Finite Group Databasebeta

← #30595897

Subgroups — #30595897

Order 15616.

528 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461747C211yesmaximal, characteristic, complemented
2#21461734C211yesmaximal, characteristic, complemented
3#21460636C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454173C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519776C411yescharacteristic
13C2×#14519773C411yescharacteristic
14C2×#14519763—21no—
15C2×#14519763—21no—
16#16839665C2211yescharacteristic
17#16839664C411yescharacteristic
18#16839663C2211yescharacteristic
19#16839662—21no—
20#16839662—21no—
21C42×Dic61C2211yescharacteristic
22C61×#390C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26C22×Dic122—21no—
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C22×C22⋊D61—21no—
30#14519776—42no—
31#14519773—42no—
32#14519763—44no—
33#14519763—42no—
34#14519763—42no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×#11758196—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49C22×D4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61—21no—
52C2×C22⋊C4×C61—21no—
53C2×C42×C61C2×C411yescharacteristic
54C24×C61—21no—
55C23×D61—21no—
56C2×D4×C61—22no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C2×C22⋊D61—42no—
64C2×C22⋊D61—42no—
65C2×C22⋊D61—42no—
66C2×C22⋊D61—42no—
67C2×C22⋊D61—42no—
68C2×C22⋊D61—42no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C2×D244—22no—
75C2×D244—41no—
76C2×D244—41no—
77C2×Dic122—42no—
78C2×Dic122—42no—
79C2×Dic122—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊C4×C61—42no—
89C42×C61—22no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C22⋊Dic61—42no—
93#11758198—42no—
94#11758198—42no—
95#11758198—41no—
96#11758198—41no—
97#11758198—42no—
98C4⋊Dic61—41no—
99#11758196—42no—
100C4×Dic61—22no—
101C4×Dic61—22no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C4×Dic61D812yes—
106C4×Dic61SD1612yes—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61C2×C22⋊C411yescharacteristic
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122D4×C61—82no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#10212yes—
134C2×C4×C61#13112yes—
135C22⋊D61—84no—
136C22⋊D61—84no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61#10012yes—
149C2×Dic61#10212yes—
150C2×Dic61C2×D811yescharacteristic
151C2×Dic61C2×SD1611yescharacteristic
152C2×Dic61AGL(1,ℤ/8)12yes—
153D244—82no—
154Dic122—84no—
155#92420—82no—
156#92420—82no—
157#7719—611nomaximal, Sylow
158C22×C61—81no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61—81no—
164C22×C61—81no—
165C22×C61#40811yescharacteristic
166C22×C61#41011yescharacteristic
167C22×C61C2×#10011yescharacteristic
168C22×C61C2×#10211yescharacteristic
169C22×C61#41811yescharacteristic
170C22×C61#42111yescharacteristic
171C22×C61#42111yescharacteristic
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C4×C61—22no—
180C4×C61—22no—
181C4×C61—41no—
182C4×C61—81no—
183Dic61—22no—
184Dic61—22no—
185Dic61—21no—
186Dic61—21no—
187Dic61—22no—
188Dic61—81no—
189#2858—611no—
190#1839—611no—
191#1831—611no—
192#1270—612no—
193#1270—612no—
194C2×C61—161no—
195C2×C61#146911yescharacteristic
196C2×C61#148011yescharacteristic
197C2×C61#149611yescharacteristic
198C2×C61#151411yescharacteristic
199C2×C61#151711yescharacteristic
200C2×C61#153311yescharacteristic
201C2×C61#154511yescharacteristic
202D61—161no—
203C2×C4⋊Q8—611no—
204C2×#127—611no—
205C2×#124—1221no—
206C2×#124—1221no—
207C2×C4⋊C8—1221no—
208#390—611no—
209#390—611no—
210#390—611no—
211#390—1221no—
212#390—1221no—
213#390#692311yescharacteristic
214C43—611no—
215#336—612no—
216#336—612no—
217#336—1221no—
218#336—1221no—
219#336—1221no—
220C61#771911yescharacteristic, complemented, Sylow
221C22×Q8—1221no—
222C22×D4—611no—
223C22×D4—1221no—
224C22×D4—1221no—
225C22×D4C2×#692311yescharacteristic
226C22×C8—1222no—
227C22×C8—1222no—
228C4⋊Q8—2442no—
229#127—2442no—
230#124—2442no—
231#124—2442no—
232#124—2444no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4C2×#692311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C42—611no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42C2×#692311yescharacteristic
251C4⋊C8—2442no—
252C24—21no—
253C24—1221no—
254C2×Q8—2442no—
255C2×Q8—2442no—
256C2×Q8—2442no—
257C2×D4—22no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—1222no—
261C2×D4—2441no—
262C2×D4—2441no—
263C2×D4—2442no—
264C2×D4—2442no—
265C2×D4—2442no—
266C2×D4—2442no—
267C2×D4—2442no—
268C2×D4—2442no—
269C22×C4—21no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—1221no—
275C22×C4C22⋊#692311yescharacteristic
276C22×C4C22⋊#692311yescharacteristic
277C22×C4C22×#692311yescharacteristic
278C2×C8—2442no—
279C2×C8—2442no—
280C2×C8—2442no—
281C2×C8—2442no—
282C2×C8—2442no—
283C2×C8—2442no—
284C4⋊C4—41no—
285C4⋊C4—2441no—
286C4⋊C4—2442no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—2442no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C22⋊C4—2442no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2442no—
296C22⋊C4—2442no—
297C42—22no—
298C42—612no—
299C42—612no—
300C42—1222no—
301C42—1222no—
302C42—2441no—
303C42—2441no—
304C42—2441no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23C2×C22⋊#692311yescharacteristic
320Q8—4884no—
321D4—82no—
322D4—4882no—
323D4—4884no—
324D4—4884no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—612no—
336C2×C4—612no—
337C2×C4—611no—
338C2×C4—611no—
339C2×C4—612no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4#1451983912yes—
352C2×C4#1451986412yes—
353C8—4882no—
354C8—4882no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22—4881no—
369C22#1684073511yescharacteristic
370C22#1684074111yescharacteristic
371C22D61⋊#10011yescharacteristic
372C22C2×#1451983911yescharacteristic
373C22#1684075411yescharacteristic
374C22#1684075911yescharacteristic
375C22#1684075911yescharacteristic
376C4—22no—
377C4—22no—
378C4—41no—
379C4—81no—
380C4—1221no—
381C4—1221no—
382C4—1222no—
383C4—1222no—
384C4—1222no—
385C4—4881no—
386C2—161no—
387C2—9761no—
388C2#2146108811yescharacteristic
389C2#2146112411yescharacteristic
390C2#2146117811yescharacteristic
391C2#2146123811yescharacteristic
392C2#2146124911yescharacteristic
393C2#2146129911yescharacteristic
394C2#2146132711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C4
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#7719
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461747C2semidirect
2. #21461734C2semidirect
3. #21460636C2semidirect
4. #21460635C2semidirect
220. C61#7719semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214617342
#214606362
#214606352
#214541732
#771961