Finite Group Databasebeta

← #30595736

Subgroups — #30595736

Order 15616.

550 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461546C211yesmaximal, characteristic, complemented
2C4×#14519834C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21454152C211yesmaximal, characteristic
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×#14519832—21no—
9C2×C4×#92420—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519762—21no—
13C2×#14519752C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839664C411yescharacteristic
16#16839663C2211yescharacteristic
17#16839658C2211yescharacteristic
18#16839652—21no—
19#16839651—21no—
20#16839640—21no—
21#16839619C411yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26#14519834—24no—
27#14519832—42no—
28C4×#92420—42no—
29C22×D244—21no—
30C22×D244C2×C411yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519762—44no—
35#14519752—42no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47C42×D61—42no—
48#14519684—21no—
49#14519684—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C42×C61C2×C411yescharacteristic
54#95×C61—21no—
55C23×D61—21no—
56C23×D61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×D244—22no—
67C2×D244—41no—
68C2×D244—41no—
69C2×D244—42no—
70C2×D244—42no—
71C2×D244—42no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×#92420—24no—
82C2×#92420—24no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61—41no—
91#11758198—42no—
92#11758198—42no—
93#11758198—42no—
94#11758198—42no—
95#11758198—42no—
96#11758198—42no—
97C4⋊Dic61—22no—
98#11758196—42no—
99C4×Dic61—22no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C23×C61C2×C22⋊C411yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61#10412yes—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61#10412yes—
131C2×C4×C61#13112yes—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61#9912yes—
142C2×Dic61#13512yes—
143C2×Dic61AGL(1,ℤ/8)12yes—
144D244—82no—
145D244—84no—
146C4×D61—44no—
147C4×D61—44no—
148C4×D61—44no—
149#92420—44no—
150#92420—44no—
151#7674—611nomaximal, Sylow
152C22×C61#40811yescharacteristic
153C22×C61C2×#9911yescharacteristic
154C22×C61#41311yescharacteristic
155C22×C61#41611yescharacteristic
156C22×C61#41811yescharacteristic
157C22×C61C2×#10411yescharacteristic
158C22×C61C2×#10411yescharacteristic
159C2×D61—22no—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—41no—
176C4×C61—81no—
177C4×C61—81no—
178Dic61—22no—
179Dic61—22no—
180Dic61—22no—
181Dic61—81no—
182#2854—611no—
183#1749—611no—
184C4×C22⋊C8—611no—
185#1271—612no—
186#1270—612no—
187C2×C61#146811yescharacteristic
188C2×C61#148411yescharacteristic
189C2×C61#149411yescharacteristic
190C2×C61#150111yescharacteristic
191C2×C61#150711yescharacteristic
192C2×C61#152411yescharacteristic
193C2×C61#155311yescharacteristic
194D61—42no—
195D61—161no—
196C2×#123—1221no—
197C2×#121—611no—
198C22×C42—611no—
199C2×C22⋊C8—1221no—
200C2×C22⋊C8—1221no—
201C2×#97—1221no—
202C2×C4×C8—1221no—
203#390—611no—
204#390—611no—
205#389—611no—
206#389#692311yescharacteristic
207#388—1221no—
208#388—1221no—
209#386—1221no—
210#380—611no—
211#336—612no—
212#336—612no—
213C61#767411yescharacteristic, complemented, Sylow
214C22×D4—611no—
215C22×D4—1221no—
216C23×C4—611no—
217C23×C4—611no—
218C23×C4—611no—
219C22×C8—1222no—
220C22×C8—1222no—
221#123—2444no—
222#121—2442no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4C2×#692311yescharacteristic
227C2×C4⋊C4C2×#692311yescharacteristic
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—2442no—
238C2×C42C2×#692311yescharacteristic
239C22⋊C8—1224no—
240C22⋊C8—1224no—
241#97—2442no—
242C4×C8—2442no—
243#95—21no—
244#95—1221no—
245#95—1221no—
246C24—611no—
247C24—1221no—
248C2×D4—1222no—
249C2×D4—2441no—
250C2×D4—2441no—
251C2×D4—2442no—
252C2×D4—2442no—
253C2×D4—2442no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4—1221no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4C22⋊#692311yescharacteristic
270C22×C4C22⋊#692311yescharacteristic
271C22×C4C22×#692311yescharacteristic
272C2×C8—1224no—
273C2×C8—1224no—
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2442no—
277C2×C8—2442no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—1222no—
282C4⋊C4—2442no—
283C22⋊C4—2442no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C22⋊C4—2442no—
287C22⋊C4—2442no—
288C22⋊C4—2442no—
289C42—41no—
290C42—1222no—
291C42—1222no—
292C42—2441no—
293C23—612no—
294C23—1221no—
295C23—1221no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23—2441no—
301C23—2441no—
302C23—2441no—
303C23—2441no—
304C23—2441no—
305C23—2441no—
306C23—2441no—
307C23C2×C22⋊#692311yescharacteristic
308D4—4882no—
309D4—4884no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—612no—
324C2×C4—612no—
325C2×C4—612no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—2444no—
333C2×C4—2444no—
334C2×C4—2444no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4#1451984212yes—
339C2×C4#1451986512yes—
340C8—2444no—
341C8—2444no—
342C22—1222no—
343C22—1222no—
344C22—1222no—
345C22—4881no—
346C22—4881no—
347C22—4881no—
348C22—4881no—
349C22—4881no—
350C22—4881no—
351C22—4881no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22#1684073711yescharacteristic
357C22D61⋊#9911yescharacteristic
358C22#1684074811yescharacteristic
359C22#1684075211yescharacteristic
360C22#1684075411yescharacteristic
361C22D61⋊#10411yescharacteristic
362C22C2×#1451984211yescharacteristic
363C4—22no—
364C4—22no—
365C4—41no—
366C4—81no—
367C4—81no—
368C4—1222no—
369C4—1222no—
370C4—1222no—
371C4—4881no—
372C2—9761no—
373C2—2442no—
374C2#2146108711yescharacteristic
375C2#2146114011yescharacteristic
376C2#2146117311yescharacteristic
377C2#2146119711yescharacteristic
378C2#2146121411yescharacteristic
379C2#2146127111yescharacteristic
380C2#2146134211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7674
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #21461546C2semidirect
2. C4×#14519834C2semidirect
3. #21460638C2semidirect
4. #21460636C2semidirect
213. C61#7674semidirect

Maximal subgroups

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

subgroupindex
#214615462
C4×#145198342
#214606382
#214606362
#214541522
#767461