Finite Group Databasebeta

← #25251683

Subgroups — #25251683

Order 11008.

548 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145181C211yesmaximal, characteristic, complemented
2#19136803C212yesmaximal, complemented
3#19136747C211yesmaximal, characteristic, complemented
4#19136742C211yesmaximal, characteristic, complemented
5#19136645C211yesmaximal, characteristic, complemented
6#19136640C211yesmaximal, characteristic, complemented
7#19136535C212yesmaximal
8#19136464C212yesmaximal, complemented
9#19136459C212yesmaximal, complemented
10#19136398C211yesmaximal, characteristic, complemented
11C4×#135×C43C211yesmaximal, characteristic
12#14583456—21no—
13C2×#13063271C2212yes—
14C2×#13063269C2212yes—
15#14583304C2211yescharacteristic
16#14583279C2211yescharacteristic
17#14583250—21no—
18#14583140—21no—
19#14583140C2212yes—
20C4×Dic172—21no—
21C4×Dic172C2212yes—
22#14582726C2212yes—
23#14582724C2212yes—
24C4⋊(C43⋊C16)C2211yescharacteristic
25C4⋊(C43⋊C16)C2211yescharacteristic
26#14582703C2212yes—
27#14582702C2212yes—
28#14582702C2212yes—
29#14582700C2212yes—
30C22⋊(C43⋊C16)C2212yes—
31#14582675C2212yes—
32C2×#135×C43C2211yescharacteristic
33C4×#41×C43—21no—
34C4×Q16×C43C2211yescharacteristic
35C4×Q16×C43C2211yescharacteristic
36C4×SD16×C43—21no—
37C4×SD16×C43—21no—
38C4×D8×C43C2211yescharacteristic
39C4×D8×C43C2211yescharacteristic
40C43×#427C2211yescharacteristic
41C43×#416—21no—
42C2×C4×C8×C43C2211yescharacteristic
43C2×Dic172—21no—
44C2×Dic172C2312yes—
45#13063325—21no—
46#13063325—21no—
47#13063317—41no—
48#13063304—22no—
49#13063304—41no—
50C4×Dic86—22no—
51C4×Dic86—41no—
52#13063284—41no—
53#13063271—24no—
54#13063269—24no—
55C2×C43⋊C16C2312yes—
56C2×C43⋊C16C2312yes—
57#13063259—21no—
58#13063259C2312yes—
59#13063250—22no—
60#13063250—22no—
61C2×#41×C43—21no—
62#135×C43—22no—
63#135×C43—22no—
64C2×Q16×C43C2311yescharacteristic
65C2×SD16×C43—21no—
66C2×D8×C43C2311yescharacteristic
67C22×C8×C43D411yescharacteristic
68C22×C8×C43C2311yescharacteristic
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—41no—
74C4×D4×C43—41no—
75#117×C43—21no—
76#117×C43—41no—
77C2×C42×C43—41no—
78C2×C42×C43D411yescharacteristic
79#107×C43C2311yescharacteristic
80#107×C43C2311yescharacteristic
81#106×C43—21no—
82#103×C43—21no—
83#103×C43—21no—
84#102×C43—21no—
85#102×C43—21no—
86C4×C8×C43D411yescharacteristic
87C4×C8×C43D411yescharacteristic
88C4×C8×C43C2311yescharacteristic
89C4×C8×C43C2311yescharacteristic
90#41×C43—24no—
91#41×C43—42no—
92C2×Q8×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43D811yescharacteristic
99C22×C4×C43D811yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C2×Dic86—22no—
102C2×Dic86—41no—
103Q16×C43—21no—
104Q16×C43#4112yes—
105SD16×C43—24no—
106D8×C43—21no—
107D8×C43#4112yes—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—41no—
111C2×C8×C43C2×D411yescharacteristic
112C2×C8×C43C2×D411yescharacteristic
113C2×C8×C43C2×D411yescharacteristic
114C2×C8×C43C2411yescharacteristic
115C4⋊C4×C43—21no—
116C4⋊C4×C43—21no—
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C42×C43—41no—
123C42×C43—41no—
124C42×C43—41no—
125C42×C43D811yescharacteristic
126C42×C43D811yescharacteristic
127C42×C43C2×D411yescharacteristic
128C42×C43C2×D411yescharacteristic
129C22⋊Dic43—42no—
130C4⋊Dic43—22no—
131C4⋊Dic43—41no—
132C4⋊Dic43—41no—
133C4⋊Dic43—41no—
134Dic43⋊C4—42no—
135Dic43⋊C4—42no—
136C4×Dic43—42no—
137Dic172—22no—
138Dic172—22no—
139Dic172—42no—
140C43⋊C16—22no—
141C43⋊C16—22no—
142C23×C43—41no—
143C23×C43C2×D811yescharacteristic
144Q8×C43—22no—
145Q8×C43—41no—
146D4×C43—22no—
147D4×C43—44no—
148D4×C43—41no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—22no—
152C2×C4×C43—41no—
153C2×C4×C43—44no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—82no—
158C2×C4×C43—82no—
159C2×C4×C43C2×D811yescharacteristic
160C2×C4×C43C2×D811yescharacteristic
161C2×C4×C43C2×D811yescharacteristic
162C2×C4×C43C2×D811yescharacteristic
163C2×C4×C43C2×D811yescharacteristic
164C2×C4×C43C22×D411yescharacteristic
165C2×Dic43—42no—
166C2×Dic43—42no—
167Dic86—42no—
168Dic86—42no—
169Dic86—82no—
170C8×C43—21no—
171C8×C43—21no—
172C8×C43—21no—
173C8×C43C2×#4111yescharacteristic
174C8×C43C2×#4111yescharacteristic
175#33676—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—42no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43C22×D811yescharacteristic
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—42no—
188C4×C43—81no—
189C4×C43—81no—
190C4×C43#51012yes—
191C4×C43#52511yescharacteristic
192C4×C43#57511yescharacteristic
193Dic43—82no—
194Dic43—82no—
195#3170—431no—
196C4×#135D4311yescharacteristic
197#2237—432no—
198#2227—431no—
199#2226—431no—
200#2209—431no—
201#2208—431no—
202#2189—432no—
203#2176—432no—
204#2175—432no—
205#2163—431no—
206C2×C43—41no—
207C2×C43—82no—
208C2×C43#310011yescharacteristic
209C2×C43C2×#51011yescharacteristic
210C2×C43#341411yescharacteristic
211C2×#135C2×D4311yescharacteristic
212#533—861no—
213C4×#41—21no—
214C2×Q32—432no—
215C2×SD32—432no—
216#500—431no—
217#494—431no—
218#487—861no—
219#467—432no—
220#467—861no—
221C4×Q16—432no—
222C4×Q16—861no—
223C4×Q16C2×D4311yescharacteristic
224C4×Q16C2×D4311yescharacteristic
225C4×SD16—21no—
226C4×SD16—21no—
227C4×D8C2×D4311yescharacteristic
228C4×D8C2×D4311yescharacteristic
229#427C2×D4311yescharacteristic
230#416—21no—
231C2×C4×C8C2×D4311yescharacteristic
232#367—432no—
233#366—432no—
234C4⋊C16—431no—
235C4⋊C16—431no—
236#358—432no—
237#358—432no—
238#358—432no—
239#357—432no—
240C22⋊C16—432no—
241#346—432no—
242C43#3367611yescharacteristic, complemented, Sylow
243C2×#41—21no—
244#135—22no—
245#135—22no—
246C2×Q16—432no—
247C2×Q16—861no—
248C2×Q16C22×D4311yescharacteristic
249C2×SD16—21no—
250C2×D8C22×D4311yescharacteristic
251C22×C8C22⋊D4311yescharacteristic
252C22×C8C22×D4311yescharacteristic
253C4⋊Q8—861no—
254C4⋊Q8—861no—
255#125—1721no—
256C22⋊Q8—862no—
257C22⋊Q8—1721no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—862no—
261C4×Q8—1721no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—41no—
265C4×D4—41no—
266#117—21no—
267#117—41no—
268#117—1721no—
269C2×C42—41no—
270C2×C42C22⋊D4311yescharacteristic
271Q32—864no—
272SD32—864no—
273C2×C16—432no—
274C2×C16—432no—
275#107—432no—
276#107—861no—
277#107C22×D4311yescharacteristic
278#107C22×D4311yescharacteristic
279#106—21no—
280#103—21no—
281#103—21no—
282#103—862no—
283#103—862no—
284#102—21no—
285#102—21no—
286C4×C8C22⋊D4311yescharacteristic
287C4×C8C22⋊D4311yescharacteristic
288C4×C8C22×D4311yescharacteristic
289C4×C8C22×D4311yescharacteristic
290#41—24no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—862no—
294C2×Q8—1721no—
295C2×D4—21no—
296C2×D4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4#1062188211yescharacteristic
301C22×C4#1062188211yescharacteristic
302C22×C4C2×C22⋊D4311yescharacteristic
303Q16—21no—
304Q16—862no—
305Q16—862no—
306Q16—1722no—
307Q16#1062189812yes—
308SD16—24no—
309D8—21no—
310D8#1062189812yes—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—41no—
314C2×C8C2×C22⋊D4311yescharacteristic
315C2×C8C2×C22⋊D4311yescharacteristic
316C2×C8C2×C22⋊D4311yescharacteristic
317C2×C8C23×D4311yescharacteristic
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—862no—
323C4⋊C4—1721no—
324C4⋊C4—1721no—
325C4⋊C4—1722no—
326C4⋊C4—1722no—
327C4⋊C4—1721no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—1722no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—1722no—
336C42#1062188211yescharacteristic
337C42#1062188211yescharacteristic
338C42C2×C22⋊D4311yescharacteristic
339C42C2×C22⋊D4311yescharacteristic
340C16—862no—
341C16—862no—
342C23—41no—
343C23C2×#1062188211yescharacteristic
344Q8—22no—
345Q8—41no—
346Q8—3442no—
347Q8—1722no—
348Q8—1722no—
349D4—22no—
350D4—44no—
351D4—41no—
352C2×C4—22no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—44no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4C2×#1062188211yescharacteristic
365C2×C4C2×#1062188211yescharacteristic
366C2×C4C2×#1062188211yescharacteristic
367C2×C4C2×#1062188211yescharacteristic
368C2×C4C2×#1062188211yescharacteristic
369C2×C4C22×C22⋊D4311yescharacteristic
370C8—21no—
371C8—21no—
372C8—21no—
373C8C2×#1062189811yescharacteristic
374C8C2×#1062189811yescharacteristic
375C22—21no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22C22×#1062188211yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—81no—
389C4—3442no—
390C4—3442no—
391C4#1458333912yes—
392C4#1458341011yescharacteristic
393C4#1458369711yescharacteristic
394C2—41no—
395C2—82no—
396C2#1914459511yescharacteristic
397C2C2×#1458333911yescharacteristic
398C2#1914772911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC4×#135×C43C2
socleC22×C43C22×D8
prime radicalC2×#135×C43C22
hypercenterC4×#135D43
hypocenterC43#33676
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #19145181C2semidirect
2. #19136803C2semidirect
3. #19136747C2semidirect
4. #19136742C2semidirect
5. #19136645C2semidirect
6. #19136640C2semidirect
8. #19136464C2semidirect
9. #19136459C2semidirect
10. #19136398C2semidirect
242. C43#33676semidirect

Maximal subgroups

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

subgroupindex
#191451812
#191368032
#191367472
#191367422
#191366452
#191366402
#191365352
#191364642
#191364592
#191363982
C4×#135×C432
#3367643