Finite Group Databasebeta

← #25252175

Subgroups — #25252175

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145165C211yesmaximal, characteristic
2#19136878C211yesmaximal, characteristic, complemented
3#19136864C211yesmaximal, characteristic, complemented
4#19136840C211yesmaximal, characteristic, complemented
5#19136834C211yesmaximal, characteristic, complemented
6#19136710C212yesmaximal
7#19136701C212yesmaximal, complemented
8C4×#13063271C212yesmaximal, complemented
9C4×#13063268C212yesmaximal, complemented
10C4×#13063265C211yesmaximal, characteristic, complemented
11C43×#3170C211yesmaximal, characteristic, complemented
12#14583433—21no—
13C2×#13063271C2212yes—
14C2×#13063268C2212yes—
15C2×#13063265C2212yes—
16#14583301C2211yescharacteristic
17#14583283C2211yescharacteristic
18#14583254—21no—
19#14583140C2211yescharacteristic
20#14583135C2211yescharacteristic
21#14583128—21no—
22C4×Dic172C2211yescharacteristic
23C4×#10621873—21no—
24C4×D344C2211yescharacteristic
25#14582726C2212yes—
26#14582724C2212yes—
27#14582703C2212yes—
28#14582703C2212yes—
29#14582702C2212yes—
30#14582699C2212yes—
31#14582675C2211yescharacteristic
32#14582675C2211yescharacteristic
33C4×C43⋊C16C2212yes—
34C43×#533—21no—
35C43×#500C2211yescharacteristic
36C43×#494C2211yescharacteristic
37C43×#487—21no—
38C43×#467—21no—
39C43×#467C2212yes—
40C4×Q16×C43—21no—
41C4×Q16×C43C2212yes—
42C2×C4×C8×C43C2211yescharacteristic
43C2×Dic172C2311yescharacteristic
44C2×#10621873—21no—
45C2×D344C2311yescharacteristic
46#13063319—41no—
47#13063317—21no—
48#13063313—21no—
49#13063308—41no—
50#13063304—21no—
51#13063299—21no—
52C4×Dic86—21no—
53C4×D172—21no—
54C4×C22⋊D43—41no—
55#13063282—41no—
56#13063271—24no—
57#13063268—24no—
58#13063265—24no—
59C2×C43⋊C16C2312yes—
60C2×C43⋊C16C2312yes—
61#13063259C2311yescharacteristic
62#13063259C2311yescharacteristic
63#13063257—21no—
64#13063250—21no—
65#13063250—21no—
66#13063247—21no—
67#13063247—21no—
68C2×Q16×C43—21no—
69C2×Q16×C43C2312yes—
70C22×C8×C43D411yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C4⋊Q8×C43—21no—
73C4⋊Q8×C43—21no—
74#125×C43—41no—
75C22⋊Q8×C43—22no—
76C22⋊Q8×C43—41no—
77C4×Q8×C43—22no—
78C4×Q8×C43—41no—
79#117×C43—41no—
80C2×C42×C43D411yescharacteristic
81#107×C43—21no—
82#107×C43C2312yes—
83#103×C43—22no—
84#103×C43—22no—
85C4×C8×C43D411yescharacteristic
86C4×C8×C43D411yescharacteristic
87C4×C8×C43C2311yescharacteristic
88C4×C8×C43C2311yescharacteristic
89C2×Q8×C43—22no—
90C2×Q8×C43—41no—
91C22×C4×C43D811yescharacteristic
92C22×C4×C43D811yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C2×C22⋊D43—41no—
95C2×D172—21no—
96C2×C4×D43—41no—
97C2×Dic86—21no—
98Q16×C43—22no—
99Q16×C43—22no—
100Q16×C43—42no—
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2411yescharacteristic
107C4⋊C4×C43—22no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—42no—
111C4⋊C4×C43—42no—
112C4⋊C4×C43—41no—
113C22⋊C4×C43—42no—
114C42×C43—42no—
115C42×C43D811yescharacteristic
116C42×C43D811yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C22⋊Dic43—41no—
120(C2×D43)⋊C4—41no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128Dic43⋊C4—41no—
129Dic43⋊C4—41no—
130C4×Dic43—41no—
131Dic172—22no—
132D344—22no—
133#10621873—42no—
134C43⋊C16—22no—
135C43⋊C16#4114yes—
136C23×C43C2×D811yescharacteristic
137C22×D43—41no—
138Q8×C43—42no—
139Q8×C43—42no—
140Q8×C43—82no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—22no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43C2×D811yescharacteristic
148C2×C4×C43C2×D811yescharacteristic
149C2×C4×C43C2×D811yescharacteristic
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43C2×D811yescharacteristic
152C2×C4×C43C22×D411yescharacteristic
153C22⋊D43—82no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157D172—41no—
158D172—41no—
159C4×D43—82no—
160Dic86—41no—
161Dic86—41no—
162C8×C43—21no—
163C8×C43—21no—
164C8×C43#13512yes—
165C8×C43C2×#4112yes—
166#33738—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43C22×D811yescharacteristic
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—82no—
179C4×C43—82no—
180C4×C43#51012yes—
181C4×C43#53211yescharacteristic
182C4×C43C2×#13511yescharacteristic
183Dic43—81no—
184Dic43—81no—
185Dic43—81no—
186#3170D4311yescharacteristic, complemented
187#3168—431no—
188#2255—431no—
189#2251—431no—
190#2245—431no—
191#2243—431no—
192#2220—432no—
193#2219—432no—
194C4×Q32—432no—
195C4×SD32—432no—
196C4×M32—431no—
197C2×C43—41no—
198C2×C43#316911yescharacteristic
199C2×C43C2×#51011yescharacteristic
200C2×C43#341411yescharacteristic
201D43—161no—
202#533—21no—
203#529—861no—
204C2×Q32—432no—
205C2×SD32—432no—
206C2×M32—432no—
207#500C2×D4311yescharacteristic
208#499—431no—
209#495—431no—
210#494C2×D4311yescharacteristic
211#488—861no—
212#487—21no—
213#467—21no—
214#467—431no—
215#467C2×D4312yes—
216#466—431no—
217#465—861no—
218C4×Q16—21no—
219C4×Q16—431no—
220C4×Q16C2×D4312yes—
221C4×SD16—861no—
222C4×D8—431no—
223C2×C4×C8C2×D4311yescharacteristic
224#367—432no—
225#366—432no—
226#358—432no—
227#358—432no—
228#358—432no—
229#357—432no—
230#346—431no—
231#346—431no—
232C4×C16—432no—
233C43#3373811yescharacteristic, complemented, Sylow
234C2×Q16—21no—
235C2×Q16—431no—
236C2×Q16C22×D4312yes—
237C2×SD16—861no—
238C2×D8—431no—
239C22×C8C22⋊D4311yescharacteristic
240C22×C8C22×D4311yescharacteristic
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243#126—1721no—
244#125—41no—
245#125—861no—
246#124—861no—
247#123—1721no—
248C22⋊Q8—22no—
249C22⋊Q8—41no—
250C22⋊Q8—861no—
251#121—861no—
252C4×Q8—22no—
253C4×Q8—41no—
254C4×Q8—861no—
255C4×D4—861no—
256C4×D4—1721no—
257#117—41no—
258#117—1721no—
259C2×C42C22⋊D4311yescharacteristic
260Q32—864no—
261SD32—864no—
262M32—864no—
263C2×C16—432no—
264C2×C16—432no—
265#107—21no—
266#107—431no—
267#107—431no—
268#107C22×D4312yes—
269#106—861no—
270#103—22no—
271#103—22no—
272#103—861no—
273#103—861no—
274#102—861no—
275#102—861no—
276C4×C8C22⋊D4311yescharacteristic
277C4×C8C22⋊D4311yescharacteristic
278C4×C8C22×D4311yescharacteristic
279C4×C8C22×D4311yescharacteristic
280C2×Q8—22no—
281C2×Q8—41no—
282C2×Q8—861no—
283C2×D4—861no—
284C2×D4—1721no—
285C22×C4—1721no—
286C22×C4#1062188211yescharacteristic
287C22×C4#1062188211yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289Q16—22no—
290Q16—22no—
291Q16—42no—
292Q16—862no—
293SD16—1722no—
294D8—862no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8C2×C22⋊D4311yescharacteristic
298C2×C8C2×C22⋊D4311yescharacteristic
299C2×C8C2×C22⋊D4311yescharacteristic
300C2×C8C23×D4311yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C22⋊C4—42no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C22⋊C4—1721no—
319C42—42no—
320C42—1721no—
321C42#1062188211yescharacteristic
322C42#1062188211yescharacteristic
323C42C2×C22⋊D4311yescharacteristic
324C42C2×C22⋊D4311yescharacteristic
325C16—434no—
326C16—862no—
327C23—1721no—
328C23C2×#1062188211yescharacteristic
329Q8—42no—
330Q8—42no—
331Q8—82no—
332Q8—1721no—
333Q8—1721no—
334D4—3442no—
335D4—1721no—
336D4—1721no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—3442no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4C2×#1062188211yescharacteristic
348C2×C4C2×#1062188211yescharacteristic
349C2×C4C2×#1062188211yescharacteristic
350C2×C4C2×#1062188211yescharacteristic
351C2×C4C2×#1062188211yescharacteristic
352C2×C4C22×C22⋊D4311yescharacteristic
353C8—21no—
354C8—21no—
355C8#1306334512yes—
356C8#41×D4312yes—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22C22×#1062188211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—82no—
370C4—3441no—
371C4—3441no—
372C4—3441no—
373C4#1458334012yes—
374C4#1458344511yescharacteristic
375C4C2×#1306334511yescharacteristic
376C2—41no—
377C2—6881no—
378C2#1914517011yescharacteristic
379C2C2×#1458334011yescharacteristic
380C2#1914772911yescharacteristic
subgroupG/H
centerC2×C4C2×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3170C2
socleC22×C43C22×D8
prime radical#14583135C22
hypercenter#3170D43
hypocenterC43#33738
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
2. #19136878C2semidirect
3. #19136864C2semidirect
4. #19136840C2semidirect
5. #19136834C2semidirect
7. #19136701C2semidirect
8. C4×#13063271C2semidirect
9. C4×#13063268C2semidirect
10. C4×#13063265C2semidirect
11. C43×#3170C2semidirect
186. #3170D43semidirect
233. C43#33738semidirect

Maximal subgroups

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

subgroupindex
#191451652
#191368782
#191368642
#191368402
#191368342
#191367102
#191367012
C4×#130632712
C4×#130632682
C4×#130632652
C43×#31702
#3373843