Finite Group Databasebeta

← #30605472

Subgroups — #30605472

Order 15616.

452 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461681C211yesmaximal, characteristic
2#21461057C211yesmaximal, characteristic
3#21460814C212yesmaximal, complemented
4#21460813C212yesmaximal, complemented
5#21450987C211yesmaximal, characteristic
6C2×#14519835—21no—
7C2×C22⋊#92420—21no—
8#16840704—21no—
9#16840640C2212yes—
10#16840608—21no—
11#16840606C2212yes—
12C2×#14519775C411yescharacteristic, complemented
13C2×#14519737C2211yescharacteristic
14#16839675C2211yescharacteristic
15#16839674C411yescharacteristic, complemented
16#16839673C2211yescharacteristic
17#16839662—21no—
18#16839626—21no—
19#16839621—21no—
20#16839620—21no—
21#16839613C411yescharacteristic, complemented
22C61×#393C411yescharacteristic, complemented
23C22×#92420—41no—
24C2×C4⋊#6923—41no—
25C2×C22⋊#6923—22no—
26#14519835—42no—
27C22⋊#92420—22no—
28C22⋊#92420—41no—
29(C2×#6923)⋊C4—41no—
30C22×Dic122C2×C411yescharacteristic
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519775—41no—
35#14519775—41no—
36#14519737—41no—
37#14519737—41no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196D411yescharacteristic
42C2×C22⋊Dic61—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198C2311yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
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×D61C2×D411yescharacteristic
59C22×#6923—42no—
60C2×Q8×C61—41no—
61C2×Q8×C61—81no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—41no—
67C2×C22⋊D61—41no—
68C2×C22⋊D61SD1612yes—
69C2×C22⋊D61Q1612yes—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—42no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—42no—
81C2×Dic122—41no—
82C2×Dic122—81no—
83C22⋊#6923—42no—
84C22⋊#6923—42no—
85C2×#92420—42no—
86C2×#92420—82no—
87C4⋊#6923—82no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—81no—
90C22⋊Dic61—81no—
91#11758198—41no—
92#11758198—81no—
93#11758198—81no—
94#11758196—41no—
95#11758196—42no—
96#11758196—42no—
97#11758196—41no—
98#11758196—41no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—42no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61#10312yes—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61C2×SD1611yescharacteristic
113C22×D61C2×Q1611yescharacteristic
114C2×#6923—82no—
115C2×#6923—82no—
116C2×#6923—82no—
117Q8×C61—82no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C22⋊D61—42no—
129C22⋊D61—42no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—22no—
133C2×Dic61—21no—
134C2×Dic61—42no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—81no—
143C2×Dic61#9911yescharacteristic
144C2×Dic61#9911yescharacteristic
145C2×Dic61#10312yes—
146C4×D61—42no—
147C4×D61—81no—
148Dic122—82no—
149#92420—82no—
150#11900—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—22no—
154C22×C61—42no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—81no—
158C22×C61C2×#9911yescharacteristic
159C22×C61C2×#10311yescharacteristic
160C22×C61#42111yescharacteristic
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—81no—
168#6923—162no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—81no—
172C4×C61—81no—
173Dic61—21no—
174Dic61—22no—
175Dic61—41no—
176Dic61—81no—
177Dic61—81no—
178Dic61#35412yes—
179#2563—611no—
180#1799—611no—
181#1459—611no—
182#1351—612no—
183#1351—612no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—42no—
187C2×C61#152011yescharacteristic
188C2×C61#212211yescharacteristic
189C2×C61C2×#35411yescharacteristic
190D61—41no—
191D61—41no—
192C2×C4⋊Q8—611no—
193C2×C4×D4—611no—
194C2×#99—1221no—
195C2×C22⋊C8—1221no—
196#393—611no—
197#393—611no—
198#393—611no—
199#393#692311yescharacteristic, complemented
200#390—1221no—
201#382—1221no—
202#380—1221no—
203#380—1221no—
204#380—1221no—
205C4×C4⋊C4—611no—
206#342—612no—
207#324—1221no—
208#323—612no—
209C61#1190011yescharacteristic, complemented, Sylow
210C22×Q8—611no—
211C22×Q8C2×#692311yescharacteristic
212C22×D4—611no—
213C23×C4—611no—
214C23×C4—611no—
215C22×C8—2441no—
216C4⋊Q8—2441no—
217C4⋊Q8—2441no—
218C4×D4—2441no—
219C4×D4—2441no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—2441no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—611no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1222no—
231C2×C22⋊C4C2×#692311yescharacteristic
232C2×C42—611no—
233C2×C42—1221no—
234#99—2442no—
235C22⋊C8—1222no—
236C22⋊C8—2441no—
237#95—21no—
238#95—611no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—2441no—
243#95C2×#692311yescharacteristic
244C24—611no—
245C24C22⋊#692311yescharacteristic
246C2×Q8—41no—
247C2×Q8—81no—
248C2×Q8—4881no—
249C2×Q8—2441no—
250C2×D4—612no—
251C2×D4—612no—
252C2×D4—2441no—
253C2×D4—2441no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4—2442no—
268C22×C4C22⋊#692311yescharacteristic
269C22×C4C22×#692311yescharacteristic
270C2×C8—4882no—
271C2×C8—2442no—
272C4⋊C4—4882no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2442no—
277C4⋊C4—2442no—
278C22⋊C4—41no—
279C22⋊C4—81no—
280C22⋊C4—4881no—
281C22⋊C4—4881no—
282C22⋊C4—4881no—
283C22⋊C4—2441no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C42—1221no—
287C42—1221no—
288C42—2442no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—611no—
294C23—611no—
295C23—1221no—
296C23—1221no—
297C23—2441no—
298C23—2441no—
299C23#1451984012yes—
300C23C2×C22⋊#692311yescharacteristic
301Q8—82no—
302Q8—4882no—
303D4—2442no—
304D4—2442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—612no—
318C2×C4—1222no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4—4882no—
325C2×C4—4882no—
326C2×C4—4882no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C8—4882no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—1221no—
345C22—1221no—
346C22—4881no—
347C22—2441no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22D61⋊#9911yescharacteristic
352C22C2×#1451984011yescharacteristic
353C22#1684075911yescharacteristic
354C4—41no—
355C4—41no—
356C4—81no—
357C4—81no—
358C4—612no—
359C4—1222no—
360C4—1221no—
361C4—9762no—
362C4—4881no—
363C4—4881no—
364C4—2441no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—2441no—
369C2—2441no—
370C2#2146125711yescharacteristic
371C2#2146207911yescharacteristic
372C2D61⋊#35411yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#393C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758198C23
hypercenter#393#6923
hypocenterC61#11900
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. #21460814C2semidirect
4. #21460813C2semidirect
12. C2×#14519775C4semidirect
15. #16839674C4semidirect
21. #16839613C4semidirect
22. C61×#393C4semidirect
199. #393#6923semidirect
209. C61#11900semidirect

Maximal subgroups

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

subgroupindex
#214616812
#214610572
#214608142
#214608132
#214509872
#1190061