Finite Group Databasebeta

← #36364427

Subgroups — #36364427

Order 22144.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26012060C211yesmaximal, characteristic, complemented
2#26012057C211yesmaximal, characteristic, complemented
3#26011818C211yesmaximal, characteristic, complemented
4#26011817C211yesmaximal, characteristic, complemented
5#26011815C211yesmaximal, characteristic, complemented
6#26011745C211yesmaximal, characteristic, complemented
7#26011743C211yesmaximal, characteristic, complemented
8#26011728C211yesmaximal, characteristic, complemented
9#26011726C211yesmaximal, characteristic, complemented
10#26011627C211yesmaximal, characteristic, complemented
11#26011626C211yesmaximal, characteristic, complemented
12#26011626C211yesmaximal, characteristic, complemented
13#26011624C211yesmaximal, characteristic, complemented
14#26011456C211yesmaximal, characteristic, complemented
15#482×C173C211yesmaximal, characteristic, complemented
16C2×#14583826C2211yescharacteristic
17C22×D692C2211yescharacteristic, complemented
18C2×D4×D173C2211yescharacteristic, complemented
19C2×D1384C2211yescharacteristic
20C2×D1384C2211yescharacteristic
21C2×#14583811C2211yescharacteristic
22C2×#14583811C2211yescharacteristic
23C2×#14583809C2211yescharacteristic, complemented
24C2×C8×D173C2211yescharacteristic, complemented
25#19149676—21no—
26#19149675—21no—
27#19149667—21no—
28#19149665—21no—
29#19149654C2211yescharacteristic
30#19149654C2211yescharacteristic
31#19149654C2211yescharacteristic, complemented
32#19149654C2211yescharacteristic, complemented
33#19149654C2211yescharacteristic, complemented
34#19149653C2211yescharacteristic
35#19149650C2211yescharacteristic, complemented
36#19149649—21no—
37#19149649—21no—
38#19149649—21no—
39#19149647—21no—
40#19149637C2211yescharacteristic, complemented
41#19149612C2211yescharacteristic, complemented
42#19149610C2211yescharacteristic, complemented
43#19149601C2211yescharacteristic, complemented
44#19149601C2211yescharacteristic, complemented
45#19149599C2211yescharacteristic, complemented
46#19149599C2211yescharacteristic, complemented
47#19149599C2211yescharacteristic, complemented
48#19149599C2211yescharacteristic, complemented
49C22⋊#13063436C2211yescharacteristic, complemented
50#19149591C2211yescharacteristic, complemented
51#19149591C2211yescharacteristic, complemented
52#121×C173C2211yescharacteristic
53#117×C173C2211yescharacteristic, complemented
54#107×C173C2211yescharacteristic, complemented
55#106×C173C2211yescharacteristic, complemented
56#102×C173C2211yescharacteristic, complemented
57#102×C173C2211yescharacteristic, complemented
58C22⋊C8×C173C2211yescharacteristic, complemented
59C23×D173—21no—
60C23×D173—21no—
61#14583826—41no—
62#14583826—41no—
63C2×Dic346D411yescharacteristic
64C2×D692—21no—
65C2×D692—21no—
66C2×D692—21no—
67C2×D692—21no—
68C2×D692—21no—
69C2×D692—21no—
70C2×D692—41no—
71C2×D692—41no—
72C2×D692D411yescharacteristic
73C2×D692C2311yescharacteristic
74C2×D692C2311yescharacteristic
75C2×D692C2311yescharacteristic
76C2×C22⋊D173—21no—
77C2×C22⋊D173—21no—
78C2×C22⋊D173—21no—
79C2×C22⋊D173D411yescharacteristic
80C2×C22⋊D173D411yescharacteristic
81D4×D173—41no—
82D4×D173—41no—
83C2×C4×D173C2311yescharacteristic
84C2×C4×D173C2311yescharacteristic
85D1384—41no—
86D1384—41no—
87#14583811—41no—
88#14583811—41no—
89#14583809—41no—
90C2×#13063436C2311yescharacteristic
91C2×#13063436C2311yescharacteristic
92C8×D173—41no—
93C4⋊Dic173C2311yescharacteristic
94C22⋊Dic173—21no—
95#14583803—21no—
96#14583803—21no—
97#14583803—21no—
98#14583803—21no—
99#14583803—21no—
100#14583803—21no—
101#14583803—21no—
102C4×Dic173—21no—
103C2×D4×C173—21no—
104C2×D4×C173C2311yescharacteristic
105C22×C4×C173C2311yescharacteristic
106C2×C8×C173C2311yescharacteristic
107C2×C8×C173C2311yescharacteristic
108C4⋊C4×C173C2311yescharacteristic
109C4⋊C4×C173C2311yescharacteristic
110C4⋊C4×C173C2311yescharacteristic
111C22⋊C4×C173—21no—
112C22⋊C4×C173—21no—
113C42×C173—21no—
114C22×D173—21no—
115C22×D173—21no—
116C22×D173—21no—
117C22×D173—42no—
118C22×D173—42no—
119C22×D173—81no—
120C22×D173—81no—
121C22×D173—81no—
122C22×D173—81no—
123C22×D173C2×D411yescharacteristic
124C22×D173C2×D411yescharacteristic
125Dic346—41no—
126D692—21no—
127D692—21no—
128D692—21no—
129D692—21no—
130D692—21no—
131D692—21no—
132D692—41no—
133D692—42no—
134D692—81no—
135D692—81no—
136D692—81no—
137D692—81no—
138D692—81no—
139C22⋊D173—41no—
140C22⋊D173—41no—
141C22⋊D173—42no—
142C22⋊D173—81no—
143C22⋊D173—81no—
144C2×Dic173—21no—
145C2×Dic173C2×D411yescharacteristic
146C2×Dic173C2×D411yescharacteristic
147C4×D173—21no—
148C4×D173—21no—
149C4×D173—21no—
150C4×D173—21no—
151#13063436—21no—
152#13063436—21no—
153C23×C173—21no—
154C23×C173C2×D411yescharacteristic
155D4×C173—21no—
156D4×C173—21no—
157D4×C173—81no—
158C2×C4×C173—21no—
159C2×C4×C173—21no—
160C2×C4×C173—21no—
161C2×C4×C173—21no—
162C2×C4×C173—21no—
163C2×C4×C173C2×D411yescharacteristic
164C2×C4×C173C2411yescharacteristic
165C8×C173—21no—
166C8×C173—21no—
167C22×C173—21no—
168C22×C173—21no—
169C22×C173—21no—
170C22×C173—41no—
171C22×C173—41no—
172C22×C173—41no—
173C22×C173C22×D411yescharacteristic
174C2×D173—21no—
175C2×D173—21no—
176C2×D173—21no—
177C2×D173—21no—
178C2×D173—21no—
179C2×D173—21no—
180C2×D173—41no—
181C2×D173—41no—
182C2×D173—41no—
183C2×D173—41no—
184C2×D173—41no—
185C2×D173—41no—
186C2×D173—41no—
187C2×D173—41no—
188C2×D173—41no—
189C2×D173—84no—
190C2×D173—84no—
191C4×C173—21no—
192C4×C173—41no—
193C4×C173—41no—
194C4×C173—41no—
195C4×C173H(5,𝔽2)11yescharacteristic
196C4×C173H(5,𝔽2)11yescharacteristic
197Dic173—21no—
198Dic173—21no—
199Dic173—41no—
200C2×C173—41no—
201C2×C173—81no—
202C2×C173#53411yescharacteristic
203C2×C173#57611yescharacteristic
204C2×C173#57611yescharacteristic
205D173—41no—
206D173—41no—
207D173—81no—
208D173—81no—
209D173—81no—
210C173#319911yescharacteristic, complemented, Sylow
211#3199—1731nomaximal, Sylow
212#535—1731no—
213#535—1731no—
214#482—1731no—
215#482—1731no—
216#482—1731no—
217#482D17311yescharacteristic, complemented
218#469—1731no—
219#469—1731no—
220#466—1731no—
221#466—1731no—
222#447—1731no—
223#447—1731no—
224#447—1731no—
225#447—1731no—
226#408—1731no—
227C2×#41—1731no—
228C22×D4—1731no—
229C22×D4—1731no—
230C2×D8—1731no—
231C2×D8—1731no—
232C2×D8—1731no—
233C2×D8—1731no—
234C2×M16—1731no—
235C22×C8—1731no—
236#127—3461no—
237#127—3461no—
238#124—3461no—
239#124—3461no—
240#121—1731no—
241#121—1731no—
242#121—1731no—
243#121—1731no—
244#121—1731no—
245#121—1731no—
246#121—1731no—
247#121C2×D17311yescharacteristic
248#120—3461no—
249#120—3461no—
250#120—3461no—
251#120—3461no—
252#117—1731no—
253#117C2×D17311yescharacteristic, complemented
254#107—1731no—
255#107C2×D17311yescharacteristic, complemented
256#106—1731no—
257#106C2×D17311yescharacteristic, complemented
258#102—1731no—
259#102—1731no—
260#102—1731no—
261#102—1731no—
262#102—1731no—
263#102—1731no—
264#102C2×D17311yescharacteristic, complemented
265#102C2×D17311yescharacteristic, complemented
266C22⋊C8—1731no—
267C22⋊C8—1731no—
268C22⋊C8—1731no—
269C22⋊C8C2×D17311yescharacteristic, complemented
270C24—3461no—
271C24—3461no—
272#41—6921no—
273#41—6921no—
274C2×Q8—1731no—
275C2×D4—21no—
276C2×D4—3461no—
277C2×D4—3461no—
278C2×D4—3461no—
279C2×D4—3461no—
280C2×D4—3461no—
281C2×D4—3461no—
282C2×D4—3461no—
283C2×D4—3461no—
284C2×D4—3461no—
285C2×D4—1731no—
286C2×D4—1731no—
287C2×D4—1731no—
288C2×D4—1731no—
289C2×D4—1731no—
290C2×D4—1731no—
291C2×D4—6921no—
292C2×D4—6921no—
293C2×D4—6921no—
294C2×D4—6921no—
295C2×D4C22×D17311yescharacteristic
296C22×C4—1731no—
297C22×C4—1731no—
298C22×C4C22×D17311yescharacteristic
299D8—6921no—
300D8—6921no—
301D8—6921no—
302D8—6921no—
303M16—6921no—
304C2×C8—1731no—
305C2×C8—1731no—
306C2×C8—6921no—
307C2×C8C22×D17311yescharacteristic
308C2×C8C22×D17311yescharacteristic
309C4⋊C4—1731no—
310C4⋊C4C22×D17311yescharacteristic
311C4⋊C4C22×D17311yescharacteristic
312C4⋊C4C22×D17311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—3461no—
316C22⋊C4—3461no—
317C22⋊C4—3461no—
318C22⋊C4—3461no—
319C22⋊C4—3461no—
320C22⋊C4—3461no—
321C22⋊C4—3461no—
322C22⋊C4—3461no—
323C42—21no—
324C42—3461no—
325C23—21no—
326C23—3461no—
327C23—3461no—
328C23—3461no—
329C23—13841no—
330C23—13841no—
331C23—13841no—
332C23—13841no—
333C23—1731no—
334C23—1731no—
335C23—6922no—
336C23—6922no—
337C23D4×D17311yescharacteristic
338Q8—6921no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—3461no—
343D4—3461no—
344D4—3461no—
345D4—3461no—
346D4—3461no—
347D4—3461no—
348D4—13841no—
349D4—13841no—
350D4—13841no—
351D4—13841no—
352D4—13841no—
353D4—13841no—
354D4—13841no—
355D4—6921no—
356D4—6922no—
357D4—6921no—
358D4—6921no—
359D4—6922no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—3461no—
366C2×C4—3461no—
367C2×C4—3461no—
368C2×C4—3461no—
369C2×C4—3461no—
370C2×C4—1731no—
371C2×C4—1731no—
372C2×C4D4×D17311yescharacteristic
373C2×C4C23×D17311yescharacteristic
374C8—21no—
375C8—21no—
376C8—3461no—
377C8—3461no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—3461no—
385C22—3461no—
386C22—3461no—
387C22—3461no—
388C22—3461no—
389C22—3461no—
390C22—13844no—
391C22—13844no—
392C22—6921no—
393C22—6921no—
394C22—6921no—
395C22—6921no—
396C22—6921no—
397C22—6921no—
398C22—6921no—
399C22—6921no—
400C22—6921no—
401C22C2×D4×D17311yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—3461no—
407C4—3461no—
408C4—6921no—
409C4#1914972511yescharacteristic
410C4#1914972511yescharacteristic
411C2—41no—
412C2—81no—
413C2—13841no—
414C2—13841no—
415C2—13841no—
416C2—6921no—
417C2—6921no—
418C2#2601205211yescharacteristic
419C2#2601229311yescharacteristic
420C2#2601229511yescharacteristic
subgroupG/H
centerC22C2×D4×D173
commutator, cosocleC2×C4×C173C24
FrattiniC2×C4C23×D173
Fitting#482×C173C2
socleC22×C173C22×D4
hypercenter#482D173
hypocenterC173#3199
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #26012060C2semidirect
2. #26012057C2semidirect
3. #26011818C2semidirect
4. #26011817C2semidirect
5. #26011815C2semidirect
6. #26011745C2semidirect
7. #26011743C2semidirect
8. #26011728C2semidirect
9. #26011726C2semidirect
10. #26011627C2semidirect
11. #26011626C2semidirect
12. #26011626C2semidirect
13. #26011624C2semidirect
14. #26011456C2semidirect
15. #482×C173C2semidirect
17. C22×D692C22semidirect
18. C2×D4×D173C22semidirect
23. C2×#14583809C22semidirect
24. C2×C8×D173C22semidirect
31. #19149654C22semidirect
32. #19149654C22semidirect
33. #19149654C22semidirect
35. #19149650C22semidirect
40. #19149637C22semidirect
41. #19149612C22semidirect
42. #19149610C22semidirect
43. #19149601C22semidirect
44. #19149601C22semidirect
45. #19149599C22semidirect
46. #19149599C22semidirect
47. #19149599C22semidirect
48. #19149599C22semidirect
49. C22⋊#13063436C22semidirect
50. #19149591C22semidirect
51. #19149591C22semidirect
53. #117×C173C22semidirect
54. #107×C173C22semidirect
55. #106×C173C22semidirect
56. #102×C173C22semidirect
57. #102×C173C22semidirect
58. C22⋊C8×C173C22semidirect
210. C173#3199semidirect
217. #482D173semidirect
253. #117C2×D173semidirect
255. #107C2×D173semidirect
257. #106C2×D173semidirect
264. #102C2×D173semidirect
265. #102C2×D173semidirect
269. C22⋊C8C2×D173semidirect

Maximal subgroups

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

subgroupindex
#260120602
#260120572
#260118182
#260118172
#260118152
#260117452
#260117432
#260117282
#260117262
#260116272
#260116262
#260116242
#260114562
#482×C1732
#3199173