Finite Group Databasebeta

← #29577382

Subgroups — #29577382

Order 15616.

506 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 117 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#21454899C211yesmaximal, characteristic
2#21450807C211yesmaximal, characteristic
3#21445812C211yesmaximal, characteristic
4#21444492C211yesmaximal, characteristic
5#21444490C211yesmaximal, characteristic
6#21443722C211yesmaximal, characteristic
7C61×#1303C211yesmaximal, characteristic
8C2×#14519777—21no—
9C2×#14519777C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11C8×Dic122—22no—
12#16839886—22no—
13#16839815C2211yescharacteristic
14#16839812—22no—
15#16839786C2211yescharacteristic
16C2×#14519695—21no—
17#16839694C414yes—
18#16839668—21no—
19#16839661—22no—
20#16839530—21no—
21#16839509—22no—
22#16839507—22no—
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C22×Dic122—21no—
27C22×Dic122D411yescharacteristic
28C2×#11758194—21no—
29#14519777—21no—
30#14519777—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777—42no—
34#14519777—42no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—24no—
41C2×C4⋊Dic61C2×C412yes—
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196C2×C412yes—
44C2×C4×Dic61D412yes—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418D412yes—
48#14519706—24no—
49#14519695—42no—
50C22⋊#92418—21no—
51C4×#92418—21no—
52C8×Dic61—24no—
53#14519684—24no—
54C2×M16×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C42×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61D412yes—
61C22⋊C8×C61—21no—
62C4×C8×C61—21no—
63#95×C61C2×C412yes—
64C22×C4×C61—22no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—22no—
69C22×Dic61C22⋊C412yes—
70C22×Dic61C22⋊C412yes—
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×Dic122D812yes—
82C2×Dic122SD1612yes—
83M16×C61—41no—
84M16×C61—41no—
85C2×C8×C61—22no—
86C2×C8×C61—41no—
87C4⋊C4×C61—24no—
88C42×C61—41no—
89C42×C61—41no—
90C42×C61C2×D411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61#4111yescharacteristic
93C42×C61#4111yescharacteristic
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—22no—
97C4⋊Dic61—22no—
98C4⋊Dic61—41no—
99C4⋊Dic61—41no—
100C4⋊Dic61—48no—
101#11758196—22no—
102#11758196—22no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105#11758194—41no—
106#11758194—41no—
107C2×#92418—22no—
108C2×#92418—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110C2×C4×C61—22no—
111C2×C4×C61—24no—
112C2×C4×C61—41no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61C4×D411yescharacteristic
116C2×C4×C61C4×D411yescharacteristic
117C2×C4×C61#12011yescharacteristic
118C2×C4×C61#12111yescharacteristic
119C2×C4×C61#12111yescharacteristic
120C2×C4×C61#12311yescharacteristic
121C2×C4×C61C2×D811yescharacteristic
122C2×C4×C61C2×SD1611yescharacteristic
123C2×C4×C61#13511yescharacteristic
124C2×C4×C61#13511yescharacteristic
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—42no—
129C2×Dic61—42no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61#10214yes—
133Dic122—22no—
134Dic122—22no—
135Dic122—22no—
136Dic122—22no—
137Dic122—81no—
138Dic122—81no—
139Dic122—81no—
140Dic122—81no—
141C8×C61—42no—
142C8×C61—81no—
143#92418—42no—
144#92418—81no—
145#9394—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#38611yescharacteristic
149C22×C61C2×#10211yescharacteristic
150C22×C61#41611yescharacteristic
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—44no—
155C4×C61#45612yes—
156C4×C61#46511yescharacteristic
157C4×C61#46511yescharacteristic
158C4×C61#46611yescharacteristic
159C4×C61#46611yescharacteristic
160Dic61—24no—
161Dic61—42no—
162Dic61—82no—
163#2982—611no—
164#2546—611no—
165#1801—611no—
166#1546—611no—
167#1546—611no—
168#1303—611no—
169#1303D6111yescharacteristic
170C2×C61—21no—
171C2×C61—21no—
172C2×C61#188611yescharacteristic
173C2×C61#189311yescharacteristic
174C2×C61#191511yescharacteristic
175C2×C4⋊Q8—611no—
176C2×C4⋊Q8—1221no—
177C2×C4×Q8—611no—
178C8×Q8—1222no—
179C8×Q8—1222no—
180#431—611no—
181#431—1222no—
182#431C2×D6111yescharacteristic
183#423—611no—
184#423C2×D6111yescharacteristic
185C2×#101—1221no—
186#398—614no—
187#391—1221no—
188#389—1222no—
189C4×C4⋊C4C2×D6111yescharacteristic
190#343—1221no—
191#332—1222no—
192#332—1222no—
193C61#939411yescharacteristic, complemented, Sylow
194C22×Q8—611no—
195C22×Q8—1221no—
196C2×M16—21no—
197C2×M16—1221no—
198C4⋊Q8—1221no—
199C4⋊Q8—1221no—
200C4⋊Q8—1221no—
201C4⋊Q8—1221no—
202C4⋊Q8—2442no—
203C4⋊Q8—2442no—
204C4×Q8—1221no—
205C4×Q8—1221no—
206C4×Q8—1221no—
207C4×Q8—1221no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—612no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—612no—
212C2×C4⋊C4—1224no—
213C2×C4⋊C4—1221no—
214C2×C42—21no—
215C2×C42—612no—
216C2×C42C22×D6111yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—612no—
220C4⋊C8—1224no—
221C4⋊C8—1221no—
222C4⋊C8—1221no—
223C4⋊C8D24412yes—
224#101—2442no—
225C22⋊C8—21no—
226C22⋊C8—1221no—
227C4×C8—21no—
228C4×C8—1224no—
229C4×C8—1221no—
230#95—1224no—
231#95C4×D6112yes—
232C2×Q8—612no—
233C2×Q8—612no—
234C2×Q8—1221no—
235C2×Q8—1221no—
236C2×Q8—1221no—
237C2×Q8—1221no—
238C2×Q8—2441no—
239C2×Q8—2441no—
240C2×Q8—2441no—
241C2×Q8—2441no—
242C2×Q8—2441no—
243C2×Q8—2441no—
244C22×C4—22no—
245C22×C4—612no—
246C22×C4—612no—
247C22×C4—1222no—
248C22×C4C2×C4×D6111yescharacteristic
249C22×C4D4×D6111yescharacteristic
250C22×C4D4×D6111yescharacteristic
251M16—41no—
252M16—41no—
253M16—2441no—
254M16—2441no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—1222no—
258C2×C8—2441no—
259C4⋊C4—24no—
260C4⋊C4—1222no—
261C4⋊C4—1222no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1222no—
265C4⋊C4—1222no—
266C4⋊C4—2448no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C42—41no—
270C42—41no—
271C42—1222no—
272C42—1222no—
273C42C2×D24411yescharacteristic
274C42#1175822211yescharacteristic
275C42D4×D6111yescharacteristic
276C42#1175822611yescharacteristic
277C23C22⋊C4×D6111yescharacteristic
278Q8—1222no—
279Q8—1222no—
280Q8—1222no—
281Q8—1222no—
282Q8—4881no—
283Q8—4881no—
284Q8—4881no—
285Q8—4881no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—614no—
292C2×C4—1222no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—2442no—
296C2×C4—2442no—
297C2×C4—2442no—
298C2×C4—2442no—
299C2×C4#1451973911yescharacteristic
300C2×C4C4×D24411yescharacteristic
301C2×C4#1451974711yescharacteristic
302C2×C4#1451975011yescharacteristic
303C2×C4#1451975211yescharacteristic
304C2×C4#1451976211yescharacteristic
305C2×C4D8×D6111yescharacteristic
306C2×C4SD16×D6111yescharacteristic
307C2×C4#1451979811yescharacteristic
308C2×C4#1451980011yescharacteristic
309C8—42no—
310C8—81no—
311C8—4881no—
312C8—2442no—
313C22—21no—
314C22—21no—
315C22#1683964011yescharacteristic
316C22#102×D6111yescharacteristic
317C22#1683975711yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—44no—
322C4—1224no—
323C4—4882no—
324C4—2442no—
325C4#1683994612yes—
326C4#1683999211yescharacteristic
327C4#1683999411yescharacteristic
328C4#1683999711yescharacteristic
329C4#1683999911yescharacteristic
330C2—21no—
331C2—21no—
332C2#2144621111yescharacteristic
333C2#2144624611yescharacteristic
334C2#2144637011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9394
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
193. C61#9394semidirect

Maximal subgroups

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

subgroupindex
#214548992
#214508072
#214458122
#214444922
#214444902
#214437222
C61×#13032
#939461