Finite Group Databasebeta

← #29590325

Subgroups — #29590325

Order 15616.

452 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 107 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#21451632C211yesmaximal, characteristic
2C2×#16839531C211yesmaximal, characteristic
3#21443850C212yesmaximal, complemented
4#21443847C212yesmaximal, complemented
5C2×C61×#324C211yesmaximal, characteristic
6C22×#11758194—21no—
7C2×#14519756C411yescharacteristic
8#16839701C411yescharacteristic
9#16839701C2211yescharacteristic
10#16839695—21no—
11#16839695—21no—
12#16839682C411yescharacteristic
13#16839682C2211yescharacteristic
14#16839635—21no—
15#16839625—21no—
16#16839622C411yescharacteristic
17#16839531—21no—
18#16839531C2212yes—
19C22×C4⋊C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C2×#11758194—24no—
25C2×#11758194—22no—
26C2×#11758194—41no—
27C2×#11758194—42no—
28C22×#92418—41no—
29#14519756—41no—
30#14519756—41no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684C2×C411yescharacteristic
45#14519684C2×C411yescharacteristic
46C23×C4×C61C2×C411yescharacteristic
47C23×C4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C22×C8×C61—41no—
50C2×C4⋊C4×C61—41no—
51C2×C4⋊C4×C61—41no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61C2311yescharacteristic
56C22⋊C8×C61—22no—
57C22⋊C8×C61—41no—
58C24×C61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—22no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—81no—
67C22×C4×C61—81no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61SD1612yes—
72C22×C4×C61Q1612yes—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C2×Dic122—41no—
81C2×Dic122—81no—
82C2×C8×C61—42no—
83C2×C8×C61—82no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C22⋊Dic61—41no—
89C22⋊Dic61—41no—
90C22⋊Dic61—42no—
91C4⋊Dic61—41no—
92C4⋊Dic61—81no—
93#11758196—42no—
94#11758196—81no—
95#11758196—81no—
96#11758194—24no—
97#11758194—44no—
98#11758194—42no—
99C2×#92418—44no—
100C2×#92418—42no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61#9911yescharacteristic
104C23×C61#9911yescharacteristic
105C23×C61#10312yes—
106C23×C61#10412yes—
107C23×C61C2×C22⋊C411yescharacteristic
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—42no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61#10312yes—
129C2×C4×C61C2×SD1611yescharacteristic
130C2×C4×C61C2×Q1611yescharacteristic
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142Dic122—82no—
143C8×C61—82no—
144#92418—44no—
145#11722—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61#32812yes—
155C22×C61#32812yes—
156C22×C61C2×#9911yescharacteristic
157C22×C61C2×#10311yescharacteristic
158C22×C61C2×#10411yescharacteristic
159C4×C61—21no—
160C4×C61—22no—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166Dic61—81no—
167Dic61—81no—
168Dic61—81no—
169Dic61—81no—
170#2627—611no—
171C2×#343—611no—
172C2×#324D6111yescharacteristic
173#1354—612no—
174#1353—612no—
175C2×C61—21no—
176C2×C61—22no—
177C2×C61—22no—
178C2×C61—21no—
179C2×C61C2×#32811yescharacteristic
180C2×C61#212111yescharacteristic
181C2×C61#213311yescharacteristic
182C22×M16—1221no—
183C2×C22⋊Q8—611no—
184C22×C4⋊C4C2×D6111yescharacteristic
185C2×C22⋊C8—21no—
186#400—611no—
187#400—611no—
188#398—1221no—
189#398—1221no—
190#395—611no—
191#395—611no—
192#385—1221no—
193#381—1221no—
194#380—611no—
195#343—612no—
196#343—1221no—
197#324—21no—
198#324C2×D6112yes—
199C61#1172211yescharacteristic, complemented, Sylow
200C22×Q8—611no—
201C23×C4C4×D6111yescharacteristic
202C23×C4D24411yescharacteristic
203C23×C4C22⋊D6111yescharacteristic
204C2×M16—1224no—
205C2×M16—1222no—
206C2×M16—2441no—
207C2×M16—2442no—
208C22×C8—41no—
209C22×C8—2441no—
210C22⋊Q8—2441no—
211C22⋊Q8—2441no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4C4×D6111yescharacteristic
220C2×C4⋊C4D24411yescharacteristic
221C2×C4⋊C4C22⋊D6111yescharacteristic
222C2×C4⋊C4C22×D6111yescharacteristic
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C22⋊C8—22no—
226C22⋊C8—41no—
227#95—611no—
228#95—611no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235C24#1175819811yescharacteristic
236C2×Q8—4881no—
237C2×Q8—2441no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4#1175819012yes—
252C22×C4Dic24412yes—
253C22×C4#1175819811yescharacteristic
254C22×C4#1175819811yescharacteristic
255C22×C4#1175819811yescharacteristic
256C22×C4C2×C4×D6111yescharacteristic
257C22×C4C2×D24411yescharacteristic
258C22×C4C2×C22⋊D6111yescharacteristic
259M16—1224no—
260M16—2444no—
261M16—2442no—
262C2×C8—42no—
263C2×C8—82no—
264C2×C8—2442no—
265C2×C8—2444no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—4881no—
271C4⋊C4—4881no—
272C4⋊C4—4881no—
273C4⋊C4—2441no—
274C4⋊C4—2442no—
275C22⋊C4—2441no—
276C22⋊C4—2441no—
277C22⋊C4—2442no—
278C23—41no—
279C23—41no—
280C23#1451969111yescharacteristic
281C23#1451969111yescharacteristic
282C23#1451970212yes—
283C23#1451970312yes—
284C23C2×#1175819811yescharacteristic
285Q8—4882no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2442no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4#1451970212yes—
318C2×C4C2×#1175819011yescharacteristic
319C2×C4C2×Dic24411yescharacteristic
320C8—82no—
321C8—2444no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22#1683950012yes—
331C22#1683950012yes—
332C22C2×#1451969111yescharacteristic
333C22C2×#1451970211yescharacteristic
334C22C2×#1451970311yescharacteristic
335C4—21no—
336C4—22no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—4881no—
343C4—4881no—
344C4—4881no—
345C4—4881no—
346C2—21no—
347C2—21no—
348C2—22no—
349C2—22no—
350C2C2×#1683950011yescharacteristic
351C2#2144746311yescharacteristic
352C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC2×C61×#324C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenterC2×#324D61
hypocenterC61#11722
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #21443850C2semidirect
4. #21443847C2semidirect
199. C61#11722semidirect

Maximal subgroups

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

subgroupindex
#214516322
C2×#168395312
#214438502
#214438472
C2×C61×#3242
#1172261