Finite Group Databasebeta

← #30595661

Subgroups — #30595661

Order 15616.

580 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 110 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
2C2×#16840628C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454145C211yesmaximal, characteristic
6C23×#92420—21no—
7C2×C22⋊#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
23C22×#92420—24no—
24C22×#92420—22no—
25C22×#92420—22no—
26C22×#92420—42no—
27C22×#92420—42no—
28C22⋊#92420—42no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519758—42no—
32#14519758—42no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C4×Dic61—42no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C22×D4×C61—21no—
51C22×D4×C61C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53#121×C61—42no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C24×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C2×D4×C61—42no—
62C2×D4×C61—42no—
63C2×D4×C61—42no—
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—41no—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61D812yes—
80C22×Dic61SD1612yes—
81C22×Dic61C2×D411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C2×#92420—24no—
84C2×#92420—48no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—42no—
92C22⋊Dic61—42no—
93C22⋊Dic61—42no—
94C22⋊Dic61—42no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97C22⋊Dic61—42no—
98C4⋊Dic61—22no—
99C4⋊Dic61—41no—
100#11758196—42no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61#9912yes—
119C23×C61#10212yes—
120C23×C61#10412yes—
121C23×C61C2×C22⋊C411yescharacteristic
122D4×C61—82no—
123D4×C61—84no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—44no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#13112yes—
134C2×Dic61—24no—
135C2×Dic61—24no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—44no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61#10212yes—
153C2×Dic61C2×D811yescharacteristic
154C2×Dic61C2×SD1611yescharacteristic
155C2×Dic61#13512yes—
156#92420—44no—
157#92420—82no—
158#7654—611nomaximal, Sylow
159C22×C61—22no—
160C22×C61—22no—
161C22×C61—22no—
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61—81no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61#32714yes—
173C22×C61#40811yescharacteristic
174C22×C61C2×#9911yescharacteristic
175C22×C61#41311yescharacteristic
176C22×C61C2×#10211yescharacteristic
177C22×C61#41611yescharacteristic
178C22×C61C2×#10411yescharacteristic
179C22×C61#42111yescharacteristic
180C4×C61—22no—
181C4×C61—41no—
182C4×C61—81no—
183Dic61—21no—
184Dic61—22no—
185Dic61—21no—
186Dic61—22no—
187Dic61—41no—
188Dic61—81no—
189Dic61—81no—
190#2854—611no—
191#1817—611no—
192C2×#336—611no—
193#1271—612no—
194#1270—612no—
195C2×C61—24no—
196C2×C61—161no—
197C2×C61#146811yescharacteristic
198C2×C61#148011yescharacteristic
199C2×C61#149411yescharacteristic
200C2×C61C2×#32711yescharacteristic
201C2×C61#151611yescharacteristic
202C2×C61#153211yescharacteristic
203C2×C61#154011yescharacteristic
204C23×C8—1221no—
205C2×#123—1221no—
206C2×#121#692311yescharacteristic
207C22×C42—611no—
208C2×C22⋊C8—1221no—
209#390—611no—
210#390—611no—
211#389—611no—
212#389—611no—
213#388—1221no—
214#388—1221no—
215#386—1221no—
216#380—611no—
217#336—612no—
218#336—612no—
219#336—1221no—
220#336—1221no—
221C61#765411yescharacteristic, complemented, Sylow
222C22×D4—21no—
223C22×D4C2×#692311yescharacteristic
224C23×C4—611no—
225C23×C4—611no—
226C23×C4C2×#692311yescharacteristic
227C22×C8—1222no—
228C22×C8—1224no—
229C22×C8—1222no—
230C22×C8—2442no—
231C22×C8—2442no—
232#123—2442no—
233#123—2442no—
234#121—42no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4C2×#692311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—2442no—
251C22⋊C8—2442no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255C24—21no—
256C24C22⋊#692311yescharacteristic
257C2×D4—22no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—42no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—612no—
268C22×C4—612no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—1222no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—2441no—
280C22×C4C22⋊#692311yescharacteristic
281C22×C4C22×#692311yescharacteristic
282C2×C8—1224no—
283C2×C8—2442no—
284C2×C8—2442no—
285C2×C8—2442no—
286C2×C8—2442no—
287C2×C8—2442no—
288C2×C8—2448no—
289C4⋊C4—41no—
290C4⋊C4—1222no—
291C4⋊C4—2441no—
292C4⋊C4—2442no—
293C4⋊C4—2441no—
294C4⋊C4—2441no—
295C22⋊C4—42no—
296C22⋊C4—2442no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C22⋊C4—2442no—
300C22⋊C4—2442no—
301C22⋊C4—2442no—
302C42—2441no—
303C42—2441no—
304C42—2441no—
305C42—2441no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23#1451983512yes—
318C23#1451983912yes—
319C23#1451984112yes—
320C23C2×C22⋊#692311yescharacteristic
321D4—82no—
322D4—84no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—44no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—612no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—612no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1224no—
343C2×C4—1224no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—2444no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4#1451986412yes—
355C8—4882no—
356C8—2444no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22#1684061314yes—
371C22#1684073511yescharacteristic
372C22C2×#1451983511yescharacteristic
373C22#1684074911yescharacteristic
374C22C2×#1451983911yescharacteristic
375C22#1684075211yescharacteristic
376C22C2×#1451984111yescharacteristic
377C22#1684075911yescharacteristic
378C4—22no—
379C4—41no—
380C4—81no—
381C4—1221no—
382C4—1222no—
383C4—1221no—
384C4—1222no—
385C4—4881no—
386C4—4881no—
387C4—2441no—
388C2—24no—
389C2—161no—
390C2#2146108411yescharacteristic
391C2#2146112411yescharacteristic
392C2#2146117011yescharacteristic
393C2C2×#1684061311yescharacteristic
394C2#2146124511yescharacteristic
395C2#2146129511yescharacteristic
396C2#2146131711yescharacteristic
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#7654
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. #21461710C2semidirect
2. C2×#16840628C2semidirect
3. #21460638C2semidirect
4. #21460635C2semidirect
221. C61#7654semidirect

Maximal subgroups

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

subgroupindex
#214617102
C2×#168406282
#214606382
#214606352
#214541452
#765461