Finite Group Databasebeta

← #30613587

Subgroups — #30613587

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462751C212yesmaximal, complemented
2#21461452C212yesmaximal, complemented
3#21461448C214yesmaximal, complemented
4Q16×#92420C212yesmaximal, complemented
5#21461376C211yesmaximal, characteristic, complemented
6#21461154C212yesmaximal, complemented
7C8×#11758217C211yesmaximal, characteristic, complemented
8#135×Dic61C211yesmaximal, characteristic
9Q8×#92420C2214yes—
10#16840797—24no—
11#16840797C2214yes—
12#16840779—22no—
13#16840779C2211yescharacteristic
14#16840765—22no—
15#16840765C2212yes—
16C4×#11758217C2211yescharacteristic
17#16840626C2212yes—
18#16840625C2212yes—
19Q8⋊#92420C2214yes—
20D4⋊#92420C2214yes—
21#92420⋊C8C2212yes—
22C8×#92420C2212yes—
23#41×Dic61C2212yes—
24Q16×Dic61C411yescharacteristic
25Q16×Dic61C2211yescharacteristic
26SD16×Dic61C412yes—
27SD16×Dic61C2212yes—
28D8×Dic61C411yescharacteristic
29D8×Dic61C2211yescharacteristic
30#16839800C411yescharacteristic
31#16839758C412yes—
32C2×C8×Dic61C2211yescharacteristic
33C2×#135×C61C411yescharacteristic
34C2×#11758217—21no—
35C2×#11758217—22no—
36C2×#11758217—24no—
37#14519844—22no—
38#14519844D411yescharacteristic
39#14519844D411yescharacteristic
40C4⋊#92420—24no—
41C4⋊#92420C2314yes—
42C22⋊#92420—24no—
43C22⋊#92420D412yes—
44#14519832—21no—
45C4×#92420—24no—
46C4×#92420C2312yes—
47C4×#92420C2312yes—
48C22×#92418C2×C411yescharacteristic
49Q8×Dic61C2×C412yes—
50Q8×Dic61C2312yes—
51D4×Dic61—22no—
52D4×Dic61—22no—
53D4×Dic61C2×C412yes—
54D4×Dic61C2312yes—
55#14519736—22no—
56#14519736C2×C412yes—
57C2×C4×Dic61—22no—
58C2×C4×Dic61C2311yescharacteristic
59#14519711C2×C411yescharacteristic
60#14519711C2×C411yescharacteristic
61#14519709C2×C412yes—
62#14519701C2×C412yes—
63#14519701C2×C412yes—
64#14519698C2×C412yes—
65#14519698C2×C412yes—
66C8×Dic61C2×C411yescharacteristic
67C8×Dic61C2×C411yescharacteristic
68C8×Dic61C2311yescharacteristic
69C8×Dic61C2311yescharacteristic
70C2×#41×C61C2×C412yes—
71#135×C61—24no—
72C2×Q16×C61C2×C411yescharacteristic
73C2×SD16×C61C2×C412yes—
74C2×D8×C61C2×C411yescharacteristic
75C22×C8×C61C2×C411yescharacteristic
76#41×C61—24no—
77#41×C61—42no—
78C2×Q8×C61C22×C412yes—
79C2×D4×C61—22no—
80C2×D4×C61C22×C412yes—
81C22×C4×C61—22no—
82C22×C4×C61C22×C411yescharacteristic
83C22×Dic61—22no—
84C22×Dic61—22no—
85C22×Dic61C2×D411yescharacteristic
86C22×Dic61#4111yescharacteristic
87#11758217—24no—
88#11758217—84no—
89#11758217—82no—
90C2×#92420—22no—
91C2×#92420—24no—
92C2×#92420C2×D412yes—
93C2×#92420C2×D412yes—
94Q16×C61M1614yescomplemented
95SD16×C61—24no—
96D8×C61—22no—
97C2×C8×C61—22no—
98C2×C8×C61C22×C411yescharacteristic
99C2×C8×C61C22×C411yescharacteristic
100C22⋊Dic61—22no—
101C22⋊Dic61—22no—
102C22⋊Dic61—22no—
103C4⋊Dic61—22no—
104C4⋊Dic61—22no—
105C4⋊Dic61C22×C412yes—
106C4⋊Dic61C22×C412yes—
107C4×Dic61—22no—
108C4×Dic61—22no—
109C4×Dic61—22no—
110C4×Dic61C22×C411yescharacteristic
111C4×Dic61C2×D411yescharacteristic
112C4×Dic61#4111yescharacteristic
113C4×Dic61C2411yescharacteristic
114C2×#92418—41no—
115C2×#92418C22×C411yescharacteristic
116C2×#92418C22×C411yescharacteristic
117C23×C61—22no—
118C23×C61C4×D411yescharacteristic
119Q8×C61—22no—
120Q8×C61C2×M1614yes—
121D4×C61—22no—
122D4×C61—22no—
123D4×C61—44no—
124C2×C4×C61—22no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—44no—
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61C23×C411yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—44no—
138C2×Dic61C4×D411yescharacteristic
139C2×Dic61C4×D411yescharacteristic
140C2×Dic61C22×D411yescharacteristic
141C2×Dic61C2×#4111yescharacteristic
142#92420—24no—
143#92420—22no—
144#92420—22no—
145#92420—44no—
146C8×C61—21no—
147C8×C61C2×M1612yes—
148#92418—21no—
149#92418—21no—
150#18059—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—42no—
155C22×C61—42no—
156C22×C61—42no—
157C22×C61C2×C4×D411yescharacteristic
158C4×C61—21no—
159C4×C61—24no—
160C4×C61C22×M1611yescharacteristic
161C4×C61#56811yescharacteristic
162Dic61—21no—
163Dic61—21no—
164Dic61—42no—
165Dic61—42no—
166Dic61#44312yes—
167Dic61#57611yescharacteristic
168Dic61#57811yescharacteristic
169#2991—612no—
170C4×#135—611no—
171#1589—612no—
172#1588—614no—
173C8×Q16—612no—
174#1567—611no—
175#1489—612no—
176C8×M16—611no—
177C2×C61—41no—
178C2×C61—82no—
179C2×C61D4×M1611yescharacteristic
180C2×C61#295111yescharacteristic
181C2×C61C2×#44311yescharacteristic
182C2×#135#692311yescharacteristic
183C4×#41—612no—
184C8×Q8—614no—
185C4×Q16—611no—
186C4×Q16—611no—
187C4×SD16—612no—
188C4×SD16—612no—
189C4×D8—611no—
190C4×D8—611no—
191#436—614no—
192#436—1224no—
193#431—611no—
194#431—1222no—
195#427—611no—
196#423—612no—
197#423—1222no—
198#416—612no—
199C4×M16—611no—
200C2×C4×C8—611no—
201#335—612no—
202#335—612no—
203Q8⋊C8—614no—
204D4⋊C8—614no—
205#322—612no—
206C82—612no—
207C61#1805911yescharacteristic, complemented, Sylow
208C2×#41C2×#692312yes—
209#135—24no—
210C2×Q16C2×#692311yescharacteristic
211C2×SD16C2×#692312yes—
212C2×D8C2×#692311yescharacteristic
213C2×M16—1224no—
214C2×M16—1221no—
215C2×M16—1222no—
216C22×C8—611no—
217C22×C8C2×#692311yescharacteristic
218C4×Q8—612no—
219C4×Q8—612no—
220C4×D4—612no—
221C4×D4—612no—
222C4×D4—1222no—
223C4×D4—1222no—
224#117—612no—
225#117—1222no—
226C2×C42—611no—
227C2×C42—1222no—
228#107—611no—
229#107—611no—
230#106—612no—
231C4⋊C8—611no—
232C4⋊C8—611no—
233C4⋊C8—614no—
234C4⋊C8—1222no—
235C4⋊C8—1224no—
236#103—612no—
237#103—612no—
238#102—612no—
239#102—612no—
240C22⋊C8—612no—
241C22⋊C8—1224no—
242#97—1221no—
243C4×C8—612no—
244C4×C8—611no—
245C4×C8—611no—
246C4×C8—611no—
247C4×C8—611no—
248C4×C8—612no—
249C4×C8—1224no—
250#41—24no—
251#41—42no—
252C2×Q8C22×#692312yes—
253C2×D4—22no—
254C2×D4C22×#692312yes—
255C22×C4—22no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4C22×#692311yescharacteristic
261Q16#1175821714yescomplemented
262SD16—24no—
263D8—22no—
264M16—1224no—
265M16—4884no—
266M16—4882no—
267C2×C8—22no—
268C2×C8—612no—
269C2×C8—612no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—1222no—
273C2×C8—1224no—
274C2×C8—2441no—
275C2×C8C22×#692311yescharacteristic
276C2×C8C22×#692311yescharacteristic
277C4⋊C4—612no—
278C4⋊C4—612no—
279C4⋊C4—1222no—
280C4⋊C4—1222no—
281C22⋊C4—1222no—
282C22⋊C4—1222no—
283C22⋊C4—1222no—
284C42—611no—
285C42—611no—
286C42—611no—
287C42—611no—
288C42—1222no—
289C42—1222no—
290C42—1222no—
291C23—22no—
292C23D4×#692311yescharacteristic
293Q8—22no—
294Q8C2×#1175821714yes—
295D4—22no—
296D4—22no—
297D4—44no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—44no—
302C2×C4—611no—
303C2×C4—611no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—1222no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2444no—
314C2×C4D4×#692311yescharacteristic
315C2×C4C23×#692311yescharacteristic
316C8—21no—
317C8—1222no—
318C8—1222no—
319C8—1224no—
320C8—1221no—
321C8—1221no—
322C8—2444no—
323C8C2×#1175821712yes—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—42no—
328C22—42no—
329C22—42no—
330C22C2×D4×#692311yescharacteristic
331C4—21no—
332C4—24no—
333C4—611no—
334C4—611no—
335C4—612no—
336C4—1221no—
337C4—1221no—
338C4—2442no—
339C4—2442no—
340C4C22×#1175821711yescharacteristic
341C4#1684084011yescharacteristic
342C2—41no—
343C2—82no—
344C2D4×#1175821711yescharacteristic
345C2#2146258111yescharacteristic
346C2D61⋊#44311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
Fitting, prime radicalC2×#135×C61C4
socleC22×C61C2×C4×D4
cosocleC4×Dic61C24
hypercenterC2×#135#6923
hypocenterC61#18059
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. #21462751C2semidirect
2. #21461452C2semidirect
3. #21461448C2semidirect
4. Q16×#92420C2semidirect
5. #21461376C2semidirect
6. #21461154C2semidirect
7. C8×#11758217C2semidirect
94. Q16×C61M16semidirect
207. C61#18059semidirect
261. Q16#11758217semidirect

Maximal subgroups

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

subgroupindex
#214627512
#214614522
#214614482
Q16×#924202
#214613762
#214611542
C8×#117582172
#135×Dic612
#1805961