Finite Group Databasebeta

← #30595680

Subgroups — #30595680

Order 15616.

544 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461674C211yesmaximal, characteristic, complemented
2C4×#14519834C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460636C212yesmaximal, complemented
5#21454152C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519834—21no—
8C2×#14519834—21no—
9C2×C4×#92420—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—
25C4⋊#92420—42no—
26#14519834—24no—
27#14519834—42no—
28C4×#92420—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—22no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61D812yes—
82C2×C4×D61SD1612yes—
83C2×#92420—24no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—42no—
92C42×C61—41no—
93#11758198—42no—
94#11758198—42no—
95#11758198—42no—
96#11758198—42no—
97#11758198—41no—
98#11758198—41no—
99#11758198—42no—
100C4⋊Dic61—22no—
101#11758196—41no—
102#11758196—41no—
103C4×Dic61—22no—
104C4×Dic61—22no—
105C4×Dic61—41no—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61—41no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61#10212yes—
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—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#10212yes—
134C2×C4×C61#10412yes—
135C2×C4×C61#13112yes—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61#9912yes—
146C2×Dic61C2×D811yescharacteristic
147C2×Dic61C2×SD1611yescharacteristic
148C2×Dic61#13512yes—
149D244—82no—
150D244—84no—
151C4×D61—42no—
152C4×D61—42no—
153C4×D61—44no—
154C4×D61—44no—
155#92420—44no—
156#92420—82no—
157#7658—611nomaximal, Sylow
158C22×C61#40811yescharacteristic
159C22×C61C2×#9911yescharacteristic
160C22×C61#41311yescharacteristic
161C22×C61C2×#10211yescharacteristic
162C22×C61#41611yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C22×C61#42111yescharacteristic
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—22no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
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—22no—
182C4×C61—81no—
183C4×C61—81no—
184Dic61—22no—
185Dic61—22no—
186Dic61—21no—
187Dic61—21no—
188Dic61—81no—
189#2854—611no—
190#1797—611no—
191C4×C22⋊C8—611no—
192#1271—612no—
193#1270—612no—
194C2×C61#146811yescharacteristic
195C2×C61#148211yescharacteristic
196C2×C61#149211yescharacteristic
197C2×C61#150111yescharacteristic
198C2×C61#151911yescharacteristic
199C2×C61#152911yescharacteristic
200C2×C61#154011yescharacteristic
201D61—42no—
202D61—161no—
203C2×#123—1221no—
204C2×#121—611no—
205C22×C42—611no—
206C2×C4⋊C8—1221no—
207C2×C22⋊C8—1221no—
208C2×C22⋊C8—1221no—
209C2×C4×C8—1221no—
210#390—611no—
211#390—611no—
212#389—611no—
213#389#692311yescharacteristic
214#388—1221no—
215#388—1221no—
216#386—1221no—
217#380—611no—
218#336—612no—
219#336—612no—
220C61#765811yescharacteristic, complemented, Sylow
221C22×D4—611no—
222C22×D4—1221no—
223C23×C4—611no—
224C23×C4—611no—
225C23×C4—611no—
226C22×C8—1222no—
227C22×C8—1222no—
228#123—2442no—
229#123—2442no—
230#121—2442no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4C2×#692311yescharacteristic
235C2×C4⋊C4C2×#692311yescharacteristic
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C22⋊C4—1221no—
239C2×C22⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—2442no—
246C2×C42C2×#692311yescharacteristic
247C4⋊C8—2442no—
248C22⋊C8—1224no—
249C22⋊C8—2442no—
250C4×C8—2442no—
251#95—21no—
252#95—1221no—
253#95—1221no—
254C24—611no—
255C24—1221no—
256C2×D4—1222no—
257C2×D4—2441no—
258C2×D4—2441no—
259C2×D4—2442no—
260C2×D4—2442no—
261C2×D4—2442no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—612no—
268C22×C4—612no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1222no—
272C22×C4—1222no—
273C22×C4—1221no—
274C22×C4—2441no—
275C22×C4—2441no—
276C22×C4—2441no—
277C22×C4—2441no—
278C22×C4C22⋊#692311yescharacteristic
279C22×C4C22⋊#692311yescharacteristic
280C22×C4C22×#692311yescharacteristic
281C2×C8—1224no—
282C2×C8—2442no—
283C2×C8—2442no—
284C2×C8—2442no—
285C2×C8—2442no—
286C2×C8—2442no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C4⋊C4—1222no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C22⋊C4—2442no—
294C22⋊C4—2442no—
295C22⋊C4—2441no—
296C22⋊C4—2441no—
297C22⋊C4—2442no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C42—41no—
301C42—1222no—
302C42—1222no—
303C42—2441no—
304C23—612no—
305C23—1221no—
306C23—1221no—
307C23—1221no—
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—2441no—
312C23—2441no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23C2×C22⋊#692311yescharacteristic
319D4—4882no—
320D4—4884no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—612no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—612no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2444no—
346C2×C4—2444no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4#1451983912yes—
351C2×C4#1451984212yes—
352C2×C4#1451986512yes—
353C8—4882no—
354C8—2444no—
355C22—1222no—
356C22—1222no—
357C22—1222no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—4881no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22#1684073711yescharacteristic
370C22D61⋊#9911yescharacteristic
371C22#1684074811yescharacteristic
372C22C2×#1451983911yescharacteristic
373C22#1684075211yescharacteristic
374C22C2×#1451984211yescharacteristic
375C22#1684075911yescharacteristic
376C4—22no—
377C4—22no—
378C4—22no—
379C4—81no—
380C4—81no—
381C4—1221no—
382C4—1221no—
383C4—1222no—
384C4—1222no—
385C4—4881no—
386C2—9761no—
387C2—2442no—
388C2#2146108711yescharacteristic
389C2#2146113311yescharacteristic
390C2#2146116611yescharacteristic
391C2#2146119711yescharacteristic
392C2#2146125411yescharacteristic
393C2#2146128611yescharacteristic
394C2#2146131611yescharacteristic
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#7658
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. #21461674C2semidirect
2. C4×#14519834C2semidirect
3. #21460638C2semidirect
4. #21460636C2semidirect
220. C61#7658semidirect

Maximal subgroups

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

subgroupindex
#214616742
C4×#145198342
#214606382
#214606362
#214541522
#765861