Finite Group Databasebeta

← #36362441

Subgroups — #36362441

Order 22144.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19149700C211yesmaximal, characteristic
2#26011973C211yesmaximal, characteristic, complemented
3#26011970C211yesmaximal, characteristic, complemented
4#26011601C211yesmaximal, characteristic, complemented
5#26011600C211yesmaximal, characteristic, complemented
6#26011596C211yesmaximal, characteristic, complemented
7#26011595C211yesmaximal, characteristic, complemented
8C4×#14583815C211yesmaximal, characteristic, complemented
9SD16×Dic173C211yesmaximal, characteristic, complemented
10#26011578C211yesmaximal, characteristic, complemented
11#106×D173C211yesmaximal, characteristic, complemented
12#26011491C211yesmaximal, characteristic, complemented
13#26011489C211yesmaximal, characteristic, complemented
14#26011445C211yesmaximal, characteristic, complemented
15C4×SD16×C173C211yesmaximal, characteristic, complemented
16C2×#14583827C2211yescharacteristic
17C2×#14583825C2211yescharacteristic
18#19149700C418yescomplemented
19C2×#14583816C2211yescharacteristic
20C2×#14583815C2211yescharacteristic
21C2×#14583811C2211yescharacteristic
22C2×#14583809C2211yescharacteristic
23C2×C8×D173C2211yescharacteristic
24Q8×Dic173C2211yescharacteristic
25C4×Dic346C2211yescharacteristic
26#19149644C2211yescharacteristic
27C4×D692—21no—
28C4×D692C2211yescharacteristic
29D4×Dic173C2211yescharacteristic
30#19149641—21no—
31#19149641C2211yescharacteristic
32C4×C22⋊D173—21no—
33#19149639—21no—
34#19149636—21no—
35#19149636C2211yescharacteristic
36#19149635—21no—
37C2×#14583805—21no—
38C4⋊C4×D173—21no—
39C4⋊C4×D173C2211yescharacteristic
40C4⋊C4×D173C2211yescharacteristic
41#19149611C2211yescharacteristic
42#19149610C2211yescharacteristic
43#19149610C2211yescharacteristic
44#19149604C2211yescharacteristic
45#19149603C2211yescharacteristic
46#19149602C2211yescharacteristic
47#19149601C2211yescharacteristic
48#19149600C2211yescharacteristic
49#19149599C2211yescharacteristic
50#19149590C2211yescharacteristic
51#19149589C2211yescharacteristic
52C8×Dic173C2211yescharacteristic
53C2×SD16×C173C2211yescharacteristic
54C4×Q8×C173C2211yescharacteristic
55C4×D4×C173C2211yescharacteristic
56#106×C173C2211yescharacteristic
57#103×C173C2211yescharacteristic
58#102×C173C2211yescharacteristic
59C4×C8×C173C2211yescharacteristic
60#14583827—22no—
61#14583827C2×C414yescomplemented
62#14583825—22no—
63#14583825C2×C414yescomplemented
64C2×Dic346C2311yescharacteristic
65C2×D692—21no—
66C2×D692C2311yescharacteristic
67C2×C22⋊D173—21no—
68C22×Dic173—21no—
69C22×Dic173—21no—
70C2×C4×D173—21no—
71C2×C4×D173—21no—
72C2×C4×D173—21no—
73C2×C4×D173—21no—
74C2×C4×D173—21no—
75C2×C4×D173C2311yescharacteristic
76#14583816C2×C414yescomplemented
77#14583815C2×C414yescomplemented
78#14583811C2×C414yescomplemented
79#14583809—22no—
80C2×#13063436C2311yescharacteristic
81C2×#13063436C2311yescharacteristic
82C8×D173C2×C414yescomplemented
83C4⋊Dic173—21no—
84C4⋊Dic173C2311yescharacteristic
85C4⋊Dic173C2311yescharacteristic
86#14583805—21no—
87#14583805—21no—
88#14583805—21no—
89#14583805—21no—
90#14583805D411yescharacteristic
91#14583805D411yescharacteristic
92C22⋊Dic173—21no—
93#14583803—21no—
94#14583803—21no—
95#14583803D411yescharacteristic
96#14583803D411yescharacteristic
97C4×Dic173—21no—
98C4×Dic173—21no—
99C4×Dic173—21no—
100C4×Dic173C2311yescharacteristic
101C2×Q8×C173C2311yescharacteristic
102C2×D4×C173C2311yescharacteristic
103C22×C4×C173—21no—
104SD16×C173C2×C414yescomplemented
105C2×C8×C173C2311yescharacteristic
106C2×C8×C173C2311yescharacteristic
107C4⋊C4×C173—21no—
108C4⋊C4×C173C2311yescharacteristic
109C4⋊C4×C173C2311yescharacteristic
110C22⋊C4×C173—21no—
111C42×C173—21no—
112C42×C173C2311yescharacteristic
113C22×D173—21no—
114C22×D173C2×D411yescharacteristic
115Dic346—21no—
116Dic346C22×C412yes—
117D692—24no—
118D692—21no—
119D692C22×C412yes—
120C22⋊D173—24no—
121C2×Dic173—21no—
122C2×Dic173—24no—
123C2×Dic173—21no—
124C2×Dic173—21no—
125C2×Dic173—81no—
126C2×Dic173C2×D411yescharacteristic
127C2×Dic173C2×D411yescharacteristic
128C2×Dic173C2×D411yescharacteristic
129C4×D173—24no—
130C4×D173—81no—
131C4×D173—81no—
132C4×D173—81no—
133C4×D173—81no—
134C4×D173C22×C412yes—
135C4×D173#4112yes—
136#13063436—21no—
137#13063436C22×C412yes—
138C23×C173—21no—
139Q8×C173—21no—
140Q8×C173C22×C412yes—
141D4×C173—21no—
142D4×C173C22×C412yes—
143C2×C4×C173—21no—
144C2×C4×C173—21no—
145C2×C4×C173—21no—
146C2×C4×C173—81no—
147C2×C4×C173C2×D411yescharacteristic
148C2×C4×C173C2×D411yescharacteristic
149C2×C4×C173C2411yescharacteristic
150C8×C173—21no—
151C8×C173C22×C412yes—
152C22×C173—22no—
153C22×C173—41no—
154C22×C173—41no—
155C22×C173C22×D411yescharacteristic
156C2×D173—21no—
157C2×D173—21no—
158C2×D173—22no—
159C2×D173—41no—
160C2×D173—41no—
161C2×D173C4×D412yes—
162C4×C173—22no—
163C4×C173—21no—
164C4×C173—21no—
165C4×C173—41no—
166C4×C173—41no—
167C4×C173C23×C411yescharacteristic
168C4×C173C2×#4111yescharacteristic
169Dic173—22no—
170Dic173—21no—
171Dic173—21no—
172Dic173—41no—
173Dic173—41no—
174Dic173C4×D412yes—
175C2×C173—42no—
176C2×C173C2×C4×D411yescharacteristic
177C2×C173#57711yescharacteristic
178C2×C173#57711yescharacteristic
179D173—22no—
180D173—42no—
181C173#295211yescharacteristic, complemented, Sylow
182#2952—1731nomaximal, Sylow
183C2×#135—1731no—
184#520—1731no—
185#520—1731no—
186#442—1731no—
187#442—1731no—
188#441—1731no—
189#441—1731no—
190C4×SD16—1731no—
191C4×SD16—1731no—
192C4×SD16—1731no—
193C4×SD16D17311yescharacteristic, complemented
194C2×#106—1731no—
195#417—1731no—
196#417—1731no—
197#405—1731no—
198C2×#41—1731no—
199C2×#41—1731no—
200#135—1738no—
201C2×Q16—1731no—
202C2×SD16—1731no—
203C2×SD16C2×D17311yescharacteristic
204C2×D8—1731no—
205C2×M16—1731no—
206C22×C8—1731no—
207C4×Q8—1731no—
208C4×Q8—1731no—
209C4×Q8—1731no—
210C4×Q8C2×D17311yescharacteristic
211C4×D4—3461no—
212C4×D4—3461no—
213C4×D4—3461no—
214C4×D4—3461no—
215C4×D4—1731no—
216C4×D4—1731no—
217C4×D4—1731no—
218C4×D4C2×D17311yescharacteristic
219#117—3461no—
220#117—3461no—
221#117—1731no—
222C2×C4⋊C4—3461no—
223C2×C4⋊C4—3461no—
224C2×C4⋊C4—1731no—
225C2×C4⋊C4—1731no—
226#106—1731no—
227#106—1731no—
228#106—1731no—
229#106C2×D17311yescharacteristic
230#103—1731no—
231#103—1731no—
232#103—1731no—
233#103C2×D17311yescharacteristic
234#102—1731no—
235#102—1731no—
236#102—1731no—
237#102C2×D17311yescharacteristic
238#97—1731no—
239#97—1731no—
240C4×C8—1731no—
241C4×C8C2×D17311yescharacteristic
242#41—3462no—
243#41—3462no—
244#41—1734no—
245#41—1734no—
246C2×Q8—1731no—
247C2×Q8C22×D17311yescharacteristic
248C2×D4—3461no—
249C2×D4—3461no—
250C2×D4—1731no—
251C2×D4C22×D17311yescharacteristic
252C22×C4—21no—
253C22×C4—3461no—
254C22×C4—3461no—
255C22×C4—3461no—
256C22×C4—3461no—
257C22×C4—3461no—
258C22×C4—3461no—
259C22×C4—3461no—
260C22×C4—1731no—
261Q16—1734no—
262SD16—1734no—
263SD16C4×D17314yescomplemented
264D8—1734no—
265M16—3462no—
266C2×C8—1731no—
267C2×C8—1731no—
268C2×C8—1734no—
269C2×C8C22×D17311yescharacteristic
270C2×C8C22×D17311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—3461no—
273C4⋊C4—3461no—
274C4⋊C4—3461no—
275C4⋊C4—3461no—
276C4⋊C4—3461no—
277C4⋊C4—1731no—
278C4⋊C4—1731no—
279C4⋊C4—1731no—
280C4⋊C4—1731no—
281C4⋊C4C22×D17311yescharacteristic
282C4⋊C4C22×D17311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—3461no—
285C22⋊C4—3461no—
286C22⋊C4—3461no—
287C22⋊C4—1731no—
288C22⋊C4—1731no—
289C42—21no—
290C42—3461no—
291C42—3461no—
292C42—3461no—
293C42—1731no—
294C42C22×D17311yescharacteristic
295C23—21no—
296C23—3461no—
297C23—1731no—
298Q8—21no—
299Q8—3461no—
300Q8—1732no—
301Q8C2×C4×D17312yes—
302D4—21no—
303D4—3464no—
304D4—3464no—
305D4—3461no—
306D4—1732no—
307D4C2×C4×D17312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—3464no—
313C2×C4—3461no—
314C2×C4—3464no—
315C2×C4—3461no—
316C2×C4—3461no—
317C2×C4—13841no—
318C2×C4—13841no—
319C2×C4—13841no—
320C2×C4—13841no—
321C2×C4—13841no—
322C2×C4—1731no—
323C2×C4—1731no—
324C2×C4—1731no—
325C2×C4—1732no—
326C2×C4—1732no—
327C2×C4D4×D17311yescharacteristic
328C2×C4D4×D17311yescharacteristic
329C2×C4C23×D17311yescharacteristic
330C8—21no—
331C8—3461no—
332C8—1732no—
333C8C2×C4×D17312yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—3461no—
338C22—3461no—
339C22—3462no—
340C22—1732no—
341C22—6921no—
342C22—6921no—
343C22C2×D4×D17311yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—3462no—
350C4—3461no—
351C4—3461no—
352C4—1732no—
353C4—6921no—
354C4—6921no—
355C4C22×C4×D17311yescharacteristic
356C4#41×D17311yescharacteristic
357C2—42no—
358C2—3462no—
359C2—6922no—
360C2C4×D4×D17311yescharacteristic
361C2#2601229711yescharacteristic
362C2#2601229811yescharacteristic
subgroupG/H
centerC22C2×D4×D173
commutatorC4×C173C23×C4
FrattiniC2×C4C23×D173
FittingC4×SD16×C173C2
socleC22×C173C22×D4
prime radicalC2×#19149700C2
cosocleC2×C4×C173C24
hypercenterC4×SD16D173
hypocenterC173#2952
LCSG ▷ C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #26011973C2semidirect
3. #26011970C2semidirect
4. #26011601C2semidirect
5. #26011600C2semidirect
6. #26011596C2semidirect
7. #26011595C2semidirect
8. C4×#14583815C2semidirect
9. SD16×Dic173C2semidirect
10. #26011578C2semidirect
11. #106×D173C2semidirect
12. #26011491C2semidirect
13. #26011489C2semidirect
14. #26011445C2semidirect
15. C4×SD16×C173C2semidirect
18. #19149700C4semidirect
61. #14583827C2×C4semidirect
63. #14583825C2×C4semidirect
76. #14583816C2×C4semidirect
77. #14583815C2×C4semidirect
78. #14583811C2×C4semidirect
82. C8×D173C2×C4semidirect
104. SD16×C173C2×C4semidirect
181. C173#2952semidirect
193. C4×SD16D173semidirect
263. SD16C4×D173semidirect

Maximal subgroups

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

subgroupindex
C2×#191497002
#260119732
#260119702
#260116012
#260116002
#260115962
#260115952
C4×#145838152
SD16×Dic1732
#260115782
#106×D1732
#260114912
#260114892
#260114452
C4×SD16×C1732
#2952173