Finite Group Databasebeta

← #29575474

Subgroups — #29575474

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454902C211yesmaximal, characteristic, complemented
2C2×#16839864C211yesmaximal, characteristic
3#21444213C211yesmaximal, characteristic, complemented
4#21444211C211yesmaximal, characteristic
5#21444139C211yesmaximal, characteristic
6#21443664C211yesmaximal, characteristic, complemented
7C61×#1275C211yesmaximal, characteristic, complemented
8C22×#11758190C411yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839892—22no—
12#16839889—22no—
13#16839864—22no—
14#16839864—22no—
15#16839816—22no—
16#16839815C2211yescharacteristic
17#16839815C2211yescharacteristic
18C2×#14519711C411yescharacteristic
19C2×#14519702C411yescharacteristic
20C2×#14519699C411yescharacteristic
21#16839492—22no—
22#16839491—22no—
23#16839485—22no—
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C2×#97×C61C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758190—22no—
31C2×#11758190—22no—
32C2×#11758190—22no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122D412yes—
36C4×Dic122D412yes—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×#11758198—21no—
45C2×C4×Dic61—21no—
46#14519711—22no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49#14519706—24no—
50#14519702—22no—
51#14519699—22no—
52C22⋊#92418—21no—
53C22⋊#92418D412yes—
54#14519687—24no—
55C4×#92418—21no—
56C4×#92418—21no—
57C22×C8×C61C2×C411yescharacteristic
58C22×C8×C61C2×C411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#97×C61—21no—
65#97×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61D412yes—
68C23×D61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61#4111yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244M1612yes—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—82no—
84C2×Dic122—21no—
85C2×Dic122—21no—
86C2×Dic122—21no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122C22⋊C412yes—
90C2×C8×C61—21no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61—22no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—41no—
97C2×C8×C61M1612yes—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102#11758198—41no—
103#11758198—41no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61C22⋊C412yes—
108#11758196—22no—
109#11758196—22no—
110C4×Dic61—22no—
111C4×Dic61—22no—
112C2×#92418—22no—
113C2×#92418—41no—
114#11758190—28no—
115C23×C61C4×D411yescharacteristic
116C22×D61—22no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—81no—
120C22×D61—81no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61C2×C22⋊C411yescharacteristic
124C2×C4×C61C4×D411yescharacteristic
125C2×C4×C61#12011yescharacteristic
126C2×C4×C61#12111yescharacteristic
127C2×C4×C61#12111yescharacteristic
128C2×C4×C61#12311yescharacteristic
129C2×C4×C61C2×M1611yescharacteristic
130C2×C4×C61C2×M1611yescharacteristic
131C2×C4×C61#13111yescharacteristic
132C2×C4×C61#13111yescharacteristic
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—81no—
139C2×Dic61—81no—
140D244—22no—
141D244—22no—
142D244—41no—
143D244—41no—
144C4×D61—82no—
145C4×D61—82no—
146Dic122—22no—
147Dic122—22no—
148Dic122—41no—
149Dic122—41no—
150C8×C61—22no—
151C8×C61—42no—
152C8×C61—41no—
153C8×C61—81no—
154#92418—42no—
155#92418—81no—
156#9094—611nomaximal, Sylow
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#38611yescharacteristic
160C22×C61#43511yescharacteristic
161C22×C61#43611yescharacteristic
162C2×D61—42no—
163C2×D61—82no—
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—82no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61#40711yescharacteristic
172C4×C61#40811yescharacteristic
173C4×C61#43511yescharacteristic
174C4×C61#43611yescharacteristic
175Dic61—42no—
176Dic61—42no—
177Dic61—81no—
178#2983—611no—
179C2×#440—611no—
180#1479—611no—
181#1478—611no—
182#1460—611no—
183#1281—611no—
184#1275D6111yescharacteristic, complemented
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#187011yescharacteristic
188C2×C61#190311yescharacteristic
189C2×C61#190511yescharacteristic
190D61—82no—
191C22×SD16—611no—
192C2×C4×Q8—611no—
193C2×C4×D4—611no—
194#446—1222no—
195#446—1222no—
196#440—1222no—
197#440—1222no—
198#432—1222no—
199#431—611no—
200#431—611no—
201#431C2×D6111yescharacteristic
202#431C2×D6111yescharacteristic
203C2×#107—611no—
204C2×#103—611no—
205C2×#102—611no—
206C2×#97C2×D6111yescharacteristic
207Q8⋊C8—1222no—
208D4⋊C8—1222no—
209#323—1222no—
210C61#909411yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C22×D4—611no—
213C23×C4—1221no—
214C2×SD16—1222no—
215C2×SD16—1222no—
216C2×SD16—1222no—
217C22×C8C4×D6111yescharacteristic
218C22×C8C4×D6111yescharacteristic
219C4×Q8—612no—
220C4×Q8—612no—
221C4×Q8—1221no—
222C4×Q8—1221no—
223C4×D4—1221no—
224C4×D4—1221no—
225C4×D4—1221no—
226C4×D4—1221no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C42—1221no—
232C2×C42C22×D6111yescharacteristic
233#107—1222no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—1224no—
237C4⋊C8—1221no—
238C4⋊C8—1221no—
239#103—1222no—
240#102—1222no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—612no—
244C22⋊C8—1221no—
245#97—21no—
246#97—21no—
247#97—1224no—
248C4×C8—21no—
249C4×C8—1221no—
250C4×C8—1221no—
251C4×C8D24412yes—
252C24—1221no—
253C2×Q8—612no—
254C2×Q8—1221no—
255C2×Q8—1221no—
256C2×Q8—1221no—
257C2×Q8—1221no—
258C2×Q8—1221no—
259C2×D4—612no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—4882no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4C2×C4×D6111yescharacteristic
272C22×C4D4×D6111yescharacteristic
273C22×C4#1175822611yescharacteristic
274SD16—1228no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—1222no—
283C2×C8—2441no—
284C2×C8#1175818912yes—
285C4⋊C4—612no—
286C4⋊C4—1221no—
287C4⋊C4—1222no—
288C4⋊C4—1222no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C42—1222no—
294C42—1222no—
295C42C2×D24411yescharacteristic
296C42#1175822211yescharacteristic
297C42D4×D6111yescharacteristic
298C42D4×D6111yescharacteristic
299C23—1222no—
300C23—4881no—
301C23—4881no—
302C23—2441no—
303C23—2441no—
304C23#1451973911yescharacteristic
305Q8—1222no—
306Q8—1222no—
307Q8—2441no—
308Q8—2441no—
309D4—1222no—
310D4—1222no—
311D4—2441no—
312D4—2441no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—4882no—
318C2×C4—4882no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4C22⋊C4×D6111yescharacteristic
325C2×C4C4×D24411yescharacteristic
326C2×C4#1451974711yescharacteristic
327C2×C4#1451975011yescharacteristic
328C2×C4#1451975211yescharacteristic
329C2×C4#1451976211yescharacteristic
330C2×C4M16×D6111yescharacteristic
331C2×C4C2×#1175818911yescharacteristic
332C2×C4#1451978311yescharacteristic
333C2×C4#1451978511yescharacteristic
334C8—22no—
335C8—42no—
336C8—41no—
337C8—81no—
338C8—4881no—
339C8—2442no—
340C22—21no—
341C22—21no—
342C22—4882no—
343C22—4882no—
344C22—4881no—
345C22—4881no—
346C22—2442no—
347C22#1683964011yescharacteristic
348C22#1683983211yescharacteristic
349C22#1683983911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—4881no—
355C4—2442no—
356C4—2442no—
357C4#1683972411yescharacteristic
358C4#1683972711yescharacteristic
359C4#1683983511yescharacteristic
360C4#1683984111yescharacteristic
361C2—21no—
362C2—21no—
363C2—4882no—
364C2#2144611511yescharacteristic
365C2#2144630011yescharacteristic
366C2#2144631411yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1275C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1275D61
hypocenterC61#9094
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
1. #21454902C2semidirect
3. #21444213C2semidirect
6. #21443664C2semidirect
7. C61×#1275C2semidirect
184. #1275D61semidirect
210. C61#9094semidirect

Maximal subgroups

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

subgroupindex
#214549022
C2×#168398642
#214442132
#214442112
#214441392
#214436642
C61×#12752
#909461