Finite Group Databasebeta

← #27182543

Subgroups — #27182543

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#20265782C211yesmaximal, characteristic, complemented
2#20265484C211yesmaximal, characteristic, complemented
3#20265477C211yesmaximal, characteristic, complemented
4#20265464C211yesmaximal, characteristic, complemented
5#20265454C211yesmaximal, characteristic, complemented
6#20265428C211yesmaximal, characteristic, complemented
7#20265425C211yesmaximal, characteristic, complemented
8#20265411C211yesmaximal, characteristic, complemented
9#20265408C211yesmaximal, characteristic, complemented
10#20265389C211yesmaximal, characteristic, complemented
11#20265389C211yesmaximal, characteristic, complemented
12#20265377C211yesmaximal, characteristic, complemented
13#20265372C211yesmaximal, characteristic, complemented
14#20265204C211yesmaximal, characteristic, complemented
15#542×C101C211yesmaximal, characteristic, complemented
16C2×#13108061C2211yescharacteristic
17C2×#13108061C2211yescharacteristic
18C2×#13108059C2211yescharacteristic
19C2×#13108059C2211yescharacteristic
20C2×#13108058C2211yescharacteristic
21C22×#11717579C2211yescharacteristic
22#15692252C2211yescharacteristic
23#15692247C2211yescharacteristic
24#15692240—21no—
25#15692240—21no—
26#15692229C2211yescharacteristic
27#15692229C2211yescharacteristic
28#15692228—21no—
29#15692228—21no—
30C4×D404C2211yescharacteristic
31C4×D404C2211yescharacteristic
32#15692188C2211yescharacteristic
33#15692188C2211yescharacteristic
34#15692186C2211yescharacteristic
35#15692186C2211yescharacteristic
36C4⋊#11717579C2211yescharacteristic
37C4⋊#11717579C2211yescharacteristic
38C4⋊#11717579C2211yescharacteristic
39C4⋊#11717579C2211yescharacteristic
40#15692179C2211yescharacteristic
41#15692179C2211yescharacteristic
42#15692176C2211yescharacteristic
43#15692176C2211yescharacteristic
44#15692175C2211yescharacteristic
45#15692175C2211yescharacteristic
46#15692175C2211yescharacteristic
47#15692175C2211yescharacteristic
48C4⋊Q8×C101C2211yescharacteristic
49#126×C101—21no—
50#124×C101—21no—
51#124×C101C2211yescharacteristic
52#123×C101—21no—
53C22⋊Q8×C101—21no—
54C22⋊Q8×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic
56C4×Q8×C101C2211yescharacteristic
57C4×D4×C101C2211yescharacteristic
58#117×C101C2211yescharacteristic
59C2×D404—21no—
60C2×D404—21no—
61C2×D404C2311yescharacteristic
62C2×D404C2311yescharacteristic
63C2×C22⋊D101—21no—
64C2×C22⋊D101—21no—
65C2×C4×D101—21no—
66C2×C4×D101—21no—
67#13108061—41no—
68#13108061—41no—
69#13108059—41no—
70#13108059—41no—
71#13108058—41no—
72C2×#11717579—41no—
73C2×#11717579C2311yescharacteristic
74C2×#11717579C2311yescharacteristic
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C4⋊Dic101C2311yescharacteristic
78C4⋊Dic101C2311yescharacteristic
79#13108053—21no—
80#13108053—21no—
81#13108051—21no—
82#13108051—21no—
83#13108051—21no—
84#13108051—21no—
85C2×Q8×C101—21no—
86C2×Q8×C101C2311yescharacteristic
87C2×D4×C101—21no—
88C2×D4×C101C2311yescharacteristic
89C22×C4×C101—21no—
90C22×C4×C101C2311yescharacteristic
91C4⋊C4×C101—21no—
92C4⋊C4×C101—21no—
93C4⋊C4×C101—21no—
94C4⋊C4×C101D411yescharacteristic
95C4⋊C4×C101D411yescharacteristic
96C4⋊C4×C101C2311yescharacteristic
97C4⋊C4×C101C2311yescharacteristic
98C22⋊C4×C101—21no—
99C22⋊C4×C101—21no—
100C22⋊C4×C101—21no—
101C22⋊C4×C101—21no—
102C22⋊C4×C101—21no—
103C22⋊C4×C101D411yescharacteristic
104C22⋊C4×C101D411yescharacteristic
105C42×C101—21no—
106C42×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C23×C101—21no—
109C23×C101C2×D411yescharacteristic
110C22×D101—21no—
111C22×D101—21no—
112Q8×C101—21no—
113Q8×C101—21no—
114Q8×C101—81no—
115D4×C101—21no—
116D4×C101—21no—
117D4×C101—81no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—81no—
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2×D411yescharacteristic
128C2×C4×C101C2×D411yescharacteristic
129C2×C4×C101C2411yescharacteristic
130C22⋊D101—81no—
131C22⋊D101—81no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134D404—21no—
135D404—21no—
136D404—21no—
137D404—21no—
138D404—81no—
139D404—81no—
140C4×D101—81no—
141C4×D101—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×C101C22×D411yescharacteristic
153C2×D101—41no—
154C2×D101—41no—
155C2×D101—41no—
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×C101—41no—
167C4×C101H(5,𝔽2)11yescharacteristic
168C4×C1012−1+411yescharacteristic
169Dic101—41no—
170Dic101—41no—
171C2×C101—41no—
172C2×C101—81no—
173C2×C101#53711yescharacteristic
174C2×C101#57611yescharacteristic
175C2×C101#57711yescharacteristic
176D101—81no—
177D101—81no—
178#3257—1011nomaximal, Sylow
179C101#325711yescharacteristic, complemented, Sylow
180#542D10111yescharacteristic, complemented
181#540—1011no—
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⋊Q8C2×D10111yescharacteristic
202#127—1011no—
203#126—21no—
204#125—1011no—
205#124—21no—
206#124C2×D10111yescharacteristic
207#123—21no—
208#123—2021no—
209#123—2021no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D10111yescharacteristic
212#121—1011no—
213#121—1011no—
214#121—2021no—
215#121—2021no—
216#121C2×D10111yescharacteristic
217C4×Q8C2×D10111yescharacteristic
218C4×D4—1011no—
219C4×D4—1011no—
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—21no—
239C2×Q8C22×D10111yescharacteristic
240C2×D4—21no—
241C2×D4—1011no—
242C2×D4—1011no—
243C2×D4—2021no—
244C2×D4—2021no—
245C2×D4—2021no—
246C2×D4—2021no—
247C2×D4C22×D10111yescharacteristic
248C22×C4—21no—
249C22×C4—2021no—
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—21no—
265C4⋊C4—1011no—
266C4⋊C4—1011no—
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—21no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C22⋊C4—2021no—
281C22⋊C4—2021no—
282C22⋊C4C22⋊D10111yescharacteristic
283C22⋊C4C22⋊D10111yescharacteristic
284C42—21no—
285C42C22×D10111yescharacteristic
286C42C22×D10111yescharacteristic
287C23—21no—
288C23—2021no—
289C23—2021no—
290C23C2×C22⋊D10111yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—8081no—
298D4—8081no—
299D4—8081no—
300D4—8081no—
301D4—2021no—
302D4—2021no—
303D4—2021no—
304D4—2021no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—8081no—
312C2×C4—8081no—
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—4041no—
332C22—4041no—
333C22—4041no—
334C22—4041no—
335C22—4041no—
336C22—4041no—
337C22C22×C22⋊D10111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—4041no—
347C4—4041no—
348C4#1569230111yescharacteristic
349C4#1569230211yescharacteristic
350C2—41no—
351C2—81no—
352C2—8081no—
353C2—8081no—
354C2#2026575511yescharacteristic
355C2#2026598011yescharacteristic
356C2#2026598511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#542×C101C2
socleC22×C101C22×D4
hypercenter#542D101
hypocenterC101#3257
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20265782C2semidirect
2. #20265484C2semidirect
3. #20265477C2semidirect
4. #20265464C2semidirect
5. #20265454C2semidirect
6. #20265428C2semidirect
7. #20265425C2semidirect
8. #20265411C2semidirect
9. #20265408C2semidirect
10. #20265389C2semidirect
11. #20265389C2semidirect
12. #20265377C2semidirect
13. #20265372C2semidirect
14. #20265204C2semidirect
15. #542×C101C2semidirect
179. C101#3257semidirect
180. #542D101semidirect

Maximal subgroups

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

subgroupindex
#202657822
#202654842
#202654772
#202654642
#202654542
#202654282
#202654252
#202654112
#202654082
#202653892
#202653772
#202653722
#202652042
#542×C1012
#3257101