Finite Group Databasebeta

← #29577385

Subgroups — #29577385

Order 15616.

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

normal subgroups only

This group has 594 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#21454842C211yesmaximal, characteristic
2#21450773C211yesmaximal, characteristic
3#21445808C211yesmaximal, characteristic
4#21444504C211yesmaximal, characteristic, complemented
5#21443721C211yesmaximal, characteristic, complemented
6#21443720C211yesmaximal, characteristic, complemented
7C61×#1549C211yesmaximal, characteristic, complemented
8C2×#14519753—22no—
9C2×C4×D244C2211yescharacteristic
10C8×D244—22no—
11#16839827—22no—
12#16839815C2211yescharacteristic
13#16839786C2211yescharacteristic
14C2×#14519693—21no—
15C22⋊C8×D61—22no—
16#16839697C414yes—
17#16839663—21no—
18#16839631—21no—
19C4×C4⋊Dic61C2211yescharacteristic
20#16839530—21no—
21#16839508—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C61×#332—22no—
26C22×D244D411yescharacteristic
27C22×C4×D61D412yes—
28C2×#11758194—21no—
29C2×C8×D61—24no—
30#14519753—48no—
31C4×D244—21no—
32C4×D244—21no—
33C4×D244—21no—
34C4×D244—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—24no—
38C2×#11758198—24no—
39C2×#11758198C2×C412yes—
40C2×C4×Dic61—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418D412yes—
44#14519693—42no—
45C22⋊#92418—21no—
46#14519689—24no—
47C4×#92418—21no—
48#14519684C2×C412yes—
49C22×Q8×C61—21no—
50C2×M16×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C412yes—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61D412yes—
61C22⋊C8×C61—21no—
62C4×C8×C61—21no—
63C23×D61C22⋊C412yes—
64C2×Q8×C61—44no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C22×C4×C61—22no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—22no—
72C22×Dic61C22⋊C412yes—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244SD1612yes—
78C2×D244Q1612yes—
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—44no—
82M16×C61—41no—
83M16×C61—41no—
84C2×C8×C61—22no—
85C2×C8×C61—41no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61C2×D411yescharacteristic
91C42×C61C2×D411yescharacteristic
92C42×C61#4111yescharacteristic
93C42×C61#4111yescharacteristic
94#11758198—22no—
95#11758198—22no—
96#11758198—48no—
97C4⋊Dic61—24no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100#11758196—48no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103#11758194—41no—
104#11758194—41no—
105C2×#92418—22no—
106C2×#92418—41no—
107C8×D61—84no—
108C23×C61C2×C22⋊C411yescharacteristic
109C22×D61—22no—
110C22×D61—22no—
111C22×D61—42no—
112C22×D61—42no—
113C22×D61#10314yes—
114Q8×C61—82no—
115Q8×C61—82no—
116C2×C4×C61—22no—
117C2×C4×C61—41no—
118C2×C4×C61—44no—
119C2×C4×C61—42no—
120C2×C4×C61C4×D411yescharacteristic
121C2×C4×C61C4×D411yescharacteristic
122C2×C4×C61#12011yescharacteristic
123C2×C4×C61#12111yescharacteristic
124C2×C4×C61#12111yescharacteristic
125C2×C4×C61#12311yescharacteristic
126C2×C4×C61C2×SD1611yescharacteristic
127C2×C4×C61C2×Q1611yescharacteristic
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61#13511yescharacteristic
130C2×Dic61—24no—
131C2×Dic61—22no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135D244—22no—
136D244—22no—
137D244—22no—
138D244—22no—
139C4×D61—44no—
140C4×D61—82no—
141C8×C61—42no—
142C8×C61—81no—
143#92418—42no—
144#92418—81no—
145#9395—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#38611yescharacteristic
149C22×C61C2×#10311yescharacteristic
150C22×C61#41611yescharacteristic
151C2×D61—24no—
152C2×D61—42no—
153C2×D61—42no—
154C2×D61—44no—
155C2×D61—82no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—82no—
160C4×C61#45312yes—
161C4×C61#46511yescharacteristic
162C4×C61#46511yescharacteristic
163C4×C61#46711yescharacteristic
164C4×C61#46711yescharacteristic
165Dic61—44no—
166Dic61—42no—
167#2972—611no—
168#2542—611no—
169#1800—611no—
170#1549—611no—
171#1549D6111yescharacteristic, complemented
172#1303—611no—
173#1303—611no—
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#188711yescharacteristic
177C2×C61#189211yescharacteristic
178C2×C61#191511yescharacteristic
179D61—44no—
180C2×C4⋊Q8C2×D6111yescharacteristic
181C2×C22⋊Q8—1222no—
182C2×C4×D4—611no—
183C8×D4—1222no—
184C8×D4—1222no—
185#431—611no—
186#431C2×D6111yescharacteristic
187#423—611no—
188#423C2×D6111yescharacteristic
189C2×#100—1221no—
190C2×C22⋊C8—1222no—
191#399—614no—
192#390—1221no—
193#384—1221no—
194C4×C4⋊C4—611no—
195#343—1221no—
196#332—22no—
197#332—1222no—
198C61#939511yescharacteristic, complemented, Sylow
199C22×Q8—21no—
200C22×D4—611no—
201C23×C4—612no—
202C2×M16—21no—
203C2×M16—1221no—
204C22×C8—1224no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C22⋊Q8—2448no—
210C4×D4—1221no—
211C4×D4—1221no—
212C4×D4—1221no—
213C4×D4—1221no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1224no—
218C2×C4⋊C4C4×D6112yes—
219C2×C22⋊C4—612no—
220C2×C22⋊C4—1224no—
221C2×C42—1221no—
222C2×C42C22×D6111yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—612no—
226C4⋊C8—1221no—
227C4⋊C8—1221no—
228C4⋊C8C22⋊D6112yes—
229#100—2442no—
230C22⋊C8—21no—
231C22⋊C8—1224no—
232C22⋊C8—1221no—
233C4×C8—21no—
234C4×C8—1221no—
235#95—612no—
236C24—612no—
237C2×Q8—44no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×D4—612no—
241C2×D4—612no—
242C2×D4—1221no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4—1221no—
246C22×C4—22no—
247C22×C4—612no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—2444no—
252C22×C4C2×C4×D6111yescharacteristic
253C22×C4D4×D6111yescharacteristic
254C22×C4D4×D6111yescharacteristic
255M16—41no—
256M16—41no—
257M16—2441no—
258M16—2441no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—1222no—
262C2×C8—4884no—
263C2×C8—2441no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—1224no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—2448no—
272C22⋊C4—1222no—
273C22⋊C4—1222no—
274C22⋊C4—2448no—
275C42—2441no—
276C42—2441no—
277C42#1175822211yescharacteristic
278C42D4×D6111yescharacteristic
279C42#1175822411yescharacteristic
280C42C2×C22⋊D6111yescharacteristic
281C23—614no—
282C23—1222no—
283C23—1222no—
284C23—2442no—
285C23—2442no—
286C23C22⋊C4×D6111yescharacteristic
287Q8—82no—
288Q8—82no—
289D4—1222no—
290D4—1222no—
291D4—1222no—
292D4—1222no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—1224no—
298C2×C4—1222no—
299C2×C4—4882no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4—2444no—
303C2×C4—2442no—
304C2×C4#1451973711yescharacteristic
305C2×C4C4×C22⋊D6111yescharacteristic
306C2×C4#1451974511yescharacteristic
307C2×C4#1451974811yescharacteristic
308C2×C4#1451975011yescharacteristic
309C2×C4#1451975911yescharacteristic
310C2×C4SD16×D6111yescharacteristic
311C2×C4Q16×D6111yescharacteristic
312C2×C4#1451979811yescharacteristic
313C2×C4#1451980011yescharacteristic
314C8—42no—
315C8—81no—
316C8—4881no—
317C8—2442no—
318C22—21no—
319C22—21no—
320C22—1224no—
321C22—4882no—
322C22—2444no—
323C22—2442no—
324C22—2442no—
325C22#1683963811yescharacteristic
326C22#103×D6111yescharacteristic
327C22#1683975711yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—82no—
332C4—2444no—
333C4—2442no—
334C4#1683992812yes—
335C4#1683998811yescharacteristic
336C4#1683999411yescharacteristic
337C4#1684000011yescharacteristic
338C4#1684000211yescharacteristic
339C2—21no—
340C2—21no—
341C2—2444no—
342C2#2144621411yescharacteristic
343C2#2144623911yescharacteristic
344C2#2144636811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1549C2
socleC22×C61#386
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1549D61
hypocenterC61#9395
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. #21444504C2semidirect
5. #21443721C2semidirect
6. #21443720C2semidirect
7. C61×#1549C2semidirect
171. #1549D61semidirect
198. C61#9395semidirect

Maximal subgroups

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

subgroupindex
#214548422
#214507732
#214458082
#214445042
#214437212
#214437202
C61×#15492
#939561