Finite Group Databasebeta

← #36363764

Subgroups — #36363764

Order 22144.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26012096C211yesmaximal, characteristic, complemented
2#26011971C211yesmaximal, characteristic, complemented
3#26011810C211yesmaximal, characteristic, complemented
4#26011805C211yesmaximal, characteristic, complemented
5#26011799C211yesmaximal, characteristic, complemented
6#26011792C211yesmaximal, characteristic, complemented
7#26011692C211yesmaximal, characteristic, complemented
8#26011687C211yesmaximal, characteristic, complemented
9#26011638C211yesmaximal, characteristic, complemented
10#26011638C211yesmaximal, characteristic, complemented
11#26011604C211yesmaximal, characteristic, complemented
12#26011593C211yesmaximal, characteristic, complemented
13C4×#14583815C211yesmaximal, characteristic, complemented
14C4×D1384C211yesmaximal, characteristic, complemented
15#433×C173C211yesmaximal, characteristic, complemented
16C2×#14583826C2211yescharacteristic
17C2×#14583815C2211yescharacteristic
18C2×#14583815C2211yescharacteristic
19C2×D1384C2211yescharacteristic
20C2×D1384C2211yescharacteristic
21#19149676C2211yescharacteristic
22#19149671C2211yescharacteristic
23#19149664—21no—
24#19149664—21no—
25#19149653C2211yescharacteristic
26#19149653C2211yescharacteristic
27#19149652—21no—
28#19149652—21no—
29C4×Dic346C2211yescharacteristic
30C4×Dic346C2211yescharacteristic
31C4×D692C2211yescharacteristic
32C4×D692C2211yescharacteristic
33C4×D692C2211yescharacteristic
34C4×D692C2211yescharacteristic
35#19149639—21no—
36#19149639—21no—
37#19149637—21no—
38C2×C4⋊Dic173C2211yescharacteristic
39C4⋊C4×D173—21no—
40#19149613C2211yescharacteristic
41#19149613C2211yescharacteristic
42#19149611C2211yescharacteristic
43#19149611C2211yescharacteristic
44#19149604C2211yescharacteristic
45#19149604C2211yescharacteristic
46#19149601C2211yescharacteristic
47#19149601C2211yescharacteristic
48#19149601C2211yescharacteristic
49#19149601C2211yescharacteristic
50#19149601C2211yescharacteristic
51#19149601C2211yescharacteristic
52#117×C173C2211yescharacteristic
53C4⋊C8×C173C2211yescharacteristic
54C4⋊C8×C173C2211yescharacteristic
55C22⋊C8×C173C2211yescharacteristic
56C22⋊C8×C173C2211yescharacteristic
57#97×C173C2211yescharacteristic
58C4×C8×C173C2211yescharacteristic
59#14583826—22no—
60#14583826—22no—
61C2×Dic346C2311yescharacteristic
62C2×D692—21no—
63C2×D692—21no—
64C2×D692C2311yescharacteristic
65C2×D692C2311yescharacteristic
66C2×D692C2311yescharacteristic
67C2×C22⋊D173—21no—
68C2×C22⋊D173—21no—
69C2×C22⋊D173—21no—
70C22×Dic173—21no—
71C2×C4×D173—21no—
72C2×C4×D173—21no—
73C2×C4×D173—21no—
74C2×C4×D173—21no—
75C2×C4×D173—21no—
76#14583815—22no—
77#14583815—22no—
78D1384—22no—
79D1384—22no—
80C4⋊Dic173—21no—
81C4⋊Dic173C2311yescharacteristic
82C4⋊Dic173C2311yescharacteristic
83C4⋊Dic173C2311yescharacteristic
84C4⋊Dic173C2311yescharacteristic
85#14583805—21no—
86#14583805—21no—
87#14583805—21no—
88#14583805—21no—
89#14583803—21no—
90#14583803—21no—
91#14583803—21no—
92#14583803—21no—
93#14583803—21no—
94#14583803—21no—
95C4×Dic173—21no—
96C4×Dic173—21no—
97C22×C4×C173C2311yescharacteristic
98C2×C8×C173C2311yescharacteristic
99C2×C8×C173C2311yescharacteristic
100C2×C8×C173C2311yescharacteristic
101C2×C8×C173C2311yescharacteristic
102C4⋊C4×C173D411yescharacteristic
103C4⋊C4×C173D411yescharacteristic
104C22⋊C4×C173D411yescharacteristic
105C22⋊C4×C173D411yescharacteristic
106C42×C173C2311yescharacteristic
107C42×C173C2311yescharacteristic
108C22×D173—21no—
109C22×D173—21no—
110C22×D173—21no—
111Dic346—21no—
112Dic346#4112yes—
113D692—21no—
114D692—21no—
115D692—21no—
116D692—21no—
117D692—21no—
118D692—81no—
119D692—81no—
120D692#4112yes—
121C22⋊D173—24no—
122C22⋊D173—81no—
123C22⋊D173—81no—
124C2×Dic173—21no—
125C2×Dic173—21no—
126C2×Dic173—21no—
127C2×Dic173—21no—
128C2×Dic173—21no—
129C2×Dic173—81no—
130C4×D173—24no—
131C4×D173—81no—
132C4×D173—81no—
133C4×D173—81no—
134C4×D173—81no—
135C23×C173C2×D411yescharacteristic
136C2×C4×C173—21no—
137C2×C4×C173—21no—
138C2×C4×C173C2×D411yescharacteristic
139C2×C4×C173C2×D411yescharacteristic
140C2×C4×C173C2×D411yescharacteristic
141C2×C4×C173C2×D411yescharacteristic
142C2×C4×C173C2×D411yescharacteristic
143C2×C4×C173C2411yescharacteristic
144C8×C173—21no—
145C8×C173—21no—
146C8×C173—21no—
147C8×C173—21no—
148C22×C173—21no—
149C22×C173—21no—
150C22×C173—21no—
151C22×C173C22×D411yescharacteristic
152C2×D173—22no—
153C2×D173—41no—
154C2×D173—41no—
155C2×D173—41no—
156C2×D173—41no—
157C2×D173—41no—
158C2×D173—41no—
159C2×D173—41no—
160C2×D173—41no—
161C4×C173—21no—
162C4×C173—21no—
163C4×C173—21no—
164C4×C173—21no—
165C4×C173—21no—
166C4×C173C2×#4111yescharacteristic
167C4×C173C2×#4111yescharacteristic
168Dic173—22no—
169Dic173—41no—
170Dic173—41no—
171Dic173—41no—
172Dic173—41no—
173C2×C173—41no—
174C2×C173#52511yescharacteristic
175C2×C173#57611yescharacteristic
176C2×C173#57711yescharacteristic
177D173—42no—
178D173—81no—
179D173—81no—
180C173#311911yescharacteristic, complemented, Sylow
181#3119—1731nomaximal, Sylow
182#540—1731no—
183#520—1731no—
184#481—1731no—
185#480—1731no—
186#479—1731no—
187#478—1731no—
188#460—1731no—
189#459—1731no—
190#449—1731no—
191#449—1731no—
192#442—1731no—
193#440—1731no—
194C4×SD16—1731no—
195C4×D8—1731no—
196#433D17311yescharacteristic, complemented
197C2×#41—1731no—
198C2×SD16—1731no—
199C2×SD16—1731no—
200C2×D8—1731no—
201C2×D8—1731no—
202#127—1731no—
203#125—1731no—
204#123—3461no—
205#123—3461no—
206#121—3461no—
207#121—3461no—
208#121—1731no—
209#121—1731no—
210C4×Q8—1731no—
211C4×Q8—1731no—
212C4×D4—3461no—
213C4×D4—3461no—
214C4×D4—1731no—
215C4×D4—1731no—
216C4×D4—1731no—
217C4×D4—1731no—
218#117—3461no—
219#117C2×D17311yescharacteristic
220C2×C4⋊C4—3461no—
221C2×C4⋊C4—1731no—
222#107—1731no—
223#107—1731no—
224#106—1731no—
225#106—1731no—
226C4⋊C8C2×D17311yescharacteristic
227C4⋊C8C2×D17311yescharacteristic
228#103—1731no—
229#103—1731no—
230#102—1731no—
231#102—1731no—
232#102—1731no—
233#102—1731no—
234#102—1731no—
235#102—1731no—
236C22⋊C8C2×D17311yescharacteristic
237C22⋊C8C2×D17311yescharacteristic
238#97C2×D17311yescharacteristic
239C4×C8C2×D17311yescharacteristic
240#41—3462no—
241#41—3462no—
242C2×Q8—1731no—
243C2×D4—3461no—
244C2×D4—3461no—
245C2×D4—3461no—
246C2×D4—3461no—
247C2×D4—3461no—
248C2×D4—1731no—
249C2×D4—1731no—
250C2×D4—1731no—
251C22×C4—3461no—
252C22×C4—3461no—
253C22×C4—3461no—
254C22×C4—3461no—
255C22×C4—3461no—
256C22×C4—3461no—
257C22×C4C22×D17311yescharacteristic
258SD16—3462no—
259SD16—3462no—
260D8—3462no—
261D8—3462no—
262C2×C8C22×D17311yescharacteristic
263C2×C8C22×D17311yescharacteristic
264C2×C8C22×D17311yescharacteristic
265C2×C8C22×D17311yescharacteristic
266C4⋊C4—3461no—
267C4⋊C4—3461no—
268C4⋊C4—3461no—
269C4⋊C4—3461no—
270C4⋊C4—3461no—
271C4⋊C4—1731no—
272C4⋊C4—1731no—
273C4⋊C4—1731no—
274C4⋊C4—1731no—
275C4⋊C4D69211yescharacteristic
276C4⋊C4D69211yescharacteristic
277C22⋊C4—3461no—
278C22⋊C4—3461no—
279C22⋊C4—3461no—
280C22⋊C4—3461no—
281C22⋊C4—3461no—
282C22⋊C4—3461no—
283C22⋊C4D69211yescharacteristic
284C22⋊C4D69211yescharacteristic
285C42—3461no—
286C42—3461no—
287C42C22×D17311yescharacteristic
288C42C22×D17311yescharacteristic
289C23—3461no—
290C23—3461no—
291C23—3461no—
292C23C2×D69211yescharacteristic
293Q8—3461no—
294Q8—1732no—
295D4—3464no—
296D4—3461no—
297D4—3461no—
298D4—3461no—
299D4—3461no—
300D4—3461no—
301D4—13841no—
302D4—13841no—
303D4—13841no—
304D4—13841no—
305D4—1732no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—3464no—
309C2×C4—3461no—
310C2×C4—3461no—
311C2×C4—3461no—
312C2×C4—3461no—
313C2×C4—3461no—
314C2×C4—13841no—
315C2×C4—13841no—
316C2×C4—13841no—
317C2×C4—13841no—
318C2×C4—13841no—
319C2×C4C2×D69211yescharacteristic
320C2×C4C2×D69211yescharacteristic
321C2×C4C2×D69211yescharacteristic
322C2×C4C2×D69211yescharacteristic
323C2×C4C2×D69211yescharacteristic
324C2×C4C23×D17311yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—3462no—
333C22—6921no—
334C22—6921no—
335C22—6921no—
336C22—6921no—
337C22—6921no—
338C22—6921no—
339C22—6921no—
340C22—6921no—
341C22C22×D69211yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—3462no—
348C4—6921no—
349C4—6921no—
350C4—6921no—
351C4—6921no—
352C4#41×D17311yescharacteristic
353C4#41×D17311yescharacteristic
354C2—41no—
355C2—13841no—
356C2—13841no—
357C2—6922no—
358C2#2601200311yescharacteristic
359C2#2601229611yescharacteristic
360C2#2601230311yescharacteristic
subgroupG/H
centerC22C22×D692
commutator, cosocleC2×C4×C173C24
FrattiniC2×C4C23×D173
Fitting#433×C173C2
socleC22×C173C22×D4
hypercenter#433D173
hypocenterC173#3119
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #26012096C2semidirect
2. #26011971C2semidirect
3. #26011810C2semidirect
4. #26011805C2semidirect
5. #26011799C2semidirect
6. #26011792C2semidirect
7. #26011692C2semidirect
8. #26011687C2semidirect
9. #26011638C2semidirect
10. #26011638C2semidirect
11. #26011604C2semidirect
12. #26011593C2semidirect
13. C4×#14583815C2semidirect
14. C4×D1384C2semidirect
15. #433×C173C2semidirect
180. C173#3119semidirect
196. #433D173semidirect

Maximal subgroups

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

subgroupindex
#260120962
#260119712
#260118102
#260118052
#260117992
#260117922
#260116922
#260116872
#260116382
#260116042
#260115932
C4×#145838152
C4×D13842
#433×C1732
#3119173