Finite Group Databasebeta

← #34080528

Subgroups — #34080528

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#23752836C211yesmaximal, characteristic, complemented
2#23752813C211yesmaximal, characteristic, complemented
3#23752518C211yesmaximal, characteristic, complemented
4#23752515C211yesmaximal, characteristic, complemented
5#23752499C211yesmaximal, characteristic, complemented
6#23752464C211yesmaximal, characteristic, complemented
7#23752459C211yesmaximal, characteristic, complemented
8#23752449C211yesmaximal, characteristic, complemented
9#23752440C211yesmaximal, characteristic, complemented
10#23752428C211yesmaximal, characteristic, complemented
11#23752427C211yesmaximal, characteristic, complemented
12#23752411C211yesmaximal, characteristic, complemented
13#23752406C211yesmaximal, characteristic, complemented
14#23752237C211yesmaximal, characteristic, complemented
15#474×C151C211yesmaximal, characteristic, complemented
16C2×#14558993C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×D1208C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012735C2211yescharacteristic
23#18012734—21no—
24#18012730C2211yescharacteristic
25#18012728—21no—
26#18012727C2211yescharacteristic
27#18012724—21no—
28#18012722—21no—
29#18012721—21no—
30#18012719C2211yescharacteristic
31#18012715—21no—
32#18012714C2211yescharacteristic
33#18012714C2211yescharacteristic
34#18012713—21no—
35#18012712—21no—
36#18012710C2211yescharacteristic
37#18012704C2211yescharacteristic
38C4×D604C2211yescharacteristic
39#18012701C2211yescharacteristic
40#18012696C2211yescharacteristic
41#18012670C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012664C2211yescharacteristic
47#18012662C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012659C2211yescharacteristic
51#18012659C2211yescharacteristic
52C4⋊Q8×C151C2211yescharacteristic
53C4×D4×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#107×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic
58#102×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C2×D604—21no—
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C4×D151—21no—
68C2×C4×D151—21no—
69C2×C4×D151C2311yescharacteristic
70#14558993—41no—
71#14558992—41no—
72D1208—41no—
73#14558989—41no—
74#14558987—41no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C8×D151—41no—
78C4⋊Dic151—21no—
79C4⋊Dic151—21no—
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84Dic151⋊C4D411yescharacteristic
85C22⋊Dic151—21no—
86(C2×D151)⋊C4—21no—
87(C2×D151)⋊C4—21no—
88(C2×D151)⋊C4—21no—
89(C2×D151)⋊C4—21no—
90(C2×D151)⋊C4—21no—
91(C2×D151)⋊C4—21no—
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4D411yescharacteristic
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151—21no—
98C2×D4×C151C2311yescharacteristic
99C22×C4×C151—21no—
100C2×C8×C151C2311yescharacteristic
101C2×C8×C151C2311yescharacteristic
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C22⋊C4×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110C22×D151C2×D411yescharacteristic
111Dic302—21no—
112Dic302—21no—
113D604—21no—
114D604—21no—
115D604—21no—
116D604—21no—
117D604—81no—
118D604—81no—
119C22⋊D151—81no—
120C22⋊D151—81no—
121C22⋊D151—81no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151C2×D411yescharacteristic
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C4×D151—21no—
128C4×D151—21no—
129C4×D151—81no—
130C4×D151—81no—
131C151⋊C8—21no—
132C151⋊C8—21no—
133C23×C151—21no—
134Q8×C151—81no—
135D4×C151—21no—
136D4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
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×C151C22×D411yescharacteristic
150C2×D151—21no—
151C2×D151—21no—
152C2×D151—21no—
153C2×D151—41no—
154C2×D151—41no—
155C2×D151—41no—
156C2×D151—41no—
157C2×D151—41no—
158C2×D151—41no—
159C4×C151—21no—
160C4×C151—21no—
161C4×C151—41no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151H(5,𝔽2)11yescharacteristic
165C4×C1512−1+411yescharacteristic
166Dic151—21no—
167Dic151—21no—
168Dic151—21no—
169Dic151—41no—
170Dic151—41no—
171C2×C151—81no—
172C2×C151#53711yescharacteristic
173C2×C151#57611yescharacteristic
174C2×C151#57711yescharacteristic
175D151—41no—
176D151—81no—
177D151—81no—
178C151#325711yescharacteristic, complemented, Sylow
179#3257—1511nomaximal, Sylow
180#542—1511no—
181#540—1511no—
182#479—1511no—
183#478—1511no—
184#476—1511no—
185#474D15111yescharacteristic, complemented
186#469—1511no—
187#468—1511no—
188#466—1511no—
189#465—1511no—
190#463—1511no—
191#463—1511no—
192#460—1511no—
193#459—1511no—
194#424—1511no—
195C2×SD16—1511no—
196C2×SD16—1511no—
197C2×D8—1511no—
198C2×D8—1511no—
199C2×M16—1511no—
200C22×C8—1511no—
201C4⋊Q8C2×D15111yescharacteristic
202#127—1511no—
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#107C2×D15111yescharacteristic
223#107C2×D15111yescharacteristic
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—21no—
239C2×Q8—1511no—
240C2×D4—3021no—
241C2×D4—3021no—
242C2×D4—3021no—
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4—1511no—
246C2×D4—1511no—
247C2×D4C22×D15111yescharacteristic
248C22×C4—21no—
249C22×C4—3021no—
250C22×C4—3021no—
251C22×C4—1511no—
252SD16—6041no—
253SD16—6041no—
254D8—6041no—
255D8—6041no—
256M16—6041no—
257C2×C8—6041no—
258C2×C8—1511no—
259C2×C8—1511no—
260C2×C8C22×D15111yescharacteristic
261C2×C8C22×D15111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—3021no—
264C4⋊C4—3021no—
265C4⋊C4—3021no—
266C4⋊C4—3021no—
267C4⋊C4—1511no—
268C4⋊C4—1511no—
269C4⋊C4—1511no—
270C4⋊C4C22×D15111yescharacteristic
271C4⋊C4C22×D15111yescharacteristic
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—3021no—
289C23—3021no—
290C23—1511no—
291Q8—81no—
292Q8—3021no—
293Q8—3021no—
294D4—21no—
295D4—21no—
296D4—3021no—
297D4—3021no—
298D4—3021no—
299D4—3021no—
300D4—12081no—
301D4—12081no—
302D4—12081no—
303D4—12081no—
304D4—12081no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
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—3021no—
329C22—3021no—
330C22—3021no—
331C22—6041no—
332C22—6041no—
333C22—6041no—
334C22—6041no—
335C22—6041no—
336C22—6041no—
337C22C2×D4×D15111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3021no—
344C4—3021no—
345C4—3021no—
346C4—6041no—
347C4—6041no—
348C4#1801278511yescharacteristic
349C4#1801278711yescharacteristic
350C2—81no—
351C2—6041no—
352C2—12081no—
353C2—12081no—
354C2#2375279211yescharacteristic
355C2#2375301311yescharacteristic
356C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#474×C151C2
socleC22×C151C22×D4
hypercenter#474D151
hypocenterC151#3257
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23752836C2semidirect
2. #23752813C2semidirect
3. #23752518C2semidirect
4. #23752515C2semidirect
5. #23752499C2semidirect
6. #23752464C2semidirect
7. #23752459C2semidirect
8. #23752449C2semidirect
9. #23752440C2semidirect
10. #23752428C2semidirect
11. #23752427C2semidirect
12. #23752411C2semidirect
13. #23752406C2semidirect
14. #23752237C2semidirect
15. #474×C151C2semidirect
178. C151#3257semidirect
185. #474D151semidirect

Maximal subgroups

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

subgroupindex
#237528362
#237528132
#237525182
#237525152
#237524992
#237524642
#237524592
#237524492
#237524402
#237524282
#237524272
#237524112
#237524062
#237522372
#474×C1512
#3257151