Finite Group Databasebeta

← #27181387

Subgroups — #27181387

Order 12928.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265794C211yesmaximal, characteristic, complemented
2#20265660C211yesmaximal, characteristic, complemented
3#20265513C211yesmaximal, characteristic, complemented
4#20265488C211yesmaximal, characteristic, complemented
5#20265470C211yesmaximal, characteristic, complemented
6#20265455C211yesmaximal, characteristic, complemented
7#20265397C211yesmaximal, characteristic, complemented
8#20265390C211yesmaximal, characteristic, complemented
9#20265339C211yesmaximal, characteristic, complemented
10#20265278C211yesmaximal, characteristic, complemented
11#20265274C211yesmaximal, characteristic, complemented
12#20265269C211yesmaximal, characteristic, complemented
13D8×Dic101C211yesmaximal, characteristic, complemented
14#20265235C211yesmaximal, characteristic, complemented
15#449×C101C211yesmaximal, characteristic
16C2×#13108064C2211yescharacteristic
17C2×#13108062C2211yescharacteristic
18#15692254C2211yescharacteristic
19#15692248—21no—
20#15692242—21no—
21#15692242C2211yescharacteristic
22#15692236—21no—
23#15692234C2211yescharacteristic
24#15692232—21no—
25Q8×Dic101C2211yescharacteristic
26Q8×Dic101C2211yescharacteristic
27#15692220C2211yescharacteristic
28D4×Dic101—21no—
29D4×Dic101—21no—
30D4×Dic101C2211yescharacteristic
31D4×Dic101C2211yescharacteristic
32D4×Dic101C2211yescharacteristic
33#15692214—21no—
34#15692214C2211yescharacteristic
35C2×C4⋊Dic101—21no—
36C2×C4⋊Dic101C2211yescharacteristic
37#15692189C2211yescharacteristic
38#15692189C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692188C2211yescharacteristic
41#15692184C2211yescharacteristic
42#15692184C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692179C2211yescharacteristic
46#15692176C2211yescharacteristic
47#15692176C2211yescharacteristic
48#15692176C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic
50#15692165C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52C2×#41×C101C2211yescharacteristic
53C2×SD16×C101C2211yescharacteristic
54C2×D8×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic
56#103×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59C2×Dic202—21no—
60C2×Dic202C2311yescharacteristic
61C22×Dic101—21no—
62C22×Dic101—21no—
63C22×Dic101—21no—
64C22×Dic101—21no—
65#13108064—22no—
66#13108062—22no—
67C2×#11717579C2311yescharacteristic
68C2×#11717579C2311yescharacteristic
69C4⋊Dic101—21no—
70C4⋊Dic101—21no—
71C4⋊Dic101—21no—
72C4⋊Dic101D411yescharacteristic
73C4⋊Dic101D411yescharacteristic
74C4⋊Dic101C2311yescharacteristic
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77#13108053—21no—
78#13108053—21no—
79#13108053—21no—
80C22⋊Dic101—21no—
81C22⋊Dic101—21no—
82C22⋊Dic101—21no—
83C22⋊Dic101—21no—
84C22⋊Dic101—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101D411yescharacteristic
87C22⋊Dic101D411yescharacteristic
88C4×Dic101—21no—
89C4×Dic101—21no—
90C4×Dic101—21no—
91C4×Dic101C2311yescharacteristic
92C4×Dic101C2311yescharacteristic
93#41×C101—22no—
94#41×C101—22no—
95C2×Q8×C101C2311yescharacteristic
96C2×D4×C101—21no—
97C2×D4×C101—21no—
98C2×D4×C101C2311yescharacteristic
99C2×D4×C101C2311yescharacteristic
100C22×C4×C101—21no—
101C22×C4×C101C2311yescharacteristic
102SD16×C101—22no—
103D8×C101—22no—
104C2×C8×C101C2311yescharacteristic
105C2×C8×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C22⋊C4×C101—21no—
108C23×C101—21no—
109C23×C101—21no—
110C23×C101C2×D411yescharacteristic
111Q8×C101—21no—
112Q8×C101#4112yes—
113D4×C101—24no—
114D4×C101—21no—
115D4×C101—21no—
116D4×C101—21no—
117D4×C101—81no—
118D4×C101#4112yes—
119C2×C4×C101—24no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101—21no—
123C2×C4×C101—21no—
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2411yescharacteristic
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101—81no—
131C2×Dic101—81no—
132C2×Dic101—81no—
133C2×Dic101—81no—
134C2×Dic101C2×D411yescharacteristic
135C2×Dic101C2×D411yescharacteristic
136C2×Dic101C2×D411yescharacteristic
137C2×Dic101C2×D411yescharacteristic
138Dic202—21no—
139Dic202—21no—
140Dic202—81no—
141C8×C101—21no—
142C8×C101—21no—
143#11717579—21no—
144#11717579—21no—
145C22×C101—21no—
146C22×C101—22no—
147C22×C101—21no—
148C22×C101—21no—
149C22×C101—41no—
150C22×C101—41no—
151C22×C101—41no—
152C22×C101—41no—
153C22×C101—41no—
154C22×C101C22×D411yescharacteristic
155C4×C101—21no—
156C4×C101—22no—
157C4×C101—41no—
158C4×C101C2×#4111yescharacteristic
159C4×C101C2×#4111yescharacteristic
160Dic101—21no—
161Dic101—21no—
162Dic101—21no—
163Dic101—21no—
164Dic101—41no—
165Dic101—41no—
166Dic101—41no—
167Dic101—41no—
168C2×C101—41no—
169C2×C101—42no—
170C2×C101—81no—
171C2×C101#52511yescharacteristic
172C2×C101#57611yescharacteristic
173C2×C101#57811yescharacteristic
174#3124—1011nomaximal, Sylow
175C101#312411yescharacteristic, complemented, Sylow
176#542—1011no—
177#520—1011no—
178#484—1011no—
179#480—1011no—
180#477—1011no—
181#474—1011no—
182#464—1011no—
183#463—1011no—
184#452—1011no—
185#449D10111yescharacteristic
186#440—1011no—
187#440—1011no—
188C4×Q16—1011no—
189C4×D8—1011no—
190#433—1011no—
191C2×#41C2×D10111yescharacteristic
192C2×Q16—1011no—
193C2×SD16—1011no—
194C2×SD16C2×D10111yescharacteristic
195C2×D8C2×D10111yescharacteristic
196C4⋊Q8—1011no—
197#126—2021no—
198#124—1011no—
199#124—2021no—
200#123—2021no—
201C22⋊Q8—1011no—
202C22⋊Q8—2021no—
203#121C2×D10111yescharacteristic
204C4×Q8—1011no—
205C4×Q8—1011no—
206C4×Q8—1011no—
207C4×D4—1011no—
208C4×D4—1011no—
209C4×D4—1011no—
210C4×D4—2021no—
211C4×D4—2021no—
212#117—1011no—
213#117—2021no—
214C2×C4⋊C4—1011no—
215C2×C4⋊C4—2021no—
216#107—1011no—
217#107—1011no—
218#107—1011no—
219#107—1011no—
220C4⋊C8—1011no—
221C4⋊C8—1011no—
222#103—1011no—
223#103—1011no—
224#103—1011no—
225#103C2×D10111yescharacteristic
226#102—1011no—
227#102—1011no—
228#102—1011no—
229#102C2×D10111yescharacteristic
230C22⋊C8—1011no—
231C22⋊C8C2×D10111yescharacteristic
232#97—1011no—
233C4×C8—1011no—
234#41—22no—
235#41—22no—
236C2×Q8—1011no—
237C2×Q8—2021no—
238C2×Q8C22×D10111yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C22×D10111yescharacteristic
242C2×D4C22×D10111yescharacteristic
243C22×C4—21no—
244C22×C4—2021no—
245C22×C4—2021no—
246C22×C4—2021no—
247C22×C4—2021no—
248C22×C4C22×D10111yescharacteristic
249Q16—2022no—
250SD16—22no—
251SD16—2022no—
252D8—22no—
253C2×C8—1011no—
254C2×C8—1011no—
255C2×C8C22×D10111yescharacteristic
256C2×C8C22×D10111yescharacteristic
257C4⋊C4—1011no—
258C4⋊C4—1011no—
259C4⋊C4—1011no—
260C4⋊C4—1011no—
261C4⋊C4—1011no—
262C4⋊C4—2021no—
263C4⋊C4—2021no—
264C4⋊C4—2021no—
265C4⋊C4—2021no—
266C4⋊C4—2021no—
267C4⋊C4—2021no—
268C4⋊C4C22×D10111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—1011no—
271C22⋊C4—1011no—
272C22⋊C4—2021no—
273C22⋊C4—2021no—
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C22⋊C4—2021no—
277C22⋊C4—2021no—
278C42—1011no—
279C42—1011no—
280C42—2021no—
281C42—2021no—
282C42—2021no—
283C23—21no—
284C23—21no—
285C23D4×D10111yescharacteristic
286Q8—21no—
287Q8—8081no—
288Q8—2021no—
289Q8—2021no—
290Q8#1310807312yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#1310807312yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—8081no—
303C2×C4—8081no—
304C2×C4—8081no—
305C2×C4—8081no—
306C2×C4—1011no—
307C2×C4—1011no—
308C2×C4—1011no—
309C2×C4—1011no—
310C2×C4—2021no—
311C2×C4—2021no—
312C2×C4—2021no—
313C2×C4—2021no—
314C2×C4D4×D10111yescharacteristic
315C2×C4C23×D10111yescharacteristic
316C8—21no—
317C8—21no—
318C8—2021no—
319C8—2021no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D10111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—4041no—
334C4—4041no—
335C4—4041no—
336C4—4041no—
337C4—2021no—
338C4—2021no—
339C4—2021no—
340C4—2021no—
341C4C2×#1310807311yescharacteristic
342C4C2×#1310807311yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#2026568311yescharacteristic
347C2#2026598111yescharacteristic
348C2#2026599111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting, prime radical#449×C101C2
socleC22×C101C22×D4
hypercenter#449D101
hypocenterC101#3124
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20265794C2semidirect
2. #20265660C2semidirect
3. #20265513C2semidirect
4. #20265488C2semidirect
5. #20265470C2semidirect
6. #20265455C2semidirect
7. #20265397C2semidirect
8. #20265390C2semidirect
9. #20265339C2semidirect
10. #20265278C2semidirect
11. #20265274C2semidirect
12. #20265269C2semidirect
13. D8×Dic101C2semidirect
14. #20265235C2semidirect
175. C101#3124semidirect

Maximal subgroups

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

subgroupindex
#202657942
#202656602
#202655132
#202654882
#202654702
#202654552
#202653972
#202653902
#202653392
#202652782
#202652742
#202652692
D8×Dic1012
#202652352
#449×C1012
#3124101