Finite Group Databasebeta

← #37545276

Subgroups — #37545276

Order 23168.

478 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×#19153845C211yesmaximal, characteristic, complemented
2#26041936C211yesmaximal, characteristic, complemented
3#26041928C211yesmaximal, characteristic, complemented
4#26041670C211yesmaximal, characteristic, complemented
5#26041522C211yesmaximal, characteristic, complemented
6#26041520C211yesmaximal, characteristic, complemented
7#26041492C211yesmaximal, characteristic, complemented
8#26041487C211yesmaximal, characteristic, complemented
9#26041441C211yesmaximal, characteristic, complemented
10#26041441C211yesmaximal, characteristic, complemented
11#26041433C211yesmaximal, characteristic, complemented
12#26041421C211yesmaximal, characteristic, complemented
13#26041380C211yesmaximal, characteristic, complemented
14#26041350C211yesmaximal, characteristic, complemented
15C2×#135×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×Q8×D181C2211yescharacteristic
18#19153845—24no—
19C2×Dic724C2211yescharacteristic
20C2×#15668439C2211yescharacteristic
21C2×#15668439C2211yescharacteristic
22C2×#15668437C2211yescharacteristic
23C2×#15668437C2211yescharacteristic
24C2×#15668432C2211yescharacteristic
25#19153814C2211yescharacteristic
26#19153803—21no—
27#19153803C2211yescharacteristic
28#19153799—21no—
29#19153797—21no—
30#19153795—21no—
31#19153795C2211yescharacteristic
32#19153795C2211yescharacteristic
33#19153792C2211yescharacteristic
34#19153788—21no—
35#19153787—21no—
36#19153787C2211yescharacteristic
37Q8×Dic181C2211yescharacteristic
38D4×Dic181C2211yescharacteristic
39C4×C22⋊D181—21no—
40C4×C22⋊D181C2211yescharacteristic
41C2×#15668428—21no—
42#19153750C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153740C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50C22⋊#13089678C2211yescharacteristic
51#19153728C2211yescharacteristic
52#19153726C2211yescharacteristic
53C2×#41×C181C2211yescharacteristic
54C2×#41×C181C2211yescharacteristic
55#135×C181—24no—
56C2×Q16×C181C2211yescharacteristic
57C2×SD16×C181C2211yescharacteristic
58C2×SD16×C181C2211yescharacteristic
59C2×D8×C181C2211yescharacteristic
60C22×C8×C181C2211yescharacteristic
61#15668448—22no—
62#15668448—41no—
63C2×Dic362—21no—
64C2×Dic362C2311yescharacteristic
65C2×Dic362C2311yescharacteristic
66Q8×D181—22no—
67Q8×D181—41no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181D411yescharacteristic
71C22×Dic181—21no—
72C22×Dic181—21no—
73C2×C4×D181—21no—
74C2×C4×D181C2311yescharacteristic
75Dic724—22no—
76#15668439—22no—
77#15668439—41no—
78#15668437—22no—
79#15668437—41no—
80#15668432—22no—
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C4⋊Dic181—21no—
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90#15668428—21no—
91#15668428D411yescharacteristic
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94C22⋊Dic181—21no—
95C22⋊Dic181—21no—
96C22⋊Dic181—21no—
97C22⋊Dic181—21no—
98C22⋊Dic181D411yescharacteristic
99#15668426—21no—
100#15668426D411yescharacteristic
101C4×Dic181—21no—
102C4×Dic181C2311yescharacteristic
103#41×C181—22no—
104#41×C181—22no—
105#41×C181—41no—
106#41×C181—41no—
107C2×Q8×C181C2311yescharacteristic
108C2×Q8×C181C2311yescharacteristic
109C2×D4×C181—21no—
110C2×D4×C181—21no—
111C2×D4×C181C2311yescharacteristic
112C2×D4×C181C2311yescharacteristic
113C22×C4×C181—21no—
114C22×C4×C181—21no—
115C22×C4×C181C2311yescharacteristic
116Q16×C181—22no—
117SD16×C181—22no—
118SD16×C181D414yescomplemented
119D8×C181—22no—
120C2×C8×C181—22no—
121C2×C8×C181C2311yescharacteristic
122C2×C8×C181C2311yescharacteristic
123C22×D181C2×D411yescharacteristic
124Dic362—21no—
125Dic362—21no—
126Dic362—21no—
127Dic362—21no—
128Dic362—42no—
129C22⋊D181—41no—
130C22⋊D181—42no—
131C22⋊D181—42no—
132C2×Dic181—21no—
133C2×Dic181—21no—
134C2×Dic181—21no—
135C2×Dic181—21no—
136C2×Dic181—42no—
137C2×Dic181—42no—
138C2×Dic181C2×D411yescharacteristic
139C2×Dic181C2×D411yescharacteristic
140C2×Dic181C2×D411yescharacteristic
141C4×D181—21no—
142C4×D181—21no—
143C4×D181—42no—
144#13089678—21no—
145#13089678—21no—
146C23×C181—21no—
147C23×C181—21no—
148C23×C181C2×D411yescharacteristic
149Q8×C181—21no—
150Q8×C181—21no—
151Q8×C181—21no—
152Q8×C181C2×D412yes—
153D4×C181—21no—
154D4×C181—21no—
155D4×C181—21no—
156D4×C181—42no—
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—42no—
164C2×C4×C181—42no—
165C2×C4×C181C2×D411yescharacteristic
166C2×C4×C181C2411yescharacteristic
167C8×C181—21no—
168C8×C181C2×D412yes—
169C22×C181—21no—
170C22×C181—22no—
171C22×C181—21no—
172C22×C181—21no—
173C22×C181—41no—
174C22×C181—41no—
175C22×C181—41no—
176C22×C181—41no—
177C22×C181—41no—
178C22×C181C22×D411yescharacteristic
179C2×D181—21no—
180C2×D181—21no—
181C2×D181—21no—
182C4×C181—21no—
183C4×C181—22no—
184C4×C181—41no—
185C4×C181C22×D411yescharacteristic
186C4×C181H(5,𝔽2)11yescharacteristic
187Dic181—21no—
188Dic181—21no—
189Dic181—21no—
190Dic181—41no—
191Dic181—41no—
192Dic181—41no—
193Dic181—41no—
194C2×C181—41no—
195C2×C181—42no—
196C2×C181—81no—
197C2×C181D4211yescharacteristic
198C2×C181#57511yescharacteristic
199C2×C181#57811yescharacteristic
200D181—41no—
201C181#326911yescharacteristic, complemented, Sylow
202#3269—1811nomaximal, Sylow
203C2×#137—1811no—
204C2×#135D18111yescharacteristic, complemented
205#548—1811no—
206#547—1811no—
207#497—1811no—
208#468—1811no—
209#467—1811no—
210#463—1811no—
211#462—1811no—
212#452—1811no—
213#452—1811no—
214#451—1811no—
215#449—1811no—
216#440—1811no—
217#435—1811no—
218C2×#41—1811no—
219C2×#41C2×D18111yescharacteristic
220C2×#41C2×D18111yescharacteristic
221C22×Q8—1811no—
222#137—3624no—
223#135—24no—
224C2×Q16—1811no—
225C2×Q16—1811no—
226C2×Q16—1811no—
227C2×Q16C2×D18111yescharacteristic
228C2×SD16—1811no—
229C2×SD16—1811no—
230C2×SD16C2×D18111yescharacteristic
231C2×SD16C2×D18111yescharacteristic
232C2×D8C2×D18111yescharacteristic
233C2×M16—1811no—
234C22×C8C2×D18111yescharacteristic
235C4⋊Q8—1811no—
236#124—3621no—
237#124—1811no—
238#123—3621no—
239#123—3621no—
240C22⋊Q8—3621no—
241C22⋊Q8—1811no—
242C22⋊Q8—1811no—
243C22⋊Q8—1811no—
244#121—3621no—
245#121—3621no—
246#121—1811no—
247C4×Q8—1811no—
248C4×D4—3621no—
249C4×D4—1811no—
250C4×D4—1811no—
251C2×C4⋊C4—3621no—
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—
262#97—1811no—
263#41—22no—
264#41—22no—
265#41—41no—
266#41—41no—
267#41—3622no—
268#41—7241no—
269C2×Q8—3621no—
270C2×Q8—3622no—
271C2×Q8—1811no—
272C2×Q8—1811no—
273C2×Q8—7241no—
274C2×Q8C22×D18111yescharacteristic
275C2×Q8C22×D18111yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—3621no—
279C2×D4—3621no—
280C2×D4—1811no—
281C2×D4C22×D18111yescharacteristic
282C2×D4C22×D18111yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—3621no—
286C22×C4—3621no—
287C22×C4—3621no—
288C22×C4—1811no—
289C22×C4C22×D18111yescharacteristic
290Q16—22no—
291Q16—3622no—
292Q16—3622no—
293Q16—7241no—
294SD16—22no—
295SD16—3622no—
296SD16—7241no—
297SD16C22⋊D18114yescomplemented
298D8—22no—
299M16—3622no—
300C2×C8—22no—
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—3621no—
310C4⋊C4—3621no—
311C4⋊C4—1811no—
312C4⋊C4—1811no—
313C4⋊C4—1811no—
314C22⋊C4—3621no—
315C22⋊C4—3621no—
316C22⋊C4—3621no—
317C22⋊C4—3621no—
318C22⋊C4—3621no—
319C22⋊C4—3621no—
320C22⋊C4—3621no—
321C22⋊C4—1811no—
322C22⋊C4—1811no—
323C42—3621no—
324C42—1811no—
325C23—21no—
326C23—21no—
327C23—1811no—
328C23D4×D18111yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—3621no—
333Q8—3621no—
334Q8—3621no—
335Q8—3621no—
336Q8—7242no—
337Q8C2×C22⋊D18112yes—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—7241no—
344D4—7242no—
345D4—7242no—
346D4C2×C22⋊D18112yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—3621no—
354C2×C4—3621no—
355C2×C4—3621no—
356C2×C4—3621no—
357C2×C4—3621no—
358C2×C4—3621no—
359C2×C4—1811no—
360C2×C4—1811no—
361C2×C4—1811no—
362C2×C4—7242no—
363C2×C4—7242no—
364C2×C4—7242no—
365C2×C4D4×D18111yescharacteristic
366C2×C4C23×D18111yescharacteristic
367C8—21no—
368C8—3621no—
369C8—3621no—
370C8C2×C22⋊D18112yes—
371C22—21no—
372C22—22no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—3621no—
381C22—3621no—
382C22—3621no—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—3621no—
388C4—3621no—
389C4—3621no—
390C4—7241no—
391C4—7241no—
392C4—7241no—
393C4—7241no—
394C4C22×C22⋊D18111yescharacteristic
395C4#1915386111yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—7241no—
400C2D4×C22⋊D18111yescharacteristic
401C2#2604207611yescharacteristic
402C2#2604209311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#135×C181C2
socleC22×C181C22×D4
hypercenterC2×#135D181
hypocenterC181#3269
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#19153845C2semidirect
2. #26041936C2semidirect
3. #26041928C2semidirect
4. #26041670C2semidirect
5. #26041522C2semidirect
6. #26041520C2semidirect
7. #26041492C2semidirect
8. #26041487C2semidirect
9. #26041441C2semidirect
10. #26041441C2semidirect
11. #26041433C2semidirect
12. #26041421C2semidirect
13. #26041380C2semidirect
14. #26041350C2semidirect
15. C2×#135×C181C2semidirect
118. SD16×C181D4semidirect
201. C181#3269semidirect
204. C2×#135D181semidirect
297. SD16C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538452
#260419362
#260419282
#260416702
#260415222
#260415202
#260414922
#260414872
#260414412
#260414332
#260414212
#260413802
#260413502
C2×#135×C1812
#3269181