Finite Group Databasebeta

← #30605492

Subgroups — #30605492

Order 15616.

440 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461684C211yesmaximal, characteristic
2#21461057C211yesmaximal, characteristic
3#21460820C212yesmaximal, complemented
4#21460817C212yesmaximal, complemented
5#21450996C211yesmaximal, characteristic
6#16840765—21no—
7C2×#14519837—21no—
8C2×C22⋊#92420—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519753C411yescharacteristic
13C2×#14519737C2211yescharacteristic
14#16839702C2211yescharacteristic
15#16839698C411yescharacteristic
16#16839681C2211yescharacteristic
17#16839644—21no—
18#16839638—21no—
19#16839634—21no—
20#16839621—21no—
21#95×D61C411yescharacteristic
22C61×#393C411yescharacteristic
23C2×#11758217—22no—
24C22×#92420—41no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519837—42no—
28C22⋊#92420—22no—
29C22⋊#92420—41no—
30C22×C22⋊D61D411yescharacteristic
31C23×Dic61D411yescharacteristic
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34#14519753—41no—
35#14519753—41no—
36#14519737—41no—
37#14519737—41no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196C2311yescharacteristic
43C2×C22⋊Dic61—21no—
44C2×#11758198—21no—
45C2×#11758198D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C22×Q8×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C2×Q8×C61—41no—
60C2×Q8×C61—81no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C2×C22⋊D61—41no—
66C2×C22⋊D61—41no—
67C2×C22⋊D61SD1612yes—
68C2×C22⋊D61Q1612yes—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—81no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—81no—
82C2×C4×D61—81no—
83#11758217—42no—
84#11758217—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—82no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—81no—
90C22⋊Dic61—42no—
91#11758198—41no—
92#11758198—42no—
93C4⋊Dic61—41no—
94#11758196—41no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98#11758196—81no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61#10312yes—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61#10312yes—
112Q8×C61—82no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C22⋊D61—42no—
124C22⋊D61—42no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—22no—
128C2×Dic61—21no—
129C2×Dic61—41no—
130C2×Dic61—42no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—81no—
138C2×Dic61#9911yescharacteristic
139C2×Dic61#9911yescharacteristic
140C2×Dic61C2×SD1611yescharacteristic
141C2×Dic61C2×Q1611yescharacteristic
142C4×D61—81no—
143C4×D61—81no—
144C4×D61—84no—
145#92420—82no—
146#92420—82no—
147#11906—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—22no—
151C22×C61—42no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—81no—
155C22×C61C2×#9911yescharacteristic
156C22×C61C2×#10311yescharacteristic
157C22×C61#42111yescharacteristic
158C2×D61—22no—
159C2×D61—42no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—42no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—81no—
166C4×C61—81no—
167Dic61—21no—
168Dic61—21no—
169Dic61—21no—
170Dic61—21no—
171Dic61—42no—
172Dic61—41no—
173Dic61—81no—
174#2564—611no—
175#1800—611no—
176#1459—611no—
177#1354—612no—
178#1353—612no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—42no—
182C2×C61#152011yescharacteristic
183C2×C61#212111yescharacteristic
184C2×C61#213211yescharacteristic
185D61—42no—
186C2×C22⋊Q8—611no—
187C2×C4×D4—611no—
188#423—1221no—
189C2×#100—1221no—
190C2×C22⋊C8—1221no—
191#400—611no—
192#399—611no—
193#395—611no—
194#393#692311yescharacteristic
195#387—1221no—
196#386—1221no—
197#385—1221no—
198#380—1221no—
199C2×#95—611no—
200#343—612no—
201#324—612no—
202#323—1221no—
203C61#1190611yescharacteristic, complemented, Sylow
204C22×Q8C2×#692311yescharacteristic
205C22×D4—611no—
206C23×C4—611no—
207C23×C4—611no—
208C23×C4—1221no—
209C2×M16—1222no—
210C22×C8—2441no—
211C22⋊Q8—2441no—
212C22⋊Q8—2441no—
213C4×D4—2441no—
214C4×D4—2441no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—611no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4C2×#692311yescharacteristic
225C2×C42—611no—
226C4⋊C8—2441no—
227C4⋊C8—2441no—
228#100—2442no—
229C22⋊C8—1222no—
230C22⋊C8—2441no—
231#95—21no—
232#95—611no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237#95C2×#692311yescharacteristic
238C24—611no—
239C24C22⋊#692311yescharacteristic
240C2×Q8—41no—
241C2×Q8—81no—
242C2×D4—612no—
243C2×D4—612no—
244C2×D4—2441no—
245C2×D4—2441no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—4881no—
258C22×C4—4881no—
259C22×C4—4881no—
260C22×C4—2442no—
261C22×C4—2442no—
262C22×C4C22⋊#692311yescharacteristic
263C22×C4C22×#692311yescharacteristic
264M16—2442no—
265M16—2442no—
266C2×C8—4882no—
267C2×C8—2442no—
268C2×C8—2442no—
269C4⋊C4—4881no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2442no—
275C22⋊C4—41no—
276C22⋊C4—81no—
277C22⋊C4—2441no—
278C22⋊C4—2442no—
279C22⋊C4—2442no—
280C42—1221no—
281C42—1221no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—612no—
287C23—1221no—
288C23—1221no—
289C23—2441no—
290C23—2441no—
291C23#1451984012yes—
292C23C2×C22⋊#692311yescharacteristic
293Q8—82no—
294D4—2442no—
295D4—2442no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—611no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1222no—
313C2×C4—1221no—
314C2×C4—4881no—
315C2×C4—4881no—
316C2×C4—4884no—
317C2×C4—4881no—
318C2×C4—2441no—
319C2×C4—2442no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C8—4882no—
327C8—4882no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—1222no—
336C22—2442no—
337C22—2442no—
338C22—2441no—
339C22—2441no—
340C22D61⋊#9911yescharacteristic
341C22C2×#1451984011yescharacteristic
342C22#1684075911yescharacteristic
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—1221no—
348C4—1221no—
349C4—1221no—
350C4—1221no—
351C4—4881no—
352C4—2442no—
353C4—2441no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—2442no—
358C2#2146125711yescharacteristic
359C2#2146207511yescharacteristic
360C2#2146211311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#393C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758196C23
hypercenter#393#6923
hypocenterC61#11906
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #393

Complements

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

NH ≅ G/Ntype
3. #21460820C2semidirect
4. #21460817C2semidirect
203. C61#11906semidirect

Maximal subgroups

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

subgroupindex
#214616842
#214610572
#214608202
#214608172
#214509962
#1190661