Finite Group Databasebeta

← #30595495

Subgroups — #30595495

Order 15616.

892 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 892 conjugacy classes of subgroups — too many to draw. Only its 118 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#21461710C211yesmaximal, characteristic, complemented
2#21461482C211yesmaximal, characteristic, complemented
3#21460636C214yesmaximal, complemented
4C2×#16839663C211yesmaximal, characteristic
5C22×#11758217—21no—
6C2×C22⋊#92420—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yescomplemented
10#16840628C2212yescomplemented
11C23×D244C411yescharacteristic
12C22×#11758198—21no—
13C22×#11758198—21no—
14C22×C4×Dic61C2211yescharacteristic
15#16839663—21no—
16#16839663—21no—
17#16839663C412yes—
18#16839663C2212yes—
19C22×C4⋊C4×C61C411yescharacteristic
20C2×#11758217—24no—
21C2×#11758217—42no—
22C2×#11758217—42no—
23C22×#92420—22no—
24C22×#92420—22no—
25C22⋊#92420—42no—
26C24×D61—21no—
27C22×D244—21no—
28C22×D244—24no—
29C22×D244—42no—
30C22×D244—42no—
31C22×D244C2×C412yes—
32C23×Dic61D411yescharacteristic
33C23×Dic61D411yescharacteristic
34C2×#11758198—22no—
35C2×#11758198—22no—
36C2×#11758198—22no—
37C2×#11758198—22no—
38C2×#11758198—44no—
39C2×#11758198—42no—
40C2×#11758198—42no—
41C2×C4×Dic61—42no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46C23×C4×C61—21no—
47C23×C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—42no—
50C2×C4⋊C4×C61C2×C412yes—
51C24×C61C22⋊C411yescharacteristic
52C23×D61—24no—
53C23×D61—22no—
54C23×D61—42no—
55C23×D61—42no—
56C23×D61—42no—
57C23×D61—42no—
58C23×D61—42no—
59C23×D61—42no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—41no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61D812yes—
77C22×Dic61SD1612yes—
78C22×Dic61C2×D411yescharacteristic
79C22×Dic61C2×D411yescharacteristic
80C2×D244—24no—
81C2×D244—22no—
82C2×D244—416no—
83C2×D244—42no—
84C2×D244—42no—
85C2×D244—42no—
86C2×D244—42no—
87C2×D244M1614yescomplemented
88#11758217—48no—
89C2×#92420—24no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C4⋊C4×C61—42no—
96C4⋊C4×C61—42no—
97#11758198—44no—
98#11758198—44no—
99#11758198—42no—
100#11758198—42no—
101#11758198—44no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C4×Dic61—41no—
105C4×Dic61—41no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61#9912yes—
111C23×C61#10212yes—
112C23×C61#10412yes—
113C23×C61C2×C22⋊C411yescharacteristic
114C22×D61—24no—
115C22×D61—48no—
116C22×D61—48no—
117C22×D61—48no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—84no—
125C22×D61—84no—
126C22×D61—84no—
127C22×D61—84no—
128C2×C4×C61—28no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—84no—
137C2×C4×C61#10012yes—
138C2×C4×C61C2×M1612yes—
139C2×Dic61—24no—
140C2×Dic61—24no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—44no—
151C2×Dic61#10212yes—
152C2×Dic61C2×D811yescharacteristic
153C2×Dic61C2×SD1611yescharacteristic
154C2×Dic61AGL(1,ℤ/8)12yes—
155D244—44no—
156D244—48no—
157D244—44no—
158#92420—44no—
159#92420—82no—
160#7606—611nomaximal, Sylow
161C22×C61—22no—
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61#32714yes—
168C22×C61#40711yescharacteristic
169C22×C61C2×#9911yescharacteristic
170C22×C61C2×#10011yescharacteristic
171C22×C61C2×#10211yescharacteristic
172C22×C61#41811yescharacteristic
173C22×C61C2×#10411yescharacteristic
174C22×C61#42111yescharacteristic
175C2×D61—44no—
176C2×D61—44no—
177C2×D61—44no—
178C2×D61—816no—
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—82no—
182C2×D61—82no—
183C4×C61—22no—
184C4×C61—22no—
185C4×C61—82no—
186Dic61—21no—
187Dic61—22no—
188Dic61—21no—
189Dic61—22no—
190Dic61—41no—
191C2×#390—611no—
192#1817—611no—
193#1728—611no—
194#1270—614no—
195C2×C61—24no—
196C2×C61#146211yescharacteristic
197C2×C61#148611yescharacteristic
198C2×C61#149011yescharacteristic
199C2×C61C2×#32711yescharacteristic
200C2×C61#151011yescharacteristic
201C2×C61#152711yescharacteristic
202C2×C61#154511yescharacteristic
203D61—84no—
204C23×D4—611no—
205C22×M16—1221no—
206C22×C4⋊C4#692311yescharacteristic
207C22×C22⋊C4—1221no—
208C22×C22⋊C4—1221no—
209C22×C42—611no—
210C2×C22⋊C8—1221no—
211#390—612no—
212#390—612no—
213#390—1221no—
214#390—1221no—
215#336—612no—
216#336—612no—
217#336—1221no—
218#336—1221no—
219C61#760611yescharacteristic, complemented, Sylow
220C25—1221no—
221C22×D4—612no—
222C22×D4—1224no—
223C22×D4—1221no—
224C22×D4—2442no—
225C22×D4—2442no—
226C23×C4—21no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4C2×#692311yescharacteristic
230C2×M16—1224no—
231C2×M16—2442no—
232C2×M16—2442no—
233C22×C8—1222no—
234C22×C8—1222no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—42no—
237C2×C4⋊C4C2×#692312yes—
238C2×C22⋊C4—1222no—
239C2×C22⋊C4—1222no—
240C2×C22⋊C4—1222no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—2442no—
243C2×C22⋊C4—2442no—
244C2×C22⋊C4—2444no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—2442no—
250C22⋊C8—2442no—
251C24—1224no—
252C24—1222no—
253C24—2442no—
254C24—2442no—
255C24—2442no—
256C24—2442no—
257C24—2442no—
258C24—2442no—
259C24C22⋊#692311yescharacteristic
260C2×D4—614no—
261C2×D4—1224no—
262C2×D4—1222no—
263C2×D4—2442no—
264C2×D4—2442no—
265C2×D4—24416no—
266C2×D4—2442no—
267C2×D4—2442no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—2441no—
286C22×C4C22⋊#692311yescharacteristic
287C22×C4C22×#692311yescharacteristic
288M16—2448no—
289C2×C8—1224no—
290C2×C8—2442no—
291C2×C8—2442no—
292C2×C8—2442no—
293C2×C8—2442no—
294C2×C8—2442no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C22⋊C4—2444no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C22⋊C4—2444no—
301C22⋊C4—2444no—
302C42—2441no—
303C42—2441no—
304C42—2441no—
305C42—2441no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—1224no—
311C23—4884no—
312C23—4884no—
313C23—4884no—
314C23—4884no—
315C23—2448no—
316C23—2448no—
317C23—2448no—
318C23—2442no—
319C23—2442no—
320C23—2442no—
321C23—2442no—
322C23—2442no—
323C23—2442no—
324C23#1451983612yes—
325C23#1451983912yes—
326C23#1451984212yes—
327C23C2×C22⋊#692311yescharacteristic
328D4—2444no—
329D4—2448no—
330D4—2444no—
331C2×C4—28no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—84no—
340C2×C4—612no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—612no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1224no—
351C2×C4—1224no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—2444no—
356C2×C4#1451983712yes—
357C2×C4D61⋊M1612yes—
358C8—4882no—
359C8—2444no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—48816no—
367C22—4882no—
368C22—4882no—
369C22—4882no—
370C22—4882no—
371C22—2444no—
372C22—2444no—
373C22—2444no—
374C22#1684061414yes—
375C22#1684073411yescharacteristic
376C22C2×#1451983611yescharacteristic
377C22C2×#1451983711yescharacteristic
378C22C2×#1451983911yescharacteristic
379C22#1684075411yescharacteristic
380C22C2×#1451984211yescharacteristic
381C22#1684076111yescharacteristic
382C4—22no—
383C4—22no—
384C4—82no—
385C4—1221no—
386C4—1222no—
387C4—1221no—
388C4—1222no—
389C4—2441no—
390C2—24no—
391C2—4884no—
392C2#2146106611yescharacteristic
393C2#2146114611yescharacteristic
394C2#2146116011yescharacteristic
395C2C2×#1684061411yescharacteristic
396C2#2146122611yescharacteristic
397C2#2146128011yescharacteristic
398C2#2146132611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#7606
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461710C2semidirect
2. #21461482C2semidirect
3. #21460636C2semidirect
9. #16840628C22semidirect
10. #16840628C22semidirect
87. C2×D244M16semidirect
219. C61#7606semidirect

Maximal subgroups

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

subgroupindex
#214617102
#214614822
#214606362
C2×#168396632
#760661