Finite Group Databasebeta

← #31817817

Subgroups — #31817817

Order 17792.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22581574C211yesmaximal, characteristic, complemented
2#22581558C211yesmaximal, characteristic, complemented
3#22581261C211yesmaximal, characteristic, complemented
4#22581254C211yesmaximal, characteristic, complemented
5#22581244C211yesmaximal, characteristic, complemented
6#22581234C211yesmaximal, characteristic, complemented
7#22581206C211yesmaximal, characteristic, complemented
8#22581199C211yesmaximal, characteristic, complemented
9#22581189C211yesmaximal, characteristic, complemented
10#22581182C211yesmaximal, characteristic, complemented
11#22581169C211yesmaximal, characteristic, complemented
12#22581169C211yesmaximal, characteristic, complemented
13#22581154C211yesmaximal, characteristic, complemented
14#22581149C211yesmaximal, characteristic, complemented
15#424×C139C211yesmaximal, characteristic, complemented
16C2×#14555774C2211yescharacteristic
17C2×#14555774C2211yescharacteristic
18C2×D1112C2211yescharacteristic
19C2×D1112C2211yescharacteristic
20#17984842C2211yescharacteristic
21#17984839C2211yescharacteristic
22#17984837—21no—
23#17984834C2211yescharacteristic
24#17984830C2211yescharacteristic
25#17984828—21no—
26#17984827—21no—
27#17984827—21no—
28#17984824—21no—
29#17984821C2211yescharacteristic
30#17984820—21no—
31#17984816C2211yescharacteristic
32#17984816C2211yescharacteristic
33#17984816C2211yescharacteristic
34#17984815—21no—
35#17984815—21no—
36C4×Dic278C2211yescharacteristic
37C4×D556C2211yescharacteristic
38C4×D556C2211yescharacteristic
39C4×D556C2211yescharacteristic
40#17984776C2211yescharacteristic
41#17984776C2211yescharacteristic
42#17984774C2211yescharacteristic
43#17984774C2211yescharacteristic
44#17984767C2211yescharacteristic
45#17984767C2211yescharacteristic
46#17984764C2211yescharacteristic
47#17984764C2211yescharacteristic
48#17984764C2211yescharacteristic
49#17984764C2211yescharacteristic
50#17984764C2211yescharacteristic
51#17984764C2211yescharacteristic
52C2×M16×C139C2211yescharacteristic
53C22×C8×C139C2211yescharacteristic
54#117×C139C2211yescharacteristic
55C4⋊C8×C139C2211yescharacteristic
56C4⋊C8×C139C2211yescharacteristic
57C4⋊C8×C139C2211yescharacteristic
58C4⋊C8×C139C2211yescharacteristic
59C2×Dic278—21no—
60C2×Dic278C2311yescharacteristic
61C2×D556—21no—
62C2×D556—21no—
63C2×D556C2311yescharacteristic
64C2×D556C2311yescharacteristic
65C2×D556C2311yescharacteristic
66C2×C22⋊D139—21no—
67C2×C22⋊D139—21no—
68C2×C22⋊D139—21no—
69C2×C4×D139—21no—
70C2×C4×D139—21no—
71C2×C4×D139—21no—
72#14555774—41no—
73#14555774—41no—
74D1112—41no—
75D1112—41no—
76C4⋊Dic139—21no—
77C4⋊Dic139C2311yescharacteristic
78C4⋊Dic139C2311yescharacteristic
79C4⋊Dic139C2311yescharacteristic
80C4⋊Dic139C2311yescharacteristic
81Dic139⋊C4—21no—
82Dic139⋊C4—21no—
83Dic139⋊C4—21no—
84Dic139⋊C4—21no—
85C22⋊Dic139—21no—
86(C2×D139)⋊C4—21no—
87(C2×D139)⋊C4—21no—
88(C2×D139)⋊C4—21no—
89(C2×D139)⋊C4—21no—
90(C2×D139)⋊C4—21no—
91(C2×D139)⋊C4—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94C4×Dic139—21no—
95C22×C4×C139C2311yescharacteristic
96M16×C139—41no—
97C2×C8×C139—41no—
98C2×C8×C139C2311yescharacteristic
99C2×C8×C139C2311yescharacteristic
100C2×C8×C139C2311yescharacteristic
101C2×C8×C139C2311yescharacteristic
102C4⋊C4×C139D411yescharacteristic
103C4⋊C4×C139D411yescharacteristic
104C22⋊C4×C139D411yescharacteristic
105C22⋊C4×C139D411yescharacteristic
106C42×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—21no—
110C22×D139—21no—
111Dic278—21no—
112Dic278—21no—
113Dic278—81no—
114D556—21no—
115D556—21no—
116D556—21no—
117D556—21no—
118D556—21no—
119D556—21no—
120D556—81no—
121D556—81no—
122C22⋊D139—81no—
123C22⋊D139—81no—
124C22⋊D139—81no—
125C2×Dic139—21no—
126C2×Dic139—21no—
127C2×Dic139—21no—
128C2×Dic139—21no—
129C2×Dic139—21no—
130C4×D139—81no—
131C4×D139—81no—
132C4×D139—81no—
133C23×C139C2×D411yescharacteristic
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139C2×D411yescharacteristic
137C2×C4×C139C2×D411yescharacteristic
138C2×C4×C139C2×D411yescharacteristic
139C2×C4×C139C2×D411yescharacteristic
140C2×C4×C139C2×D411yescharacteristic
141C2×C4×C139C2411yescharacteristic
142C8×C139—21no—
143C8×C139—21no—
144C8×C139—21no—
145C8×C139—21no—
146C22×C139—21no—
147C22×C139—21no—
148C22×C139—21no—
149C22×C139C22×D411yescharacteristic
150C2×D139—41no—
151C2×D139—41no—
152C2×D139—41no—
153C2×D139—41no—
154C2×D139—41no—
155C2×D139—41no—
156C2×D139—41no—
157C2×D139—41no—
158C2×D139—41no—
159C4×C139—21no—
160C4×C139—21no—
161C4×C139—21no—
162C4×C139—21no—
163C4×C139—21no—
164C4×C139H(5,𝔽2)11yescharacteristic
165C4×C1392−1+411yescharacteristic
166Dic139—41no—
167Dic139—41no—
168Dic139—41no—
169Dic139—41no—
170Dic139—41no—
171C2×C139—41no—
172C2×C139#53711yescharacteristic
173C2×C139#57611yescharacteristic
174C2×C139#57711yescharacteristic
175D139—81no—
176D139—81no—
177D139—81no—
178C139#325711yescharacteristic, complemented, Sylow
179#3257—1391nomaximal, Sylow
180#542—1391no—
181#540—1391no—
182#479—1391no—
183#478—1391no—
184#476—1391no—
185#474—1391no—
186#469—1391no—
187#468—1391no—
188#466—1391no—
189#465—1391no—
190#463—1391no—
191#463—1391no—
192#460—1391no—
193#459—1391no—
194#424D13911yescharacteristic, complemented
195C2×SD16—1391no—
196C2×SD16—1391no—
197C2×D8—1391no—
198C2×D8—1391no—
199C2×M16C2×D13911yescharacteristic
200C22×C8C2×D13911yescharacteristic
201C4⋊Q8—1391no—
202#127—1391no—
203#126—2781no—
204#125—1391no—
205#124—2781no—
206#124—1391no—
207#123—2781no—
208#123—2781no—
209#123—2781no—
210C22⋊Q8—2781no—
211C22⋊Q8—1391no—
212#121—2781no—
213#121—2781no—
214#121—1391no—
215#121—1391no—
216#121—1391no—
217C4×Q8—1391no—
218C4×D4—1391no—
219C4×D4—1391no—
220C4×D4—1391no—
221#117C2×D13911yescharacteristic
222#107—1391no—
223#107—1391no—
224#106—1391no—
225#106—1391no—
226C4⋊C8C2×D13911yescharacteristic
227C4⋊C8C2×D13911yescharacteristic
228C4⋊C8C2×D13911yescharacteristic
229C4⋊C8C2×D13911yescharacteristic
230#103—1391no—
231#103—1391no—
232#102—1391no—
233#102—1391no—
234#102—1391no—
235#102—1391no—
236#102—1391no—
237#102—1391no—
238C2×Q8—2781no—
239C2×Q8—1391no—
240C2×D4—2781no—
241C2×D4—2781no—
242C2×D4—2781no—
243C2×D4—2781no—
244C2×D4—2781no—
245C2×D4—1391no—
246C2×D4—1391no—
247C2×D4—1391no—
248C22×C4—2781no—
249C22×C4—2781no—
250C22×C4—2781no—
251C22×C4C22×D13911yescharacteristic
252SD16—5561no—
253SD16—5561no—
254D8—5561no—
255D8—5561no—
256M16—41no—
257C2×C8—41no—
258C2×C8C22×D13911yescharacteristic
259C2×C8C22×D13911yescharacteristic
260C2×C8C22×D13911yescharacteristic
261C2×C8C22×D13911yescharacteristic
262C4⋊C4—2781no—
263C4⋊C4—2781no—
264C4⋊C4—2781no—
265C4⋊C4—2781no—
266C4⋊C4—2781no—
267C4⋊C4—1391no—
268C4⋊C4—1391no—
269C4⋊C4—1391no—
270C4⋊C4—1391no—
271C4⋊C4D55611yescharacteristic
272C4⋊C4D55611yescharacteristic
273C22⋊C4—2781no—
274C22⋊C4—2781no—
275C22⋊C4—2781no—
276C22⋊C4—2781no—
277C22⋊C4—2781no—
278C22⋊C4—2781no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4D55611yescharacteristic
283C22⋊C4D55611yescharacteristic
284C42—2781no—
285C42C22×D13911yescharacteristic
286C42C22×D13911yescharacteristic
287C23—2781no—
288C23—2781no—
289C23—2781no—
290C23C2×D55611yescharacteristic
291Q8—2781no—
292Q8—2781no—
293Q8—11121no—
294D4—2781no—
295D4—2781no—
296D4—2781no—
297D4—2781no—
298D4—2781no—
299D4—2781no—
300D4—11121no—
301D4—11121no—
302D4—11121no—
303D4—11121no—
304D4—11121no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—2781no—
308C2×C4—2781no—
309C2×C4—2781no—
310C2×C4—2781no—
311C2×C4—2781no—
312C2×C4—11121no—
313C2×C4—11121no—
314C2×C4—11121no—
315C2×C4C2×D55611yescharacteristic
316C2×C4C2×D55611yescharacteristic
317C2×C4C2×D55611yescharacteristic
318C2×C4C2×D55611yescharacteristic
319C2×C4C2×D55611yescharacteristic
320C2×C4C23×D13911yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—5561no—
329C22—5561no—
330C22—5561no—
331C22—5561no—
332C22—5561no—
333C22—5561no—
334C22—5561no—
335C22—5561no—
336C22—5561no—
337C22C22×D55611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—5561no—
344C4—5561no—
345C4—5561no—
346C4—5561no—
347C4—5561no—
348C4#1798488711yescharacteristic
349C4#1798489011yescharacteristic
350C2—41no—
351C2—11121no—
352C2—11121no—
353C2—11121no—
354C2#2258153411yescharacteristic
355C2#2258175811yescharacteristic
356C2#2258176511yescharacteristic
subgroupG/H
centerC22C22×D556
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#424×C139C2
socleC22×C139C22×D4
hypercenter#424D139
hypocenterC139#3257
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #22581574C2semidirect
2. #22581558C2semidirect
3. #22581261C2semidirect
4. #22581254C2semidirect
5. #22581244C2semidirect
6. #22581234C2semidirect
7. #22581206C2semidirect
8. #22581199C2semidirect
9. #22581189C2semidirect
10. #22581182C2semidirect
11. #22581169C2semidirect
12. #22581169C2semidirect
13. #22581154C2semidirect
14. #22581149C2semidirect
15. #424×C139C2semidirect
178. C139#3257semidirect
194. #424D139semidirect

Maximal subgroups

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

subgroupindex
#225815742
#225815582
#225812612
#225812542
#225812442
#225812342
#225812062
#225811992
#225811892
#225811822
#225811692
#225811542
#225811492
#424×C1392
#3257139