Finite Group Databasebeta

← #30597561

Subgroups — #30597561

Order 15616.

698 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461605C211yesmaximal, characteristic, complemented
2#21461534C211yesmaximal, characteristic, complemented
3C2×D4⋊#92420C212yesmaximal
4#21460655C212yesmaximal, complemented
5C4×D4×Dic61C211yesmaximal, characteristic
6C2×C4⋊#92420C2212yes—
7C2×#14519832—21no—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11#16840628—21no—
12D4⋊#92420C418yescomplemented
13C2×D4×Dic61C411yescharacteristic
14C2×D4×Dic61C2211yescharacteristic
15C22×C4×Dic61—21no—
16C4⋊C4×Dic61C411yescharacteristic
17C4⋊C4×Dic61C2211yescharacteristic
18C4×C4⋊Dic61C411yescharacteristic
19C22⋊C4×Dic61—21no—
20C22⋊C4×Dic61—21no—
21C4×C22⋊Dic61—21no—
22C42×Dic61C2211yescharacteristic
23C2×C4×D4×C61C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26C4⋊#92420—22no—
27C4⋊#92420C2×C414yescomplemented
28#14519832—42no—
29C4×#92420—22no—
30C4×#92420C2×C414yescomplemented
31C23×Dic61—21no—
32C23×Dic61—21no—
33D4×Dic61—22no—
34D4×Dic61—22no—
35D4×Dic61—22no—
36D4×Dic61C2×C414yes—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61—42no—
45C2×C4×Dic61—42no—
46C2×C4×Dic61C2×C411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61C2311yescharacteristic
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C22×D4×C61C2×C411yescharacteristic
56C23×C4×C61—21no—
57C4×D4×C61—22no—
58C4×D4×C61—22no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C42×C61C2×C411yescharacteristic
62C24×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61C4212yes—
67C2×D4×C61M1612yes—
68C2×D4×C61M1612yes—
69C22×C4×C61—24no—
70C22×C4×C61—21no—
71C22×C4×C61—42no—
72C22×C4×C61—42no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×Dic61—24no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—24no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—42no—
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C2×D411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C2×#92420—24no—
90C2×#92420—24no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61M1612yes—
97C22⋊C4×C61—24no—
98C42×C61—21no—
99C42×C61—21no—
100C22⋊Dic61—24no—
101C22⋊Dic61—24no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C4212yes—
105C4⋊Dic61M1612yes—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—22no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C4×Dic61—42no—
112C4×Dic61—42no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C4×Dic61D812yes—
116C4×Dic61SD1612yes—
117C4×Dic61C22×C412yes—
118C4×Dic61#4112yes—
119C23×C61—22no—
120C23×C61—22no—
121C23×C61—22no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61C2×C22⋊C411yescharacteristic
127D4×C61—22no—
128D4×C61—22no—
129D4×C61—22no—
130D4×C61#9714yescomplemented
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—22no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—48no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61#10212yes—
141C2×C4×C61C2×C4211yescharacteristic
142C2×C4×C61#11711yescharacteristic
143C2×C4×C61C2×M1611yescharacteristic
144C2×C4×C61C2×M1611yescharacteristic
145C2×C4×C61C2×M1611yescharacteristic
146C2×C4×C61C2×M1611yescharacteristic
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—22no—
152C2×Dic61—21no—
153C2×Dic61—22no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—48no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—44no—
162C2×Dic61—44no—
163C2×Dic61#10212yes—
164C2×Dic61C4×D412yes—
165C2×Dic61C4×D412yes—
166C2×Dic61C2×D811yescharacteristic
167C2×Dic61C2×SD1611yescharacteristic
168C2×Dic61#13512yes—
169#92420—44no—
170#92420—44no—
171#8174—611nomaximal, Sylow
172C22×C61—24no—
173C22×C61—42no—
174C22×C61—42no—
175C22×C61—42no—
176C22×C61—42no—
177C22×C61—42no—
178C22×C61—42no—
179C22×C61C4×C22⋊C411yescharacteristic
180C22×C61#40711yescharacteristic
181C22×C61#40711yescharacteristic
182C22×C61C2×#10211yescharacteristic
183C22×C61#41611yescharacteristic
184C22×C61#42111yescharacteristic
185C22×C61#42111yescharacteristic
186C4×C61—22no—
187C4×C61—42no—
188C4×C61—41no—
189C4×C61C2×#9711yescharacteristic
190C4×C61C4×M1611yescharacteristic
191C4×C61#43211yescharacteristic
192C4×C61#43211yescharacteristic
193Dic61—22no—
194Dic61—22no—
195Dic61—42no—
196Dic61—41no—
197Dic61—42no—
198Dic61C4×D812yes—
199Dic61C4×SD1612yes—
200C42×D4—611no—
201#1767—611no—
202#1744—611no—
203C2×D4⋊C8—612no—
204#1279—612no—
205C2×C61—44no—
206C2×C61#148611yescharacteristic
207C2×C61#148611yescharacteristic
208C2×C61#148811yescharacteristic
209C2×C61#148811yescharacteristic
210C2×C61#174911yescharacteristic
211C2×C61#175911yescharacteristic
212C2×C61C4×#10211yescharacteristic
213C2×C4×D4—611no—
214C2×C4×D4—611no—
215C2×C4×D4#692311yescharacteristic
216C22×C42—1221no—
217C2×C4⋊C8—612no—
218C2×#97—1221no—
219C2×C4×C8—612no—
220C4×C4⋊C4—611no—
221C4×C4⋊C4—611no—
222C4×C4⋊C4—611no—
223C4×C22⋊C4—1221no—
224C4×C22⋊C4—1221no—
225C4×C22⋊C4—1221no—
226C43—611no—
227#336—1221no—
228#336—1221no—
229#336—1221no—
230D4⋊C8—618no—
231C61#817411yescharacteristic, complemented, Sylow
232C22×D4C2×#692311yescharacteristic
233C23×C4—21no—
234C23×C4—1221no—
235C23×C4—1221no—
236C22×C8—1222no—
237C22×C8—1222no—
238C4×D4—22no—
239C4×D4—22no—
240C4×D4—614no—
241C4×D4—1222no—
242C4×D4—1222no—
243C4×D4—1222no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4C2×#692311yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—611no—
256C2×C42—1221no—
257C2×C42—1221no—
258C2×C42—1221no—
259C2×C42—2442no—
260C2×C42—2442no—
261C2×C42C2×#692311yescharacteristic
262C4⋊C8—614no—
263C4⋊C8—1222no—
264#97—2442no—
265C4×C8—614no—
266C4×C8—1222no—
267#95—1221no—
268#95—1221no—
269#95—1221no—
270C24—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4#1175821312yes—
275C2×D4C4×#692312yes—
276C2×D4#1175821712yes—
277C22×C4—24no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1224no—
286C22×C4—1224no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—2441no—
290C22×C4—2441no—
291C22×C4—2442no—
292C22×C4—2442no—
293C22×C4—2442no—
294C22×C4C22⋊#692311yescharacteristic
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22×#692311yescharacteristic
297C2×C8—1224no—
298C2×C8—1224no—
299C2×C8—2442no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C4⋊C4—21no—
304C4⋊C4—612no—
305C4⋊C4—612no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4#1175821712yes—
309C22⋊C4—24no—
310C22⋊C4—1224no—
311C22⋊C4—1224no—
312C42—21no—
313C42—21no—
314C42—612no—
315C42—612no—
316C42—612no—
317C42—612no—
318C42—1222no—
319C42—1221no—
320C42—1221no—
321C42—2441no—
322C42—2441no—
323C42—2441no—
324C42—2441no—
325C42—2442no—
326C42—2442no—
327C23—22no—
328C23—22no—
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23C2×C22⋊#692311yescharacteristic
335D4—22no—
336D4—22no—
337D4—22no—
338D4#1451983214yescomplemented
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—48no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—612no—
351C2×C4—612no—
352C2×C4—612no—
353C2×C4—612no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1222no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1222no—
363C2×C4—2444no—
364C2×C4—2444no—
365C2×C4—2448no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4#1451983912yes—
371C2×C4C2×C4×#692311yescharacteristic
372C2×C4#1451985611yescharacteristic
373C2×C4C2×#1175821711yescharacteristic
374C2×C4C2×#1175821711yescharacteristic
375C2×C4D61⋊M1611yescharacteristic
376C2×C4C2×#1175821311yescharacteristic
377C8—2444no—
378C8—2444no—
379C22—24no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22C4×C22⋊#692311yescharacteristic
387C22#1684073211yescharacteristic
388C22#1684073311yescharacteristic
389C22C2×#1451983911yescharacteristic
390C22#1684075211yescharacteristic
391C22#1684075911yescharacteristic
392C22#1684076011yescharacteristic
393C4—22no—
394C4—42no—
395C4—41no—
396C4—612no—
397C4—612no—
398C4—1222no—
399C4—1222no—
400C4—2442no—
401C4—2442no—
402C4—2441no—
403C4C2×#1451983211yescharacteristic
404C4C4×#1175821711yescharacteristic
405C4#1684078211yescharacteristic
406C4#1684078311yescharacteristic
407C2—44no—
408C2#2146114411yescharacteristic
409C2#2146114511yescharacteristic
410C2#2146115011yescharacteristic
411C2#2146115111yescharacteristic
412C2#2146154511yescharacteristic
413C2#2146158211yescharacteristic
414C2C4×#1451983911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#8174
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461605C2semidirect
2. #21461534C2semidirect
4. #21460655C2semidirect
12. D4⋊#92420C4semidirect
27. C4⋊#92420C2×C4semidirect
30. C4×#92420C2×C4semidirect
130. D4×C61#97semidirect
231. C61#8174semidirect
338. D4#14519832semidirect

Maximal subgroups

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

subgroupindex
#214616052
#214615342
C2×D4⋊#924202
#214606552
C4×D4×Dic612
#817461