Finite Group Databasebeta

← #30595749

Subgroups — #30595749

Order 15616.

630 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461482C211yesmaximal, characteristic, complemented
2C2×#16840628C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454145C211yesmaximal, characteristic
6C22×#11758217—21no—
7C23×#92420—21no—
8#16840628—21no—
9#16840628—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
23C2×#11758217—24no—
24C2×#11758217—42no—
25C2×#11758217—42no—
26C22×#92420—24no—
27C22×#92420—22no—
28C22×#92420—22no—
29C22×#92420—42no—
30C22×#92420—42no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519758—42no—
34#14519758—42no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52C22×D4×C61—21no—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61C2×C411yescharacteristic
55#121×C61—42no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C24×C61—21no—
59C24×C61C22⋊C411yescharacteristic
60C2×D4×C61—22no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C2×D4×C61—42no—
64C2×D4×C61—42no—
65C2×D4×C61—42no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—22no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61D812yes—
83C22×Dic61SD1612yes—
84C22×Dic61C2×D411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86#11758217—48no—
87C2×#92420—24no—
88C2×#92420—24no—
89C2×#92420—48no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C4⋊C4×C61—41no—
95C22⋊C4×C61—42no—
96C22⋊Dic61—42no—
97C22⋊Dic61—42no—
98C22⋊Dic61—42no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103C4⋊Dic61—22no—
104C4⋊Dic61—41no—
105#11758196—42no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—41no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C4×Dic61—41no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61—41no—
122C23×C61—41no—
123C23×C61#9912yes—
124C23×C61#10212yes—
125C23×C61#10412yes—
126C23×C61C2×C22⋊C411yescharacteristic
127D4×C61—82no—
128D4×C61—84no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—44no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61#13112yes—
139C2×Dic61—24no—
140C2×Dic61—24no—
141C2×Dic61—24no—
142C2×Dic61—24no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#10212yes—
158C2×Dic61#10412yes—
159C2×Dic61C2×D811yescharacteristic
160C2×Dic61C2×SD1611yescharacteristic
161C2×Dic61AGL(1,ℤ/8)11yescharacteristic
162C2×Dic61#13711yescharacteristic
163#92420—44no—
164#92420—44no—
165#7678—611nomaximal, Sylow
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—22no—
170C22×C61—22no—
171C22×C61—22no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61—81no—
179C22×C61#32714yes—
180C22×C61#40811yescharacteristic
181C22×C61C2×#9911yescharacteristic
182C22×C61#41311yescharacteristic
183C22×C61C2×#10211yescharacteristic
184C22×C61#41711yescharacteristic
185C22×C61C2×#10411yescharacteristic
186C22×C61C2×#10411yescharacteristic
187C4×C61—22no—
188C4×C61—41no—
189C4×C61—81no—
190Dic61—21no—
191Dic61—22no—
192Dic61—21no—
193Dic61—21no—
194Dic61—22no—
195Dic61—21no—
196Dic61—81no—
197Dic61—81no—
198#2854—611no—
199#1728—611no—
200C2×#336—611no—
201#1271—612no—
202#1270—612no—
203C2×C61—24no—
204C2×C61—161no—
205C2×C61#146811yescharacteristic
206C2×C61#148311yescharacteristic
207C2×C61#149211yescharacteristic
208C2×C61C2×#32711yescharacteristic
209C2×C61#150411yescharacteristic
210C2×C61#152411yescharacteristic
211C2×C61#154711yescharacteristic
212C22×M16—1221no—
213C23×C8—1221no—
214C2×#123—1221no—
215C2×#121#692311yescharacteristic
216C22×C42—611no—
217#390—611no—
218#390—611no—
219#389—611no—
220#389—611no—
221#388—1221no—
222#388—1221no—
223#386—1221no—
224#380—611no—
225#336—612no—
226#336—612no—
227#336—1221no—
228#336—1221no—
229C61#767811yescharacteristic, complemented, Sylow
230C22×D4—21no—
231C22×D4C2×#692311yescharacteristic
232C23×C4—611no—
233C23×C4—611no—
234C23×C4C2×#692311yescharacteristic
235C2×M16—1224no—
236C2×M16—2442no—
237C2×M16—2442no—
238C22×C8—1222no—
239C22×C8—1222no—
240C22×C8—1224no—
241C22×C8—2442no—
242C22×C8—2442no—
243#123—2442no—
244#123—2442no—
245#121—42no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4C2×#692311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4—1221no—
257C2×C42—611no—
258C2×C42—611no—
259C2×C42—611no—
260C2×C42—611no—
261C2×C42—2442no—
262#95—1221no—
263#95—1221no—
264#95—1221no—
265C24—21no—
266C24C22⋊#692311yescharacteristic
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—1222no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1222no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4C22⋊#692311yescharacteristic
292C22×C4C22×#692311yescharacteristic
293M16—2448no—
294C2×C8—1224no—
295C2×C8—1224no—
296C2×C8—2442no—
297C2×C8—2442no—
298C2×C8—2448no—
299C2×C8—2442no—
300C2×C8—2442no—
301C4⋊C4—41no—
302C4⋊C4—1222no—
303C4⋊C4—2441no—
304C4⋊C4—2442no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C22⋊C4—42no—
308C22⋊C4—2442no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2441no—
313C22⋊C4—2442no—
314C22⋊C4—2442no—
315C42—2441no—
316C42—2441no—
317C42—2441no—
318C42—2441no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23#1451983512yes—
331C23#1451983912yes—
332C23#1451984112yes—
333C23C2×C22⋊#692311yescharacteristic
334D4—82no—
335D4—84no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—44no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—612no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—612no—
351C2×C4—1224no—
352C2×C4—1224no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1224no—
362C2×C4—1224no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4#1451986412yes—
370C8—2444no—
371C8—2444no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22#1684061314yes—
386C22#1684073511yescharacteristic
387C22C2×#1451983511yescharacteristic
388C22#1684074911yescharacteristic
389C22C2×#1451983911yescharacteristic
390C22#1684075311yescharacteristic
391C22C2×#1451984111yescharacteristic
392C22D61⋊#10411yescharacteristic
393C4—22no—
394C4—41no—
395C4—81no—
396C4—1221no—
397C4—1222no—
398C4—1221no—
399C4—1221no—
400C4—1222no—
401C4—1221no—
402C4—4881no—
403C4—4881no—
404C2—24no—
405C2—161no—
406C2#2146108411yescharacteristic
407C2#2146113411yescharacteristic
408C2#2146116411yescharacteristic
409C2C2×#1684061311yescharacteristic
410C2#2146120511yescharacteristic
411C2#2146127011yescharacteristic
412C2#2146133111yescharacteristic
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#7678
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. #21461482C2semidirect
2. C2×#16840628C2semidirect
3. #21460638C2semidirect
4. #21460635C2semidirect
229. C61#7678semidirect

Maximal subgroups

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

subgroupindex
#214614822
C2×#168406282
#214606382
#214606352
#214541452
#767861