Finite Group Databasebeta

← #25254660

Subgroups — #25254660

Order 11008.

510 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#19147601C211yesmaximal, characteristic, complemented
2#19136867C212yesmaximal, complemented
3#19136850C211yesmaximal, characteristic
4#19136654C212yesmaximal, complemented
5#19136645C211yesmaximal, characteristic, complemented
6#19136640C212yesmaximal, complemented
7#19136632C211yesmaximal, characteristic
8#19136504C211yesmaximal, characteristic, complemented
9#19136459C212yesmaximal, complemented
10C4×#13063271C211yesmaximal, characteristic, complemented
11C43×#3396C211yesmaximal, characteristic
12#14583628—21no—
13C2×#13063271C2211yescharacteristic
14C2×#13063271C2212yes—
15C2×#13063269C2212yes—
16C2×#13063269C2212yes—
17C2×#13063269C2212yes—
18#14583279C2211yescharacteristic
19#14583279C2212yes—
20#14583110—21no—
21#14583110—22no—
22C4×Dic172C2211yescharacteristic
23C4×Dic172C2212yes—
24#14582724C2211yescharacteristic
25C4⋊(C43⋊C16)C2211yescharacteristic
26C4⋊(C43⋊C16)C2212yes—
27#14582703C2211yescharacteristic
28#14582702C2211yescharacteristic
29#14582702C2212yes—
30#14582700C2212yes—
31#14582675C2212yes—
32C4×C43⋊C16C2211yescharacteristic
33C43×#559—21no—
34C43×#495C2212yes—
35C43×#493C2211yescharacteristic
36C43×#463—22no—
37C43×#460—21no—
38C8×Q8×C43C2211yescharacteristic
39C4×Q16×C43C2211yescharacteristic
40C4×D8×C43C2212yes—
41C2×Dic172—22no—
42C2×Dic172—21no—
43C2×Dic172C2312yes—
44C2×Dic172C2311yescharacteristic
45#13063325—22no—
46#13063325—21no—
47#13063316—41no—
48#13063316—42no—
49Q8×Dic43—41no—
50C4×Dic86—22no—
51C4×Dic86—21no—
52#13063271—22no—
53#13063271—42no—
54#13063269—24no—
55#13063269—42no—
56#13063269—42no—
57C2×C43⋊C16C2311yescharacteristic
58C2×C43⋊C16C2312yes—
59C2×C43⋊C16C2311yescharacteristic
60#13063259C2311yescharacteristic
61#13063250—22no—
62#13063250—21no—
63C2×Q16×C43C2311yescharacteristic
64C2×SD16×C43—22no—
65C2×D8×C43—21no—
66C2×D8×C43C2312yes—
67#127×C43—21no—
68#124×C43—22no—
69#124×C43—41no—
70#123×C43—42no—
71C4×Q8×C43—21no—
72C4×Q8×C43D411yescharacteristic
73C4×D4×C43—22no—
74C4×D4×C43—41no—
75#107×C43C2311yescharacteristic
76C4⋊C8×C43D411yescharacteristic
77C4⋊C8×C43D412yes—
78#103×C43—21no—
79#102×C43—22no—
80C4×C8×C43C2311yescharacteristic
81C4×C8×C43C2312yes—
82C2×Q8×C43—21no—
83C2×Q8×C43D811yescharacteristic
84C2×D4×C43—22no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C22×C4×C43—42no—
88C2×Dic86—22no—
89C2×Dic86—21no—
90Q16×C43—21no—
91Q16×C43—21no—
92SD16×C43—82no—
93D8×C43—22no—
94D8×C43—22no—
95D8×C43—81no—
96C2×C8×C43C2×D412yes—
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2411yescharacteristic
99C4⋊C4×C43—21no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43D811yescharacteristic
102C4⋊C4×C43D812yes—
103C22⋊C4×C43—42no—
104C22⋊C4×C43—42no—
105C22⋊C4×C43—42no—
106C42×C43—41no—
107C42×C43C2×D412yes—
108C42×C43C2×D411yescharacteristic
109C4⋊Dic43—21no—
110C4⋊Dic43—42no—
111C4⋊Dic43—41no—
112C4⋊Dic43—42no—
113C4⋊Dic43—41no—
114Dic43⋊C4—42no—
115Dic43⋊C4—41no—
116C4×Dic43—42no—
117C4×Dic43—41no—
118Dic172—22no—
119Dic172—21no—
120Dic172—21no—
121Dic172—22no—
122Dic172—81no—
123Dic172—82no—
124C43⋊C16—21no—
125C43⋊C16—22no—
126C43⋊C16#4112yes—
127C23×C43—42no—
128Q8×C43—22no—
129Q8×C43—41no—
130Q8×C43—41no—
131D4×C43—42no—
132D4×C43—42no—
133D4×C43—82no—
134D4×C43—161no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—162no—
138C2×C4×C43C2×D812yes—
139C2×C4×C43C2×D812yes—
140C2×C4×C43C2×D811yescharacteristic
141C2×C4×C43C2×D811yescharacteristic
142C2×C4×C43C22×D411yescharacteristic
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146Dic86—42no—
147Dic86—41no—
148Dic86—42no—
149Dic86—41no—
150C8×C43—21no—
151C8×C43—22no—
152C8×C43C2×#4111yescharacteristic
153C8×C43H(5,𝔽2)11yescharacteristic
154#33967—431nomaximal, Sylow
155C22×C43—82no—
156C22×C43—82no—
157C22×C43—82no—
158C22×C43C22×D811yescharacteristic
159C4×C43—22no—
160C4×C43—22no—
161C4×C43—21no—
162C4×C43—81no—
163C4×C43—81no—
164C4×C43#51012yes—
165C4×C43#55011yescharacteristic
166C4×C43#57611yescharacteristic
167Dic43—82no—
168Dic43—81no—
169Dic43—81no—
170#3396D4311yescharacteristic
171#3395—431no—
172#2251—432no—
173#2248—431no—
174#2211—432no—
175#2209—431no—
176#2208—432no—
177#2207—431no—
178#2183—431no—
179#2175—432no—
180C4×Q32—431no—
181C2×C43—162no—
182C2×C43#339111yescharacteristic
183C2×C43C2×#51011yescharacteristic
184C2×C43#341611yescharacteristic
185#559—21no—
186#557—861no—
187C2×Q32—431no—
188C2×Q32—432no—
189C2×SD32—432no—
190C2×SD32—432no—
191C2×SD32—432no—
192#495C2×D4312yes—
193#494—432no—
194#494—431no—
195#493C2×D4311yescharacteristic
196#463—22no—
197#462—861no—
198#462—862no—
199#460—21no—
200C8×Q8C2×D4311yescharacteristic
201C4×Q16—431no—
202C4×Q16—432no—
203C4×Q16C2×D4311yescharacteristic
204C4×D8C2×D4312yes—
205#366—431no—
206C4⋊C16—431no—
207C4⋊C16—432no—
208#358—431no—
209#358—431no—
210#358—432no—
211#357—432no—
212#346—432no—
213C4×C16—431no—
214C43#3396711yescharacteristic, complemented, Sylow
215C2×Q16—432no—
216C2×Q16—431no—
217C2×Q16—862no—
218C2×Q16—861no—
219C2×Q16C22×D4311yescharacteristic
220C2×SD16—22no—
221C2×D8—21no—
222C2×D8C22×D4312yes—
223C4⋊Q8—862no—
224C4⋊Q8—861no—
225#127—21no—
226#125—1721no—
227#125—1722no—
228#124—22no—
229#124—41no—
230#123—42no—
231C4×Q8—21no—
232C4×Q8—862no—
233C4×Q8—861no—
234C4×Q8—1721no—
235C4×Q8C22⋊D4311yescharacteristic
236C4×D4—22no—
237C4×D4—41no—
238Q32—862no—
239Q32—1722no—
240SD32—864no—
241SD32—1722no—
242SD32—1722no—
243C2×C16—431no—
244C2×C16—431no—
245C2×C16—432no—
246#107—431no—
247#107C22×D4311yescharacteristic
248C4⋊C8C22⋊D4311yescharacteristic
249C4⋊C8C22⋊D4312yes—
250#103—21no—
251#103—862no—
252#103—861no—
253#102—22no—
254C4×C8C22×D4311yescharacteristic
255C4×C8C22×D4312yes—
256C2×Q8—21no—
257C2×Q8—862no—
258C2×Q8—861no—
259C2×Q8#1062188211yescharacteristic
260C2×D4—22no—
261C2×D4—41no—
262C2×D4—41no—
263C22×C4—42no—
264Q16—21no—
265Q16—21no—
266Q16—862no—
267Q16—861no—
268Q16—861no—
269Q16—862no—
270Q16—3441no—
271Q16—3442no—
272SD16—82no—
273D8—22no—
274D8—22no—
275D8—81no—
276C2×C8C2×C22⋊D4312yes—
277C2×C8C2×C22⋊D4311yescharacteristic
278C2×C8C23×D4311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—861no—
282C4⋊C4—1722no—
283C4⋊C4—1721no—
284C4⋊C4—1722no—
285C4⋊C4—1721no—
286C4⋊C4—1722no—
287C4⋊C4—1721no—
288C4⋊C4#1062188211yescharacteristic
289C4⋊C4#1062188212yes—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C42—41no—
294C42—1722no—
295C42—1721no—
296C42C2×C22⋊D4312yes—
297C42C2×C22⋊D4311yescharacteristic
298C16—432no—
299C16—861no—
300C16—862no—
301C23—42no—
302Q8—22no—
303Q8—41no—
304Q8—41no—
305Q8—1722no—
306Q8—1721no—
307Q8—1722no—
308Q8—1721no—
309D4—42no—
310D4—42no—
311D4—82no—
312D4—161no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—162no—
316C2×C4—1721no—
317C2×C4—1722no—
318C2×C4—1721no—
319C2×C4C2×#1062188212yes—
320C2×C4C2×#1062188212yes—
321C2×C4C2×#1062188211yescharacteristic
322C2×C4C2×#1062188211yescharacteristic
323C2×C4C22×C22⋊D4311yescharacteristic
324C8—21no—
325C8—22no—
326C8#41×D4311yescharacteristic
327C8#1306337111yescharacteristic
328C22—82no—
329C22—82no—
330C22—82no—
331C22C22×#1062188211yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—81no—
336C4—81no—
337C4—3442no—
338C4—3441no—
339C4—3441no—
340C4#1458333912yes—
341C4#1458356811yescharacteristic
342C4#1458370211yescharacteristic
343C2—162no—
344C2#1914756711yescharacteristic
345C2C2×#1458333911yescharacteristic
346C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3396C2
socleC22×C43C22×D8
prime radicalC43×#493C22
hypercenter#3396D43
hypocenterC43#33967
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
1. #19147601C2semidirect
2. #19136867C2semidirect
4. #19136654C2semidirect
5. #19136645C2semidirect
6. #19136640C2semidirect
8. #19136504C2semidirect
9. #19136459C2semidirect
10. C4×#13063271C2semidirect
214. C43#33967semidirect

Maximal subgroups

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

subgroupindex
#191476012
#191368672
#191368502
#191366542
#191366452
#191366402
#191366322
#191365042
#191364592
C4×#130632712
C43×#33962
#3396743