Finite Group Databasebeta

← #30595895

Subgroups — #30595895

Order 15616.

506 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461710C211yesmaximal, characteristic, complemented
2#21461709C211yesmaximal, characteristic, complemented
3#21460637C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21454151C211yesmaximal, characteristic
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519761—21no—
13C2×#14519751C411yescharacteristic
14C22×C4×Dic61C2211yescharacteristic
15#16839663C411yescharacteristic
16#16839663C2211yescharacteristic
17#16839661C411yescharacteristic
18#16839661C2211yescharacteristic
19#16839654—21no—
20#16839654—21no—
21#16839639—21no—
22C61×#380C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C22⋊#92420—42no—
26C22⋊#92420—42no—
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519761—44no—
32#14519751—42no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48C23×C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61—21no—
52#95×C61—21no—
53C24×C61C22⋊C411yescharacteristic
54C23×D61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—41no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C2×C22⋊D61—42no—
63C2×C22⋊D61—42no—
64C2×C22⋊D61—42no—
65C22×Dic61—22no—
66C22×Dic61—22no—
67C22×Dic61—22no—
68C22×Dic61—22no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×D244—22no—
77C2×D244—41no—
78C2×D244—41no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—22no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88#11758198—42no—
89#11758198—42no—
90#11758198—42no—
91#11758198—42no—
92#11758198—42no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96C4×Dic61—41no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61#9912yes—
107C23×C61C2×C22⋊C411yescharacteristic
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—44no—
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#13112yes—
128C22⋊D61—84no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—44no—
140C2×Dic61—44no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#13512yes—
145C2×Dic61AGL(1,ℤ/8)12yes—
146D244—82no—
147#92420—82no—
148#92420—82no—
149#7718—611nomaximal, Sylow
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61#40811yescharacteristic
158C22×C61C2×#9911yescharacteristic
159C22×C61#41311yescharacteristic
160C22×C61#41611yescharacteristic
161C22×C61#41811yescharacteristic
162C22×C61#42111yescharacteristic
163C22×C61#42111yescharacteristic
164C2×D61—81no—
165C2×D61—81no—
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—22no—
172C4×C61—41no—
173C4×C61—81no—
174C4×C61—81no—
175Dic61—22no—
176Dic61—22no—
177Dic61—41no—
178Dic61—41no—
179Dic61—81no—
180#2854—611no—
181#1817—611no—
182#1817—611no—
183#1271—612no—
184#1270—612no—
185C2×C61—42no—
186C2×C61#146811yescharacteristic
187C2×C61#148211yescharacteristic
188C2×C61#149611yescharacteristic
189C2×C61#151011yescharacteristic
190C2×C61#151611yescharacteristic
191C2×C61#153511yescharacteristic
192C2×C61#155311yescharacteristic
193D61—161no—
194C2×#123—1221no—
195C2×#121—611no—
196C22×C42—611no—
197C2×C22⋊C8—1221no—
198C2×C22⋊C8—1221no—
199#390—611no—
200#390—611no—
201#389—611no—
202#389—611no—
203#388—1221no—
204#388—1221no—
205#386—1221no—
206#380#692311yescharacteristic
207#336—612no—
208#336—612no—
209#336—1221no—
210#336—1221no—
211C61#771811yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C22×D4—1221no—
214C23×C4—611no—
215C23×C4—611no—
216C23×C4C2×#692311yescharacteristic
217C22×C8—1222no—
218C22×C8—1222no—
219#123—2444no—
220#121—2442no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4C2×#692311yescharacteristic
225C2×C4⋊C4C2×#692311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—2442no—
237C22⋊C8—2442no—
238C22⋊C8—2442no—
239#95—21no—
240#95—1221no—
241#95—1221no—
242C24—1221no—
243C24C22⋊#692311yescharacteristic
244C2×D4—1222no—
245C2×D4—2441no—
246C2×D4—2441no—
247C2×D4—2442no—
248C2×D4—2442no—
249C2×D4—2442no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—1221no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4C22⋊#692311yescharacteristic
267C22×C4C22×#692311yescharacteristic
268C2×C8—2442no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C2×C8—2442no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—2441no—
277C4⋊C4—2442no—
278C4⋊C4—2442no—
279C22⋊C4—42no—
280C22⋊C4—2442no—
281C22⋊C4—2442no—
282C22⋊C4—2442no—
283C22⋊C4—2442no—
284C22⋊C4—2442no—
285C42—2441no—
286C42—2441no—
287C42—2441no—
288C42—2441no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—2441no—
296C23—2441no—
297C23—2441no—
298C23—2441no—
299C23—2441no—
300C23—2441no—
301C23—2441no—
302C23#1451983612yes—
303C23C2×C22⋊#692311yescharacteristic
304D4—4882no—
305D4—4884no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—612no—
319C2×C4—612no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—2444no—
331C2×C4—2444no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4#1451986412yes—
336C8—4882no—
337C8—4882no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—4881no—
346C22—4881no—
347C22—4881no—
348C22—4881no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22#1684073511yescharacteristic
353C22C2×#1451983611yescharacteristic
354C22#1684074911yescharacteristic
355C22#1684075211yescharacteristic
356C22#1684075411yescharacteristic
357C22#1684075911yescharacteristic
358C22#1684076111yescharacteristic
359C4—22no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—1222no—
364C4—1222no—
365C4—4881no—
366C4—2441no—
367C4—2441no—
368C2—42no—
369C2—9761no—
370C2#2146108611yescharacteristic
371C2#2146113211yescharacteristic
372C2#2146117811yescharacteristic
373C2#2146122611yescharacteristic
374C2#2146124711yescharacteristic
375C2#2146130611yescharacteristic
376C2#2146134311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7718
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #21461710C2semidirect
2. #21461709C2semidirect
3. #21460637C2semidirect
4. #21460636C2semidirect
211. C61#7718semidirect

Maximal subgroups

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

subgroupindex
#214617102
#214617092
#214606372
#214606362
#214541512
#771861