Finite Group Databasebeta

← #30595384

Subgroups — #30595384

Order 15616.

668 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 126 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
2C4×#14519834C211yesmaximal, characteristic
3#21460640C212yesmaximal, complemented
4#21460639C212yesmaximal, complemented
5#391×D61C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×#14519834—21no—
8C2×#14519834—21no—
9C2×C4×#92420—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C22×Q8×D61C411yescharacteristic
13C2×C4⋊C4×D61C411yescharacteristic
14C2×C42×D61C2211yescharacteristic
15#16839669C2211yescharacteristic
16#16839668C411yescharacteristic
17#16839667C2211yescharacteristic
18#16839666—21no—
19#16839666—21no—
20#95×D61—21no—
21#95×D61—21no—
22C61×#391C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—42no—
26#14519834—24no—
27#14519834—42no—
28C4×#92420—42no—
29C22×Dic122—21no—
30C22×Dic122C2×C411yescharacteristic
31C2×Q8×D61—22no—
32C2×Q8×D61—42no—
33C2×Q8×D61—42no—
34C2×Q8×D61C814yescomplemented
35C22×C4×D61—21no—
36C22×C4×D61—21no—
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×#11758196—21no—
42C4⋊C4×D61—42no—
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61C2311yescharacteristic
46C42×D61—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×Q8×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2×C411yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58C23×D61C22⋊C411yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2×C812yes—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C22×Dic61C2×D411yescharacteristic
73Q8×D61—48no—
74Q8×D61—48no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—24no—
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61—42no—
88C2×C4×D61C2×C812yes—
89C2×C4×D61M1612yes—
90C2×C4×D61SD1612yes—
91C2×C4×D61Q1612yes—
92C2×Dic122—21no—
93C2×Dic122—24no—
94C2×Dic122—42no—
95C2×Dic122—42no—
96C2×Dic122—41no—
97C2×Dic122—41no—
98C2×Dic122C2×C812yes—
99C2×#92420—24no—
100C2×#92420—42no—
101C2×#92420—42no—
102C2×#92420—42no—
103C2×#92420—42no—
104C2×#92420—42no—
105C4⋊C4×C61—41no—
106C42×C61—41no—
107C4⋊Dic61—41no—
108#11758196—42no—
109C4×Dic61—22no—
110C4×Dic61—22no—
111C4×Dic61—41no—
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61C22⋊C812yes—
118C22×D61#10312yes—
119C22×D61#10412yes—
120Q8×C61—42no—
121Q8×C61—42no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
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#10312yes—
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—22no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61C22⋊C812yes—
149C2×Dic61#9912yes—
150C2×Dic61#10012yes—
151C2×Dic61C2×SD1611yescharacteristic
152C2×Dic61C2×Q1611yescharacteristic
153C2×Dic61#13712yes—
154C4×D61—24no—
155C4×D61—24no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—44no—
159C4×D61—48no—
160C4×D61—84no—
161Dic122—42no—
162Dic122—48no—
163Dic122—42no—
164#92420—44no—
165#92420—82no—
166#7575—611nomaximal, Sylow
167C22×C61C2×C22⋊C811yescharacteristic
168C22×C61C2×#9911yescharacteristic
169C22×C61C2×#10011yescharacteristic
170C22×C61C2×#10311yescharacteristic
171C22×C61#41911yescharacteristic
172C22×C61C2×#10411yescharacteristic
173C22×C61#42111yescharacteristic
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—22no—
180C2×D61Q8⋊C814yes—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—22no—
184C4×C61—42no—
185C4×C61—41no—
186C4×C61—81no—
187Dic61—22no—
188Dic61—21no—
189Dic61—21no—
190Dic61—42no—
191Dic61—81no—
192Dic61#32314yes—
193C2×#391—611no—
194#1797—611no—
195C4×C22⋊C8—611no—
196#1272—612no—
197#1272—612no—
198C2×C61C2×#32311yescharacteristic
199C2×C61C2×Q8⋊C811yescharacteristic
200C2×C61#147911yescharacteristic
201C2×C61#150811yescharacteristic
202C2×C61#152011yescharacteristic
203C2×C61#152711yescharacteristic
204C2×C61#154811yescharacteristic
205D61—24no—
206C23×Q8—611no—
207C22×C4⋊C4—611no—
208C22×C42—611no—
209C2×C4⋊C8—1221no—
210C2×C22⋊C8—1221no—
211C2×C22⋊C8—1221no—
212C2×C4×C8—1221no—
213#391—611no—
214#391—611no—
215#391—611no—
216#391—1221no—
217#391—1221no—
218#391#692311yescharacteristic
219C2×#95—1221no—
220C2×#95—1221no—
221#336—612no—
222#336—612no—
223C61#757511yescharacteristic, complemented, Sylow
224C22×Q8—614no—
225C22×Q8—611no—
226C22×Q8—1221no—
227C22×Q8—1222no—
228C22×Q8—2442no—
229C22×Q8—2442no—
230C22×Q8C2×#692311yescharacteristic
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—611no—
234C23×C4—1221no—
235C23×C4—1221no—
236C22×C8—1222no—
237C22×C8—1222no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4—2442no—
241C2×C4⋊C4C2×#692311yescharacteristic
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—21no—
253#95—1221no—
254#95—1221no—
255#95—1221no—
256#95—1221no—
257#95—1221no—
258#95—1221no—
259C24—611no—
260C2×Q8—21no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—612no—
264C2×Q8—1224no—
265C2×Q8—1221no—
266C2×Q8—2441no—
267C2×Q8—2441no—
268C2×Q8—2442no—
269C2×Q8—2442no—
270C2×Q8—2448no—
271C2×Q8—2448no—
272C2×Q8D61⋊C812yes—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—612no—
279C22×C4—612no—
280C22×C4—612no—
281C22×C4—612no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4—1222no—
286C22×C4—1224no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4—2442no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4C22⋊#692311yescharacteristic
298C22×C4C22⋊#692311yescharacteristic
299C22×C4C22×#692311yescharacteristic
300C2×C8—1224no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8—2442no—
304C2×C8—2442no—
305C2×C8—2442no—
306C4⋊C4—41no—
307C4⋊C4—2441no—
308C4⋊C4—2442no—
309C42—41no—
310C42—1222no—
311C42—1222no—
312C42—2441no—
313C23—612no—
314C23—612no—
315C23—612no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—1221no—
320C23C2×C22⋊#692311yescharacteristic
321Q8—42no—
322Q8—42no—
323Q8—2442no—
324Q8—2442no—
325Q8—2448no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—612no—
340C2×C4—612no—
341C2×C4—612no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—612no—
345C2×C4—1224no—
346C2×C4—1224no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1222no—
352C2×C4—4884no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2444no—
356C2×C4—2448no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4#1451984012yes—
363C2×C4C2×D61⋊C811yescharacteristic
364C2×C4D61⋊M1611yescharacteristic
365C8—4882no—
366C8—2444no—
367C22—614no—
368C22—1222no—
369C22—1222no—
370C22—1222no—
371C22—1222no—
372C22—1222no—
373C22—1222no—
374C22D61⋊(C22⋊C8)11yescharacteristic
375C22D61⋊#9911yescharacteristic
376C22D61⋊#10011yescharacteristic
377C22C2×#1451984011yescharacteristic
378C22#1684075511yescharacteristic
379C22D61⋊#10411yescharacteristic
380C22#1684075911yescharacteristic
381C4—22no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—41no—
386C4—81no—
387C4—614no—
388C4—1221no—
389C4—1221no—
390C4—1222no—
391C4—4881no—
392C4—2442no—
393C2—1224no—
394C2D61⋊#32311yescharacteristic
395C2D61⋊(Q8⋊C8)11yescharacteristic
396C2#2146112211yescharacteristic
397C2#2146121711yescharacteristic
398C2#2146125711yescharacteristic
399C2#2146127911yescharacteristic
400C2#2146133311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#7575
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
4. #21460639C2semidirect
34. C2×Q8×D61C8semidirect
223. C61#7575semidirect

Maximal subgroups

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

subgroupindex
#214616762
C4×#145198342
#214606402
#214606392
#391×D612
#757561