Finite Group Databasebeta

← #37545132

Subgroups — #37545132

Order 23168.

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#26041884C211yesmaximal, characteristic, complemented
2#26041586C211yesmaximal, characteristic, complemented
3#26041579C211yesmaximal, characteristic, complemented
4#26041566C211yesmaximal, characteristic, complemented
5#26041556C211yesmaximal, characteristic, complemented
6#26041530C211yesmaximal, characteristic, complemented
7#26041527C211yesmaximal, characteristic, complemented
8#26041513C211yesmaximal, characteristic, complemented
9#26041510C211yesmaximal, characteristic, complemented
10#26041491C211yesmaximal, characteristic, complemented
11#26041491C211yesmaximal, characteristic, complemented
12#26041479C211yesmaximal, characteristic, complemented
13#26041474C211yesmaximal, characteristic, complemented
14#26041306C211yesmaximal, characteristic, complemented
15#542×C181C211yesmaximal, characteristic, complemented
16C2×#15668436C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668433C2211yescharacteristic
21C22×#13089678C2211yescharacteristic
22#19153813C2211yescharacteristic
23#19153808C2211yescharacteristic
24#19153801—21no—
25#19153801—21no—
26#19153790C2211yescharacteristic
27#19153790C2211yescharacteristic
28#19153789—21no—
29#19153789—21no—
30C4×D724C2211yescharacteristic
31C4×D724C2211yescharacteristic
32#19153749C2211yescharacteristic
33#19153749C2211yescharacteristic
34#19153747C2211yescharacteristic
35#19153747C2211yescharacteristic
36C4⋊#13089678C2211yescharacteristic
37C4⋊#13089678C2211yescharacteristic
38C4⋊#13089678C2211yescharacteristic
39C4⋊#13089678C2211yescharacteristic
40#19153740C2211yescharacteristic
41#19153740C2211yescharacteristic
42#19153737C2211yescharacteristic
43#19153737C2211yescharacteristic
44#19153736C2211yescharacteristic
45#19153736C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic
48C4⋊Q8×C181C2211yescharacteristic
49#126×C181—21no—
50#124×C181—21no—
51#124×C181C2211yescharacteristic
52#123×C181—21no—
53C22⋊Q8×C181—21no—
54C22⋊Q8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56C4×Q8×C181C2211yescharacteristic
57C4×D4×C181C2211yescharacteristic
58#117×C181C2211yescharacteristic
59C2×D724—21no—
60C2×D724—21no—
61C2×D724C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181—21no—
67#15668436—41no—
68#15668436—41no—
69#15668434—41no—
70#15668434—41no—
71#15668433—41no—
72C2×#13089678—41no—
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81#15668426—21no—
82#15668426—21no—
83#15668426—21no—
84#15668426—21no—
85C2×Q8×C181—21no—
86C2×Q8×C181C2311yescharacteristic
87C2×D4×C181—21no—
88C2×D4×C181C2311yescharacteristic
89C22×C4×C181—21no—
90C22×C4×C181C2311yescharacteristic
91C4⋊C4×C181—21no—
92C4⋊C4×C181—21no—
93C4⋊C4×C181—21no—
94C4⋊C4×C181D411yescharacteristic
95C4⋊C4×C181D411yescharacteristic
96C4⋊C4×C181C2311yescharacteristic
97C4⋊C4×C181C2311yescharacteristic
98C22⋊C4×C181—21no—
99C22⋊C4×C181—21no—
100C22⋊C4×C181—21no—
101C22⋊C4×C181—21no—
102C22⋊C4×C181—21no—
103C22⋊C4×C181D411yescharacteristic
104C22⋊C4×C181D411yescharacteristic
105C42×C181—21no—
106C42×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—21no—
110D724—21no—
111D724—21no—
112D724—21no—
113D724—21no—
114D724—81no—
115D724—81no—
116C22⋊D181—81no—
117C22⋊D181—81no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C4×D181—81no—
121C4×D181—81no—
122#13089678—21no—
123#13089678—21no—
124#13089678—21no—
125#13089678—21no—
126C23×C181—21no—
127C23×C181C2×D411yescharacteristic
128Q8×C181—21no—
129Q8×C181—21no—
130Q8×C181—81no—
131D4×C181—21no—
132D4×C181—21no—
133D4×C181—81no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—81no—
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2411yescharacteristic
146C22×C181—21no—
147C22×C181—21no—
148C22×C181—21no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181C22×D411yescharacteristic
153C2×D181—41no—
154C2×D181—41no—
155C2×D181—41no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—21no—
162C4×C181—21no—
163C4×C181—21no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181—41no—
167C4×C181H(5,𝔽2)11yescharacteristic
168C4×C1812−1+411yescharacteristic
169Dic181—41no—
170Dic181—41no—
171C2×C181—41no—
172C2×C181—81no—
173C2×C181#53711yescharacteristic
174C2×C181#57611yescharacteristic
175C2×C181#57711yescharacteristic
176D181—81no—
177D181—81no—
178C181#325711yescharacteristic, complemented, Sylow
179#3257—1811nomaximal, Sylow
180#542D18111yescharacteristic, complemented
181#540—1811no—
182#479—1811no—
183#478—1811no—
184#476—1811no—
185#474—1811no—
186#469—1811no—
187#468—1811no—
188#466—1811no—
189#465—1811no—
190#463—1811no—
191#463—1811no—
192#460—1811no—
193#459—1811no—
194#424—1811no—
195C2×SD16—1811no—
196C2×SD16—1811no—
197C2×D8—1811no—
198C2×D8—1811no—
199C2×M16—1811no—
200C22×C8—1811no—
201C4⋊Q8C2×D18111yescharacteristic
202#127—1811no—
203#126—21no—
204#125—1811no—
205#124—21no—
206#124C2×D18111yescharacteristic
207#123—21no—
208#123—3621no—
209#123—3621no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D18111yescharacteristic
212#121—3621no—
213#121—3621no—
214#121—1811no—
215#121—1811no—
216#121C2×D18111yescharacteristic
217C4×Q8C2×D18111yescharacteristic
218C4×D4—1811no—
219C4×D4—1811no—
220C4×D4C2×D18111yescharacteristic
221#117C2×D18111yescharacteristic
222#107—1811no—
223#107—1811no—
224#106—1811no—
225#106—1811no—
226C4⋊C8—1811no—
227C4⋊C8—1811no—
228C4⋊C8—1811no—
229C4⋊C8—1811no—
230#103—1811no—
231#103—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102—1811no—
236#102—1811no—
237#102—1811no—
238C2×Q8—21no—
239C2×Q8C22×D18111yescharacteristic
240C2×D4—21no—
241C2×D4—3621no—
242C2×D4—3621no—
243C2×D4—3621no—
244C2×D4—3621no—
245C2×D4—1811no—
246C2×D4—1811no—
247C2×D4C22×D18111yescharacteristic
248C22×C4—21no—
249C22×C4—3621no—
250C22×C4—3621no—
251C22×C4C22×D18111yescharacteristic
252SD16—7241no—
253SD16—7241no—
254D8—7241no—
255D8—7241no—
256M16—7241no—
257C2×C8—1811no—
258C2×C8—1811no—
259C2×C8—1811no—
260C2×C8—1811no—
261C2×C8—7241no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—1811no—
268C4⋊C4—1811no—
269C4⋊C4C22⋊D18111yescharacteristic
270C4⋊C4C22⋊D18111yescharacteristic
271C4⋊C4C22×D18111yescharacteristic
272C4⋊C4C22×D18111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4C22⋊D18111yescharacteristic
283C22⋊C4C22⋊D18111yescharacteristic
284C42—21no—
285C42C22×D18111yescharacteristic
286C42C22×D18111yescharacteristic
287C23—21no—
288C23—3621no—
289C23—3621no—
290C23C2×C22⋊D18111yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—3621no—
298D4—3621no—
299D4—3621no—
300D4—3621no—
301D4—14481no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—14481no—
314C2×C4—14481no—
315C2×C4C2×C22⋊D18111yescharacteristic
316C2×C4C2×C22⋊D18111yescharacteristic
317C2×C4C2×C22⋊D18111yescharacteristic
318C2×C4C2×C22⋊D18111yescharacteristic
319C2×C4C2×C22⋊D18111yescharacteristic
320C2×C4C23×D18111yescharacteristic
321C8—3621no—
322C8—3621no—
323C8—3621no—
324C8—3621no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—7241no—
332C22—7241no—
333C22—7241no—
334C22—7241no—
335C22—7241no—
336C22—7241no—
337C22C22×C22⋊D18111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—7241no—
347C4—7241no—
348C4#1915386211yescharacteristic
349C4#1915386311yescharacteristic
350C2—41no—
351C2—81no—
352C2—14481no—
353C2—14481no—
354C2#2604185711yescharacteristic
355C2#2604208211yescharacteristic
356C2#2604208711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#542×C181C2
socleC22×C181C22×D4
hypercenter#542D181
hypocenterC181#3257
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #26041884C2semidirect
2. #26041586C2semidirect
3. #26041579C2semidirect
4. #26041566C2semidirect
5. #26041556C2semidirect
6. #26041530C2semidirect
7. #26041527C2semidirect
8. #26041513C2semidirect
9. #26041510C2semidirect
10. #26041491C2semidirect
11. #26041491C2semidirect
12. #26041479C2semidirect
13. #26041474C2semidirect
14. #26041306C2semidirect
15. #542×C181C2semidirect
178. C181#3257semidirect
180. #542D181semidirect

Maximal subgroups

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

subgroupindex
#260418842
#260415862
#260415792
#260415662
#260415562
#260415302
#260415272
#260415132
#260415102
#260414912
#260414792
#260414742
#260413062
#542×C1812
#3257181