Finite Group Databasebeta

← #36364674

Subgroups — #36364674

Order 22144.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26012112C211yesmaximal, characteristic, complemented
2#26012067C211yesmaximal, characteristic, complemented
3#26011885C211yesmaximal, characteristic, complemented
4#26011875C211yesmaximal, characteristic, complemented
5#26011851C211yesmaximal, characteristic, complemented
6#26011842C211yesmaximal, characteristic, complemented
7#26011714C211yesmaximal, characteristic, complemented
8#26011707C211yesmaximal, characteristic, complemented
9#26011702C211yesmaximal, characteristic, complemented
10#26011697C211yesmaximal, characteristic, complemented
11#26011655C211yesmaximal, characteristic, complemented
12#26011649C211yesmaximal, characteristic, complemented
13#26011638C211yesmaximal, characteristic
14#26011632C211yesmaximal, characteristic, complemented
15#433×C173C211yesmaximal, characteristic, complemented
16C2×#14583826C2211yescharacteristic
17C22×Dic346C2211yescharacteristic
18C2×Dic692C2211yescharacteristic
19C2×Dic692C2211yescharacteristic
20C2×Dic692C2211yescharacteristic
21C2×#14583815C2211yescharacteristic
22C2×#14583815C2211yescharacteristic
23C2×#14583815C2211yescharacteristic
24C2×#14583815C2211yescharacteristic
25C2×D1384C2211yescharacteristic
26#19149679C2211yescharacteristic
27#19149679C2211yescharacteristic
28#19149679C2211yescharacteristic
29#19149674—21no—
30#19149667C2211yescharacteristic
31#19149667C2211yescharacteristic
32#19149667C2211yescharacteristic
33#19149665—21no—
34#19149663—21no—
35#19149663—21no—
36#19149661—21no—
37#19149659—21no—
38#19149659—21no—
39#19149658C2211yescharacteristic
40#19149657—21no—
41#19149653C2211yescharacteristic
42C4×Dic346C2211yescharacteristic
43C4×D692C2211yescharacteristic
44#19149604C2211yescharacteristic
45#19149604C2211yescharacteristic
46#19149604C2211yescharacteristic
47#19149604C2211yescharacteristic
48#19149604C2211yescharacteristic
49#19149604C2211yescharacteristic
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—41no—
60#14583826—41no—
61C2×Dic346—21no—
62C2×Dic346—21no—
63C2×Dic346—41no—
64C2×Dic346—41no—
65C2×Dic346C2311yescharacteristic
66C2×Dic346C2311yescharacteristic
67C2×Dic346C2311yescharacteristic
68C2×Dic346C2311yescharacteristic
69C2×D692C2311yescharacteristic
70C2×D692C2311yescharacteristic
71C2×C22⋊D173—21no—
72C2×C22⋊D173—21no—
73C22×Dic173—21no—
74C2×C4×D173—21no—
75C2×C4×D173—21no—
76Dic692—41no—
77Dic692—41no—
78Dic692—41no—
79#14583815—41no—
80#14583815—41no—
81#14583815—41no—
82#14583815—41no—
83D1384—41no—
84C4⋊Dic173—21no—
85C4⋊Dic173—21no—
86C4⋊Dic173—21no—
87C4⋊Dic173—21no—
88C4⋊Dic173—21no—
89C4⋊Dic173C2311yescharacteristic
90C4⋊Dic173C2311yescharacteristic
91#14583805—21no—
92#14583805—21no—
93C22⋊Dic173—21no—
94#14583803—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—
103C22×C4×C173C2311yescharacteristic
104C2×C8×C173C2311yescharacteristic
105C2×C8×C173C2311yescharacteristic
106C2×C8×C173C2311yescharacteristic
107C2×C8×C173C2311yescharacteristic
108C4⋊C4×C173D411yescharacteristic
109C4⋊C4×C173D411yescharacteristic
110C22⋊C4×C173D411yescharacteristic
111C22⋊C4×C173D411yescharacteristic
112C42×C173C2311yescharacteristic
113C42×C173C2311yescharacteristic
114C22×D173—21no—
115C22×D173—21no—
116Dic346—21no—
117Dic346—21no—
118Dic346—21no—
119Dic346—21no—
120Dic346—21no—
121Dic346—21no—
122Dic346—21no—
123Dic346—21no—
124Dic346—42no—
125Dic346—81no—
126D692—21no—
127D692—21no—
128D692—21no—
129D692—21no—
130C22⋊D173—42no—
131C22⋊D173—81no—
132C2×Dic173—21no—
133C2×Dic173—21no—
134C2×Dic173—21no—
135C2×Dic173—21no—
136C2×Dic173—21no—
137C2×Dic173—21no—
138C2×Dic173—42no—
139C4×D173—42no—
140C4×D173—81no—
141C23×C173C2×D411yescharacteristic
142C2×C4×C173—21no—
143C2×C4×C173—21no—
144C2×C4×C173C2×D411yescharacteristic
145C2×C4×C173C2×D411yescharacteristic
146C2×C4×C173C2×D411yescharacteristic
147C2×C4×C173C2×D411yescharacteristic
148C2×C4×C173C2×D411yescharacteristic
149C2×C4×C173C2411yescharacteristic
150C8×C173—21no—
151C8×C173—21no—
152C8×C173—21no—
153C8×C173—21no—
154C22×C173—21no—
155C22×C173—21no—
156C22×C173—21no—
157C22×C173C22×D411yescharacteristic
158C2×D173—41no—
159C2×D173—41no—
160C2×D173—41no—
161C2×D173—41no—
162C2×D173—41no—
163C2×D173—41no—
164C4×C173—21no—
165C4×C173—21no—
166C4×C173—21no—
167C4×C173—21no—
168C4×C173—21no—
169C4×C173H(5,𝔽2)11yescharacteristic
170C4×C173H(5,𝔽2)11yescharacteristic
171Dic173—41no—
172Dic173—41no—
173Dic173—41no—
174Dic173—41no—
175Dic173—41no—
176Dic173—41no—
177C2×C173—41no—
178C2×C173#53511yescharacteristic
179C2×C173#57711yescharacteristic
180C2×C173#57811yescharacteristic
181D173—81no—
182D173—81no—
183C173#322511yescharacteristic, complemented, Sylow
184#3225—1731nomaximal, Sylow
185#542—1731no—
186#536—1731no—
187#497—1731no—
188#495—1731no—
189#489—1731no—
190#487—1731no—
191#464—1731no—
192#463—1731no—
193#462—1731no—
194#461—1731no—
195#452—1731no—
196#451—1731no—
197#449—1731no—
198#448—1731no—
199#433D17311yescharacteristic, complemented
200C2×#41—1731no—
201C22×Q8—1731no—
202C2×Q16—1731no—
203C2×Q16—1731no—
204C2×Q16—1731no—
205C2×SD16—1731no—
206C2×SD16—1731no—
207C2×SD16—1731no—
208C2×SD16—1731no—
209C2×D8—1731no—
210C4⋊Q8—1731no—
211C4⋊Q8—1731no—
212C4⋊Q8—1731no—
213#126—3461no—
214#124—3461no—
215#124—1731no—
216#124—1731no—
217#124—1731no—
218#123—3461no—
219#123—3461no—
220#123—3461no—
221C22⋊Q8—3461no—
222C22⋊Q8—3461no—
223C22⋊Q8—3461no—
224C22⋊Q8—1731no—
225#121—1731no—
226C4×Q8—1731no—
227C4×D4—1731no—
228#117C2×D17311yescharacteristic
229C4⋊C8C2×D17311yescharacteristic
230C4⋊C8C2×D17311yescharacteristic
231#103—1731no—
232#103—1731no—
233#103—1731no—
234#103—1731no—
235#103—1731no—
236#103—1731no—
237#102—1731no—
238#102—1731no—
239C22⋊C8C2×D17311yescharacteristic
240C22⋊C8C2×D17311yescharacteristic
241#97C2×D17311yescharacteristic
242C4×C8C2×D17311yescharacteristic
243#41—6921no—
244#41—6921no—
245C2×Q8—3461no—
246C2×Q8—3461no—
247C2×Q8—1731no—
248C2×Q8—1731no—
249C2×Q8—1731no—
250C2×Q8—1731no—
251C2×Q8—6921no—
252C2×Q8—6921no—
253C2×D4—3461no—
254C2×D4—3461no—
255C2×D4—1731no—
256C2×D4—1731no—
257C22×C4—3461no—
258C22×C4—3461no—
259C22×C4—3461no—
260C22×C4C22×D17311yescharacteristic
261Q16—6921no—
262Q16—6921no—
263Q16—6921no—
264SD16—6921no—
265SD16—6921no—
266SD16—6921no—
267SD16—6921no—
268D8—6921no—
269C2×C8C22×D17311yescharacteristic
270C2×C8C22×D17311yescharacteristic
271C2×C8C22×D17311yescharacteristic
272C2×C8C22×D17311yescharacteristic
273C4⋊C4—3461no—
274C4⋊C4—3461no—
275C4⋊C4—3461no—
276C4⋊C4—3461no—
277C4⋊C4—3461no—
278C4⋊C4—3461no—
279C4⋊C4—3461no—
280C4⋊C4—1731no—
281C4⋊C4—1731no—
282C4⋊C4D69211yescharacteristic
283C4⋊C4D69211yescharacteristic
284C22⋊C4—3461no—
285C22⋊C4—3461no—
286C22⋊C4—3461no—
287C22⋊C4—3461no—
288C22⋊C4—3461no—
289C22⋊C4—3461no—
290C22⋊C4—3461no—
291C22⋊C4—3461no—
292C22⋊C4—3461no—
293C22⋊C4D69211yescharacteristic
294C22⋊C4D69211yescharacteristic
295C42—3461no—
296C42C22×D17311yescharacteristic
297C42C22×D17311yescharacteristic
298C23—3461no—
299C23—3461no—
300C23C2×D69211yescharacteristic
301Q8—3461no—
302Q8—3461no—
303Q8—3461no—
304Q8—3461no—
305Q8—3461no—
306Q8—3461no—
307Q8—3461no—
308Q8—3461no—
309Q8—13841no—
310Q8—6922no—
311D4—3461no—
312D4—3461no—
313D4—3461no—
314D4—3461no—
315D4—13841no—
316D4—6922no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—3461no—
320C2×C4—3461no—
321C2×C4—3461no—
322C2×C4—3461no—
323C2×C4—3461no—
324C2×C4—3461no—
325C2×C4—13841no—
326C2×C4—6922no—
327C2×C4—6922no—
328C2×C4C2×D69211yescharacteristic
329C2×C4C2×D69211yescharacteristic
330C2×C4C2×D69211yescharacteristic
331C2×C4C2×D69211yescharacteristic
332C2×C4C2×D69211yescharacteristic
333C2×C4C23×D17311yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—6921no—
342C22—6921no—
343C22—6921no—
344C22—6921no—
345C22—6921no—
346C22—6921no—
347C22C22×D69211yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—6921no—
354C4—6921no—
355C4—6921no—
356C4—6921no—
357C4—6921no—
358C4—6921no—
359C4#1914972511yescharacteristic
360C4#1914972511yescharacteristic
361C2—41no—
362C2—13841no—
363C2—13841no—
364C2#2601206011yescharacteristic
365C2#2601230311yescharacteristic
366C2#2601230811yescharacteristic
subgroupG/H
centerC22C22×D692
commutator, cosocleC2×C4×C173C24
FrattiniC2×C4C23×D173
Fitting#433×C173C2
socleC22×C173C22×D4
prime radical#26011638C2
hypercenter#433D173
hypocenterC173#3225
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. #26012067C2semidirect
3. #26011885C2semidirect
4. #26011875C2semidirect
5. #26011851C2semidirect
6. #26011842C2semidirect
7. #26011714C2semidirect
8. #26011707C2semidirect
9. #26011702C2semidirect
10. #26011697C2semidirect
11. #26011655C2semidirect
12. #26011649C2semidirect
14. #26011632C2semidirect
15. #433×C173C2semidirect
183. C173#3225semidirect
199. #433D173semidirect

Maximal subgroups

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

subgroupindex
#260121122
#260120672
#260118852
#260118752
#260118512
#260118422
#260117142
#260117072
#260117022
#260116972
#260116552
#260116492
#260116382
#260116322
#433×C1732
#3225173