Finite Group Databasebeta

← #30604758

Subgroups — #30604758

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#21460804C212yesmaximal, complemented
4#21460802C212yesmaximal, complemented
5#21451564C211yesmaximal, characteristic
6C22×#11758217—21no—
7C2×C22⋊#92420—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519761—21no—
13C2×#14519751C411yescharacteristic
14C22×#11758196C2211yescharacteristic
15#16839694C411yescharacteristic
16#16839694C2211yescharacteristic
17#16839684—21no—
18#16839684—21no—
19#16839680C411yescharacteristic
20#16839680C2211yescharacteristic
21#16839639—21no—
22C61×#380C411yescharacteristic
23C2×#11758217—24no—
24C2×#11758217—22no—
25C2×#11758217—41no—
26C2×#11758217—42no—
27C22×#92420—41no—
28C22×#92420—41no—
29C22⋊#92420—22no—
30C22⋊#92420—41no—
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C23×Dic61D411yescharacteristic
34C23×Dic61D411yescharacteristic
35#14519761—42no—
36#14519761—42no—
37#14519751—41no—
38#14519751—41no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196—41no—
43C2×#11758196—41no—
44C2×#11758196C2×C411yescharacteristic
45C2×#11758196D411yescharacteristic
46C2×#11758196D411yescharacteristic
47C2×#11758196C2311yescharacteristic
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53#14519684—21no—
54#14519684—21no—
55C23×C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58#95×C61C2×C411yescharacteristic
59#95×C61C2×C411yescharacteristic
60C24×C61C22⋊C411yescharacteristic
61C23×D61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—81no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—41no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61—42no—
72C2×C22⋊D61—42no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—22no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—81no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61D812yes—
83C22×Dic61SD1612yes—
84C22×Dic61C2×D411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86C2×D244—41no—
87C2×D244—81no—
88#11758217—24no—
89#11758217—44no—
90#11758217—42no—
91C2×#92420—44no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—82no—
95C4⋊C4×C61—81no—
96C22⋊C4×C61—42no—
97#11758198—42no—
98#11758198—42no—
99#11758198—41no—
100#11758198—41no—
101#11758198—81no—
102#11758198—81no—
103C4⋊Dic61—42no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107#11758196—41no—
108#11758196—41no—
109#11758196—41no—
110#11758196—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61#9911yescharacteristic
114C23×C61#9911yescharacteristic
115C23×C61#10212yes—
116C23×C61#10412yes—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C22×D61—41no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
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—
137C22⋊D61—82no—
138C22⋊D61—82no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—81no—
156C2×Dic61#10212yes—
157C2×Dic61C2×D811yescharacteristic
158C2×Dic61C2×SD1611yescharacteristic
159D244—82no—
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#32712yes—
172C22×C61#32712yes—
173C22×C61C2×#9911yescharacteristic
174C22×C61C2×#10211yescharacteristic
175C22×C61C2×#10411yescharacteristic
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C4×C61—41no—
184C4×C61—41no—
185C4×C61—81no—
186C4×C61—81no—
187Dic61—21no—
188Dic61—22no—
189Dic61—21no—
190Dic61—41no—
191Dic61—41no—
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×C61C2×#32711yescharacteristic
203C2×C61#212111yescharacteristic
204C2×C61#213311yescharacteristic
205D61—161no—
206C22×M16—1221no—
207C2×#123—1221no—
208C2×#121—611no—
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#692311yescharacteristic
219#343—612no—
220#343—1221no—
221#324—612no—
222#324—1221no—
223C61#1169811yescharacteristic, complemented, Sylow
224C22×D4—611no—
225C22×D4—1221no—
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—2441no—
238#121—2441no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—2441no—
248C2×C4⋊C4—2441no—
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—1221no—
258#95—1221no—
259#95C2×#692311yescharacteristic
260#95C2×#692311yescharacteristic
261C24—1221no—
262C24C22⋊#692311yescharacteristic
263C2×D4—4881no—
264C2×D4—2441no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2442no—
268C2×D4—2442no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—81no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1222no—
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—81no—
297C4⋊C4—2441no—
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—2442no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C23—41no—
313C23—41no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23#1451983611yescharacteristic
322C23#1451983611yescharacteristic
323C23#1451983912yes—
324C23#1451984212yes—
325C23C2×C22⋊#692311yescharacteristic
326D4—4882no—
327D4—4882no—
328D4—4882no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—612no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—4881no—
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—4881no—
372C22—4881no—
373C22—4881no—
374C22—4881no—
375C22—4881no—
376C22—4881no—
377C22—4881no—
378C22#1684061412yes—
379C22#1684061412yes—
380C22C2×#1451983611yescharacteristic
381C22C2×#1451983911yescharacteristic
382C22C2×#1451984211yescharacteristic
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—1221no—
388C4—1222no—
389C4—1221no—
390C4—4881no—
391C4—2441no—
392C4—2441no—
393C2—21no—
394C2—21no—
395C2—22no—
396C2—22no—
397C2—9761no—
398C2C2×#1684061411yescharacteristic
399C2#2146207611yescharacteristic
400C2#2146211611yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61C2×#99
prime radicalC2×#14519751C4
cosocleC2×#11758196C23
hypercenter#380#6923
hypocenterC61#11698
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#16840642C2semidirect
2. C2×#16840608C2semidirect
3. #21460804C2semidirect
4. #21460802C2semidirect
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
#214608042
#214608022
#214515642
#1169861