Finite Group Databasebeta

← #34080206

Subgroups — #34080206

Order 19328.

408 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#23752833C211yesmaximal, characteristic, complemented
2#23752781C211yesmaximal, characteristic, complemented
3#23752601C211yesmaximal, characteristic, complemented
4#23752596C211yesmaximal, characteristic, complemented
5#23752572C211yesmaximal, characteristic, complemented
6#23752559C211yesmaximal, characteristic, complemented
7#23752435C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752413C211yesmaximal, characteristic, complemented
10#23752408C211yesmaximal, characteristic, complemented
11#23752376C211yesmaximal, characteristic, complemented
12#23752365C211yesmaximal, characteristic, complemented
13#23752359C211yesmaximal, characteristic, complemented
14#23752348C211yesmaximal, characteristic, complemented
15#433×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C2×Dic604C2211yescharacteristic, complemented
19C2×#14558993C2211yescharacteristic
20C2×#14558993C2211yescharacteristic
21C2×#14558993C2211yescharacteristic, complemented
22C2×#14558993C2211yescharacteristic, complemented
23C2×D1208C2211yescharacteristic
24C2×D1208C2211yescharacteristic
25C2×D1208C2211yescharacteristic, complemented
26#18012739C2211yescharacteristic, complemented
27#18012736C2211yescharacteristic
28#18012736C2211yescharacteristic
29#18012734—21no—
30#18012727C2211yescharacteristic
31#18012727C2211yescharacteristic
32#18012727C2211yescharacteristic, complemented
33#18012725—21no—
34#18012721—21no—
35#18012718C2211yescharacteristic
36#18012717—21no—
37#18012714—21no—
38#18012714—21no—
39#18012713C2211yescharacteristic
40#18012709—21no—
41#18012709—21no—
42C4×Dic302C2211yescharacteristic, complemented
43C4×D604C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012664C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic
48#18012661C2211yescharacteristic
49#18012661C2211yescharacteristic
50#18012661C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic, complemented
52#117×C151C2211yescharacteristic
53C4⋊C8×C151C2211yescharacteristic, complemented
54C4⋊C8×C151C2211yescharacteristic, complemented
55C22⋊C8×C151C2211yescharacteristic
56C22⋊C8×C151C2211yescharacteristic
57#97×C151C2211yescharacteristic, complemented
58C4×C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60#14559004—41no—
61#14559004—41no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64C2×Dic302C2311yescharacteristic
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604—41no—
71C2×D604—41no—
72C2×D604C2311yescharacteristic
73C2×D604C2311yescharacteristic
74C2×D604C2311yescharacteristic
75C2×D604C2311yescharacteristic
76C2×C22⋊D151—21no—
77C2×C22⋊D151—21no—
78C2×C4×D151—21no—
79C2×C4×D151—21no—
80Dic604—41no—
81#14558993—41no—
82#14558993—41no—
83#14558993—41no—
84#14558993—41no—
85D1208—41no—
86D1208—41no—
87D1208—41no—
88C4⋊Dic151—21no—
89C4⋊Dic151C2311yescharacteristic
90C4⋊Dic151C2311yescharacteristic
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93C22⋊Dic151—21no—
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4—21no—
102C4×Dic151—21no—
103C22×C4×C151C2311yescharacteristic
104C2×C8×C151C2311yescharacteristic
105C2×C8×C151C2311yescharacteristic
106C2×C8×C151C2311yescharacteristic
107C2×C8×C151C2311yescharacteristic
108C4⋊C4×C151D411yescharacteristic
109C4⋊C4×C151D411yescharacteristic
110C22⋊C4×C151D411yescharacteristic
111C22⋊C4×C151D411yescharacteristic
112C42×C151C2311yescharacteristic
113C42×C151C2311yescharacteristic
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—21no—
118C22×D151—42no—
119C22×D151—81no—
120C22×D151—81no—
121Dic302—21no—
122Dic302—21no—
123Dic302—21no—
124Dic302—21no—
125Dic302—81no—
126D604—21no—
127D604—21no—
128D604—21no—
129D604—21no—
130D604—21no—
131D604—21no—
132D604—21no—
133D604—21no—
134D604—42no—
135D604—81no—
136D604—81no—
137D604—81no—
138D604—81no—
139C22⋊D151—42no—
140C22⋊D151—81no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—21no—
145C4×D151—42no—
146C4×D151—81no—
147C23×C151C2×D411yescharacteristic
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151C2×D411yescharacteristic
151C2×C4×C151C2×D411yescharacteristic
152C2×C4×C151C2×D411yescharacteristic
153C2×C4×C151C2×D411yescharacteristic
154C2×C4×C151C2×D411yescharacteristic
155C2×C4×C151C2411yescharacteristic
156C8×C151—21no—
157C8×C151—21no—
158C8×C151—21no—
159C8×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151C22×D411yescharacteristic
164C2×D151—41no—
165C2×D151—41no—
166C2×D151—41no—
167C2×D151—41no—
168C2×D151—41no—
169C2×D151—41no—
170C2×D151—41no—
171C2×D151—41no—
172C2×D151—41no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—84no—
177C4×C151—21no—
178C4×C151—21no—
179C4×C151—21no—
180C4×C151—21no—
181C4×C151—21no—
182C4×C151H(5,𝔽2)11yescharacteristic
183C4×C151H(5,𝔽2)11yescharacteristic
184Dic151—41no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188C2×C151—41no—
189C2×C151#53511yescharacteristic
190C2×C151#57611yescharacteristic
191C2×C151#57711yescharacteristic
192D151—81no—
193D151—81no—
194D151—81no—
195D151—81no—
196C151#322411yescharacteristic, complemented, Sylow
197#3224—1511nomaximal, Sylow
198#542—1511no—
199#535—1511no—
200#496—1511no—
201#495—1511no—
202#489—1511no—
203#486—1511no—
204#464—1511no—
205#463—1511no—
206#460—1511no—
207#459—1511no—
208#452—1511no—
209#450—1511no—
210#449—1511no—
211#447—1511no—
212#433D15111yescharacteristic, complemented
213C2×#41—1511no—
214C22×D4—1511no—
215C2×Q16—1511no—
216C2×SD16—1511no—
217C2×SD16—1511no—
218C2×SD16—1511no—
219C2×SD16—1511no—
220C2×D8—1511no—
221C2×D8—1511no—
222C2×D8—1511no—
223C4⋊Q8—1511no—
224#127—1511no—
225#127—1511no—
226#126—3021no—
227#124—3021no—
228#124—1511no—
229#124—1511no—
230#124—1511no—
231#123—3021no—
232C22⋊Q8—3021no—
233C22⋊Q8—1511no—
234#121—3021no—
235#121—3021no—
236#121—1511no—
237#120—3021no—
238#120—3021no—
239C4×Q8—1511no—
240C4×D4—1511no—
241#117C2×D15111yescharacteristic
242C4⋊C8C2×D15111yescharacteristic, complemented
243C4⋊C8C2×D15111yescharacteristic, complemented
244#103—1511no—
245#103—1511no—
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102—1511no—
251#102—1511no—
252C22⋊C8C2×D15111yescharacteristic
253C22⋊C8C2×D15111yescharacteristic
254#97C2×D15111yescharacteristic, complemented
255C4×C8C2×D15111yescharacteristic, complemented
256C24—3021no—
257#41—6041no—
258#41—6041no—
259C2×Q8—3021no—
260C2×Q8—1511no—
261C2×Q8—1511no—
262C2×D4—3021no—
263C2×D4—3021no—
264C2×D4—3021no—
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—6041no—
270C2×D4—6041no—
271C2×D4—1511no—
272C2×D4—1511no—
273C2×D4—1511no—
274C2×D4—1511no—
275C22×C4—3021no—
276C22×C4—3021no—
277C22×C4C22×D15111yescharacteristic
278Q16—6041no—
279SD16—6041no—
280SD16—6041no—
281SD16—6041no—
282SD16—6041no—
283D8—6041no—
284D8—6041no—
285D8—6041no—
286C2×C8C22×D15111yescharacteristic
287C2×C8C22×D15111yescharacteristic
288C2×C8C22×D15111yescharacteristic
289C2×C8C22×D15111yescharacteristic
290C4⋊C4—3021no—
291C4⋊C4—3021no—
292C4⋊C4—3021no—
293C4⋊C4—1511no—
294C4⋊C4—1511no—
295C4⋊C4D60411yescharacteristic
296C4⋊C4D60411yescharacteristic
297C22⋊C4—3021no—
298C22⋊C4—3021no—
299C22⋊C4—3021no—
300C22⋊C4—3021no—
301C22⋊C4—3021no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4D60411yescharacteristic
307C22⋊C4D60411yescharacteristic
308C42—3021no—
309C42C22×D15111yescharacteristic
310C42C22×D15111yescharacteristic
311C23—3021no—
312C23—3021no—
313C23—3021no—
314C23—3021no—
315C23—6042no—
316C23—12081no—
317C23—12081no—
318C23C2×D60411yescharacteristic
319Q8—3021no—
320Q8—3021no—
321Q8—3021no—
322Q8—3021no—
323Q8—12081no—
324D4—3021no—
325D4—3021no—
326D4—3021no—
327D4—3021no—
328D4—3021no—
329D4—3021no—
330D4—3021no—
331D4—3021no—
332D4—6042no—
333D4—6042no—
334D4—12081no—
335D4—12081no—
336D4—12081no—
337D4—12081no—
338D4—12081no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—6042no—
346C2×C4—12081no—
347C2×C4C2×D60411yescharacteristic
348C2×C4C2×D60411yescharacteristic
349C2×C4C2×D60411yescharacteristic
350C2×C4C2×D60411yescharacteristic
351C2×C4C2×D60411yescharacteristic
352C2×C4C23×D15111yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—6041no—
361C22—6041no—
362C22—6041no—
363C22—6041no—
364C22—6041no—
365C22—6041no—
366C22—6041no—
367C22—6041no—
368C22—6041no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—12084no—
373C22C22×D60411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—6041no—
380C4—6041no—
381C4—6041no—
382C4—6041no—
383C4#1801278511yescharacteristic
384C4#1801278511yescharacteristic
385C2—41no—
386C2—12081no—
387C2—12081no—
388C2—12081no—
389C2—12081no—
390C2#2375278111yescharacteristic
391C2#2375301711yescharacteristic
392C2#2375302411yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
hypercenter#433D151
hypocenterC151#3224
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23752833C2semidirect
2. #23752781C2semidirect
3. #23752601C2semidirect
4. #23752596C2semidirect
5. #23752572C2semidirect
6. #23752559C2semidirect
7. #23752435C2semidirect
8. #23752428C2semidirect
9. #23752413C2semidirect
10. #23752408C2semidirect
11. #23752376C2semidirect
12. #23752365C2semidirect
13. #23752359C2semidirect
14. #23752348C2semidirect
15. #433×C151C2semidirect
18. C2×Dic604C22semidirect
21. C2×#14558993C22semidirect
22. C2×#14558993C22semidirect
25. C2×D1208C22semidirect
26. #18012739C22semidirect
32. #18012727C22semidirect
42. C4×Dic302C22semidirect
43. C4×D604C22semidirect
44. #18012664C22semidirect
45. #18012664C22semidirect
50. #18012661C22semidirect
51. #18012661C22semidirect
53. C4⋊C8×C151C22semidirect
54. C4⋊C8×C151C22semidirect
57. #97×C151C22semidirect
58. C4×C8×C151C22semidirect
196. C151#3224semidirect
212. #433D151semidirect
242. C4⋊C8C2×D151semidirect
243. C4⋊C8C2×D151semidirect
254. #97C2×D151semidirect
255. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528332
#237527812
#237526012
#237525962
#237525722
#237525592
#237524352
#237524282
#237524132
#237524082
#237523762
#237523652
#237523592
#237523482
#433×C1512
#3224151