Finite Group Databasebeta

← #30599232

Subgroups — #30599232

Order 15616.

680 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461674C211yesmaximal, characteristic
2C4×#14519834C211yesmaximal, characteristic
3#21460655C212yesmaximal, complemented
4#21460655C212yesmaximal, complemented
5C4×C4⋊C4×D61C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×#14519834—21no—
8C2×#14519834—21no—
9C2×C4×#92420C2212yes—
10#16840628—21no—
11#16840628—21no—
12C2×C4⋊C4×D61C411yescharacteristic
13C2×C4⋊C4×D61C411yescharacteristic
14C2×C42×D61—21no—
15C2×C42×D61C2211yescharacteristic
16C4⋊C4×Dic61C2211yescharacteristic
17C4⋊C4×Dic61C2211yescharacteristic
18C4×#11758196—21no—
19C4×C4⋊Dic61C411yescharacteristic
20#16839613—21no—
21#95×D61—21no—
22C4×C4⋊C4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—22no—
26C4⋊#92420—22no—
27#14519834—24no—
28#14519834—42no—
29C4×#92420—22no—
30C4×#92420—22no—
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C22×C4×D61C2×C411yescharacteristic
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C4⋊C4×D61—22no—
41C4⋊C4×D61—22no—
42C4⋊C4×D61—22no—
43C4⋊C4×D61C814yescomplemented
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61C2311yescharacteristic
50C42×D61—22no—
51C42×D61—22no—
52C42×D61—44no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C42×C61—21no—
59C2×C42×C61C2×C411yescharacteristic
60#95×C61—21no—
61C23×D61C22⋊C411yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22×C411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—24no—
79C2×C4×D61—24no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—41no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
86C2×C4×D61—42no—
87C2×C4×D61C2×C812yes—
88C2×C4×D61M1612yes—
89C2×C4×D61SD1612yes—
90C2×C4×D61Q1612yes—
91C2×#92420—24no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61C2×C812yes—
100C4⋊C4×C61M1612yes—
101C42×C61—21no—
102C42×C61—21no—
103C42×C61—42no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61C2×C812yes—
107C4⋊Dic61M1612yes—
108#11758196—24no—
109#11758196—24no—
110C4×Dic61—22no—
111C4×Dic61—22no—
112C4×Dic61—42no—
113C4×Dic61—42no—
114C4×Dic61—42no—
115C4×Dic61#4112yes—
116C4×Dic61#4112yes—
117C23×C61C2×C22⋊C411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61C22⋊C812yes—
123C22×D61#10312yes—
124C22×D61#10412yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61#10312yes—
137C2×C4×C61#11711yescharacteristic
138C2×C4×C61#11711yescharacteristic
139C2×C4×C61C22×C811yescharacteristic
140C2×C4×C61C2×M1611yescharacteristic
141C2×C4×C61C2×M1611yescharacteristic
142C2×C4×C61C2×M1611yescharacteristic
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61C22⋊C812yes—
154C2×Dic61#12312yes—
155C2×Dic61#12312yes—
156C2×Dic61C2×SD1611yescharacteristic
157C2×Dic61C2×Q1611yescharacteristic
158C2×Dic61AGL(1,ℤ/8)12yes—
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—22no—
162C4×D61—22no—
163C4×D61—24no—
164C4×D61—24no—
165C4×D61—44no—
166C4×D61—48no—
167C4×D61—48no—
168#92420—44no—
169#92420—82no—
170#8707—611nomaximal, Sylow
171C22×C61#38111yescharacteristic
172C22×C61C2×C22⋊C811yescharacteristic
173C22×C61#40711yescharacteristic
174C22×C61C2×#10311yescharacteristic
175C22×C61#41811yescharacteristic
176C22×C61C2×#10411yescharacteristic
177C22×C61#42111yescharacteristic
178C2×D61—22no—
179C2×D61—22no—
180C2×D61—22no—
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—22no—
184C2×D61Q8⋊C814yes—
185C4×C61—22no—
186C4×C61—41no—
187C4×C61—42no—
188C4×C61—42no—
189C4×C61#43111yescharacteristic
190C4×C61#43111yescharacteristic
191C4×C61#43211yescharacteristic
192C4×C61#43211yescharacteristic
193Dic61—22no—
194Dic61—22no—
195Dic61—42no—
196Dic61—42no—
197Dic61#48112yes—
198Dic61#48412yes—
199C2×C4×C4⋊C4—611no—
200#1797—611no—
201C4×C22⋊C8—611no—
202#1279—612no—
203#1279—612no—
204C2×C61C2×Q8⋊C811yescharacteristic
205C2×C61#147811yescharacteristic
206C2×C61#148711yescharacteristic
207C2×C61#149011yescharacteristic
208C2×C61#181711yescharacteristic
209C2×C61#182411yescharacteristic
210C2×C61#182611yescharacteristic
211D61—24no—
212C22×C4⋊C4—611no—
213C22×C4⋊C4—611no—
214C22×C42—611no—
215C22×C42—1221no—
216C2×C4⋊C8—612no—
217C2×C22⋊C8—1221no—
218C2×C22⋊C8—1221no—
219C2×C4×C8—612no—
220C4×C4⋊C4—611no—
221C4×C4⋊C4—611no—
222C4×C4⋊C4—611no—
223C4×C4⋊C4—1221no—
224C4×C4⋊C4—1221no—
225C4×C4⋊C4#692311yescharacteristic
226C2×#95—1221no—
227#336—1221no—
228#336—1221no—
229C61#870711yescharacteristic, complemented, Sylow
230C23×C4—611no—
231C23×C4—611no—
232C23×C4—611no—
233C23×C4—1221no—
234C23×C4—1221no—
235C22×C8—1222no—
236C22×C8—1222no—
237C2×C4⋊C4—611no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—614no—
240C2×C4⋊C4—1222no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1222no—
245C2×C4⋊C4C2×#692311yescharacteristic
246C2×C4⋊C4C2×#692311yescharacteristic
247C2×C42—21no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—1222no—
252C2×C42—1222no—
253C2×C42—1221no—
254C2×C42—1221no—
255C2×C42—1221no—
256C2×C42—2444no—
257C2×C42C2×#692311yescharacteristic
258C4⋊C8—1222no—
259C4⋊C8—1222no—
260C22⋊C8—1224no—
261C22⋊C8—2442no—
262C4×C8—1222no—
263C4×C8—1222no—
264#95—21no—
265#95—1221no—
266#95—1221no—
267#95—1221no—
268C24—611no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—612no—
275C22×C4—612no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—1222no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1224no—
283C22×C4—1224no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4—2442no—
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298C2×C8—1224no—
299C2×C8—2442no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8—2442no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—612no—
307C4⋊C4—612no—
308C4⋊C4—1224no—
309C4⋊C4—1224no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4D61⋊C812yes—
313C4⋊C4#1175821312yes—
314C42—21no—
315C42—21no—
316C42—42no—
317C42—612no—
318C42—612no—
319C42—1222no—
320C42—1222no—
321C42—2442no—
322C42—2442no—
323C42—2442no—
324C23—612no—
325C23—612no—
326C23—612no—
327C23—1221no—
328C23—1221no—
329C23—1221no—
330C23—1221no—
331C23C2×C22⋊#692311yescharacteristic
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—612no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—612no—
349C2×C4—1224no—
350C2×C4—1224no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—1222no—
361C2×C4—2444no—
362C2×C4—2448no—
363C2×C4—2448no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4#1451984012yes—
369C2×C4#1451985611yescharacteristic
370C2×C4#1451985611yescharacteristic
371C2×C4C2×D61⋊C811yescharacteristic
372C2×C4D61⋊M1611yescharacteristic
373C2×C4D61⋊M1611yescharacteristic
374C2×C4C2×#1175821311yescharacteristic
375C8—4882no—
376C8—2444no—
377C22—614no—
378C22—1222no—
379C22—1222no—
380C22—1222no—
381C22—1222no—
382C22—1222no—
383C22—1222no—
384C22#1684070511yescharacteristic
385C22D61⋊(C22⋊C8)11yescharacteristic
386C22#1684073311yescharacteristic
387C22C2×#1451984011yescharacteristic
388C22#1684075411yescharacteristic
389C22D61⋊#10411yescharacteristic
390C22#1684075911yescharacteristic
391C4—22no—
392C4—42no—
393C4—42no—
394C4—41no—
395C4—612no—
396C4—612no—
397C4—1222no—
398C4—1222no—
399C4—2442no—
400C4—2442no—
401C4#1684078011yescharacteristic
402C4#1684078111yescharacteristic
403C4#1684078411yescharacteristic
404C4#1684078511yescharacteristic
405C2—1224no—
406C2D61⋊(Q8⋊C8)11yescharacteristic
407C2#2146111911yescharacteristic
408C2#2146114811yescharacteristic
409C2#2146115911yescharacteristic
410C2#2146171111yescharacteristic
411C2#2146172311yescharacteristic
412C2#2146172711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8707
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460655C2semidirect
4. #21460655C2semidirect
43. C4⋊C4×D61C8semidirect
229. C61#8707semidirect

Maximal subgroups

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

subgroupindex
#214616742
C4×#145198342
#214606552
C4×C4⋊C4×D612
#870761