Finite Group Databasebeta

← #30604366

Subgroups — #30604366

Order 15616.

552 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461075C211yesmaximal, characteristic
2#21461059C211yesmaximal, characteristic
3#21460764C212yesmaximal, complemented
4#21460763C212yesmaximal, complemented
5#21449181C211yesmaximal, characteristic
6#16840778—21no—
7#16840732—21no—
8#16840607—21no—
9#16840605—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C23×Dic122C411yescharacteristic
13C2×#14519754—21no—
14C2×D4×Dic61C2211yescharacteristic
15#16839683—21no—
16#16839674—21no—
17#16839666—21no—
18#16839642C411yescharacteristic
19#16839637C2211yescharacteristic
20#16839635C2211yescharacteristic
21#16839620C411yescharacteristic
22C61×#386C411yescharacteristic
23C2×#11758217—41no—
24C4⋊#92420—41no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C4×#92420—41no—
29C22×Dic122—21no—
30C22×Dic122—21no—
31C22×Dic122—44no—
32C22×Dic122—41no—
33C22×Dic122—41no—
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61D411yescharacteristic
37#14519754—44no—
38D4×Dic61—41no—
39D4×Dic61—41no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61C2×C411yescharacteristic
46C2×C22⋊Dic61D411yescharacteristic
47C2×C22⋊Dic61C2311yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×D4×C61C2×C411yescharacteristic
54C23×C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58C24×C61C22⋊C411yescharacteristic
59C24×C61C22×C411yescharacteristic
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—41no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—42no—
66C22×C4×C61—41no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×Dic122—24no—
83C2×Dic122—42no—
84C2×Dic122—42no—
85C2×Dic122—42no—
86C2×Dic122—42no—
87C2×Dic122—44no—
88C2×Dic122—44no—
89C2×Dic122—44no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—44no—
93#11758217—82no—
94C2×#92420—42no—
95C2×#92420—42no—
96C22⋊C4×C61—22no—
97C22⋊C4×C61—42no—
98C22⋊Dic61—22no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—42no—
102C4⋊Dic61—41no—
103C4⋊Dic61—42no—
104#11758196—42no—
105#11758196—42no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C23×C61#13112yes—
119D4×C61—44no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—22no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61#10112yes—
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—42no—
137C2×Dic61—41no—
138C2×Dic61—42no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—81no—
150C2×Dic61#9911yescharacteristic
151C2×Dic61#9911yescharacteristic
152Dic122—44no—
153Dic122—48no—
154Dic122—44no—
155#92420—82no—
156#92420—82no—
157#11580—611nomaximal, Sylow
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—22no—
161C22×C61—42no—
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—81no—
170C22×C61#40811yescharacteristic
171C22×C61C2×#9911yescharacteristic
172C22×C61C2×#10111yescharacteristic
173C4×C61—22no—
174C4×C61—42no—
175C4×C61—81no—
176Dic61—21no—
177Dic61—41no—
178Dic61—42no—
179Dic61—41no—
180Dic61—41no—
181Dic61—81no—
182Dic61AΣL(1,𝔽16)12yes—
183#2409—611no—
184#1465—611no—
185#1460—611no—
186#1326—612no—
187#1326—612no—
188C2×C61—21no—
189C2×C61—21no—
190C2×C61—42no—
191C2×C61—81no—
192C2×C61#147211yescharacteristic
193C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
194C2×C61#212311yescharacteristic
195C23×Q8—611no—
196C2×C22⋊Q8—1221no—
197C2×C4×D4—611no—
198#431—1221no—
199#407—1221no—
200#395—1221no—
201#393—1221no—
202#391—1221no—
203#386—611no—
204#386#692311yescharacteristic
205#385—611no—
206#385—611no—
207#380—611no—
208#324—1221no—
209#323—612no—
210#323—612no—
211#323—1221no—
212C61#1158011yescharacteristic, complemented, Sylow
213C22×Q8—1221no—
214C22×Q8—1221no—
215C22×Q8—2441no—
216C22×Q8—2441no—
217C22×Q8—2444no—
218C22×D4C2×#692311yescharacteristic
219C23×C4—611no—
220C23×C4—611no—
221C23×C4—611no—
222C23×C4C2×#692311yescharacteristic
223C2×M16—2441no—
224C22⋊Q8—2444no—
225C4×D4—2441no—
226C4×D4—2441no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C4⋊C4—1221no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4C2×#692311yescharacteristic
237C2×C42—611no—
238C4⋊C8—2441no—
239C22⋊C8—1222no—
240C22⋊C8—1222no—
241C22⋊C8—2441no—
242C4×C8—2441no—
243#95—21no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248C24C22⋊#692311yescharacteristic
249C24C22×#692311yescharacteristic
250C2×Q8—1224no—
251C2×Q8—2442no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×Q8—2442no—
255C2×Q8—2442no—
256C2×Q8—2442no—
257C2×Q8—2444no—
258C2×Q8—2444no—
259C2×Q8—2444no—
260C2×Q8—2444no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—41no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—2442no—
279C22×C4—2442no—
280C22×C4—2442no—
281C22×C4—2441no—
282C22×C4C22⋊#692311yescharacteristic
283M16—4882no—
284C2×C8—2442no—
285C2×C8—2442no—
286C4⋊C4—2441no—
287C4⋊C4—2442no—
288C4⋊C4—2442no—
289C4⋊C4—2442no—
290C22⋊C4—22no—
291C22⋊C4—42no—
292C22⋊C4—1222no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2442no—
296C42—1221no—
297C42—1221no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23C2×C22⋊#692311yescharacteristic
308C23#1451986412yes—
309Q8—2444no—
310Q8—2444no—
311Q8—2448no—
312D4—44no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—4881no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2442no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2442no—
344C2×C4#1451983812yes—
345C8—4882no—
346C8—4882no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22#1684073511yescharacteristic
360C22D61⋊#9911yescharacteristic
361C22C2×#1451983811yescharacteristic
362C4—22no—
363C4—42no—
364C4—81no—
365C4—612no—
366C4—1221no—
367C4—4881no—
368C4—2441no—
369C4—2442no—
370C4—2441no—
371C4—2441no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—81no—
376C2#2146109811yescharacteristic
377C2D61⋊AΣL(1,𝔽16)11yescharacteristic
378C2#2146208211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC61×#386C4
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenter#386#6923
hypocenterC61#11580
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #21460764C2semidirect
4. #21460763C2semidirect
212. C61#11580semidirect

Maximal subgroups

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

subgroupindex
#214610752
#214610592
#214607642
#214607632
#214491812
#1158061