×D61—82no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—41no—
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12311yescharacteristic
147C2×C4×C61C2×SD1611yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61#13711yescharacteristic
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—42no—
156C2×Dic61—81no—
157D244—42no—
158D244—42no—
159D244—82no—
160D244—82no—
161D244—82no—
162D244—81no—
163D244—81no—
164D244—81no—
165D244—81no—
166Dic122—21no—
167Dic122—21no—
168Dic122—21no—
169Dic122—42no—
170Dic122#10012yescomplemented
171C8×C61—42no—
172C8×C61—42no—
173C8×C61—81no—
174#92418—22no—
175#92418—41no—
176#92418—81no—
177#9254—611nomaximal, Sylow
178C22×C61—21no—
179C22×C61—21no—
180C22×C61#38611yescharacteristic
181C22×C61C4×SD1611yescharacteristic
182C22×C61#44011yescharacteristic
183C2×D61—82no—
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—162no—
187C2×D61—162no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61C2×#10011yescharacteristic
192C4×C61#41311yescharacteristic
193C4×C61#44811yescharacteristic
194C4×C61#44911yescharacteristic
195C4×C61#46011yescharacteristic
196C4×C61#46411yescharacteristic
197Dic61—22no—
198Dic61—41no—
199Dic61—41no—
200Dic61—41no—
201C2×#460—611no—
202Q8×M16—611no—
203#1965—611no—
204#1545—611no—
205#1487—611no—
206#1292D6111yescharacteristic, complemented
207#1283—611no—
208C2×C61—21no—
209C2×C61—21no—
210C2×C61#188011yescharacteristic
211C2×C61#190011yescharacteristic
212C2×C61#190311yescharacteristic
213D61—162no—
214C22×SD16—612no—
215C2×#127—611no—
216C2×C4×Q8—611no—
217#460—1221no—
218#460—1221no—
219#460—1221no—
220#460—1221no—
221#446—1221no—
222#446—1222no—
223C8×Q8—1221no—
224#431—611no—
225#423—1221no—
226#423C2×D6111yescharacteristic
227#423C2×D6111yescharacteristic
228C2×C4⋊C8C2×D6111yescharacteristic
229C2×#102—612no—
230C2×#100—1221no—
231C2×#100—1221no—
232C4×M16—611no—
233C4×M16—1221no—
234#331—1222no—
235Q8⋊C8—1221no—
236Q8⋊C8—1221no—
237C61#925411yescharacteristic, complemented, Sylow
238C22×Q8—611no—
239C22×D4—612no—
240C22×D4—1221no—
241C22×D4—1221no—
242C2×SD16—1222no—
243C2×SD16—1222no—
244C2×SD16—2444no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—611no—
248C2×M16—611no—
249C22×C8C4×D6112yes—
250#127—1221no—
251#127—1221no—
252#127—1221no—
253#127—1221no—
254C4×Q8—611no—
255C4×Q8—611no—
256C4×Q8—611no—
257C4×Q8—611no—
258C4×Q8—1221no—
259C4×Q8—1221no—
260C2×C4⋊C4—611no—
261C2×C4⋊C4—1221no—
262C2×C42—1221no—
263C2×C42C22×D6111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—1222no—
270C4⋊C8—1222no—
271C4⋊C8—1221no—
272C4⋊C8D24412yes—
273#102—1222no—
274#102—1222no—
275#100—2442no—
276#100—2442no—
277C22⋊C8—1221no—
278#97—1222no—
279#97—1221no—
280C4×C8—1222no—
281C4×C8—1221no—
282C4×C8—1221no—
283C24—1222no—
284C2×Q8—611no—
285C2×Q8—611no—
286C2×Q8—1222no—
287C2×Q8—1221no—
288C2×Q8—2441no—
289C2×D4—1222no—
290C2×D4—1222no—
291C2×D4—4882no—
292C2×D4—2442no—
293C2×D4—2442no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2441no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4C2×C4×D6111yescharacteristic
305C22×C4D4×D6111yescharacteristic
306C22×C4#1175822611yescharacteristic
307SD16—2444no—
308SD16—2444no—
309M16—41no—
310M16—41no—
311M16—41no—
312M16—41no—
313M16—612no—
314M16—1221no—
315M16—1221no—
316M16—1221no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—42no—
320C2×C8—41no—
321C2×C8—1221no—
322C2×C8—1221no—
323C2×C8—2441no—
324C4⋊C4—611no—
325C4⋊C4—611no—
326C4⋊C4—1221no—
327C4⋊C4—1221no—
328C4⋊C4—1221no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C42—1221no—
332C42—1221no—
333C42—1221no—
334C42—1221no—
335C42C2×D24411yescharacteristic
336C42#1175822211yescharacteristic
337C42D4×D6111yescharacteristic
338C42D4×D6111yescharacteristic
339C23—4882no—
340C23—4882no—
341C23—2442no—
342C23—2442no—
343C23—2442no—
344C23#1451973911yescharacteristic
345Q8—612no—
346Q8—1221no—
347Q8—1221no—
348Q8—1221no—
349Q8—2442no—
350D4—4882no—
351D4—4882no—
352D4—4882no—
353D4—4881no—
354D4—4881no—
355D4—4881no—
356D4—4881no—
357D4—2442no—
358D4—2442no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—4881no—
367C2×C4—2442no—
368C2×C4C22⋊C4×D6111yescharacteristic
369C2×C4C4×D24411yescharacteristic
370C2×C4#1451974711yescharacteristic
371C2×C4#1451975011yescharacteristic
372C2×C4#1451975211yescharacteristic
373C2×C4#1451976211yescharacteristic
374C2×C4SD16×D6111yescharacteristic
375C2×C4#1451979811yescharacteristic
376C2×C4#1451980111yescharacteristic
377C2×C4#1451980911yescharacteristic
378C8—42no—
379C8—42no—
380C8—81no—
381C8—1222no—
382C8—4881no—
383C8—2441no—
384C22—21no—
385C22—21no—
386C22—9762no—
387C22—9762no—
388C22—4882no—
389C22—4882no—
390C22—4882no—
391C22#1683964011yescharacteristic
392C22#1683984911yescharacteristic
393C22#1683986111yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—1222no—
398C4—2441no—
399C4—2441no—
400C4—2441no—
401C4#100×D6111yescharacteristic
402C4#1683974511yescharacteristic
403C4#1683990211yescharacteristic
404C4#1683990811yescharacteristic
405C4#1683996111yescharacteristic
406C4#1683998711yescharacteristic
407C2—21no—
408C2—21no—
409C2—9762no—
410C2#2144617511yescharacteristic
411C2#2144628111yescharacteristic
412C2#2144630011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1292C2
socleC22×C61#386
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1292D61
hypocenterC61#9254
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
2. #21454770C2semidirect
5. #21444247C2semidirect
6. #21443669C2semidirect
7. C61×#1292C2semidirect
126. #11758194SD16semidirect
170. Dic122#100semidirect
206. #1292D61semidirect
237. C61#9254semidirect

Maximal subgroups

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

subgroupindex
C2×#168399632
#214547702
#214466582
#214444882
#214442472
#214436692
C61×#12922
#925461