Finite Group Databasebeta

← #27179351

Subgroups — #27179351

Order 12928.

400 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265115C211yesmaximal, characteristic, complemented
2#20265112C211yesmaximal, characteristic, complemented
3#20265112C211yesmaximal, characteristic, complemented
4#20265110C211yesmaximal, characteristic, complemented
5#20265107C211yesmaximal, characteristic, complemented
6#20265105C211yesmaximal, characteristic, complemented
7#20265104C211yesmaximal, characteristic, complemented
8#20265100C211yesmaximal, characteristic, complemented
9#20265093C211yesmaximal, characteristic
10#20265092C211yesmaximal, characteristic
11#20265092C211yesmaximal, characteristic
12#20265074C211yesmaximal, characteristic, complemented
13#20265067C211yesmaximal, characteristic, complemented
14#20265065C211yesmaximal, characteristic, complemented
15#396×C101C211yesmaximal, characteristic, complemented
16C22×C22⋊D101C2211yescharacteristic
17C2×C4⋊Dic101C2211yescharacteristic
18C2×C4⋊Dic101C2211yescharacteristic
19C2×#13108053C2211yescharacteristic
20C2×#13108053C2211yescharacteristic
21C2×#13108053C2211yescharacteristic
22C2×#13108053C2211yescharacteristic
23C2×#13108053C2211yescharacteristic
24C2×#13108053C2211yescharacteristic
25C2×C22⋊Dic101C2211yescharacteristic
26C2×C22⋊Dic101C2211yescharacteristic
27C2×C22⋊Dic101C2211yescharacteristic
28C2×#13108051C2211yescharacteristic
29C2×#13108051C2211yescharacteristic
30C2×#13108051C2211yescharacteristic
31C2×#13108051C2211yescharacteristic
32C2×#13108051C2211yescharacteristic
33C2×#13108051C2211yescharacteristic
34C2×C4×Dic101C2211yescharacteristic
35#15692162C2211yescharacteristic
36#15692162C2211yescharacteristic
37#15692162C2211yescharacteristic
38#15692162C2211yescharacteristic
39#15692162C2211yescharacteristic
40#15692162C2211yescharacteristic
41#15692162C2211yescharacteristic
42#15692162C2211yescharacteristic
43#15692162C2211yescharacteristic
44C2×C4⋊C4×C101C2211yescharacteristic
45C2×C4⋊C4×C101C2211yescharacteristic
46C2×C4⋊C4×C101C2211yescharacteristic
47C2×C22⋊C4×C101C2211yescharacteristic
48C2×C22⋊C4×C101C2211yescharacteristic
49C2×C22⋊C4×C101C2211yescharacteristic
50#95×C101C2211yescharacteristic
51C23×D101C2311yescharacteristic
52C2×C22⋊D101—41no—
53C2×C22⋊D101—41no—
54C2×C22⋊D101—41no—
55C22×Dic101C2311yescharacteristic
56C22×Dic101C2311yescharacteristic
57C22×Dic101C2311yescharacteristic
58C22×Dic101C2311yescharacteristic
59C22×Dic101C2311yescharacteristic
60C22×Dic101C2311yescharacteristic
61C22×Dic101C2311yescharacteristic
62C4⋊Dic101—41no—
63C4⋊Dic101—41no—
64#13108053—22no—
65#13108053—41no—
66#13108053—41no—
67#13108053—41no—
68#13108053—41no—
69#13108053—41no—
70C22⋊Dic101—22no—
71C22⋊Dic101—41no—
72C22⋊Dic101—41no—
73#13108051—22no—
74#13108051—41no—
75#13108051—41no—
76#13108051—41no—
77#13108051—41no—
78#13108051—41no—
79C4×Dic101—41no—
80C24×C101C2311yescharacteristic
81C22×C4×C101C2311yescharacteristic
82C22×C4×C101C2311yescharacteristic
83C22×C4×C101C2311yescharacteristic
84C22×C4×C101C2311yescharacteristic
85C22×C4×C101C2311yescharacteristic
86C22×C4×C101C2311yescharacteristic
87C4⋊C4×C101—41no—
88C4⋊C4×C101—41no—
89C4⋊C4×C101—41no—
90C22⋊C4×C101—41no—
91C22⋊C4×C101—41no—
92C22⋊C4×C101—41no—
93C23×C101—21no—
94C23×C101—21no—
95C23×C101—21no—
96C23×C101—21no—
97C23×C101—21no—
98C23×C101—21no—
99C23×C101—21no—
100C23×C101C2411yescharacteristic
101C22×D101—21no—
102C22×D101—21no—
103C22×D101—21no—
104C22×D101—21no—
105C22×D101—21no—
106C22×D101—21no—
107C22×D101—21no—
108C2×C4×C101—21no—
109C2×C4×C101—21no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C22⋊D101—44no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136C2×Dic101—21no—
137C2×Dic101—21no—
138C2×Dic101—21no—
139C2×Dic101—21no—
140C2×Dic101—21no—
141C2×Dic101—21no—
142C2×Dic101—21no—
143C2×Dic101—21no—
144C2×Dic101—21no—
145C2×Dic101—21no—
146C2×Dic101—21no—
147C2×Dic101#4112yes—
148C22×C101—41no—
149C22×C101—41no—
150C22×C101—41no—
151C22×C101—41no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101—41no—
155C22×C101C2×#4111yescharacteristic
156C22×C101H(5,𝔽2)11yescharacteristic
157C22×C101H(5,𝔽2)11yescharacteristic
158C22×C101H(5,𝔽2)11yescharacteristic
159C22×C101H(5,𝔽2)11yescharacteristic
160C22×C1012−1+411yescharacteristic
161C22×C1012−1+411yescharacteristic
162C2×D101—41no—
163C2×D101—41no—
164C2×D101—41no—
165C2×D101—41no—
166C2×D101—41no—
167C2×D101—41no—
168C2×D101—41no—
169C4×C101—41no—
170C4×C101—41no—
171C4×C101—41no—
172C4×C101—41no—
173C4×C101—41no—
174C4×C101—41no—
175Dic101—22no—
176Dic101—41no—
177Dic101—41no—
178Dic101—41no—
179Dic101—41no—
180Dic101—41no—
181Dic101—41no—
182C2×C101—81no—
183C2×C101#53911yescharacteristic
184C2×C101#54011yescharacteristic
185C2×C101#54211yescharacteristic
186C2×C101#56011yescharacteristic
187C2×C101#56211yescharacteristic
188C2×C101#56211yescharacteristic
189C2×C101#56311yescharacteristic
190D101—81no—
191#2837—1011nomaximal, Sylow
192C101#283711yescharacteristic, complemented, Sylow
193#400—1011no—
194#399—1011no—
195#399—1011no—
196#398—1011no—
197#398—1011no—
198#397—1011no—
199#397—1011no—
200#396—1011no—
201#396D10111yescharacteristic, complemented
202#394—1011no—
203#394—1011no—
204#394—1011no—
205#389—1011no—
206#388—1011no—
207#388—1011no—
208C22×D4—1011no—
209C2×C4⋊C4—1011no—
210C2×C4⋊C4—1011no—
211C2×C4⋊C4—1011no—
212C2×C4⋊C4—1011no—
213C2×C4⋊C4—1011no—
214C2×C4⋊C4—1011no—
215C2×C4⋊C4—1011no—
216C2×C4⋊C4—1011no—
217C2×C4⋊C4C2×D10111yescharacteristic
218C2×C4⋊C4C2×D10111yescharacteristic
219C2×C4⋊C4C2×D10111yescharacteristic
220C2×C22⋊C4—1011no—
221C2×C22⋊C4—1011no—
222C2×C22⋊C4—1011no—
223C2×C22⋊C4—1011no—
224C2×C22⋊C4—1011no—
225C2×C22⋊C4—1011no—
226C2×C22⋊C4—1011no—
227C2×C22⋊C4—1011no—
228C2×C22⋊C4—1011no—
229C2×C22⋊C4C2×D10111yescharacteristic
230C2×C22⋊C4C2×D10111yescharacteristic
231C2×C22⋊C4C2×D10111yescharacteristic
232C2×C42—1011no—
233#95—1011no—
234#95—1011no—
235#95—1011no—
236#95—1011no—
237#95—1011no—
238#95—1011no—
239#95—1011no—
240#95—1011no—
241#95—1011no—
242#95C2×D10111yescharacteristic
243C24—1011no—
244C24C22×D10111yescharacteristic
245C2×D4—4041no—
246C2×D4—4041no—
247C2×D4—4041no—
248C22×C4—1011no—
249C22×C4—1011no—
250C22×C4—1011no—
251C22×C4—1011no—
252C22×C4—1011no—
253C22×C4—1011no—
254C22×C4—1011no—
255C22×C4C22×D10111yescharacteristic
256C22×C4C22×D10111yescharacteristic
257C22×C4C22×D10111yescharacteristic
258C22×C4C22×D10111yescharacteristic
259C22×C4C22×D10111yescharacteristic
260C22×C4C22×D10111yescharacteristic
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—4041no—
265C4⋊C4—4041no—
266C4⋊C4—4041no—
267C4⋊C4—4041no—
268C4⋊C4—4041no—
269C4⋊C4—4041no—
270C4⋊C4—4041no—
271C4⋊C4—2022no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—4041no—
276C22⋊C4—4041no—
277C22⋊C4—4041no—
278C22⋊C4—4041no—
279C22⋊C4—4041no—
280C22⋊C4—4041no—
281C22⋊C4—4041no—
282C22⋊C4—2022no—
283C22⋊C4—2022no—
284C42—4041no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—2021no—
293C23—2021no—
294C23—2021no—
295C23—2021no—
296C23—2021no—
297C23—2021no—
298C23—2021no—
299C23C23×D10111yescharacteristic
300D4—4044no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
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—1012no—
320C2×C4—2021no—
321C2×C4—2021no—
322C2×C4—2021no—
323C2×C4—2021no—
324C2×C4—2021no—
325C2×C4—2021no—
326C2×C4—2021no—
327C2×C4—2021no—
328C2×C4—2021no—
329C2×C4—2021no—
330C2×C4—2021no—
331C2×C4—2021no—
332C2×C4—2021no—
333C2×C4—2021no—
334C2×C4—2021no—
335C2×C4—2021no—
336C2×C4—2021no—
337C2×C4—2021no—
338C2×C4—2021no—
339C2×C4—2021no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—4041no—
348C22—4041no—
349C22—4041no—
350C22—4041no—
351C22—4041no—
352C22—4041no—
353C22—4041no—
354C22#41×D10111yescharacteristic
355C22#1569230011yescharacteristic
356C22#1569230011yescharacteristic
357C22#1569230011yescharacteristic
358C22#1569230111yescharacteristic
359C22#1569230211yescharacteristic
360C22#1569230311yescharacteristic
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—4041no—
368C4—4041no—
369C4—4041no—
370C4—4041no—
371C4—4041no—
372C4—4041no—
373C4—2022no—
374C2—81no—
375C2—8081no—
376C2#2026577311yescharacteristic
377C2#2026577711yescharacteristic
378C2#2026579311yescharacteristic
379C2#2026591511yescharacteristic
380C2#2026592211yescharacteristic
381C2#2026592311yescharacteristic
382C2#2026592811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, cosocleC23×C101C24
Fitting#396×C101C2
prime radicalC22×C22⋊D101C22
hypercenter#396D101
hypocenterC101#2837
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #20265115C2semidirect
2. #20265112C2semidirect
3. #20265112C2semidirect
4. #20265110C2semidirect
5. #20265107C2semidirect
6. #20265105C2semidirect
7. #20265104C2semidirect
8. #20265100C2semidirect
12. #20265074C2semidirect
13. #20265067C2semidirect
14. #20265065C2semidirect
15. #396×C101C2semidirect
192. C101#2837semidirect
201. #396D101semidirect

Maximal subgroups

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

subgroupindex
#202651152
#202651122
#202651102
#202651072
#202651052
#202651042
#202651002
#202650932
#202650922
#202650742
#202650672
#202650652
#396×C1012
#2837101