Finite Group Databasebeta

← #30604756

Subgroups — #30604756

Order 15616.

514 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×#16840642C211yesmaximal, characteristic, complemented
2C2×#16840608C211yesmaximal, characteristic, complemented
3#21460803C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21451563C211yesmaximal, characteristic
6C22×#11758217—21no—
7C2×C22⋊#92420—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519758—21no—
13C22×#11758196C2211yescharacteristic
14#16839693C411yescharacteristic
15#16839693C2211yescharacteristic
16#16839685—21no—
17#16839685—21no—
18#16839676C411yescharacteristic
19#16839676C2211yescharacteristic
20#16839642—21no—
21#16839622C411yescharacteristic
22C2×#121×C61C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—22no—
25C2×#11758217—41no—
26C2×#11758217—42no—
27C22×#92420—41no—
28C22×#92420—41no—
29C22⋊#92420—22no—
30C22⋊#92420—41no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519758—42no—
34#14519758—42no—
35C2×C4⋊Dic61—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—41no—
39C2×#11758196—41no—
40C2×#11758196C2×C411yescharacteristic
41C2×#11758196D411yescharacteristic
42C2×#11758196D411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52#14519684C2×C411yescharacteristic
53C22×D4×C61—21no—
54C22×D4×C61C2×C411yescharacteristic
55C23×C4×C61C2×C411yescharacteristic
56#121×C61—41no—
57#121×C61—41no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C22⋊C4×C61—21no—
60C24×C61—21no—
61C24×C61C22⋊C411yescharacteristic
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61—41no—
65C2×D4×C61—42no—
66C2×D4×C61—42no—
67C2×D4×C61—81no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—81no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—22no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—81no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61D812yes—
85C22×Dic61SD1612yes—
86C22×Dic61C2×D411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88#11758217—24no—
89#11758217—44no—
90#11758217—42no—
91C2×#92420—44no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—82no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—42no—
97C22⋊Dic61—42no—
98C22⋊Dic61—42no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—81no—
102C22⋊Dic61—81no—
103C4⋊Dic61—81no—
104#11758196—41no—
105#11758196—41no—
106#11758196—41no—
107#11758196—41no—
108#11758196—42no—
109#11758196—41no—
110#11758196—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61—41no—
120C23×C61#9911yescharacteristic
121C23×C61#9911yescharacteristic
122C23×C61#10212yes—
123C23×C61#10412yes—
124C23×C61C2×C22⋊C411yescharacteristic
125D4×C61—82no—
126D4×C61—82no—
127D4×C61—82no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—42no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—81no—
157C2×Dic61#10212yes—
158C2×Dic61C2×D811yescharacteristic
159C2×Dic61C2×SD1611yescharacteristic
160#92420—44no—
161#92420—82no—
162#11698—611nomaximal, Sylow
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—81no—
176C22×C61—81no—
177C22×C61—81no—
178C22×C61#32712yes—
179C22×C61#32712yes—
180C22×C61C2×#9911yescharacteristic
181C22×C61C2×#10211yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—81no—
186Dic61—21no—
187Dic61—22no—
188Dic61—21no—
189Dic61—41no—
190Dic61—41no—
191Dic61—81no—
192Dic61—81no—
193#2618—611no—
194C2×#343—611no—
195C2×#324—611no—
196#1346—612no—
197#1345—612no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61—22no—
201C2×C61—22no—
202C2×C61—161no—
203C2×C61C2×#32711yescharacteristic
204C2×C61#212111yescharacteristic
205C2×C61#213311yescharacteristic
206C22×M16—1221no—
207C2×#123—1221no—
208C2×#121#692311yescharacteristic
209C22×C4⋊C4—611no—
210C2×C22⋊C8—1221no—
211#398—611no—
212#398—611no—
213#396—1221no—
214#396—1221no—
215#394—611no—
216#394—611no—
217#386—1221no—
218#380—611no—
219#343—612no—
220#343—1221no—
221#324—612no—
222#324—1221no—
223C61#1169811yescharacteristic, complemented, Sylow
224C22×D4—21no—
225C22×D4C2×#692311yescharacteristic
226C23×C4—611no—
227C23×C4—611no—
228C23×C4C2×#692311yescharacteristic
229C2×M16—1222no—
230C2×M16—1224no—
231C2×M16—2442no—
232C2×M16—2441no—
233C22×C8—2441no—
234C22×C8—2441no—
235#123—2442no—
236#123—2442no—
237#121—41no—
238#121—41no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—2441no—
247C2×C4⋊C4—2441no—
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×C22⋊C4—1221no—
255C22⋊C8—1222no—
256C22⋊C8—2441no—
257#95—611no—
258#95—611no—
259#95—1221no—
260#95—1221no—
261C24—21no—
262C24C22⋊#692311yescharacteristic
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—42no—
268C2×D4—81no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—81no—
273C22×C4—612no—
274C22×C4—612no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—1221no—
280C22×C4—1221no—
281C22×C4—1222no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—4881no—
287C22×C4C22⋊#692311yescharacteristic
288C22×C4C22×#692311yescharacteristic
289M16—1224no—
290M16—2442no—
291M16—2444no—
292C2×C8—4882no—
293C2×C8—2442no—
294C2×C8—2442no—
295C2×C8—2444no—
296C4⋊C4—41no—
297C4⋊C4—4881no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2442no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C22⋊C4—42no—
306C22⋊C4—4881no—
307C22⋊C4—4881no—
308C22⋊C4—2442no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C22⋊C4—2442no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23#1451983511yescharacteristic
322C23#1451983511yescharacteristic
323C23#1451983912yes—
324C23#1451984112yes—
325C23C2×C22⋊#692311yescharacteristic
326D4—82no—
327D4—82no—
328D4—82no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—612no—
339C2×C4—611no—
340C2×C4—611no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—4881no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2442no—
359C2×C4—2441no—
360C2×C4—2441no—
361C8—4882no—
362C8—2444no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22#1684061312yes—
379C22#1684061312yes—
380C22C2×#1451983511yescharacteristic
381C22C2×#1451983911yescharacteristic
382C22C2×#1451984111yescharacteristic
383C4—41no—
384C4—41no—
385C4—81no—
386C4—1221no—
387C4—1222no—
388C4—1221no—
389C4—4881no—
390C4—4881no—
391C4—2441no—
392C4—2441no—
393C2—21no—
394C2—21no—
395C2—22no—
396C2—22no—
397C2—161no—
398C2C2×#1684061311yescharacteristic
399C2#2146207411yescharacteristic
400C2#2146211411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#121×C61C4
socleC22×C61C2×#99
cosocleC2×#11758196C23
hypercenterC2×#121#6923
hypocenterC61#11698
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16840642C2semidirect
2. C2×#16840608C2semidirect
3. #21460803C2semidirect
4. #21460801C2semidirect
223. C61#11698semidirect

Maximal subgroups

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

subgroupindex
C2×#168406422
C2×#168406082
#214608032
#214608012
#214515632
#1169861