Finite Group Databasebeta

← #30599233

Subgroups — #30599233

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461673C211yesmaximal, characteristic
2C4×C22⋊#92420C211yesmaximal, characteristic
3#21460655C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5#117×Dic61C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×C22⋊#92420—21no—
8C2×C22⋊#92420—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×#14519736C411yescharacteristic
13C22×C4×Dic61C2211yescharacteristic
14C4⋊C4×Dic61C411yescharacteristic
15C4⋊C4×Dic61C411yescharacteristic
16C4⋊C4×Dic61C2211yescharacteristic
17C4⋊C4×Dic61C2211yescharacteristic
18C22⋊C4×Dic61—21no—
19C22⋊C4×Dic61—21no—
20#16839608—21no—
21C42×Dic61—21no—
22C2×#117×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—22no—
26C4⋊#92420—22no—
27C22⋊#92420—24no—
28C22⋊#92420—42no—
29C4×#92420—22no—
30C4×#92420—22no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33#14519736—22no—
34#14519736—22no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61—22no—
40C2×C4×Dic61—22no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61C2311yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C23×C4×C61C2×C411yescharacteristic
54#117×C61—22no—
55#117×C61C814yescomplemented
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C22⋊C4×C61—21no—
59C2×C42×C61—21no—
60C24×C61C22⋊C411yescharacteristic
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C2×C812yes—
69C22×C4×C61M1612yes—
70C22×C4×C61C22×C411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—22no—
76C22×Dic61—22no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—41no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C2×#92420—24no—
85C2×#92420—42no—
86C2×#92420—42no—
87C2×#92420—42no—
88C2×#92420—42no—
89C2×#92420—42no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61C2×C812yes—
93C4⋊C4×C61C2×C812yes—
94C22⋊C4×C61—24no—
95C42×C61—24no—
96C22⋊Dic61—24no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61M1612yes—
100C4⋊Dic61M1612yes—
101C4×Dic61—24no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—22no—
105C4×Dic61—22no—
106C4×Dic61—42no—
107C4×Dic61—42no—
108C4×Dic61—42no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C4×Dic61#4112yes—
112C4×Dic61#4112yes—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61C22⋊C812yes—
120C23×C61C2×C22⋊C411yescharacteristic
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C22⋊C812yes—
134C2×C4×C61#11711yescharacteristic
135C2×C4×C61#11711yescharacteristic
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61C2×M1611yescharacteristic
139C2×C4×C61C2×M1611yescharacteristic
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—44no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61#10412yes—
157C2×Dic61#12312yes—
158C2×Dic61#12312yes—
159C2×Dic61#13512yes—
160C2×Dic61AGL(1,ℤ/8)11yescharacteristic
161C2×Dic61#13711yescharacteristic
162#92420—44no—
163#92420—82no—
164#8708—611nomaximal, Sylow
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61#38111yescharacteristic
173C22×C61C2×C22⋊C811yescharacteristic
174C22×C61#40711yescharacteristic
175C22×C61#41611yescharacteristic
176C22×C61#41711yescharacteristic
177C22×C61C2×#10411yescharacteristic
178C22×C61#42111yescharacteristic
179C4×C61—22no—
180C4×C61—42no—
181C4×C61—42no—
182C4×C61#43111yescharacteristic
183C4×C61#43111yescharacteristic
184C4×C61#43211yescharacteristic
185C4×C61#43211yescharacteristic
186Dic61—22no—
187Dic61—22no—
188Dic61—41no—
189Dic61—42no—
190Dic61—42no—
191Dic61#48212yes—
192Dic61#48512yes—
193C4×#117—611no—
194#1797—611no—
195C4×C22⋊C8—611no—
196#1279—612no—
197#1279—612no—
198C2×C61—42no—
199C2×C61#147611yescharacteristic
200C2×C61#147711yescharacteristic
201C2×C61#148811yescharacteristic
202C2×C61#148911yescharacteristic
203C2×C61#181711yescharacteristic
204C2×C61#182511yescharacteristic
205C2×C61#182611yescharacteristic
206C2×#117—611no—
207C2×#117#692311yescharacteristic
208C22×C42—611no—
209C2×C4⋊C8—612no—
210C2×C22⋊C8—1221no—
211C2×C22⋊C8—1221no—
212C2×C4×C8—612no—
213C4×C4⋊C4—611no—
214C4×C4⋊C4—611no—
215C4×C4⋊C4—611no—
216C4×C4⋊C4—611no—
217C4×C22⋊C4—1221no—
218C4×C22⋊C4—1221no—
219#376—1221no—
220C43—1221no—
221#336—1221no—
222#336—1221no—
223C61#870811yescharacteristic, complemented, Sylow
224C23×C4—611no—
225C23×C4—611no—
226C23×C4C2×#692311yescharacteristic
227C22×C8—1222no—
228C22×C8—1222no—
229#117—22no—
230#117—1222no—
231#117—1222no—
232#117#9242014yescomplemented
233C2×C4⋊C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4C2×#692311yescharacteristic
236C2×C4⋊C4C2×#692311yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—1221no—
239C2×C42—21no—
240C2×C42—611no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—1222no—
245C2×C42—1222no—
246C2×C42—1221no—
247C2×C42—1221no—
248C2×C42—1221no—
249C2×C42—1221no—
250C2×C42—1221no—
251C4⋊C8—1222no—
252C4⋊C8—1222no—
253C22⋊C8—1224no—
254C22⋊C8—2442no—
255C4×C8—1222no—
256C4×C8—1222no—
257#95—1221no—
258#95—1221no—
259#95—1221no—
260#95—1221no—
261C24C22⋊#692311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1222no—
273C22×C4—1221no—
274C22×C4—1222no—
275C22×C4—1222no—
276C22×C4—1222no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4—1221no—
280C22×C4—2441no—
281C22×C4C2×#9242012yes—
282C22×C4#1175821712yes—
283C22×C4C22⋊#692311yescharacteristic
284C22×C4C22×#692311yescharacteristic
285C2×C8—1224no—
286C2×C8—2442no—
287C2×C8—2442no—
288C2×C8—2442no—
289C2×C8—2442no—
290C2×C8—2442no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—612no—
294C4⋊C4—612no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4C2×#9242012yes—
298C4⋊C4C2×#9242012yes—
299C22⋊C4—24no—
300C22⋊C4—1224no—
301C42—24no—
302C42—612no—
303C42—612no—
304C42—1222no—
305C42—1222no—
306C42—1224no—
307C42—1221no—
308C42—1221no—
309C42—2442no—
310C42—2441no—
311C42—2441no—
312C42—2442no—
313C42—2442no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C22⋊#9242012yes—
321C23C2×C22⋊#692311yescharacteristic
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—612no—
335C2×C4—612no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—612no—
339C2×C4—612no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—2442no—
350C2×C4—2442no—
351C2×C4—2444no—
352C2×C4—2441no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4C22⋊#9242012yes—
357C2×C4#1451985611yescharacteristic
358C2×C4#1451985611yescharacteristic
359C2×C4C22×#9242011yescharacteristic
360C2×C4C2×#1175821711yescharacteristic
361C2×C4D61⋊M1611yescharacteristic
362C2×C4D61⋊M1611yescharacteristic
363C8—4882no—
364C8—2444no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22#1684070511yescharacteristic
373C22C2×C22⋊#9242011yescharacteristic
374C22#1684073411yescharacteristic
375C22#1684075211yescharacteristic
376C22#1684075311yescharacteristic
377C22D61⋊#10411yescharacteristic
378C22#1684075911yescharacteristic
379C4—22no—
380C4—42no—
381C4—42no—
382C4—612no—
383C4—612no—
384C4—1222no—
385C4—1222no—
386C4—2442no—
387C4—2442no—
388C4—2441no—
389C4#1684077811yescharacteristic
390C4#1684077811yescharacteristic
391C4#1684078211yescharacteristic
392C4#1684078211yescharacteristic
393C2—42no—
394C2#2146111011yescharacteristic
395C2#2146111411yescharacteristic
396C2#2146115211yescharacteristic
397C2#2146115611yescharacteristic
398C2#2146170911yescharacteristic
399C2#2146172411yescharacteristic
400C2#2146172711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8708
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #21460655C2semidirect
4. #21460655C2semidirect
55. #117×C61C8semidirect
223. C61#8708semidirect
232. #117#92420semidirect

Maximal subgroups

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

subgroupindex
#214616732
C4×C22⋊#924202
#214606552
#117×Dic612
#870861