Finite Group Databasebeta

← #27182537

Subgroups — #27182537

Order 12928.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265798C211yesmaximal, characteristic, complemented
2#20265481C211yesmaximal, characteristic, complemented
3#20265474C211yesmaximal, characteristic, complemented
4#20265467C211yesmaximal, characteristic, complemented
5#20265457C211yesmaximal, characteristic, complemented
6#20265428C211yesmaximal, characteristic, complemented
7#20265421C211yesmaximal, characteristic, complemented
8#20265411C211yesmaximal, characteristic, complemented
9#20265404C211yesmaximal, characteristic, complemented
10#20265392C211yesmaximal, characteristic, complemented
11#20265392C211yesmaximal, characteristic, complemented
12#20265374C211yesmaximal, characteristic, complemented
13#20265369C211yesmaximal, characteristic, complemented
14#20265204C211yesmaximal, characteristic, complemented
15#540×C101C211yesmaximal, characteristic, complemented
16C2×#13108062C2211yescharacteristic
17C2×#13108062C2211yescharacteristic
18C2×#13108059C2211yescharacteristic
19C2×#13108059C2211yescharacteristic
20C2×#13108058C2211yescharacteristic
21C22×#11717579C2211yescharacteristic
22#15692255C2211yescharacteristic
23#15692250—21no—
24#15692243C2211yescharacteristic
25#15692241—21no—
26#15692237—21no—
27#15692234C2211yescharacteristic
28#15692233—21no—
29#15692229C2211yescharacteristic
30C4×Dic202C2211yescharacteristic
31C4×D404C2211yescharacteristic
32#15692188C2211yescharacteristic
33#15692188C2211yescharacteristic
34#15692186C2211yescharacteristic
35#15692186C2211yescharacteristic
36C4⋊#11717579C2211yescharacteristic
37C4⋊#11717579C2211yescharacteristic
38C4⋊#11717579C2211yescharacteristic
39C4⋊#11717579C2211yescharacteristic
40#15692178C2211yescharacteristic
41#15692178C2211yescharacteristic
42#15692176C2211yescharacteristic
43#15692176C2211yescharacteristic
44#15692176C2211yescharacteristic
45#15692176C2211yescharacteristic
46#15692175C2211yescharacteristic
47#15692175C2211yescharacteristic
48#127×C101C2211yescharacteristic
49#125×C101C2211yescharacteristic
50#123×C101—21no—
51#123×C101—21no—
52#121×C101—21no—
53#121×C101—21no—
54#121×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic
56C4×D4×C101C2211yescharacteristic
57C4×D4×C101C2211yescharacteristic
58#117×C101C2211yescharacteristic
59C2×Dic202—21no—
60C2×Dic202C2311yescharacteristic
61C2×D404C2311yescharacteristic
62C2×C22⋊D101—21no—
63C2×C4×D101—21no—
64#13108062—41no—
65#13108062—41no—
66#13108059—41no—
67#13108059—41no—
68#13108058—41no—
69C2×#11717579—41no—
70C2×#11717579C2311yescharacteristic
71C2×#11717579C2311yescharacteristic
72C2×#11717579C2311yescharacteristic
73C2×#11717579C2311yescharacteristic
74C4⋊Dic101—21no—
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77#13108053—21no—
78#13108053—21no—
79C22⋊Dic101—21no—
80#13108051—21no—
81#13108051—21no—
82#13108051—21no—
83#13108051—21no—
84C4×Dic101—21no—
85C2×D4×C101—21no—
86C2×D4×C101—21no—
87C2×D4×C101—21no—
88C2×D4×C101—21no—
89C2×D4×C101C2311yescharacteristic
90C2×D4×C101C2311yescharacteristic
91C22×C4×C101—21no—
92C22×C4×C101—21no—
93C22×C4×C101C2311yescharacteristic
94C4⋊C4×C101—21no—
95C4⋊C4×C101—21no—
96C4⋊C4×C101D411yescharacteristic
97C4⋊C4×C101D411yescharacteristic
98C4⋊C4×C101C2311yescharacteristic
99C4⋊C4×C101C2311yescharacteristic
100C22⋊C4×C101—21no—
101C22⋊C4×C101—21no—
102C22⋊C4×C101—21no—
103C22⋊C4×C101—21no—
104C22⋊C4×C101D411yescharacteristic
105C22⋊C4×C101D411yescharacteristic
106C42×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C23×C101—21no—
109C23×C101—21no—
110C23×C101C2×D411yescharacteristic
111C22×D101—21no—
112D4×C101—21no—
113D4×C101—21no—
114D4×C101—21no—
115D4×C101—21no—
116D4×C101—81no—
117D4×C101—81no—
118D4×C101—81no—
119D4×C101—81no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101—81no—
125C2×C4×C101—81no—
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2×D411yescharacteristic
128C2×C4×C101C2×D411yescharacteristic
129C2×C4×C101C2×D411yescharacteristic
130C2×C4×C101C2×D411yescharacteristic
131C2×C4×C101C2411yescharacteristic
132C22⋊D101—81no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136D404—21no—
137D404—21no—
138C4×D101—81no—
139Dic202—21no—
140Dic202—21no—
141Dic202—81no—
142#11717579—21no—
143#11717579—21no—
144#11717579—21no—
145#11717579—21no—
146C22×C101—21no—
147C22×C101—21no—
148C22×C101—21no—
149C22×C101—41no—
150C22×C101—41no—
151C22×C101—41no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101—41no—
155C22×C101C22×D411yescharacteristic
156C2×D101—41no—
157C2×D101—41no—
158C2×D101—41no—
159C4×C101—21no—
160C4×C101—21no—
161C4×C101—21no—
162C4×C101—21no—
163C4×C101—21no—
164C4×C101—41no—
165C4×C101—41no—
166C4×C101H(5,𝔽2)11yescharacteristic
167C4×C1012−1+411yescharacteristic
168Dic101—41no—
169Dic101—41no—
170Dic101—41no—
171C2×C101—41no—
172C2×C101—81no—
173C2×C101—81no—
174C2×C101#53711yescharacteristic
175C2×C101#57611yescharacteristic
176C2×C101#57711yescharacteristic
177D101—81no—
178#3257—1011nomaximal, Sylow
179C101#325711yescharacteristic, complemented, Sylow
180#542—1011no—
181#540D10111yescharacteristic, complemented
182#479—1011no—
183#478—1011no—
184#476—1011no—
185#474—1011no—
186#469—1011no—
187#468—1011no—
188#466—1011no—
189#465—1011no—
190#463—1011no—
191#463—1011no—
192#460—1011no—
193#459—1011no—
194#424—1011no—
195C2×SD16—1011no—
196C2×SD16—1011no—
197C2×D8—1011no—
198C2×D8—1011no—
199C2×M16—1011no—
200C22×C8—1011no—
201C4⋊Q8—1011no—
202#127C2×D10111yescharacteristic
203#126—2021no—
204#125C2×D10111yescharacteristic
205#124—1011no—
206#124—2021no—
207#123—21no—
208#123—21no—
209#123—2021no—
210C22⋊Q8—1011no—
211C22⋊Q8—2021no—
212#121—21no—
213#121—21no—
214#121—1011no—
215#121C2×D10111yescharacteristic
216#121C2×D10111yescharacteristic
217C4×Q8—1011no—
218C4×D4—1011no—
219C4×D4C2×D10111yescharacteristic
220C4×D4C2×D10111yescharacteristic
221#117C2×D10111yescharacteristic
222#107—1011no—
223#107—1011no—
224#106—1011no—
225#106—1011no—
226C4⋊C8—1011no—
227C4⋊C8—1011no—
228C4⋊C8—1011no—
229C4⋊C8—1011no—
230#103—1011no—
231#103—1011no—
232#102—1011no—
233#102—1011no—
234#102—1011no—
235#102—1011no—
236#102—1011no—
237#102—1011no—
238C2×Q8—1011no—
239C2×Q8—2021no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—1011no—
245C2×D4—2021no—
246C2×D4C22×D10111yescharacteristic
247C2×D4C22×D10111yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—2021no—
251C22×C4C22×D10111yescharacteristic
252SD16—4041no—
253SD16—4041no—
254D8—4041no—
255D8—4041no—
256M16—4041no—
257C2×C8—1011no—
258C2×C8—1011no—
259C2×C8—1011no—
260C2×C8—1011no—
261C2×C8—4041no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—1011no—
265C4⋊C4—1011no—
266C4⋊C4—2021no—
267C4⋊C4—2021no—
268C4⋊C4—2021no—
269C4⋊C4C22⋊D10111yescharacteristic
270C4⋊C4C22⋊D10111yescharacteristic
271C4⋊C4C22×D10111yescharacteristic
272C4⋊C4C22×D10111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2021no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C22⋊C4—2021no—
281C22⋊C4—2021no—
282C22⋊C4C22⋊D10111yescharacteristic
283C22⋊C4C22⋊D10111yescharacteristic
284C42—2021no—
285C42C22×D10111yescharacteristic
286C42C22×D10111yescharacteristic
287C23—21no—
288C23—21no—
289C23—2021no—
290C23C2×C22⋊D10111yescharacteristic
291Q8—8081no—
292Q8—2021no—
293Q8—2021no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—8081no—
303D4—2021no—
304D4—2021no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—8081no—
312C2×C4—2021no—
313C2×C4—2021no—
314C2×C4—2021no—
315C2×C4C2×C22⋊D10111yescharacteristic
316C2×C4C2×C22⋊D10111yescharacteristic
317C2×C4C2×C22⋊D10111yescharacteristic
318C2×C4C2×C22⋊D10111yescharacteristic
319C2×C4C2×C22⋊D10111yescharacteristic
320C2×C4C23×D10111yescharacteristic
321C8—2021no—
322C8—2021no—
323C8—2021no—
324C8—2021no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—4041no—
335C22—4041no—
336C22—4041no—
337C22C22×C22⋊D10111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—4041no—
346C4—4041no—
347C4—4041no—
348C4#1569230111yescharacteristic
349C4#1569230211yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—8081no—
354C2#2026575511yescharacteristic
355C2#2026598011yescharacteristic
356C2#2026598811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#540×C101C2
socleC22×C101C22×D4
hypercenter#540D101
hypocenterC101#3257
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20265798C2semidirect
2. #20265481C2semidirect
3. #20265474C2semidirect
4. #20265467C2semidirect
5. #20265457C2semidirect
6. #20265428C2semidirect
7. #20265421C2semidirect
8. #20265411C2semidirect
9. #20265404C2semidirect
10. #20265392C2semidirect
11. #20265392C2semidirect
12. #20265374C2semidirect
13. #20265369C2semidirect
14. #20265204C2semidirect
15. #540×C101C2semidirect
179. C101#3257semidirect
181. #540D101semidirect

Maximal subgroups

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

subgroupindex
#202657982
#202654812
#202654742
#202654672
#202654572
#202654282
#202654212
#202654112
#202654042
#202653922
#202653742
#202653692
#202652042
#540×C1012
#3257101