Finite Group Databasebeta

← #30605409

Subgroups — #30605409

Order 15616.

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

normal subgroups only

This group has 460 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#21461684C211yesmaximal, characteristic
2#21461057C211yesmaximal, characteristic
3#21460804C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#21450120C211yesmaximal, characteristic
6#16840765—21no—
7C2×#14519837—21no—
8C2×C22⋊#92420—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519759—21no—
13C2×#14519737C2211yescharacteristic
14C2×C4⋊C4×D61C411yescharacteristic
15#16839694C2211yescharacteristic
16#16839693C2211yescharacteristic
17#16839687C411yescharacteristic
18#16839659—21no—
19#16839624—21no—
20#16839621C411yescharacteristic
21#16839620—21no—
22C61×#397C411yescharacteristic
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#14519759—42no—
35#14519759—42no—
36#14519737—41no—
37#14519737—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196C2311yescharacteristic
44C4⋊C4×D61—41no—
45C4⋊C4×D61—41no—
46C2×C22⋊Dic61—21no—
47C2×#11758198—21no—
48C2×#11758198D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61C2×C411yescharacteristic
59C24×C61C22⋊C411yescharacteristic
60C23×D61C22⋊C411yescharacteristic
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⋊D61D812yes—
68C2×C22⋊D61SD1612yes—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—42no—
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—42no—
82C2×C4×D61—42no—
83#11758217—42no—
84#11758217—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—82no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—42no—
91C22⋊Dic61—42no—
92#11758198—41no—
93#11758198—42no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97#11758196—41no—
98#11758196—42no—
99#11758196—41no—
100#11758196—41no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61#10212yes—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61#10212yes—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C22⋊D61—42no—
127C22⋊D61—42no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—22no—
131C2×Dic61—21no—
132C2×Dic61—42no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—81no—
141C2×Dic61#9911yescharacteristic
142C2×Dic61#9911yescharacteristic
143C2×Dic61C2×D811yescharacteristic
144C2×Dic61C2×SD1611yescharacteristic
145C4×D61—42no—
146C4×D61—42no—
147C4×D61—84no—
148#92420—82no—
149#92420—82no—
150#11881—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×#10211yescharacteristic
160C22×C61#42111yescharacteristic
161C2×D61—22no—
162C2×D61—42no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—42no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—81no—
169C4×C61—81no—
170Dic61—21no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—81no—
175Dic61—81no—
176Dic61#35212yes—
177#2486—611no—
178#1800—611no—
179#1459—611no—
180#1346—612no—
181#1346—612no—
182C2×C61—21no—
183C2×C61—21no—
184C2×C61—42no—
185C2×C61#151911yescharacteristic
186C2×C61C2×#35211yescharacteristic
187C2×C61#213511yescharacteristic
188D61—42no—
189C2×#123—1221no—
190C2×C4×D4—611no—
191C22×C4⋊C4—611no—
192#423—1221no—
193C2×#100—1221no—
194C2×C22⋊C8—1221no—
195#398—611no—
196#398—611no—
197#397—611no—
198#397#692311yescharacteristic
199#389—1221no—
200#381—1221no—
201#380—611no—
202#380—1221no—
203#343—612no—
204#324—612no—
205#323—1221no—
206C61#1188111yescharacteristic, complemented, Sylow
207C22×D4—611no—
208C23×C4—611no—
209C23×C4—611no—
210C23×C4—1221no—
211C2×M16—1222no—
212C22×C8—2441no—
213#123—2442no—
214#123—2442no—
215C4×D4—2441no—
216C4×D4—2441no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—2441no—
224C2×C4⋊C4—2441no—
225C2×C4⋊C4C2×#692311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—611no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4C2×#692311yescharacteristic
231C2×C42—611no—
232C4⋊C8—2441no—
233C4⋊C8—2441no—
234#100—2442no—
235C22⋊C8—1222no—
236C22⋊C8—2441no—
237#95—21no—
238#95—611no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95C2×#692311yescharacteristic
243C24—611no—
244C24C22⋊#692311yescharacteristic
245C2×D4—612no—
246C2×D4—612no—
247C2×D4—2441no—
248C2×D4—2441no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—2442no—
261C22×C4—2442no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4—2442no—
265C22×C4C22⋊#692311yescharacteristic
266C22×C4C22×#692311yescharacteristic
267M16—2442no—
268M16—2442no—
269C2×C8—4882no—
270C2×C8—2442no—
271C2×C8—2442no—
272C4⋊C4—41no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2442no—
282C22⋊C4—41no—
283C22⋊C4—42no—
284C22⋊C4—2441no—
285C22⋊C4—2442no—
286C22⋊C4—2442no—
287C42—1221no—
288C42—1221no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—612no—
294C23—1221no—
295C23—1221no—
296C23—2441no—
297C23—2441no—
298C23#1451983912yes—
299C23C2×C22⋊#692311yescharacteristic
300D4—2442no—
301D4—2442no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—1222no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—4884no—
321C2×C4—4881no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C8—4882no—
333C8—4882no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—1222no—
342C22—2442no—
343C22—2442no—
344C22—2441no—
345C22—2441no—
346C22D61⋊#9911yescharacteristic
347C22C2×#1451983911yescharacteristic
348C22#1684075911yescharacteristic
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—612no—
354C4—1221no—
355C4—1221no—
356C4—1221no—
357C4—4881no—
358C4—4881no—
359C4—2441no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—2442no—
364C2#2146125411yescharacteristic
365C2D61⋊#35211yescharacteristic
366C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758196C23
hypercenter#397#6923
hypocenterC61#11881
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #21460804C2semidirect
4. #21460803C2semidirect
206. C61#11881semidirect

Maximal subgroups

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

subgroupindex
#214616842
#214610572
#214608042
#214608032
#214501202
#1188161