Finite Group Databasebeta

← #27179873

Subgroups — #27179873

Order 12928.

492 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692263C211yesmaximal, characteristic, complemented
2C2×#15692261C211yesmaximal, characteristic, complemented
3#20265724C211yesmaximal, characteristic
4#20265253C211yesmaximal, characteristic, complemented
5#20265252C211yesmaximal, characteristic, complemented
6#20265250C211yesmaximal, characteristic, complemented
7#20265249C211yesmaximal, characteristic, complemented
8#20265247C211yesmaximal, characteristic, complemented
9C8×C22⋊D101C211yesmaximal, characteristic, complemented
10#20265240C211yesmaximal, characteristic, complemented
11C4⋊C8×D101C211yesmaximal, characteristic, complemented
12#20265142C211yesmaximal, characteristic, complemented
13#20265142C211yesmaximal, characteristic, complemented
14#20265129C211yesmaximal, characteristic, complemented
15#435×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×#13108074C2211yescharacteristic
18#15692263—24no—
19#15692261—24no—
20C2×#13108058C2211yescharacteristic
21C2×#13108057C2211yescharacteristic
22C2×#13108057C2211yescharacteristic
23C2×#13108057C2211yescharacteristic
24C2×#13108057C2211yescharacteristic
25C22×#11717579C2211yescharacteristic
26C2×C8×D101C2211yescharacteristic
27C2×C8×D101C2211yescharacteristic
28C2×C8×D101C2211yescharacteristic
29C2×C8×D101C2211yescharacteristic
30#15692254C411yescharacteristic
31#15692251C411yescharacteristic
32#15692241C411yescharacteristic
33#15692241C411yescharacteristic
34#15692230C411yescharacteristic
35#15692228C411yescharacteristic
36#15692228C411yescharacteristic
37#15692226C411yescharacteristic
38C4×D404C2211yescharacteristic
39C4×C22⋊D101C2211yescharacteristic
40C4×C22⋊D101C2211yescharacteristic
41C42×D101C2211yescharacteristic
42C4⋊#11717579C2211yescharacteristic
43#15692184C2211yescharacteristic
44#15692184C2211yescharacteristic
45C22⋊#11717579C2211yescharacteristic
46C22⋊#11717579C2211yescharacteristic
47#15692167C2211yescharacteristic
48#15692167C2211yescharacteristic
49#15692167C2211yescharacteristic
50#15692167C2211yescharacteristic
51#15692166C2211yescharacteristic
52C8×Dic101C2211yescharacteristic
53C8×Dic101C2211yescharacteristic
54C2×M16×C101C2211yescharacteristic
55C22×C8×C101C2211yescharacteristic
56C4×D4×C101C2211yescharacteristic
57C4⋊C8×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59C22⋊C8×C101C2211yescharacteristic
60#97×C101C2211yescharacteristic
61#13108074—22no—
62#13108074—22no—
63#13108074—22no—
64#13108074—22no—
65C2×Dic202C2×C411yescharacteristic
66C2×Dic202C2×C411yescharacteristic
67C2×D404C2×C411yescharacteristic
68C2×D404C2×C411yescharacteristic
69C2×D404C2×C411yescharacteristic
70C2×C22⋊D101C2×C411yescharacteristic
71C2×C22⋊D101C2×C411yescharacteristic
72C2×C22⋊D101C2×C411yescharacteristic
73C2×C22⋊D101C2×C411yescharacteristic
74C2×C22⋊D101C2×C411yescharacteristic
75C2×C22⋊D101C2×C411yescharacteristic
76C2×C4×D101C2×C411yescharacteristic
77C2×C4×D101C2×C411yescharacteristic
78C2×C4×D101C2311yescharacteristic
79C2×C4×D101C2311yescharacteristic
80C2×C4×D101C2311yescharacteristic
81#13108058—22no—
82#13108057—22no—
83#13108057—22no—
84#13108057—22no—
85#13108057D414yescomplemented
86C2×#11717579—22no—
87C2×#11717579C2311yescharacteristic
88C2×#11717579C2311yescharacteristic
89C2×#11717579C2311yescharacteristic
90C2×#11717579C2311yescharacteristic
91C8×D101—22no—
92C8×D101—22no—
93C8×D101—22no—
94C8×D101—22no—
95C4⋊Dic101C2×C411yescharacteristic
96#13108053C2×C411yescharacteristic
97#13108053C2×C411yescharacteristic
98C22⋊Dic101C2×C411yescharacteristic
99C22⋊Dic101C2×C411yescharacteristic
100#13108051C2×C411yescharacteristic
101#13108051C2×C411yescharacteristic
102#13108051C2×C411yescharacteristic
103#13108051C2×C411yescharacteristic
104C4×Dic101C2×C411yescharacteristic
105C4×Dic101C2×C411yescharacteristic
106C4×Dic101C2311yescharacteristic
107C2×D4×C101C2×C411yescharacteristic
108C22×C4×C101C2311yescharacteristic
109C22×C4×C101C2311yescharacteristic
110M16×C101—22no—
111C2×C8×C101—22no—
112C2×C8×C101C2311yescharacteristic
113C2×C8×C101C2311yescharacteristic
114C2×C8×C101C2311yescharacteristic
115C2×C8×C101C2311yescharacteristic
116C4⋊C4×C101C2×C411yescharacteristic
117C22⋊C4×C101C2×C411yescharacteristic
118C22⋊C4×C101C2×C411yescharacteristic
119C42×C101C2311yescharacteristic
120C23×C101C22×C411yescharacteristic
121C23×C101C22×C411yescharacteristic
122C22×D101C22×C411yescharacteristic
123C22×D101C22×C411yescharacteristic
124C22×D101C22×C411yescharacteristic
125D4×C101—41no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—21no—
129C2×C4×C101—21no—
130C2×C4×C101C22×C411yescharacteristic
131C2×C4×C101C22×C411yescharacteristic
132C2×C4×C101C22×C411yescharacteristic
133C2×C4×C101C22×C411yescharacteristic
134C2×C4×C101C2411yescharacteristic
135C22⋊D101—22no—
136C22⋊D101—22no—
137C22⋊D101—22no—
138C22⋊D101—22no—
139C22⋊D101—22no—
140C22⋊D101—22no—
141C2×Dic101C22×C411yescharacteristic
142C2×Dic101C22×C411yescharacteristic
143C2×Dic101C22×C411yescharacteristic
144C2×Dic101C22×C411yescharacteristic
145C2×Dic101C22×C411yescharacteristic
146D404—22no—
147D404—22no—
148D404—41no—
149C4×D101—21no—
150C4×D101—21no—
151C4×D101—21no—
152C4×D101—21no—
153C4×D101—22no—
154C4×D101—41no—
155C4×D101C2×D412yes—
156C4×D101#4112yes—
157Dic202—22no—
158Dic202—22no—
159C8×C101—21no—
160C8×C101—21no—
161C8×C101—21no—
162C8×C101C2×D412yes—
163#11717579—21no—
164#11717579—21no—
165#11717579—21no—
166#11717579C2×D412yes—
167C22×C101—21no—
168C22×C101—21no—
169C22×C101—21no—
170C22×C101—21no—
171C22×C101—21no—
172C22×C101—21no—
173C22×C101C23×C411yescharacteristic
174C2×D101—21no—
175C2×D101—21no—
176C2×D101—21no—
177C2×D101—21no—
178C2×D101—21no—
179C2×D101—21no—
180C2×D101—21no—
181C2×D101—21no—
182C2×D101C4×D412yes—
183C4×C101—21no—
184C4×C101—21no—
185C4×C101—21no—
186C4×C101—21no—
187C4×C101C22×D411yescharacteristic
188C4×C101C2×#4111yescharacteristic
189Dic101—21no—
190Dic101—21no—
191Dic101—21no—
192Dic101C4×D412yes—
193Dic101#13112yescomplemented
194C2×C101—41no—
195C2×C101—41no—
196C2×C101C2×C4×D411yescharacteristic
197C2×C101C2×#13111yescharacteristic
198C2×C101#56811yescharacteristic
199D101—22no—
200D101—41no—
201D101—41no—
202#2935—1011nomaximal, Sylow
203C101#293511yescharacteristic, complemented, Sylow
204C2×#131—1011no—
205C2×#131—1011no—
206#532—1011no—
207#436—1011no—
208#436—1011no—
209#435—1011no—
210#435—1011no—
211#435—1011no—
212#435D10111yescharacteristic, complemented
213C8×D4—1011no—
214C8×D4—1011no—
215C2×C4⋊C8—1011no—
216#408—1011no—
217#408—1011no—
218C4×M16—1011no—
219C2×#41—1011no—
220C2×#41—1011no—
221#131—2024no—
222#131—2024no—
223C2×M16—1011no—
224C2×M16—1011no—
225C2×M16—1011no—
226C2×M16—1011no—
227C2×M16—1011no—
228C2×M16C2×D10111yescharacteristic
229C22×C8—1011no—
230C22×C8—1011no—
231C22×C8—1011no—
232C22×C8—1011no—
233C22×C8—1011no—
234C22×C8C2×D10111yescharacteristic
235C4⋊Q8—1011no—
236#127—1011no—
237#124—1011no—
238#124—1011no—
239#121—1011no—
240#121—1011no—
241#121—1011no—
242#121—1011no—
243C4×D4—1011no—
244C4×D4—1011no—
245C4×D4—1011no—
246C4×D4C2×D10111yescharacteristic
247C2×C42—1011no—
248C4⋊C8—1011no—
249C4⋊C8—1011no—
250C4⋊C8—1011no—
251C4⋊C8C2×D10111yescharacteristic
252C22⋊C8—1011no—
253C22⋊C8—1011no—
254C22⋊C8—1011no—
255C22⋊C8—1011no—
256C22⋊C8—1011no—
257C22⋊C8—1011no—
258C22⋊C8C2×D10111yescharacteristic
259C22⋊C8C2×D10111yescharacteristic
260#97—1011no—
261#97C2×D10111yescharacteristic
262C4×C8—1011no—
263C4×C8—1011no—
264#41—2022no—
265#41—2022no—
266#41—2022no—
267#41—2022no—
268C2×Q8—1011no—
269C2×Q8—1011no—
270C2×D4—1011no—
271C2×D4—1011no—
272C2×D4—1011no—
273C2×D4—1011no—
274C2×D4—1011no—
275C2×D4—1011no—
276C2×D4—1011no—
277C2×D4—1011no—
278C2×D4—1011no—
279C2×D4C4×D10111yescharacteristic
280C22×C4—1011no—
281C22×C4—1011no—
282C22×C4—1011no—
283C22×C4—1011no—
284C22×C4—1011no—
285C22×C4C22×D10111yescharacteristic
286C22×C4C22×D10111yescharacteristic
287M16—22no—
288M16—1014no—
289M16—2022no—
290M16—2022no—
291M16—2022no—
292M16—2022no—
293C2×C8—22no—
294C2×C8—1011no—
295C2×C8—1011no—
296C2×C8—1011no—
297C2×C8—1011no—
298C2×C8—2022no—
299C2×C8—2022no—
300C2×C8—2022no—
301C2×C8—2022no—
302C2×C8—2022no—
303C2×C8C22×D10111yescharacteristic
304C2×C8C22×D10111yescharacteristic
305C2×C8C22×D10111yescharacteristic
306C2×C8C22×D10111yescharacteristic
307C4⋊C4—1011no—
308C4⋊C4—1011no—
309C4⋊C4—1011no—
310C4⋊C4C4×D10111yescharacteristic
311C22⋊C4—1011no—
312C22⋊C4—1011no—
313C22⋊C4—1011no—
314C22⋊C4—1011no—
315C22⋊C4—1011no—
316C22⋊C4—1011no—
317C22⋊C4C4×D10111yescharacteristic
318C22⋊C4C4×D10111yescharacteristic
319C42—1011no—
320C42—1011no—
321C42—1011no—
322C42C22×D10111yescharacteristic
323C23—1011no—
324C23—1011no—
325C23—1011no—
326C23C2×C4×D10111yescharacteristic
327C23C2×C4×D10111yescharacteristic
328Q8—2022no—
329Q8—2022no—
330D4—41no—
331D4—4041no—
332D4—2022no—
333D4—2022no—
334D4—2022no—
335D4—2022no—
336D4—2022no—
337D4—2022no—
338D4—2022no—
339D4—2022no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—1011no—
345C2×C4—1011no—
346C2×C4—1012no—
347C2×C4—1012no—
348C2×C4—1011no—
349C2×C4—1011no—
350C2×C4—1011no—
351C2×C4—4041no—
352C2×C4—2022no—
353C2×C4—2021no—
354C2×C4—2021no—
355C2×C4—2021no—
356C2×C4—2021no—
357C2×C4C2×C4×D10111yescharacteristic
358C2×C4C2×C4×D10111yescharacteristic
359C2×C4C2×C4×D10111yescharacteristic
360C2×C4C2×C4×D10111yescharacteristic
361C2×C4C23×D10111yescharacteristic
362C8—21no—
363C8—21no—
364C8—21no—
365C8—1012no—
366C8—2021no—
367C8—2021no—
368C8—2021no—
369C8D4×D10112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—1012no—
377C22—2021no—
378C22—2021no—
379C22—2021no—
380C22—2021no—
381C22—2021no—
382C22—2021no—
383C22—2021no—
384C22—2021no—
385C22C22×C4×D10111yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—1012no—
391C4—1012no—
392C4—2021no—
393C4—2021no—
394C4—2021no—
395C4C2×D4×D10111yescharacteristic
396C4#41×D10111yescharacteristic
397C2—41no—
398C2—41no—
399C2—4041no—
400C2—4041no—
401C2—2022no—
402C2C4×D4×D10111yescharacteristic
403C2#131×D10111yescharacteristic
404C2#2026594311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D101
commutator, socleC22×C101C23×C4
Fitting#435×C101C2
prime radical#20265724C2
cosocleC2×C4×C101C24
hypercenter#435D101
hypocenterC101#2935
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#15692263C2semidirect
2. C2×#15692261C2semidirect
4. #20265253C2semidirect
5. #20265252C2semidirect
6. #20265250C2semidirect
7. #20265249C2semidirect
8. #20265247C2semidirect
9. C8×C22⋊D101C2semidirect
10. #20265240C2semidirect
11. C4⋊C8×D101C2semidirect
12. #20265142C2semidirect
13. #20265142C2semidirect
14. #20265129C2semidirect
15. #435×C101C2semidirect
85. #13108057D4semidirect
193. Dic101#131semidirect
203. C101#2935semidirect
212. #435D101semidirect

Maximal subgroups

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

subgroupindex
C2×#156922632
C2×#156922612
#202657242
#202652532
#202652522
#202652502
#202652492
#202652472
C8×C22⋊D1012
#202652402
C4⋊C8×D1012
#202651422
#202651292
#435×C1012
#2935101