Finite Group Databasebeta

← #30606844

Subgroups — #30606844

Order 15616.

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

normal subgroups only

This group has 962 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
1C2×#16840673C212yesmaximal, complemented
2C2×#16840670C212yesmaximal, complemented
3#21461654C212yesmaximal, complemented
4C2×#16840332C211yesmaximal, characteristic
5C2×#14519838—22no—
6C2×#14519838C2214yes—
7#16840734—22no—
8#16840673—24no—
9#16840670—24no—
10C22×#11758224C411yescharacteristic
11C22×Q8×D61C2211yescharacteristic
12#16840332—24no—
13#16840332—24no—
14C2×#14519777C2211yescharacteristic
15C2×#14519775C411yescharacteristic
16C2×#14519764C2211yescharacteristic
17C2×#14519759—22no—
18C2×#14519754—22no—
19C2×#14519734C411yescharacteristic
20C2×#124×C61C411yescharacteristic
21C2×#11758217—24no—
22#14519838—24no—
23#14519838—24no—
24#14519838—44no—
25#14519834—44no—
26C2×#11758224—22no—
27C2×#11758224—22no—
28C2×#11758224—42no—
29C2×#11758224—42no—
30C22×Dic122C2×C411yescharacteristic
31C22×Dic122D412yes—
32C22×Dic122C2311yescharacteristic
33C2×Q8×D61—22no—
34C2×Q8×D61—22no—
35C2×Q8×D61—42no—
36C2×Q8×D61—42no—
37C22×C22⋊D61—21no—
38C23×Dic61—21no—
39C22×C4×D61C2×C411yescharacteristic
40C22×C4×D61D412yes—
41#14519777—22no—
42#14519777D414yes—
43#14519775—22no—
44#14519775—22no—
45#14519764—22no—
46#14519764D414yes—
47#14519759—216no—
48#14519754—216no—
49#14519734—22no—
50#14519734—22no—
51C2×C4⋊Dic61—22no—
52C2×#11758196—22no—
53C2×#11758196—21no—
54C2×C22⋊Dic61—22no—
55C2×#11758198—21no—
56C2×C4×Dic61C2×C411yescharacteristic
57C22×Q8×C61C2×C411yescharacteristic
58C22×D4×C61C2×C411yescharacteristic
59#124×C61—22no—
60#124×C61—22no—
61C2×C22⋊C4×C61—22no—
62C2×C42×C61C2×C411yescharacteristic
63C24×C61—21no—
64C23×D61C22⋊C411yescharacteristic
65C2×Q8×C61—21no—
66C2×Q8×C61—21no—
67C2×Q8×C61—41no—
68C2×Q8×C61—41no—
69C2×D4×C61—21no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61C22⋊C412yes—
73C22×C4×C61—21no—
74C22×C4×C61C22⋊C412yes—
75C22×C4×C61C22×C411yescharacteristic
76C2×C22⋊D61—24no—
77C2×C22⋊D61—42no—
78C2×C22⋊D61—42no—
79C22×Dic61—24no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—42no—
83C22×Dic61—42no—
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C2×D412yes—
86Q8×D61—48no—
87Q8×D61—48no—
88#11758224—48no—
89#11758224—48no—
90C2×C4×D61—22no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61—22no—
94C2×C4×D61—24no—
95C2×C4×D61—24no—
96C2×C4×D61—42no—
97C2×Dic122—21no—
98C2×Dic122—24no—
99C2×Dic122—24no—
100C2×Dic122—42no—
101C2×Dic122—41no—
102C2×Dic122—41no—
103C2×Dic122—41no—
104C2×Dic122—41no—
105C2×Dic122C22⋊C412yes—
106C2×Dic122C2×D412yes—
107C2×Dic122C2×D412yes—
108#11758217—44no—
109#11758217—44no—
110C2×#92420—44no—
111C22⋊C4×C61—28no—
112C42×C61—21no—
113C42×C61C22⋊C412yes—
114C22⋊Dic61—28no—
115#11758198—24no—
116C4⋊Dic61—28no—
117#11758196—24no—
118#11758196—28no—
119C4×Dic61—21no—
120C4×Dic61C22⋊C412yes—
121C23×C61—22no—
122C23×C61—44no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61C2×C22⋊C411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—42no—
129C22×D61#9912yes—
130Q8×C61—42no—
131Q8×C61—42no—
132D4×C61—42no—
133D4×C61—42no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—42no—
141C2×C4×C61C2×C22⋊C411yescharacteristic
142C2×C4×C61C2×C22⋊C411yescharacteristic
143C22⋊D61—48no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—21no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—48no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61#9912yes—
155C2×Dic61#12014yes—
156C4×D61—24no—
157C4×D61—24no—
158C4×D61—48no—
159Dic122—42no—
160Dic122—42no—
161Dic122—48no—
162Dic122—42no—
163Dic122—42no—
164#92420—84no—
165#12702—611nomaximal, Sylow
166C22×C61—22no—
167C22×C61—44no—
168C22×C61—42no—
169C22×C61—82no—
170C22×C61—82no—
171C22×C61#37911yescharacteristic
172C22×C61C2×#9911yescharacteristic
173C22×C61C2×#9911yescharacteristic
174C2×D61—24no—
175C2×D61—22no—
176C2×D61—42no—
177C2×D61—42no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—42no—
181C4×C61—42no—
182Dic61—24no—
183Dic61—22no—
184Dic61—42no—
185Dic61—42no—
186C2×#536—611no—
187C2×#356—612no—
188C2×#355—612no—
189#1784—612no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61—82no—
193C2×C61#178111yescharacteristic
194C2×C61#213312yes—
195D61—42no—
196C22×#41—611no—
197C23×Q8—611no—
198#536—1224no—
199#536—1224no—
200C2×C4⋊Q8—611no—
201C2×C4⋊Q8—611no—
202C2×#124—611no—
203C2×#124#692311yescharacteristic
204C2×#123—1222no—
205C2×C22⋊Q8—1222no—
206C2×#117—611no—
207C2×#101—614no—
208C2×#101—1222no—
209#407—1222no—
210#356—1224no—
211#355—1224no—
212C61#1270211yescharacteristic, complemented, Sylow
213C2×#41—1222no—
214C2×#41—1222no—
215C2×#41—2442no—
216C2×#41—2442no—
217C22×Q8—612no—
218C22×Q8—611no—
219C22×Q8—611no—
220C22×Q8—1222no—
221C22×Q8—1222no—
222C22×Q8—2442no—
223C22×Q8—2442no—
224C22×Q8C2×#692311yescharacteristic
225C22×D4—1221no—
226C22×D4C2×#692311yescharacteristic
227C23×C4—611no—
228C23×C4—612no—
229C23×C4—1221no—
230C2×M16—1224no—
231C4⋊Q8—614no—
232C4⋊Q8—1222no—
233C4⋊Q8—1222no—
234C4⋊Q8—1222no—
235#124—22no—
236#124—22no—
237#124—614no—
238#124—1222no—
239#123—12216no—
240C22⋊Q8—12216no—
241#117—1222no—
242#117—1222no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1222no—
245C2×C4⋊C4—1222no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1222no—
249C2×C42—611no—
250C2×C42C2×#692311yescharacteristic
251#101—1224no—
252#101—1224no—
253#101—2444no—
254C22⋊C8—2444no—
255C24—21no—
256C24—611no—
257#41—2448no—
258#41—2448no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—612no—
264C2×Q8—612no—
265C2×Q8—612no—
266C2×Q8—1224no—
267C2×Q8—1224no—
268C2×Q8—1221no—
269C2×Q8—2441no—
270C2×Q8—2441no—
271C2×Q8—2442no—
272C2×Q8—2441no—
273C2×Q8—2441no—
274C2×Q8—2448no—
275C2×Q8—2448no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—1224no—
280C2×D4—2442no—
281C2×D4—2442no—
282C2×D4C22⋊#692312yes—
283C22×C4—21no—
284C22×C4—612no—
285C22×C4—611no—
286C22×C4—1222no—
287C22×C4—1224no—
288C22×C4—1222no—
289C22×C4—1224no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1224no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4—2442no—
298C22×C4C22⋊#692312yes—
299C22×C4C22×#692311yescharacteristic
300M16—2444no—
301M16—2444no—
302C2×C8—2444no—
303C4⋊C4—1228no—
304C4⋊C4—1224no—
305C4⋊C4—1228no—
306C22⋊C4—28no—
307C22⋊C4—1224no—
308C22⋊C4—1228no—
309C42—21no—
310C42—612no—
311C42—1221no—
312C42C22⋊#692312yes—
313C23—22no—
314C23—44no—
315C23—41no—
316C23—41no—
317C23—612no—
318C23—1221no—
319C23—1221no—
320C23—2442no—
321C23C2×C22⋊#692311yescharacteristic
322Q8—42no—
323Q8—42no—
324Q8—2442no—
325Q8—2442no—
326Q8—2442no—
327Q8—2442no—
328Q8—2448no—
329D4—42no—
330D4—42no—
331D4—2448no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—42no—
339C2×C4—612no—
340C2×C4—614no—
341C2×C4—1224no—
342C2×C4—1224no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—2448no—
350C2×C4—2448no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4C2×C22⋊#692311yescharacteristic
355C2×C4C2×C22⋊#692311yescharacteristic
356C8—4884no—
357C22—22no—
358C22—44no—
359C22—42no—
360C22—82no—
361C22—82no—
362C22—1224no—
363C22—1222no—
364C22—2442no—
365C22—2442no—
366C22#1684070311yescharacteristic
367C22D61⋊#9911yescharacteristic
368C22D61⋊#9911yescharacteristic
369C4—21no—
370C4—21no—
371C4—42no—
372C4—42no—
373C4—1224no—
374C4—1222no—
375C4—2442no—
376C4—2442no—
377C2—21no—
378C2—21no—
379C2—82no—
380C2—2442no—
381C2#2146164611yescharacteristic
382C2#2146211512yes—
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#124×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758224C4
cosocleC22×Dic122C23
hypercenterC2×#124#6923
hypocenterC61#12702
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16840673C2semidirect
2. C2×#16840670C2semidirect
3. #21461654C2semidirect
212. C61#12702semidirect

Maximal subgroups

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

subgroupindex
C2×#168406732
C2×#168406702
#214616542
C2×#168403322
#1270261