Finite Group Databasebeta

← #27179450

Subgroups — #27179450

Order 12928.

582 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692250C211yesmaximal, characteristic, complemented
2C2×C42×D101C211yesmaximal, characteristic, complemented
3#20265068C211yesmaximal, characteristic, complemented
4#20265067C211yesmaximal, characteristic, complemented
5#20265066C211yesmaximal, characteristic, complemented
6#20265064C211yesmaximal, characteristic, complemented
7#20265059C211yesmaximal, characteristic, complemented
8#20265055C211yesmaximal, characteristic
9#20265055C211yesmaximal, characteristic
10#20265055C211yesmaximal, characteristic
11#20265051C211yesmaximal, characteristic, complemented
12#20265048C211yesmaximal, characteristic, complemented
13#20265048C211yesmaximal, characteristic, complemented
14#20265044C211yesmaximal, characteristic, complemented
15#387×C101C211yesmaximal, characteristic, complemented
16C22×D404C2211yescharacteristic
17C22×C4×D101C2211yescharacteristic
18C22×C4×D101C2211yescharacteristic
19C22×C4×D101C2211yescharacteristic
20#15692250—24no—
21C2×C4⋊Dic101C2211yescharacteristic
22C2×#13108053C2211yescharacteristic
23C2×#13108053C2211yescharacteristic
24C2×#13108053C2211yescharacteristic
25C2×#13108051C2211yescharacteristic
26C2×#13108051C2211yescharacteristic
27C2×#13108051C2211yescharacteristic
28C2×#13108051C2211yescharacteristic
29C2×#13108051C2211yescharacteristic
30C2×#13108051C2211yescharacteristic
31C2×#13108051C2211yescharacteristic
32C2×#13108051C2211yescharacteristic
33C2×#13108051C2211yescharacteristic
34C2×C4×Dic101C2211yescharacteristic
35C2×C4×Dic101C2211yescharacteristic
36C2×C4×Dic101C2211yescharacteristic
37C42×D101—24no—
38#15692162C2211yescharacteristic
39#15692162C2211yescharacteristic
40#15692162C2211yescharacteristic
41#15692162C2211yescharacteristic
42#15692162C2211yescharacteristic
43#15692162C2211yescharacteristic
44#15692162C2211yescharacteristic
45#15692162C2211yescharacteristic
46C2×C4⋊C4×C101C2211yescharacteristic
47C2×C4⋊C4×C101C2211yescharacteristic
48C2×C42×C101C2211yescharacteristic
49#95×C101C2211yescharacteristic
50#95×C101C2211yescharacteristic
51#95×C101C2211yescharacteristic
52#95×C101C2211yescharacteristic
53C23×D101C2311yescharacteristic
54C23×D101C2311yescharacteristic
55C2×D404—22no—
56C2×D404—22no—
57C2×D404—22no—
58C22×Dic101C2311yescharacteristic
59C22×Dic101C2311yescharacteristic
60C22×Dic101C2311yescharacteristic
61C22×Dic101C2311yescharacteristic
62C22×Dic101C2311yescharacteristic
63C22×Dic101C2311yescharacteristic
64C2×C4×D101—22no—
65C2×C4×D101—22no—
66C2×C4×D101—22no—
67C2×C4×D101—22no—
68C2×C4×D101—22no—
69C2×C4×D101—22no—
70C2×C4×D101—22no—
71C2×C4×D101—22no—
72C2×C4×D101—22no—
73C4⋊Dic101—22no—
74#13108053—22no—
75#13108053—22no—
76#13108053—22no—
77#13108051—22no—
78#13108051—22no—
79#13108051—22no—
80#13108051—22no—
81#13108051—22no—
82#13108051—22no—
83#13108051—22no—
84#13108051—22no—
85#13108051—22no—
86C4×Dic101—22no—
87C4×Dic101—22no—
88C4×Dic101D414yescomplemented
89C22×C4×C101C2311yescharacteristic
90C22×C4×C101C2311yescharacteristic
91C22×C4×C101C2311yescharacteristic
92C22×C4×C101C2311yescharacteristic
93C22×C4×C101C2311yescharacteristic
94C22×C4×C101C2311yescharacteristic
95C22×C4×C101C2311yescharacteristic
96C4⋊C4×C101—22no—
97C4⋊C4×C101—22no—
98C42×C101—22no—
99C23×C101C2411yescharacteristic
100C22×D101—21no—
101C22×D101—21no—
102C22×D101—21no—
103C22×D101—21no—
104C22×D101—21no—
105C22×D101—21no—
106C22×D101—21no—
107C22×D101—21no—
108C22×D101—21no—
109C22×D101—21no—
110C22×D101—21no—
111C22×D101#4112yes—
112C22×D101#4112yes—
113C22×D101#4112yes—
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—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—21no—
129C2×C4×C101—21no—
130C2×C4×C101—21no—
131C2×C4×C101—21no—
132C2×C4×C101C2×D412yes—
133C2×C4×C101#4112yes—
134C2×C4×C101#4112yes—
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—21no—
148C2×Dic101—21no—
149C2×Dic101—21no—
150C2×Dic101C2×D412yes—
151C2×Dic101C2×D412yes—
152C2×Dic101#4112yes—
153D404—44no—
154C4×D101—28no—
155C4×D101—28no—
156C4×D101—28no—
157C22×C101C22×D411yescharacteristic
158C22×C101C2×#4111yescharacteristic
159C22×C101C2×#4111yescharacteristic
160C22×C101C2×#4111yescharacteristic
161C22×C101C2×#4111yescharacteristic
162C22×C101C2×#4111yescharacteristic
163C22×C101C2×#4111yescharacteristic
164C2×D101—22no—
165C2×D101—22no—
166C2×D101—22no—
167C2×D101—22no—
168C2×D101—22no—
169C2×D101—22no—
170C2×D101—41no—
171C2×D101—41no—
172C2×D101—41no—
173C2×D101—41no—
174C2×D101—41no—
175C2×D101—41no—
176C2×D101—41no—
177C2×D101#12614yescomplemented
178C4×C101—22no—
179C4×C101—22no—
180C4×C101—22no—
181C4×C101—41no—
182C4×C101—41no—
183C4×C101—41no—
184C4×C101—41no—
185Dic101—22no—
186Dic101—22no—
187Dic101—22no—
188Dic101—41no—
189Dic101—41no—
190Dic101—41no—
191C2×C101#52511yescharacteristic
192C2×C101#52511yescharacteristic
193C2×C101#52511yescharacteristic
194C2×C101C2×#12611yescharacteristic
195C2×C101#52911yescharacteristic
196C2×C101#52911yescharacteristic
197C2×C101#52911yescharacteristic
198D101—24no—
199D101—81no—
200#2852—1011nomaximal, Sylow
201C101#285211yescharacteristic, complemented, Sylow
202C2×#126—1011no—
203C22×C42—1011no—
204#388—1011no—
205#388—1011no—
206#388—1011no—
207#387—1011no—
208#387—1011no—
209#387D10111yescharacteristic, complemented
210#386—1011no—
211#386—1011no—
212#386—1011no—
213#385—1011no—
214#385—1011no—
215#385—1011no—
216#383—1011no—
217C22×D4—1011no—
218C23×C4—1011no—
219C23×C4—1011no—
220C23×C4—1011no—
221#126—2024no—
222C2×C4⋊C4—1011no—
223C2×C4⋊C4—1011no—
224C2×C4⋊C4—1011no—
225C2×C4⋊C4—1011no—
226C2×C4⋊C4C2×D10111yescharacteristic
227C2×C4⋊C4C2×D10111yescharacteristic
228C2×C22⋊C4—1011no—
229C2×C22⋊C4—1011no—
230C2×C22⋊C4—1011no—
231C2×C22⋊C4—1011no—
232C2×C22⋊C4—1011no—
233C2×C22⋊C4—1011no—
234C2×C22⋊C4—1011no—
235C2×C22⋊C4—1011no—
236C2×C22⋊C4—1011no—
237C2×C42—1011no—
238C2×C42—1011no—
239C2×C42—1011no—
240C2×C42—2024no—
241C2×C42C2×D10111yescharacteristic
242#95—1011no—
243#95—1011no—
244#95—1011no—
245#95—1011no—
246#95—1011no—
247#95—1011no—
248#95—1011no—
249#95—1011no—
250#95C2×D10111yescharacteristic
251#95C2×D10111yescharacteristic
252#95C2×D10111yescharacteristic
253#95C2×D10111yescharacteristic
254C24—1011no—
255C24—1011no—
256C2×D4—2022no—
257C2×D4—2022no—
258C2×D4—2022no—
259C22×C4—1011no—
260C22×C4—1011no—
261C22×C4—1011no—
262C22×C4—1011no—
263C22×C4—1011no—
264C22×C4—1011no—
265C22×C4—2022no—
266C22×C4—2022no—
267C22×C4—2022no—
268C22×C4—2022no—
269C22×C4—2022no—
270C22×C4—2022no—
271C22×C4—2022no—
272C22×C4—2022no—
273C22×C4—2022no—
274C22×C4C22×D10111yescharacteristic
275C22×C4C22×D10111yescharacteristic
276C22×C4C22×D10111yescharacteristic
277C22×C4C22×D10111yescharacteristic
278C22×C4C22×D10111yescharacteristic
279C22×C4C22×D10111yescharacteristic
280C22×C4C22×D10111yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—2022no—
284C4⋊C4—2022no—
285C4⋊C4—2022no—
286C4⋊C4—2022no—
287C22⋊C4—2022no—
288C22⋊C4—2022no—
289C22⋊C4—2022no—
290C22⋊C4—2022no—
291C22⋊C4—2022no—
292C22⋊C4—2022no—
293C22⋊C4—2022no—
294C22⋊C4—2022no—
295C22⋊C4—2022no—
296C42—22no—
297C42—1014no—
298C42—2022no—
299C42—2022no—
300C23—1012no—
301C23—1012no—
302C23—1012no—
303C23—2021no—
304C23—2021no—
305C23—2021no—
306C23—2021no—
307C23—2021no—
308C23—2021no—
309C23—2021no—
310C23—2021no—
311C23—2021no—
312C23—2021no—
313C23—2021no—
314C23C23×D10111yescharacteristic
315D4—4044no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—1012no—
335C2×C4—1012no—
336C2×C4—1012no—
337C2×C4—2028no—
338C2×C4—2028no—
339C2×C4—2028no—
340C2×C4—2021no—
341C2×C4—2021no—
342C2×C4—2021no—
343C2×C4—2021no—
344C2×C4—2021no—
345C2×C4—2021no—
346C2×C4—2021no—
347C2×C4—2021no—
348C2×C4—2021no—
349C2×C4—2021no—
350C2×C4—2021no—
351C2×C4—2021no—
352C2×C4—2021no—
353C2×C4—2021no—
354C2×C4—2021no—
355C2×C4D4×D10112yes—
356C2×C4#1310807412yes—
357C2×C4#1310807512yes—
358C22—1014no—
359C22—4041no—
360C22—4041no—
361C22—4041no—
362C22—4041no—
363C22—4041no—
364C22—4041no—
365C22—4041no—
366C22—2022no—
367C22—2022no—
368C22—2022no—
369C22—2022no—
370C22—2022no—
371C22—2022no—
372C22C2×D4×D10111yescharacteristic
373C22#41×D10111yescharacteristic
374C22#41×D10111yescharacteristic
375C22#41×D10111yescharacteristic
376C22#41×D10111yescharacteristic
377C22C2×#1310807411yescharacteristic
378C22C2×#1310807511yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—4041no—
387C4—4041no—
388C4—4041no—
389C4—2022no—
390C4—2022no—
391C4—2022no—
392C2—8081no—
393C2—2024no—
394C2#2026568511yescharacteristic
395C2#2026568611yescharacteristic
396C2#2026569011yescharacteristic
397C2#126×D10111yescharacteristic
398C2#2026570511yescharacteristic
399C2#2026571211yescharacteristic
400C2#2026571411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutator, socle, cosocleC23×C101C24
Fitting#387×C101C2
prime radicalC22×D404C22
hypercenter#387D101
hypocenterC101#2852
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#15692250C2semidirect
2. C2×C42×D101C2semidirect
3. #20265068C2semidirect
4. #20265067C2semidirect
5. #20265066C2semidirect
6. #20265064C2semidirect
7. #20265059C2semidirect
11. #20265051C2semidirect
12. #20265048C2semidirect
13. #20265048C2semidirect
14. #20265044C2semidirect
15. #387×C101C2semidirect
88. C4×Dic101D4semidirect
177. C2×D101#126semidirect
201. C101#2852semidirect
209. #387D101semidirect

Maximal subgroups

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

subgroupindex
C2×#156922502
C2×C42×D1012
#202650682
#202650672
#202650662
#202650642
#202650592
#202650552
#202650512
#202650482
#202650442
#387×C1012
#2852101