Finite Group Databasebeta

← #37545372

Subgroups — #37545372

Order 23168.

476 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×#19153848C211yesmaximal, characteristic, complemented
2#26041940C211yesmaximal, characteristic, complemented
3#26041936C211yesmaximal, characteristic, complemented
4#26041660C211yesmaximal, characteristic, complemented
5#26041525C211yesmaximal, characteristic, complemented
6#26041522C211yesmaximal, characteristic, complemented
7#26041503C211yesmaximal, characteristic, complemented
8#26041499C211yesmaximal, characteristic, complemented
9#26041435C211yesmaximal, characteristic, complemented
10#26041433C211yesmaximal, characteristic, complemented
11#26041424C211yesmaximal, characteristic, complemented
12#26041423C211yesmaximal, characteristic, complemented
13Q16×Dic181C211yesmaximal, characteristic, complemented
14#26041355C211yesmaximal, characteristic, complemented
15C2×#137×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×Q8×D181C2211yescharacteristic
18#19153848—24no—
19C2×#15668439C2211yescharacteristic
20C2×#15668439C2211yescharacteristic
21C2×#15668438C2211yescharacteristic
22C2×#15668436C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24C2×#15668432C2211yescharacteristic
25#19153805—21no—
26#19153805C2211yescharacteristic
27#19153803—21no—
28#19153803C2211yescharacteristic
29#19153795—21no—
30#19153795C2211yescharacteristic
31#19153792—21no—
32#19153792C2211yescharacteristic
33#19153790—21no—
34#19153790C2211yescharacteristic
35#19153787—21no—
36#19153787C2211yescharacteristic
37Q8×Dic181C2211yescharacteristic
38Q8×Dic181C2211yescharacteristic
39C4×C22⋊D181—21no—
40C4×C22⋊D181—21no—
41C4×C22⋊D181C2211yescharacteristic
42#19153750C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153740C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153737C2211yescharacteristic
50C22⋊#13089678C2211yescharacteristic
51#19153728C2211yescharacteristic
52C8×Dic181C2211yescharacteristic
53C2×#41×C181C2211yescharacteristic
54C22×Q8×C181C2211yescharacteristic
55#137×C181—24no—
56C2×Q16×C181C2211yescharacteristic
57C2×Q16×C181C2211yescharacteristic
58C2×SD16×C181C2211yescharacteristic
59C2×SD16×C181C2211yescharacteristic
60C2×M16×C181C2211yescharacteristic
61#15668450—22no—
62#15668450—41no—
63C2×Dic362—21no—
64C2×Dic362C2311yescharacteristic
65Q8×D181—22no—
66Q8×D181—41no—
67C2×D724—21no—
68C2×D724C2311yescharacteristic
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181D411yescharacteristic
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181C2311yescharacteristic
75#15668439—22no—
76#15668439—41no—
77#15668438—22no—
78#15668436—22no—
79#15668434—41no—
80#15668432—22no—
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C4⋊Dic181—21no—
84C4⋊Dic181—21no—
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94C22⋊Dic181D411yescharacteristic
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426—21no—
99#15668426D411yescharacteristic
100C4×Dic181—21no—
101C4×Dic181—21no—
102C4×Dic181C2311yescharacteristic
103#41×C181—22no—
104#41×C181—41no—
105C2×Q8×C181—21no—
106C2×Q8×C181—22no—
107C2×Q8×C181—41no—
108C2×Q8×C181C2311yescharacteristic
109C2×Q8×C181C2311yescharacteristic
110C2×Q8×C181C2311yescharacteristic
111C2×D4×C181—21no—
112C2×D4×C181C2311yescharacteristic
113C22×C4×C181—21no—
114C22×C4×C181—21no—
115C22×C4×C181C2311yescharacteristic
116Q16×C181—22no—
117Q16×C181D414yescomplemented
118SD16×C181—22no—
119SD16×C181—22no—
120M16×C181—22no—
121C2×C8×C181C2311yescharacteristic
122C2×C8×C181C2311yescharacteristic
123C22×D181—21no—
124C22×D181C2×D411yescharacteristic
125Dic362—21no—
126Dic362—21no—
127Dic362—42no—
128D724—21no—
129D724—21no—
130D724—42no—
131C22⋊D181—41no—
132C22⋊D181—42no—
133C22⋊D181—42no—
134C2×Dic181—21no—
135C2×Dic181—21no—
136C2×Dic181—21no—
137C2×Dic181C2×D411yescharacteristic
138C2×Dic181C2×D411yescharacteristic
139C2×Dic181C2×D411yescharacteristic
140C4×D181—21no—
141C4×D181—21no—
142C4×D181—42no—
143C4×D181—42no—
144#13089678—21no—
145#13089678—21no—
146C23×C181—21no—
147C23×C181C2×D411yescharacteristic
148Q8×C181—21no—
149Q8×C181—21no—
150Q8×C181—21no—
151Q8×C181—21no—
152Q8×C181—42no—
153Q8×C181C2×D412yes—
154Q8×C181C2×D412yes—
155D4×C181—21no—
156D4×C181—21no—
157D4×C181—42no—
158C2×C4×C181—21no—
159C2×C4×C181—21no—
160C2×C4×C181—21no—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181—42no—
164C2×C4×C181—42no—
165C2×C4×C181C2×D411yescharacteristic
166C2×C4×C181C2411yescharacteristic
167C8×C181—21no—
168C8×C181C2×D412yes—
169C22×C181—21no—
170C22×C181—21no—
171C22×C181—21no—
172C22×C181—41no—
173C22×C181—41no—
174C22×C181—41no—
175C22×C181C22×D411yescharacteristic
176C2×D181—21no—
177C2×D181—21no—
178C2×D181—21no—
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C4×C181—21no—
183C4×C181—22no—
184C4×C181—22no—
185C4×C181—41no—
186C4×C181C22×D411yescharacteristic
187C4×C181H(5,𝔽2)11yescharacteristic
188Dic181—21no—
189Dic181—21no—
190Dic181—21no—
191Dic181—41no—
192Dic181—41no—
193Dic181—41no—
194C2×C181—41no—
195C2×C181—81no—
196C2×C181D4211yescharacteristic
197C2×C181#57511yescharacteristic
198C2×C181#57811yescharacteristic
199D181—41no—
200D181—81no—
201C181#327711yescharacteristic, complemented, Sylow
202#3277—1811nomaximal, Sylow
203C2×#137—1811no—
204C2×#137D18111yescharacteristic, complemented
205#548—1811no—
206#548—1811no—
207#495—1811no—
208#468—1811no—
209#468—1811no—
210#464—1811no—
211#464—1811no—
212#451—1811no—
213#451—1811no—
214#449—1811no—
215#449—1811no—
216C4×Q16—1811no—
217#436—1811no—
218C2×#41—1811no—
219C2×#41C2×D18111yescharacteristic
220C22×Q8—1811no—
221C22×Q8C2×D18111yescharacteristic
222#137—24no—
223#137—3624no—
224C2×Q16—1811no—
225C2×Q16—1811no—
226C2×Q16C2×D18111yescharacteristic
227C2×Q16C2×D18111yescharacteristic
228C2×SD16—1811no—
229C2×SD16—1811no—
230C2×SD16C2×D18111yescharacteristic
231C2×SD16C2×D18111yescharacteristic
232C2×D8—1811no—
233C2×M16—1811no—
234C2×M16C2×D18111yescharacteristic
235#124—3621no—
236#124—3621no—
237#124—1811no—
238#124—1811no—
239C22⋊Q8—3621no—
240C22⋊Q8—3621no—
241C22⋊Q8—1811no—
242C22⋊Q8—1811no—
243#121—3621no—
244#121—3621no—
245#121—1811no—
246#121—1811no—
247C4×Q8—1811no—
248C4×Q8—1811no—
249C4×D4—3621no—
250C4×D4—3621no—
251C4×D4—1811no—
252#107—1811no—
253C4⋊C8—1811no—
254#103—1811no—
255#103—1811no—
256#103—1811no—
257#103—1811no—
258#102—1811no—
259#102—1811no—
260C22⋊C8—1811no—
261C22⋊C8—1811no—
262C4×C8—1811no—
263#41—22no—
264#41—41no—
265#41—3622no—
266#41—7241no—
267C2×Q8—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—3621no—
271C2×Q8—3622no—
272C2×Q8—1811no—
273C2×Q8—7241no—
274C2×Q8C22×D18111yescharacteristic
275C2×Q8C22×D18111yescharacteristic
276C2×Q8C22×D18111yescharacteristic
277C2×D4—21no—
278C2×D4—3621no—
279C2×D4—3621no—
280C2×D4—3621no—
281C2×D4—1811no—
282C2×D4—1811no—
283C2×D4C22×D18111yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—3621no—
287C22×C4—3621no—
288C22×C4—1811no—
289C22×C4C22×D18111yescharacteristic
290Q16—22no—
291Q16—3622no—
292Q16—7241no—
293Q16C22⋊D18114yescomplemented
294SD16—22no—
295SD16—22no—
296SD16—3622no—
297SD16—3622no—
298D8—7241no—
299M16—22no—
300M16—3622no—
301C2×C8—1811no—
302C2×C8—1811no—
303C2×C8C22×D18111yescharacteristic
304C2×C8C22×D18111yescharacteristic
305C4⋊C4—3621no—
306C4⋊C4—3621no—
307C4⋊C4—3621no—
308C4⋊C4—3621no—
309C4⋊C4—1811no—
310C4⋊C4—1811no—
311C4⋊C4—1811no—
312C22⋊C4—3621no—
313C22⋊C4—3621no—
314C22⋊C4—3621no—
315C22⋊C4—3621no—
316C22⋊C4—3621no—
317C22⋊C4—3621no—
318C22⋊C4—3621no—
319C22⋊C4—3621no—
320C22⋊C4—1811no—
321C22⋊C4—1811no—
322C42—3621no—
323C42—3621no—
324C42—1811no—
325C23—21no—
326C23—3621no—
327C23—1811no—
328C23D4×D18111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—42no—
334Q8—3621no—
335Q8—3621no—
336Q8—7242no—
337Q8C2×C22⋊D18112yes—
338Q8C2×C22⋊D18112yes—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—3621no—
343D4—3621no—
344D4—7242no—
345D4—7241no—
346D4—7242no—
347D4—7242no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—3621no—
356C2×C4—3621no—
357C2×C4—3621no—
358C2×C4—3621no—
359C2×C4—3621no—
360C2×C4—1811no—
361C2×C4—1811no—
362C2×C4—1811no—
363C2×C4—7242no—
364C2×C4—7242no—
365C2×C4D4×D18111yescharacteristic
366C2×C4C23×D18111yescharacteristic
367C8—21no—
368C8—3621no—
369C8—3621no—
370C8C2×C22⋊D18112yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—3621no—
378C22—3621no—
379C22—3621no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—22no—
386C4—22no—
387C4—41no—
388C4—3621no—
389C4—3621no—
390C4—3621no—
391C4—7241no—
392C4—7241no—
393C4—7241no—
394C4C22×C22⋊D18111yescharacteristic
395C4#1915386111yescharacteristic
396C2—41no—
397C2—81no—
398C2—14481no—
399C2—7241no—
400C2D4×C22⋊D18111yescharacteristic
401C2#2604207811yescharacteristic
402C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#137×C181C2
socleC22×C181C22×D4
hypercenterC2×#137D181
hypocenterC181#3277
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#19153848C2semidirect
2. #26041940C2semidirect
3. #26041936C2semidirect
4. #26041660C2semidirect
5. #26041525C2semidirect
6. #26041522C2semidirect
7. #26041503C2semidirect
8. #26041499C2semidirect
9. #26041435C2semidirect
10. #26041433C2semidirect
11. #26041424C2semidirect
12. #26041423C2semidirect
13. Q16×Dic181C2semidirect
14. #26041355C2semidirect
15. C2×#137×C181C2semidirect
117. Q16×C181D4semidirect
201. C181#3277semidirect
204. C2×#137D181semidirect
293. Q16C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538482
#260419402
#260419362
#260416602
#260415252
#260415222
#260415032
#260414992
#260414352
#260414332
#260414242
#260414232
Q16×Dic1812
#260413552
C2×#137×C1812
#3277181