Finite Group Databasebeta

← #30598138

Subgroups — #30598138

Order 15616.

1238 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 128 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#21461642C212yesmaximal, complemented
2C2×#16840608C212yesmaximal, complemented
3C2×#16840606C212yesmaximal, complemented
4C22×#14519762C211yesmaximal, characteristic
5C2×#14519834—24no—
6C2×C22⋊#92420C2214yes—
7#16840608—24no—
8#16840606—24no—
9C23×D244C411yescharacteristic
10C23×C4×D61C2211yescharacteristic
11C2×#14519762—24no—
12C2×#14519762—24no—
13C2×#14519762—24no—
14C22×#11758196C2211yescharacteristic
15C22×#11758198C411yescharacteristic
16C22×#11758198C411yescharacteristic
17C22×#11758198C2211yescharacteristic
18C22×C4⋊C4×C61C411yescharacteristic
19C22×#92420—24no—
20#14519834—48no—
21C22⋊#92420—24no—
22C22⋊#92420—24no—
23C24×D61C2×C411yescharacteristic
24C24×D61C2×C411yescharacteristic
25C22×D244—22no—
26C22×D244—22no—
27C22×D244—22no—
28C22×D244—44no—
29C23×Dic61C2×C411yescharacteristic
30C23×Dic61C2311yescharacteristic
31C22×C4×D61—22no—
32C22×C4×D61—22no—
33C22×C4×D61—44no—
34C22×C4×D61D414yes—
35#14519762—232no—
36C2×#11758196—22no—
37C2×#11758196—22no—
38C2×#11758196D414yes—
39C2×#11758198—22no—
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×#11758198—22no—
43C2×#11758198—22no—
44C2×#11758198—22no—
45C2×#11758198—22no—
46C2×#11758198—22no—
47C2×#11758198D414yes—
48C23×C4×C61C2×C411yescharacteristic
49C23×C4×C61C2×C411yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61—22no—
52C2×C4⋊C4×C61—22no—
53C2×C4⋊C4×C61—22no—
54C24×C61C22×C411yescharacteristic
55C23×D61—21no—
56C23×D61—21no—
57C23×D61—24no—
58C23×D61—21no—
59C23×D61—21no—
60C23×D61—24no—
61C23×D61—24no—
62C23×D61—42no—
63C23×D61—42no—
64C23×D61—42no—
65C23×D61C22⋊C412yes—
66C23×D61C22⋊C412yes—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—42no—
74C22×C4×C61—42no—
75C22×C4×C61—42no—
76C22×C4×C61C22⋊C412yes—
77C22×C4×C61C22⋊C412yes—
78C22×C4×C61C22⋊C412yes—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—24no—
82C22×Dic61—42no—
83C22×Dic61C22⋊C412yes—
84C22×Dic61C2×D412yes—
85C22×Dic61C2×D412yes—
86C22×Dic61C2×D412yes—
87C2×D244—28no—
88C2×D244—48no—
89C2×D244—44no—
90C2×D244—48no—
91C2×D244—44no—
92C2×C4×D61—28no—
93C2×C4×D61—28no—
94C2×C4×D61—44no—
95C2×C4×D61—48no—
96C2×C4×D61—48no—
97C2×#92420—48no—
98C2×#92420—44no—
99C4⋊C4×C61—28no—
100#11758198—28no—
101#11758198—28no—
102#11758198—28no—
103#11758196—28no—
104C23×C61—22no—
105C23×C61—22no—
106C23×C61C2×C22⋊C411yescharacteristic
107C23×C61C2×C22⋊C411yescharacteristic
108C23×C61C2×C22⋊C411yescharacteristic
109C23×C61#13114yes—
110C22×D61—24no—
111C22×D61—24no—
112C22×D61—22no—
113C22×D61—24no—
114C22×D61—22no—
115C22×D61—24no—
116C22×D61—22no—
117C22×D61—24no—
118C22×D61—416no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61—42no—
126C22×D61—42no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—88no—
132C22×D61#9914yes—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—24no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61—42no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×Dic61—24no—
146C2×Dic61—22no—
147C2×Dic61—24no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61#12014yes—
153D244—416no—
154C4×D61—416no—
155#92420—84no—
156#8304—611nomaximal, Sylow
157C22×C61—28no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#37911yescharacteristic
163C22×C61#40812yes—
164C22×C61#40812yes—
165C22×C61#40812yes—
166C22×C61C2×#9912yes—
167C22×C61#41312yes—
168C2×D61—28no—
169C2×D61—24no—
170C2×D61—48no—
171C2×D61—48no—
172C2×D61—44no—
173C2×D61—42no—
174C2×D61—42no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61—42no—
178C2×D61—84no—
179C2×D61—84no—
180C2×D61—84no—
181C4×C61—42no—
182C4×C61—42no—
183C4×C61—42no—
184Dic61—24no—
185Dic61—42no—
186C22×#123—611no—
187#1779—612no—
188C2×#324—612no—
189C2×#323—612no—
190C2×C61—22no—
191C2×C61—22no—
192C2×C61#146814yes—
193C2×C61#178011yescharacteristic
194C2×C61#178111yescharacteristic
195C2×C61#178511yescharacteristic
196D61—44no—
197D61—82no—
198C23×D4—611no—
199C24×C4—611no—
200C2×#123—1224no—
201C2×#123—1224no—
202C2×#123—1224no—
203C22×C4⋊C4—611no—
204C22×C4⋊C4#692311yescharacteristic
205C22×C22⋊C4—611no—
206C22×C22⋊C4—611no—
207C22×C22⋊C4—611no—
208C2×C22⋊C8—614no—
209C2×C22⋊C8—1224no—
210#324—1224no—
211#323—1224no—
212C61#830411yescharacteristic, complemented, Sylow
213C25—611no—
214C25—611no—
215C22×D4—1222no—
216C22×D4—1222no—
217C22×D4—1222no—
218C22×D4—2444no—
219C23×C4—611no—
220C23×C4—611no—
221C23×C4—614no—
222C23×C4—1222no—
223C23×C4—1222no—
224C23×C4—2444no—
225C23×C4C2×#692311yescharacteristic
226C23×C4C2×#692311yescharacteristic
227C23×C4C2×#692311yescharacteristic
228C22×C8—1224no—
229#123—12232no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—614no—
234C2×C4⋊C4—1222no—
235C2×C4⋊C4—1222no—
236C2×C22⋊C4—614no—
237C2×C22⋊C4—1222no—
238C2×C22⋊C4—1222no—
239C2×C22⋊C4—1222no—
240C2×C22⋊C4—1222no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1222no—
244C2×C22⋊C4—1222no—
245C22⋊C8—1224no—
246C22⋊C8—1224no—
247C22⋊C8—2448no—
248C24—612no—
249C24—612no—
250C24—1224no—
251C24—1221no—
252C24—1221no—
253C24—1224no—
254C24—1221no—
255C24—1221no—
256C24—1224no—
257C24—2442no—
258C24—2442no—
259C24—2442no—
260C24C22×#692311yescharacteristic
261C2×D4—1228no—
262C2×D4—2444no—
263C2×D4—2448no—
264C2×D4—2444no—
265C2×D4—2448no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—1228no—
280C22×C4—1228no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1224no—
284C22×C4—2444no—
285C22×C4—2448no—
286C22×C4—2448no—
287C22×C4—2442no—
288C22×C4C22⋊#692312yes—
289C22×C4C22⋊#692312yes—
290C22×C4C22⋊#692312yes—
291C2×C8—2444no—
292C2×C8—2448no—
293C4⋊C4—28no—
294C4⋊C4—1228no—
295C22⋊C4—1228no—
296C22⋊C4—1228no—
297C22⋊C4—1228no—
298C23—22no—
299C23—22no—
300C23—614no—
301C23—1224no—
302C23—1224no—
303C23—1224no—
304C23—1222no—
305C23—1224no—
306C23—1222no—
307C23—1224no—
308C23—1222no—
309C23—4888no—
310C23—24416no—
311C23—2442no—
312C23—2442no—
313C23—2442no—
314C23—2442no—
315C23—2442no—
316C23—2442no—
317C23—2442no—
318C23—2442no—
319C23—2442no—
320C23—2442no—
321C23—2442no—
322C23—2442no—
323C23C2×C22⋊#692311yescharacteristic
324C23C2×C22⋊#692311yescharacteristic
325C23C2×C22⋊#692311yescharacteristic
326C23#1451986514yes—
327D4—24416no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—614no—
341C2×C4—1224no—
342C2×C4—1224no—
343C2×C4—1222no—
344C2×C4—24416no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2442no—
349C8—4884no—
350C22—28no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—1228no—
356C22—1224no—
357C22—4884no—
358C22—4884no—
359C22—4884no—
360C22—2448no—
361C22—2448no—
362C22—2442no—
363C22—2442no—
364C22—2442no—
365C22—2444no—
366C22—2442no—
367C22—2442no—
368C22#1684070311yescharacteristic
369C22#1684073712yes—
370C22#1684073712yes—
371C22#1684073712yes—
372C22D61⋊#9912yes—
373C22#1684074812yes—
374C4—42no—
375C4—42no—
376C4—42no—
377C4—1224no—
378C4—2442no—
379C2—22no—
380C2—22no—
381C2—4882no—
382C2—2444no—
383C2#2146108714yes—
384C2#2146164411yescharacteristic
385C2#2146164611yescharacteristic
386C2#2146165511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8304
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461642C2semidirect
2. C2×#16840608C2semidirect
3. C2×#16840606C2semidirect
212. C61#8304semidirect

Maximal subgroups

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

subgroupindex
#214616422
C2×#168406082
C2×#168406062
C22×#145197622
#830461