Finite Group Databasebeta

← #34080527

Subgroups — #34080527

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#23752834C211yesmaximal, characteristic, complemented
2#23752818C211yesmaximal, characteristic, complemented
3#23752509C211yesmaximal, characteristic, complemented
4#23752501C211yesmaximal, characteristic, complemented
5#23752491C211yesmaximal, characteristic, complemented
6#23752466C211yesmaximal, characteristic, complemented
7#23752461C211yesmaximal, characteristic, complemented
8#23752449C211yesmaximal, characteristic, complemented
9#23752444C211yesmaximal, characteristic, complemented
10#23752430C211yesmaximal, characteristic, complemented
11#23752430C211yesmaximal, characteristic, complemented
12#23752412C211yesmaximal, characteristic, complemented
13#23752408C211yesmaximal, characteristic, complemented
14#23752237C211yesmaximal, characteristic, complemented
15#479×C151C211yesmaximal, characteristic, complemented
16C2×#14558991C2211yescharacteristic
17C2×#14558991C2211yescharacteristic
18C2×D1208C2211yescharacteristic
19C2×D1208C2211yescharacteristic
20C2×#14558987C2211yescharacteristic
21C2×C8×D151C2211yescharacteristic
22#18012738C2211yescharacteristic
23#18012736C2211yescharacteristic
24#18012733—21no—
25#18012728C2211yescharacteristic
26#18012727—21no—
27#18012724—21no—
28#18012724—21no—
29#18012724—21no—
30#18012717—21no—
31#18012715C2211yescharacteristic
32#18012714—21no—
33#18012714—21no—
34#18012714C2211yescharacteristic
35#18012714C2211yescharacteristic
36#18012714C2211yescharacteristic
37C4×D604C2211yescharacteristic
38#18012701C2211yescharacteristic
39#18012701C2211yescharacteristic
40#18012696C2211yescharacteristic
41#18012672C2211yescharacteristic
42#18012670C2211yescharacteristic
43C4⋊(C151⋊C8)C2211yescharacteristic
44Dic151⋊C8C2211yescharacteristic
45Dic151⋊C8C2211yescharacteristic
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012659C2211yescharacteristic
49#18012659C2211yescharacteristic
50#18012659C2211yescharacteristic
51#18012659C2211yescharacteristic
52#125×C151C2211yescharacteristic
53C4×Q8×C151C2211yescharacteristic
54#107×C151C2211yescharacteristic
55#106×C151C2211yescharacteristic
56C4⋊C8×C151C2211yescharacteristic
57#103×C151C2211yescharacteristic
58#103×C151C2211yescharacteristic
59C2×Dic302—21no—
60C2×D604—21no—
61C2×D604—21no—
62C2×D604—21no—
63C2×D604—21no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×D604C2311yescharacteristic
68C2×C4×D151—21no—
69C2×C4×D151—21no—
70C2×C4×D151—21no—
71C2×C4×D151C2311yescharacteristic
72#14558991—41no—
73#14558991—41no—
74D1208—41no—
75D1208—41no—
76#14558987—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C8×D151—41no—
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83Dic151⋊C4D411yescharacteristic
84Dic151⋊C4D411yescharacteristic
85(C2×D151)⋊C4—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)⋊C4—21no—
94(C2×D151)⋊C4D411yescharacteristic
95(C2×D151)⋊C4D411yescharacteristic
96C4×Dic151C2311yescharacteristic
97C2×Q8×C151C2311yescharacteristic
98C2×C8×C151C2311yescharacteristic
99C2×C8×C151C2311yescharacteristic
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151C2311yescharacteristic
104C4⋊C4×C151C2311yescharacteristic
105C4⋊C4×C151C2311yescharacteristic
106C42×C151—21no—
107C42×C151C2311yescharacteristic
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—21no—
111C22×D151C2×D411yescharacteristic
112Dic302—81no—
113D604—21no—
114D604—21no—
115D604—21no—
116D604—21no—
117D604—21no—
118D604—21no—
119D604—81no—
120D604—81no—
121D604—81no—
122D604—81no—
123D604—81no—
124C2×Dic151—21no—
125C2×Dic151C2×D411yescharacteristic
126C2×Dic151C2×D411yescharacteristic
127C2×Dic151C2×D411yescharacteristic
128C4×D151—21no—
129C4×D151—21no—
130C4×D151—81no—
131C4×D151—81no—
132C4×D151—81no—
133C151⋊C8—21no—
134C151⋊C8—21no—
135Q8×C151—21no—
136Q8×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151C2×D411yescharacteristic
142C2×C4×C151C2×D411yescharacteristic
143C2×C4×C151C2411yescharacteristic
144C8×C151—21no—
145C8×C151—21no—
146C22×C151C22×D411yescharacteristic
147C2×D151—21no—
148C2×D151—21no—
149C2×D151—21no—
150C2×D151—41no—
151C2×D151—41no—
152C2×D151—41no—
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×C151—41no—
165C4×C151H(5,𝔽2)11yescharacteristic
166C4×C1512−1+411yescharacteristic
167Dic151—21no—
168Dic151—21no—
169Dic151—21no—
170Dic151—41no—
171C2×C151#53711yescharacteristic
172C2×C151#57611yescharacteristic
173C2×C151#57711yescharacteristic
174D151—41no—
175D151—81no—
176D151—81no—
177D151—81no—
178C151#325711yescharacteristic, complemented, Sylow
179#3257—1511nomaximal, Sylow
180#542—1511no—
181#540—1511no—
182#479D15111yescharacteristic, complemented
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#459—1511no—
194#424—1511no—
195C2×SD16—1511no—
196C2×SD16—1511no—
197C2×D8—1511no—
198C2×D8—1511no—
199C2×M16—1511no—
200C22×C8—1511no—
201C4⋊Q8—1511no—
202#127—1511no—
203#126—3021no—
204#125C2×D15111yescharacteristic
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×Q8C2×D15111yescharacteristic
218C4×D4—1511no—
219C4×D4—1511no—
220C4×D4—1511no—
221#117—1511no—
222#107—1511no—
223#107C2×D15111yescharacteristic
224#106—1511no—
225#106C2×D15111yescharacteristic
226C4⋊C8—1511no—
227C4⋊C8—1511no—
228C4⋊C8—1511no—
229C4⋊C8C2×D15111yescharacteristic
230#103C2×D15111yescharacteristic
231#103C2×D15111yescharacteristic
232#102—1511no—
233#102—1511no—
234#102—1511no—
235#102—1511no—
236#102—1511no—
237#102—1511no—
238C2×Q8—3021no—
239C2×Q8C22×D15111yescharacteristic
240C2×D4—3021no—
241C2×D4—3021no—
242C2×D4—3021no—
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4—1511no—
246C2×D4—1511no—
247C2×D4—1511no—
248C22×C4—3021no—
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—21no—
264C4⋊C4—21no—
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—3021no—
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—21no—
285C42—1511no—
286C42C22×D15111yescharacteristic
287C23—3021no—
288C23—3021no—
289C23—3021no—
290C23—1511no—
291Q8—21no—
292Q8—21no—
293Q8—12081no—
294D4—3021no—
295D4—3021no—
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—21no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—1511no—
313C2×C4—1511no—
314C2×C4—1511no—
315C2×C4—12081no—
316C2×C4—12081no—
317C2×C4—12081no—
318C2×C4D4×D15111yescharacteristic
319C2×C4D4×D15111yescharacteristic
320C2×C4C23×D15111yescharacteristic
321C8—21no—
322C8—21no—
323C8—3021no—
324C8—3021no—
325C22—3021no—
326C22—3021no—
327C22—3021no—
328C22—6041no—
329C22—6041no—
330C22—6041no—
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—41no—
344C4—3021no—
345C4—3021no—
346C4—3021no—
347C4—6041no—
348C4#1801278511yescharacteristic
349C4#1801278711yescharacteristic
350C2—6041no—
351C2—12081no—
352C2—12081no—
353C2—12081no—
354C2#2375279211yescharacteristic
355C2#2375301411yescharacteristic
356C2#2375302111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#479×C151C2
socleC22×C151C22×D4
hypercenter#479D151
hypocenterC151#3257
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #23752834C2semidirect
2. #23752818C2semidirect
3. #23752509C2semidirect
4. #23752501C2semidirect
5. #23752491C2semidirect
6. #23752466C2semidirect
7. #23752461C2semidirect
8. #23752449C2semidirect
9. #23752444C2semidirect
10. #23752430C2semidirect
11. #23752430C2semidirect
12. #23752412C2semidirect
13. #23752408C2semidirect
14. #23752237C2semidirect
15. #479×C151C2semidirect
178. C151#3257semidirect
182. #479D151semidirect

Maximal subgroups

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

subgroupindex
#237528342
#237528182
#237525092
#237525012
#237524912
#237524662
#237524612
#237524492
#237524442
#237524302
#237524122
#237524082
#237522372
#479×C1512
#3257151