Finite Group Databasebeta

← #30607426

Subgroups — #30607426

Order 15616.

388 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462580C211yesmaximal, characteristic
2#21462171C211yesmaximal, characteristic
3C2×#16840675C211yesmaximal, characteristic
4#21461937C211yesmaximal, characteristic
5#21460882C211yesmaximal, characteristic
6#21460875C211yesmaximal, characteristic
7#362×D61C211yesmaximal, characteristic
8#16840830—21no—
9C2×D61⋊C16C2211yescharacteristic
10#16840802—22no—
11Q16×#6923—21no—
12Q16×#6923—21no—
13#16840773—21no—
14#16840772C2211yescharacteristic
15C2×#14519846C2211yescharacteristic
16#16840755—21no—
17#16840725C2211yescharacteristic
18#16840689—21no—
19#16840688—21no—
20#16840675—22no—
21#16840641—21no—
22C2×Q16×D61C2211yescharacteristic
23M32×D61C2211yescharacteristic
24#108×D61C2211yescharacteristic
25#16839579C411yescharacteristic, complemented
26#16839578C411yescharacteristic, complemented
27#16839577C411yescharacteristic, complemented
28C61×#362C411yescharacteristic, complemented
29D61⋊M16D411yescharacteristic
30Q8×#6923—22no—
31Q8×#6923—22no—
32Q8×#6923—41no—
33Q8×#6923—41no—
34#14519856—21no—
35#14519856—42no—
36#14519856D411yescharacteristic
37C2×C4⋊#6923—21no—
38D61⋊C16—21no—
39D61⋊C16—21no—
40C2×#11758187—21no—
41#14519846—21no—
42#14519846—21no—
43#14519846—41no—
44#14519846D411yescharacteristic
45#14519846D411yescharacteristic
46#14519845—21no—
47#14519845—41no—
48#14519840—22no—
49#14519840—22no—
50#14519831—21no—
51C8×#6923—21no—
52C2×Q8×D61—21no—
53C2×Dic244C2×C411yescharacteristic
54C2×#11758202—21no—
55Q16×D61—21no—
56Q16×D61—21no—
57Q16×D61D412yes—
58Q16×D61Q812yes—
59M16×D61—21no—
60C2×C8×D61C2311yescharacteristic
61#14519717C2×C411yescharacteristic
62#14519716—21no—
63C16×D61—21no—
64#14519713C2×C411yescharacteristic
65#14519712—21no—
66C2×Q16×C61C2×C411yescharacteristic
67M32×C61C2×C411yescharacteristic
68#108×C61C2×C411yescharacteristic
69C22×#6923—41no—
70C2×Q8×C61—21no—
71Q8×D61—22no—
72Q8×D61—22no—
73Q8×D61—41no—
74Q8×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61C2×D411yescharacteristic
77C2×Dic122—21no—
78C2×Dic122—41no—
79C22⋊#6923—21no—
80C22⋊#6923—41no—
81#11758217—21no—
82C4⋊#6923—21no—
83C4⋊#6923—21no—
84C4⋊#6923—42no—
85C4⋊#6923—42no—
86C4⋊#6923—41no—
87C4⋊#6923—41no—
88C4⋊#6923D811yescharacteristic
89C4⋊#6923D811yescharacteristic
90C4×#6923—21no—
91C4×#6923—42no—
92C4×#6923—42no—
93C4×#6923—41no—
94#11758213—21no—
95D61⋊C8—21no—
96Q16×C61—21no—
97Q16×C61C4⋊C412yes—
98M16×C61—21no—
99C2×C8×C61C22×C411yescharacteristic
100#11758202—22no—
101#11758202—22no—
102#11758194—21no—
103C2×#92418#4111yescharacteristic
104Dic244—21no—
105Dic244C4⋊C412yes—
106#11758189—41no—
107C8×D61—41no—
108C8×D61C2×D411yescharacteristic
109C8×D61C2×D411yescharacteristic
110C8×D61C2×Q811yescharacteristic
111C8×D61#4111yescharacteristic
112#11758187—41no—
113C16×C61—21no—
114#11758185—21no—
115C22×D61AGL(1,ℤ/8)11yescharacteristic
116C2×#6923—21no—
117C2×#6923—21no—
118C2×#6923—41no—
119C2×#6923—41no—
120C2×#6923—81no—
121C2×#6923—161no—
122Q8×C61—22no—
123Q8×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61C4×D411yescharacteristic
126C2×Dic61—41no—
127C2×Dic61#13711yescharacteristic
128C4×D61—42no—
129C4×D61—42no—
130C4×D61#12011yescharacteristic
131C4×D61C22⋊Q811yescharacteristic
132C4×D61C2×D811yescharacteristic
133C4×D61#13511yescharacteristic
134Dic122—22no—
135Dic122—41no—
136Dic122—42no—
137Dic122—42no—
138#92420—41no—
139C8×C61—41no—
140C8×C61C2×C4⋊C411yescharacteristic
141C8×C61C4×D411yescharacteristic
142#92418—41no—
143#92418C22⋊Q811yescharacteristic
144#92418#12311yescharacteristic
145#12941—611nomaximal, Sylow
146C22×C61#44011yescharacteristic
147C2×D61—21no—
148C2×D61—21no—
149C2×D61#44711yescharacteristic
150C2×D61#47811yescharacteristic
151#6923—41no—
152#6923—41no—
153#6923—81no—
154#6923—81no—
155#6923—161no—
156C4×C61—42no—
157C4×C61#38511yescharacteristic
158C4×C61C4×D811yescharacteristic
159Dic61—42no—
160Dic61#45211yescharacteristic
161Dic61#47411yescharacteristic
162#2950—611no—
163#2159—611no—
164C2×#362—611no—
165C2×#358—611no—
166#1952—611no—
167#1382—611no—
168#1379—611no—
169C2×C61—21no—
170C2×C61#186211yescharacteristic
171D61—21no—
172D61#219311yescharacteristic
173D61#219511yescharacteristic
174C22×Q16—611no—
175#519—1221no—
176C2×M32—611no—
177C22×C16—611no—
178#441—1222no—
179C4×Q16—1221no—
180C4×Q16—1221no—
181C2×#108—611no—
182#428—1221no—
183#427—611no—
184C2×#107—611no—
185#419—1221no—
186#405—611no—
187#367—1221no—
188#366—1221no—
189#362—611no—
190#362—611no—
191#362—611no—
192#362#692311yescharacteristic, complemented
193#358—1222no—
194#343—1221no—
195C61#1294111yescharacteristic, complemented, Sylow
196C22×Q8—1221no—
197C2×Q16—612no—
198C2×Q16—612no—
199C2×Q16—611no—
200C2×Q16—1221no—
201C2×Q16—1221no—
202C2×Q16—1221no—
203C2×Q16C2×#692311yescharacteristic
204C2×M16—611no—
205C2×M16—1221no—
206C22×C8—611no—
207C4×Q8—1222no—
208C4×Q8—1222no—
209C4×Q8—2441no—
210C4×Q8—2441no—
211#117—611no—
212#117—1221no—
213#117—2442no—
214C2×C4⋊C4—1221no—
215M32—611no—
216M32—1221no—
217M32C2×#692311yescharacteristic
218C2×C16—1221no—
219C2×C16—1221no—
220C2×C16—1221no—
221C2×C16—1221no—
222#108—611no—
223#108—1221no—
224#108C2×#692311yescharacteristic
225#107—611no—
226#107—611no—
227#107—1221no—
228#107—1221no—
229#107—2441no—
230#106—1221no—
231#106—2441no—
232#103—1222no—
233#103—1222no—
234#97—1221no—
235C4×C8—1221no—
236C2×Q8—21no—
237C2×Q8—1222no—
238C2×Q8—1222no—
239C2×Q8—1221no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C22×C4—611no—
244C22×C4—2441no—
245C22×C4—2441no—
246Q16—21no—
247Q16—612no—
248Q16—1222no—
249Q16—1222no—
250Q16—1221no—
251Q16C4⋊#692312yes—
252M16—21no—
253M16—1221no—
254M16—1221no—
255M16—1221no—
256M16—2441no—
257C2×C8—611no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—611no—
262C2×C8—1221no—
263C2×C8—2441no—
264C2×C8C22×#692311yescharacteristic
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C4⋊C4—2442no—
273C22⋊C4—1221no—
274C22⋊C4—2441no—
275C42—1221no—
276C42—2441no—
277C42—2442no—
278C42—2442no—
279C16—21no—
280C16—1221no—
281C16—2441no—
282C23—611no—
283Q8—22no—
284Q8—41no—
285Q8—1222no—
286Q8—2442no—
287Q8—2442no—
288Q8—2441no—
289C2×C4—41no—
290C2×C4—611no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—611no—
294C2×C4—611no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—9761no—
298C2×C4—4881no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4D4×#692311yescharacteristic
305C8—41no—
306C8—611no—
307C8—611no—
308C8—2441no—
309C8—2441no—
310C8C2×C4⋊#692311yescharacteristic
311C8D4×#692311yescharacteristic
312C22—611no—
313C22—611no—
314C22—1221no—
315C22—1221no—
316C22#1684080111yescharacteristic
317C4—42no—
318C4—611no—
319C4—611no—
320C4—9761no—
321C4—4881no—
322C4—4881no—
323C4—2441no—
324C4—2441no—
325C4—2442no—
326C4#1684070911yescharacteristic
327C4D8×#692311yescharacteristic
328C2—21no—
329C2—611no—
330C2—611no—
331C2—1221no—
332C2#2146178211yescharacteristic
subgroupG/H
centerC2#21461782
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#362C4
socleC2×C61#1862
prime radicalC22×D61AGL(1,ℤ/8)
cosocleC2×C8×D61C23
hypercenter#362#6923
hypocenterC61#12941
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
25. #16839579C4semidirect
26. #16839578C4semidirect
27. #16839577C4semidirect
28. C61×#362C4semidirect
192. #362#6923semidirect
195. C61#12941semidirect

Maximal subgroups

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

subgroupindex
#214625802
#214621712
C2×#168406752
#214619372
#214608822
#214608752
#362×D612
#1294161