Finite Group Databasebeta

← #34078829

Subgroups — #34078829

Order 19328.

452 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753012C211yesmaximal, characteristic, complemented
2#23753010C211yesmaximal, characteristic, complemented
3C2×#18012759C211yesmaximal, characteristic, complemented
4C2×#18012747C211yesmaximal, characteristic, complemented
5#23752486C212yesmaximal, complemented
6#23752481C212yesmaximal, complemented
7#23752478C212yesmaximal, complemented
8#23752474C212yesmaximal, complemented
9C2×#18012674C211yesmaximal, characteristic, complemented
10#23752194C211yesmaximal, characteristic, complemented
11#413×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C2×#14559004C2211yescharacteristic
14#18012772—21no—
15#18012772C2212yes—
16#18012770C2212yes—
17#18012769—21no—
18#18012767—21no—
19#18012767C2212yes—
20#18012765C2212yes—
21#18012764—21no—
22#18012761—22no—
23#18012759—22no—
24#18012759—21no—
25#18012759—21no—
26#18012759—21no—
27#18012759—21no—
28C2×#14558994C2211yescharacteristic, complemented
29C2×#14558992C2211yescharacteristic, complemented
30C2×#14558991C2211yescharacteristic, complemented
31C2×#14558989C2211yescharacteristic, complemented
32#18012747—21no—
33#18012747—21no—
34#18012747C2212yes—
35#18012747C2212yes—
36C2×#14558988C2211yescharacteristic
37C2×#14558987—21no—
38C22×C151⋊C8C2211yescharacteristic
39C2×C8×D151—21no—
40#18012674C2212yescomplemented
41#18012674C2212yescomplemented
42#18012657C2212yescomplemented
43#18012655C2212yescomplemented
44C2×#41×C151C2211yescharacteristic
45C2×M16×C151C2211yescharacteristic
46C2×M16×C151C2211yescharacteristic
47#101×C151C2212yescomplemented
48#100×C151C2212yescomplemented
49#14559004—21no—
50#14559004—21no—
51#14559004—21no—
52#14559004—21no—
53#14559004—21no—
54#14559004—21no—
55#14559004D412yes—
56#14559004C2312yes—
57C2×Dic302D411yescharacteristic
58C2×Dic302C2311yescharacteristic
59C2×D604D411yescharacteristic
60C2×D604C2311yescharacteristic
61C2×C22⋊D151—21no—
62C2×C22⋊D151—21no—
63C2×C4×D151—21no—
64C2×C4×D151—21no—
65Dic604—22no—
66#14558994—22no—
67#14558994—21no—
68#14558994—21no—
69#14558993—22no—
70#14558993—22no—
71#14558992—22no—
72#14558992—21no—
73#14558992—21no—
74#14558991—22no—
75#14558991—21no—
76#14558991—21no—
77D1208—22no—
78#14558989—22no—
79#14558989—21no—
80#14558989—21no—
81#14558988—21no—
82#14558988C2312yes—
83#14558987—22no—
84#14558987—22no—
85C2×C151⋊C8—21no—
86C2×C151⋊C8D411yescharacteristic
87C2×C151⋊C8D411yescharacteristic
88C2×C151⋊C8D411yescharacteristic
89C2×C151⋊C8D411yescharacteristic
90C2×C151⋊C8C2311yescharacteristic
91C2×C151⋊C8C2311yescharacteristic
92C8×D151—22no—
93C8×D151—22no—
94#41×C151—21no—
95#41×C151—21no—
96#41×C151—21no—
97#41×C151—21no—
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151—21no—
100C2×D4×C151C2311yescharacteristic
101C22×C4×C151—21no—
102C22×C4×C151C2311yescharacteristic
103M16×C151—21no—
104M16×C151—21no—
105M16×C151C2312yes—
106M16×C151C2312yes—
107C2×C8×C151—21no—
108C2×C8×C151—21no—
109C22×D151—21no—
110C22×D151—21no—
111Dic302—21no—
112Dic302—21no—
113Dic302—21no—
114Dic302C2×D412yes—
115D604—21no—
116D604—21no—
117D604—21no—
118D604C2×D412yes—
119C22⋊D151—22no—
120C22⋊D151—22no—
121C22⋊D151—41no—
122C22⋊D151—41no—
123C2×Dic151—21no—
124C2×Dic151—21no—
125C4×D151—22no—
126C4×D151—22no—
127C4×D151—41no—
128C4×D151—41no—
129C151⋊C8—22no—
130C151⋊C8C2×D411yescharacteristic
131C151⋊C8C2×D411yescharacteristic
132C151⋊C8C2×D411yescharacteristic
133C151⋊C8C2×D411yescharacteristic
134C23×C151—21no—
135C23×C151#4111yescharacteristic
136Q8×C151—21no—
137Q8×C151—21no—
138D4×C151—21no—
139D4×C151—21no—
140D4×C151—41no—
141D4×C151—41no—
142C2×C4×C151—21no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151#4111yescharacteristic
150C2×C4×C151C2411yescharacteristic
151C8×C151—22no—
152C8×C151—22no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—81no—
156C22×C151#12111yescharacteristic
157C22×C151#12111yescharacteristic
158C22×C151C2×#4111yescharacteristic
159C2×D151—22no—
160C2×D151—42no—
161C2×D151—41no—
162C2×D151—81no—
163C4×C151—41no—
164C4×C151#12111yescharacteristic
165C4×C151#12111yescharacteristic
166C4×C151C22×D411yescharacteristic
167C4×C151C22×D411yescharacteristic
168Dic151—22no—
169Dic151—41no—
170C2×C151—21no—
171C2×C151—21no—
172C2×C151—21no—
173C2×C151—81no—
174C2×C151C2×#12111yescharacteristic
175D151—42no—
176D151—81no—
177C151#306711yescharacteristic, complemented, Sylow
178#3067—1511nomaximal, Sylow
179#575—1511no—
180#575—1511no—
181C2×#135—1511no—
182C2×#131—1511no—
183#473—1512no—
184#472—1512no—
185#471—1512no—
186#471—1512no—
187C2×#108—1511no—
188#413—1511no—
189#413D15111yescharacteristic, complemented
190C2×#41—1511no—
191C2×#41—1511no—
192C2×#41C2×D15111yescharacteristic
193#137—3021no—
194#137—3021no—
195#137—1512no—
196#137—1512no—
197AGL(1,ℤ/8)—3021no—
198AGL(1,ℤ/8)—3021no—
199AGL(1,ℤ/8)—1512no—
200AGL(1,ℤ/8)—1512no—
201#135—3022no—
202#135—3022no—
203#135—3021no—
204#135—3021no—
205#135—3021no—
206#135—3021no—
207C2×Q16—1511no—
208C2×SD16—1511no—
209C2×SD16—1511no—
210C2×D8—1511no—
211#131—3021no—
212#131—3021no—
213#131—1512no—
214#131—1512no—
215C2×M16—3021no—
216C2×M16—1511no—
217C2×M16C2×D15111yescharacteristic
218C2×M16C2×D15111yescharacteristic
219C22×C8—3021no—
220C22×C8—1511no—
221#108—1512no—
222#108—1512no—
223#101—1512no—
224#101C2×D15112yescomplemented
225#100—1512no—
226#100C2×D15112yescomplemented
227#41—21no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—3021no—
232#41—3021no—
233#41—3021no—
234#41—3021no—
235#41—3021no—
236#41—3021no—
237#41—1512no—
238#41—1512no—
239C2×Q8—1511no—
240C2×Q8—1511no—
241C2×Q8C22×D15111yescharacteristic
242C2×D4—21no—
243C2×D4—3021no—
244C2×D4—3021no—
245C2×D4—1511no—
246C2×D4—1511no—
247C2×D4C22×D15111yescharacteristic
248C22×C4—21no—
249C22×C4—3021no—
250C22×C4—3021no—
251C22×C4C22×D15111yescharacteristic
252Q16—3022no—
253Q16—3022no—
254Q16—3021no—
255Q16—3021no—
256SD16—3022no—
257SD16—3022no—
258SD16—3022no—
259SD16—3022no—
260SD16—3021no—
261SD16—3021no—
262SD16—3021no—
263SD16—3021no—
264D8—3022no—
265D8—3022no—
266D8—3021no—
267D8—3021no—
268M16—21no—
269M16—21no—
270M16—3022no—
271M16—3022no—
272M16—3021no—
273M16—1512no—
274M16C22×D15112yes—
275M16C22×D15112yes—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—3022no—
279C2×C8—3022no—
280C2×C8—3021no—
281C2×C8—1511no—
282C2×C8—1511no—
283C2×C8—1511no—
284C2×C8—1511no—
285C2×C8—1511no—
286C2×C8—1511no—
287C23—21no—
288C23—3021no—
289C23—3021no—
290C23#1455900411yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—3021no—
294Q8—3021no—
295Q8—3021no—
296Q8—1512no—
297D4—21no—
298D4—21no—
299D4—41no—
300D4—41no—
301D4—3022no—
302D4—3022no—
303D4—3021no—
304D4—3021no—
305D4—3021no—
306D4—6041no—
307D4—6041no—
308D4—1512no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—3021no—
313C2×C4—3022no—
314C2×C4—3022no—
315C2×C4—3021no—
316C2×C4—6041no—
317C2×C4—6041no—
318C2×C4D4×D15111yescharacteristic
319C2×C4D4×D15111yescharacteristic
320C2×C4D4×D15111yescharacteristic
321C2×C4D4×D15111yescharacteristic
322C2×C4#1455900411yescharacteristic
323C2×C4C23×D15111yescharacteristic
324C8—22no—
325C8—22no—
326C8—3022no—
327C8—1511no—
328C8—1511no—
329C8—1511no—
330C8—1511no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—3022no—
335C22—6042no—
336C22—6041no—
337C22—12081no—
338C22#1801271211yescharacteristic
339C22#1801271211yescharacteristic
340C22C2×#1455900411yescharacteristic
341C4—41no—
342C4—3022no—
343C4—6041no—
344C4#1801271211yescharacteristic
345C4#1801271211yescharacteristic
346C4C2×D4×D15111yescharacteristic
347C4C2×D4×D15111yescharacteristic
348C2—21no—
349C2—21no—
350C2—21no—
351C2—81no—
352C2—6042no—
353C2—12081no—
354C2C2×#1801271211yescharacteristic
subgroupG/H
centerC4#18012712
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#413×C151C2
socleC2×C151C2×#121
hypercenter#413D151
hypocenterC151#3067
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #23753012C2semidirect
2. #23753010C2semidirect
3. C2×#18012759C2semidirect
4. C2×#18012747C2semidirect
5. #23752486C2semidirect
6. #23752481C2semidirect
7. #23752478C2semidirect
8. #23752474C2semidirect
9. C2×#18012674C2semidirect
10. #23752194C2semidirect
11. #413×C151C2semidirect
28. C2×#14558994C22semidirect
29. C2×#14558992C22semidirect
30. C2×#14558991C22semidirect
31. C2×#14558989C22semidirect
40. #18012674C22semidirect
41. #18012674C22semidirect
42. #18012657C22semidirect
43. #18012655C22semidirect
47. #101×C151C22semidirect
48. #100×C151C22semidirect
177. C151#3067semidirect
189. #413D151semidirect
224. #101C2×D151semidirect
226. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530122
#237530102
C2×#180127592
C2×#180127472
#237524862
#237524812
#237524782
#237524742
C2×#180126742
#237521942
#413×C1512
#3067151