Finite Group Databasebeta

← #13117838

Subgroups — #13117838

Order 1664.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88150C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic
3C2×#88141C211yesmaximal, characteristic, complemented
4C13×#389C211yesmaximal, characteristic, complemented
5#11718650C211yesmaximal, characteristic
6#11718650C211yesmaximal, characteristic
7#11718642C211yesmaximal, characteristic, complemented
8#11718639C211yesmaximal, characteristic, complemented
9#11718633C211yesmaximal, characteristic, complemented
10C4×#6103C211yesmaximal, characteristic
11C4×#6101C211yesmaximal, characteristic, complemented
12#11718327C211yesmaximal, characteristic
13#11718327C211yesmaximal, characteristic
14#11718308C211yesmaximal, characteristic, complemented
15#11718307C211yesmaximal, characteristic, complemented
16C22×C4×D13C2211yescharacteristic
17C22×C4×D13C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×C13×C4⋊C4C2211yescharacteristic
23C2×C13×C4⋊C4C2211yescharacteristic
24C2×C42×C13C2211yescharacteristic
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2211yescharacteristic
28C2×#6103C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C2×#6101C2211yescharacteristic
34C2×#6101C2211yescharacteristic
35C2×#6101C2211yescharacteristic
36C2×C4×Dic13C2211yescharacteristic
37C2×C4×Dic13C2211yescharacteristic
38C2×C4×Dic13C2211yescharacteristic
39C2×C4×Dic13C2211yescharacteristic
40C2×C4×Dic13C2211yescharacteristic
41#88150C418yescomplemented
42C4⋊C4×D13—24no—
43#88141—24no—
44C13×#95C2211yescharacteristic
45C13×#95C2211yescharacteristic
46#88071C2211yescharacteristic
47#88071C2211yescharacteristic
48#88071C2211yescharacteristic
49#88071C2211yescharacteristic
50#88071C2211yescharacteristic
51#88071C2211yescharacteristic
52#88071C2211yescharacteristic
53#88071C2211yescharacteristic
54C23×D13C2311yescharacteristic
55C22×C4×C13C2311yescharacteristic
56C22×C4×C13C2311yescharacteristic
57C22×C4×C13C2311yescharacteristic
58C22×C4×C13C2311yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×Dic13C2311yescharacteristic
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C22×Dic13C2311yescharacteristic
67C22×Dic13C2311yescharacteristic
68C22×Dic13C2311yescharacteristic
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—22no—
73C2×C4×D13—22no—
74C2×C4×D13—22no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13C2×C414yes—
78C2×Dic26—22no—
79C2×Dic26—22no—
80C2×Dic26C2×C414yescomplemented
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4C2×C414yescomplemented
85C42×C13—41no—
86#6103—22no—
87#6103C2×C414yes—
88#6103C2×C414yes—
89#6103Q814yescomplemented
90C4⋊Dic13—22no—
91#6101—22no—
92#6101—22no—
93#6101—41no—
94#6101C2×C414yescomplemented
95#6101C2×C414yescomplemented
96#6101D414yes—
97C4×Dic13—22no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13—41no—
102#2360—131nomaximal, Sylow
103C23×C13C2411yescharacteristic
104C22×D13—21no—
105C22×D13—21no—
106C22×D13—21no—
107C22×D13—21no—
108C22×D13C22×C412yes—
109C22×D13C2×Q812yes—
110C22×D13#4112yes—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13C22×C412yes—
128C2×C4×C13C22×C412yes—
129C2×C4×C13C22×C412yes—
130C2×C4×C13C2×D412yes—
131C2×C4×C13C2×Q812yes—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13C22×C412yes—
147C2×Dic13C22×C412yes—
148C2×Dic13C22×C412yes—
149C2×Dic13C2×D412yes—
150C2×Dic13C2×D412yes—
151C2×Dic13C2×Q812yes—
152C2×Dic13#4112yes—
153C4×D13—28no—
154C4×D13—44no—
155C4×D13—44no—
156Dic26—28no—
157C2×C22⋊Q8—131no—
158C2×C4×Q8—131no—
159C22×C4⋊C4—131no—
160#391—131no—
161#389—131no—
162#389—131no—
163#389D1311yescharacteristic, complemented
164#387—131no—
165#387—131no—
166#385—131no—
167#385—131no—
168C4×C4⋊C4—131no—
169C4×C22⋊C4—131no—
170C4×C22⋊C4—131no—
171C4×C22⋊C4—131no—
172C22×C13C23×C411yescharacteristic
173C22×C13C22×D411yescharacteristic
174C22×C13C22×Q811yescharacteristic
175C22×C13C2×#4111yescharacteristic
176C22×C13C2×#4111yescharacteristic
177C22×C13H(5,𝔽2)11yescharacteristic
178C22×C132−1+411yescharacteristic
179C2×D13—22no—
180C2×D13—22no—
181C2×D13—22no—
182C2×D13—22no—
183C2×D13—22no—
184C2×D13—22no—
185C2×D13C4×Q814yescomplemented
186C4×C13—22no—
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—22no—
190C4×C13—22no—
191C4×C13—41no—
192C4×C13—41no—
193Dic13—22no—
194Dic13—22no—
195Dic13—22no—
196Dic13—22no—
197Dic13—41no—
198Dic13—41no—
199Dic13C4×D414yes—
200C22×Q8—131no—
201C23×C4—131no—
202C23×C4—131no—
203C23×C4—131no—
204C22⋊Q8—138no—
205C4×Q8—264no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—264no—
214C2×C4⋊C4C2×D1311yescharacteristic
215C2×C4⋊C4C2×D1311yescharacteristic
216C2×C4⋊C4C2×D1311yescharacteristic
217C2×C4⋊C4C2×D1311yescharacteristic
218C2×C22⋊C4—131no—
219C2×C22⋊C4—131no—
220C2×C22⋊C4—131no—
221C2×C22⋊C4—131no—
222C2×C42—131no—
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42C2×D1311yescharacteristic
228#95—131no—
229#95—131no—
230#95—131no—
231#95—131no—
232#95—131no—
233#95—131no—
234#95—131no—
235#95—131no—
236#95C2×D1311yescharacteristic
237#95C2×D1311yescharacteristic
238C2×C13C2×C4×D411yescharacteristic
239C2×C13C2×C4×Q811yescharacteristic
240C2×C13#52011yescharacteristic
241C2×C13#54611yescharacteristic
242C2×C13D4×Q811yescharacteristic
243C2×C13#55211yescharacteristic
244C2×C13#55411yescharacteristic
245D13—24no—
246C24—131no—
247C2×Q8—134no—
248C2×Q8—262no—
249C2×Q8—262no—
250C22×C4—131no—
251C22×C4—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—134no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—262no—
259C22×C4—262no—
260C22×C4—262no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4—262no—
264C22×C4—521no—
265C22×C4—521no—
266C22×C4C22×D1311yescharacteristic
267C22×C4C22×D1311yescharacteristic
268C22×C4C22×D1311yescharacteristic
269C22×C4C22×D1311yescharacteristic
270C22×C4C22×D1311yescharacteristic
271C22×C4C22×D1311yescharacteristic
272C22×C4C22×D1311yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—134no—
277C4⋊C4—134no—
278C4⋊C4—134no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—521no—
283C4⋊C4C4×D1314yescomplemented
284C22⋊C4—134no—
285C22⋊C4—134no—
286C22⋊C4—134no—
287C22⋊C4—262no—
288C42—41no—
289C42—262no—
290C42—262no—
291C42—262no—
292C42—262no—
293C42—521no—
294C13#236011yescharacteristic, complemented, Sylow
295C23—132no—
296C23—132no—
297C23—132no—
298C23—261no—
299C23—261no—
300C23—261no—
301C23—261no—
302C23C23×D1311yescharacteristic
303Q8—268no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—132no—
321C2×C4—132no—
322C2×C4—132no—
323C2×C4—132no—
324C2×C4—132no—
325C2×C4—132no—
326C2×C4—132no—
327C2×C4—268no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—261no—
340C2×C4—261no—
341C2×C4—261no—
342C2×C4—524no—
343C2×C4—524no—
344C2×C4C2×C4×D1312yes—
345C2×C4C2×C4×D1312yes—
346C2×C4C2×C4×D1312yes—
347C2×C4D4×D1312yes—
348C2×C4Q8×D1312yes—
349C22—134no—
350C22—262no—
351C22—262no—
352C22—262no—
353C22—262no—
354C22—262no—
355C22—262no—
356C22C22×C4×D1311yescharacteristic
357C22C2×D4×D1311yescharacteristic
358C22#8825111yescharacteristic
359C22C2×Q8×D1311yescharacteristic
360C22#8825411yescharacteristic
361C22#41×D1311yescharacteristic
362C22#41×D1311yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—134no—
371C4—262no—
372C4—262no—
373C4—262no—
374C4—262no—
375C4—521no—
376C4—521no—
377C2—264no—
378C2#1171920911yescharacteristic
379C2C4×D4×D1311yescharacteristic
380C2C4×Q8×D1311yescharacteristic
381C2#1171931511yescharacteristic
382C2#1171934111yescharacteristic
383C2#1171939811yescharacteristic
384C2#1171943211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutatorC22×C13C23×C4
FittingC13×#389C2
socle, cosocleC23×C13C24
prime radicalC23×D13C23
hypercenter#389D13
hypocenterC13#2360
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C2×#88141C2semidirect
4. C13×#389C2semidirect
7. #11718642C2semidirect
8. #11718639C2semidirect
9. #11718633C2semidirect
11. C4×#6101C2semidirect
14. #11718308C2semidirect
15. #11718307C2semidirect
41. #88150C4semidirect
80. C2×Dic26C2×C4semidirect
84. C13×C4⋊C4C2×C4semidirect
89. #6103Q8semidirect
94. #6101C2×C4semidirect
95. #6101C2×C4semidirect
163. #389D13semidirect
185. C2×D13C4×Q8semidirect
283. C4⋊C4C4×D13semidirect
294. C13#2360semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×C4⋊C4×D132
C2×#881412
C13×#3892
#117186502
#117186422
#117186392
#117186332
C4×#61032
C4×#61012
#117183272
#117183082
#117183072
#236013