Finite Group Databasebeta

← #30595825

Subgroups — #30595825

Order 15616.

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

normal subgroups only

This group has 534 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
1#21461746C211yesmaximal, characteristic, complemented
2#21461536C211yesmaximal, characteristic, complemented
3#21460636C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5#21454173C211yesmaximal, characteristic
6C2×#14519832—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—
25#14519832—24no—
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—44no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48C22×D4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C22⋊C4×C61—21no—
51C2×C22⋊C4×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53C24×C61—21no—
54C23×D61—21no—
55C2×D4×C61—22no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C2×C22⋊D61—42no—
63C2×C22⋊D61—42no—
64C2×C22⋊D61—42no—
65C2×C22⋊D61—42no—
66C2×C22⋊D61—42no—
67C2×C22⋊D61—42no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73C2×D244—22no—
74C2×D244—41no—
75C2×D244—41no—
76C2×Dic122—42no—
77C2×Dic122—42no—
78C2×Dic122—42no—
79C2×#92420—24no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—41no—
86C22⋊C4×C61—42no—
87C22⋊C4×C61—42no—
88C42×C61—22no—
89C22⋊Dic61—42no—
90C22⋊Dic61—42no—
91#11758198—42no—
92#11758198—42no—
93#11758198—42no—
94#11758198—42no—
95C4⋊Dic61—41no—
96#11758196—42no—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C4×Dic61—22no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C4×Dic61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—41no—
112C22×D61—41no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118D4×C61—82no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61#13112yes—
131C22⋊D61—84no—
132C22⋊D61—84no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#10012yes—
145C2×Dic61#10412yes—
146C2×Dic61AGL(1,ℤ/8)12yes—
147C2×Dic61AGL(1,ℤ/8)12yes—
148D244—82no—
149Dic122—84no—
150#92420—44no—
151#92420—82no—
152#7699—611nomaximal, Sylow
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61#40811yescharacteristic
161C22×C61#41011yescharacteristic
162C22×C61C2×#10011yescharacteristic
163C22×C61#41811yescharacteristic
164C22×C61#41811yescharacteristic
165C22×C61C2×#10411yescharacteristic
166C22×C61#42111yescharacteristic
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C2×D61—81no—
173C2×D61—81no—
174C4×C61—22no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—81no—
178Dic61—22no—
179Dic61—22no—
180Dic61—22no—
181Dic61—22no—
182Dic61—81no—
183#2858—611no—
184#1839—611no—
185#1745—611no—
186#1270—612no—
187#1270—612no—
188C2×C61—161no—
189C2×C61#146911yescharacteristic
190C2×C61#148411yescharacteristic
191C2×C61#149611yescharacteristic
192C2×C61#150511yescharacteristic
193C2×C61#151411yescharacteristic
194C2×C61#152711yescharacteristic
195C2×C61#155511yescharacteristic
196D61—161no—
197C2×C4⋊Q8—611no—
198C2×#127—611no—
199C2×#124—1221no—
200C2×#124—1221no—
201C2×#97—1221no—
202#390—611no—
203#390—611no—
204#390—611no—
205#390—1221no—
206#390—1221no—
207#390#692311yescharacteristic
208C43—611no—
209#336—612no—
210#336—612no—
211#336—1221no—
212#336—1221no—
213#336—1221no—
214C61#769911yescharacteristic, complemented, Sylow
215C22×Q8—1221no—
216C22×D4—611no—
217C22×D4—1221no—
218C22×D4—1221no—
219C22×D4C2×#692311yescharacteristic
220C22×C8—1222no—
221C22×C8—1222no—
222C4⋊Q8—2442no—
223#127—2442no—
224#124—2444no—
225#124—2444no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C22⋊C4—1221no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42C2×#692311yescharacteristic
244#97—1224no—
245C24—21no—
246C24—1221no—
247C2×Q8—2442no—
248C2×Q8—2442no—
249C2×Q8—2442no—
250C2×D4—22no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—1222no—
254C2×D4—2441no—
255C2×D4—2441no—
256C2×D4—2442no—
257C2×D4—2442no—
258C2×D4—2442no—
259C2×D4—2442no—
260C2×D4—2442no—
261C2×D4—2442no—
262C22×C4—21no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4C22⋊#692311yescharacteristic
269C22×C4C22⋊#692311yescharacteristic
270C22×C4C22×#692311yescharacteristic
271C2×C8—1224no—
272C2×C8—2442no—
273C2×C8—2442no—
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2442no—
277C4⋊C4—41no—
278C4⋊C4—2441no—
279C4⋊C4—2442no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—2442no—
283C22⋊C4—2442no—
284C22⋊C4—2442no—
285C22⋊C4—2442no—
286C22⋊C4—2442no—
287C22⋊C4—2442no—
288C42—22no—
289C42—1222no—
290C42—1222no—
291C42—1222no—
292C42—1222no—
293C42—2441no—
294C42—2441no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—2441no—
303C23—2441no—
304C23—2441no—
305C23—2441no—
306C23—2441no—
307C23—2441no—
308C23—2441no—
309C23C2×C22⋊#692311yescharacteristic
310Q8—4884no—
311D4—82no—
312D4—4882no—
313D4—4884no—
314D4—4884no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—612no—
327C2×C4—612no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4#1451986412yes—
342C8—4882no—
343C8—2444no—
344C22—81no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—4881no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22—4881no—
356C22—4881no—
357C22—4881no—
358C22#1684073511yescharacteristic
359C22#1684074111yescharacteristic
360C22D61⋊#10011yescharacteristic
361C22#1684075411yescharacteristic
362C22#1684075411yescharacteristic
363C22D61⋊#10411yescharacteristic
364C22#1684075911yescharacteristic
365C4—22no—
366C4—41no—
367C4—41no—
368C4—81no—
369C4—1222no—
370C4—1222no—
371C4—1222no—
372C4—1222no—
373C4—4881no—
374C2—161no—
375C2—9761no—
376C2#2146108811yescharacteristic
377C2#2146113811yescharacteristic
378C2#2146117811yescharacteristic
379C2#2146120911yescharacteristic
380C2#2146123811yescharacteristic
381C2#2146127911yescharacteristic
382C2#2146134711yescharacteristic
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#7699
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. #21461746C2semidirect
2. #21461536C2semidirect
3. #21460636C2semidirect
4. #21460635C2semidirect
214. C61#7699semidirect

Maximal subgroups

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

subgroupindex
#214617462
#214615362
#214606362
#214606352
#214541732
#769961