Finite Group Databasebeta

← #31819470

Subgroups — #31819470

Order 17792.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581688C211yesmaximal, characteristic, complemented
2#22581345C211yesmaximal, characteristic, complemented
3#22581343C211yesmaximal, characteristic
4#22581335C211yesmaximal, characteristic, complemented
5#22581175C211yesmaximal, characteristic, complemented
6#22581172C211yesmaximal, characteristic, complemented
7#22581168C211yesmaximal, characteristic, complemented
8#22581165C211yesmaximal, characteristic, complemented
9#22581155C211yesmaximal, characteristic, complemented
10#22581153C211yesmaximal, characteristic, complemented
11#22581084C211yesmaximal, characteristic, complemented
12#22581063C211yesmaximal, characteristic, complemented
13#22581058C211yesmaximal, characteristic, complemented
14C4×#14555772C211yesmaximal, characteristic, complemented
15#556×C139C211yesmaximal, characteristic, complemented
16C2×#14555775C2211yescharacteristic
17C2×#14555775C2211yescharacteristic
18C2×#14555773C2211yescharacteristic
19C2×#14555772C2211yescharacteristic
20C2×#14555772C2211yescharacteristic
21C2×#14555772C2211yescharacteristic
22C2×#14555772C2211yescharacteristic
23C2×#14555770C2211yescharacteristic
24C2×#14555770C2211yescharacteristic
25#17984839C2211yescharacteristic
26#17984831—21no—
27#17984830C2211yescharacteristic
28#17984830C2211yescharacteristic
29#17984827—21no—
30#17984827—21no—
31C4×Dic278C2211yescharacteristic
32C4×D556C2211yescharacteristic
33C4×D556C2211yescharacteristic
34#17984804—21no—
35#17984773C2211yescharacteristic
36C4⋊(C139⋊C8)C2211yescharacteristic
37C4⋊(C139⋊C8)C2211yescharacteristic
38C4⋊(C139⋊C8)C2211yescharacteristic
39#17984766C2211yescharacteristic
40#17984766C2211yescharacteristic
41#17984765C2211yescharacteristic
42#17984763C2211yescharacteristic
43#17984762C2211yescharacteristic
44#17984762C2211yescharacteristic
45#17984753C2211yescharacteristic
46#17984753C2211yescharacteristic
47C4×C139⋊C8C2211yescharacteristic
48C4⋊Q8×C139C2211yescharacteristic
49#126×C139—21no—
50#126×C139—21no—
51#124×C139C2211yescharacteristic
52#124×C139C2211yescharacteristic
53C22⋊Q8×C139—21no—
54C4×Q8×C139C2211yescharacteristic
55C4×Q8×C139C2211yescharacteristic
56C4×Q8×C139C2211yescharacteristic
57C4×D4×C139C2211yescharacteristic
58#117×C139—21no—
59C2×Dic278C2311yescharacteristic
60C2×D556—21no—
61C2×D556—21no—
62C2×D556C2311yescharacteristic
63C2×D556C2311yescharacteristic
64C2×C4×D139—21no—
65C2×C4×D139—21no—
66#14555775—22no—
67#14555775—41no—
68#14555773—41no—
69#14555772—22no—
70#14555772—41no—
71#14555772—41no—
72#14555772—41no—
73#14555770—22no—
74#14555770—41no—
75C2×C139⋊C8C2311yescharacteristic
76C2×C139⋊C8C2311yescharacteristic
77C2×C139⋊C8C2311yescharacteristic
78C2×C139⋊C8C2311yescharacteristic
79C4⋊Dic139C2311yescharacteristic
80Dic139⋊C4—21no—
81(C2×D139)⋊C4—21no—
82(C2×D139)⋊C4—21no—
83(C2×D139)⋊C4—21no—
84(C2×D139)⋊C4—21no—
85(C2×D139)⋊C4—21no—
86(C2×D139)⋊C4—21no—
87C4×Dic139—21no—
88C2×Q8×C139D411yescharacteristic
89C2×Q8×C139C2311yescharacteristic
90C2×Q8×C139C2311yescharacteristic
91C2×D4×C139C2311yescharacteristic
92C22×C4×C139—21no—
93C4⋊C4×C139—21no—
94C4⋊C4×C139—21no—
95C4⋊C4×C139—21no—
96C4⋊C4×C139—21no—
97C4⋊C4×C139D411yescharacteristic
98C4⋊C4×C139D411yescharacteristic
99C4⋊C4×C139D411yescharacteristic
100C4⋊C4×C139C2311yescharacteristic
101C22⋊C4×C139—21no—
102C22⋊C4×C139—21no—
103C22⋊C4×C139—21no—
104C22⋊C4×C139—21no—
105C22⋊C4×C139—21no—
106C42×C139—21no—
107C42×C139—21no—
108C42×C139C2311yescharacteristic
109C42×C139C2311yescharacteristic
110C42×C139C2311yescharacteristic
111C22×D139—21no—
112C22×D139—21no—
113Dic278—21no—
114Dic278—21no—
115D556—21no—
116D556—21no—
117D556—21no—
118D556—21no—
119D556—42no—
120D556—81no—
121C2×Dic139—21no—
122C2×Dic139—21no—
123C4×D139—81no—
124C4×D139—81no—
125C139⋊C8—21no—
126C139⋊C8—21no—
127C139⋊C8—21no—
128C139⋊C8#4112yes—
129C23×C139—21no—
130Q8×C139—21no—
131Q8×C139—21no—
132Q8×C139—21no—
133Q8×C139—21no—
134Q8×C139—41no—
135D4×C139—21no—
136D4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—21no—
139C2×C4×C139—21no—
140C2×C4×C139—42no—
141C2×C4×C139C2×D411yescharacteristic
142C2×C4×C139C2×D411yescharacteristic
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2×D411yescharacteristic
145C2×C4×C139C2×D411yescharacteristic
146C2×C4×C139C2×D411yescharacteristic
147C2×C4×C139C2411yescharacteristic
148C22×C139—41no—
149C22×C139—41no—
150C22×C139—41no—
151C22×C139C22×D411yescharacteristic
152C2×D139—41no—
153C2×D139—41no—
154C2×D139—41no—
155C2×D139—41no—
156C2×D139—41no—
157C2×D139—41no—
158C4×C139—21no—
159C4×C139—21no—
160C4×C139—21no—
161C4×C139—21no—
162C4×C139—21no—
163C4×C139—21no—
164C4×C139—41no—
165C4×C139—41no—
166C4×C139—41no—
167C4×C139C2×#4111yescharacteristic
168C4×C139H(5,𝔽2)11yescharacteristic
169Dic139—41no—
170Dic139—41no—
171C2×C139—81no—
172C2×C139#55011yescharacteristic
173C2×C139#57511yescharacteristic
174C2×C139#57711yescharacteristic
175D139—81no—
176D139—81no—
177C139#340111yescharacteristic, complemented, Sylow
178#3401—1391nomaximal, Sylow
179#559—1391no—
180#556D13911yescharacteristic, complemented
181#497—1391no—
182#496—1391no—
183#495—1391no—
184#464—1391no—
185#464—1391no—
186#463—1391no—
187#463—1391no—
188#461—1391no—
189#460—1391no—
190#446—1391no—
191#442—1391no—
192#441—1391no—
193C4×SD16—1391no—
194C2×Q16—1391no—
195C2×Q16—1391no—
196C2×SD16—1391no—
197C2×SD16—1391no—
198C2×SD16—1391no—
199C2×SD16—1391no—
200C2×SD16—1391no—
201C2×D8—1391no—
202C2×D8—1391no—
203C4⋊Q8C2×D13911yescharacteristic
204#127—1391no—
205#126—21no—
206#126—21no—
207#124—2781no—
208#124—1391no—
209#124—1391no—
210#124C2×D13911yescharacteristic
211#124C2×D13911yescharacteristic
212#123—2781no—
213#123—2781no—
214C22⋊Q8—21no—
215C4×Q8—1391no—
216C4×Q8C2×D13911yescharacteristic
217C4×Q8C2×D13911yescharacteristic
218C4×Q8C2×D13911yescharacteristic
219C4×D4—2781no—
220C4×D4—1391no—
221C4×D4—1391no—
222C4×D4C2×D13911yescharacteristic
223#117—21no—
224#106—1391no—
225C4⋊C8—1391no—
226C4⋊C8—1391no—
227C4⋊C8—1391no—
228#103—1391no—
229#103—1391no—
230#103—1391no—
231#102—1391no—
232#102—1391no—
233#102—1391no—
234#97—1391no—
235#97—1391no—
236C4×C8—1391no—
237C2×Q8—1391no—
238C2×Q8C22⋊D13911yescharacteristic
239C2×Q8C22×D13911yescharacteristic
240C2×Q8C22×D13911yescharacteristic
241C2×D4—2781no—
242C2×D4—2781no—
243C2×D4—1391no—
244C2×D4—1391no—
245C2×D4C22×D13911yescharacteristic
246C22×C4—21no—
247C22×C4—2781no—
248C22×C4—2781no—
249Q16—2782no—
250Q16—5561no—
251SD16—2782no—
252SD16—5561no—
253SD16—5561no—
254SD16—5561no—
255SD16—5561no—
256D8—2782no—
257D8—5561no—
258C2×C8—1391no—
259C2×C8—1391no—
260C2×C8—1391no—
261C2×C8—1391no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—2781no—
267C4⋊C4—1391no—
268C4⋊C4C22⋊D13911yescharacteristic
269C4⋊C4C22⋊D13911yescharacteristic
270C4⋊C4C22⋊D13911yescharacteristic
271C4⋊C4C22×D13911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2781no—
278C22⋊C4—2781no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4—2781no—
283C42—21no—
284C42—21no—
285C42—2781no—
286C42C22×D13911yescharacteristic
287C42C22×D13911yescharacteristic
288C42C22×D13911yescharacteristic
289C23—21no—
290C23—2781no—
291C23—2781no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—41no—
297Q8—2781no—
298Q8—2781no—
299D4—21no—
300D4—21no—
301D4—2781no—
302D4—2781no—
303D4—2781no—
304D4—2781no—
305D4—5562no—
306D4—11121no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—2781no—
312C2×C4—2781no—
313C2×C4—11121no—
314C2×C4—11121no—
315C2×C4C2×C22⋊D13911yescharacteristic
316C2×C4C2×C22⋊D13911yescharacteristic
317C2×C4C2×C22⋊D13911yescharacteristic
318C2×C4C2×C22⋊D13911yescharacteristic
319C2×C4C2×C22⋊D13911yescharacteristic
320C2×C4C2×C22⋊D13911yescharacteristic
321C2×C4C23×D13911yescharacteristic
322C8—2781no—
323C8—2781no—
324C8—2781no—
325C8—1392no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—5561no—
330C22—5561no—
331C22—5561no—
332C22—5561no—
333C22—5561no—
334C22—5561no—
335C22C22×C22⋊D13911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—5561no—
346C4—5561no—
347C4#41×D13911yescharacteristic
348C4#1798488811yescharacteristic
349C2—81no—
350C2—11121no—
351C2—11121no—
352C2#2258162211yescharacteristic
353C2#2258175111yescharacteristic
354C2#2258176111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#556×C139C2
socleC22×C139C22×D4
prime radical#22581343C2
hypercenter#556D139
hypocenterC139#3401
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #22581688C2semidirect
2. #22581345C2semidirect
4. #22581335C2semidirect
5. #22581175C2semidirect
6. #22581172C2semidirect
7. #22581168C2semidirect
8. #22581165C2semidirect
9. #22581155C2semidirect
10. #22581153C2semidirect
11. #22581084C2semidirect
12. #22581063C2semidirect
13. #22581058C2semidirect
14. C4×#14555772C2semidirect
15. #556×C139C2semidirect
177. C139#3401semidirect
180. #556D139semidirect

Maximal subgroups

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

subgroupindex
#225816882
#225813452
#225813432
#225813352
#225811752
#225811722
#225811682
#225811652
#225811552
#225811532
#225810842
#225810632
#225810582
C4×#145557722
#556×C1392
#3401139