Finite Group Databasebeta

← #34078845

Subgroups — #34078845

Order 19328.

446 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753011C211yesmaximal, characteristic
2C2×#18012771C211yesmaximal, characteristic, complemented
3#137×D151C211yesmaximal, characteristic, complemented
4#23752977C211yesmaximal, characteristic, complemented
5#23752486C211yesmaximal, characteristic, complemented
6#23752485C211yesmaximal, characteristic, complemented
7#23752484C211yesmaximal, characteristic, complemented
8#23752478C211yesmaximal, characteristic, complemented
9#23752477C211yesmaximal, characteristic, complemented
10#23752476C211yesmaximal, characteristic, complemented
11#23752475C211yesmaximal, characteristic, complemented
12#23752259C211yesmaximal, characteristic, complemented
13#23752195C211yesmaximal, characteristic, complemented
14#101×D151C211yesmaximal, characteristic, complemented
15#473×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic
17#41×D151C2211yescharacteristic
18C2×Q8×D151C2211yescharacteristic
19#18012772C2211yescharacteristic
20#18012771—21no—
21#18012771—21no—
22#18012771—21no—
23#18012771—21no—
24#18012771—21no—
25#18012771—21no—
26#18012770C2211yescharacteristic
27#18012770C2211yescharacteristic
28#18012769C2211yescharacteristic
29#18012768—21no—
30#18012767C2211yescharacteristic
31#18012766—21no—
32#18012764C2211yescharacteristic
33#18012762—21no—
34#18012760—21no—
35C2×#14558994C2211yescharacteristic, complemented
36Q16×D151—21no—
37C2×#14558993C2211yescharacteristic, complemented
38C2×#14558991C2211yescharacteristic, complemented
39SD16×D151—21no—
40#18012747—21no—
41#18012747C2211yescharacteristic
42#18012746C2211yescharacteristic
43#18012745—21no—
44#18012745C2211yescharacteristic
45C2×#14558987—21no—
46C2×#14558987C2211yescharacteristic
47M16×D151—21no—
48M16×D151C2211yescharacteristic
49M16×D151C2211yescharacteristic
50M16×D151C2211yescharacteristic
51#18012675C2211yescharacteristic, complemented
52#18012674C2211yescharacteristic, complemented
53#18012674C2211yescharacteristic, complemented
54#18012658C2211yescharacteristic, complemented
55#18012658C2211yescharacteristic, complemented
56#18012657C2211yescharacteristic, complemented
57#18012657C2211yescharacteristic, complemented
58#18012655C2211yescharacteristic, complemented
59#18012655C2211yescharacteristic, complemented
60#137×C151C2211yescharacteristic
61#137×C151C2211yescharacteristic
62C2×Q16×C151C2211yescharacteristic, complemented
63#131×C151C2211yescharacteristic
64#108×C151C2211yescharacteristic, complemented
65#101×C151C2211yescharacteristic, complemented
66#101×C151C2211yescharacteristic, complemented
67#14559005—21no—
68#14559005—21no—
69#14559005—21no—
70#14559005—21no—
71#14559005D411yescharacteristic
72#14559004—21no—
73#14559004C2311yescharacteristic
74#14559003—21no—
75#14559003D411yescharacteristic
76C2×Dic302—21no—
77C2×Dic302C2311yescharacteristic
78Q8×D151—21no—
79Q8×D151—21no—
80Q8×D151—21no—
81Q8×D151—21no—
82Q8×D151D411yescharacteristic
83C2×D604—21no—
84C2×D604C2311yescharacteristic
85D4×D151—21no—
86D4×D151D411yescharacteristic
87C2×C4×D151—21no—
88C2×C4×D151—21no—
89C2×C4×D151—21no—
90C2×C4×D151C2311yescharacteristic
91Dic604—21no—
92#14558994—21no—
93#14558994—21no—
94#14558994—21no—
95#14558994—21no—
96#14558994—21no—
97#14558993—21no—
98#14558993—21no—
99#14558993—21no—
100#14558993—21no—
101#14558992—21no—
102#14558991—21no—
103#14558991—21no—
104#14558991—21no—
105#14558991—21no—
106#14558991—21no—
107D1208—21no—
108#14558989—21no—
109#14558988—21no—
110#14558988C2311yescharacteristic
111#14558988C2311yescharacteristic
112#14558988C2311yescharacteristic
113#14558987—21no—
114#14558987—21no—
115#14558987—21no—
116#14558987—21no—
117#14558987—21no—
118#14558987D411yescharacteristic
119#14558987D411yescharacteristic
120#14558987D411yescharacteristic
121#14558987D411yescharacteristic
122C2×C151⋊C8—21no—
123C2×C151⋊C8C2311yescharacteristic
124C8×D151—21no—
125C8×D151—21no—
126C8×D151—21no—
127C8×D151—21no—
128C8×D151—21no—
129#41×C151C2311yescharacteristic
130C2×Q8×C151C2311yescharacteristic
131C2×Q8×C151C2311yescharacteristic
132Q16×C151—21no—
133Q16×C151—21no—
134Q16×C151—21no—
135Q16×C151—21no—
136SD16×C151—21no—
137SD16×C151—21no—
138M16×C151—21no—
139M16×C151C2311yescharacteristic
140M16×C151C2311yescharacteristic
141M16×C151C2311yescharacteristic
142C2×C8×C151—21no—
143C2×C8×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—21no—
146C22×D151#4111yescharacteristic
147Dic302—21no—
148Dic302—21no—
149Dic302—21no—
150Dic302—41no—
151Dic302—41no—
152Dic302C2×D411yescharacteristic
153D604—21no—
154D604—21no—
155D604—21no—
156D604—41no—
157D604—41no—
158D604C2×D411yescharacteristic
159C22⋊D151—21no—
160C22⋊D151—21no—
161C22⋊D151—21no—
162C2×Dic151—21no—
163C2×Dic151—21no—
164C2×Dic151#4111yescharacteristic
165C4×D151—21no—
166C4×D151—21no—
167C4×D151—21no—
168C4×D151—41no—
169C4×D151—41no—
170C4×D151—41no—
171C4×D151—41no—
172C4×D151C2×D411yescharacteristic
173C4×D151C2×D411yescharacteristic
174C4×D151C2×D411yescharacteristic
175C4×D151C2×D411yescharacteristic
176C151⋊C8—21no—
177C151⋊C8—21no—
178C151⋊C8—21no—
179C151⋊C8C2×D411yescharacteristic
180C151⋊C8C2×D411yescharacteristic
181Q8×C151—21no—
182Q8×C151—21no—
183Q8×C151—21no—
184Q8×C151—21no—
185Q8×C151C2×D411yescharacteristic
186D4×C151—21no—
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×C151—21no—
195C8×C151C2×D411yescharacteristic
196C8×C151C2×D411yescharacteristic
197C22×C151—21no—
198C22×C151C2×#4111yescharacteristic
199C2×D151—21no—
200C2×D151—41no—
201C2×D151—41no—
202C2×D151—81no—
203C2×D151—81no—
204C2×D151#12111yescharacteristic
205C2×D151#12111yescharacteristic
206C4×C151—21no—
207C4×C151—41no—
208C4×C151—41no—
209C4×C151C22×D411yescharacteristic
210C4×C151C22×D411yescharacteristic
211Dic151—21no—
212Dic151—41no—
213Dic151#12111yescharacteristic
214Dic151#12111yescharacteristic
215C2×C151—21no—
216C2×C151—41no—
217C2×C151C2×#12111yescharacteristic
218D151—21no—
219D151—21no—
220D151—41no—
221D151—81no—
222C151#306911yescharacteristic, complemented, Sylow
223#3069—1511nomaximal, Sylow
224#575—1511no—
225C2×#137—1511no—
226C2×#137—1511no—
227#568—1511no—
228#473—1511no—
229#473—1511no—
230#473—1511no—
231#473D15111yescharacteristic, complemented
232#471—1511no—
233#471—1511no—
234#471—1511no—
235#471—1511no—
236#430—1511no—
237#413—1511no—
238C2×#101—1511no—
239C2×#41—1511no—
240C2×#41—1511no—
241C22×Q8—1511no—
242#137—3021no—
243#137—3021no—
244#137—3021no—
245#137—3021no—
246#137—3021no—
247#137—3021no—
248#137—3021no—
249#137—1511no—
250#137—1511no—
251#137—1511no—
252#137—1511no—
253#137C2×D15111yescharacteristic
254#137C2×D15111yescharacteristic
255AGL(1,ℤ/8)—3021no—
256AGL(1,ℤ/8)—1511no—
257AGL(1,ℤ/8)—1511no—
258#135—3021no—
259#135—3021no—
260C2×Q16—3021no—
261C2×Q16—1511no—
262C2×Q16C2×D15111yescharacteristic, complemented
263C2×SD16—3021no—
264C2×SD16—1511no—
265C2×SD16—1511no—
266#131—3021no—
267#131—3021no—
268#131—1511no—
269#131—1511no—
270#131—1511no—
271#131C2×D15111yescharacteristic
272C2×M16—3021no—
273C2×M16—3021no—
274C2×M16—1511no—
275C2×M16—1511no—
276C2×M16—1511no—
277C2×M16—1511no—
278#108—1511no—
279#108—1511no—
280#108—1511no—
281#108C2×D15111yescharacteristic, complemented
282#101—1511no—
283#101—1511no—
284#101—1511no—
285#101—1511no—
286#101C2×D15111yescharacteristic, complemented
287#101C2×D15111yescharacteristic, complemented
288#100—1511no—
289#100—1511no—
290#41—3021no—
291#41—3021no—
292#41—3021no—
293#41—3021no—
294#41—3021no—
295#41—3021no—
296#41—1511no—
297#41—1511no—
298#41—1511no—
299#41C22×D15111yescharacteristic
300C2×Q8—3021no—
301C2×Q8—3021no—
302C2×Q8—3021no—
303C2×Q8—3021no—
304C2×Q8—3021no—
305C2×Q8—1511no—
306C2×Q8—1511no—
307C2×Q8C22×D15111yescharacteristic
308C2×Q8C22×D15111yescharacteristic
309C2×D4—3021no—
310C2×D4—3021no—
311C2×D4—1511no—
312C2×D4—1511no—
313C22×C4—3021no—
314C22×C4—3021no—
315C22×C4—3021no—
316C22×C4—1511no—
317Q16—21no—
318Q16—21no—
319Q16—21no—
320Q16—21no—
321Q16—3021no—
322Q16—3021no—
323Q16—3021no—
324Q16—3021no—
325Q16—3021no—
326Q16—3021no—
327SD16—21no—
328SD16—21no—
329SD16—3021no—
330SD16—3021no—
331SD16—3021no—
332SD16—3021no—
333SD16—3021no—
334SD16—3021no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338SD16—3021no—
339D8—3021no—
340D8—3021no—
341M16—21no—
342M16—3021no—
343M16—3021no—
344M16—3021no—
345M16—3021no—
346M16—3021no—
347M16—3021no—
348M16—1511no—
349M16—1511no—
350M16—1511no—
351M16—1511no—
352M16—1511no—
353M16—1511no—
354M16—1511no—
355M16C22×D15111yescharacteristic
356M16C22×D15111yescharacteristic
357M16C22×D15111yescharacteristic
358C2×C8—21no—
359C2×C8—3021no—
360C2×C8—3021no—
361C2×C8—3021no—
362C2×C8—3021no—
363C2×C8—3021no—
364C2×C8—3021no—
365C2×C8—1511no—
366C2×C8C22×D15111yescharacteristic
367C23—3021no—
368C23—3021no—
369C23—1511no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—3021no—
375Q8—3021no—
376Q8—3021no—
377Q8—6041no—
378Q8—6041no—
379Q8—1511no—
380Q8D4×D15111yescharacteristic
381D4—21no—
382D4—3021no—
383D4—3021no—
384D4—3021no—
385D4—3021no—
386D4—3021no—
387D4—3021no—
388D4—6041no—
389D4—6041no—
390D4—1511no—
391D4D4×D15111yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—3021no—
396C2×C4—3021no—
397C2×C4—3021no—
398C2×C4—3021no—
399C2×C4—3021no—
400C2×C4—6041no—
401C2×C4—6041no—
402C2×C4—6041no—
403C2×C4—6041no—
404C2×C4—1511no—
405C2×C4—1511no—
406C2×C4—1511no—
407C2×C4—1511no—
408C2×C4—1511no—
409C2×C4C23×D15111yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—3021no—
414C8—3021no—
415C8—3021no—
416C8—1511no—
417C8—1511no—
418C8D4×D15111yescharacteristic
419C8D4×D15111yescharacteristic
420C22—21no—
421C22—3021no—
422C22—6041no—
423C22—6041no—
424C22—1511no—
425C22—1511no—
426C22—12081no—
427C22—12081no—
428C22#41×D15111yescharacteristic
429C4—21no—
430C4—41no—
431C4—41no—
432C4—3021no—
433C4—6041no—
434C4—1511no—
435C4—1511no—
436C4C2×D4×D15111yescharacteristic
437C4C2×D4×D15111yescharacteristic
438C2—21no—
439C2—41no—
440C2—3021no—
441C2—3021no—
442C2—6041no—
443C2—12081no—
444C2#121×D15111yescharacteristic
subgroupG/H
centerC2#121×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#473×C151C2
socleC2×C151C2×#121
prime radical#23753011C2
hypercenter#473D151
hypocenterC151#3069
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
2. C2×#18012771C2semidirect
3. #137×D151C2semidirect
4. #23752977C2semidirect
5. #23752486C2semidirect
6. #23752485C2semidirect
7. #23752484C2semidirect
8. #23752478C2semidirect
9. #23752477C2semidirect
10. #23752476C2semidirect
11. #23752475C2semidirect
12. #23752259C2semidirect
13. #23752195C2semidirect
14. #101×D151C2semidirect
15. #473×C151C2semidirect
35. C2×#14558994C22semidirect
37. C2×#14558993C22semidirect
38. C2×#14558991C22semidirect
51. #18012675C22semidirect
52. #18012674C22semidirect
53. #18012674C22semidirect
54. #18012658C22semidirect
55. #18012658C22semidirect
56. #18012657C22semidirect
57. #18012657C22semidirect
58. #18012655C22semidirect
59. #18012655C22semidirect
62. C2×Q16×C151C22semidirect
64. #108×C151C22semidirect
65. #101×C151C22semidirect
66. #101×C151C22semidirect
222. C151#3069semidirect
231. #473D151semidirect
262. C2×Q16C2×D151semidirect
281. #108C2×D151semidirect
286. #101C2×D151semidirect
287. #101C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530112
C2×#180127712
#137×D1512
#237529772
#237524862
#237524852
#237524842
#237524782
#237524772
#237524762
#237524752
#237522592
#237521952
#101×D1512
#473×C1512
#3069151