Finite Group Databasebeta

← #31814625

Subgroups — #31814625

Order 17792.

400 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22580890C211yesmaximal, characteristic, complemented
2#22580888C211yesmaximal, characteristic, complemented
3#22580887C211yesmaximal, characteristic, complemented
4#22580887C211yesmaximal, characteristic, complemented
5#22580882C211yesmaximal, characteristic, complemented
6#22580882C211yesmaximal, characteristic, complemented
7#22580875C211yesmaximal, characteristic, complemented
8#22580875C211yesmaximal, characteristic, complemented
9#22580871C211yesmaximal, characteristic
10#22580871C211yesmaximal, characteristic
11#22580871C211yesmaximal, characteristic
12#22580850C211yesmaximal, characteristic, complemented
13#22580845C211yesmaximal, characteristic, complemented
14#22580843C211yesmaximal, characteristic, complemented
15#400×C139C211yesmaximal, characteristic, complemented
16C22×D556C2211yescharacteristic
17C2×C4⋊Dic139C2211yescharacteristic
18C2×C4⋊Dic139C2211yescharacteristic
19C2×C4⋊Dic139C2211yescharacteristic
20C2×Dic139⋊C4C2211yescharacteristic
21C2×Dic139⋊C4C2211yescharacteristic
22C2×Dic139⋊C4C2211yescharacteristic
23C2×Dic139⋊C4C2211yescharacteristic
24C2×Dic139⋊C4C2211yescharacteristic
25C2×Dic139⋊C4C2211yescharacteristic
26C2×(C2×D139)⋊C4C2211yescharacteristic
27C2×(C2×D139)⋊C4C2211yescharacteristic
28C2×(C2×D139)⋊C4C2211yescharacteristic
29C2×(C2×D139)⋊C4C2211yescharacteristic
30C2×(C2×D139)⋊C4C2211yescharacteristic
31C2×(C2×D139)⋊C4C2211yescharacteristic
32C2×(C2×D139)⋊C4C2211yescharacteristic
33C2×(C2×D139)⋊C4C2211yescharacteristic
34C2×(C2×D139)⋊C4C2211yescharacteristic
35C2×(C2×D139)⋊C4C2211yescharacteristic
36C2×(C2×D139)⋊C4C2211yescharacteristic
37C2×(C2×D139)⋊C4C2211yescharacteristic
38C2×C4×Dic139C2211yescharacteristic
39C139⋊#95C2211yescharacteristic
40C139⋊#95C2211yescharacteristic
41C139⋊#95C2211yescharacteristic
42C139⋊#95C2211yescharacteristic
43C139⋊#95C2211yescharacteristic
44C2×C4⋊C4×C139C2211yescharacteristic
45C2×C4⋊C4×C139C2211yescharacteristic
46#95×C139C2211yescharacteristic
47#95×C139C2211yescharacteristic
48#95×C139C2211yescharacteristic
49#95×C139C2211yescharacteristic
50#95×C139C2211yescharacteristic
51C23×D139C2311yescharacteristic
52C23×D139C2311yescharacteristic
53C2×D556—41no—
54C2×D556—41no—
55C2×D556—41no—
56C22×Dic139C2311yescharacteristic
57C22×Dic139C2311yescharacteristic
58C22×Dic139C2311yescharacteristic
59C22×Dic139C2311yescharacteristic
60C22×Dic139C2311yescharacteristic
61C22×Dic139C2311yescharacteristic
62C4⋊Dic139—41no—
63C4⋊Dic139—41no—
64C4⋊Dic139—41no—
65Dic139⋊C4—22no—
66Dic139⋊C4—41no—
67Dic139⋊C4—41no—
68Dic139⋊C4—41no—
69Dic139⋊C4—41no—
70Dic139⋊C4—41no—
71(C2×D139)⋊C4—22no—
72(C2×D139)⋊C4—22no—
73(C2×D139)⋊C4—41no—
74(C2×D139)⋊C4—41no—
75(C2×D139)⋊C4—41no—
76(C2×D139)⋊C4—41no—
77(C2×D139)⋊C4—41no—
78(C2×D139)⋊C4—41no—
79(C2×D139)⋊C4—41no—
80(C2×D139)⋊C4—41no—
81(C2×D139)⋊C4—41no—
82(C2×D139)⋊C4—41no—
83C4×Dic139—41no—
84C22×C4×C139C2311yescharacteristic
85C22×C4×C139C2311yescharacteristic
86C22×C4×C139C2311yescharacteristic
87C22×C4×C139C2311yescharacteristic
88C22×C4×C139C2311yescharacteristic
89C22×C4×C139C2311yescharacteristic
90C22×C4×C139C2311yescharacteristic
91C4⋊C4×C139—41no—
92C4⋊C4×C139—41no—
93C22×D139—21no—
94C22×D139—21no—
95C22×D139—21no—
96C22×D139—21no—
97C22×D139—21no—
98C22×D139—21no—
99C22×D139—21no—
100C22×D139—21no—
101C22×D139—21no—
102C22×D139—21no—
103C22×D139—21no—
104C22×D139—21no—
105C22×D139—21no—
106C22×D139—21no—
107D556—44no—
108C2×Dic139—21no—
109C2×Dic139—21no—
110C2×Dic139—21no—
111C2×Dic139—21no—
112C2×Dic139—21no—
113C2×Dic139—21no—
114C2×Dic139—21no—
115C2×Dic139—21no—
116C2×Dic139—21no—
117C2×Dic139—21no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C2×Dic139—21no—
122C2×Dic139—21no—
123C2×Dic139—21no—
124C2×Dic139—21no—
125C2×Dic139#4112yes—
126C23×C139C2411yescharacteristic
127C2×C4×C139—21no—
128C2×C4×C139—21no—
129C2×C4×C139—21no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—21no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—21no—
145C2×C4×C139—21no—
146C2×C4×C139—21no—
147C2×C4×C139—21no—
148C22×C139C2×#4111yescharacteristic
149C22×C139H(5,𝔽2)11yescharacteristic
150C22×C139H(5,𝔽2)11yescharacteristic
151C22×C139H(5,𝔽2)11yescharacteristic
152C22×C139H(5,𝔽2)11yescharacteristic
153C22×C1392−1+411yescharacteristic
154C22×C1392−1+411yescharacteristic
155C2×D139—41no—
156C2×D139—41no—
157C2×D139—41no—
158C2×D139—41no—
159C2×D139—41no—
160C2×D139—41no—
161C2×D139—41no—
162C2×D139—41no—
163C2×D139—41no—
164C2×D139—41no—
165C2×D139—41no—
166C2×D139—41no—
167C2×D139—41no—
168C2×D139—41no—
169C4×C139—41no—
170C4×C139—41no—
171C4×C139—41no—
172C4×C139—41no—
173C4×C139—41no—
174C4×C139—41no—
175C4×C139—41no—
176Dic139—22no—
177Dic139—41no—
178Dic139—41no—
179Dic139—41no—
180Dic139—41no—
181Dic139—41no—
182C2×C139#53911yescharacteristic
183C2×C139#54011yescharacteristic
184C2×C139#54211yescharacteristic
185C2×C139#56011yescharacteristic
186C2×C139#56211yescharacteristic
187C2×C139#56211yescharacteristic
188C2×C139#56311yescharacteristic
189D139—81no—
190D139—81no—
191C139#283711yescharacteristic, complemented, Sylow
192#2837—1391nomaximal, Sylow
193#400D13911yescharacteristic, complemented
194#399—1391no—
195#399—1391no—
196#398—1391no—
197#398—1391no—
198#397—1391no—
199#397—1391no—
200#396—1391no—
201#396—1391no—
202#394—1391no—
203#394—1391no—
204#394—1391no—
205#389—1391no—
206#388—1391no—
207#388—1391no—
208C22×D4—1391no—
209C2×C4⋊C4—1391no—
210C2×C4⋊C4—1391no—
211C2×C4⋊C4—1391no—
212C2×C4⋊C4—1391no—
213C2×C4⋊C4—1391no—
214C2×C4⋊C4—1391no—
215C2×C4⋊C4—1391no—
216C2×C4⋊C4—1391no—
217C2×C4⋊C4—1391no—
218C2×C4⋊C4C2×D13911yescharacteristic
219C2×C4⋊C4C2×D13911yescharacteristic
220C2×C22⋊C4—1391no—
221C2×C22⋊C4—1391no—
222C2×C22⋊C4—1391no—
223C2×C22⋊C4—1391no—
224C2×C22⋊C4—1391no—
225C2×C22⋊C4—1391no—
226C2×C22⋊C4—1391no—
227C2×C22⋊C4—1391no—
228C2×C22⋊C4—1391no—
229C2×C22⋊C4—1391no—
230C2×C22⋊C4—1391no—
231C2×C22⋊C4—1391no—
232C2×C42—1391no—
233#95—1391no—
234#95—1391no—
235#95—1391no—
236#95—1391no—
237#95—1391no—
238#95C2×D13911yescharacteristic
239#95C2×D13911yescharacteristic
240#95C2×D13911yescharacteristic
241#95C2×D13911yescharacteristic
242#95C2×D13911yescharacteristic
243C24—1391no—
244C24—1391no—
245C2×D4—5561no—
246C2×D4—5561no—
247C2×D4—5561no—
248C22×C4—1391no—
249C22×C4—1391no—
250C22×C4—1391no—
251C22×C4—1391no—
252C22×C4—1391no—
253C22×C4—1391no—
254C22×C4C22×D13911yescharacteristic
255C22×C4C22×D13911yescharacteristic
256C22×C4C22×D13911yescharacteristic
257C22×C4C22×D13911yescharacteristic
258C22×C4C22×D13911yescharacteristic
259C22×C4C22×D13911yescharacteristic
260C22×C4C22×D13911yescharacteristic
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—2782no—
264C4⋊C4—5561no—
265C4⋊C4—5561no—
266C4⋊C4—5561no—
267C4⋊C4—5561no—
268C4⋊C4—5561no—
269C4⋊C4—5561no—
270C4⋊C4—5561no—
271C4⋊C4—5561no—
272C22⋊C4—2782no—
273C22⋊C4—2782no—
274C22⋊C4—5561no—
275C22⋊C4—5561no—
276C22⋊C4—5561no—
277C22⋊C4—5561no—
278C22⋊C4—5561no—
279C22⋊C4—5561no—
280C22⋊C4—5561no—
281C22⋊C4—5561no—
282C22⋊C4—5561no—
283C22⋊C4—5561no—
284C42—5561no—
285C23—2781no—
286C23—2781no—
287C23—2781no—
288C23—2781no—
289C23—2781no—
290C23—2781no—
291C23—2781no—
292C23—2781no—
293C23—2781no—
294C23—2781no—
295C23—2781no—
296C23—2781no—
297C23—2781no—
298C23—2781no—
299C23C23×D13911yescharacteristic
300D4—5564no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—2781no—
323C2×C4—2781no—
324C2×C4—2781no—
325C2×C4—2781no—
326C2×C4—2781no—
327C2×C4—2781no—
328C2×C4—2781no—
329C2×C4—2781no—
330C2×C4—2781no—
331C2×C4—2781no—
332C2×C4—2781no—
333C2×C4—2781no—
334C2×C4—2781no—
335C2×C4—2781no—
336C2×C4—2781no—
337C2×C4—2781no—
338C2×C4—2781no—
339C2×C4—1392no—
340C22—5561no—
341C22—5561no—
342C22—5561no—
343C22—5561no—
344C22—5561no—
345C22—5561no—
346C22—5561no—
347C22—5561no—
348C22—5561no—
349C22—5561no—
350C22—5561no—
351C22—5561no—
352C22—5561no—
353C22—5561no—
354C22#41×D13911yescharacteristic
355C22#1798488711yescharacteristic
356C22#1798488811yescharacteristic
357C22#1798488811yescharacteristic
358C22#1798488811yescharacteristic
359C22#1798488911yescharacteristic
360C22#1798489011yescharacteristic
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2782no—
369C4—5561no—
370C4—5561no—
371C4—5561no—
372C4—5561no—
373C4—5561no—
374C2—11121no—
375C2—11121no—
376C2#2258155111yescharacteristic
377C2#2258155511yescharacteristic
378C2#2258156911yescharacteristic
379C2#2258169411yescharacteristic
380C2#2258169711yescharacteristic
381C2#2258169911yescharacteristic
382C2#2258170711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, cosocleC23×C139C24
Fitting#400×C139C2
prime radicalC22×D556C22
hypercenter#400D139
hypocenterC139#2837
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #22580890C2semidirect
2. #22580888C2semidirect
3. #22580887C2semidirect
4. #22580887C2semidirect
5. #22580882C2semidirect
6. #22580882C2semidirect
7. #22580875C2semidirect
8. #22580875C2semidirect
12. #22580850C2semidirect
13. #22580845C2semidirect
14. #22580843C2semidirect
15. #400×C139C2semidirect
191. C139#2837semidirect
193. #400D139semidirect

Maximal subgroups

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

subgroupindex
#225808902
#225808882
#225808872
#225808822
#225808752
#225808712
#225808502
#225808452
#225808432
#400×C1392
#2837139