Finite Group Databasebeta

← #30601738

Subgroups — #30601738

Order 15616.

584 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461605C211yesmaximal, characteristic, complemented
2C4×#14519844C211yesmaximal, characteristic, complemented
3C2×#16840612C212yesmaximal, complemented
4C2×#16840610C212yesmaximal
5#21448358C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420C2212yes—
8C2×#14519832—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12#16840612—24no—
13#16840610—24no—
14C2×#14519765C411yescharacteristic
15C2×#14519742C2211yescharacteristic
16C2×#14519739C2211yescharacteristic
17#16839667C411yescharacteristic
18#16839663C411yescharacteristic
19#16839651—21no—
20#16839651—21no—
21#16839609—21no—
22#16839609—21no—
23C42×Dic61C2211yescharacteristic
24C61×#382C411yescharacteristic
25C22×#92420—22no—
26C22×#92420—22no—
27#14519844—24no—
28C4⋊#92420—22no—
29C4⋊#92420D414yes—
30#14519832—42no—
31C4×#92420—22no—
32C4×#92420—22no—
33C22×Dic122C2×C411yescharacteristic
34C22×D244C2×C411yescharacteristic
35C22×C4×D61—21no—
36#14519765—22no—
37#14519765—22no—
38#14519742—22no—
39#14519742—22no—
40#14519739—22no—
41#14519739—22no—
42C2×#11758196—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61C2311yescharacteristic
55#14519684—21no—
56#14519684—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C42×C61C2×C411yescharacteristic
60#95×C61—21no—
61#95×C61—21no—
62C23×D61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—21no—
76C2×D244M1612yes—
77C2×C4×D61—42no—
78C2×C4×D61—42no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×Dic122—22no—
82C2×Dic122—22no—
83C2×Dic122—21no—
84C2×Dic122M1612yes—
85C2×#92420—24no—
86C2×#92420—24no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C2×#92420—42no—
91C4⋊C4×C61—22no—
92C4⋊C4×C61—22no—
93C42×C61—21no—
94C42×C61—21no—
95#11758198—24no—
96#11758198—24no—
97#11758198—42no—
98#11758198—42no—
99#11758198—41no—
100#11758198—41no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—22no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—41no—
109C4×Dic61—42no—
110C4×Dic61C2×D412yes—
111C4×Dic61#4112yes—
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—22no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61C4×D412yes—
133C2×C4×C61C2×M1611yescharacteristic
134C2×C4×C61C2×M1611yescharacteristic
135C2×C4×C61#13112yes—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—22no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61#10412yes—
147C2×Dic61#12112yes—
148C2×Dic61#12411yescharacteristic
149C2×Dic61#12711yescharacteristic
150C2×Dic61#13512yes—
151C2×Dic61AGL(1,ℤ/8)11yescharacteristic
152C2×Dic61#13711yescharacteristic
153D244—24no—
154D244—42no—
155C4×D61—82no—
156C4×D61—82no—
157Dic122—24no—
158Dic122—42no—
159#92420—44no—
160#92420—44no—
161#9676—611nomaximal, Sylow
162C22×C61#39011yescharacteristic
163C22×C61#40711yescharacteristic
164C22×C61#40811yescharacteristic
165C22×C61#41611yescharacteristic
166C22×C61#41711yescharacteristic
167C22×C61C2×#10411yescharacteristic
168C22×C61#42111yescharacteristic
169C2×D61—42no—
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—81no—
179C4×C61—81no—
180C4×C61#43512yes—
181C4×C61#43512yes—
182Dic61—21no—
183Dic61—21no—
184Dic61—22no—
185Dic61—42no—
186Dic61—41no—
187Dic61#46312yes—
188Dic61#46412yes—
189C4×#124—611no—
190#1767—611no—
191C4×C4⋊C8—611no—
192C2×Q8⋊C8—612no—
193C2×D4⋊C8—612no—
194C2×C61#148811yescharacteristic
195C2×C61#148911yescharacteristic
196C2×C61#149411yescharacteristic
197C2×C61#149511yescharacteristic
198C2×C61#195511yescharacteristic
199C2×C61#198011yescharacteristic
200C2×C61#198311yescharacteristic
201D61—82no—
202C2×#124—611no—
203C2×C4×Q8—611no—
204C2×C4×D4—611no—
205C2×C4⋊C8—612no—
206C2×C4⋊C8—1221no—
207C2×#97—1221no—
208C2×C4×C8—612no—
209#391—611no—
210#390—611no—
211#388—1221no—
212#388—1221no—
213#382#692311yescharacteristic
214C4×C22⋊C4—1221no—
215C4×C22⋊C4—1221no—
216C43—611no—
217#336—1221no—
218#336—1221no—
219Q8⋊C8—1224no—
220D4⋊C8—1224no—
221C61#967611yescharacteristic, complemented, Sylow
222C22×Q8—611no—
223C22×D4—611no—
224C23×C4—1221no—
225C22×C8—1222no—
226C22×C8—1222no—
227#124—1222no—
228#124—1222no—
229C4×Q8—1222no—
230C4×Q8—1222no—
231C4×D4—1222no—
232C4×D4—1222no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4C2×#692311yescharacteristic
235C2×C4⋊C4C2×#692311yescharacteristic
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—1221no—
248C2×C42C2×#692311yescharacteristic
249C4⋊C8—614no—
250C4⋊C8—1222no—
251C4⋊C8—1224no—
252#97—2442no—
253C4×C8—1222no—
254C4×C8—1222no—
255#95—21no—
256#95—21no—
257#95—1221no—
258#95—1221no—
259C24—1221no—
260C2×Q8—612no—
261C2×Q8—1221no—
262C2×Q8—1222no—
263C2×Q8—1222no—
264C2×D4—612no—
265C2×D4—1222no—
266C2×D4—1221no—
267C2×D4—1222no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—1221no—
275C22×C4—2442no—
276C22×C4—2442no—
277C22×C4—2441no—
278C22×C4—2441no—
279C22×C4C22⋊#692311yescharacteristic
280C22×C4C22⋊#692311yescharacteristic
281C22×C4C22×#692311yescharacteristic
282C2×C8—1224no—
283C2×C8—1224no—
284C2×C8—2442no—
285C2×C8—2442no—
286C2×C8—2442no—
287C2×C8—2442no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—2441no—
291C4⋊C4—2441no—
292C22⋊C4—1224no—
293C22⋊C4—1224no—
294C22⋊C4—2441no—
295C22⋊C4—2441no—
296C22⋊C4—2442no—
297C22⋊C4—2442no—
298C42—21no—
299C42—21no—
300C42—612no—
301C42—612no—
302C42—1221no—
303C42—1222no—
304C42—1222no—
305C42—1221no—
306C42—1222no—
307C42—2441no—
308C42—2442no—
309C23—1222no—
310C23—2441no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23C2×C22⋊#692311yescharacteristic
317Q8—1224no—
318Q8—2442no—
319D4—1224no—
320D4—2442no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—612no—
334C2×C4—612no—
335C2×C4—611no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—612no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1222no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—4882no—
349C2×C4—4882no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4D4×#692312yes—
353C2×C4D61⋊M1611yescharacteristic
354C2×C4D61⋊M1611yescharacteristic
355C2×C4#1451986512yes—
356C8—2444no—
357C8—2444no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—2442no—
363C22—2442no—
364C22—2442no—
365C22#1684071411yescharacteristic
366C22#1684073411yescharacteristic
367C22#1684073711yescharacteristic
368C22#1684075211yescharacteristic
369C22#1684075311yescharacteristic
370C22D61⋊#10411yescharacteristic
371C22#1684075911yescharacteristic
372C4—41no—
373C4—41no—
374C4—81no—
375C4—81no—
376C4—612no—
377C4—612no—
378C4—1222no—
379C4—1221no—
380C4—1221no—
381C4—2441no—
382C4—2442no—
383C4#1684079212yes—
384C4#1684079212yes—
385C2—4882no—
386C2#2146115211yescharacteristic
387C2#2146115611yescharacteristic
388C2#2146117311yescharacteristic
389C2#2146117711yescharacteristic
390C2#2146194511yescharacteristic
391C2#2146198411yescharacteristic
392C2#2146198711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#9676
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #21461605C2semidirect
2. C4×#14519844C2semidirect
3. C2×#16840612C2semidirect
221. C61#9676semidirect

Maximal subgroups

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

subgroupindex
#214616052
C4×#145198442
C2×#168406122
C2×#168406102
#214483582
#967661