Finite Group Databasebeta

← #37545436

Subgroups — #37545436

Order 23168.

484 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153837C211yesmaximal, characteristic, complemented
2C2×#19153836C211yesmaximal, characteristic, complemented
3#26041931C211yesmaximal, characteristic, complemented
4#26041928C211yesmaximal, characteristic, complemented
5#26041657C211yesmaximal, characteristic, complemented
6#26041519C211yesmaximal, characteristic, complemented
7#26041518C211yesmaximal, characteristic, complemented
8#26041483C211yesmaximal, characteristic, complemented
9#26041482C211yesmaximal, characteristic, complemented
10#26041443C211yesmaximal, characteristic, complemented
11#26041442C211yesmaximal, characteristic, complemented
12#26041440C211yesmaximal, characteristic, complemented
13#26041359C211yesmaximal, characteristic, complemented
14#26041342C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×#15668448C2211yescharacteristic
19#19153837—24no—
20#19153836—24no—
21C2×Dic724C2211yescharacteristic
22C2×#15668439C2211yescharacteristic
23C2×#15668439C2211yescharacteristic
24C2×#15668438C2211yescharacteristic
25C2×#15668437C2211yescharacteristic
26C2×#15668436C2211yescharacteristic
27C2×#15668434C2211yescharacteristic
28C22×#13089678C2211yescharacteristic
29C2×C8×D181C2211yescharacteristic
30#19153814C2211yescharacteristic
31#19153814C2211yescharacteristic
32#19153801—21no—
33#19153799—21no—
34#19153798—21no—
35#19153797—21no—
36#19153796C2211yescharacteristic
37#19153795C2211yescharacteristic
38#19153792C2211yescharacteristic
39#19153789—21no—
40#19153788—21no—
41D4×Dic181C2211yescharacteristic
42#19153778C2211yescharacteristic
43C4×C22⋊D181C2211yescharacteristic
44C2×#15668428—21no—
45C4⋊C4×D181—21no—
46#19153749C2211yescharacteristic
47#19153745C2211yescharacteristic
48#19153741C2211yescharacteristic
49#19153740C2211yescharacteristic
50#19153739C2211yescharacteristic
51#19153738C2211yescharacteristic
52#19153728C2211yescharacteristic
53C8×Dic181C2211yescharacteristic
54C2×#41×C181C2211yescharacteristic
55C2×Q16×C181C2211yescharacteristic
56C2×SD16×C181C2211yescharacteristic
57C22⋊Q8×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59#102×C181C2211yescharacteristic
60C22⋊C8×C181C2211yescharacteristic
61#15668450—22no—
62#15668450—41no—
63#15668449—22no—
64#15668449—41no—
65#15668448—22no—
66#15668448—41no—
67C2×Dic362C2311yescharacteristic
68C2×Dic362C2311yescharacteristic
69C2×D724—21no—
70C2×D724C2311yescharacteristic
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C2×C22⋊D181D411yescharacteristic
74C22×Dic181—21no—
75C22×Dic181—21no—
76C2×C4×D181—21no—
77C2×C4×D181—21no—
78C2×C4×D181—21no—
79C2×C4×D181C2311yescharacteristic
80Dic724—41no—
81#15668439—22no—
82#15668439—22no—
83#15668438—22no—
84#15668437—22no—
85#15668436—22no—
86#15668434D414yescomplemented
87C2×#13089678—22no—
88C2×#13089678C2311yescharacteristic
89C2×#13089678C2311yescharacteristic
90C8×D181—22no—
91C4⋊Dic181—21no—
92C4⋊Dic181C2311yescharacteristic
93#15668428—21no—
94#15668428—21no—
95#15668428—21no—
96#15668428—21no—
97#15668428—21no—
98#15668428—21no—
99#15668428D411yescharacteristic
100C22⋊Dic181—21no—
101C22⋊Dic181—21no—
102C22⋊Dic181D411yescharacteristic
103#15668426—21no—
104#15668426—21no—
105#15668426—21no—
106#15668426D411yescharacteristic
107C4×Dic181C2311yescharacteristic
108#41×C181—22no—
109#41×C181—41no—
110C2×Q8×C181C2311yescharacteristic
111C2×Q8×C181C2311yescharacteristic
112C2×D4×C181—21no—
113C2×D4×C181C2311yescharacteristic
114C22×C4×C181—21no—
115C22×C4×C181C2311yescharacteristic
116Q16×C181—41no—
117SD16×C181—22no—
118C2×C8×C181C2311yescharacteristic
119C2×C8×C181C2311yescharacteristic
120C4⋊C4×C181—21no—
121C4⋊C4×C181C2311yescharacteristic
122C22⋊C4×C181—21no—
123C22×D181—21no—
124C22×D181C2×D411yescharacteristic
125Dic362—21no—
126Dic362—21no—
127Dic362—21no—
128Dic362—21no—
129D724—21no—
130D724—42no—
131D724C2×D412yes—
132C22⋊D181—22no—
133C22⋊D181—42no—
134C22⋊D181—42no—
135C2×Dic181—21no—
136C2×Dic181—21no—
137C2×Dic181—21no—
138C2×Dic181—42no—
139C2×Dic181—42no—
140C2×Dic181C2×D411yescharacteristic
141C2×Dic181C2×D411yescharacteristic
142C2×Dic181C2×D411yescharacteristic
143C4×D181—21no—
144C4×D181—21no—
145C4×D181—42no—
146C4×D181—42no—
147C4×D181—42no—
148#13089678—21no—
149#13089678C2×D412yes—
150C23×C181—21no—
151C23×C181C2×D411yescharacteristic
152Q8×C181—21no—
153Q8×C181—21no—
154Q8×C181—21no—
155Q8×C181—21no—
156D4×C181—21no—
157D4×C181—42no—
158D4×C181C2×D412yes—
159C2×C4×C181—21no—
160C2×C4×C181—21no—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181—21no—
164C2×C4×C181—42no—
165C2×C4×C181C2×D411yescharacteristic
166C2×C4×C181C2411yescharacteristic
167C8×C181—21no—
168C8×C181—21no—
169C22×C181—21no—
170C22×C181—22no—
171C22×C181—21no—
172C22×C181—21no—
173C22×C181—41no—
174C22×C181—41no—
175C22×C181C22×D411yescharacteristic
176C2×D181—21no—
177C2×D181—22no—
178C2×D181—21no—
179C2×D181—21no—
180C2×D181—41no—
181C2×D181—41no—
182C4×C181—21no—
183C4×C181—41no—
184C4×C181—41no—
185C4×C181—41no—
186C4×C181C22×D411yescharacteristic
187C4×C181H(5,𝔽2)11yescharacteristic
188Dic181—21no—
189Dic181—21no—
190Dic181—41no—
191Dic181—41no—
192Dic181—41no—
193Dic181#13512yescomplemented
194C2×C181—41no—
195C2×C181—42no—
196C2×C181D4211yescharacteristic
197C2×C181C2×#13511yescharacteristic
198C2×C181#57811yescharacteristic
199D181—41no—
200D181—42no—
201C181#328311yescharacteristic, complemented, Sylow
202#3283—1811nomaximal, Sylow
203C2×#135—1811no—
204C2×#135—1811no—
205#547—1811no—
206#547—1811no—
207#494—1811no—
208#467—1811no—
209#467—1811no—
210#461—1811no—
211#461—1811no—
212#452—1811no—
213#452—1811no—
214#452—1811no—
215#452D18111yescharacteristic, complemented
216C4×D8—1811no—
217C8×D4—1811no—
218C2×#41—1811no—
219C2×#41—1811no—
220C2×#41—1811no—
221C2×#41C2×D18111yescharacteristic
222#135—3624no—
223#135—3624no—
224C2×Q16—1811no—
225C2×Q16—1811no—
226C2×Q16—1811no—
227C2×Q16C2×D18111yescharacteristic
228C2×SD16—1811no—
229C2×SD16—1811no—
230C2×SD16—1811no—
231C2×SD16C2×D18111yescharacteristic
232C2×D8—1811no—
233C22×C8—1811no—
234C22×C8—1811no—
235C4⋊Q8—1811no—
236C4⋊Q8—1811no—
237#123—3621no—
238#123—3621no—
239#123—3621no—
240#123—3621no—
241C22⋊Q8—1811no—
242C22⋊Q8—1811no—
243C22⋊Q8—1811no—
244C22⋊Q8C2×D18111yescharacteristic
245#121—3621no—
246#121—3621no—
247C4×D4—1811no—
248C4×D4—1811no—
249C4×D4—1811no—
250C2×C4⋊C4—3621no—
251C2×C4⋊C4—3621no—
252#107—1811no—
253C4⋊C8—1811no—
254#103—1811no—
255#103—1811no—
256#103—1811no—
257#103C2×D18111yescharacteristic
258#102—1811no—
259#102C2×D18111yescharacteristic
260C22⋊C8—1811no—
261C22⋊C8C2×D18111yescharacteristic
262C4×C8—1811no—
263#41—22no—
264#41—41no—
265#41—3622no—
266#41—3622no—
267#41—3622no—
268#41—7241no—
269#41—7241no—
270#41—7241no—
271C2×Q8—1811no—
272C2×Q8—1811no—
273C2×Q8C22×D18111yescharacteristic
274C2×Q8C22×D18111yescharacteristic
275C2×D4—21no—
276C2×D4—3621no—
277C2×D4—3621no—
278C2×D4—3621no—
279C2×D4—1811no—
280C2×D4—1811no—
281C2×D4C22×D18111yescharacteristic
282C22×C4—21no—
283C22×C4—3621no—
284C22×C4—3621no—
285C22×C4—3621no—
286C22×C4—3621no—
287C22×C4—3621no—
288C22×C4—1811no—
289C22×C4C22×D18111yescharacteristic
290Q16—41no—
291Q16—3622no—
292Q16—3622no—
293Q16—7241no—
294SD16—22no—
295SD16—3622no—
296SD16—3622no—
297SD16—3622no—
298D8—1814no—
299C2×C8—3622no—
300C2×C8—3622no—
301C2×C8—1811no—
302C2×C8—1811no—
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—3621no—
312C4⋊C4—3621no—
313C4⋊C4—1811no—
314C4⋊C4—1811no—
315C4⋊C4C22×D18111yescharacteristic
316C22⋊C4—21no—
317C22⋊C4—3621no—
318C22⋊C4—3621no—
319C22⋊C4—3621no—
320C22⋊C4—3621no—
321C22⋊C4—3621no—
322C22⋊C4—1811no—
323C22⋊C4—1811no—
324C42—1811no—
325C23—21no—
326C23—3621no—
327C23—1811no—
328C23D4×D18111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—3621no—
334Q8—3621no—
335Q8—3621no—
336Q8—3621no—
337D4—21no—
338D4—42no—
339D4—3622no—
340D4—3621no—
341D4—1812no—
342D4—7242no—
343D4—7242no—
344D4—7242no—
345D4D4×D18112yes—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—3621no—
353C2×C4—3621no—
354C2×C4—3621no—
355C2×C4—3621no—
356C2×C4—3621no—
357C2×C4—1811no—
358C2×C4—1811no—
359C2×C4—1811no—
360C2×C4—7242no—
361C2×C4—7242no—
362C2×C4—7242no—
363C2×C4—7242no—
364C2×C4—7242no—
365C2×C4D4×D18111yescharacteristic
366C2×C4C23×D18111yescharacteristic
367C8—21no—
368C8—21no—
369C8—3621no—
370C8—1812no—
371C22—21no—
372C22—22no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—3621no—
378C22—3622no—
379C22—3621no—
380C22—3621no—
381C22—7241no—
382C22—7241no—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—3621no—
389C4—3621no—
390C4—1812no—
391C4—7241no—
392C4—7241no—
393C4—7241no—
394C4C2×D4×D18111yescharacteristic
395C4#1915386111yescharacteristic
396C2—41no—
397C2—42no—
398C2—7241no—
399C2—7242no—
400C2#2604191111yescharacteristic
401C2#135×D18111yescharacteristic
402C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
hypercenter#452D181
hypocenterC181#3283
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#19153837C2semidirect
2. C2×#19153836C2semidirect
3. #26041931C2semidirect
4. #26041928C2semidirect
5. #26041657C2semidirect
6. #26041519C2semidirect
7. #26041518C2semidirect
8. #26041483C2semidirect
9. #26041482C2semidirect
10. #26041443C2semidirect
11. #26041442C2semidirect
12. #26041440C2semidirect
13. #26041359C2semidirect
14. #26041342C2semidirect
15. #452×C181C2semidirect
86. #15668434D4semidirect
193. Dic181#135semidirect
201. C181#3283semidirect
215. #452D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538372
C2×#191538362
#260419312
#260419282
#260416572
#260415192
#260415182
#260414832
#260414822
#260414432
#260414422
#260414402
#260413592
#260413422
#452×C1812
#3283181