Finite Group Databasebeta

← #25251321

Subgroups — #25251321

Order 11008.

534 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145131C211yesmaximal, characteristic, complemented
2#19143471C211yesmaximal, characteristic
3#19136761C212yesmaximal, complemented
4#19136750C212yesmaximal, complemented
5#19136740C212yesmaximal, complemented
6#19136735C212yesmaximal, complemented
7#19136383C211yesmaximal, characteristic, complemented
8C2×#14582726C211yesmaximal, characteristic, complemented
9#19136355C211yesmaximal, characteristic, complemented
10#19136302C211yesmaximal, characteristic
11C43×#2139C211yesmaximal, characteristic
12#14583530—21no—
13#14583382—21no—
14C22×C43⋊C16C2211yescharacteristic
15#14583307—22no—
16#14583303C2212yes—
17#14583300C2212yes—
18#14583000—22no—
19Q16×Dic43C2212yes—
20D8×Dic43C2212yes—
21#14582939—21no—
22#14582937C2211yescharacteristic
23C2×#13063259C2211yescharacteristic
24#14582900—21no—
25#14582854C2211yescharacteristic
26#14582727C2212yes—
27#14582726C2212yes—
28#14582726C2212yes—
29#14582725C2212yes—
30Dic43⋊C16C2212yes—
31Dic43⋊C16C2212yes—
32#14582703C2211yescharacteristic
33#14582703C2211yescharacteristic
34#14582700C2211yescharacteristic
35#14582700C2211yescharacteristic
36C2×#135×C43C2211yescharacteristic
37C2×M32×C43C2211yescharacteristic
38C2×#107×C43C2211yescharacteristic
39C43×#358C2212yes—
40C43×#357C2212yes—
41C2×#10621877D411yescharacteristic
42#13063324—22no—
43#13063324—41no—
44#13063316—22no—
45#13063316—41no—
46#13063304—42no—
47Q8×Dic43—22no—
48D4×Dic43—22no—
49D4×Dic43—42no—
50#13063284—21no—
51#13063284—41no—
52#13063284D411yescharacteristic
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—41no—
55C2×C43⋊C16—22no—
56C2×C43⋊C16C2311yescharacteristic
57C2×C43⋊C16C2311yescharacteristic
58#13063259—21no—
59#13063259C2311yescharacteristic
60#13063259C2311yescharacteristic
61#13063259C2312yes—
62#13063258—22no—
63#13063257—21no—
64#13063256—22no—
65#13063249—22no—
66#13063246—22no—
67#13063235D412yes—
68C8×Dic43C2312yes—
69C2×#41×C43—21no—
70#135×C43—22no—
71#135×C43Q814yescomplemented
72C2×Q16×C43C2311yescharacteristic
73C2×SD16×C43—21no—
74C2×D8×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C2×C4⋊C4×C43—21no—
77M32×C43—22no—
78C2×C16×C43C2312yes—
79#107×C43—21no—
80#107×C43C2312yes—
81#41×C43—24no—
82#41×C43—42no—
83C2×Q8×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C2×D411yescharacteristic
89C22×Dic43—42no—
90C22×Dic43—41no—
91C2×Dic86—42no—
92Q16×C43—21no—
93Q16×C43C2×Q812yes—
94SD16×C43—24no—
95D8×C43—21no—
96D8×C43C2×Q812yes—
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×Q812yes—
99C2×C8×C43#4112yes—
100C2×C8×C43C2411yescharacteristic
101C4⋊C4×C43—22no—
102C4⋊C4×C43—41no—
103C22⋊Dic43—42no—
104C22⋊Dic43—41no—
105C22⋊Dic43D812yes—
106C4⋊Dic43—22no—
107C4⋊Dic43—21no—
108C4⋊Dic43—21no—
109C4⋊Dic43—41no—
110C4⋊Dic43—42no—
111C4⋊Dic43—42no—
112C4⋊Dic43D811yescharacteristic
113C4⋊Dic43D811yescharacteristic
114Dic43⋊C4—42no—
115Dic43⋊C4—42no—
116C4×Dic43—41no—
117C4×Dic43—42no—
118C4×Dic43C2×D412yes—
119#10621877—22no—
120C2×C43⋊C8C2×D412yes—
121C16×C43—22no—
122C43⋊C16—21no—
123C43⋊C16—21no—
124C23×C43—41no—
125C23×C43C2×D811yescharacteristic
126Q8×C43—22no—
127Q8×C43—41no—
128D4×C43—22no—
129D4×C43—44no—
130D4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—44no—
133C2×C4×C43—42no—
134C2×C4×C43—161no—
135C2×C4×C43C22⋊Q812yes—
136C2×C4×C43C2×D811yescharacteristic
137C2×C4×C43#13712yes—
138C2×C4×C43C22×D411yescharacteristic
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—42no—
142C2×Dic43—162no—
143C2×Dic43—161no—
144C2×Dic43C2×D812yes—
145C2×Dic43C2×D812yes—
146Dic86—162no—
147C8×C43C22⋊Q812yes—
148C8×C43C22×Q811yescharacteristic
149C8×C43C2×#4111yescharacteristic
150C43⋊C8—22no—
151#33634—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—42no—
155C22×C43—81no—
156C22×C43—81no—
157C22×C43#47412yes—
158C22×C43C22×D811yescharacteristic
159C4×C43—42no—
160C4×C43—82no—
161C4×C43#47412yes—
162C4×C43C2×C22⋊Q811yescharacteristic
163C4×C43C2×#13711yescharacteristic
164Dic43—22no—
165Dic43—22no—
166Dic43—81no—
167Dic43—81no—
168Dic43—82no—
169#3164—431no—
170#2951—431no—
171#2229—432no—
172#2228—432no—
173#2226—432no—
174#2225—432no—
175#2159—431no—
176C2×#367—431no—
177#2151—431no—
178#2139D4311yescharacteristic
179#2138—431no—
180C2×C43—22no—
181C2×C43—82no—
182C2×C43C2×#47411yescharacteristic
183C2×C43#341611yescharacteristic
184C2×C43#341611yescharacteristic
185C2×#135C2×D4311yescharacteristic
186#544—861no—
187#520—861no—
188C2×M32C2×D4311yescharacteristic
189C22×C16—431no—
190#501—862no—
191#500—432no—
192#499—432no—
193#440—862no—
194C4×Q16—432no—
195C4×D8—432no—
196#428—861no—
197#427—431no—
198C2×#107—431no—
199C2×#107C2×D4311yescharacteristic
200#417—861no—
201#405—431no—
202#367—432no—
203#367—432no—
204#367—432no—
205#366—432no—
206C4⋊C16—432no—
207C4⋊C16—432no—
208#358—431no—
209#358—431no—
210#358C2×D4312yes—
211#357—431no—
212#357—431no—
213#357C2×D4312yes—
214C43#3363411yescharacteristic, complemented, Sylow
215C2×#41—21no—
216#135—22no—
217#135Dic8614yescomplemented
218C2×Q16C22×D4311yescharacteristic
219C2×SD16—21no—
220C2×D8C22×D4311yescharacteristic
221C2×M16—431no—
222C22×C8C22×D4311yescharacteristic
223C4⋊Q8—862no—
224C4⋊Q8—1721no—
225#125—862no—
226#125—1721no—
227C22⋊Q8—1722no—
228C4×Q8—862no—
229C4×D4—862no—
230C4×D4—1722no—
231#117—431no—
232#117—861no—
233#117—1721no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—1721no—
237M32—22no—
238C2×C16—431no—
239C2×C16—431no—
240C2×C16—862no—
241C2×C16C22×D4312yes—
242#107—21no—
243#107—431no—
244#107—431no—
245#107—432no—
246#107—862no—
247#107—861no—
248#107C22×D4312yes—
249#106—862no—
250#106—861no—
251#103—862no—
252#102—862no—
253#97—432no—
254C4×C8—432no—
255#41—24no—
256#41—42no—
257C2×Q8—21no—
258C2×Q8—1722no—
259C2×D4—21no—
260C2×D4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—1722no—
264C22×C4—1721no—
265C22×C4D4×D4311yescharacteristic
266Q16—21no—
267Q16C2×Dic8612yes—
268SD16—24no—
269D8—21no—
270D8C2×Dic8612yes—
271M16—862no—
272C2×C8—432no—
273C2×C8C2×Dic8612yes—
274C2×C8D4×D4311yescharacteristic
275C2×C8#1062190012yes—
276C2×C8C23×D4311yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—431no—
280C4⋊C4—431no—
281C4⋊C4—862no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—1722no—
285C4⋊C4—1722no—
286C4⋊C4—1722no—
287C4⋊C4—1722no—
288C4⋊C4—1721no—
289C22⋊C4—432no—
290C22⋊C4—1722no—
291C22⋊C4—1721no—
292C42—432no—
293C42—1722no—
294C42—1721no—
295C16—22no—
296C16—861no—
297C16—861no—
298C23—41no—
299C23D8×D4311yescharacteristic
300Q8—22no—
301Q8—41no—
302Q8—6882no—
303D4—22no—
304D4—44no—
305D4—41no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—161no—
310C2×C4—432no—
311C2×C4—432no—
312C2×C4—1721no—
313C2×C4—1722no—
314C2×C4—1721no—
315C2×C4—6882no—
316C2×C4—6881no—
317C2×C4#1306330212yes—
318C2×C4D8×D4311yescharacteristic
319C2×C4#1306335412yes—
320C2×C4C2×D4×D4311yescharacteristic
321C8—862no—
322C8#1306330212yes—
323C8C22×Dic8611yescharacteristic
324C8C2×#1062190011yescharacteristic
325C22—21no—
326C22—21no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22#1458317712yes—
331C22C2×D8×D4311yescharacteristic
332C4—42no—
333C4—82no—
334C4—862no—
335C4—862no—
336C4—3442no—
337C4—3441no—
338C4—3441no—
339C4#1458317712yes—
340C4C2×#1306330211yescharacteristic
341C4C2×#1306335411yescharacteristic
342C2—22no—
343C2—82no—
344C2C2×#1458317711yescharacteristic
345C2#1914774011yescharacteristic
346C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2139C2
socleC22×C43C22×D8
prime radicalC2×#135×C43C22
hypercenter#2139D43
hypocenterC43#33634
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
1. #19145131C2semidirect
3. #19136761C2semidirect
4. #19136750C2semidirect
5. #19136740C2semidirect
6. #19136735C2semidirect
7. #19136383C2semidirect
8. C2×#14582726C2semidirect
9. #19136355C2semidirect
71. #135×C43Q8semidirect
214. C43#33634semidirect
217. #135Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451312
#191434712
#191367612
#191367502
#191367402
#191367352
#191363832
C2×#145827262
#191363552
#191363022
C43×#21392
#3363443