Finite Group Databasebeta

← #30595640

Subgroups — #30595640

Order 15616.

584 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 100 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
2#21461675C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21448325C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519751C411yescharacteristic
13C2×#14519739C411yescharacteristic
14C2×#14519737—21no—
15C22×C4×Dic61C2211yescharacteristic
16#16839663C2211yescharacteristic
17#16839658C2211yescharacteristic
18#16839651—21no—
19#16839639—21no—
20C4⋊C4×Dic61C411yescharacteristic
21#16839609—21no—
22C61×#380C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C22⋊#92420—42no—
27C22⋊#92420—42no—
28C22×D244C2×C411yescharacteristic
29C22×C22⋊D61—21no—
30C23×Dic61D411yescharacteristic
31C23×Dic61D411yescharacteristic
32C22×C4×D61—21no—
33#14519751—22no—
34#14519751—22no—
35#14519739—42no—
36#14519737—42no—
37#14519737—42no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61—42no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50#14519684—21no—
51#14519684—21no—
52C23×C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56#95×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C23×D61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C2×C22⋊D61—24no—
68C2×C22⋊D61—42no—
69C2×C22⋊D61—42no—
70C22×Dic61—21no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61D812yes—
79C22×Dic61SD1612yes—
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×D244—21no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244M1612yes—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61—42no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—42no—
98#11758198—24no—
99#11758198—42no—
100#11758198—41no—
101#11758198—41no—
102#11758198—42no—
103C4⋊Dic61—21no—
104C4⋊Dic61M1612yes—
105#11758196—41no—
106#11758196—41no—
107C4×Dic61—22no—
108C4×Dic61—22no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C4×Dic61—42no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61#10212yes—
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—22no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61C2×M1611yescharacteristic
141C2×C4×C61C2×M1611yescharacteristic
142C22⋊D61—48no—
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—22no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—44no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#9912yes—
158C2×Dic61#10212yes—
159C2×Dic61C2×D811yescharacteristic
160C2×Dic61C2×SD1611yescharacteristic
161C2×Dic61#13512yes—
162D244—42no—
163D244—42no—
164C4×D61—84no—
165#92420—82no—
166#92420—82no—
167#7647—611nomaximal, Sylow
168C22×C61—22no—
169C22×C61—22no—
170C22×C61—22no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61#40711yescharacteristic
176C22×C61C2×#9911yescharacteristic
177C22×C61#41311yescharacteristic
178C22×C61C2×#10211yescharacteristic
179C22×C61#41611yescharacteristic
180C22×C61#42111yescharacteristic
181C22×C61#42111yescharacteristic
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—81no—
193C4×C61—81no—
194Dic61—22no—
195Dic61—22no—
196Dic61—21no—
197Dic61—22no—
198Dic61—21no—
199Dic61—42no—
200C4×#121—611no—
201#1817—611no—
202#1797—611no—
203#1271—612no—
204#1270—612no—
205C2×C61—42no—
206C2×C61#146511yescharacteristic
207C2×C61#148611yescharacteristic
208C2×C61#148811yescharacteristic
209C2×C61#151611yescharacteristic
210C2×C61#151911yescharacteristic
211C2×C61#153511yescharacteristic
212C2×C61#154011yescharacteristic
213D61—82no—
214C2×#121—611no—
215C2×C4×D4—611no—
216C2×C4×D4—1221no—
217C22×C42—611no—
218C2×C4⋊C8—1221no—
219C2×C22⋊C8—1221no—
220C2×C22⋊C8—1221no—
221#390—611no—
222#389—611no—
223#388—1221no—
224#386—1221no—
225#380#692311yescharacteristic
226C4×C4⋊C4—611no—
227C4×C22⋊C4—1221no—
228#336—612no—
229#336—612no—
230#336—1221no—
231C61#764711yescharacteristic, complemented, Sylow
232C22×D4—611no—
233C22×D4—1221no—
234C23×C4—611no—
235C23×C4—611no—
236C23×C4—1221no—
237C23×C4C2×#692311yescharacteristic
238C22×C8—1222no—
239C22×C8—1222no—
240#121—1222no—
241#121—1222no—
242C4×D4—2442no—
243C4×D4—2442no—
244C4×D4—2442no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4C2×#692311yescharacteristic
248C2×C4⋊C4C2×#692311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C42—611no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42—611no—
258C2×C42—1221no—
259C2×C42—2442no—
260C4⋊C8—2442no—
261C22⋊C8—2442no—
262C22⋊C8—2442no—
263#95—21no—
264#95—1221no—
265#95—1221no—
266C24—1221no—
267C24C22⋊#692311yescharacteristic
268C2×D4—612no—
269C2×D4—1224no—
270C2×D4—1221no—
271C2×D4—2441no—
272C2×D4—2441no—
273C2×D4—2442no—
274C2×D4—2442no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—612no—
286C22×C4—612no—
287C22×C4—1222no—
288C22×C4—1222no—
289C22×C4—1221no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298C2×C8—2442no—
299C2×C8—2442no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8—2442no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—612no—
307C4⋊C4—1221no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C22⋊C4—42no—
311C22⋊C4—1224no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C22⋊C4—2442no—
315C22⋊C4—2442no—
316C42—1222no—
317C42—1222no—
318C42—2441no—
319C42—2441no—
320C42—2442no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—1222no—
328C23—2441no—
329C23—2441no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23#1451983912yes—
335C23C2×C22⋊#692311yescharacteristic
336D4—2442no—
337D4—2442no—
338D4—2448no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—612no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1222no—
366C2×C4—4884no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2444no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4D61⋊M1611yescharacteristic
373C2×C4D61⋊M1611yescharacteristic
374C8—4882no—
375C8—4882no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—4881no—
384C22—4881no—
385C22—4881no—
386C22—4881no—
387C22—2442no—
388C22—2442no—
389C22—2442no—
390C22#1684073411yescharacteristic
391C22D61⋊#9911yescharacteristic
392C22#1684074911yescharacteristic
393C22C2×#1451983911yescharacteristic
394C22#1684075211yescharacteristic
395C22#1684075911yescharacteristic
396C22#1684076111yescharacteristic
397C4—21no—
398C4—21no—
399C4—41no—
400C4—81no—
401C4—81no—
402C4—1221no—
403C4—1222no—
404C4—1221no—
405C4—1222no—
406C4—1222no—
407C4—2442no—
408C2—42no—
409C2—4882no—
410C2#2146107711yescharacteristic
411C2#2146114611yescharacteristic
412C2#2146115211yescharacteristic
413C2#2146124611yescharacteristic
414C2#2146125411yescharacteristic
415C2#2146130611yescharacteristic
416C2#2146131711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#7647
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #21461710C2semidirect
2. #21461675C2semidirect
3. #21460638C2semidirect
4. #21460636C2semidirect
231. C61#7647semidirect

Maximal subgroups

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

subgroupindex
#214617102
#214616752
#214606382
#214606362
#214483252
#764761