Finite Group Databasebeta

← #31819479

Subgroups — #31819479

Order 17792.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581676C211yesmaximal, characteristic, complemented
2#22581348C211yesmaximal, characteristic, complemented
3#22581345C211yesmaximal, characteristic, complemented
4#22581335C211yesmaximal, characteristic
5#22581175C211yesmaximal, characteristic, complemented
6#22581172C211yesmaximal, characteristic, complemented
7#22581168C211yesmaximal, characteristic
8#22581165C211yesmaximal, characteristic
9#22581163C211yesmaximal, characteristic, complemented
10#22581160C211yesmaximal, characteristic, complemented
11#22581084C211yesmaximal, characteristic, complemented
12#22581053C211yesmaximal, characteristic, complemented
13#22581051C211yesmaximal, characteristic, complemented
14C4×#14555775C211yesmaximal, characteristic, complemented
15#556×C139C211yesmaximal, characteristic, complemented
16C2×#14555775C2211yescharacteristic
17C2×#14555775C2211yescharacteristic
18C2×#14555775C2211yescharacteristic
19C2×#14555775C2211yescharacteristic
20C2×#14555773C2211yescharacteristic
21C2×#14555773C2211yescharacteristic
22C2×#14555772C2211yescharacteristic
23C2×#14555772C2211yescharacteristic
24C2×#14555770C2211yescharacteristic
25#17984842C2211yescharacteristic
26#17984837—21no—
27#17984837—21no—
28#17984830C2211yescharacteristic
29#17984830C2211yescharacteristic
30#17984818—21no—
31C4×Dic278C2211yescharacteristic
32C4×Dic278C2211yescharacteristic
33C4×D556C2211yescharacteristic
34#17984800—21no—
35#17984775C2211yescharacteristic
36C4⋊(C139⋊C8)C2211yescharacteristic
37C4⋊(C139⋊C8)C2211yescharacteristic
38C4⋊(C139⋊C8)C2211yescharacteristic
39#17984766C2211yescharacteristic
40#17984766C2211yescharacteristic
41#17984765C2211yescharacteristic
42#17984765C2211yescharacteristic
43#17984763C2211yescharacteristic
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×Dic278C2311yescharacteristic
61C2×D556C2311yescharacteristic
62C2×C4×D139—21no—
63#14555775—22no—
64#14555775—41no—
65#14555775—41no—
66#14555775—41no—
67#14555773—22no—
68#14555773—41no—
69#14555772—22no—
70#14555772—41no—
71#14555770—41no—
72C2×C139⋊C8C2311yescharacteristic
73C2×C139⋊C8C2311yescharacteristic
74C2×C139⋊C8C2311yescharacteristic
75C2×C139⋊C8C2311yescharacteristic
76C4⋊Dic139—21no—
77C4⋊Dic139—21no—
78C4⋊Dic139C2311yescharacteristic
79Dic139⋊C4—21no—
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—
86C4×Dic139—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—
112Dic278—21no—
113Dic278—21no—
114Dic278—21no—
115Dic278—21no—
116D556—21no—
117D556—21no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C2×Dic139—21no—
121C4×D139—42no—
122C139⋊C8—21no—
123C139⋊C8—21no—
124C139⋊C8—21no—
125C139⋊C8#4112yes—
126C23×C139—21no—
127Q8×C139—21no—
128Q8×C139—21no—
129Q8×C139—21no—
130Q8×C139—21no—
131Q8×C139—41no—
132D4×C139—21no—
133D4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—42no—
138C2×C4×C139C2×D411yescharacteristic
139C2×C4×C139C2×D411yescharacteristic
140C2×C4×C139C2×D411yescharacteristic
141C2×C4×C139C2×D411yescharacteristic
142C2×C4×C139C2×D411yescharacteristic
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2411yescharacteristic
145C22×C139—41no—
146C22×C139—41no—
147C22×C139—41no—
148C22×C139C22×D411yescharacteristic
149C2×D139—41no—
150C2×D139—41no—
151C2×D139—41no—
152C4×C139—21no—
153C4×C139—21no—
154C4×C139—21no—
155C4×C139—21no—
156C4×C139—21no—
157C4×C139—21no—
158C4×C139—41no—
159C4×C139—41no—
160C4×C139—41no—
161C4×C139C2×#4111yescharacteristic
162C4×C139H(5,𝔽2)11yescharacteristic
163Dic139—41no—
164Dic139—41no—
165Dic139—41no—
166C2×C139—81no—
167C2×C139#55011yescharacteristic
168C2×C139#57511yescharacteristic
169C2×C139#57811yescharacteristic
170D139—81no—
171C139#340211yescharacteristic, complemented, Sylow
172#3402—1391nomaximal, Sylow
173#556—1391no—
174#556D13911yescharacteristic, complemented
175#497—1391no—
176#497—1391no—
177#495—1391no—
178#464—1391no—
179#464—1391no—
180#463—1391no—
181#463—1391no—
182#462—1391no—
183#462—1391no—
184#446—1391no—
185#440—1391no—
186#440—1391no—
187C4×Q16—1391no—
188C2×Q16—1391no—
189C2×Q16—1391no—
190C2×Q16—1391no—
191C2×Q16—1391no—
192C2×SD16—1391no—
193C2×SD16—1391no—
194C2×SD16—1391no—
195C2×SD16—1391no—
196C2×D8—1391no—
197C4⋊Q8—1391no—
198C4⋊Q8C2×D13911yescharacteristic
199#126—21no—
200#126—21no—
201#126—2781no—
202#126—2781no—
203#124—1391no—
204#124—1391no—
205#124C2×D13911yescharacteristic
206#124C2×D13911yescharacteristic
207C22⋊Q8—21no—
208C22⋊Q8—2781no—
209C4×Q8—1391no—
210C4×Q8—1391no—
211C4×Q8C2×D13911yescharacteristic
212C4×Q8C2×D13911yescharacteristic
213C4×Q8C2×D13911yescharacteristic
214C4×D4—1391no—
215C4×D4C2×D13911yescharacteristic
216#117—21no—
217#117—2781no—
218#107—1391no—
219C4⋊C8—1391no—
220C4⋊C8—1391no—
221C4⋊C8—1391no—
222#103—1391no—
223#103—1391no—
224#103—1391no—
225#103—1391no—
226#102—1391no—
227#102—1391no—
228#97—1391no—
229#97—1391no—
230C4×C8—1391no—
231C2×Q8—1391no—
232C2×Q8—1391no—
233C2×Q8C22⋊D13911yescharacteristic
234C2×Q8C22×D13911yescharacteristic
235C2×Q8C22×D13911yescharacteristic
236C2×D4—1391no—
237C2×D4C22×D13911yescharacteristic
238C22×C4—21no—
239C22×C4—2781no—
240Q16—2782no—
241Q16—5561no—
242Q16—5561no—
243Q16—5561no—
244SD16—2782no—
245SD16—2782no—
246SD16—5561no—
247SD16—5561no—
248D8—5561no—
249C2×C8—1391no—
250C2×C8—1391no—
251C2×C8—1391no—
252C2×C8—1391no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—2781no—
258C4⋊C4—2781no—
259C4⋊C4—2781no—
260C4⋊C4—2781no—
261C4⋊C4—1391no—
262C4⋊C4C22⋊D13911yescharacteristic
263C4⋊C4C22⋊D13911yescharacteristic
264C4⋊C4C22⋊D13911yescharacteristic
265C4⋊C4C22×D13911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—2781no—
272C22⋊C4—2781no—
273C22⋊C4—2781no—
274C22⋊C4—2781no—
275C22⋊C4—2781no—
276C42—21no—
277C42—21no—
278C42—2781no—
279C42—2781no—
280C42C22×D13911yescharacteristic
281C42C22×D13911yescharacteristic
282C42C22×D13911yescharacteristic
283C23—21no—
284C23—2781no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—41no—
290Q8—2781no—
291Q8—2781no—
292Q8—2781no—
293Q8—2781no—
294D4—21no—
295D4—21no—
296D4—2781no—
297D4—2781no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—2781no—
303C2×C4—2781no—
304C2×C4—2781no—
305C2×C4—5562no—
306C2×C4C2×C22⋊D13911yescharacteristic
307C2×C4C2×C22⋊D13911yescharacteristic
308C2×C4C2×C22⋊D13911yescharacteristic
309C2×C4C2×C22⋊D13911yescharacteristic
310C2×C4C2×C22⋊D13911yescharacteristic
311C2×C4C2×C22⋊D13911yescharacteristic
312C2×C4C23×D13911yescharacteristic
313C8—2781no—
314C8—2781no—
315C8—2781no—
316C8—1392no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—5561no—
321C22—5561no—
322C22—5561no—
323C22C22×C22⋊D13911yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—5561no—
334C4—5561no—
335C4—5561no—
336C4#41×D13911yescharacteristic
337C4#1798488811yescharacteristic
338C2—81no—
339C2—11121no—
340C2#2258162211yescharacteristic
341C2#2258175111yescharacteristic
342C2#2258176811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#556×C139C2
socleC22×C139C22×D4
prime radicalC2×#14555770C22
hypercenter#556D139
hypocenterC139#3402
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. #22581676C2semidirect
2. #22581348C2semidirect
3. #22581345C2semidirect
5. #22581175C2semidirect
6. #22581172C2semidirect
9. #22581163C2semidirect
10. #22581160C2semidirect
11. #22581084C2semidirect
12. #22581053C2semidirect
13. #22581051C2semidirect
14. C4×#14555775C2semidirect
15. #556×C139C2semidirect
171. C139#3402semidirect
174. #556D139semidirect

Maximal subgroups

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

subgroupindex
#225816762
#225813482
#225813452
#225813352
#225811752
#225811722
#225811682
#225811652
#225811632
#225811602
#225810842
#225810532
#225810512
C4×#145557752
#556×C1392
#3402139