Finite Group Databasebeta

← #34072250

Subgroups — #34072250

Order 19328.

688 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012709C211yesmaximal, characteristic
2#23752114C211yesmaximal, characteristic, complemented
3#23752113C211yesmaximal, characteristic, complemented
4#23752112C211yesmaximal, characteristic, complemented
5#23752105C211yesmaximal, characteristic, complemented
6#23752104C211yesmaximal, characteristic, complemented
7#23752103C211yesmaximal, characteristic, complemented
8#23752102C211yesmaximal, characteristic, complemented
9#23752101C211yesmaximal, characteristic, complemented
10#23752090C211yesmaximal, characteristic, complemented
11#23752090C211yesmaximal, characteristic, complemented
12#23752088C211yesmaximal, characteristic, complemented
13#23752067C211yesmaximal, characteristic, complemented
14#23752067C211yesmaximal, characteristic, complemented
15#388×C151C211yesmaximal, characteristic, complemented
16C24×D151C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C22×D604C2211yescharacteristic
19C22×C22⋊D151C2211yescharacteristic
20C22×C4×D151C2211yescharacteristic, complemented
21#18012709C418yescomplemented
22C2×C4⋊Dic151C2211yescharacteristic, complemented
23C2×Dic151⋊C4C2211yescharacteristic, complemented
24C2×C22⋊Dic151C2211yescharacteristic
25C2×C22⋊Dic151C2211yescharacteristic
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
35C2×(C2×D151)⋊C4C2211yescharacteristic
36C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D151)⋊C4C2211yescharacteristic, complemented
39C2×C4×Dic151C2211yescharacteristic, complemented
40C2×C4×Dic151C2211yescharacteristic, 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—41no—
53C23×D151—41no—
54C23×D151—41no—
55C23×D151—41no—
56C23×D151—41no—
57C23×D151—41no—
58C23×D151C2×C414yescomplemented
59C23×D151C2311yescharacteristic
60C23×D151C2311yescharacteristic
61C23×D151C2311yescharacteristic
62C2×D604—41no—
63C2×D604—41no—
64C2×D604—41no—
65C2×D604—41no—
66C2×D604C2×C414yes—
67C2×D604C2×C414yes—
68C2×C22⋊D151—41no—
69C2×C22⋊D151—41no—
70C2×C22⋊D151C2×C414yes—
71C22×Dic151C2311yescharacteristic
72C22×Dic151C2311yescharacteristic
73C22×Dic151C2311yescharacteristic
74C22×Dic151C2311yescharacteristic
75C22×Dic151C2311yescharacteristic
76C2×C4×D151—41no—
77C2×C4×D151—41no—
78C2×C4×D151—41no—
79C4⋊Dic151—41no—
80Dic151⋊C4—41no—
81C22⋊Dic151—41no—
82C22⋊Dic151—41no—
83(C2×D151)⋊C4—41no—
84(C2×D151)⋊C4—41no—
85(C2×D151)⋊C4—41no—
86(C2×D151)⋊C4—41no—
87(C2×D151)⋊C4—41no—
88(C2×D151)⋊C4—41no—
89(C2×D151)⋊C4—41no—
90(C2×D151)⋊C4—41no—
91(C2×D151)⋊C4—41no—
92(C2×D151)⋊C4—41no—
93(C2×D151)⋊C4—41no—
94(C2×D151)⋊C4C2×C414yescomplemented
95(C2×D151)⋊C4C2×C414yescomplemented
96C4×Dic151—41no—
97C4×Dic151—41no—
98C24×C151C2311yescharacteristic
99C22×C4×C151C2311yescharacteristic
100C22×C4×C151C2311yescharacteristic
101C22×C4×C151C2311yescharacteristic
102C22×C4×C151C2311yescharacteristic
103C22×C4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105C4⋊C4×C151—41no—
106C22⋊C4×C151—41no—
107C22⋊C4×C151—41no—
108C22⋊C4×C151C2×C414yescomplemented
109C42×C151—41no—
110C22×D151—21no—
111C22×D151—21no—
112C22×D151—21no—
113C22×D151—21no—
114C22×D151—21no—
115C22×D151—21no—
116C22×D151—21no—
117C22×D151—21no—
118C22×D151—21no—
119C22×D151—21no—
120C22×D151—21no—
121C22×D151—21no—
122C22×D151—21no—
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—21no—
127C22×D151—21no—
128C22×D151—44no—
129C22×D151—44no—
130C22×D151—44no—
131C22×D151—44no—
132C22×D151—44no—
133C22×D151—44no—
134C22×D151—44no—
135C22×D151C22×C412yes—
136C22×D151C22×C412yes—
137C22×D151C22×C412yes—
138D604—44no—
139D604—44no—
140C22⋊D151—44no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—21no—
145C2×Dic151—21no—
146C2×Dic151—21no—
147C2×Dic151—21no—
148C2×Dic151—21no—
149C2×Dic151—21no—
150C2×Dic151—21no—
151C2×Dic151—21no—
152C2×Dic151—21no—
153C2×Dic151—21no—
154C2×Dic151—21no—
155C2×Dic151C22×C412yes—
156C4×D151—44no—
157C23×C151—21no—
158C23×C151—21no—
159C23×C151—21no—
160C23×C151—21no—
161C23×C151—21no—
162C23×C151—21no—
163C23×C151C22×C412yes—
164C23×C151C2411yescharacteristic
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—21no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151C22×C412yes—
182C2×C4×C151C22×C412yes—
183C22×C151—22no—
184C22×C151—22no—
185C22×C151—22no—
186C22×C151—41no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151—41no—
190C22×C151C23×C411yescharacteristic
191C22×C151H(5,𝔽2)11yescharacteristic
192C22×C151H(5,𝔽2)11yescharacteristic
193C22×C151H(5,𝔽2)11yescharacteristic
194C22×C151H(5,𝔽2)11yescharacteristic
195C22×C151H(5,𝔽2)11yescharacteristic
196C22×C151H(5,𝔽2)11yescharacteristic
197C2×D151—22no—
198C2×D151—22no—
199C2×D151—22no—
200C2×D151—22no—
201C2×D151—22no—
202C2×D151—22no—
203C2×D151—22no—
204C2×D151—22no—
205C2×D151—22no—
206C2×D151—416no—
207C2×D151—41no—
208C2×D151—41no—
209C2×D151—41no—
210C2×D151—41no—
211C2×D151—41no—
212C2×D151—41no—
213C2×D151—41no—
214C2×D151—41no—
215C2×D151—41no—
216C2×D151—41no—
217C2×D151—41no—
218C2×D151—41no—
219C4×C151—22no—
220C4×C151—22no—
221C4×C151—41no—
222C4×C151—41no—
223C4×C151—41no—
224C4×C151—41no—
225Dic151—22no—
226Dic151—41no—
227Dic151—41no—
228Dic151—41no—
229Dic151—41no—
230C2×C151—42no—
231C2×C151#51811yescharacteristic
232C2×C151#51811yescharacteristic
233C2×C151#51811yescharacteristic
234C2×C151#56011yescharacteristic
235C2×C151#56011yescharacteristic
236C2×C151#56011yescharacteristic
237C2×C151H(3,𝔽4)11yescharacteristic
238D151—42no—
239D151—42no—
240D151—42no—
241C151#237511yescharacteristic, complemented, Sylow
242#2375—1511nomaximal, Sylow
243C2×#120—1511no—
244#390—1511no—
245#390—1511no—
246#390—1511no—
247#388—1511no—
248#388—1511no—
249#388—1511no—
250#388—1511no—
251#388—1511no—
252#388D15111yescharacteristic, complemented
253#386—1511no—
254#386—1511no—
255#386—1511no—
256#379—1511no—
257#379—1511no—
258C25—1511no—
259C22×D4—1511no—
260C22×D4—1511no—
261C22×D4—1511no—
262C23×C4—1511no—
263#120—1518no—
264C2×C4⋊C4—1511no—
265C2×C4⋊C4—1511no—
266C2×C4⋊C4C2×D15111yescharacteristic, complemented
267C2×C22⋊C4—1511no—
268C2×C22⋊C4—1511no—
269C2×C22⋊C4—1511no—
270C2×C22⋊C4—1511no—
271C2×C22⋊C4—1511no—
272C2×C22⋊C4—1511no—
273C2×C22⋊C4—1511no—
274C2×C22⋊C4—1511no—
275C2×C22⋊C4—1511no—
276C2×C22⋊C4—1511no—
277C2×C22⋊C4—1511no—
278C2×C22⋊C4—1511no—
279C2×C22⋊C4—1511no—
280C2×C22⋊C4—1511no—
281C2×C22⋊C4—1511no—
282C2×C22⋊C4C2×D15111yescharacteristic
283C2×C22⋊C4C2×D15111yescharacteristic
284C2×C22⋊C4C2×D15111yescharacteristic
285C2×C42—1511no—
286C2×C42—1511no—
287C2×C42C2×D15111yescharacteristic, complemented
288#95—1511no—
289#95—1511no—
290#95—1511no—
291#95—1511no—
292#95C2×D15111yescharacteristic, complemented
293#95C2×D15111yescharacteristic, complemented
294C24—6041no—
295C24—6041no—
296C24—6041no—
297C24—6041no—
298C24—6041no—
299C24—6041no—
300C24—1511no—
301C24—1511no—
302C24—1511no—
303C24—1514no—
304C24C22×D15111yescharacteristic
305C2×D4—6041no—
306C2×D4—6041no—
307C2×D4—6041no—
308C2×D4—6041no—
309C2×D4—6041no—
310C2×D4—6041no—
311C2×D4—1514no—
312C2×D4—1514no—
313C2×D4—1514no—
314C22×C4—6041no—
315C22×C4—6041no—
316C22×C4—6041no—
317C22×C4—1511no—
318C22×C4—1511no—
319C22×C4—1511no—
320C22×C4—1511no—
321C22×C4—1511no—
322C22×C4C22×D15111yescharacteristic
323C22×C4C22×D15111yescharacteristic
324C22×C4C22×D15111yescharacteristic
325C22×C4C22×D15111yescharacteristic
326C22×C4C22×D15111yescharacteristic
327C22×C4C22×D15111yescharacteristic
328C4⋊C4—41no—
329C4⋊C4—6041no—
330C4⋊C4—6041no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—6041no—
334C22⋊C4—6041no—
335C22⋊C4—6041no—
336C22⋊C4—6041no—
337C22⋊C4—6041no—
338C22⋊C4—6041no—
339C22⋊C4—6041no—
340C22⋊C4—6041no—
341C22⋊C4—6041no—
342C22⋊C4—6041no—
343C22⋊C4—6041no—
344C22⋊C4—6041no—
345C22⋊C4—6041no—
346C22⋊C4—1514no—
347C22⋊C4—1514no—
348C22⋊C4C4×D15114yescomplemented
349C42—41no—
350C42—6041no—
351C42—6041no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—3021no—
359C23—3021no—
360C23—3021no—
361C23—3021no—
362C23—3021no—
363C23—3021no—
364C23—3021no—
365C23—3021no—
366C23—3021no—
367C23—3021no—
368C23—3021no—
369C23—3021no—
370C23—3021no—
371C23—3021no—
372C23—3021no—
373C23—3021no—
374C23—3021no—
375C23—3021no—
376C23—6044no—
377C23—6044no—
378C23—6044no—
379C23—6044no—
380C23—6044no—
381C23—6044no—
382C23—6044no—
383C23—1512no—
384C23—1512no—
385C23—1512no—
386C23C2×C4×D15112yes—
387C23C23×D15111yescharacteristic
388D4—6044no—
389D4—6044no—
390D4—6044no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—3021no—
408C2×C4—3021no—
409C2×C4—3021no—
410C2×C4—3021no—
411C2×C4—3021no—
412C2×C4—3021no—
413C2×C4—3021no—
414C2×C4—3021no—
415C2×C4—3021no—
416C2×C4—3021no—
417C2×C4—3021no—
418C2×C4—3021no—
419C2×C4—3021no—
420C2×C4—3021no—
421C2×C4—6044no—
422C2×C4—1512no—
423C2×C4C2×C4×D15112yes—
424C2×C4C2×C4×D15112yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—3022no—
433C22—3022no—
434C22—3022no—
435C22—3022no—
436C22—3022no—
437C22—3022no—
438C22—3022no—
439C22—3022no—
440C22—3022no—
441C22—60416no—
442C22—6041no—
443C22—6041no—
444C22—6041no—
445C22—6041no—
446C22—6041no—
447C22—6041no—
448C22—6041no—
449C22—6041no—
450C22—6041no—
451C22—6041no—
452C22—6041no—
453C22—6041no—
454C22C22×C4×D15111yescharacteristic
455C22#1801278411yescharacteristic
456C22#1801278411yescharacteristic
457C22#1801278511yescharacteristic
458C22#1801278511yescharacteristic
459C22#1801278511yescharacteristic
460C22#1801278511yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—3022no—
468C4—6041no—
469C4—6041no—
470C4—6041no—
471C4—6041no—
472C2—42no—
473C2—6042no—
474C2—6042no—
475C2—6042no—
476C2#2375268411yescharacteristic
477C2#2375268411yescharacteristic
478C2#2375268611yescharacteristic
479C2#2375295011yescharacteristic
480C2#2375295211yescharacteristic
481C2#2375295311yescharacteristic
482C2#2375295411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#388×C151C2
socle, cosocleC23×C151C24
prime radicalC2×#18012709C2
hypercenter#388D151
hypocenterC151#2375
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #23752114C2semidirect
3. #23752113C2semidirect
4. #23752112C2semidirect
5. #23752105C2semidirect
6. #23752104C2semidirect
7. #23752103C2semidirect
8. #23752102C2semidirect
9. #23752101C2semidirect
10. #23752090C2semidirect
11. #23752090C2semidirect
12. #23752088C2semidirect
13. #23752067C2semidirect
14. #23752067C2semidirect
15. #388×C151C2semidirect
20. C22×C4×D151C22semidirect
21. #18012709C4semidirect
22. C2×C4⋊Dic151C22semidirect
23. C2×Dic151⋊C4C22semidirect
36. C2×(C2×D151)⋊C4C22semidirect
37. C2×(C2×D151)⋊C4C22semidirect
38. C2×(C2×D151)⋊C4C22semidirect
39. C2×C4×Dic151C22semidirect
40. C2×C4×Dic151C22semidirect
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
58. C23×D151C2×C4semidirect
94. (C2×D151)⋊C4C2×C4semidirect
95. (C2×D151)⋊C4C2×C4semidirect
108. C22⋊C4×C151C2×C4semidirect
241. C151#2375semidirect
252. #388D151semidirect
266. C2×C4⋊C4C2×D151semidirect
287. C2×C42C2×D151semidirect
292. #95C2×D151semidirect
293. #95C2×D151semidirect
348. C22⋊C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127092
#237521142
#237521132
#237521122
#237521052
#237521042
#237521032
#237521022
#237521012
#237520902
#237520882
#237520672
#388×C1512
#2375151