Finite Group Databasebeta

← #37543389

Subgroups — #37543389

Order 23168.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153837C211yesmaximal, characteristic, complemented
2C2×#19153824C211yesmaximal, characteristic, complemented
3#26041859C211yesmaximal, characteristic, complemented
4#26041858C211yesmaximal, characteristic, complemented
5#26041526C211yesmaximal, characteristic, complemented
6#26041525C211yesmaximal, characteristic, complemented
7#26041522C211yesmaximal, characteristic, complemented
8#26041519C211yesmaximal, characteristic, complemented
9#26041518C211yesmaximal, characteristic, complemented
10#26041514C211yesmaximal, characteristic, complemented
11#26041513C211yesmaximal, characteristic, complemented
12#107×D181C211yesmaximal, characteristic, complemented
13#26041279C211yesmaximal, characteristic, complemented
14#26041277C211yesmaximal, characteristic, complemented
15#468×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×#15668448C2211yescharacteristic
19#19153837—24no—
20C2×#15668439C2211yescharacteristic
21C2×#15668438C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23#19153824—24no—
24C2×#15668432C2211yescharacteristic
25C2×#15668432C2211yescharacteristic
26C22×#13089678C2211yescharacteristic
27C2×C8×D181C2211yescharacteristic
28C2×C8×D181C2211yescharacteristic
29#19153796C2211yescharacteristic
30#19153795C2211yescharacteristic
31#19153794—21no—
32#19153793—21no—
33#19153792C2211yescharacteristic
34#19153791—21no—
35#19153791C2211yescharacteristic
36#19153790C2211yescharacteristic
37#19153789—21no—
38#19153789—21no—
39#19153789—21no—
40#19153788—21no—
41#19153787—21no—
42#19153787C2211yescharacteristic
43C4⋊C4×D181C2211yescharacteristic
44C4⋊C4×D181C2211yescharacteristic
45#19153750C2211yescharacteristic
46#19153749C2211yescharacteristic
47#19153749C2211yescharacteristic
48#19153741C2211yescharacteristic
49#19153740C2211yescharacteristic
50#19153739C2211yescharacteristic
51#19153738C2211yescharacteristic
52#19153737C2211yescharacteristic
53#19153736C2211yescharacteristic
54C2×SD16×C181C2211yescharacteristic
55C2×M16×C181C2211yescharacteristic
56C22⋊Q8×C181C2211yescharacteristic
57#121×C181C2211yescharacteristic
58#107×C181C2211yescharacteristic
59#103×C181C2211yescharacteristic
60#102×C181C2211yescharacteristic
61#15668450—22no—
62#15668450—22no—
63#15668449—22no—
64#15668449—22no—
65#15668448—22no—
66#15668448—22no—
67C2×Dic362D411yescharacteristic
68C2×Dic362C2311yescharacteristic
69C2×D724—21no—
70C2×D724—21no—
71C2×D724D411yescharacteristic
72C2×D724C2311yescharacteristic
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181—21no—
76C2×C22⋊D181D411yescharacteristic
77C2×C22⋊D181D411yescharacteristic
78C22×Dic181—21no—
79C2×C4×D181—21no—
80C2×C4×D181—21no—
81C2×C4×D181—21no—
82C2×C4×D181C2311yescharacteristic
83C2×C4×D181C2311yescharacteristic
84#15668439—22no—
85#15668438—22no—
86#15668434—22no—
87#15668432—22no—
88#15668432—22no—
89C2×#13089678—22no—
90C2×#13089678C2311yescharacteristic
91C2×#13089678C2311yescharacteristic
92C8×D181—22no—
93C8×D181D414yescomplemented
94C4⋊Dic181—21no—
95C4⋊Dic181C2311yescharacteristic
96C4⋊Dic181C2311yescharacteristic
97#15668428—21no—
98#15668428—21no—
99#15668428—21no—
100#15668428—21no—
101C22⋊Dic181—21no—
102C22⋊Dic181—21no—
103#15668426—21no—
104#15668426—21no—
105#15668426—21no—
106#15668426—21no—
107C2×Q8×C181C2311yescharacteristic
108C2×D4×C181—21no—
109C2×D4×C181C2311yescharacteristic
110C22×C4×C181C2311yescharacteristic
111SD16×C181—22no—
112M16×C181—22no—
113C2×C8×C181C2311yescharacteristic
114C2×C8×C181C2311yescharacteristic
115C4⋊C4×C181—21no—
116C4⋊C4×C181C2311yescharacteristic
117C4⋊C4×C181C2311yescharacteristic
118C22⋊C4×C181—21no—
119C22⋊C4×C181—21no—
120C22×D181—21no—
121C22×D181C2×D411yescharacteristic
122C22×D181C2×D411yescharacteristic
123Dic362—22no—
124Dic362—21no—
125Dic362—21no—
126D724—22no—
127D724—21no—
128D724—21no—
129D724—42no—
130D724—81no—
131C22⋊D181—22no—
132C22⋊D181—22no—
133C22⋊D181—42no—
134C22⋊D181—81no—
135C22⋊D181—81no—
136C2×Dic181—21no—
137C2×Dic181—21no—
138C2×Dic181—21no—
139C2×Dic181—42no—
140C2×Dic181C2×D411yescharacteristic
141C2×Dic181C2×D411yescharacteristic
142C4×D181—21no—
143C4×D181—21no—
144C4×D181—42no—
145C4×D181—81no—
146C4×D181—81no—
147C4×D181C2×D412yes—
148C4×D181#4112yes—
149#13089678—21no—
150#13089678C2×D412yes—
151C23×C181—21no—
152C23×C181C2×D411yescharacteristic
153Q8×C181—21no—
154Q8×C181—21no—
155D4×C181—21no—
156D4×C181—21no—
157D4×C181—81no—
158C2×C4×C181—21no—
159C2×C4×C181—21no—
160C2×C4×C181—21no—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181C2×D411yescharacteristic
164C2×C4×C181C2411yescharacteristic
165C8×C181—21no—
166C8×C181C2×D412yes—
167C22×C181—21no—
168C22×C181—21no—
169C22×C181—21no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181—41no—
173C22×C181C22×D411yescharacteristic
174C2×D181—21no—
175C2×D181—21no—
176C2×D181—21no—
177C2×D181—21no—
178C2×D181—21no—
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181#12112yes—
183C4×C181—21no—
184C4×C181—41no—
185C4×C181—41no—
186C4×C181—41no—
187C4×C181C22×D411yescharacteristic
188C4×C181C2×#4111yescharacteristic
189Dic181—21no—
190Dic181—41no—
191Dic181—41no—
192Dic181—41no—
193Dic181#12112yes—
194C2×C181—41no—
195C2×C181—81no—
196C2×C181C2×#12111yescharacteristic
197C2×C181#57611yescharacteristic
198C2×C181#57811yescharacteristic
199D181—22no—
200D181—41no—
201D181—81no—
202C181#306111yescharacteristic, complemented, Sylow
203#3061—1811nomaximal, Sylow
204C2×#135—1811no—
205C2×#131—1811no—
206#537—1811no—
207#537—1811no—
208#468—1811no—
209#468—1811no—
210#468—1811no—
211#468D18111yescharacteristic, complemented
212#467—1811no—
213#467—1811no—
214#466—1811no—
215#466—1811no—
216C2×#107—1811no—
217#417—1811no—
218#417—1811no—
219C2×#41—1811no—
220C2×#41—1811no—
221C2×#41—1811no—
222#135—3624no—
223C2×Q16—1811no—
224C2×SD16—1811no—
225C2×SD16C2×D18111yescharacteristic
226C2×D8—1811no—
227#131—3624no—
228C2×M16—1811no—
229C2×M16—1811no—
230C2×M16C2×D18111yescharacteristic
231C22×C8—1811no—
232C22×C8—1811no—
233C22×C8—1811no—
234C22⋊Q8—3621no—
235C22⋊Q8—3621no—
236C22⋊Q8—1811no—
237C22⋊Q8—1811no—
238C22⋊Q8—1811no—
239C22⋊Q8C2×D18111yescharacteristic
240#121—3621no—
241#121—3621no—
242#121—3621no—
243#121—3621no—
244#121—3621no—
245#121—3621no—
246#121—1811no—
247#121—1811no—
248#121—1811no—
249#121C2×D18111yescharacteristic
250C2×C4⋊C4—1811no—
251C2×C4⋊C4—1811no—
252#107—1811no—
253#107—1811no—
254#107—1811no—
255#107C2×D18111yescharacteristic
256#103—1811no—
257#103—1811no—
258#103—1811no—
259#103C2×D18111yescharacteristic
260#102—1811no—
261#102—1811no—
262#102—1811no—
263#102C2×D18111yescharacteristic
264#41—3622no—
265#41—3622no—
266#41—3622no—
267#41—3622no—
268#41—3622no—
269#41—3622no—
270C2×Q8—1811no—
271C2×Q8—1811no—
272C2×Q8C22×D18111yescharacteristic
273C2×D4—21no—
274C2×D4—3621no—
275C2×D4—3621no—
276C2×D4—3621no—
277C2×D4—3621no—
278C2×D4—3621no—
279C2×D4—1811no—
280C2×D4—1811no—
281C2×D4—1811no—
282C2×D4—1811no—
283C2×D4C22×D18111yescharacteristic
284C22×C4—3621no—
285C22×C4—3621no—
286C22×C4—3621no—
287C22×C4—3621no—
288C22×C4—1811no—
289C22×C4—1811no—
290C22×C4C22×D18111yescharacteristic
291Q16—3622no—
292SD16—22no—
293SD16—3622no—
294D8—3622no—
295M16—22no—
296M16—3622no—
297M16—3622no—
298C2×C8—3622no—
299C2×C8—3622no—
300C2×C8—1811no—
301C2×C8—1811no—
302C2×C8—1814no—
303C2×C8C22×D18111yescharacteristic
304C2×C8C22×D18111yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—3621no—
307C4⋊C4—3621no—
308C4⋊C4—3621no—
309C4⋊C4—3621no—
310C4⋊C4—3621no—
311C4⋊C4—1811no—
312C4⋊C4—1811no—
313C4⋊C4C22×D18111yescharacteristic
314C4⋊C4C22×D18111yescharacteristic
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—3621no—
318C22⋊C4—3621no—
319C22⋊C4—3621no—
320C22⋊C4—3621no—
321C22⋊C4—3621no—
322C22⋊C4—3621no—
323C23—21no—
324C23—3621no—
325C23—1811no—
326C23—1811no—
327C23D4×D18111yescharacteristic
328Q8—21no—
329Q8—21no—
330Q8—3622no—
331Q8—3621no—
332Q8—3621no—
333D4—21no—
334D4—21no—
335D4—81no—
336D4—3622no—
337D4—3622no—
338D4—3622no—
339D4—3621no—
340D4—3621no—
341D4—14481no—
342D4—14481no—
343D4—14481no—
344D4—7242no—
345D4—7242no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3621no—
352C2×C4—3621no—
353C2×C4—3621no—
354C2×C4—3621no—
355C2×C4—3621no—
356C2×C4—14481no—
357C2×C4—14481no—
358C2×C4—1811no—
359C2×C4—1811no—
360C2×C4—1812no—
361C2×C4—1812no—
362C2×C4—7242no—
363C2×C4—7242no—
364C2×C4D4×D18111yescharacteristic
365C2×C4C23×D18111yescharacteristic
366C8—21no—
367C8—3621no—
368C8—1812no—
369C8D4×D18112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3621no—
377C22—3621no—
378C22—3621no—
379C22—3621no—
380C22—3621no—
381C22—1812no—
382C22—7241no—
383C22—7241no—
384C22—7241no—
385C22C2×D4×D18111yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—3621no—
391C4—1812no—
392C4—7241no—
393C4—7241no—
394C4—7241no—
395C4C2×D4×D18111yescharacteristic
396C4#41×D18111yescharacteristic
397C2—41no—
398C2—81no—
399C2—3622no—
400C2—14481no—
401C2—7241no—
402C2#121×D18111yescharacteristic
403C2#2604208311yescharacteristic
404C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#468×C181C2
socleC22×C181C22×D4
hypercenter#468D181
hypocenterC181#3061
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#19153837C2semidirect
2. C2×#19153824C2semidirect
3. #26041859C2semidirect
4. #26041858C2semidirect
5. #26041526C2semidirect
6. #26041525C2semidirect
7. #26041522C2semidirect
8. #26041519C2semidirect
9. #26041518C2semidirect
10. #26041514C2semidirect
11. #26041513C2semidirect
12. #107×D181C2semidirect
13. #26041279C2semidirect
14. #26041277C2semidirect
15. #468×C181C2semidirect
93. C8×D181D4semidirect
202. C181#3061semidirect
211. #468D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538372
C2×#191538242
#260418592
#260418582
#260415262
#260415252
#260415222
#260415192
#260415182
#260415142
#260415132
#107×D1812
#260412792
#260412772
#468×C1812
#3061181