Finite Group Databasebeta

← #29577427

Subgroups — #29577427

Order 15616.

570 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 109 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#21454859C211yesmaximal, characteristic
2#21450768C211yesmaximal, characteristic
3#21445808C211yesmaximal, characteristic
4#21444505C211yesmaximal, characteristic, complemented
5#21444503C211yesmaximal, characteristic, complemented
6#21443722C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519757—22no—
10C2×C4×D244C2211yescharacteristic
11#16839841—22no—
12#16839839—22no—
13#16839815C2211yescharacteristic
14#16839786C2211yescharacteristic
15C2×#14519693—21no—
16#16839724—22no—
17#16839699C414yes—
18#16839664—21no—
19#16839632—21no—
20#16839530—21no—
21#16839509—22no—
22#16839507—22no—
23C61×#431C2211yescharacteristic
24C61×#423C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C22×Dic122—21no—
27C22×D244D411yescharacteristic
28C22×C4×D61D412yes—
29C2×#11758194—21no—
30C2×#11758189—24no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519757—48no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—24no—
42C2×C4⋊Dic61C2×C412yes—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758198—24no—
45C2×#11758198C2×C412yes—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418D412yes—
49#14519693—42no—
50C22⋊#92418—21no—
51#14519689—24no—
52C4×#92418—21no—
53C2×M16×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C42×C61—21no—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61D412yes—
60C22⋊C8×C61—21no—
61C4×C8×C61—21no—
62#95×C61C2×C412yes—
63C23×D61C22⋊C412yes—
64C22×C4×C61—22no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—22no—
69C22×Dic61C22⋊C412yes—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—44no—
79C2×Dic122—44no—
80C2×Dic122—41no—
81C2×Dic122—41no—
82M16×C61—41no—
83M16×C61—41no—
84C2×C8×C61—22no—
85C2×C8×C61—41no—
86C4⋊C4×C61—24no—
87C42×C61—41no—
88C42×C61—41no—
89C42×C61C2×D411yescharacteristic
90C42×C61C2×D411yescharacteristic
91C42×C61#4111yescharacteristic
92C42×C61#4111yescharacteristic
93#11758198—22no—
94#11758198—22no—
95#11758198—48no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—22no—
99C4⋊Dic61—22no—
100C4⋊Dic61—48no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103#11758194—41no—
104#11758194—41no—
105C2×#92418—22no—
106C2×#92418—41no—
107#11758189—84no—
108C23×C61C2×C22⋊C411yescharacteristic
109C22×D61—22no—
110C22×D61—22no—
111C22×D61—22no—
112C22×D61—42no—
113C22×D61—42no—
114C2×C4×C61—22no—
115C2×C4×C61—24no—
116C2×C4×C61—41no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61C4×D411yescharacteristic
120C2×C4×C61C4×D411yescharacteristic
121C2×C4×C61#12011yescharacteristic
122C2×C4×C61#12111yescharacteristic
123C2×C4×C61#12111yescharacteristic
124C2×C4×C61#12311yescharacteristic
125C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C61#13711yescharacteristic
127C2×C4×C61#13711yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×Dic61—22no—
130C2×Dic61—42no—
131C2×Dic61—44no—
132C2×Dic61—42no—
133D244—41no—
134D244—41no—
135D244—41no—
136D244—41no—
137C4×D61—44no—
138C4×D61—82no—
139Dic122—82no—
140Dic122—82no—
141C8×C61—42no—
142C8×C61—81no—
143#92418—42no—
144#92418—81no—
145#9403—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#38611yescharacteristic
149C22×C61#41711yescharacteristic
150C22×C61#41911yescharacteristic
151C2×D61—44no—
152C2×D61—42no—
153C2×D61—42no—
154C2×D61—42no—
155C2×D61—82no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—44no—
160C4×C61#45312yes—
161C4×C61#46811yescharacteristic
162C4×C61#46811yescharacteristic
163C4×C61#47011yescharacteristic
164C4×C61#47011yescharacteristic
165Dic61—42no—
166Dic61—82no—
167#2975—611no—
168#2542—611no—
169#1800—611no—
170#1549—611no—
171#1549—611no—
172#1303—611no—
173#1303D6111yescharacteristic, complemented
174C2×C61—21no—
175C2×C61—21no—
176C2×C61#188711yescharacteristic
177C2×C61#189411yescharacteristic
178C2×C61#191511yescharacteristic
179D61—82no—
180C2×C4⋊Q8—611no—
181C2×C22⋊Q8—1222no—
182C2×C4×D4—611no—
183#436—1222no—
184#436—1222no—
185#431—611no—
186#431C2×D6111yescharacteristic
187#423—611no—
188#423C2×D6111yescharacteristic
189C2×#100—1221no—
190#407—1222no—
191#399—614no—
192#390—1221no—
193#384—1221no—
194C4×C4⋊C4C2×D6111yescharacteristic
195#343—1221no—
196#332—1222no—
197#332—1222no—
198C61#940311yescharacteristic, complemented, Sylow
199C22×Q8—1221no—
200C22×D4—611no—
201C23×C4—612no—
202C2×M16—21no—
203C2×M16—1224no—
204C2×M16—1221no—
205C4⋊Q8—1221no—
206C4⋊Q8—1221no—
207C4⋊Q8—1221no—
208C4⋊Q8—1221no—
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—612no—
217C2×C4⋊C4—1224no—
218C2×C4⋊C4—1221no—
219C2×C22⋊C4—612no—
220C2×C22⋊C4—1224no—
221C2×C42—21no—
222C2×C42C22×D6111yescharacteristic
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—612no—
226C4⋊C8—1221no—
227C4⋊C8—1221no—
228C4⋊C8D24412yes—
229#100—2442no—
230C22⋊C8—21no—
231C22⋊C8—1224no—
232C22⋊C8—1221no—
233C4×C8—21no—
234C4×C8—1221no—
235#95C4×D6112yes—
236C24—612no—
237C2×Q8—2444no—
238C2×Q8—2441no—
239C2×Q8—2441no—
240C2×D4—1221no—
241C2×D4—1221no—
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—4884no—
258M16—2441no—
259M16—2441no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—1222no—
263C2×C8—2441no—
264C4⋊C4—24no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1222no—
268C4⋊C4—1222no—
269C4⋊C4—2448no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C22⋊C4—1222no—
273C22⋊C4—1222no—
274C22⋊C4—2448no—
275C42—41no—
276C42—41no—
277C42C2×D24411yescharacteristic
278C42#1175822211yescharacteristic
279C42D4×D6111yescharacteristic
280C42#1175822611yescharacteristic
281C23—1222no—
282C23—1222no—
283C23—1222no—
284C23—2442no—
285C23—2442no—
286C23C22⋊C4×D6111yescharacteristic
287Q8—4882no—
288Q8—4882no—
289D4—2441no—
290D4—2441no—
291D4—2441no—
292D4—2441no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—1222no—
299C2×C4—4882no—
300C2×C4—2444no—
301C2×C4—2442no—
302C2×C4—2444no—
303C2×C4—2442no—
304C2×C4#1451973911yescharacteristic
305C2×C4C4×D24411yescharacteristic
306C2×C4#1451974711yescharacteristic
307C2×C4#1451975011yescharacteristic
308C2×C4#1451975211yescharacteristic
309C2×C4#1451976211yescharacteristic
310C2×C4#1451980111yescharacteristic
311C2×C4#1451980611yescharacteristic
312C2×C4#1451980611yescharacteristic
313C2×C4#1451980911yescharacteristic
314C8—42no—
315C8—81no—
316C8—4881no—
317C8—2442no—
318C22—21no—
319C22—21no—
320C22—4882no—
321C22—2444no—
322C22—2442no—
323C22—2442no—
324C22—2442no—
325C22#1683964011yescharacteristic
326C22#1683976011yescharacteristic
327C22#1683976911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—44no—
332C4—4882no—
333C4—2442no—
334C4#1683993112yes—
335C4#1684000711yescharacteristic
336C4#1684000911yescharacteristic
337C4#1684001911yescharacteristic
338C4#1684002111yescharacteristic
339C2—21no—
340C2—21no—
341C2—4882no—
342C2#2144621611yescharacteristic
343C2#2144625111yescharacteristic
344C2#2144637011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#386
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#9403
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
4. #21444505C2semidirect
5. #21444503C2semidirect
6. #21443722C2semidirect
7. C61×#1303C2semidirect
173. #1303D61semidirect
198. C61#9403semidirect

Maximal subgroups

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

subgroupindex
#214548592
#214507682
#214458082
#214445052
#214445032
#214437222
C61×#13032
#940361