Finite Group Databasebeta

← #34080007

Subgroups — #34080007

Order 19328.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752790C211yesmaximal, characteristic, complemented
2#23752547C211yesmaximal, characteristic, complemented
3#23752545C211yesmaximal, characteristic, complemented
4#23752525C211yesmaximal, characteristic, complemented
5#23752523C211yesmaximal, characteristic, complemented
6#23752460C211yesmaximal, characteristic, complemented
7#23752456C211yesmaximal, characteristic, complemented
8#23752451C211yesmaximal, characteristic, complemented
9#23752446C211yesmaximal, characteristic, complemented
10#23752374C211yesmaximal, characteristic, complemented
11#23752372C211yesmaximal, characteristic, complemented
12#23752357C211yesmaximal, characteristic, complemented
13#23752355C211yesmaximal, characteristic, complemented
14#23752179C211yesmaximal, characteristic, complemented
15#537×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C2×#14558994C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558989C2211yescharacteristic
21C2×#14558988C2211yescharacteristic
22C22×C151⋊C8C2211yescharacteristic
23#18012718C2211yescharacteristic
24#18012718C2211yescharacteristic
25#18012715—21no—
26#18012713C2211yescharacteristic
27#18012713C2211yescharacteristic
28#18012711—21no—
29#18012711—21no—
30#18012710—21no—
31C2×C4⋊Dic151C2211yescharacteristic
32#18012672C2211yescharacteristic
33#18012672C2211yescharacteristic
34#18012672C2211yescharacteristic
35#18012672C2211yescharacteristic
36#18012663C2211yescharacteristic
37#18012663C2211yescharacteristic
38#18012662C2211yescharacteristic
39#18012662C2211yescharacteristic
40#18012660C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012659C2211yescharacteristic
43#18012659C2211yescharacteristic
44C22⋊(C151⋊C8)C2211yescharacteristic
45C22⋊(C151⋊C8)C2211yescharacteristic
46C22⋊(C151⋊C8)C2211yescharacteristic
47C22⋊(C151⋊C8)C2211yescharacteristic
48C2×#41×C151C2211yescharacteristic
49C2×#41×C151C2211yescharacteristic
50C22⋊Q8×C151—21no—
51C22⋊Q8×C151C2211yescharacteristic
52C22⋊Q8×C151C2211yescharacteristic
53#121×C151—21no—
54#121×C151—21no—
55#121×C151—21no—
56#121×C151C2211yescharacteristic
57#121×C151C2211yescharacteristic
58C2×C4⋊C4×C151C2211yescharacteristic
59#14559004—41no—
60#14559004—41no—
61C2×Dic302C2311yescharacteristic
62C2×D604C2311yescharacteristic
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C22×Dic151—21no—
67C2×C4×D151—21no—
68#14558994—41no—
69#14558992—41no—
70#14558991—41no—
71#14558989—41no—
72#14558988—41no—
73C2×C151⋊C8—41no—
74C2×C151⋊C8C2311yescharacteristic
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C4⋊Dic151—21no—
79C4⋊Dic151C2311yescharacteristic
80C4⋊Dic151C2311yescharacteristic
81Dic151⋊C4—21no—
82Dic151⋊C4—21no—
83C22⋊Dic151—21no—
84C22⋊Dic151—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87#41×C151—41no—
88#41×C151—41no—
89#41×C151—41no—
90#41×C151—41no—
91C2×Q8×C151D411yescharacteristic
92C2×Q8×C151C2311yescharacteristic
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—21no—
96C2×D4×C151D411yescharacteristic
97C2×D4×C151D411yescharacteristic
98C2×D4×C151D411yescharacteristic
99C2×D4×C151C2311yescharacteristic
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151C2311yescharacteristic
103C22×C4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151C2311yescharacteristic
109C4⋊C4×C151C2311yescharacteristic
110C22⋊C4×C151—21no—
111C22⋊C4×C151—21no—
112C22⋊C4×C151—21no—
113C22⋊C4×C151—21no—
114C22×D151—21no—
115Dic302—21no—
116Dic302—21no—
117D604—21no—
118D604—21no—
119C22⋊D151—42no—
120C22⋊D151—81no—
121C22⋊D151—81no—
122C2×Dic151—21no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C2×Dic151—81no—
126C4×D151—42no—
127C151⋊C8—21no—
128C151⋊C8—21no—
129C151⋊C8—21no—
130C151⋊C8—21no—
131C23×C151—21no—
132C23×C151C2×D411yescharacteristic
133C23×C151C2×D411yescharacteristic
134C23×C151C2×D411yescharacteristic
135Q8×C151—21no—
136Q8×C151—21no—
137Q8×C151—41no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—41no—
141D4×C151—41no—
142D4×C151—41no—
143D4×C151—42no—
144D4×C151—81no—
145D4×C151—81no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—21no—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—42no—
156C2×C4×C151—81no—
157C2×C4×C151C2×D411yescharacteristic
158C2×C4×C151C2×D411yescharacteristic
159C2×C4×C151C2×D411yescharacteristic
160C2×C4×C151C2411yescharacteristic
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—21no—
164C22×C151—21no—
165C22×C151—21no—
166C22×C151—21no—
167C22×C151—21no—
168C22×C151—21no—
169C22×C151—21no—
170C22×C151—41no—
171C22×C151—41no—
172C22×C151—41no—
173C22×C151C22×D411yescharacteristic
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C4×C151—21no—
178C4×C151—21no—
179C4×C151—21no—
180C4×C151—41no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151H(5,𝔽2)11yescharacteristic
184C4×C151H(5,𝔽2)11yescharacteristic
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—41no—
189C2×C151—41no—
190C2×C151—41no—
191C2×C151—81no—
192C2×C151#53411yescharacteristic
193C2×C151#57611yescharacteristic
194C2×C151#57811yescharacteristic
195D151—81no—
196C151#320311yescharacteristic, complemented, Sylow
197#3203—1511nomaximal, Sylow
198#537—1511no—
199#537D15111yescharacteristic, complemented
200#484—1511no—
201#484—1511no—
202#480—1511no—
203#480—1511no—
204#468—1511no—
205#468—1511no—
206#467—1511no—
207#466—1511no—
208#452—1511no—
209#452—1511no—
210#449—1511no—
211#449—1511no—
212#408—1511no—
213C2×#41—1511no—
214C2×#41C2×D15111yescharacteristic
215C2×#41C2×D15111yescharacteristic
216C2×Q16—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×D8—1511no—
220C2×M16—1511no—
221C22×C8—1511no—
222C22⋊Q8—21no—
223C22⋊Q8—3021no—
224C22⋊Q8—1511no—
225C22⋊Q8—1511no—
226C22⋊Q8C2×D15111yescharacteristic
227C22⋊Q8C2×D15111yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—3021no—
232#121—3021no—
233#121—3021no—
234#121—1511no—
235#121—1511no—
236#121C2×D15111yescharacteristic
237#121C2×D15111yescharacteristic
238C2×C4⋊C4—1511no—
239C2×C4⋊C4C2×D15111yescharacteristic
240#107—1511no—
241#107—1511no—
242#107—1511no—
243#107—1511no—
244#103—1511no—
245#103—1511no—
246#103—1511no—
247#103—1511no—
248#102—1511no—
249#102—1511no—
250#102—1511no—
251#102—1511no—
252C22⋊C8—1511no—
253C22⋊C8—1511no—
254C22⋊C8—1511no—
255C22⋊C8—1511no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—6041no—
261#41—6041no—
262C2×Q8—1511no—
263C2×Q8C22⋊D15111yescharacteristic
264C2×Q8C22×D15111yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—3021no—
271C2×D4—1511no—
272C2×D4C22⋊D15111yescharacteristic
273C2×D4C22⋊D15111yescharacteristic
274C2×D4C22⋊D15111yescharacteristic
275C2×D4C22×D15111yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—3021no—
279C22×C4—3021no—
280C22×C4C22×D15111yescharacteristic
281C22×C4C22×D15111yescharacteristic
282C22×C4C22×D15111yescharacteristic
283Q16—6041no—
284SD16—6041no—
285SD16—6041no—
286D8—6041no—
287M16—6041no—
288C2×C8—6041no—
289C2×C8—1511no—
290C2×C8—1511no—
291C2×C8—1511no—
292C2×C8—1511no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—3021no—
297C4⋊C4—3021no—
298C4⋊C4—3021no—
299C4⋊C4—1511no—
300C4⋊C4—1511no—
301C4⋊C4C22×D15111yescharacteristic
302C4⋊C4C22×D15111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C23—21no—
312C23—3021no—
313C23C2×C22⋊D15111yescharacteristic
314C23C2×C22⋊D15111yescharacteristic
315C23C2×C22⋊D15111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—3021no—
320Q8—3021no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—3021no—
330D4—3021no—
331D4—6042no—
332D4—12081no—
333D4—12081no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—3021no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—6042no—
349C2×C4—12081no—
350C2×C4C2×C22⋊D15111yescharacteristic
351C2×C4C2×C22⋊D15111yescharacteristic
352C2×C4C2×C22⋊D15111yescharacteristic
353C2×C4C23×D15111yescharacteristic
354C8—3021no—
355C8—3021no—
356C8—3021no—
357C8—3021no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—6041no—
371C22—6041no—
372C22—6041no—
373C22C22×C22⋊D15111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—6041no—
381C4—6041no—
382C4—6041no—
383C4#1801278411yescharacteristic
384C4#1801278411yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—12081no—
390C2#2375277111yescharacteristic
391C2#2375301511yescharacteristic
392C2#2375302711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#537×C151C2
socleC22×C151C22×D4
hypercenter#537D151
hypocenterC151#3203
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #23752790C2semidirect
2. #23752547C2semidirect
3. #23752545C2semidirect
4. #23752525C2semidirect
5. #23752523C2semidirect
6. #23752460C2semidirect
7. #23752456C2semidirect
8. #23752451C2semidirect
9. #23752446C2semidirect
10. #23752374C2semidirect
11. #23752372C2semidirect
12. #23752357C2semidirect
13. #23752355C2semidirect
14. #23752179C2semidirect
15. #537×C151C2semidirect
196. C151#3203semidirect
199. #537D151semidirect

Maximal subgroups

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

subgroupindex
#237527902
#237525472
#237525452
#237525252
#237525232
#237524602
#237524562
#237524512
#237524462
#237523742
#237523722
#237523572
#237523552
#237521792
#537×C1512
#3203151