Finite Group Databasebeta

← #31817815

Subgroups — #31817815

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#22581558C211yesmaximal, characteristic, complemented
2#22581260C211yesmaximal, characteristic, complemented
3#22581253C211yesmaximal, characteristic, complemented
4#22581240C211yesmaximal, characteristic, complemented
5#22581230C211yesmaximal, characteristic, complemented
6#22581204C211yesmaximal, characteristic, complemented
7#22581201C211yesmaximal, characteristic, complemented
8#22581187C211yesmaximal, characteristic, complemented
9#22581184C211yesmaximal, characteristic, complemented
10#22581165C211yesmaximal, characteristic, complemented
11#22581165C211yesmaximal, characteristic, complemented
12#22581153C211yesmaximal, characteristic, complemented
13#22581148C211yesmaximal, characteristic, complemented
14#22580980C211yesmaximal, characteristic, complemented
15#542×C139C211yesmaximal, characteristic, complemented
16C2×#14555772C2211yescharacteristic
17C2×#14555772C2211yescharacteristic
18C2×#14555770C2211yescharacteristic
19C2×#14555770C2211yescharacteristic
20C2×#14555769C2211yescharacteristic
21C22×C139⋊C8C2211yescharacteristic
22#17984839C2211yescharacteristic
23#17984834C2211yescharacteristic
24#17984827—21no—
25#17984827—21no—
26#17984816C2211yescharacteristic
27#17984816C2211yescharacteristic
28#17984815—21no—
29#17984815—21no—
30C4×D556C2211yescharacteristic
31C4×D556C2211yescharacteristic
32#17984775C2211yescharacteristic
33#17984775C2211yescharacteristic
34#17984773C2211yescharacteristic
35#17984773C2211yescharacteristic
36C4⋊(C139⋊C8)C2211yescharacteristic
37C4⋊(C139⋊C8)C2211yescharacteristic
38C4⋊(C139⋊C8)C2211yescharacteristic
39C4⋊(C139⋊C8)C2211yescharacteristic
40#17984766C2211yescharacteristic
41#17984766C2211yescharacteristic
42#17984763C2211yescharacteristic
43#17984763C2211yescharacteristic
44#17984762C2211yescharacteristic
45#17984762C2211yescharacteristic
46#17984762C2211yescharacteristic
47#17984762C2211yescharacteristic
48C4⋊Q8×C139C2211yescharacteristic
49#126×C139—21no—
50#124×C139—21no—
51#124×C139C2211yescharacteristic
52#123×C139—21no—
53C22⋊Q8×C139—21no—
54C22⋊Q8×C139C2211yescharacteristic
55#121×C139C2211yescharacteristic
56C4×Q8×C139C2211yescharacteristic
57C4×D4×C139C2211yescharacteristic
58#117×C139C2211yescharacteristic
59C2×D556—21no—
60C2×D556—21no—
61C2×D556C2311yescharacteristic
62C2×D556C2311yescharacteristic
63C2×C22⋊D139—21no—
64C2×C22⋊D139—21no—
65C2×C4×D139—21no—
66C2×C4×D139—21no—
67#14555772—41no—
68#14555772—41no—
69#14555770—41no—
70#14555770—41no—
71#14555769—41no—
72C2×C139⋊C8—41no—
73C2×C139⋊C8C2311yescharacteristic
74C2×C139⋊C8C2311yescharacteristic
75C2×C139⋊C8C2311yescharacteristic
76C2×C139⋊C8C2311yescharacteristic
77C4⋊Dic139C2311yescharacteristic
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—
85C2×Q8×C139—21no—
86C2×Q8×C139C2311yescharacteristic
87C2×D4×C139—21no—
88C2×D4×C139C2311yescharacteristic
89C22×C4×C139—21no—
90C22×C4×C139C2311yescharacteristic
91C4⋊C4×C139—21no—
92C4⋊C4×C139—21no—
93C4⋊C4×C139—21no—
94C4⋊C4×C139D411yescharacteristic
95C4⋊C4×C139D411yescharacteristic
96C4⋊C4×C139C2311yescharacteristic
97C4⋊C4×C139C2311yescharacteristic
98C22⋊C4×C139—21no—
99C22⋊C4×C139—21no—
100C22⋊C4×C139—21no—
101C22⋊C4×C139—21no—
102C22⋊C4×C139—21no—
103C22⋊C4×C139D411yescharacteristic
104C22⋊C4×C139D411yescharacteristic
105C42×C139—21no—
106C42×C139C2311yescharacteristic
107C42×C139C2311yescharacteristic
108C22×D139—21no—
109C22×D139—21no—
110D556—21no—
111D556—21no—
112D556—21no—
113D556—21no—
114D556—81no—
115D556—81no—
116C22⋊D139—81no—
117C22⋊D139—81no—
118C2×Dic139—21no—
119C2×Dic139—21no—
120C4×D139—81no—
121C4×D139—81no—
122C139⋊C8—21no—
123C139⋊C8—21no—
124C139⋊C8—21no—
125C139⋊C8—21no—
126C23×C139—21no—
127C23×C139C2×D411yescharacteristic
128Q8×C139—21no—
129Q8×C139—21no—
130Q8×C139—81no—
131D4×C139—21no—
132D4×C139—21no—
133D4×C139—81no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
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×C139C2×D411yescharacteristic
143C2×C4×C139C2×D411yescharacteristic
144C2×C4×C139C2×D411yescharacteristic
145C2×C4×C139C2411yescharacteristic
146C22×C139—21no—
147C22×C139—21no—
148C22×C139—21no—
149C22×C139—41no—
150C22×C139—41no—
151C22×C139—41no—
152C22×C139C22×D411yescharacteristic
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×C139—41no—
165C4×C139—41no—
166C4×C139—41no—
167C4×C139H(5,𝔽2)11yescharacteristic
168C4×C1392−1+411yescharacteristic
169Dic139—41no—
170Dic139—41no—
171C2×C139—41no—
172C2×C139—81no—
173C2×C139#53711yescharacteristic
174C2×C139#57611yescharacteristic
175C2×C139#57711yescharacteristic
176D139—81no—
177D139—81no—
178C139#325711yescharacteristic, complemented, Sylow
179#3257—1391nomaximal, Sylow
180#542D13911yescharacteristic, complemented
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#424—1391no—
195C2×SD16—1391no—
196C2×SD16—1391no—
197C2×D8—1391no—
198C2×D8—1391no—
199C2×M16—1391no—
200C22×C8—1391no—
201C4⋊Q8C2×D13911yescharacteristic
202#127—1391no—
203#126—21no—
204#125—1391no—
205#124—21no—
206#124C2×D13911yescharacteristic
207#123—21no—
208#123—2781no—
209#123—2781no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D13911yescharacteristic
212#121—2781no—
213#121—2781no—
214#121—1391no—
215#121—1391no—
216#121C2×D13911yescharacteristic
217C4×Q8C2×D13911yescharacteristic
218C4×D4—1391no—
219C4×D4—1391no—
220C4×D4C2×D13911yescharacteristic
221#117C2×D13911yescharacteristic
222#107—1391no—
223#107—1391no—
224#106—1391no—
225#106—1391no—
226C4⋊C8—1391no—
227C4⋊C8—1391no—
228C4⋊C8—1391no—
229C4⋊C8—1391no—
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—21no—
239C2×Q8C22×D13911yescharacteristic
240C2×D4—21no—
241C2×D4—2781no—
242C2×D4—2781no—
243C2×D4—2781no—
244C2×D4—2781no—
245C2×D4—1391no—
246C2×D4—1391no—
247C2×D4C22×D13911yescharacteristic
248C22×C4—21no—
249C22×C4—2781no—
250C22×C4—2781no—
251C22×C4C22×D13911yescharacteristic
252SD16—5561no—
253SD16—5561no—
254D8—5561no—
255D8—5561no—
256M16—5561no—
257C2×C8—5561no—
258C2×C8—1391no—
259C2×C8—1391no—
260C2×C8—1391no—
261C2×C8—1391no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—2781no—
266C4⋊C4—2781no—
267C4⋊C4—1391no—
268C4⋊C4—1391no—
269C4⋊C4C22⋊D13911yescharacteristic
270C4⋊C4C22⋊D13911yescharacteristic
271C4⋊C4C22×D13911yescharacteristic
272C4⋊C4C22×D13911yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—2781no—
279C22⋊C4—2781no—
280C22⋊C4—2781no—
281C22⋊C4—2781no—
282C22⋊C4C22⋊D13911yescharacteristic
283C22⋊C4C22⋊D13911yescharacteristic
284C42—21no—
285C42C22×D13911yescharacteristic
286C42C22×D13911yescharacteristic
287C23—21no—
288C23—2781no—
289C23—2781no—
290C23C2×C22⋊D13911yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—2781no—
298D4—2781no—
299D4—2781no—
300D4—2781no—
301D4—11121no—
302D4—11121no—
303D4—11121no—
304D4—11121no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
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×C4C23×D13911yescharacteristic
321C8—2781no—
322C8—2781no—
323C8—2781no—
324C8—2781no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—5561no—
332C22—5561no—
333C22—5561no—
334C22—5561no—
335C22—5561no—
336C22—5561no—
337C22C22×C22⋊D13911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—5561no—
347C4—5561no—
348C4#1798488811yescharacteristic
349C4#1798488911yescharacteristic
350C2—41no—
351C2—81no—
352C2—11121no—
353C2—11121no—
354C2#2258153111yescharacteristic
355C2#2258175611yescharacteristic
356C2#2258176111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#542×C139C2
socleC22×C139C22×D4
hypercenter#542D139
hypocenterC139#3257
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #22581558C2semidirect
2. #22581260C2semidirect
3. #22581253C2semidirect
4. #22581240C2semidirect
5. #22581230C2semidirect
6. #22581204C2semidirect
7. #22581201C2semidirect
8. #22581187C2semidirect
9. #22581184C2semidirect
10. #22581165C2semidirect
11. #22581165C2semidirect
12. #22581153C2semidirect
13. #22581148C2semidirect
14. #22580980C2semidirect
15. #542×C139C2semidirect
178. C139#3257semidirect
180. #542D139semidirect

Maximal subgroups

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

subgroupindex
#225815582
#225812602
#225812532
#225812402
#225812302
#225812042
#225812012
#225811872
#225811842
#225811652
#225811532
#225811482
#225809802
#542×C1392
#3257139