Finite Group Databasebeta

← #34080650

Subgroups — #34080650

Order 19328.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012766C211yesmaximal, characteristic, complemented
2#23752881C211yesmaximal, characteristic, complemented
3#23752850C211yesmaximal, characteristic, complemented
4#23752598C211yesmaximal, characteristic, complemented
5#23752455C211yesmaximal, characteristic, complemented
6#23752448C211yesmaximal, characteristic, complemented
7#23752436C211yesmaximal, characteristic, complemented
8#23752405C211yesmaximal, characteristic, complemented
9#23752373C211yesmaximal, characteristic, complemented
10#23752357C211yesmaximal, characteristic, complemented
11#23752357C211yesmaximal, characteristic, complemented
12#23752344C211yesmaximal, characteristic, complemented
13#23752313C211yesmaximal, characteristic, complemented
14#23752283C211yesmaximal, characteristic, complemented
15C2×#135×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17C2×D4×D151C2211yescharacteristic
18#18012766—24no—
19C2×#14558991C2211yescharacteristic
20C2×#14558991C2211yescharacteristic, complemented
21C2×D1208C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24C2×#14558987C2211yescharacteristic
25#18012735—21no—
26#18012735C2211yescharacteristic, complemented
27#18012728C2211yescharacteristic
28#18012722—21no—
29#18012715C2211yescharacteristic
30#18012713—21no—
31#18012713C2211yescharacteristic
32#18012713C2211yescharacteristic, complemented
33#18012711—21no—
34#18012710—21no—
35#18012710C2211yescharacteristic
36#18012707—21no—
37Q8×Dic151C2211yescharacteristic, complemented
38D4×Dic151C2211yescharacteristic
39C4×C22⋊D151—21no—
40C4×C22⋊D151C2211yescharacteristic
41C2×(C2×D151)⋊C4—21no—
42#18012673C2211yescharacteristic, complemented
43Dic151⋊C8C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic
47#18012661C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic, complemented
50C22⋊(C151⋊C8)C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic
52#18012649C2211yescharacteristic, complemented
53C2×#41×C151C2211yescharacteristic
54C2×#41×C151C2211yescharacteristic, complemented
55#135×C151—24no—
56C2×Q16×C151C2211yescharacteristic, complemented
57C2×SD16×C151C2211yescharacteristic
58C2×SD16×C151C2211yescharacteristic, complemented
59C2×D8×C151C2211yescharacteristic
60C22×C8×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559005—22no—
63#14559005—41no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151D411yescharacteristic
74D4×D151—22no—
75D4×D151—41no—
76C22×Dic151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79#14558991—22no—
80#14558991—41no—
81D1208—22no—
82#14558989—22no—
83#14558989—41no—
84#14558987—22no—
85C2×C151⋊C8C2311yescharacteristic
86C2×C151⋊C8C2311yescharacteristic
87C4⋊Dic151—21no—
88C4⋊Dic151C2311yescharacteristic
89C4⋊Dic151C2311yescharacteristic
90Dic151⋊C4—21no—
91Dic151⋊C4D411yescharacteristic
92C22⋊Dic151—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151D411yescharacteristic
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)⋊C4D411yescharacteristic
101C4×Dic151—21no—
102C4×Dic151C2311yescharacteristic
103#41×C151—22no—
104#41×C151—22no—
105#41×C151—41no—
106#41×C151—41no—
107C2×Q8×C151C2311yescharacteristic
108C2×Q8×C151C2311yescharacteristic
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151C2311yescharacteristic
116Q16×C151—22no—
117SD16×C151—22no—
118SD16×C151D414yescomplemented
119D8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151C2311yescharacteristic
122C2×C8×C151C2311yescharacteristic
123C22×D151—21no—
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—81no—
128C22×D151C2×D411yescharacteristic
129D604—21no—
130D604—21no—
131D604—21no—
132D604—21no—
133D604—42no—
134C22⋊D151—41no—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C22⋊D151—81no—
138C22⋊D151—81no—
139C22⋊D151—81no—
140C22⋊D151—81no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—81no—
144C2×Dic151C2×D411yescharacteristic
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C4×D151—21no—
148C4×D151—21no—
149C4×D151—42no—
150C151⋊C8—21no—
151C151⋊C8—21no—
152C23×C151—21no—
153C23×C151—21no—
154C23×C151C2×D411yescharacteristic
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151—21no—
158Q8×C151C2×D412yes—
159D4×C151—21no—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—42no—
163D4×C151—42no—
164D4×C151C2×D412yes—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151C2×D411yescharacteristic
172C2×C4×C151C2411yescharacteristic
173C8×C151—21no—
174C8×C151C2×D412yes—
175C22×C151—21no—
176C22×C151—22no—
177C22×C151—21no—
178C22×C151—21no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151C22×D411yescharacteristic
185C2×D151—21no—
186C2×D151—21no—
187C2×D151—21no—
188C2×D151—41no—
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—84no—
195C4×C151—21no—
196C4×C151—22no—
197C4×C151—41no—
198C4×C151C22×D411yescharacteristic
199C4×C151H(5,𝔽2)11yescharacteristic
200Dic151—21no—
201Dic151—21no—
202Dic151—21no—
203Dic151—41no—
204Dic151—41no—
205C2×C151—42no—
206C2×C151—41no—
207C2×C151—81no—
208C2×C151D4211yescharacteristic
209C2×C151#57511yescharacteristic
210C2×C151#57611yescharacteristic
211D151—41no—
212D151—81no—
213D151—81no—
214C151#326811yescharacteristic, complemented, Sylow
215#3268—1511nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1511no—
217C2×#135D15111yescharacteristic, complemented
218#550—1511no—
219#546—1511no—
220#496—1511no—
221#468—1511no—
222#466—1511no—
223#464—1511no—
224#459—1511no—
225#452—1511no—
226#449—1511no—
227#449—1511no—
228#447—1511no—
229#440—1511no—
230#435—1511no—
231C2×#41—1511no—
232C2×#41C2×D15111yescharacteristic
233C2×#41C2×D15111yescharacteristic, complemented
234C22×D4—1511no—
235AGL(1,ℤ/8)—3024no—
236#135—24no—
237C2×Q16C2×D15111yescharacteristic, complemented
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16C2×D15111yescharacteristic
241C2×SD16C2×D15111yescharacteristic, complemented
242C2×D8—1511no—
243C2×D8—1511no—
244C2×D8—1511no—
245C2×D8C2×D15111yescharacteristic
246C2×M16—1511no—
247C22×C8C2×D15111yescharacteristic, complemented
248#127—3021no—
249#127—1511no—
250#124—1511no—
251#123—3021no—
252C22⋊Q8—1511no—
253#121—3021no—
254#121—3021no—
255#121—3021no—
256#121—1511no—
257#121—1511no—
258#121—1511no—
259#120—3021no—
260C4×Q8—1511no—
261C4×D4—3021no—
262C4×D4—1511no—
263C4×D4—1511no—
264C2×C22⋊C4—3021no—
265#107—1511no—
266C4⋊C8—1511no—
267#103—1511no—
268#103—1511no—
269#102—1511no—
270#102—1511no—
271#102—1511no—
272#102—1511no—
273C22⋊C8—1511no—
274C22⋊C8—1511no—
275#97—1511no—
276C24—3021no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—3022no—
282#41—6041no—
283C2×Q8C22×D15111yescharacteristic
284C2×Q8C22×D15111yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—3021no—
288C2×D4—3022no—
289C2×D4—3021no—
290C2×D4—3021no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—6041no—
296C2×D4—1511no—
297C2×D4—1511no—
298C2×D4—1511no—
299C2×D4C22×D15111yescharacteristic
300C2×D4C22×D15111yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4—1511no—
306C22×C4C22×D15111yescharacteristic
307Q16—22no—
308SD16—22no—
309SD16—3022no—
310SD16—6041no—
311SD16C22⋊D15114yescomplemented
312D8—22no—
313D8—3022no—
314D8—3022no—
315D8—6041no—
316M16—3022no—
317C2×C8—22no—
318C2×C8—1511no—
319C2×C8—1511no—
320C2×C8C22×D15111yescharacteristic
321C2×C8C22×D15111yescharacteristic
322C4⋊C4—3021no—
323C4⋊C4—3021no—
324C4⋊C4—1511no—
325C4⋊C4—1511no—
326C4⋊C4—1511no—
327C22⋊C4—3021no—
328C22⋊C4—3021no—
329C22⋊C4—3021no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—1511no—
335C22⋊C4—1511no—
336C42—3021no—
337C42—1511no—
338C23—21no—
339C23—21no—
340C23—3021no—
341C23—3021no—
342C23—6042no—
343C23—6042no—
344C23—1511no—
345C23—12081no—
346C23D4×D15111yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8C2×C22⋊D15112yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—42no—
356D4—3021no—
357D4—3021no—
358D4—3021no—
359D4—3021no—
360D4—6042no—
361D4—6041no—
362D4—6042no—
363D4—6042no—
364D4—12081no—
365D4—12081no—
366D4—12081no—
367D4—12081no—
368D4C2×C22⋊D15112yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—3021no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—3021no—
379C2×C4—6042no—
380C2×C4—1511no—
381C2×C4—1511no—
382C2×C4—1511no—
383C2×C4—12081no—
384C2×C4D4×D15111yescharacteristic
385C2×C4C23×D15111yescharacteristic
386C8—21no—
387C8—3021no—
388C8—3021no—
389C8C2×C22⋊D15112yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—3021no—
400C22—3021no—
401C22—3021no—
402C22—6041no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—6041no—
407C22—6041no—
408C22—12084no—
409C22C2×D4×D15111yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—3021no—
414C4—3021no—
415C4—3021no—
416C4—6041no—
417C4—6041no—
418C4C22×C22⋊D15111yescharacteristic
419C4#1801278411yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—6041no—
424C2—12081no—
425C2—12081no—
426C2D4×C22⋊D15111yescharacteristic
427C2#2375300911yescharacteristic
428C2#2375301411yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#135×C151C2
socleC22×C151C22×D4
hypercenterC2×#135D151
hypocenterC151#3268
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#18012766C2semidirect
2. #23752881C2semidirect
3. #23752850C2semidirect
4. #23752598C2semidirect
5. #23752455C2semidirect
6. #23752448C2semidirect
7. #23752436C2semidirect
8. #23752405C2semidirect
9. #23752373C2semidirect
10. #23752357C2semidirect
11. #23752357C2semidirect
12. #23752344C2semidirect
13. #23752313C2semidirect
14. #23752283C2semidirect
15. C2×#135×C151C2semidirect
20. C2×#14558991C22semidirect
26. #18012735C22semidirect
32. #18012713C22semidirect
37. Q8×Dic151C22semidirect
42. #18012673C22semidirect
43. Dic151⋊C8C22semidirect
44. #18012663C22semidirect
45. #18012663C22semidirect
47. #18012661C22semidirect
49. #18012660C22semidirect
50. C22⋊(C151⋊C8)C22semidirect
52. #18012649C22semidirect
54. C2×#41×C151C22semidirect
56. C2×Q16×C151C22semidirect
58. C2×SD16×C151C22semidirect
60. C22×C8×C151C22semidirect
118. SD16×C151D4semidirect
214. C151#3268semidirect
217. C2×#135D151semidirect
233. C2×#41C2×D151semidirect
237. C2×Q16C2×D151semidirect
241. C2×SD16C2×D151semidirect
247. C22×C8C2×D151semidirect
311. SD16C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127662
#237528812
#237528502
#237525982
#237524552
#237524482
#237524362
#237524052
#237523732
#237523572
#237523442
#237523132
#237522832
C2×#135×C1512
#3268151