Finite Group Databasebeta

← #30599229

Subgroups — #30599229

Order 15616.

680 conjugacy classes of subgroups.

The subgroup lattice has 420 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—42no—
53C42×D61—42no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C2×C4⋊C4×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2×C411yescharacteristic
61#95×C61—21no—
62C23×D61C22⋊C411yescharacteristic
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
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—24no—
80C2×C4×D61—24no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—41no—
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×D61D812yes—
91C2×C4×D61SD1612yes—
92C2×#92420—24no—
93C2×#92420—42no—
94C2×#92420—42no—
95C2×#92420—42no—
96C2×#92420—42no—
97C2×#92420—42no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61C2×C812yes—
101C4⋊C4×C61M1612yes—
102C42×C61—21no—
103C42×C61—21no—
104C42×C61—42no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61C2×C812yes—
108C4⋊Dic61M1612yes—
109#11758196—24no—
110#11758196—24no—
111C4×Dic61—22no—
112C4×Dic61—22no—
113C4×Dic61—42no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C4×Dic61—41no—
117C4×Dic61—41no—
118C4×Dic61#4112yes—
119C4×Dic61#4112yes—
120C23×C61C2×C22⋊C411yescharacteristic
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61C22⋊C812yes—
126C22×D61#10212yes—
127C22×D61#10412yes—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61#10212yes—
140C2×C4×C61#11711yescharacteristic
141C2×C4×C61#11711yescharacteristic
142C2×C4×C61C22×C811yescharacteristic
143C2×C4×C61C2×M1611yescharacteristic
144C2×C4×C61C2×M1611yescharacteristic
145C2×C4×C61C2×M1611yescharacteristic
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61C22⋊C812yes—
157C2×Dic61#12312yes—
158C2×Dic61#12312yes—
159C2×Dic61C2×D811yescharacteristic
160C2×Dic61C2×SD1611yescharacteristic
161C2×Dic61#13712yes—
162C4×D61—22no—
163C4×D61—22no—
164C4×D61—22no—
165C4×D61—22no—
166C4×D61—24no—
167C4×D61—24no—
168C4×D61—44no—
169C4×D61—48no—
170C4×D61—48no—
171#92420—44no—
172#92420—82no—
173#8706—611nomaximal, Sylow
174C22×C61#38111yescharacteristic
175C22×C61C2×C22⋊C811yescharacteristic
176C22×C61#40711yescharacteristic
177C22×C61C2×#10211yescharacteristic
178C22×C61#41911yescharacteristic
179C22×C61C2×#10411yescharacteristic
180C22×C61#42111yescharacteristic
181C2×D61—22no—
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—22no—
186C2×D61—22no—
187C2×D61D4⋊C814yes—
188C4×C61—22no—
189C4×C61—41no—
190C4×C61—42no—
191C4×C61—42no—
192C4×C61#43111yescharacteristic
193C4×C61#43111yescharacteristic
194C4×C61#43211yescharacteristic
195C4×C61#43211yescharacteristic
196Dic61—22no—
197Dic61—22no—
198Dic61—42no—
199Dic61—42no—
200Dic61#48012yes—
201Dic61#48312yes—
202C2×C4×C4⋊C4—611no—
203#1797—611no—
204C4×C22⋊C8—611no—
205#1279—612no—
206#1279—612no—
207C2×C61C2×D4⋊C811yescharacteristic
208C2×C61#147911yescharacteristic
209C2×C61#148611yescharacteristic
210C2×C61#149111yescharacteristic
211C2×C61#181711yescharacteristic
212C2×C61#182311yescharacteristic
213C2×C61#182611yescharacteristic
214D61—24no—
215C22×C4⋊C4—611no—
216C22×C4⋊C4—611no—
217C22×C42—611no—
218C22×C42—1221no—
219C2×C4⋊C8—612no—
220C2×C22⋊C8—1221no—
221C2×C22⋊C8—1221no—
222C2×C4×C8—612no—
223C4×C4⋊C4—611no—
224C4×C4⋊C4—611no—
225C4×C4⋊C4—611no—
226C4×C4⋊C4—1221no—
227C4×C4⋊C4—1221no—
228C4×C4⋊C4#692311yescharacteristic
229C2×#95—1221no—
230#336—1221no—
231#336—1221no—
232C61#870611yescharacteristic, complemented, Sylow
233C23×C4—611no—
234C23×C4—611no—
235C23×C4—611no—
236C23×C4—1221no—
237C23×C4—1221no—
238C22×C8—1222no—
239C22×C8—1222no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—614no—
243C2×C4⋊C4—1222no—
244C2×C4⋊C4—1222no—
245C2×C4⋊C4—1221no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1222no—
248C2×C4⋊C4C2×#692311yescharacteristic
249C2×C4⋊C4C2×#692311yescharacteristic
250C2×C42—21no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—1222no—
255C2×C42—1222no—
256C2×C42—1221no—
257C2×C42—1221no—
258C2×C42—1221no—
259C2×C42—2442no—
260C2×C42—2442no—
261C2×C42C2×#692311yescharacteristic
262C4⋊C8—1222no—
263C4⋊C8—1222no—
264C22⋊C8—1224no—
265C22⋊C8—2442no—
266C4×C8—1222no—
267C4×C8—1222no—
268#95—21no—
269#95—1221no—
270#95—1221no—
271#95—1221no—
272C24—611no—
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—1224no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—2441no—
295C22×C4—2442no—
296C22×C4—2442no—
297C22×C4—2442no—
298C22×C4—2442no—
299C22×C4C22⋊#692311yescharacteristic
300C22×C4C22⋊#692311yescharacteristic
301C22×C4C22×#692311yescharacteristic
302C2×C8—1224no—
303C2×C8—2442no—
304C2×C8—2442no—
305C2×C8—2442no—
306C2×C8—2442no—
307C2×C8—2442no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—612no—
311C4⋊C4—612no—
312C4⋊C4—1224no—
313C4⋊C4—1224no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4D61⋊C812yes—
317C4⋊C4#1175821312yes—
318C42—21no—
319C42—21no—
320C42—42no—
321C42—612no—
322C42—612no—
323C42—1222no—
324C42—1222no—
325C42—2441no—
326C42—2441no—
327C42—2441no—
328C42—2441no—
329C42—2442no—
330C23—612no—
331C23—612no—
332C23—612no—
333C23—1221no—
334C23—1221no—
335C23—1221no—
336C23—1221no—
337C23C2×C22⋊#692311yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—612no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—612no—
355C2×C4—1224no—
356C2×C4—1224no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—1222no—
365C2×C4—1222no—
366C2×C4—1222no—
367C2×C4—2444no—
368C2×C4—2448no—
369C2×C4—2448no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4—2441no—
374C2×C4#1451983912yes—
375C2×C4#1451985611yescharacteristic
376C2×C4#1451985611yescharacteristic
377C2×C4C2×D61⋊C811yescharacteristic
378C2×C4D61⋊M1611yescharacteristic
379C2×C4D61⋊M1611yescharacteristic
380C2×C4C2×#1175821311yescharacteristic
381C8—4882no—
382C8—2444no—
383C22—614no—
384C22—1222no—
385C22—1222no—
386C22—1222no—
387C22—1222no—
388C22—1222no—
389C22—1222no—
390C22#1684070511yescharacteristic
391C22D61⋊(C22⋊C8)11yescharacteristic
392C22#1684073311yescharacteristic
393C22C2×#1451983911yescharacteristic
394C22#1684075511yescharacteristic
395C22D61⋊#10411yescharacteristic
396C22#1684075911yescharacteristic
397C4—22no—
398C4—42no—
399C4—42no—
400C4—41no—
401C4—612no—
402C4—612no—
403C4—1222no—
404C4—1222no—
405C4—2442no—
406C4—2442no—
407C4#1684078011yescharacteristic
408C4#1684078111yescharacteristic
409C4#1684078411yescharacteristic
410C4#1684078511yescharacteristic
411C2—1224no—
412C2D61⋊(D4⋊C8)11yescharacteristic
413C2#2146112211yescharacteristic
414C2#2146114511yescharacteristic
415C2#2146116211yescharacteristic
416C2#2146171111yescharacteristic
417C2#2146172211yescharacteristic
418C2#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#8706
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
232. C61#8706semidirect

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
#870661