Finite Group Databasebeta

← #34080817

Subgroups — #34080817

Order 19328.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012760C211yesmaximal, characteristic, complemented
2#23752873C211yesmaximal, characteristic, complemented
3#23752856C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752441C211yesmaximal, characteristic, complemented
6#23752438C211yesmaximal, characteristic, complemented
7#23752432C211yesmaximal, characteristic, complemented
8#23752429C211yesmaximal, characteristic, complemented
9#23752371C211yesmaximal, characteristic, complemented
10#23752368C211yesmaximal, characteristic, complemented
11#23752356C211yesmaximal, characteristic, complemented
12#23752346C211yesmaximal, characteristic, complemented
13SD16×Dic151C211yesmaximal, characteristic, complemented
14C8×C22⋊D151C211yesmaximal, characteristic, complemented
15C22×SD16×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic, complemented
17C2×#14559003C2211yescharacteristic
18#18012760—24no—
19C2×#14558994C2211yescharacteristic, complemented
20C2×#14558994C2211yescharacteristic, complemented
21C2×#14558993C2211yescharacteristic, complemented
22C2×#14558989C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24C2×C8×D151C2211yescharacteristic, complemented
25#18012728—21no—
26#18012728C2211yescharacteristic, complemented
27#18012726C2211yescharacteristic
28#18012720—21no—
29#18012718C2211yescharacteristic
30#18012715—21no—
31#18012715C2211yescharacteristic, complemented
32#18012713—21no—
33#18012713C2211yescharacteristic
34#18012711—21no—
35#18012710C2211yescharacteristic
36#18012708—21no—
37Q8×Dic151C2211yescharacteristic, complemented
38D4×Dic151C2211yescharacteristic
39C4×C22⋊D151—21no—
40C4×C22⋊D151C2211yescharacteristic
41C2×C22⋊Dic151—21no—
42#18012671C2211yescharacteristic, complemented
43Dic151⋊C8C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012663C2211yescharacteristic, complemented
47#18012661C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic
50C22⋊(C151⋊C8)C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C8×Dic151C2211yescharacteristic, complemented
53C22×Q8×C151C2211yescharacteristic
54C22×D4×C151C2211yescharacteristic
55C2×SD16×C151—24no—
56C2×SD16×C151C2211yescharacteristic
57C2×SD16×C151C2211yescharacteristic
58C2×SD16×C151C2211yescharacteristic
59C2×SD16×C151C2211yescharacteristic
60C22×C8×C151C2211yescharacteristic
61#14559005—22no—
62#14559005—41no—
63#14559003—22no—
64#14559003—41no—
65C2×Dic302C2311yescharacteristic
66C2×D604—21no—
67C2×D604C2311yescharacteristic
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151D411yescharacteristic
72C22×Dic151—21no—
73C22×Dic151—21no—
74C2×C4×D151—21no—
75C2×C4×D151C2311yescharacteristic
76#14558994—22no—
77#14558994—41no—
78#14558993—22no—
79#14558989—22no—
80#14558989—41no—
81C2×C151⋊C8C2311yescharacteristic
82C2×C151⋊C8C2311yescharacteristic
83C8×D151—22no—
84C4⋊Dic151—21no—
85C4⋊Dic151C2311yescharacteristic
86C4⋊Dic151C2311yescharacteristic
87Dic151⋊C4—21no—
88Dic151⋊C4—21no—
89Dic151⋊C4D411yescharacteristic
90C22⋊Dic151—21no—
91C22⋊Dic151—21no—
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151D411yescharacteristic
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4D411yescharacteristic
101C4×Dic151—21no—
102C4×Dic151C2311yescharacteristic
103C24×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151—22no—
106C2×Q8×C151—41no—
107C2×Q8×C151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151—22no—
110C2×D4×C151—21no—
111C2×D4×C151—41no—
112C2×D4×C151C2311yescharacteristic
113C2×D4×C151C2311yescharacteristic
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116SD16×C151—22no—
117SD16×C151—22no—
118SD16×C151—22no—
119SD16×C151D414yescomplemented
120C2×C8×C151—22no—
121C2×C8×C151C2311yescharacteristic
122C2×C8×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127D604—21no—
128D604—21no—
129D604—42no—
130C22⋊D151—22no—
131C22⋊D151—42no—
132C22⋊D151—42no—
133C22⋊D151—81no—
134C2×Dic151—21no—
135C2×Dic151—21no—
136C2×Dic151—21no—
137C2×Dic151—42no—
138C2×Dic151—81no—
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C4×D151—21no—
143C4×D151—21no—
144C4×D151—42no—
145C151⋊C8—21no—
146C151⋊C8—21no—
147C23×C151—21no—
148C23×C151—21no—
149C23×C151—42no—
150C23×C151—42no—
151C23×C151—81no—
152C23×C151C2×D411yescharacteristic
153Q8×C151—21no—
154Q8×C151—21no—
155Q8×C151—21no—
156Q8×C151—42no—
157Q8×C151C2×D412yes—
158D4×C151—21no—
159D4×C151—21no—
160D4×C151—21no—
161D4×C151—42no—
162D4×C151C2×D412yes—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—42no—
168C2×C4×C151C2×D411yescharacteristic
169C2×C4×C151C2411yescharacteristic
170C8×C151—21no—
171C8×C151C2×D412yes—
172C22×C151—21no—
173C22×C151—21no—
174C22×C151—22no—
175C22×C151—41no—
176C22×C151—41no—
177C22×C151—41no—
178C22×C151—41no—
179C22×C151—41no—
180C22×C151—84no—
181C22×C151#13512yescomplemented
182C22×C151C22×D411yescharacteristic
183C2×D151—21no—
184C2×D151—21no—
185C2×D151—21no—
186C2×D151—41no—
187C2×D151—41no—
188C2×D151—41no—
189C4×C151—21no—
190C4×C151—22no—
191C4×C151—41no—
192C4×C151C22×D411yescharacteristic
193C4×C151H(5,𝔽2)11yescharacteristic
194Dic151—21no—
195Dic151—21no—
196Dic151—21no—
197Dic151—41no—
198Dic151—41no—
199Dic151—41no—
200C2×C151—22no—
201C2×C151—42no—
202C2×C151—81no—
203C2×C151D4211yescharacteristic
204C2×C151C2×#13511yescharacteristic
205C2×C151#57711yescharacteristic
206D151—41no—
207D151—81no—
208C151#328211yescharacteristic, complemented, Sylow
209#3282—1511nomaximal, Sylow
210C2×#135—1511no—
211C22×SD16D15111yescharacteristic, complemented
212#548—1511no—
213#546—1511no—
214#495—1511no—
215#465—1511no—
216#465—1511no—
217#464—1511no—
218#463—1511no—
219#452—1511no—
220#451—1511no—
221#449—1511no—
222#447—1511no—
223C4×SD16—1511no—
224C8×D4—1511no—
225C2×#41—1511no—
226C2×#41—1511no—
227C22×Q8C2×D15111yescharacteristic
228C22×D4C2×D15111yescharacteristic
229#135—3024no—
230C2×Q16—1511no—
231C2×Q16—1511no—
232C2×SD16—24no—
233C2×SD16—1511no—
234C2×SD16C2×D15111yescharacteristic
235C2×SD16C2×D15111yescharacteristic
236C2×SD16C2×D15111yescharacteristic
237C2×SD16C2×D15111yescharacteristic
238C2×D8—1511no—
239C2×D8—1511no—
240C22×C8—1511no—
241C22×C8C2×D15111yescharacteristic
242#124—3021no—
243#124—1511no—
244#124—1511no—
245#123—3021no—
246C22⋊Q8—3021no—
247C22⋊Q8—1511no—
248C22⋊Q8—1511no—
249#121—3021no—
250#121—3021no—
251#121—1511no—
252#121—1511no—
253#120—3021no—
254C4×Q8—1511no—
255C4×D4—3021no—
256C4×D4—1511no—
257C4×D4—1511no—
258C2×C22⋊C4—3021no—
259#106—1511no—
260C4⋊C8—1511no—
261#103—1511no—
262#103—1511no—
263#103—1511no—
264#102—1511no—
265#102—1511no—
266#102—1511no—
267C22⋊C8—1511no—
268C22⋊C8—1511no—
269C4×C8—1511no—
270C24—21no—
271#41—3022no—
272#41—3022no—
273#41—6041no—
274#41—6041no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—1511no—
279C2×Q8C22×D15111yescharacteristic
280C2×Q8C22×D15111yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—3021no—
285C2×D4—3021no—
286C2×D4—3021no—
287C2×D4—3021no—
288C2×D4—1511no—
289C2×D4—1511no—
290C2×D4C22×D15111yescharacteristic
291C2×D4C22×D15111yescharacteristic
292C22×C4—21no—
293C22×C4—3021no—
294C22×C4—3021no—
295C22×C4—3021no—
296C22×C4—1511no—
297C22×C4C22×D15111yescharacteristic
298Q16—3022no—
299Q16—6041no—
300SD16—22no—
301SD16—22no—
302SD16—22no—
303SD16—3022no—
304SD16C22⋊D15114yescomplemented
305D8—3022no—
306D8—6041no—
307C2×C8—22no—
308C2×C8—3022no—
309C2×C8—1511no—
310C2×C8—1511no—
311C2×C8C22×D15111yescharacteristic
312C2×C8C22×D15111yescharacteristic
313C4⋊C4—3021no—
314C4⋊C4—3021no—
315C4⋊C4—3021no—
316C4⋊C4—1511no—
317C4⋊C4—1511no—
318C4⋊C4—1511no—
319C22⋊C4—3021no—
320C22⋊C4—3021no—
321C22⋊C4—3021no—
322C22⋊C4—3021no—
323C22⋊C4—3021no—
324C22⋊C4—3021no—
325C22⋊C4—3021no—
326C22⋊C4—3021no—
327C22⋊C4—3021no—
328C22⋊C4—1511no—
329C22⋊C4—1511no—
330C42—3021no—
331C42—1511no—
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—3021no—
338C23—1511no—
339C23D4×D15111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—3021no—
345Q8—3021no—
346Q8C2×C22⋊D15112yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—3022no—
352D4—3021no—
353D4—3021no—
354D4—6042no—
355D4—6042no—
356D4—6042no—
357D4—12081no—
358D4C2×C22⋊D15112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—3021no—
365C2×C4—3021no—
366C2×C4—3021no—
367C2×C4—3021no—
368C2×C4—3021no—
369C2×C4—6042no—
370C2×C4—6042no—
371C2×C4—1511no—
372C2×C4—1511no—
373C2×C4—1511no—
374C2×C4—12081no—
375C2×C4D4×D15111yescharacteristic
376C2×C4C23×D15111yescharacteristic
377C8—21no—
378C8—3021no—
379C8—3021no—
380C8C2×C22⋊D15112yes—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—84no—
390C22—3021no—
391C22—3021no—
392C22—3021no—
393C22—6041no—
394C22—6041no—
395C22—6041no—
396C22#1801276012yescomplemented
397C22C2×D4×D15111yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—3021no—
402C4—3021no—
403C4—3021no—
404C4—6041no—
405C4—6041no—
406C4—6041no—
407C4C22×C22⋊D15111yescharacteristic
408C4#1801278411yescharacteristic
409C2—22no—
410C2—42no—
411C2—81no—
412C2—6041no—
413C2—12081no—
414C2D4×C22⋊D15111yescharacteristic
415C2C2×#1801276011yescharacteristic
416C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×SD16×C151C2
socleC22×C151C22×D4
hypercenterC22×SD16D151
hypocenterC151#3282
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#18012760C2semidirect
2. #23752873C2semidirect
3. #23752856C2semidirect
4. #23752593C2semidirect
5. #23752441C2semidirect
6. #23752438C2semidirect
7. #23752432C2semidirect
8. #23752429C2semidirect
9. #23752371C2semidirect
10. #23752368C2semidirect
11. #23752356C2semidirect
12. #23752346C2semidirect
13. SD16×Dic151C2semidirect
14. C8×C22⋊D151C2semidirect
15. C22×SD16×C151C2semidirect
16. C2×#14559005C22semidirect
19. C2×#14558994C22semidirect
20. C2×#14558994C22semidirect
21. C2×#14558993C22semidirect
24. C2×C8×D151C22semidirect
26. #18012728C22semidirect
31. #18012715C22semidirect
37. Q8×Dic151C22semidirect
42. #18012671C22semidirect
43. Dic151⋊C8C22semidirect
44. #18012664C22semidirect
45. #18012663C22semidirect
46. #18012663C22semidirect
47. #18012661C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. C8×Dic151C22semidirect
119. SD16×C151D4semidirect
181. C22×C151#135semidirect
208. C151#3282semidirect
211. C22×SD16D151semidirect
304. SD16C22⋊D151semidirect
396. C22#18012760semidirect

Maximal subgroups

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

subgroupindex
C2×#180127602
#237528732
#237528562
#237525932
#237524412
#237524382
#237524322
#237524292
#237523712
#237523682
#237523562
#237523462
SD16×Dic1512
C8×C22⋊D1512
C22×SD16×C1512
#3282151