Finite Group Databasebeta

← #31816654

Subgroups — #31816654

Order 17792.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581564C211yesmaximal, characteristic, complemented
2#22581425C211yesmaximal, characteristic
3#22581293C211yesmaximal, characteristic, complemented
4#22581292C211yesmaximal, characteristic, complemented
5#22581254C211yesmaximal, characteristic, complemented
6#22581253C211yesmaximal, characteristic, complemented
7#22581155C211yesmaximal, characteristic, complemented
8#22581102C211yesmaximal, characteristic
9#22581102C211yesmaximal, characteristic
10#22581056C211yesmaximal, characteristic, complemented
11#22581054C211yesmaximal, characteristic, complemented
12SD16×Dic139C211yesmaximal, characteristic, complemented
13#22581038C211yesmaximal, characteristic, complemented
14#22581013C211yesmaximal, characteristic, complemented
15#461×C139C211yesmaximal, characteristic, complemented
16C2×D4×D139C2211yescharacteristic
17C2×#14555772C2211yescharacteristic
18C2×#14555772C2211yescharacteristic
19#17984837—21no—
20#17984837—21no—
21#17984834C2211yescharacteristic, complemented
22#17984832—21no—
23#17984832—21no—
24#17984818C2211yescharacteristic
25#17984818C2211yescharacteristic
26Q8×Dic139C2211yescharacteristic, complemented
27Q8×Dic139C2211yescharacteristic, complemented
28C4×D556C2211yescharacteristic
29D4×Dic139C2211yescharacteristic
30#17984804C2211yescharacteristic
31C4×C22⋊D139—21no—
32(C22⋊D139)⋊C4—21no—
33#17984800C2211yescharacteristic
34#17984799C2211yescharacteristic
35C2×(C2×D139)⋊C4—21no—
36C22⋊C4×D139—21no—
37#17984776C2211yescharacteristic, complemented
38#17984775C2211yescharacteristic, complemented
39#17984774C2211yescharacteristic, complemented
40#17984773C2211yescharacteristic, complemented
41C4⋊(C139⋊C8)C2211yescharacteristic, complemented
42#17984766C2211yescharacteristic, complemented
43#17984766C2211yescharacteristic, complemented
44#17984764C2211yescharacteristic
45#17984764C2211yescharacteristic
46#17984763C2211yescharacteristic
47#17984763C2211yescharacteristic
48(C2×D139)⋊C8C2211yescharacteristic
49(C2×D139)⋊C8C2211yescharacteristic
50#17984752C2211yescharacteristic, complemented
51C8×Dic139C2211yescharacteristic, complemented
52C2×SD16×C139C2211yescharacteristic
53C2×SD16×C139C2211yescharacteristic
54C4⋊Q8×C139C2211yescharacteristic, complemented
55C4×D4×C139C2211yescharacteristic
56C4⋊C8×C139C2211yescharacteristic, complemented
57#103×C139C2211yescharacteristic, complemented
58#103×C139C2211yescharacteristic, complemented
59C23×D139—21no—
60C2×D556C2311yescharacteristic
61C2×C22⋊D139—21no—
62D4×D139—22no—
63D4×D139—22no—
64C22×Dic139—21no—
65C2×C4×D139—21no—
66C2×C4×D139—21no—
67C2×C4×D139C2311yescharacteristic
68#14555772—22no—
69#14555772—22no—
70C2×C139⋊C8C2311yescharacteristic
71C2×C139⋊C8C2311yescharacteristic
72C4⋊Dic139—21no—
73C4⋊Dic139—21no—
74C4⋊Dic139C2311yescharacteristic
75C4⋊Dic139C2311yescharacteristic
76C4⋊Dic139C2311yescharacteristic
77Dic139⋊C4—21no—
78Dic139⋊C4—21no—
79Dic139⋊C4—21no—
80Dic139⋊C4—21no—
81Dic139⋊C4D411yescharacteristic
82Dic139⋊C4D411yescharacteristic
83C22⋊Dic139—21no—
84(C2×D139)⋊C4—21no—
85(C2×D139)⋊C4—21no—
86(C2×D139)⋊C4—21no—
87(C2×D139)⋊C4—21no—
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4D411yescharacteristic
90(C2×D139)⋊C4D411yescharacteristic
91C4×Dic139—21no—
92C4×Dic139—21no—
93C4×Dic139—21no—
94C4×Dic139C2311yescharacteristic
95C2×Q8×C139C2311yescharacteristic
96C2×Q8×C139C2311yescharacteristic
97C2×D4×C139C2311yescharacteristic
98C22×C4×C139—21no—
99SD16×C139—22no—
100SD16×C139—22no—
101C2×C8×C139C2311yescharacteristic
102C2×C8×C139C2311yescharacteristic
103C4⋊C4×C139—21no—
104C4⋊C4×C139—21no—
105C4⋊C4×C139C2311yescharacteristic
106C22⋊C4×C139—21no—
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—24no—
110C22×D139—81no—
111C22×D139—81no—
112C22×D139C2×D411yescharacteristic
113D556—21no—
114D556#4112yes—
115C22⋊D139—24no—
116C2×Dic139—21no—
117C2×Dic139—21no—
118C2×Dic139—21no—
119C2×Dic139—81no—
120C2×Dic139C2×D411yescharacteristic
121C2×Dic139C2×D411yescharacteristic
122C2×Dic139C2×D411yescharacteristic
123C4×D139—21no—
124C4×D139—21no—
125C4×D139—81no—
126C4×D139—81no—
127C139⋊C8—21no—
128C139⋊C8—21no—
129C23×C139—21no—
130Q8×C139—21no—
131Q8×C139—21no—
132Q8×C139—21no—
133Q8×C139—21no—
134D4×C139—21no—
135D4×C139#4112yes—
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—21no—
139C2×C4×C139—81no—
140C2×C4×C139C2×D411yescharacteristic
141C2×C4×C139C2×D411yescharacteristic
142C2×C4×C139C2411yescharacteristic
143C8×C139—21no—
144C8×C139—21no—
145C22×C139—22no—
146C22×C139—41no—
147C22×C139—41no—
148C22×C139C22×D411yescharacteristic
149C2×D139—21no—
150C2×D139—22no—
151C2×D139—21no—
152C2×D139—21no—
153C2×D139—41no—
154C2×D139—41no—
155C2×D139—84no—
156C4×C139—21no—
157C4×C139—21no—
158C4×C139—41no—
159C4×C139—41no—
160C4×C139—41no—
161C4×C139C2×#4111yescharacteristic
162C4×C139C2×#4111yescharacteristic
163Dic139—21no—
164Dic139—21no—
165Dic139—21no—
166Dic139—41no—
167Dic139—41no—
168Dic139—41no—
169C2×C139—42no—
170C2×C139#52511yescharacteristic
171C2×C139#57711yescharacteristic
172C2×C139#57711yescharacteristic
173D139—41no—
174D139—42no—
175C139#312311yescharacteristic, complemented, Sylow
176#3123—1391nomaximal, Sylow
177#541—1391no—
178#518—1391no—
179#485—1391no—
180#485—1391no—
181#478—1391no—
182#478—1391no—
183#461—1391no—
184#461D13911yescharacteristic, complemented
185#450—1391no—
186#450—1391no—
187#440—1391no—
188#440—1391no—
189C4×SD16—1391no—
190C4×SD16—1391no—
191#433—1391no—
192C22×D4—1391no—
193C2×SD16—1391no—
194C2×SD16—1391no—
195C2×SD16C2×D13911yescharacteristic
196C2×SD16C2×D13911yescharacteristic
197C4⋊Q8C2×D13911yescharacteristic, complemented
198#126—2781no—
199#126—2781no—
200#125—2781no—
201#125—2781no—
202#125—1391no—
203C22⋊Q8—1391no—
204C22⋊Q8—1391no—
205C4×Q8—1391no—
206C4×Q8—1391no—
207C4×D4—2781no—
208C4×D4—2781no—
209C4×D4—1391no—
210C4×D4—1391no—
211C4×D4—1391no—
212C4×D4C2×D13911yescharacteristic
213#117—1391no—
214#117—1391no—
215C2×C22⋊C4—2781no—
216C2×C22⋊C4—2781no—
217#107—1391no—
218#107—1391no—
219#106—1391no—
220#106—1391no—
221C4⋊C8—1391no—
222C4⋊C8C2×D13911yescharacteristic, complemented
223#103—1391no—
224#103—1391no—
225#103C2×D13911yescharacteristic, complemented
226#103C2×D13911yescharacteristic, complemented
227#102—1391no—
228#102—1391no—
229#102—1391no—
230#102—1391no—
231C22⋊C8—1391no—
232C22⋊C8—1391no—
233#97—1391no—
234C4×C8—1391no—
235C24—2781no—
236C2×Q8C22×D13911yescharacteristic
237C2×Q8C22×D13911yescharacteristic
238C2×D4—2782no—
239C2×D4—2782no—
240C2×D4—2781no—
241C2×D4—1391no—
242C2×D4C22×D13911yescharacteristic
243C22×C4—21no—
244C22×C4—2781no—
245C22×C4—2781no—
246C22×C4—2781no—
247C22×C4—1391no—
248SD16—22no—
249SD16—22no—
250SD16—2782no—
251SD16—2782no—
252C2×C8—1391no—
253C2×C8—1391no—
254C2×C8C22×D13911yescharacteristic
255C2×C8C22×D13911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—2781no—
259C4⋊C4—2781no—
260C4⋊C4—2781no—
261C4⋊C4—2781no—
262C4⋊C4—2781no—
263C4⋊C4—2781no—
264C4⋊C4—1391no—
265C4⋊C4—1391no—
266C4⋊C4—1391no—
267C4⋊C4—1391no—
268C4⋊C4—1391no—
269C4⋊C4C22×D13911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—2781no—
272C22⋊C4—2781no—
273C22⋊C4—2781no—
274C22⋊C4—2781no—
275C22⋊C4—2781no—
276C22⋊C4—2781no—
277C22⋊C4—1391no—
278C22⋊C4—1391no—
279C42—2781no—
280C42—2781no—
281C42—2781no—
282C42—1391no—
283C42C22×D13911yescharacteristic
284C23—21no—
285C23—2784no—
286C23—2781no—
287C23—11121no—
288C23—11121no—
289C23—1391no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—2784no—
296D4—2781no—
297D4—1392no—
298D4#1455578412yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—2781no—
304C2×C4—2781no—
305C2×C4—2781no—
306C2×C4—2781no—
307C2×C4—2781no—
308C2×C4—11121no—
309C2×C4—11121no—
310C2×C4—11121no—
311C2×C4—1391no—
312C2×C4—1391no—
313C2×C4—1391no—
314C2×C4D4×D13911yescharacteristic
315C2×C4D4×D13911yescharacteristic
316C2×C4C23×D13911yescharacteristic
317C8—21no—
318C8—21no—
319C8—2781no—
320C8—2781no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—2781no—
325C22—2781no—
326C22—2782no—
327C22—2781no—
328C22—5561no—
329C22—5561no—
330C22—11124no—
331C22C2×D4×D13911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2781no—
338C4—2781no—
339C4—2781no—
340C4—5561no—
341C4—5561no—
342C4—5561no—
343C4#41×D13911yescharacteristic
344C4C2×#1455578411yescharacteristic
345C2—42no—
346C2—5561no—
347C2—5562no—
348C2#2258146311yescharacteristic
349C2#2258175911yescharacteristic
350C2#2258176211yescharacteristic
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#461×C139C2
socleC22×C139C22×D4
prime radicalC2×D4×D139C22
hypercenter#461D139
hypocenterC139#3123
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #22581564C2semidirect
3. #22581293C2semidirect
4. #22581292C2semidirect
5. #22581254C2semidirect
6. #22581253C2semidirect
7. #22581155C2semidirect
10. #22581056C2semidirect
11. #22581054C2semidirect
12. SD16×Dic139C2semidirect
13. #22581038C2semidirect
14. #22581013C2semidirect
15. #461×C139C2semidirect
21. #17984834C22semidirect
26. Q8×Dic139C22semidirect
27. Q8×Dic139C22semidirect
37. #17984776C22semidirect
38. #17984775C22semidirect
39. #17984774C22semidirect
40. #17984773C22semidirect
41. C4⋊(C139⋊C8)C22semidirect
42. #17984766C22semidirect
43. #17984766C22semidirect
50. #17984752C22semidirect
51. C8×Dic139C22semidirect
54. C4⋊Q8×C139C22semidirect
56. C4⋊C8×C139C22semidirect
57. #103×C139C22semidirect
58. #103×C139C22semidirect
175. C139#3123semidirect
184. #461D139semidirect
197. C4⋊Q8C2×D139semidirect
222. C4⋊C8C2×D139semidirect
225. #103C2×D139semidirect
226. #103C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815642
#225814252
#225812932
#225812922
#225812542
#225812532
#225811552
#225811022
#225810562
#225810542
SD16×Dic1392
#225810382
#225810132
#461×C1392
#3123139