Finite Group Databasebeta

← #30604895

Subgroups — #30604895

Order 15616.

470 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461569C211yesmaximal, characteristic, complemented
2#21461057C211yesmaximal, characteristic, complemented
3#21460817C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21451708C211yesmaximal, characteristic
6C2×#14519837—21no—
7C2×C22⋊#92420—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519748C411yescharacteristic
13C2×#14519737C2211yescharacteristic
14#16839702C2211yescharacteristic
15#16839698C411yescharacteristic
16#16839677—21no—
17#16839676C2211yescharacteristic
18#16839670—21no—
19#16839656—21no—
20#16839642—21no—
21#16839624C411yescharacteristic
22C61×#392C411yescharacteristic
23C2×#11758217—22no—
24C22×#92420—41no—
25#14519837—24no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28#14519832—41no—
29C4×#92420—41no—
30C22×C22⋊D61—21no—
31C22×C22⋊D61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C22×C4×D61C2×C411yescharacteristic
34#14519748—41no—
35#14519748—41no—
36#14519737—41no—
37#14519737—41no—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196C2311yescharacteristic
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×#11758198—21no—
46C2×#11758198D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C22×D4×C61—21no—
53C22×D4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61C2×C411yescharacteristic
56#95×C61C2×C411yescharacteristic
57C24×C61—21no—
58C24×C61C22⋊C411yescharacteristic
59C23×D61C22⋊C411yescharacteristic
60C2×D4×C61—41no—
61C2×D4×C61—42no—
62C2×D4×C61—81no—
63C2×D4×C61—81no—
64C2×D4×C61—81no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61—42no—
72C2×C22⋊D61—81no—
73C2×C22⋊D61—81no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—81no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—81no—
85#11758217—24no—
86#11758217—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—82no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—81no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—42no—
95C22⋊Dic61—81no—
96C22⋊Dic61—81no—
97#11758198—41no—
98#11758198—81no—
99C4⋊Dic61—41no—
100#11758196—41no—
101#11758196—81no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61#10412yes—
116C23×C61C2×C22⋊C411yescharacteristic
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122D4×C61—82no—
123D4×C61—84no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C22⋊D61—44no—
132C22⋊D61—84no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61#9911yescharacteristic
147C2×Dic61#9911yescharacteristic
148C2×Dic61#13512yes—
149C4×D61—81no—
150C4×D61—81no—
151#92420—44no—
152#92420—82no—
153#11737—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—22no—
157C22×C61—42no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61—81no—
166C22×C61—81no—
167C22×C61—81no—
168C22×C61C2×#9911yescharacteristic
169C22×C61#41611yescharacteristic
170C22×C61C2×#10411yescharacteristic
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—81no—
175C2×D61—81no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—81no—
179Dic61—21no—
180Dic61—21no—
181Dic61—22no—
182Dic61—41no—
183Dic61—81no—
184Dic61—81no—
185#2635—611no—
186C4×#100—611no—
187#1459—611no—
188#1353—612no—
189#1345—612no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—42no—
193C2×C61—161no—
194C2×C61#150111yescharacteristic
195C2×C61#212111yescharacteristic
196C2×C61#213411yescharacteristic
197D61—81no—
198C2×#121—611no—
199C2×C4×D4—611no—
200C2×#100—1221no—
201C2×C22⋊C8—1221no—
202C4×M16—1221no—
203#400—611no—
204#399—611no—
205#394—611no—
206#394—1221no—
207#392—1221no—
208#392#692311yescharacteristic
209#388—1221no—
210#386—1221no—
211#381—611no—
212#343—612no—
213#324—612no—
214#323—1221no—
215C61#1173711yescharacteristic, complemented, Sylow
216C22×D4—21no—
217C22×D4—611no—
218C22×D4—1221no—
219C22×D4C2×#692311yescharacteristic
220C23×C4—611no—
221C23×C4—611no—
222C2×M16—1222no—
223C22×C8—2441no—
224#121—2441no—
225#121—2441no—
226C4×D4—2441no—
227C4×D4—2441no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4C2×#692311yescharacteristic
239C2×C42—611no—
240#100—1224no—
241C22⋊C8—1222no—
242C22⋊C8—2441no—
243#97—2441no—
244C4×C8—2441no—
245#95—611no—
246#95—1221no—
247#95—1221no—
248#95—1221no—
249#95C2×#692311yescharacteristic
250C24—21no—
251C24—611no—
252C24C22⋊#692311yescharacteristic
253C2×D4—41no—
254C2×D4—42no—
255C2×D4—81no—
256C2×D4—81no—
257C2×D4—81no—
258C2×D4—1222no—
259C2×D4—1222no—
260C2×D4—4881no—
261C2×D4—4881no—
262C2×D4—2441no—
263C2×D4—2442no—
264C22×C4—21no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—4881no—
275C22×C4—4881no—
276C22×C4C22⋊#692311yescharacteristic
277C22×C4C22×#692311yescharacteristic
278M16—1224no—
279M16—2442no—
280C2×C8—4882no—
281C2×C8—2442no—
282C2×C8—2442no—
283C4⋊C4—4881no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C22⋊C4—41no—
287C22⋊C4—81no—
288C22⋊C4—4881no—
289C22⋊C4—4881no—
290C22⋊C4—4881no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2442no—
295C42—1221no—
296C42—1221no—
297C23—21no—
298C23—21no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—2441no—
312C23—2441no—
313C23#1451984112yes—
314C23C2×C22⋊#692311yescharacteristic
315D4—82no—
316D4—84no—
317D4—4884no—
318D4—2444no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—612no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—2441no—
336C2×C4—2442no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2441no—
344C8—4882no—
345C8—2444no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—4881no—
361C22—4881no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22D61⋊#9911yescharacteristic
366C22#1684075211yescharacteristic
367C22C2×#1451984111yescharacteristic
368C4—41no—
369C4—41no—
370C4—81no—
371C4—1221no—
372C4—1221no—
373C4—1222no—
374C4—4881no—
375C4—4881no—
376C4—2441no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—161no—
381C2—4881no—
382C2#2146119511yescharacteristic
383C2#2146207511yescharacteristic
384C2#2146211911yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#392C4
socleC22×C61C2×#99
prime radical#21451708C2
cosocleC2×#11758196C23
hypercenter#392#6923
hypocenterC61#11737
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #21461569C2semidirect
2. #21461057C2semidirect
3. #21460817C2semidirect
4. #21460801C2semidirect
215. C61#11737semidirect

Maximal subgroups

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

subgroupindex
#214615692
#214610572
#214608172
#214608012
#214517082
#1173761