Finite Group Databasebeta

← #34072129

Subgroups — #34072129

Order 19328.

788 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012712C211yesmaximal, characteristic
2C2×#18012701C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D151C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D151C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×D151C211yesmaximal, characteristic, complemented
6#23752112C211yesmaximal, characteristic, complemented
7#23752107C211yesmaximal, characteristic, complemented
8#23752105C211yesmaximal, characteristic, complemented
9#23752102C211yesmaximal, characteristic, complemented
10#23752090C211yesmaximal, characteristic, complemented
11#23752088C211yesmaximal, characteristic, complemented
12#23752086C211yesmaximal, characteristic, complemented
13#23752063C211yesmaximal, characteristic, complemented
14#23752059C211yesmaximal, characteristic, complemented
15#385×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic
17C22×C22⋊D151C2211yescharacteristic
18C22×C22⋊D151C2211yescharacteristic
19C22×C4×D151C2211yescharacteristic
20C22×C4×D151C2211yescharacteristic
21C22×C4×D151C2211yescharacteristic
22C22×C4×D151C2211yescharacteristic
23#18012712C418yescomplemented
24#18012701—24no—
25C4×C22⋊D151—24no—
26C4×C22⋊D151—24no—
27C2×C4⋊Dic151C2211yescharacteristic
28C2×Dic151⋊C4C2211yescharacteristic
29C2×Dic151⋊C4C2211yescharacteristic
30C2×Dic151⋊C4C2211yescharacteristic
31C2×Dic151⋊C4C2211yescharacteristic
32C4⋊C4×D151—24no—
33C2×C22⋊Dic151C2211yescharacteristic
34C2×C22⋊Dic151C2211yescharacteristic
35C2×(C2×D151)⋊C4C2211yescharacteristic
36C2×(C2×D151)⋊C4C2211yescharacteristic
37C2×(C2×D151)⋊C4C2211yescharacteristic
38C2×(C2×D151)⋊C4C2211yescharacteristic
39C2×(C2×D151)⋊C4C2211yescharacteristic
40C2×(C2×D151)⋊C4C2211yescharacteristic
41C2×C4×Dic151C2211yescharacteristic
42C2×C4×Dic151C2211yescharacteristic
43C2×C4×Dic151C2211yescharacteristic
44C2×C4×Dic151C2211yescharacteristic
45C151⋊#95C2211yescharacteristic
46C151⋊#95C2211yescharacteristic
47C151⋊#95C2211yescharacteristic
48C151⋊#95C2211yescharacteristic
49C23×C4×C151C2211yescharacteristic
50C2×C4⋊C4×C151C2211yescharacteristic
51C2×C4⋊C4×C151C2211yescharacteristic
52C2×C22⋊C4×C151C2211yescharacteristic
53C2×C22⋊C4×C151C2211yescharacteristic
54#95×C151C2211yescharacteristic
55#95×C151C2211yescharacteristic
56C23×D151C2311yescharacteristic
57C23×D151C2311yescharacteristic
58C2×D604—22no—
59C2×D604—22no—
60C2×D604C2×C414yescomplemented
61C2×C22⋊D151—22no—
62C2×C22⋊D151—22no—
63C2×C22⋊D151—22no—
64C2×C22⋊D151—22no—
65C2×C22⋊D151C2×C414yescomplemented
66C2×C22⋊D151C2×C414yescomplemented
67C22×Dic151C2311yescharacteristic
68C22×Dic151C2311yescharacteristic
69C22×Dic151C2311yescharacteristic
70C22×Dic151C2311yescharacteristic
71C22×Dic151C2311yescharacteristic
72C22×Dic151C2311yescharacteristic
73C2×C4×D151—22no—
74C2×C4×D151—22no—
75C2×C4×D151—22no—
76C2×C4×D151—22no—
77C2×C4×D151—22no—
78C2×C4×D151—22no—
79C2×C4×D151—22no—
80C2×C4×D151—22no—
81C2×C4×D151—41no—
82C2×C4×D151—41no—
83C2×C4×D151—41no—
84C2×C4×D151C2×C414yescomplemented
85C4⋊Dic151—22no—
86Dic151⋊C4—22no—
87Dic151⋊C4—22no—
88Dic151⋊C4C2×C414yescomplemented
89Dic151⋊C4D414yescomplemented
90C22⋊Dic151—22no—
91C22⋊Dic151—22no—
92(C2×D151)⋊C4—22no—
93(C2×D151)⋊C4—22no—
94(C2×D151)⋊C4—22no—
95(C2×D151)⋊C4—41no—
96(C2×D151)⋊C4C2×C414yescomplemented
97(C2×D151)⋊C4D414yescomplemented
98C4×Dic151—22no—
99C4×Dic151—22no—
100C4×Dic151—22no—
101C4×Dic151—22no—
102C24×C151C2311yescharacteristic
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—41no—
106C22×C4×C151C2311yescharacteristic
107C22×C4×C151C2311yescharacteristic
108C22×C4×C151C2311yescharacteristic
109C22×C4×C151C2311yescharacteristic
110C22×C4×C151C2311yescharacteristic
111C22×C4×C151C2311yescharacteristic
112C4⋊C4×C151—22no—
113C4⋊C4×C151—22no—
114C22⋊C4×C151—41no—
115C22⋊C4×C151C2×C414yescomplemented
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×D151C22×C412yes—
127C22×D151C22×C412yes—
128C22×D151C2×D412yes—
129C22×D151#4112yes—
130D604—28no—
131C22⋊D151—28no—
132C22⋊D151—28no—
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×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—21no—
145C2×Dic151C22×C412yes—
146C2×Dic151C22×C412yes—
147C2×Dic151C2×D412yes—
148C2×Dic151C2×D412yes—
149C2×Dic151C2×D412yes—
150C2×Dic151#4112yes—
151C4×D151—28no—
152C4×D151—44no—
153C4×D151—44no—
154C4×D151—44no—
155C23×C151—21no—
156C23×C151—21no—
157C23×C151—21no—
158C23×C151—21no—
159C23×C151—21no—
160C23×C151—21no—
161C23×C151C22×C412yes—
162C23×C151C2411yescharacteristic
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×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—44no—
178C2×C4×C151C22×C412yes—
179C2×C4×C151C22×C412yes—
180C2×C4×C151C2×D412yes—
181C2×C4×C151C2×D412yes—
182C22×C151—22no—
183C22×C151—22no—
184C22×C151—22no—
185C22×C151—41no—
186C22×C151—41no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151C23×C411yescharacteristic
190C22×C151C22×D411yescharacteristic
191C22×C151C22×D411yescharacteristic
192C22×C151C2×#4111yescharacteristic
193C22×C151C2×#4111yescharacteristic
194C22×C151H(5,𝔽2)11yescharacteristic
195C22×C1512−1+411yescharacteristic
196C2×D151—22no—
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—41no—
206C2×D151—41no—
207C2×D151—41no—
208C2×D151—41no—
209C2×D151C4×D414yescomplemented
210C4×C151—22no—
211C4×C151—22no—
212C4×C151—22no—
213C4×C151—22no—
214C4×C151—41no—
215C4×C151—41no—
216Dic151—22no—
217Dic151—22no—
218Dic151—22no—
219Dic151—41no—
220Dic151—41no—
221Dic151C4×D414yescomplemented
222C2×C151—42no—
223C2×C151C2×C4×D411yescharacteristic
224C2×C151C2×C4×D411yescharacteristic
225C2×C151#52011yescharacteristic
226C2×C151D4211yescharacteristic
227C2×C151#54711yescharacteristic
228C2×C151#54811yescharacteristic
229C2×C151#55311yescharacteristic
230D151—24no—
231D151—42no—
232C151#236111yescharacteristic, complemented, Sylow
233#2361—1511nomaximal, Sylow
234C2×#121—1511no—
235C2×C4×D4—1511no—
236C2×C4×D4—1511no—
237C2×C4×D4—1511no—
238C22×C4⋊C4—1511no—
239#390—1511no—
240#389—1511no—
241#388—1511no—
242#388—1511no—
243#386—1511no—
244#386—1511no—
245#385—1511no—
246#385D15111yescharacteristic, complemented
247C4×C4⋊C4—1511no—
248C4×C22⋊C4—1511no—
249C22×D4—1511no—
250C22×D4—1511no—
251C22×D4—1511no—
252C23×C4—1511no—
253C23×C4—1511no—
254C23×C4—1511no—
255C23×C4—1511no—
256C23×C4C2×D15111yescharacteristic
257#121—1518no—
258C4×D4—3024no—
259C4×D4—3024no—
260C4×D4—3024no—
261C2×C4⋊C4—3024no—
262C2×C4⋊C4—1511no—
263C2×C4⋊C4—1511no—
264C2×C4⋊C4—1511no—
265C2×C4⋊C4—1511no—
266C2×C4⋊C4—1511no—
267C2×C4⋊C4C2×D15111yescharacteristic
268C2×C4⋊C4C2×D15111yescharacteristic
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⋊C4C2×D15111yescharacteristic
278C2×C22⋊C4C2×D15111yescharacteristic
279C2×C42—1511no—
280C2×C42—1511no—
281C2×C42—1511no—
282C2×C42—1511no—
283#95—1511no—
284#95—1511no—
285#95—1511no—
286#95—1511no—
287#95C2×D15111yescharacteristic
288#95C2×D15111yescharacteristic
289C24—1511no—
290C24—1511no—
291C24C22×D15111yescharacteristic
292C2×D4—3022no—
293C2×D4—3022no—
294C2×D4—3022no—
295C2×D4—3022no—
296C2×D4—3022no—
297C2×D4—3022no—
298C2×D4—1514no—
299C2×D4—1514no—
300C2×D4—1514no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—3022no—
305C22×C4—3022no—
306C22×C4—3022no—
307C22×C4—3022no—
308C22×C4—3022no—
309C22×C4—3022no—
310C22×C4—3022no—
311C22×C4—3022no—
312C22×C4—6041no—
313C22×C4—6041no—
314C22×C4—6041no—
315C22×C4—1511no—
316C22×C4—1511no—
317C22×C4—1511no—
318C22×C4—1511no—
319C22×C4—1511no—
320C22×C4—1514no—
321C22×C4—1511no—
322C22×C4C22×D15111yescharacteristic
323C22×C4C22×D15111yescharacteristic
324C22×C4C22×D15111yescharacteristic
325C22×C4C22×D15111yescharacteristic
326C22×C4C22×D15111yescharacteristic
327C22×C4C22×D15111yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—3022no—
331C4⋊C4—3022no—
332C4⋊C4—3022no—
333C4⋊C4—1514no—
334C4⋊C4—1514no—
335C22⋊C4—41no—
336C22⋊C4—3022no—
337C22⋊C4—3022no—
338C22⋊C4—3022no—
339C22⋊C4—3022no—
340C22⋊C4—3022no—
341C22⋊C4—6041no—
342C22⋊C4—1514no—
343C22⋊C4—1514no—
344C22⋊C4C4×D15114yescomplemented
345C42—3022no—
346C42—3022no—
347C42—3022no—
348C42—3022no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—3021no—
356C23—3021no—
357C23—3021no—
358C23—3021no—
359C23—3021no—
360C23—3021no—
361C23—3021no—
362C23—3021no—
363C23—3021no—
364C23—3021no—
365C23—1512no—
366C23—1512no—
367C23—1512no—
368C23—1512no—
369C23C2×C4×D15112yes—
370C23C23×D15111yescharacteristic
371D4—3028no—
372D4—3028no—
373D4—3028no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—44no—
389C2×C4—3028no—
390C2×C4—3021no—
391C2×C4—3021no—
392C2×C4—3021no—
393C2×C4—3021no—
394C2×C4—3021no—
395C2×C4—3021no—
396C2×C4—3021no—
397C2×C4—3021no—
398C2×C4—3021no—
399C2×C4—3021no—
400C2×C4—3021no—
401C2×C4—3021no—
402C2×C4—6044no—
403C2×C4—6044no—
404C2×C4—6044no—
405C2×C4—1512no—
406C2×C4—1512no—
407C2×C4—1512no—
408C2×C4—1512no—
409C2×C4—1512no—
410C2×C4—1512no—
411C2×C4C2×C4×D15112yes—
412C2×C4C2×C4×D15112yes—
413C2×C4D4×D15112yes—
414C2×C4D4×D15112yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—3022no—
423C22—3022no—
424C22—3022no—
425C22—3022no—
426C22—3022no—
427C22—3022no—
428C22—3022no—
429C22—3022no—
430C22—3022no—
431C22—6041no—
432C22—6041no—
433C22—6041no—
434C22—6041no—
435C22—1514no—
436C22C22×C4×D15111yescharacteristic
437C22C2×D4×D15111yescharacteristic
438C22C2×D4×D15111yescharacteristic
439C22#41×D15111yescharacteristic
440C22#41×D15111yescharacteristic
441C22#1801278411yescharacteristic
442C22#1801278711yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—41no—
449C4—3022no—
450C4—3022no—
451C4—3022no—
452C4—6041no—
453C4—6041no—
454C4—1514no—
455C2—42no—
456C2—3024no—
457C2—6042no—
458C2C4×D4×D15111yescharacteristic
459C2C4×D4×D15111yescharacteristic
460C2#2375269311yescharacteristic
461C2#2375284411yescharacteristic
462C2#2375286411yescharacteristic
463C2#2375287211yescharacteristic
464C2#2375290711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#385×C151C2
socle, cosocleC23×C151C24
prime radicalC2×#18012712C2
hypercenter#385D151
hypocenterC151#2361
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#18012701C2semidirect
3. C2×C4×C22⋊D151C2semidirect
4. C2×C4×C22⋊D151C2semidirect
5. C2×C4⋊C4×D151C2semidirect
6. #23752112C2semidirect
7. #23752107C2semidirect
8. #23752105C2semidirect
9. #23752102C2semidirect
10. #23752090C2semidirect
11. #23752088C2semidirect
12. #23752086C2semidirect
13. #23752063C2semidirect
14. #23752059C2semidirect
15. #385×C151C2semidirect
23. #18012712C4semidirect
60. C2×D604C2×C4semidirect
65. C2×C22⋊D151C2×C4semidirect
66. C2×C22⋊D151C2×C4semidirect
84. C2×C4×D151C2×C4semidirect
88. Dic151⋊C4C2×C4semidirect
89. Dic151⋊C4D4semidirect
96. (C2×D151)⋊C4C2×C4semidirect
97. (C2×D151)⋊C4D4semidirect
115. C22⋊C4×C151C2×C4semidirect
209. C2×D151C4×D4semidirect
221. Dic151C4×D4semidirect
232. C151#2361semidirect
246. #385D151semidirect
344. C22⋊C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127122
C2×#180127012
C2×C4×C22⋊D1512
C2×C4⋊C4×D1512
#237521122
#237521072
#237521052
#237521022
#237520902
#237520882
#237520862
#237520632
#237520592
#385×C1512
#2361151