Finite Group Databasebeta

← #27184216

Subgroups — #27184216

Order 12928.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265912C211yesmaximal, characteristic, complemented
2#20265567C211yesmaximal, characteristic, complemented
3#20265564C211yesmaximal, characteristic, complemented
4#20265559C211yesmaximal, characteristic, complemented
5#20265399C211yesmaximal, characteristic, complemented
6#20265396C211yesmaximal, characteristic, complemented
7#20265392C211yesmaximal, characteristic, complemented
8#20265389C211yesmaximal, characteristic, complemented
9#20265372C211yesmaximal, characteristic, complemented
10#20265369C211yesmaximal, characteristic, complemented
11#20265308C211yesmaximal, characteristic, complemented
12#20265277C211yesmaximal, characteristic, complemented
13#20265275C211yesmaximal, characteristic, complemented
14C4×#13108059C211yesmaximal, characteristic, complemented
15#559×C101C211yesmaximal, characteristic, complemented
16C2×#13108064C2211yescharacteristic
17C2×#13108062C2211yescharacteristic
18C2×#13108062C2211yescharacteristic
19C2×#13108061C2211yescharacteristic
20C2×#13108061C2211yescharacteristic
21C2×#13108059C2211yescharacteristic
22C2×#13108059C2211yescharacteristic
23C2×#13108059C2211yescharacteristic
24C2×#13108059C2211yescharacteristic
25#15692252C2211yescharacteristic
26#15692244—21no—
27#15692243C2211yescharacteristic
28#15692243C2211yescharacteristic
29#15692240—21no—
30#15692240—21no—
31C4×Dic202C2211yescharacteristic
32C4×D404C2211yescharacteristic
33C4×D404C2211yescharacteristic
34#15692217—21no—
35#15692188C2211yescharacteristic
36C4⋊#11717579C2211yescharacteristic
37C4⋊#11717579C2211yescharacteristic
38C4⋊#11717579C2211yescharacteristic
39#15692179C2211yescharacteristic
40#15692178C2211yescharacteristic
41#15692176C2211yescharacteristic
42#15692176C2211yescharacteristic
43#15692175C2211yescharacteristic
44#15692175C2211yescharacteristic
45#15692166C2211yescharacteristic
46#15692166C2211yescharacteristic
47C4×#11717579C2211yescharacteristic
48#127×C101C2211yescharacteristic
49#124×C101—21no—
50#124×C101C2211yescharacteristic
51#124×C101C2211yescharacteristic
52#123×C101—21no—
53#123×C101—21no—
54C4×Q8×C101C2211yescharacteristic
55C4×Q8×C101C2211yescharacteristic
56C4×D4×C101—21no—
57C4×D4×C101C2211yescharacteristic
58C4×D4×C101C2211yescharacteristic
59C2×Dic202C2311yescharacteristic
60C2×D404—21no—
61C2×D404—21no—
62C2×D404C2311yescharacteristic
63C2×D404C2311yescharacteristic
64C2×C4×D101—21no—
65C2×C4×D101—21no—
66#13108064—41no—
67#13108062—22no—
68#13108062—41no—
69#13108061—22no—
70#13108061—41no—
71#13108059—22no—
72#13108059—41no—
73#13108059—41no—
74#13108059—41no—
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C2×#11717579C2311yescharacteristic
78C2×#11717579C2311yescharacteristic
79C4⋊Dic101C2311yescharacteristic
80#13108053—21no—
81#13108051—21no—
82#13108051—21no—
83#13108051—21no—
84#13108051—21no—
85#13108051—21no—
86#13108051—21no—
87C4×Dic101—21no—
88C2×Q8×C101D411yescharacteristic
89C2×Q8×C101C2311yescharacteristic
90C2×D4×C101—21no—
91C2×D4×C101—21no—
92C2×D4×C101C2311yescharacteristic
93C2×D4×C101C2311yescharacteristic
94C22×C4×C101—21no—
95C22×C4×C101—21no—
96C4⋊C4×C101—21no—
97C4⋊C4×C101D411yescharacteristic
98C4⋊C4×C101D411yescharacteristic
99C4⋊C4×C101D411yescharacteristic
100C4⋊C4×C101C2311yescharacteristic
101C22⋊C4×C101—21no—
102C22⋊C4×C101—21no—
103C22⋊C4×C101—21no—
104C22⋊C4×C101—21no—
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C42×C101—21no—
108C42×C101C2311yescharacteristic
109C42×C101C2311yescharacteristic
110C42×C101C2311yescharacteristic
111C23×C101—21no—
112C23×C101—21no—
113C22×D101—21no—
114C22×D101—21no—
115Q8×C101—21no—
116Q8×C101—21no—
117Q8×C101—41no—
118D4×C101—21no—
119D4×C101—21no—
120D4×C101—21no—
121D4×C101—21no—
122D4×C101—42no—
123D4×C101—81no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101—81no—
127C2×C4×C101—81no—
128C2×C4×C101C2×D411yescharacteristic
129C2×C4×C101C2×D411yescharacteristic
130C2×C4×C101C2×D411yescharacteristic
131C2×C4×C101C2×D411yescharacteristic
132C2×C4×C101C2×D411yescharacteristic
133C2×C4×C101C2×D411yescharacteristic
134C2×C4×C101C2411yescharacteristic
135C2×Dic101—21no—
136C2×Dic101—21no—
137D404—21no—
138D404—21no—
139D404—21no—
140D404—21no—
141D404—42no—
142D404—81no—
143C4×D101—81no—
144C4×D101—81no—
145Dic202—21no—
146Dic202—21no—
147#11717579—21no—
148#11717579—21no—
149#11717579—21no—
150#11717579#4112yes—
151C22×C101—41no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101—41no—
155C22×C101—41no—
156C22×C101—41no—
157C22×C101C22×D411yescharacteristic
158C2×D101—41no—
159C2×D101—41no—
160C2×D101—41no—
161C2×D101—41no—
162C2×D101—41no—
163C2×D101—41no—
164C4×C101—21no—
165C4×C101—21no—
166C4×C101—21no—
167C4×C101—21no—
168C4×C101—21no—
169C4×C101—21no—
170C4×C101—41no—
171C4×C101—41no—
172C4×C101C2×#4111yescharacteristic
173C4×C101H(5,𝔽2)11yescharacteristic
174Dic101—41no—
175Dic101—41no—
176C2×C101—81no—
177C2×C101—81no—
178C2×C101#55011yescharacteristic
179C2×C101#57511yescharacteristic
180C2×C101#57611yescharacteristic
181D101—81no—
182D101—81no—
183#3403—1011nomaximal, Sylow
184C101#340311yescharacteristic, complemented, Sylow
185#559—1011no—
186#559D10111yescharacteristic, complemented
187#496—1011no—
188#496—1011no—
189#495—1011no—
190#464—1011no—
191#464—1011no—
192#463—1011no—
193#463—1011no—
194#459—1011no—
195#459—1011no—
196#446—1011no—
197#440—1011no—
198#440—1011no—
199C4×D8—1011no—
200C2×Q16—1011no—
201C2×SD16—1011no—
202C2×SD16—1011no—
203C2×SD16—1011no—
204C2×SD16—1011no—
205C2×D8—1011no—
206C2×D8—1011no—
207C2×D8—1011no—
208C2×D8—1011no—
209#127—1011no—
210#127C2×D10111yescharacteristic
211#124—21no—
212#124—1011no—
213#124—1011no—
214#124—2021no—
215#124C2×D10111yescharacteristic
216#124C2×D10111yescharacteristic
217#123—21no—
218#123—21no—
219#123—2021no—
220#123—2021no—
221C4×Q8—1011no—
222C4×Q8C2×D10111yescharacteristic
223C4×Q8C2×D10111yescharacteristic
224C4×D4—21no—
225C4×D4—1011no—
226C4×D4—1011no—
227C4×D4—2021no—
228C4×D4C2×D10111yescharacteristic
229C4×D4C2×D10111yescharacteristic
230#107—1011no—
231C4⋊C8—1011no—
232C4⋊C8—1011no—
233C4⋊C8—1011no—
234#103—1011no—
235#103—1011no—
236#102—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#97—1011no—
241#97—1011no—
242C4×C8—1011no—
243C2×Q8—1011no—
244C2×Q8C22⋊D10111yescharacteristic
245C2×Q8C22×D10111yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—1011no—
249C2×D4—1011no—
250C2×D4—2021no—
251C2×D4—2021no—
252C2×D4C22×D10111yescharacteristic
253C2×D4C22×D10111yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—2021no—
257C22×C4—2021no—
258Q16—4041no—
259SD16—4041no—
260SD16—4041no—
261SD16—2022no—
262SD16—2022no—
263D8—4041no—
264D8—4041no—
265D8—4041no—
266D8—2022no—
267C2×C8—1011no—
268C2×C8—1011no—
269C2×C8—1011no—
270C2×C8—1011no—
271C4⋊C4—21no—
272C4⋊C4—1011no—
273C4⋊C4—2021no—
274C4⋊C4C22⋊D10111yescharacteristic
275C4⋊C4C22⋊D10111yescharacteristic
276C4⋊C4C22⋊D10111yescharacteristic
277C4⋊C4C22×D10111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—2021no—
285C22⋊C4—2021no—
286C22⋊C4—2021no—
287C22⋊C4—2021no—
288C22⋊C4—2021no—
289C22⋊C4—2021no—
290C42—21no—
291C42—2021no—
292C42C22×D10111yescharacteristic
293C42C22×D10111yescharacteristic
294C42C22×D10111yescharacteristic
295C23—21no—
296C23—21no—
297C23—2021no—
298C23—2021no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—2021no—
303Q8—2021no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—8081no—
311D4—4042no—
312D4—2021no—
313D4—2021no—
314D4—2021no—
315D4—2021no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—8081no—
321C2×C4—8081no—
322C2×C4—2021no—
323C2×C4—2021no—
324C2×C4C2×C22⋊D10111yescharacteristic
325C2×C4C2×C22⋊D10111yescharacteristic
326C2×C4C2×C22⋊D10111yescharacteristic
327C2×C4C2×C22⋊D10111yescharacteristic
328C2×C4C2×C22⋊D10111yescharacteristic
329C2×C4C2×C22⋊D10111yescharacteristic
330C2×C4C23×D10111yescharacteristic
331C8—1012no—
332C8—2021no—
333C8—2021no—
334C8—2021no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—4041no—
342C22—4041no—
343C22—4041no—
344C22—4041no—
345C22—4041no—
346C22—4041no—
347C22C22×C22⋊D10111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—4041no—
357C4—4041no—
358C4#41×D10111yescharacteristic
359C4#1569230111yescharacteristic
360C2—81no—
361C2—81no—
362C2—8081no—
363C2—8081no—
364C2#2026584611yescharacteristic
365C2#2026597511yescharacteristic
366C2#2026598011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#559×C101C2
socleC22×C101C22×D4
hypercenter#559D101
hypocenterC101#3403
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #20265912C2semidirect
2. #20265567C2semidirect
3. #20265564C2semidirect
4. #20265559C2semidirect
5. #20265399C2semidirect
6. #20265396C2semidirect
7. #20265392C2semidirect
8. #20265389C2semidirect
9. #20265372C2semidirect
10. #20265369C2semidirect
11. #20265308C2semidirect
12. #20265277C2semidirect
13. #20265275C2semidirect
14. C4×#13108059C2semidirect
15. #559×C101C2semidirect
184. C101#3403semidirect
186. #559D101semidirect

Maximal subgroups

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

subgroupindex
#202659122
#202655672
#202655642
#202655592
#202653992
#202653962
#202653922
#202653892
#202653722
#202653692
#202653082
#202652772
#202652752
C4×#131080592
#559×C1012
#3403101