Finite Group Databasebeta

← #30595880

Subgroups — #30595880

Order 15616.

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

normal subgroups only

This group has 526 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#21461676C211yesmaximal, characteristic, complemented
2#21461674C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21454152C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420—21no—
8C2×#14519834—21no—
9C2×#14519834—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519762—21no—
13C2×#14519752C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839664C411yescharacteristic
16#16839663C2211yescharacteristic
17#16839658C2211yescharacteristic
18#16839652—21no—
19#16839651—21no—
20#16839640—21no—
21#16839619C411yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26C4⋊#92420—42no—
27#14519834—42no—
28#14519834—42no—
29C22×D244—21no—
30C22×D244C2×C411yescharacteristic
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519762—42no—
35#14519762—42no—
36#14519752—42no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61C2311yescharacteristic
48C42×D61—42no—
49#14519684—21no—
50#14519684—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55#95×C61—21no—
56C23×D61—21no—
57C23×D61C22⋊C411yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×D244—22no—
68C2×D244—41no—
69C2×D244—41no—
70C2×D244—42no—
71C2×D244—42no—
72C2×D244—42no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61D812yes—
83C2×C4×D61SD1612yes—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—42no—
93C42×C61—41no—
94#11758198—42no—
95#11758198—42no—
96#11758198—42no—
97#11758198—42no—
98#11758198—41no—
99#11758198—41no—
100#11758198—41no—
101#11758198—41no—
102C4⋊Dic61—22no—
103#11758196—41no—
104#11758196—41no—
105C4×Dic61—22no—
106C4×Dic61—22no—
107C4×Dic61—41no—
108C23×C61C2×C22⋊C411yescharacteristic
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61#10212yes—
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—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61#10212yes—
137C2×C4×C61#13112yes—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61#9912yes—
148C2×Dic61C2×D811yescharacteristic
149C2×Dic61C2×SD1611yescharacteristic
150C2×Dic61AGL(1,ℤ/8)11yescharacteristic
151C2×Dic61#13711yescharacteristic
152D244—82no—
153D244—84no—
154C4×D61—42no—
155C4×D61—42no—
156C4×D61—44no—
157C4×D61—42no—
158C4×D61—42no—
159#92420—82no—
160#92420—82no—
161#7714—611nomaximal, Sylow
162C22×C61#40811yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61#41311yescharacteristic
165C22×C61C2×#10211yescharacteristic
166C22×C61#41711yescharacteristic
167C22×C61#42111yescharacteristic
168C22×C61#42111yescharacteristic
169C2×D61—22no—
170C2×D61—22no—
171C2×D61—22no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—81no—
177C2×D61—81no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C2×D61—81no—
183C4×C61—22no—
184C4×C61—22no—
185C4×C61—41no—
186C4×C61—81no—
187C4×C61—81no—
188Dic61—22no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—81no—
194#2854—611no—
195#1797—611no—
196#1797—611no—
197#1271—612no—
198#1270—612no—
199C2×C61#146811yescharacteristic
200C2×C61#148011yescharacteristic
201C2×C61#149511yescharacteristic
202C2×C61#151311yescharacteristic
203C2×C61#151911yescharacteristic
204C2×C61#153511yescharacteristic
205C2×C61#154711yescharacteristic
206D61—42no—
207D61—161no—
208C2×#123—1221no—
209C2×#121—611no—
210C22×C42—611no—
211C2×C4⋊C8—1221no—
212C2×C4⋊C8—1221no—
213C2×C22⋊C8—1221no—
214C2×C22⋊C8—1221no—
215#390—611no—
216#390—611no—
217#389—611no—
218#389#692311yescharacteristic
219#388—1221no—
220#388—1221no—
221#386—1221no—
222#380—611no—
223#336—612no—
224#336—612no—
225C61#771411yescharacteristic, complemented, Sylow
226C22×D4—611no—
227C22×D4—1221no—
228C23×C4—611no—
229C23×C4—611no—
230C23×C4—611no—
231C22×C8—1222no—
232C22×C8—1222no—
233#123—2442no—
234#123—2442no—
235#121—2442no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4C2×#692311yescharacteristic
240C2×C4⋊C4C2×#692311yescharacteristic
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1221no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—2442no—
251C2×C42C2×#692311yescharacteristic
252C4⋊C8—2442no—
253C4⋊C8—2442no—
254C22⋊C8—2442no—
255C22⋊C8—2442no—
256#95—21no—
257#95—1221no—
258#95—1221no—
259C24—611no—
260C24—1221no—
261C2×D4—1222no—
262C2×D4—2441no—
263C2×D4—2441no—
264C2×D4—2442no—
265C2×D4—2442no—
266C2×D4—2442no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—612no—
273C22×C4—612no—
274C22×C4—1221no—
275C22×C4—1222no—
276C22×C4—1221no—
277C22×C4—1222no—
278C22×C4—1221no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4—2441no—
283C22×C4—2441no—
284C22×C4C22⋊#692311yescharacteristic
285C22×C4C22⋊#692311yescharacteristic
286C22×C4C22×#692311yescharacteristic
287C2×C8—2442no—
288C2×C8—2442no—
289C2×C8—2442no—
290C2×C8—2442no—
291C2×C8—2442no—
292C2×C8—2442no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—42no—
296C4⋊C4—1222no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C22⋊C4—2442no—
300C22⋊C4—2441no—
301C22⋊C4—2441no—
302C22⋊C4—2442no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2442no—
306C22⋊C4—2442no—
307C42—41no—
308C42—1222no—
309C42—1222no—
310C42—2441no—
311C23—612no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—2441no—
319C23—2441no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23—2441no—
324C23—2441no—
325C23C2×C22⋊#692311yescharacteristic
326D4—4882no—
327D4—4884no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—612no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2444no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4#1451983912yes—
361C2×C4#1451986512yes—
362C8—4882no—
363C8—4882no—
364C22—1222no—
365C22—1222no—
366C22—1222no—
367C22—4881no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22—4881no—
372C22—4881no—
373C22—4881no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22—2441no—
378C22#1684073711yescharacteristic
379C22D61⋊#9911yescharacteristic
380C22#1684074811yescharacteristic
381C22C2×#1451983911yescharacteristic
382C22#1684075311yescharacteristic
383C22#1684075911yescharacteristic
384C22#1684076111yescharacteristic
385C4—22no—
386C4—22no—
387C4—41no—
388C4—81no—
389C4—81no—
390C4—1221no—
391C4—1221no—
392C4—1222no—
393C4—1221no—
394C4—1221no—
395C4—4881no—
396C2—9761no—
397C2—2442no—
398C2#2146108711yescharacteristic
399C2#2146112611yescharacteristic
400C2#2146117711yescharacteristic
401C2#2146123711yescharacteristic
402C2#2146125411yescharacteristic
403C2#2146130511yescharacteristic
404C2#2146133011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7714
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
1. #21461676C2semidirect
2. #21461674C2semidirect
3. #21460638C2semidirect
4. #21460636C2semidirect
225. C61#7714semidirect

Maximal subgroups

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

subgroupindex
#214616762
#214616742
#214606382
#214606362
#214541522
#771461