Finite Group Databasebeta

← #36363827

Subgroups — #36363827

Order 22144.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26012112C211yesmaximal, characteristic, complemented
2#26011971C211yesmaximal, characteristic, complemented
3#26011827C211yesmaximal, characteristic, complemented
4#26011805C211yesmaximal, characteristic, complemented
5#26011787C211yesmaximal, characteristic, complemented
6#26011772C211yesmaximal, characteristic, complemented
7#26011714C211yesmaximal, characteristic, complemented
8#26011707C211yesmaximal, characteristic, complemented
9#26011655C211yesmaximal, characteristic, complemented
10#26011638C211yesmaximal, characteristic
11#26011593C211yesmaximal, characteristic, complemented
12#26011593C211yesmaximal, characteristic, complemented
13C4×Dic692C211yesmaximal, characteristic, complemented
14C4×D1384C211yesmaximal, characteristic, complemented
15#433×C173C211yesmaximal, characteristic, complemented
16C2×#14583826C2211yescharacteristic
17C2×Dic692C2211yescharacteristic
18C2×#14583815C2211yescharacteristic
19C2×#14583815C2211yescharacteristic
20C2×D1384C2211yescharacteristic
21#19149679C2211yescharacteristic
22#19149674—21no—
23#19149667C2211yescharacteristic
24#19149665—21no—
25#19149661—21no—
26#19149658C2211yescharacteristic
27#19149657—21no—
28#19149653C2211yescharacteristic
29C4×Dic346C2211yescharacteristic
30C4×Dic346C2211yescharacteristic
31C4×Dic346C2211yescharacteristic
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#19149613C2211yescharacteristic
43#19149613C2211yescharacteristic
44#19149604C2211yescharacteristic
45#19149604C2211yescharacteristic
46#19149604C2211yescharacteristic
47#19149604C2211yescharacteristic
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×Dic346—21no—
62C2×Dic346C2311yescharacteristic
63C2×Dic346C2311yescharacteristic
64C2×D692C2311yescharacteristic
65C2×D692C2311yescharacteristic
66C2×C22⋊D173—21no—
67C2×C22⋊D173—21no—
68C22×Dic173—21no—
69C2×C4×D173—21no—
70C2×C4×D173—21no—
71C2×C4×D173—21no—
72C2×C4×D173—21no—
73Dic692—22no—
74#14583815—22no—
75#14583815—22no—
76D1384—22no—
77C4⋊Dic173—21no—
78C4⋊Dic173—21no—
79C4⋊Dic173C2311yescharacteristic
80C4⋊Dic173C2311yescharacteristic
81C4⋊Dic173C2311yescharacteristic
82C4⋊Dic173C2311yescharacteristic
83#14583805—21no—
84#14583805—21no—
85#14583805—21no—
86#14583805—21no—
87C22⋊Dic173—21no—
88#14583803—21no—
89#14583803—21no—
90#14583803—21no—
91#14583803—21no—
92#14583803—21no—
93#14583803—21no—
94C4×Dic173—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—
110Dic346—21no—
111Dic346—21no—
112Dic346—21no—
113Dic346—81no—
114Dic346#4112yes—
115D692—21no—
116D692—21no—
117D692—21no—
118D692#4112yes—
119C22⋊D173—24no—
120C22⋊D173—81no—
121C2×Dic173—21no—
122C2×Dic173—21no—
123C2×Dic173—21no—
124C2×Dic173—21no—
125C2×Dic173—21no—
126C2×Dic173—21no—
127C2×Dic173—81no—
128C4×D173—24no—
129C4×D173—81no—
130C4×D173—81no—
131C4×D173—81no—
132C23×C173C2×D411yescharacteristic
133C2×C4×C173—21no—
134C2×C4×C173—21no—
135C2×C4×C173C2×D411yescharacteristic
136C2×C4×C173C2×D411yescharacteristic
137C2×C4×C173C2×D411yescharacteristic
138C2×C4×C173C2×D411yescharacteristic
139C2×C4×C173C2×D411yescharacteristic
140C2×C4×C173C2411yescharacteristic
141C8×C173—21no—
142C8×C173—21no—
143C8×C173—21no—
144C8×C173—21no—
145C22×C173—21no—
146C22×C173—21no—
147C22×C173—21no—
148C22×C173C22×D411yescharacteristic
149C2×D173—22no—
150C2×D173—41no—
151C2×D173—41no—
152C2×D173—41no—
153C2×D173—41no—
154C2×D173—41no—
155C4×C173—21no—
156C4×C173—21no—
157C4×C173—21no—
158C4×C173—21no—
159C4×C173—21no—
160C4×C173C2×#4111yescharacteristic
161C4×C173C2×#4111yescharacteristic
162Dic173—22no—
163Dic173—41no—
164Dic173—41no—
165Dic173—41no—
166Dic173—41no—
167Dic173—41no—
168C2×C173—41no—
169C2×C173#52511yescharacteristic
170C2×C173#57611yescharacteristic
171C2×C173#57811yescharacteristic
172D173—42no—
173D173—81no—
174C173#312411yescharacteristic, complemented, Sylow
175#3124—1731nomaximal, Sylow
176#542—1731no—
177#520—1731no—
178#484—1731no—
179#480—1731no—
180#477—1731no—
181#474—1731no—
182#464—1731no—
183#463—1731no—
184#452—1731no—
185#449—1731no—
186#440—1731no—
187#440—1731no—
188C4×Q16—1731no—
189C4×D8—1731no—
190#433D17311yescharacteristic, complemented
191C2×#41—1731no—
192C2×Q16—1731no—
193C2×SD16—1731no—
194C2×SD16—1731no—
195C2×D8—1731no—
196C4⋊Q8—1731no—
197#126—3461no—
198#124—3461no—
199#124—1731no—
200#123—3461no—
201C22⋊Q8—3461no—
202C22⋊Q8—1731no—
203#121—1731no—
204C4×Q8—1731no—
205C4×Q8—1731no—
206C4×Q8—1731no—
207C4×D4—3461no—
208C4×D4—3461no—
209C4×D4—1731no—
210C4×D4—1731no—
211C4×D4—1731no—
212#117—3461no—
213#117C2×D17311yescharacteristic
214C2×C4⋊C4—3461no—
215C2×C4⋊C4—1731no—
216#107—1731no—
217#107—1731no—
218#107—1731no—
219#107—1731no—
220C4⋊C8C2×D17311yescharacteristic
221C4⋊C8C2×D17311yescharacteristic
222#103—1731no—
223#103—1731no—
224#103—1731no—
225#103—1731no—
226#102—1731no—
227#102—1731no—
228#102—1731no—
229#102—1731no—
230C22⋊C8C2×D17311yescharacteristic
231C22⋊C8C2×D17311yescharacteristic
232#97C2×D17311yescharacteristic
233C4×C8C2×D17311yescharacteristic
234#41—3462no—
235#41—3462no—
236C2×Q8—3461no—
237C2×Q8—1731no—
238C2×Q8—1731no—
239C2×D4—3461no—
240C2×D4—3461no—
241C2×D4—1731no—
242C2×D4—1731no—
243C22×C4—3461no—
244C22×C4—3461no—
245C22×C4—3461no—
246C22×C4—3461no—
247C22×C4—3461no—
248C22×C4C22×D17311yescharacteristic
249Q16—3462no—
250SD16—3462no—
251SD16—3462no—
252D8—3462no—
253C2×C8C22×D17311yescharacteristic
254C2×C8C22×D17311yescharacteristic
255C2×C8C22×D17311yescharacteristic
256C2×C8C22×D17311yescharacteristic
257C4⋊C4—3461no—
258C4⋊C4—3461no—
259C4⋊C4—3461no—
260C4⋊C4—3461no—
261C4⋊C4—3461no—
262C4⋊C4—3461no—
263C4⋊C4—1731no—
264C4⋊C4—1731no—
265C4⋊C4—1731no—
266C4⋊C4—1731no—
267C4⋊C4D69211yescharacteristic
268C4⋊C4D69211yescharacteristic
269C22⋊C4—3461no—
270C22⋊C4—3461no—
271C22⋊C4—3461no—
272C22⋊C4—3461no—
273C22⋊C4—3461no—
274C22⋊C4—3461no—
275C22⋊C4—3461no—
276C22⋊C4D69211yescharacteristic
277C22⋊C4D69211yescharacteristic
278C42—3461no—
279C42—3461no—
280C42—3461no—
281C42C22×D17311yescharacteristic
282C42C22×D17311yescharacteristic
283C23—3461no—
284C23—3461no—
285C23C2×D69211yescharacteristic
286Q8—3461no—
287Q8—3461no—
288Q8—3461no—
289Q8—13841no—
290Q8—1732no—
291D4—3464no—
292D4—3461no—
293D4—3461no—
294D4—3461no—
295D4—13841no—
296D4—1732no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—3464no—
300C2×C4—3461no—
301C2×C4—3461no—
302C2×C4—3461no—
303C2×C4—3461no—
304C2×C4—3461no—
305C2×C4—3461no—
306C2×C4—13841no—
307C2×C4—13841no—
308C2×C4—13841no—
309C2×C4—13841no—
310C2×C4C2×D69211yescharacteristic
311C2×C4C2×D69211yescharacteristic
312C2×C4C2×D69211yescharacteristic
313C2×C4C2×D69211yescharacteristic
314C2×C4C2×D69211yescharacteristic
315C2×C4C23×D17311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—3462no—
324C22—6921no—
325C22—6921no—
326C22—6921no—
327C22—6921no—
328C22—6921no—
329C22C22×D69211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—3462no—
336C4—6921no—
337C4—6921no—
338C4—6921no—
339C4—6921no—
340C4—6921no—
341C4#41×D17311yescharacteristic
342C4#41×D17311yescharacteristic
343C2—41no—
344C2—13841no—
345C2—6922no—
346C2#2601200311yescharacteristic
347C2#2601229611yescharacteristic
348C2#2601230811yescharacteristic
subgroupG/H
centerC22C22×D692
commutator, cosocleC2×C4×C173C24
FrattiniC2×C4C23×D173
Fitting#433×C173C2
socleC22×C173C22×D4
prime radical#26011638C2
hypercenter#433D173
hypocenterC173#3124
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. #26012112C2semidirect
2. #26011971C2semidirect
3. #26011827C2semidirect
4. #26011805C2semidirect
5. #26011787C2semidirect
6. #26011772C2semidirect
7. #26011714C2semidirect
8. #26011707C2semidirect
9. #26011655C2semidirect
11. #26011593C2semidirect
12. #26011593C2semidirect
13. C4×Dic692C2semidirect
14. C4×D1384C2semidirect
15. #433×C173C2semidirect
174. C173#3124semidirect
190. #433D173semidirect

Maximal subgroups

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

subgroupindex
#260121122
#260119712
#260118272
#260118052
#260117872
#260117722
#260117142
#260117072
#260116552
#260116382
#260115932
C4×Dic6922
C4×D13842
#433×C1732
#3124173