Finite Group Databasebeta

← #34079303

Subgroups — #34079303

Order 19328.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752692C211yesmaximal, characteristic, complemented
2#23752528C211yesmaximal, characteristic, complemented
3#23752523C211yesmaximal, characteristic, complemented
4#23752516C211yesmaximal, characteristic, complemented
5#23752509C211yesmaximal, characteristic, complemented
6#23752409C211yesmaximal, characteristic, complemented
7#23752404C211yesmaximal, characteristic, complemented
8#23752355C211yesmaximal, characteristic, complemented
9#23752355C211yesmaximal, characteristic, complemented
10#23752322C211yesmaximal, characteristic, complemented
11#23752312C211yesmaximal, characteristic, complemented
12C4×#14558992C211yesmaximal, characteristic, complemented
13C4×#14558989C211yesmaximal, characteristic, complemented
14#23752273C211yesmaximal, characteristic, complemented
15#540×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558989C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C4×Dic302C2211yescharacteristic
22C4×Dic302C2211yescharacteristic
23C4×D604C2211yescharacteristic
24C4×D604C2211yescharacteristic
25(C22⋊D151)⋊C4—21no—
26(C22⋊D151)⋊C4—21no—
27#18012697—21no—
28C2×C4⋊Dic151C2211yescharacteristic
29C4⋊C4×D151—21no—
30#18012672C2211yescharacteristic
31#18012672C2211yescharacteristic
32#18012670C2211yescharacteristic
33#18012670C2211yescharacteristic
34C4⋊(C151⋊C8)C2211yescharacteristic
35C4⋊(C151⋊C8)C2211yescharacteristic
36#18012662C2211yescharacteristic
37#18012662C2211yescharacteristic
38#18012660C2211yescharacteristic
39#18012660C2211yescharacteristic
40#18012660C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46#18012650C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48#127×C151C2211yescharacteristic
49#125×C151C2211yescharacteristic
50#123×C151—21no—
51#123×C151—21no—
52#121×C151—21no—
53#121×C151—21no—
54#121×C151C2211yescharacteristic
55#121×C151C2211yescharacteristic
56C4×D4×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic
58#117×C151C2211yescharacteristic
59#14559004—22no—
60#14559004—22no—
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C22×Dic151—21no—
65C2×C4×D151—21no—
66C2×C4×D151—21no—
67C2×C4×D151—21no—
68#14558992—22no—
69#14558992—22no—
70#14558989—22no—
71#14558989—22no—
72C2×C151⋊C8C2311yescharacteristic
73C2×C151⋊C8C2311yescharacteristic
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C4⋊Dic151—21no—
77C4⋊Dic151C2311yescharacteristic
78C4⋊Dic151C2311yescharacteristic
79Dic151⋊C4—21no—
80Dic151⋊C4—21no—
81(C2×D151)⋊C4—21no—
82(C2×D151)⋊C4—21no—
83C4×Dic151—21no—
84C4×Dic151—21no—
85C2×D4×C151—21no—
86C2×D4×C151—21no—
87C2×D4×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151C2311yescharacteristic
90C2×D4×C151C2311yescharacteristic
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151C2311yescharacteristic
94C4⋊C4×C151—21no—
95C4⋊C4×C151—21no—
96C4⋊C4×C151D411yescharacteristic
97C4⋊C4×C151D411yescharacteristic
98C4⋊C4×C151C2311yescharacteristic
99C4⋊C4×C151C2311yescharacteristic
100C22⋊C4×C151—21no—
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C22⋊C4×C151—21no—
104C22⋊C4×C151D411yescharacteristic
105C22⋊C4×C151D411yescharacteristic
106C42×C151C2311yescharacteristic
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109Dic302—21no—
110Dic302#4112yes—
111D604—21no—
112D604#4112yes—
113C22⋊D151—24no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151—21no—
117C2×Dic151—81no—
118C4×D151—24no—
119C4×D151—81no—
120C4×D151—81no—
121C151⋊C8—21no—
122C151⋊C8—21no—
123C151⋊C8—21no—
124C151⋊C8—21no—
125C23×C151—21no—
126C23×C151—21no—
127C23×C151C2×D411yescharacteristic
128D4×C151—21no—
129D4×C151—21no—
130D4×C151—21no—
131D4×C151—21no—
132D4×C151—81no—
133D4×C151—81no—
134D4×C151—81no—
135D4×C151—81no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—81no—
141C2×C4×C151—81no—
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2×D411yescharacteristic
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2411yescharacteristic
148C22×C151—21no—
149C22×C151—21no—
150C22×C151—21no—
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151C22×D411yescharacteristic
158C2×D151—22no—
159C2×D151—41no—
160C2×D151—41no—
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—41no—
167C4×C151—41no—
168C4×C151C2×#4111yescharacteristic
169C4×C151C2×#4111yescharacteristic
170Dic151—22no—
171Dic151—41no—
172Dic151—41no—
173C2×C151—41no—
174C2×C151—81no—
175C2×C151—81no—
176C2×C151#52511yescharacteristic
177C2×C151#57611yescharacteristic
178C2×C151#57711yescharacteristic
179D151—42no—
180C151#311911yescharacteristic, complemented, Sylow
181#3119—1511nomaximal, Sylow
182#540D15111yescharacteristic, complemented
183#520—1511no—
184#481—1511no—
185#480—1511no—
186#479—1511no—
187#478—1511no—
188#460—1511no—
189#459—1511no—
190#449—1511no—
191#449—1511no—
192#442—1511no—
193#440—1511no—
194C4×SD16—1511no—
195C4×D8—1511no—
196#433—1511no—
197C2×#41—1511no—
198C2×SD16—1511no—
199C2×SD16—1511no—
200C2×D8—1511no—
201C2×D8—1511no—
202#127C2×D15111yescharacteristic
203#125C2×D15111yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D15111yescharacteristic
209#121C2×D15111yescharacteristic
210C4×Q8—1511no—
211C4×Q8—1511no—
212C4×D4—3021no—
213C4×D4—3021no—
214C4×D4—1511no—
215C4×D4—1511no—
216C4×D4C2×D15111yescharacteristic
217C4×D4C2×D15111yescharacteristic
218#117—3021no—
219#117C2×D15111yescharacteristic
220C2×C4⋊C4—3021no—
221C2×C4⋊C4—1511no—
222#107—1511no—
223#107—1511no—
224#106—1511no—
225#106—1511no—
226C4⋊C8—1511no—
227C4⋊C8—1511no—
228#103—1511no—
229#103—1511no—
230#102—1511no—
231#102—1511no—
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236C22⋊C8—1511no—
237C22⋊C8—1511no—
238#97—1511no—
239C4×C8—1511no—
240#41—3022no—
241#41—3022no—
242C2×Q8—1511no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—3021no—
248C2×D4—1511no—
249C2×D4C22×D15111yescharacteristic
250C2×D4C22×D15111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—3021no—
254C22×C4—3021no—
255C22×C4—3021no—
256C22×C4—3021no—
257C22×C4C22×D15111yescharacteristic
258SD16—3022no—
259SD16—3022no—
260D8—3022no—
261D8—3022no—
262C2×C8—1511no—
263C2×C8—1511no—
264C2×C8—1511no—
265C2×C8—1511no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—3021no—
269C4⋊C4—3021no—
270C4⋊C4—3021no—
271C4⋊C4—1511no—
272C4⋊C4—1511no—
273C4⋊C4C22⋊D15111yescharacteristic
274C4⋊C4C22⋊D15111yescharacteristic
275C4⋊C4C22×D15111yescharacteristic
276C4⋊C4C22×D15111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—3021no—
282C22⋊C4—3021no—
283C22⋊C4C22⋊D15111yescharacteristic
284C22⋊C4C22⋊D15111yescharacteristic
285C42—3021no—
286C42—3021no—
287C42C22×D15111yescharacteristic
288C42C22×D15111yescharacteristic
289C23—21no—
290C23—21no—
291C23—3021no—
292C23C2×C22⋊D15111yescharacteristic
293Q8—3021no—
294Q8—1512no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—3024no—
304D4—3021no—
305D4—1512no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—3024no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—12081no—
317C2×C4—12081no—
318C2×C4—12081no—
319C2×C4C2×C22⋊D15111yescharacteristic
320C2×C4C2×C22⋊D15111yescharacteristic
321C2×C4C2×C22⋊D15111yescharacteristic
322C2×C4C2×C22⋊D15111yescharacteristic
323C2×C4C2×C22⋊D15111yescharacteristic
324C2×C4C23×D15111yescharacteristic
325C8—3021no—
326C8—3021no—
327C8—3021no—
328C8—3021no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—3022no—
339C22—6041no—
340C22—6041no—
341C22C22×C22⋊D15111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—3022no—
350C4—6041no—
351C4—6041no—
352C4#41×D15111yescharacteristic
353C4#41×D15111yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—6042no—
358C2#2375271911yescharacteristic
359C2#2375301511yescharacteristic
360C2#2375302311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#540×C151C2
socleC22×C151C22×D4
hypercenter#540D151
hypocenterC151#3119
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23752692C2semidirect
2. #23752528C2semidirect
3. #23752523C2semidirect
4. #23752516C2semidirect
5. #23752509C2semidirect
6. #23752409C2semidirect
7. #23752404C2semidirect
8. #23752355C2semidirect
9. #23752355C2semidirect
10. #23752322C2semidirect
11. #23752312C2semidirect
12. C4×#14558992C2semidirect
13. C4×#14558989C2semidirect
14. #23752273C2semidirect
15. #540×C151C2semidirect
180. C151#3119semidirect
182. #540D151semidirect

Maximal subgroups

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

subgroupindex
#237526922
#237525282
#237525232
#237525162
#237525092
#237524092
#237524042
#237523552
#237523222
#237523122
C4×#145589922
C4×#145589892
#237522732
#540×C1512
#3119151