Finite Group Databasebeta

← #29581325

Subgroups — #29581325

Order 15616.

526 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16840132C211yesmaximal, characteristic, complemented
2C2×#16840122C211yesmaximal, characteristic
3#21453869C211yesmaximal, characteristic
4#21446792C211yesmaximal, characteristic, complemented
5C2×#16839501C211yesmaximal, characteristic
6#21443701C211yesmaximal, characteristic, complemented
7C2×C61×#330C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519765C2211yescharacteristic
10#16840132—22no—
11#16840132—22no—
12#16840122—22no—
13#16840122—22no—
14C2×#14519702—21no—
15C2×#14519700—21no—
16C2×#14519700—21no—
17C2×#14519699—21no—
18C2×#14519688C2211yescharacteristic
19#16839697—21no—
20#16839688—21no—
21#16839684—22no—
22#16839682—21no—
23#16839679—21no—
24#16839628C2211yescharacteristic
25#16839525—22no—
26#16839501—22no—
27C2×#125×C61C2211yescharacteristic
28C2×#97×C61C2211yescharacteristic
29C2×#97×C61C2211yescharacteristic
30C61×#330—22no—
31C22×Dic122—21no—
32C22×Dic122D411yescharacteristic
33C22×D244D411yescharacteristic
34C22×#92418—21no—
35#14519777—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777D412yes—
39#14519765—21no—
40#14519765—21no—
41#14519765—21no—
42#14519765—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61D412yes—
46C2×#11758196—22no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—22no—
50C2×#11758198—22no—
51#14519702—24no—
52#14519700—24no—
53#14519700—24no—
54#14519699—24no—
55#14519688—21no—
56#14519688D412yes—
57#14519684—22no—
58#14519684—21no—
59#14519684—21no—
60C22×C8×C61—21no—
61C22×C8×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64#125×C61—21no—
65#125×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C42×C61C2311yescharacteristic
71#97×C61—21no—
72#97×C61—21no—
73#97×C61—21no—
74#97×C61D412yes—
75C23×D61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×Dic61—21no—
82C22×Dic61—22no—
83C22×Dic61—41no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—42no—
87C2×Dic122—22no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—42no—
91C2×Dic122—44no—
92C2×Dic122—41no—
93C2×C8×C61—22no—
94C2×C8×C61—22no—
95C2×C8×C61—41no—
96C2×C8×C61—42no—
97C2×C8×C61—41no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61C2×D411yescharacteristic
109C42×C61#4111yescharacteristic
110#11758198—41no—
111#11758198—41no—
112#11758198—41no—
113#11758198—41no—
114#11758198—82no—
115#11758198—82no—
116C4⋊Dic61—22no—
117C4⋊Dic61—22no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—42no—
121#11758196—82no—
122C2×#92418—22no—
123C2×#92418—42no—
124C23×C61#12011yescharacteristic
125C22×D61—41no—
126C22×D61—42no—
127C22×D61—41no—
128C22×D61—42no—
129C22×D61—41no—
130C2×C4×C61—22no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—21no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—42no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12711yescharacteristic
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—82no—
152D244—42no—
153D244—81no—
154Dic122—44no—
155Dic122—42no—
156Dic122—82no—
157Dic122—81no—
158C8×C61—42no—
159C8×C61—42no—
160#92418—42no—
161#10083—611nomaximal, Sylow
162C22×C61#39211yescharacteristic
163C22×C61#45412yes—
164C22×C61#45511yescharacteristic
165C22×C61#45512yes—
166C22×C61#45611yescharacteristic
167C2×D61—82no—
168C2×D61—82no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—81no—
179C4×C61—81no—
180Dic61—82no—
181Dic61—82no—
182Dic61—81no—
183C2×#491—611no—
184C2×#489—611no—
185#2820—611no—
186#1993—611no—
187C2×#330D6111yescharacteristic, complemented
188C2×#329—611no—
189#1295—611no—
190C2×C61#166212yes—
191C2×C61#166412yes—
192C2×C61#200311yescharacteristic
193C2×C61#200411yescharacteristic
194C2×C61#200711yescharacteristic
195D61—161no—
196C2×C4⋊Q8—611no—
197C2×#125C2×D6111yescharacteristic
198C2×#124—611no—
199#491—1222no—
200#491—1222no—
201#489—1222no—
202#489—1222no—
203C2×#103—1221no—
204C2×#103—1221no—
205C2×#103—1221no—
206C2×#102—1221no—
207C2×#97—611no—
208C2×#97C2×D6111yescharacteristic
209C2×#97C2×D6111yescharacteristic
210#399—1221no—
211#397—1221no—
212#396—1222no—
213#395—1221no—
214#394—1221no—
215#382—611no—
216#340—1222no—
217#330—22no—
218#329—1222no—
219C61#1008311yescharacteristic, complemented, Sylow
220C22×Q8—611no—
221C22×Q8—1221no—
222C22×D4—611no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—1221no—
226C4⋊Q8—612no—
227C4⋊Q8—1221no—
228C4⋊Q8—1221no—
229C4⋊Q8—1221no—
230#125—21no—
231#125—21no—
232#125—21no—
233#125—21no—
234#124—1221no—
235#124—1221no—
236#124—1221no—
237#124—1221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—612no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1222no—
244C2×C4⋊C4D24411yescharacteristic
245C2×C4⋊C4D24411yescharacteristic
246C2×C22⋊C4—1222no—
247C2×C22⋊C4—1222no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C42C22×D6111yescharacteristic
251#103—1224no—
252#103—1224no—
253#103—1224no—
254#102—1224no—
255#97—21no—
256#97—21no—
257#97—21no—
258#97—612no—
259#97—1221no—
260#97C22⋊D6112yes—
261#95—1222no—
262#95—1221no—
263#95—1221no—
264C24—1221no—
265C2×Q8—1221no—
266C2×Q8—1222no—
267C2×Q8—1221no—
268C2×Q8—2444no—
269C2×Q8—2442no—
270C2×Q8—2441no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2442no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—1222no—
277C22×C4—1221no—
278C22×C4—2441no—
279C22×C4C2×D24411yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C22×C4D4×D6111yescharacteristic
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—42no—
286C2×C8—41no—
287C2×C8—1222no—
288C2×C8—2442no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—1222no—
298C4⋊C4—1222no—
299C4⋊C4—4882no—
300C4⋊C4—2442no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C22⋊C4—4882no—
304C22⋊C4—4882no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42#1175822211yescharacteristic
310C42D4×D6111yescharacteristic
311C42D4×D6111yescharacteristic
312C42C2×C22⋊D6111yescharacteristic
313C23—2442no—
314C23—2441no—
315C23—2442no—
316C23—2441no—
317C23—2441no—
318C23#1451974711yescharacteristic
319Q8—4881no—
320Q8—4882no—
321Q8—2444no—
322Q8—2442no—
323D4—4881no—
324D4—2442no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—4882no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2441no—
340C2×C4—2442no—
341C2×C4#1451974511yescharacteristic
342C2×C4#1451974711yescharacteristic
343C2×C4#1451975011yescharacteristic
344C2×C4#1451975011yescharacteristic
345C2×C4#1451975111yescharacteristic
346C2×C4#1451977311yescharacteristic
347C8—42no—
348C8—42no—
349C8—2442no—
350C22—4882no—
351C22—4882no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22#1683967111yescharacteristic
356C22#1683993712yes—
357C22#1683994111yescharacteristic
358C22#1683994112yes—
359C22#1683994611yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—81no—
367C4—81no—
368C4—4882no—
369C4—4882no—
370C4—4881no—
371C2—9761no—
372C2#2144514312yes—
373C2#2144515412yes—
374C2#2144684311yescharacteristic
375C2#2144684711yescharacteristic
376C2#2144686711yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenterC2×#330D61
hypocenterC61#10083
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
1. C2×#16840132C2semidirect
4. #21446792C2semidirect
6. #21443701C2semidirect
7. C2×C61×#330C2semidirect
187. C2×#330D61semidirect
219. C61#10083semidirect

Maximal subgroups

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

subgroupindex
C2×#168401322
C2×#168401222
#214538692
#214467922
C2×#168395012
#214437012
C2×C61×#3302
#1008361