Finite Group Databasebeta

← #30596264

Subgroups — #30596264

Order 15616.

666 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840783C211yesmaximal, characteristic
2C2×#16840779C211yesmaximal, characteristic
3#21460657C214yesmaximal
4C2×#16839627C211yesmaximal, characteristic
5#16840783—22no—
6#16840783C414yescomplemented
7#16840779—22no—
8#16840779C414yescomplemented
9C2×#14519844—21no—
10C2×C4⋊#92420—21no—
11C2×C22⋊#92420C2212yes—
12C2×C22⋊#92420C2212yes—
13C2×#14519832—21no—
14C2×C4×#92420—21no—
15C22×C4⋊Dic61C411yescharacteristic
16C22×C4×Dic61C2211yescharacteristic
17#16839627—21no—
18#16839627—21no—
19#16839627—21no—
20#16839627—21no—
21C2×#14519684C412yes—
22C2×#14519684C2212yes—
23C22×C4⋊C4×C61C411yescharacteristic
24C22×#92420—22no—
25C22×#92420—22no—
26#14519844—24no—
27C4⋊#92420—24no—
28C22⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420C2×C414yes—
31C22⋊#92420C2×C414yes—
32#14519832—24no—
33C4×#92420—24no—
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2×C412yes—
36C23×Dic61C2311yescharacteristic
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—42no—
40C2×C4×Dic61C2×C412yes—
41C2×C4×Dic61C2×C412yes—
42C2×C4×Dic61D412yes—
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61Q812yes—
48#14519684—22no—
49#14519684—22no—
50#14519684—22no—
51#14519684—22no—
52C23×C4×C61C2×C412yes—
53C23×C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—42no—
57C24×C61C22×C411yescharacteristic
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—24no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61C4212yes—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C4⋊C412yes—
68C22×Dic61—22no—
69C22×Dic61—22no—
70C22×Dic61—22no—
71C22×Dic61—24no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61—42no—
75C22×Dic61—42no—
76C22×Dic61C4212yes—
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C4⋊C412yes—
80C22×Dic61C22×C411yescharacteristic
81C22×Dic61C22×C411yescharacteristic
82C22×Dic61C2×D411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85C22×Dic61C2×Q811yescharacteristic
86C2×#92420—24no—
87C2×#92420—24no—
88C2×#92420—42no—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C4⋊C4×C61—42no—
93C4⋊C4×C61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61—42no—
96C4×Dic61C22⋊C412yes—
97C4×Dic61C22⋊C412yes—
98C4×Dic61C22⋊C412yes—
99C4×Dic61C22⋊C412yes—
100C4×Dic61C4⋊C412yes—
101C4×Dic61C4⋊C412yes—
102C4×Dic61C4⋊C412yes—
103C4×Dic61C4⋊C412yes—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61C2×C4211yescharacteristic
109C23×C61C2×C22⋊C411yescharacteristic
110C23×C61C2×C4⋊C411yescharacteristic
111C23×C61#13112yes—
112C23×C61#13112yes—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—24no—
116C2×C4×C61—24no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×C4×C61—84no—
121C2×C4×C61#9512yes—
122C2×C4×C61#9512yes—
123C2×C4×C61#10012yes—
124C2×C4×C61#10112yes—
125C2×Dic61—24no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—24no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—84no—
143C2×Dic61#9512yes—
144C2×Dic61#9512yes—
145C2×Dic61C2×C22⋊C411yescharacteristic
146C2×Dic61C2×C22⋊C411yescharacteristic
147C2×Dic61C2×C4⋊C411yescharacteristic
148C2×Dic61C2×C4⋊C411yescharacteristic
149#92420—44no—
150#92420—44no—
151#7914—611nomaximal, Sylow
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61C2×#9511yescharacteristic
161C22×C61#40512yes—
162C22×C61#40811yescharacteristic
163C22×C61#40811yescharacteristic
164C22×C61#41011yescharacteristic
165C22×C61#41011yescharacteristic
166C22×C61C2×#10011yescharacteristic
167C22×C61C2×#10111yescharacteristic
168C22×C61#42412yes—
169C4×C61—22no—
170C4×C61—82no—
171C4×C61#34314yes—
172Dic61—22no—
173Dic61—22no—
174Dic61—21no—
175Dic61—21no—
176Dic61—21no—
177Dic61—21no—
178Dic61—82no—
179C2×#432—611no—
180C2×#431—611no—
181C2×#382—611no—
182#1280—614no—
183C2×C61—22no—
184C2×C61—22no—
185C2×C61#146911yescharacteristic
186C2×C61#146911yescharacteristic
187C2×C61#147011yescharacteristic
188C2×C61#147011yescharacteristic
189C2×C61#172911yescharacteristic
190C2×C61#174011yescharacteristic
191C2×C61C2×#34311yescharacteristic
192C22×C4⋊C4—611no—
193C22×C4⋊C4#692311yescharacteristic
194C22×C42—611no—
195#432—614no—
196#432—1222no—
197#431—614no—
198#431—1222no—
199C2×C4⋊C8—1221no—
200C2×C4⋊C8—1221no—
201C2×C22⋊C8—612no—
202C2×C22⋊C8—612no—
203C2×#97—1221no—
204C2×C4×C8—1221no—
205#382—1221no—
206#382—1221no—
207#382—1221no—
208#382—1221no—
209C2×#95—612no—
210C2×#95—612no—
211C61#791411yescharacteristic, complemented, Sylow
212C23×C4—611no—
213C23×C4—611no—
214C23×C4—612no—
215C23×C4C2×#692312yes—
216C23×C4C2×#692311yescharacteristic
217C22×C8—1222no—
218C22×C8—1222no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—42no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—2442no—
225C2×C42—612no—
226C2×C42—612no—
227C2×C42—612no—
228C2×C42—612no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—611no—
233C4⋊C8—1224no—
234C4⋊C8—1224no—
235C22⋊C8—614no—
236C22⋊C8—614no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239#97—1224no—
240C4×C8—1224no—
241#95—1222no—
242#95—1222no—
243#95—1222no—
244#95—1222no—
245C24C22×#692311yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—24no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—612no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—612no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1224no—
265C22×C4—1222no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2442no—
269C22×C4—2442no—
270C22×C4C4×#692312yes—
271C22×C4C4⋊#692312yes—
272C22×C4C22⋊#692311yescharacteristic
273C22×C4C22⋊#692311yescharacteristic
274C2×C8—1224no—
275C2×C8—1224no—
276C2×C8—2442no—
277C2×C8—2442no—
278C2×C8—2442no—
279C2×C8—2442no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—2442no—
283C4⋊C4—2442no—
284C42—612no—
285C42—612no—
286C42—612no—
287C42—612no—
288C42—612no—
289C42—612no—
290C42—612no—
291C42—612no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23C2×C4×#692311yescharacteristic
297C23C2×C22⋊#692311yescharacteristic
298C23C2×C4⋊#692311yescharacteristic
299C23#1451986412yes—
300C23#1451986512yes—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—84no—
309C2×C4—612no—
310C2×C4—612no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—1224no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1224no—
325C2×C4—4884no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4(C2×#6923)⋊C412yes—
334C2×C4(C2×#6923)⋊C412yes—
335C2×C4#1451983712yes—
336C2×C4#1451983812yes—
337C8—2444no—
338C8—2444no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22C2×(C2×#6923)⋊C411yescharacteristic
348C22#1684072712yes—
349C22#1684073611yescharacteristic
350C22#1684073711yescharacteristic
351C22#1684074211yescharacteristic
352C22#1684074311yescharacteristic
353C22C2×#1451983711yescharacteristic
354C22C2×#1451983811yescharacteristic
355C22#1684076912yes—
356C4—22no—
357C4—82no—
358C4—1221no—
359C4—1221no—
360C4—1221no—
361C4—1221no—
362C4—1222no—
363C4—1222no—
364C4—4882no—
365C4#1684064214yes—
366C2—22no—
367C2—22no—
368C2#2146108911yescharacteristic
369C2#2146109011yescharacteristic
370C2#2146109211yescharacteristic
371C2#2146109311yescharacteristic
372C2#2146148611yescharacteristic
373C2#2146151911yescharacteristic
374C2C2×#1684064211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#7914
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #16840783C4semidirect
8. #16840779C4semidirect
211. C61#7914semidirect

Maximal subgroups

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

subgroupindex
C2×#168407832
C2×#168407792
#214606572
C2×#168396272
#791461