Finite Group Databasebeta

← #34080886

Subgroups — #34080886

Order 19328.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753029C211yesmaximal, characteristic, complemented
2#23753026C211yesmaximal, characteristic, complemented
3#23753024C211yesmaximal, characteristic, complemented
4#23753019C211yesmaximal, characteristic, complemented
5#23752606C211yesmaximal, characteristic, complemented
6#23752488C211yesmaximal, characteristic, complemented
7#23752487C211yesmaximal, characteristic, complemented
8#23752476C211yesmaximal, characteristic, complemented
9#23752475C211yesmaximal, characteristic, complemented
10#23752396C211yesmaximal, characteristic, complemented
11#23752396C211yesmaximal, characteristic, complemented
12#23752391C211yesmaximal, characteristic, complemented
13#23752386C211yesmaximal, characteristic, complemented
14#23752335C211yesmaximal, characteristic, complemented
15#444×C151C211yesmaximal, characteristic, complemented
16#18012786C2211yescharacteristic
17#18012786C2211yescharacteristic
18#18012786C2211yescharacteristic, complemented
19#18012785C2211yescharacteristic
20#18012772—21no—
21#18012772—21no—
22#18012772—21no—
23#18012772C2211yescharacteristic
24#18012772C2211yescharacteristic
25#18012772C2211yescharacteristic, complemented
26#18012771—21no—
27#18012769C2211yescharacteristic
28#18012769C2211yescharacteristic
29#18012769C2211yescharacteristic, complemented
30#18012768—21no—
31#18012768—21no—
32#18012767—21no—
33#18012767C2211yescharacteristic
34#18012764C2211yescharacteristic
35#18012763—21no—
36#18012761—21no—
37#18012761—21no—
38#18012761C2211yescharacteristic
39#18012760—21no—
40#18012758—21no—
41C2×Dic604—21no—
42C2×Dic604C2211yescharacteristic, complemented
43C2×Dic604C2211yescharacteristic, complemented
44Q16×D151—21no—
45C2×#14558993—21no—
46C2×#14558993C2211yescharacteristic
47C2×#14558993C2211yescharacteristic
48SD16×D151—21no—
49#18012745C2211yescharacteristic
50#18012745C2211yescharacteristic, complemented
51#18012739C2211yescharacteristic, complemented
52#18012727C2211yescharacteristic
53#18012675C2211yescharacteristic, complemented
54#18012667C2211yescharacteristic
55#18012667C2211yescharacteristic, complemented
56#18012657C2211yescharacteristic, complemented
57#18012657C2211yescharacteristic, complemented
58#18012657C2211yescharacteristic, complemented
59#18012655C2211yescharacteristic
60#135×C151C2211yescharacteristic
61#131×C151C2211yescharacteristic
62#131×C151C2211yescharacteristic, complemented
63#108×C151C2211yescharacteristic, complemented
64#104×C151C2211yescharacteristic
65#104×C151C2211yescharacteristic, complemented
66#97×C151C2211yescharacteristic, complemented
67#14559005—21no—
68#14559004—21no—
69#14559004—21no—
70#14559004—21no—
71#14559004—21no—
72#14559004C2311yescharacteristic
73#14559004C2311yescharacteristic
74#14559003—21no—
75#14559003—21no—
76#14559003—21no—
77#14559003—41no—
78#14559003—41no—
79#14559003—41no—
80C2×Dic302—21no—
81C2×Dic302—21no—
82C2×Dic302—21no—
83C2×Dic302C2311yescharacteristic
84C2×Dic302C2311yescharacteristic
85C2×Dic302C2311yescharacteristic
86Q8×D151—21no—
87Q8×D151—21no—
88Q8×D151—21no—
89C2×D604—21no—
90C2×D604C2311yescharacteristic
91D4×D151—21no—
92D4×D151—41no—
93Dic604—21no—
94Dic604—21no—
95Dic604—21no—
96Dic604—21no—
97Dic604—21no—
98Dic604—21no—
99Dic604—21no—
100Dic604D411yescharacteristic
101#14558994—21no—
102#14558994—21no—
103#14558994—21no—
104#14558993—21no—
105#14558993—21no—
106#14558993—21no—
107#14558993—21no—
108#14558993—21no—
109#14558993—21no—
110#14558993—21no—
111#14558993—21no—
112#14558993D411yescharacteristic
113#14558993D411yescharacteristic
114#14558992—21no—
115#14558992—21no—
116#14558992—21no—
117#14558991—21no—
118D1208—21no—
119D1208D411yescharacteristic
120#14558989—21no—
121#14558988C2311yescharacteristic
122#14558988C2311yescharacteristic
123#14558987—21no—
124#14558987—21no—
125C8×D151—21no—
126C8×D151—21no—
127C4⋊Dic151—41no—
128(C2×D151)⋊C4—41no—
129#41×C151C2311yescharacteristic
130#41×C151C2311yescharacteristic
131Q16×C151D411yescharacteristic
132SD16×C151D411yescharacteristic
133SD16×C151D411yescharacteristic
134D8×C151D411yescharacteristic
135M16×C151—21no—
136M16×C151—21no—
137M16×C151C2311yescharacteristic
138M16×C151C2311yescharacteristic
139C2×C8×C151—21no—
140C2×C8×C151—21no—
141C2×C8×C151C2311yescharacteristic
142C2×C8×C151C2311yescharacteristic
143C42×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—41no—
146Dic302—21no—
147Dic302—21no—
148Dic302—21no—
149Dic302—21no—
150Dic302—21no—
151Dic302—21no—
152Dic302—41no—
153Dic302—41no—
154Dic302—41no—
155Dic302C2×D411yescharacteristic
156Dic302C2×D411yescharacteristic
157D604—21no—
158D604—21no—
159D604—41no—
160D604C2×D411yescharacteristic
161D604C2×D411yescharacteristic
162C22⋊D151—21no—
163C22⋊D151—21no—
164C22⋊D151—41no—
165C22⋊D151—41no—
166C22⋊D151—41no—
167C22⋊D151—41no—
168C2×Dic151—21no—
169C2×Dic151—21no—
170C2×Dic151—21no—
171C2×Dic151—41no—
172C2×Dic151—41no—
173C2×Dic151—41no—
174C4×D151—21no—
175C4×D151—21no—
176C4×D151—41no—
177C4×D151—41no—
178C4×D151—41no—
179C4×D151—41no—
180C151⋊C8—21no—
181C151⋊C8—21no—
182Q8×C151C2×D411yescharacteristic
183Q8×C151C2×D411yescharacteristic
184D4×C151—21no—
185D4×C151—21no—
186D4×C151C2×D411yescharacteristic
187D4×C151C2×D411yescharacteristic
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151C2411yescharacteristic
192C8×C151—21no—
193C8×C151—21no—
194C8×C151C2×D411yescharacteristic
195C8×C151C2×D411yescharacteristic
196C8×C151C2×D411yescharacteristic
197C8×C151C2×D411yescharacteristic
198C22×C151—21no—
199C22×C151—21no—
200C22×C151H(5,𝔽2)11yescharacteristic
201C2×D151—21no—
202C2×D151—21no—
203C2×D151—41no—
204C2×D151—81no—
205C2×D151—161no—
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—41no—
209C4×C151C22×D411yescharacteristic
210C4×C151C22×D411yescharacteristic
211Dic151—21no—
212Dic151—21no—
213Dic151—41no—
214Dic151—41no—
215Dic151—41no—
216C2×C151—21no—
217C2×C151—41no—
218C2×C151—41no—
219C2×C151D4211yescharacteristic
220D151—41no—
221D151—41no—
222D151—81no—
223C151#328911yescharacteristic, complemented, Sylow
224#3289—1511nomaximal, Sylow
225#578—1511no—
226#578—1511no—
227#577—1511no—
228#577—1511no—
229#497—1511no—
230#473—1511no—
231#473—1511no—
232#471—1511no—
233#471—1511no—
234#456—1511no—
235#456—1511no—
236#455—1511no—
237#454—1511no—
238#444—1511no—
239#444D15111yescharacteristic, complemented
2402−1+4—1511no—
2412−1+4—1511no—
2422−1+4—1511no—
243H(5,𝔽2)—1511no—
244#137—3021no—
245#137—3021no—
246#137—3021no—
247#137—3021no—
248#137—3021no—
249#137—3021no—
250#137—1511no—
251#137—1511no—
252#137—1511no—
253#137—1511no—
254#137—1511no—
255#137—1511no—
256AGL(1,ℤ/8)—3021no—
257AGL(1,ℤ/8)—3021no—
258AGL(1,ℤ/8)—1511no—
259AGL(1,ℤ/8)—1511no—
260#135—3021no—
261#135—3021no—
262#135—3021no—
263#135—3021no—
264#135—1511no—
265#135C2×D15111yescharacteristic
266C2×Q16—3021no—
267C2×Q16—3021no—
268C2×Q16—1511no—
269C2×Q16—1511no—
270C2×SD16—3021no—
271C2×SD16—3021no—
272C2×SD16—1511no—
273C2×SD16—1511no—
274#131—1511no—
275#131—1511no—
276#131C2×D15111yescharacteristic
277#131C2×D15111yescharacteristic, complemented
278C4⋊Q8—1511no—
279#124—1511no—
280#108—1511no—
281#108C2×D15111yescharacteristic, complemented
282#104—1511no—
283#104—1511no—
284#104C2×D15111yescharacteristic
285#104C2×D15111yescharacteristic, complemented
286#101—1511no—
287#101—1511no—
288#101—1511no—
289#100—1511no—
290#97C2×D15111yescharacteristic, complemented
291#41—3021no—
292#41—3021no—
293#41—3021no—
294#41—3021no—
295#41—3021no—
296#41—3021no—
297#41—3021no—
298#41—3021no—
299#41—6041no—
300#41—6041no—
301#41—6041no—
302#41—1511no—
303#41—1511no—
304#41C22×D15111yescharacteristic
305#41C22×D15111yescharacteristic
306C2×Q8—3021no—
307C2×Q8—3021no—
308C2×Q8—3021no—
309C2×Q8—3021no—
310C2×Q8—3021no—
311C2×Q8—3021no—
312C2×Q8—1511no—
313C2×Q8—1511no—
314C2×Q8—1511no—
315C2×D4—3021no—
316C2×D4—3021no—
317C2×D4—6041no—
318C2×D4—1511no—
319Q16—3021no—
320Q16—3021no—
321Q16—3021no—
322Q16—3021no—
323Q16—3021no—
324Q16—3021no—
325Q16—3021no—
326Q16—3021no—
327Q16—3021no—
328Q16—3021no—
329Q16—1511no—
330Q16D60411yescharacteristic
331SD16—3021no—
332SD16—3021no—
333SD16—3021no—
334SD16—3021no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338SD16—3021no—
339SD16—3021no—
340SD16—3021no—
341SD16—3021no—
342SD16—3021no—
343SD16—1511no—
344SD16—1511no—
345SD16D60411yescharacteristic
346SD16D60411yescharacteristic
347D8—3021no—
348D8—3021no—
349D8—1511no—
350D8D60411yescharacteristic
351M16—21no—
352M16—21no—
353M16—3021no—
354M16—3021no—
355M16—1511no—
356M16—1511no—
357M16C22×D15111yescharacteristic
358M16C22×D15111yescharacteristic
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—3021no—
362C2×C8—3021no—
363C2×C8C22×D15111yescharacteristic
364C2×C8C22×D15111yescharacteristic
365C4⋊C4—6041no—
366C22⋊C4—6041no—
367C42C22×D15111yescharacteristic
368C23—3021no—
369C23—6041no—
370Q8—3021no—
371Q8—3021no—
372Q8—3021no—
373Q8—3021no—
374Q8—3021no—
375Q8—3021no—
376Q8—6041no—
377Q8—6041no—
378Q8—6041no—
379Q8—1511no—
380Q8—1511no—
381Q8C2×D60411yescharacteristic
382Q8C2×D60411yescharacteristic
383D4—21no—
384D4—21no—
385D4—3021no—
386D4—3021no—
387D4—3021no—
388D4—3021no—
389D4—6041no—
390D4—6041no—
391D4—6041no—
392D4—6041no—
393D4—6041no—
394D4—1511no—
395D4—1511no—
396D4C2×D60411yescharacteristic
397D4C2×D60411yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—3021no—
402C2×C4—3021no—
403C2×C4—3021no—
404C2×C4—3021no—
405C2×C4—3021no—
406C2×C4—6041no—
407C2×C4—6041no—
408C2×C4—6041no—
409C2×C4—6041no—
410C2×C4—6041no—
411C2×C4—6041no—
412C2×C4—6041no—
413C2×C4C23×D15111yescharacteristic
414C8—21no—
415C8—21no—
416C8—3021no—
417C8—3021no—
418C8D4×D15111yescharacteristic
419C8D4×D15111yescharacteristic
420C8C2×D60411yescharacteristic
421C8C2×D60411yescharacteristic
422C22—21no—
423C22—21no—
424C22—3021no—
425C22—3021no—
426C22—6041no—
427C22—24161no—
428C22—12081no—
429C22#1801278511yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—3021no—
434C4—3021no—
435C4—6041no—
436C4—6041no—
437C4—6041no—
438C4C2×D4×D15111yescharacteristic
439C4C22×D60411yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—6041no—
444C2—6041no—
445C2—12081no—
446C2D4×D60411yescharacteristic
subgroupG/H
centerC2D4×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#444×C151C2
socleC2×C151D42
hypercenter#444D151
hypocenterC151#3289
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #23753029C2semidirect
2. #23753026C2semidirect
3. #23753024C2semidirect
4. #23753019C2semidirect
5. #23752606C2semidirect
6. #23752488C2semidirect
7. #23752487C2semidirect
8. #23752476C2semidirect
9. #23752475C2semidirect
10. #23752396C2semidirect
11. #23752396C2semidirect
12. #23752391C2semidirect
13. #23752386C2semidirect
14. #23752335C2semidirect
15. #444×C151C2semidirect
18. #18012786C22semidirect
25. #18012772C22semidirect
29. #18012769C22semidirect
42. C2×Dic604C22semidirect
43. C2×Dic604C22semidirect
50. #18012745C22semidirect
51. #18012739C22semidirect
53. #18012675C22semidirect
55. #18012667C22semidirect
56. #18012657C22semidirect
57. #18012657C22semidirect
58. #18012657C22semidirect
62. #131×C151C22semidirect
63. #108×C151C22semidirect
65. #104×C151C22semidirect
66. #97×C151C22semidirect
223. C151#3289semidirect
239. #444D151semidirect
277. #131C2×D151semidirect
281. #108C2×D151semidirect
285. #104C2×D151semidirect
290. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530292
#237530262
#237530242
#237530192
#237526062
#237524882
#237524872
#237524762
#237524752
#237523962
#237523912
#237523862
#237523352
#444×C1512
#3289151