Finite Group Databasebeta

← #30595877

Subgroups — #30595877

Order 15616.

526 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461675C211yesmaximal, characteristic, complemented
2#21461673C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454145C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420—21no—
8C2×C22⋊#92420—21no—
9C2×C22⋊#92420—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—
25#14519844—42no—
26C4⋊#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—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61D812yes—
81C22×Dic61SD1612yes—
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C2×#92420—42no—
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—41no—
98C22⋊Dic61—41no—
99C4⋊Dic61—22no—
100C4⋊Dic61—41no—
101#11758196—42no—
102#11758196—41no—
103#11758196—41no—
104C4×Dic61—22no—
105C4×Dic61—22no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61—41no—
121C23×C61#10212yes—
122C23×C61C2×C22⋊C411yescharacteristic
123D4×C61—82no—
124D4×C61—84no—
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#9912yes—
134C2×C4×C61#13112yes—
135C2×Dic61—21no—
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—42no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61#10212yes—
155C2×Dic61C2×D811yescharacteristic
156C2×Dic61C2×SD1611yescharacteristic
157C2×Dic61AGL(1,ℤ/8)11yescharacteristic
158C2×Dic61#13711yescharacteristic
159#92420—82no—
160#92420—82no—
161#7714—611nomaximal, Sylow
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—81no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61#40811yescharacteristic
177C22×C61C2×#9911yescharacteristic
178C22×C61#41311yescharacteristic
179C22×C61C2×#10211yescharacteristic
180C22×C61#41711yescharacteristic
181C22×C61#42111yescharacteristic
182C22×C61#42111yescharacteristic
183C4×C61—22no—
184C4×C61—22no—
185C4×C61—81no—
186Dic61—21no—
187Dic61—21no—
188Dic61—21no—
189Dic61—22no—
190Dic61—21no—
191Dic61—41no—
192Dic61—81no—
193Dic61—81no—
194#2854—611no—
195#1797—611no—
196#1797—611no—
197#1271—612no—
198#1270—612no—
199C2×C61—42no—
200C2×C61—161no—
201C2×C61#146811yescharacteristic
202C2×C61#148011yescharacteristic
203C2×C61#149511yescharacteristic
204C2×C61#151311yescharacteristic
205C2×C61#151911yescharacteristic
206C2×C61#153511yescharacteristic
207C2×C61#154711yescharacteristic
208C2×#123—1221no—
209C2×#121#692311yescharacteristic
210C22×C42—611no—
211C2×C4⋊C8—1221no—
212C2×C4⋊C8—1221no—
213C2×C22⋊C8—1221no—
214C2×C22⋊C8—1221no—
215#390—611no—
216#390—611no—
217#389—611no—
218#389—611no—
219#388—1221no—
220#388—1221no—
221#386—1221no—
222#380—611no—
223#336—612no—
224#336—612no—
225C61#771411yescharacteristic, complemented, Sylow
226C22×D4—21no—
227C22×D4C2×#692311yescharacteristic
228C23×C4—611no—
229C23×C4—611no—
230C23×C4C2×#692311yescharacteristic
231C22×C8—1222no—
232C22×C8—1222no—
233#123—2442no—
234#123—2442no—
235#121—42no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C2×#692311yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—2442no—
252C4⋊C8—2442no—
253C4⋊C8—2442no—
254C22⋊C8—2442no—
255C22⋊C8—2442no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259C24—21no—
260C24C22⋊#692311yescharacteristic
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—42no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—611no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4—2441no—
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287C2×C8—2442no—
288C2×C8—2442no—
289C2×C8—2442no—
290C2×C8—2442no—
291C2×C8—2442no—
292C2×C8—2442no—
293C4⋊C4—41no—
294C4⋊C4—1222no—
295C4⋊C4—2441no—
296C4⋊C4—2442no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C22⋊C4—42no—
300C22⋊C4—2442no—
301C22⋊C4—2441no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C42—1222no—
308C42—1222no—
309C42—2441no—
310C42—2441no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23#1451983912yes—
325C23C2×C22⋊#692311yescharacteristic
326D4—82no—
327D4—84no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—612no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4#1451983512yes—
361C2×C4#1451986412yes—
362C8—4882no—
363C8—4882no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1684073511yescharacteristic
379C22C2×#1451983511yescharacteristic
380C22#1684074911yescharacteristic
381C22C2×#1451983911yescharacteristic
382C22#1684075311yescharacteristic
383C22#1684075911yescharacteristic
384C22#1684076011yescharacteristic
385C4—22no—
386C4—22no—
387C4—81no—
388C4—1221no—
389C4—1222no—
390C4—1221no—
391C4—1221no—
392C4—1221no—
393C4—4881no—
394C4—4881no—
395C4—2441no—
396C2—42no—
397C2—161no—
398C2#2146108411yescharacteristic
399C2#2146112411yescharacteristic
400C2#2146117411yescharacteristic
401C2#2146123411yescharacteristic
402C2#2146125511yescharacteristic
403C2#2146130411yescharacteristic
404C2#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#7714
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. #21461675C2semidirect
2. #21461673C2semidirect
3. #21460638C2semidirect
4. #21460635C2semidirect
225. C61#7714semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214616732
#214606382
#214606352
#214541452
#771461