Finite Group Databasebeta

← #30595821

Subgroups — #30595821

Order 15616.

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

normal subgroups only

This group has 532 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#21461673C211yesmaximal, characteristic, complemented
2#21461545C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454145C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9C2×#14519832—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519758—21no—
13C22×C4×Dic61C2211yescharacteristic
14#16839665C411yescharacteristic
15#16839665C2211yescharacteristic
16#16839658C411yescharacteristic
17#16839658C2211yescharacteristic
18#16839650—21no—
19#16839650—21no—
20#16839642—21no—
21#16839622C411yescharacteristic
22C2×#121×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C22⋊#92420—24no—
27C22⋊#92420—42no—
28#14519832—42no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519758—44no—
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×D4×C61—21no—
50C22×D4×C61C2×C411yescharacteristic
51C23×C4×C61C2×C411yescharacteristic
52#121×C61—42no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C24×C61—21no—
56C24×C61C22⋊C411yescharacteristic
57C2×D4×C61—22no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C2×D4×C61—42no—
61C2×D4×C61—42no—
62C2×D4×C61—42no—
63C22×C4×C61—22no—
64C22×C4×C61—22no—
65C22×C4×C61—21no—
66C22×C4×C61—41no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—22no—
70C22×Dic61—21no—
71C22×Dic61—22no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×#92420—24no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—42no—
90C22⋊Dic61—42no—
91C22⋊Dic61—42no—
92C22⋊Dic61—42no—
93C22⋊Dic61—41no—
94C22⋊Dic61—42no—
95C22⋊Dic61—41no—
96C4⋊Dic61—22no—
97C4⋊Dic61—41no—
98#11758196—42no—
99#11758196—42no—
100C4×Dic61—22no—
101C4×Dic61—22no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61#10412yes—
118C23×C61C2×C22⋊C411yescharacteristic
119D4×C61—82no—
120D4×C61—84no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—44no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61#9912yes—
130C2×C4×C61#13112yes—
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—21no—
140C2×Dic61—21no—
141C2×Dic61—44no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61AGL(1,ℤ/8)11yescharacteristic
151C2×Dic61AGL(1,ℤ/8)12yes—
152C2×Dic61#13711yescharacteristic
153#92420—44no—
154#92420—82no—
155#7698—611nomaximal, Sylow
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61#40811yescharacteristic
171C22×C61C2×#9911yescharacteristic
172C22×C61#41311yescharacteristic
173C22×C61#41711yescharacteristic
174C22×C61#41811yescharacteristic
175C22×C61C2×#10411yescharacteristic
176C22×C61#42111yescharacteristic
177C4×C61—22no—
178C4×C61—22no—
179C4×C61—81no—
180Dic61—22no—
181Dic61—21no—
182Dic61—21no—
183Dic61—41no—
184Dic61—41no—
185Dic61—81no—
186Dic61—81no—
187#2854—611no—
188#1797—611no—
189#1749—611no—
190#1271—612no—
191#1270—612no—
192C2×C61—42no—
193C2×C61—161no—
194C2×C61#146811yescharacteristic
195C2×C61#148311yescharacteristic
196C2×C61#149611yescharacteristic
197C2×C61#150711yescharacteristic
198C2×C61#151311yescharacteristic
199C2×C61#153211yescharacteristic
200C2×C61#155711yescharacteristic
201C2×#123—1221no—
202C2×#121#692311yescharacteristic
203C22×C42—611no—
204C2×C4⋊C8—1221no—
205C2×C22⋊C8—1221no—
206C2×C22⋊C8—1221no—
207C2×#97—1221no—
208#390—611no—
209#390—611no—
210#389—611no—
211#389—611no—
212#388—1221no—
213#388—1221no—
214#386—1221no—
215#380—611no—
216#336—612no—
217#336—612no—
218C61#769811yescharacteristic, complemented, Sylow
219C22×D4—21no—
220C22×D4C2×#692311yescharacteristic
221C23×C4—611no—
222C23×C4—611no—
223C23×C4C2×#692311yescharacteristic
224C22×C8—1222no—
225C22×C8—1222no—
226#123—2444no—
227#121—42no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4C2×#692311yescharacteristic
233C2×C22⋊C4—21no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—2442no—
244C4⋊C8—2442no—
245C22⋊C8—1224no—
246C22⋊C8—2442no—
247#97—2442no—
248#95—1221no—
249#95—1221no—
250#95—1221no—
251C24—21no—
252C24C22⋊#692311yescharacteristic
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—42no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1222no—
269C22×C4—1221no—
270C22×C4—1222no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4C22⋊#692311yescharacteristic
277C22×C4C22×#692311yescharacteristic
278C2×C8—1224no—
279C2×C8—2442no—
280C2×C8—2442no—
281C2×C8—2442no—
282C2×C8—2442no—
283C2×C8—2442no—
284C4⋊C4—41no—
285C4⋊C4—1222no—
286C4⋊C4—2441no—
287C4⋊C4—2442no—
288C4⋊C4—2442no—
289C22⋊C4—42no—
290C22⋊C4—2442no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2442no—
296C42—1222no—
297C42—1222no—
298C42—2441no—
299C42—2441no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#1451984112yes—
314C23C2×C22⋊#692311yescharacteristic
315D4—82no—
316D4—84no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—44no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—612no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—2444no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4#1451983512yes—
348C2×C4#1451986412yes—
349C8—4882no—
350C8—2444no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22#1684073511yescharacteristic
366C22C2×#1451983511yescharacteristic
367C22#1684074911yescharacteristic
368C22#1684075311yescharacteristic
369C22#1684075411yescharacteristic
370C22C2×#1451984111yescharacteristic
371C22#1684075911yescharacteristic
372C4—22no—
373C4—22no—
374C4—81no—
375C4—1222no—
376C4—1221no—
377C4—1221no—
378C4—4881no—
379C4—4881no—
380C4—2441no—
381C4—2441no—
382C2—42no—
383C2—161no—
384C2#2146108411yescharacteristic
385C2#2146113411yescharacteristic
386C2#2146117811yescharacteristic
387C2#2146121511yescharacteristic
388C2#2146123411yescharacteristic
389C2#2146129511yescharacteristic
390C2#2146135111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#121×C61C4
socleC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#121#6923
hypocenterC61#7698
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #21461673C2semidirect
2. #21461545C2semidirect
3. #21460638C2semidirect
4. #21460635C2semidirect
218. C61#7698semidirect

Maximal subgroups

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

subgroupindex
#214616732
#214615452
#214606382
#214606352
#214541452
#769861