Finite Group Databasebeta

← #34080517

Subgroups — #34080517

Order 19328.

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#23752827C211yesmaximal, characteristic, complemented
2#23752816C211yesmaximal, characteristic, complemented
3#23752520C211yesmaximal, characteristic, complemented
4#23752512C211yesmaximal, characteristic, complemented
5#23752500C211yesmaximal, characteristic, complemented
6#23752490C211yesmaximal, characteristic, complemented
7#23752462C211yesmaximal, characteristic, complemented
8#23752457C211yesmaximal, characteristic, complemented
9#23752445C211yesmaximal, characteristic, complemented
10#23752440C211yesmaximal, characteristic, complemented
11#23752425C211yesmaximal, characteristic, complemented
12#23752425C211yesmaximal, characteristic, complemented
13#23752409C211yesmaximal, characteristic, complemented
14#23752237C211yesmaximal, characteristic, complemented
15#459×C151C211yesmaximal, characteristic, complemented
16C2×#14558992C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558987C2211yescharacteristic
19C2×C8×D151C2211yescharacteristic
20#18012738C2211yescharacteristic
21#18012732—21no—
22#18012731C2211yescharacteristic
23#18012726C2211yescharacteristic
24#18012725—21no—
25#18012722—21no—
26#18012720—21no—
27#18012720—21no—
28#18012719C2211yescharacteristic
29#18012718—21no—
30#18012711—21no—
31#18012711—21no—
32#18012710C2211yescharacteristic
33#18012710C2211yescharacteristic
34#18012710C2211yescharacteristic
35C4×Dic302C2211yescharacteristic
36D4×Dic151C2211yescharacteristic
37D4×Dic151C2211yescharacteristic
38#18012696C2211yescharacteristic
39#18012673C2211yescharacteristic
40#18012672C2211yescharacteristic
41#18012671C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012664C2211yescharacteristic
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic
50#18012660C2211yescharacteristic
51#18012660C2211yescharacteristic
52C2×D8×C151C2211yescharacteristic
53C2×D8×C151C2211yescharacteristic
54#127×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×Dic302C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C22×Dic151—21no—
66C2×C4×D151C2311yescharacteristic
67#14558992—41no—
68#14558992—41no—
69#14558987—41no—
70C2×C151⋊C8C2311yescharacteristic
71C2×C151⋊C8C2311yescharacteristic
72C8×D151—41no—
73C4⋊Dic151—21no—
74C4⋊Dic151C2311yescharacteristic
75C4⋊Dic151C2311yescharacteristic
76C4⋊Dic151C2311yescharacteristic
77Dic151⋊C4—21no—
78Dic151⋊C4—21no—
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81Dic151⋊C4D411yescharacteristic
82Dic151⋊C4D411yescharacteristic
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85C22⋊Dic151—21no—
86C22⋊Dic151—21no—
87C22⋊Dic151—21no—
88C22⋊Dic151—21no—
89C22⋊Dic151—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4D411yescharacteristic
92(C2×D151)⋊C4D411yescharacteristic
93C4×Dic151—21no—
94C4×Dic151C2311yescharacteristic
95C2×D4×C151—21no—
96C2×D4×C151—21no—
97C2×D4×C151C2311yescharacteristic
98C2×D4×C151C2311yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C22×C4×C151—21no—
101D8×C151—41no—
102D8×C151—41no—
103C2×C8×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151C2×D411yescharacteristic
109Dic302—21no—
110Dic302—21no—
111Dic302—81no—
112C22⋊D151—81no—
113C22⋊D151—81no—
114C22⋊D151—81no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—81no—
120C2×Dic151—81no—
121C2×Dic151C2×D411yescharacteristic
122C2×Dic151C2×D411yescharacteristic
123C2×Dic151C2×D411yescharacteristic
124C4×D151—21no—
125C4×D151—21no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C23×C151—21no—
129C23×C151—21no—
130C23×C151—21no—
131D4×C151—21no—
132D4×C151—21no—
133D4×C151—21no—
134D4×C151—21no—
135D4×C151—21no—
136D4×C151—21no—
137D4×C151—81no—
138D4×C151—81no—
139C2×C4×C151—21no—
140C2×C4×C151—81no—
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2411yescharacteristic
144C8×C151—21no—
145C8×C151—21no—
146C22×C151—41no—
147C22×C151—41no—
148C22×C151—41no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151C22×D411yescharacteristic
156C2×D151—21no—
157C2×D151—21no—
158C2×D151—21no—
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—41no—
162C4×C151H(5,𝔽2)11yescharacteristic
163C4×C1512−1+411yescharacteristic
164Dic151—21no—
165Dic151—21no—
166Dic151—21no—
167Dic151—41no—
168Dic151—41no—
169Dic151—41no—
170Dic151—41no—
171C2×C151—81no—
172C2×C151—81no—
173C2×C151—81no—
174C2×C151#53711yescharacteristic
175C2×C151#57611yescharacteristic
176C2×C151#57711yescharacteristic
177D151—41no—
178C151#325711yescharacteristic, complemented, Sylow
179#3257—1511nomaximal, Sylow
180#542—1511no—
181#540—1511no—
182#479—1511no—
183#478—1511no—
184#476—1511no—
185#474—1511no—
186#469—1511no—
187#468—1511no—
188#466—1511no—
189#465—1511no—
190#463—1511no—
191#463—1511no—
192#460—1511no—
193#459D15111yescharacteristic, complemented
194#424—1511no—
195C2×SD16—1511no—
196C2×SD16—1511no—
197C2×D8C2×D15111yescharacteristic
198C2×D8C2×D15111yescharacteristic
199C2×M16—1511no—
200C22×C8—1511no—
201C4⋊Q8—1511no—
202#127C2×D15111yescharacteristic
203#126—3021no—
204#125—1511no—
205#124—3021no—
206#124—1511no—
207#123—3021no—
208#123—3021no—
209#123—3021no—
210C22⋊Q8—3021no—
211C22⋊Q8—1511no—
212#121—3021no—
213#121—3021no—
214#121—1511no—
215#121—1511no—
216#121—1511no—
217C4×Q8—1511no—
218C4×D4—1511no—
219C4×D4—1511no—
220C4×D4C2×D15111yescharacteristic
221#117—1511no—
222#107—1511no—
223#107—1511no—
224#106—1511no—
225#106—1511no—
226C4⋊C8—1511no—
227C4⋊C8—1511no—
228C4⋊C8—1511no—
229C4⋊C8C2×D15111yescharacteristic
230#103—1511no—
231#103—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102C2×D15111yescharacteristic
237#102C2×D15111yescharacteristic
238C2×Q8—3021no—
239C2×Q8—1511no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—3021no—
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4C22×D15111yescharacteristic
246C2×D4C22×D15111yescharacteristic
247C2×D4C22×D15111yescharacteristic
248C22×C4—21no—
249C22×C4—3021no—
250C22×C4—3021no—
251C22×C4—1511no—
252SD16—6041no—
253SD16—6041no—
254D8—41no—
255D8—41no—
256M16—6041no—
257C2×C8—6041no—
258C2×C8—1511no—
259C2×C8—1511no—
260C2×C8C22×D15111yescharacteristic
261C2×C8C22×D15111yescharacteristic
262C4⋊C4—3021no—
263C4⋊C4—3021no—
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—1511no—
268C4⋊C4—1511no—
269C4⋊C4—1511no—
270C4⋊C4—1511no—
271C4⋊C4—1511no—
272C4⋊C4C22×D15111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—3021no—
275C22⋊C4—3021no—
276C22⋊C4—3021no—
277C22⋊C4—3021no—
278C22⋊C4—3021no—
279C22⋊C4—3021no—
280C22⋊C4—3021no—
281C22⋊C4—3021no—
282C22⋊C4—1511no—
283C22⋊C4—1511no—
284C42—3021no—
285C42—1511no—
286C42C22×D15111yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—1511no—
291Q8—3021no—
292Q8—3021no—
293Q8—12081no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—12081no—
303D4—12081no—
304D4—12081no—
305C2×C4—21no—
306C2×C4—81no—
307C2×C4—3021no—
308C2×C4—3021no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—1511no—
314C2×C4—1511no—
315C2×C4—1511no—
316C2×C4—12081no—
317C2×C4—12081no—
318C2×C4D4×D15111yescharacteristic
319C2×C4D4×D15111yescharacteristic
320C2×C4C23×D15111yescharacteristic
321C8—21no—
322C8—21no—
323C8—3021no—
324C8—3021no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—3021no—
335C22—3021no—
336C22—3021no—
337C22C2×D4×D15111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—3021no—
342C4—3021no—
343C4—3021no—
344C4—6041no—
345C4—6041no—
346C4—6041no—
347C4—6041no—
348C4#1801278411yescharacteristic
349C4#1801278611yescharacteristic
350C2—81no—
351C2—81no—
352C2—81no—
353C2—6041no—
354C2#2375279111yescharacteristic
355C2#2375301311yescharacteristic
356C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#459×C151C2
socleC22×C151C22×D4
hypercenter#459D151
hypocenterC151#3257
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23752827C2semidirect
2. #23752816C2semidirect
3. #23752520C2semidirect
4. #23752512C2semidirect
5. #23752500C2semidirect
6. #23752490C2semidirect
7. #23752462C2semidirect
8. #23752457C2semidirect
9. #23752445C2semidirect
10. #23752440C2semidirect
11. #23752425C2semidirect
12. #23752425C2semidirect
13. #23752409C2semidirect
14. #23752237C2semidirect
15. #459×C151C2semidirect
178. C151#3257semidirect
193. #459D151semidirect

Maximal subgroups

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

subgroupindex
#237528272
#237528162
#237525202
#237525122
#237525002
#237524902
#237524622
#237524572
#237524452
#237524402
#237524252
#237524092
#237522372
#459×C1512
#3257151