Finite Group Databasebeta

← #34071704

Subgroups — #34071704

Order 19328.

672 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×D151C211yesmaximal, characteristic
2#23752106C211yesmaximal, characteristic, complemented
3#23752105C211yesmaximal, characteristic, complemented
4#23752104C211yesmaximal, characteristic, complemented
5#23752103C211yesmaximal, characteristic, complemented
6#23752102C211yesmaximal, characteristic, complemented
7#23752101C211yesmaximal, characteristic, complemented
8#23752100C211yesmaximal, characteristic, complemented
9#23752071C211yesmaximal, characteristic, complemented
10#23752069C211yesmaximal, characteristic, complemented
11#23752067C211yesmaximal, characteristic
12#23752067C211yesmaximal, characteristic
13C4×(C2×D151)⋊C4C211yesmaximal, characteristic, complemented
14#23752059C211yesmaximal, characteristic, complemented
15#388×C151C211yesmaximal, characteristic, complemented
16C24×D151C2211yescharacteristic
17C22×C4×D151C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19C2×C4⋊Dic151C2211yescharacteristic, complemented
20C2×Dic151⋊C4C2211yescharacteristic, complemented
21C2×Dic151⋊C4C2211yescharacteristic, complemented
22C2×C22⋊Dic151C2211yescharacteristic
23C2×C22⋊Dic151C2211yescharacteristic
24C2×C22⋊Dic151C2211yescharacteristic
25C2×(C2×D151)⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2211yescharacteristic
27C2×(C2×D151)⋊C4C2211yescharacteristic
28C2×(C2×D151)⋊C4C2211yescharacteristic
29C2×(C2×D151)⋊C4C2211yescharacteristic
30C2×(C2×D151)⋊C4C2211yescharacteristic
31C2×(C2×D151)⋊C4C2211yescharacteristic
32C2×(C2×D151)⋊C4C2211yescharacteristic
33C2×(C2×D151)⋊C4C2211yescharacteristic
34C2×(C2×D151)⋊C4C2211yescharacteristic
35C22⋊C4×D151C418yescomplemented
36C2×C4×Dic151C2211yescharacteristic, complemented
37C2×C4×Dic151C2211yescharacteristic, complemented
38C2×C4×Dic151C2211yescharacteristic, complemented
39C151⋊#95C2211yescharacteristic, complemented
40C151⋊#95C2211yescharacteristic, complemented
41C151⋊#95C2211yescharacteristic, complemented
42C151⋊#95C2211yescharacteristic, complemented
43C151⋊#95C2211yescharacteristic, complemented
44C151⋊#95C2211yescharacteristic, complemented
45C2×C4⋊C4×C151C2211yescharacteristic, complemented
46C2×C22⋊C4×C151C2211yescharacteristic
47C2×C22⋊C4×C151C2211yescharacteristic
48C2×C22⋊C4×C151C2211yescharacteristic
49C2×C42×C151C2211yescharacteristic, complemented
50#95×C151C2211yescharacteristic, complemented
51#95×C151C2211yescharacteristic, complemented
52C23×D151—22no—
53C23×D151—22no—
54C23×D151—41no—
55C23×D151—41no—
56C23×D151—41no—
57C23×D151—41no—
58C23×D151C2×C414yes—
59C23×D151C2311yescharacteristic
60C23×D151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C22×Dic151C2311yescharacteristic
64C22×Dic151C2311yescharacteristic
65C22×Dic151C2311yescharacteristic
66C22×Dic151C2311yescharacteristic
67C2×C4×D151—41no—
68C2×C4×D151—41no—
69C2×C4×D151—41no—
70C2×C4×D151—41no—
71C2×C4×D151C2×C414yes—
72C2×C4×D151C2×C414yes—
73C4⋊Dic151—41no—
74Dic151⋊C4—41no—
75Dic151⋊C4—41no—
76C22⋊Dic151—41no—
77C22⋊Dic151—41no—
78C22⋊Dic151C2×C414yes—
79(C2×D151)⋊C4—22no—
80(C2×D151)⋊C4—22no—
81(C2×D151)⋊C4—22no—
82(C2×D151)⋊C4—22no—
83(C2×D151)⋊C4—41no—
84(C2×D151)⋊C4—41no—
85(C2×D151)⋊C4—41no—
86(C2×D151)⋊C4—41no—
87(C2×D151)⋊C4C2×C414yes—
88(C2×D151)⋊C4C2×C414yes—
89C4×Dic151—41no—
90C4×Dic151—41no—
91C4×Dic151—41no—
92C24×C151C2311yescharacteristic
93C22×C4×C151C2311yescharacteristic
94C22×C4×C151C2311yescharacteristic
95C22×C4×C151C2311yescharacteristic
96C22×C4×C151C2311yescharacteristic
97C22×C4×C151C2311yescharacteristic
98C22×C4×C151C2311yescharacteristic
99C4⋊C4×C151—41no—
100C22⋊C4×C151—41no—
101C22⋊C4×C151—41no—
102C22⋊C4×C151C2×C414yes—
103C42×C151—41no—
104C22×D151—21no—
105C22×D151—21no—
106C22×D151—21no—
107C22×D151—21no—
108C22×D151—21no—
109C22×D151—21no—
110C22×D151—21no—
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—28no—
115C22×D151—44no—
116C22×D151—44no—
117C22×D151—44no—
118C22×D151—44no—
119C22×D151—44no—
120C22×D151—44no—
121C22×D151C22×C412yes—
122C22×D151C22×C412yes—
123C22×D151#4112yes—
124C22×D151#4112yes—
125C2×Dic151—21no—
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—21no—
130C2×Dic151—21no—
131C2×Dic151—21no—
132C2×Dic151—21no—
133C2×Dic151—21no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C2×Dic151—21no—
140C2×Dic151—21no—
141C2×Dic151C22×C412yes—
142C2×Dic151C22×C412yes—
143C4×D151—44no—
144C4×D151—44no—
145C23×C151—21no—
146C23×C151—21no—
147C23×C151—21no—
148C23×C151—21no—
149C23×C151—21no—
150C23×C151—21no—
151C23×C151C22×C412yes—
152C23×C151C2411yescharacteristic
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151C22×C412yes—
170C2×C4×C151C22×C412yes—
171C22×C151—22no—
172C22×C151—22no—
173C22×C151—22no—
174C22×C151—41no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151C23×C411yescharacteristic
179C22×C151C2×#4111yescharacteristic
180C22×C151C2×#4111yescharacteristic
181C22×C151H(5,𝔽2)11yescharacteristic
182C22×C151H(5,𝔽2)11yescharacteristic
183C22×C151H(5,𝔽2)11yescharacteristic
184C22×C151H(5,𝔽2)11yescharacteristic
185C2×D151—22no—
186C2×D151—22no—
187C2×D151—22no—
188C2×D151—22no—
189C2×D151—22no—
190C2×D151—22no—
191C2×D151—22no—
192C2×D151—22no—
193C2×D151—22no—
194C2×D151—416no—
195C2×D151—41no—
196C2×D151—41no—
197C2×D151—41no—
198C2×D151—41no—
199C2×D151#11714yes—
200C4×C151—22no—
201C4×C151—22no—
202C4×C151—41no—
203C4×C151—41no—
204C4×C151—41no—
205C4×C151—41no—
206Dic151—22no—
207Dic151—22no—
208Dic151—41no—
209Dic151—41no—
210Dic151—41no—
211Dic151—41no—
212C2×C151—42no—
213C2×C151C2×#11711yescharacteristic
214C2×C151#51811yescharacteristic
215C2×C151#51811yescharacteristic
216C2×C151#53811yescharacteristic
217C2×C151#53811yescharacteristic
218C2×C151#53811yescharacteristic
219C2×C151#53811yescharacteristic
220D151—24no—
221D151—42no—
222C151#231211yescharacteristic, complemented, Sylow
223#2312—1511nomaximal, Sylow
224C22×C22⋊C4—1511no—
225#388—1511no—
226#388—1511no—
227#388—1511no—
228#388—1511no—
229#388—1511no—
230#388—1511no—
231#388—1511no—
232#388D15111yescharacteristic, complemented
233#380—1511no—
234#380—1511no—
235#379—1511no—
236#379—1511no—
237C4×C22⋊C4—1511no—
238C4×C22⋊C4—1511no—
239C25—1511no—
240C23×C4—1511no—
241C23×C4—1511no—
242C2×C4⋊C4—1511no—
243C2×C4⋊C4—1511no—
244C2×C4⋊C4—1511no—
245C2×C4⋊C4C2×D15111yescharacteristic, complemented
246C2×C22⋊C4—1511no—
247C2×C22⋊C4—1511no—
248C2×C22⋊C4—1511no—
249C2×C22⋊C4—1511no—
250C2×C22⋊C4—1511no—
251C2×C22⋊C4—1511no—
252C2×C22⋊C4—1511no—
253C2×C22⋊C4—1511no—
254C2×C22⋊C4—1511no—
255C2×C22⋊C4—1511no—
256C2×C22⋊C4—1511no—
257C2×C22⋊C4—1511no—
258C2×C22⋊C4—1511no—
259C2×C22⋊C4—1518no—
260C2×C22⋊C4C2×D15111yescharacteristic
261C2×C22⋊C4C2×D15111yescharacteristic
262C2×C22⋊C4C2×D15111yescharacteristic
263C2×C42—1511no—
264C2×C42—1511no—
265C2×C42—1511no—
266C2×C42C2×D15111yescharacteristic, complemented
267#95—1511no—
268#95—1511no—
269#95—1511no—
270#95—1511no—
271#95—1511no—
272#95—1511no—
273#95C2×D15111yescharacteristic, complemented
274#95C2×D15111yescharacteristic, complemented
275C24—3022no—
276C24—3022no—
277C24—6041no—
278C24—6041no—
279C24—6041no—
280C24—6041no—
281C24—1511no—
282C24—1511no—
283C24—1514no—
284C24C22×D15111yescharacteristic
285C22×C4—6041no—
286C22×C4—6041no—
287C22×C4—6041no—
288C22×C4—6041no—
289C22×C4—1511no—
290C22×C4—1511no—
291C22×C4—1511no—
292C22×C4—1511no—
293C22×C4—1511no—
294C22×C4—1511no—
295C22×C4—1514no—
296C22×C4—1514no—
297C22×C4C22×D15111yescharacteristic
298C22×C4C22×D15111yescharacteristic
299C22×C4C22×D15111yescharacteristic
300C22×C4C22×D15111yescharacteristic
301C22×C4C22×D15111yescharacteristic
302C22×C4C22×D15111yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—6041no—
305C4⋊C4—6041no—
306C4⋊C4—6041no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—3022no—
310C22⋊C4—3022no—
311C22⋊C4—3022no—
312C22⋊C4—3022no—
313C22⋊C4—6041no—
314C22⋊C4—6041no—
315C22⋊C4—6041no—
316C22⋊C4—6041no—
317C22⋊C4—6041no—
318C22⋊C4—6041no—
319C22⋊C4—1514no—
320C22⋊C4—1514no—
321C22⋊C4—1514no—
322C22⋊C4C4×D15114yes—
323C42—41no—
324C42—6041no—
325C42—6041no—
326C42—6041no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—3028no—
334C23—3021no—
335C23—3021no—
336C23—3021no—
337C23—3021no—
338C23—3021no—
339C23—3021no—
340C23—3021no—
341C23—3021no—
342C23—3021no—
343C23—3021no—
344C23—6044no—
345C23—6044no—
346C23—6044no—
347C23—6044no—
348C23—6044no—
349C23—6044no—
350C23—1512no—
351C23—1512no—
352C23—1512no—
353C23—1512no—
354C23C2×C4×D15112yes—
355C23C23×D15111yescharacteristic
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—3021no—
373C2×C4—3021no—
374C2×C4—3021no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—3021no—
379C2×C4—3021no—
380C2×C4—3021no—
381C2×C4—3021no—
382C2×C4—3021no—
383C2×C4—3021no—
384C2×C4—3021no—
385C2×C4—3021no—
386C2×C4—3021no—
387C2×C4—3021no—
388C2×C4—6044no—
389C2×C4—6044no—
390C2×C4—1512no—
391C2×C4—1512no—
392C2×C4C2×C4×D15112yes—
393C2×C4C2×C4×D15112yes—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—3022no—
402C22—3022no—
403C22—3022no—
404C22—3022no—
405C22—3022no—
406C22—3022no—
407C22—3022no—
408C22—3022no—
409C22—3022no—
410C22—60416no—
411C22—6041no—
412C22—6041no—
413C22—6041no—
414C22—6041no—
415C22—1514no—
416C22C22×C4×D15111yescharacteristic
417C22#41×D15111yescharacteristic
418C22#41×D15111yescharacteristic
419C22#1801278411yescharacteristic
420C22#1801278411yescharacteristic
421C22#1801278511yescharacteristic
422C22#1801278511yescharacteristic
423C4—22no—
424C4—22no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—3022no—
430C4—3022no—
431C4—6041no—
432C4—6041no—
433C4—6041no—
434C4—6041no—
435C2—42no—
436C2—3024no—
437C2—6042no—
438C2#117×D15111yescharacteristic
439C2#2375268411yescharacteristic
440C2#2375268411yescharacteristic
441C2#2375279411yescharacteristic
442C2#2375279611yescharacteristic
443C2#2375279811yescharacteristic
444C2#2375280111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#388×C151C2
socle, cosocleC23×C151C24
prime radicalC24×D151C22
hypercenter#388D151
hypocenterC151#2312
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #23752106C2semidirect
3. #23752105C2semidirect
4. #23752104C2semidirect
5. #23752103C2semidirect
6. #23752102C2semidirect
7. #23752101C2semidirect
8. #23752100C2semidirect
9. #23752071C2semidirect
10. #23752069C2semidirect
13. C4×(C2×D151)⋊C4C2semidirect
14. #23752059C2semidirect
15. #388×C151C2semidirect
19. C2×C4⋊Dic151C22semidirect
20. C2×Dic151⋊C4C22semidirect
21. C2×Dic151⋊C4C22semidirect
35. C22⋊C4×D151C4semidirect
36. C2×C4×Dic151C22semidirect
37. C2×C4×Dic151C22semidirect
38. C2×C4×Dic151C22semidirect
39. C151⋊#95C22semidirect
40. C151⋊#95C22semidirect
41. C151⋊#95C22semidirect
42. C151⋊#95C22semidirect
43. C151⋊#95C22semidirect
44. C151⋊#95C22semidirect
45. C2×C4⋊C4×C151C22semidirect
49. C2×C42×C151C22semidirect
50. #95×C151C22semidirect
51. #95×C151C22semidirect
222. C151#2312semidirect
232. #388D151semidirect
245. C2×C4⋊C4C2×D151semidirect
266. C2×C42C2×D151semidirect
273. #95C2×D151semidirect
274. #95C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D1512
#237521062
#237521052
#237521042
#237521032
#237521022
#237521012
#237521002
#237520712
#237520692
#237520672
C4×(C2×D151)⋊C42
#237520592
#388×C1512
#2312151