Finite Group Databasebeta

← #25080470

Subgroups — #25080470

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145179C211yesmaximal, characteristic
2#19144727C212yesmaximal
3C8×Q8×D43C211yesmaximal, characteristic
4#19134024C212yesmaximal, complemented
5#19134023C212yesmaximal, complemented
6#19133990C211yesmaximal, characteristic, complemented
7#19133989C211yesmaximal, characteristic, complemented
8#19133962C211yesmaximal, characteristic, complemented
9#19133357C211yesmaximal, characteristic
10#19133294C212yesmaximal
11C43×#1670C211yesmaximal, characteristic, complemented
12#14583454C2212yes—
13C4×Q8×D43C2211yescharacteristic
14#14583304C2211yescharacteristic
15#14583249C2212yes—
16#14583231—22no—
17#14583181C2212yes—
18#14583137—21no—
19#14583137—21no—
20#14583110C2212yes—
21#14583109C2212yes—
22#14583056—22no—
23Q8×C43⋊C8C2211yescharacteristic
24C8×Dic86—21no—
25C8×Dic86C2211yescharacteristic
26#14583023—21no—
27#14583023C2211yescharacteristic
28#14583005—22no—
29#14583003—22no—
30Q16×Dic43—21no—
31Q16×Dic43—21no—
32#14582955C2212yes—
33C4⋊C8×D43—21no—
34C4⋊C8×D43C2211yescharacteristic
35C4×C8×D43—21no—
36C4×C8×D43C2211yescharacteristic
37#14582652C2211yescharacteristic
38#14582649C2212yes—
39#14582646C2212yes—
40#14582645C2212yes—
41#14582644C2212yes—
42C43×#494C2211yescharacteristic
43C43×#475C2212yes—
44C8×Q8×C43C2211yescharacteristic
45C43×#335C2211yescharacteristic
46C43×#332C2212yes—
47C2×Q8×D43D411yescharacteristic
48C2×Dic172—22no—
49C2×#10621885—22no—
50C2×C8×D43—21no—
51C2×C8×D43D411yescharacteristic
52C2×C8×D43D411yescharacteristic
53#13063325C2312yes—
54#13063316—22no—
55#13063305—22no—
56#13063301—22no—
57Q8×Dic43—22no—
58Q8×Dic43D411yescharacteristic
59C4×Dic86—21no—
60C4×Dic86C2311yescharacteristic
61#13063290—21no—
62#13063290—22no—
63#13063290D411yescharacteristic
64#13063283—22no—
65C4⋊C4×D43—21no—
66C4⋊C4×D43D411yescharacteristic
67C42×D43—21no—
68C42×D43C2311yescharacteristic
69#13063259—21no—
70#13063259—21no—
71#13063256—22no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)C2312yes—
74C4⋊(C43⋊C8)C2311yescharacteristic
75Dic43⋊C8—21no—
76Dic43⋊C8—21no—
77Dic43⋊C8—21no—
78#13063250—22no—
79#13063249—22no—
80#13063249—22no—
81#13063248—22no—
82#13063248—22no—
83(C2×D43)⋊C8—22no—
84#13063235—22no—
85C4×C43⋊C8—21no—
86C4×C43⋊C8C2311yescharacteristic
87C8×Dic43—21no—
88C8×Dic43—21no—
89C8×Dic43D411yescharacteristic
90C8×Dic43D411yescharacteristic
91C2×Q16×C43—21no—
92C2×Q16×C43—21no—
93C4⋊Q8×C43C2312yes—
94C4×Q8×C43C2311yescharacteristic
95#106×C43—22no—
96C4⋊C8×C43—21no—
97C4⋊C8×C43C2312yes—
98C4⋊C8×C43C2311yescharacteristic
99#103×C43—22no—
100C4×C8×C43—21no—
101C4×C8×C43C2311yescharacteristic
102C2×Q8×C43—22no—
103C2×Q8×C43C2×D411yescharacteristic
104Q8×D43—22no—
105Q8×D43—22no—
106C2×C4×D43—21no—
107C2×C4×D43—21no—
108C2×C4×D43C2×D411yescharacteristic
109C2×C4×D43C2×D411yescharacteristic
110C2×C4×D43#4111yescharacteristic
111C2×Dic86—21no—
112C2×Dic86—22no—
113C2×Dic86C2×D411yescharacteristic
114Q16×C43—42no—
115Q16×C43—42no—
116C2×C8×C43—21no—
117C2×C8×C43—22no—
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43C2×D411yescharacteristic
120C4⋊C4×C43—21no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43C2×D411yescharacteristic
124C42×C43—21no—
125C42×C43C2411yescharacteristic
126#10621885—44no—
127(C2×D43)⋊C4—42no—
128C4⋊Dic43—21no—
129C4⋊Dic43—22no—
130C4⋊Dic43—22no—
131C4⋊Dic43—42no—
132C4⋊Dic43C2×D411yescharacteristic
133Dic43⋊C4—21no—
134Dic43⋊C4—21no—
135Dic43⋊C4—21no—
136Dic43⋊C4—42no—
137C4×Dic43—21no—
138C4×Dic43—21no—
139C4×Dic43—21no—
140C4×Dic43—42no—
141C4×Dic43C2×D411yescharacteristic
142C4×Dic43C2×D411yescharacteristic
143C4×Dic43#4111yescharacteristic
144C2×C43⋊C8—21no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8C2×D411yescharacteristic
147C2×C43⋊C8C2×D411yescharacteristic
148Dic172—44no—
149C8×D43—22no—
150C8×D43—41no—
151C8×D43—42no—
152C22×D43#12111yescharacteristic
153Q8×C43—21no—
154Q8×C43—42no—
155Q8×C43—42no—
156Q8×C43#13512yes—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—42no—
160C2×C4×C43C22×D411yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C2×C4×C43C2×#4111yescharacteristic
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—42no—
166C2×Dic43#12111yescharacteristic
167C2×Dic43#12111yescharacteristic
168C2×Dic43#12111yescharacteristic
169C4×D43—24no—
170C4×D43—22no—
171C4×D43—21no—
172C4×D43—21no—
173C4×D43—21no—
174C4×D43—21no—
175C4×D43—42no—
176Dic86—24no—
177Dic86—21no—
178Dic86—42no—
179Dic86—42no—
180Dic86#13512yes—
181C8×C43—21no—
182C8×C43—42no—
183C8×C43—41no—
184C8×C43#13712yes—
185C43⋊C8—21no—
186C43⋊C8—21no—
187C43⋊C8—42no—
188C43⋊C8—41no—
189#19265—431nomaximal, Sylow
190C22×C43C2×#12111yescharacteristic
191C2×D43—21no—
192C2×D43—21no—
193C2×D43#47312yes—
194C4×C43—22no—
195C4×C43—21no—
196C4×C43—41no—
197C4×C43—82no—
198C4×C43C2×#13511yescharacteristic
199C4×C43C2×#13511yescharacteristic
200C4×C43C2×#13711yescharacteristic
201C4×C43#57511yescharacteristic
202Dic43—21no—
203Dic43—21no—
204Dic43—22no—
205Dic43—21no—
206Dic43—41no—
207Dic43—82no—
208#3170—431no—
209#3113—432no—
210C2×C8×Q8—431no—
211#1680—432no—
212#1680—432no—
213#1674—431no—
214#1674—431no—
215#1670—431no—
216#1670D4311yescharacteristic, complemented
217#1568—431no—
218#1552—432no—
219C2×C43#303711yescharacteristic
220C2×C43#305011yescharacteristic
221C2×C43C2×#47311yescharacteristic
222D43—22no—
223#533—432no—
224C2×C4×Q8—431no—
225#500—431no—
226#494C2×D4311yescharacteristic
227#487—432no—
228#483—862no—
229#475—432no—
230#475C2×D4312yes—
231#467—861no—
232#467—861no—
233#462—432no—
234#462—432no—
235#451—862no—
236C8×Q8—431no—
237C8×Q8—431no—
238C8×Q8—431no—
239C8×Q8—861no—
240C8×Q8—861no—
241C8×Q8C2×D4311yescharacteristic
242#441—862no—
243#441—862no—
244C4×Q16—861no—
245C4×Q16—861no—
246#432—432no—
247C2×C4⋊C8—431no—
248C2×C4⋊C8—861no—
249C2×C4×C8—431no—
250C2×C4×C8—861no—
251#335—431no—
252#335C2×D4311yescharacteristic
253#334—432no—
254#332—432no—
255#332—432no—
256#332—432no—
257#332C2×D4312yes—
258C43#1926511yescharacteristic, complemented, Sylow
259C22×Q8—431no—
260C2×Q16—21no—
261C2×Q16—21no—
262C2×Q16—862no—
263C2×Q16—862no—
264C22×C8—431no—
265C22×C8—431no—
266C22×C8—861no—
267C4⋊Q8—432no—
268C4⋊Q8C22×D4312yes—
269#125—862no—
270C22⋊Q8—862no—
271C22⋊Q8—862no—
272C4×Q8—431no—
273C4×Q8—431no—
274C4×Q8—431no—
275C4×Q8—861no—
276C4×Q8—861no—
277C4×Q8—862no—
278C4×Q8—862no—
279C4×Q8C22×D4311yescharacteristic
280#117—862no—
281C2×C4⋊C4—431no—
282C2×C4⋊C4—861no—
283C2×C42—431no—
284C2×C42—861no—
285#107—861no—
286#107—861no—
287#106—22no—
288#106—862no—
289C4⋊C8—21no—
290C4⋊C8—431no—
291C4⋊C8—432no—
292C4⋊C8—861no—
293C4⋊C8—861no—
294C4⋊C8—861no—
295C4⋊C8—861no—
296C4⋊C8C22×D4311yescharacteristic
297C4⋊C8C22×D4312yes—
298#103—22no—
299#103—862no—
300#103—862no—
301#103—862no—
302#103—862no—
303#103—862no—
304C22⋊C8—862no—
305#97—862no—
306C4×C8—21no—
307C4×C8—431no—
308C4×C8—431no—
309C4×C8—431no—
310C4×C8—861no—
311C4×C8—861no—
312C4×C8—861no—
313C4×C8C22×D4311yescharacteristic
314C2×Q8—22no—
315C2×Q8—431no—
316C2×Q8—861no—
317C2×Q8—862no—
318C2×Q8—862no—
319C2×Q8—862no—
320C2×Q8D4×D4311yescharacteristic
321C22×C4—431no—
322C22×C4—431no—
323C22×C4—431no—
324C22×C4—861no—
325C22×C4—861no—
326Q16—42no—
327Q16—42no—
328Q16—1724no—
329Q16—1724no—
330C2×C8—21no—
331C2×C8—22no—
332C2×C8—431no—
333C2×C8—431no—
334C2×C8—862no—
335C2×C8—861no—
336C2×C8—862no—
337C2×C8—1721no—
338C2×C8—1722no—
339C2×C8D4×D4311yescharacteristic
340C2×C8D4×D4311yescharacteristic
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—431no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—862no—
350C4⋊C4—862no—
351C4⋊C4—1722no—
352C4⋊C4—1722no—
353C4⋊C4D4×D4311yescharacteristic
354C22⋊C4—1722no—
355C42—21no—
356C42—431no—
357C42—431no—
358C42—431no—
359C42—861no—
360C42—861no—
361C42—861no—
362C42—1722no—
363C42C23×D4311yescharacteristic
364C23—431no—
365Q8—21no—
366Q8—42no—
367Q8—42no—
368Q8—432no—
369Q8—864no—
370Q8—861no—
371Q8—1722no—
372Q8—1722no—
373Q8#1306334812yes—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—431no—
378C2×C4—431no—
379C2×C4—431no—
380C2×C4—862no—
381C2×C4—864no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4C2×D4×D4311yescharacteristic
391C2×C4C2×D4×D4311yescharacteristic
392C2×C4#41×D4311yescharacteristic
393C8—21no—
394C8—42no—
395C8—41no—
396C8—861no—
397C8—861no—
398C8—1722no—
399C8—1721no—
400C8#1306335412yes—
401C22—432no—
402C22—861no—
403C22—861no—
404C22#121×D4311yescharacteristic
405C4—21no—
406C4—22no—
407C4—41no—
408C4—82no—
409C4—861no—
410C4—861no—
411C4—861no—
412C4—862no—
413C4—3442no—
414C4—1721no—
415C4#135×D4311yescharacteristic
416C4C2×#1306334811yescharacteristic
417C4C2×#1306335411yescharacteristic
418C4#1458369511yescharacteristic
419C2—862no—
420C2#1914406211yescharacteristic
421C2#1914417811yescharacteristic
422C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1670C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1670D43
hypocenterC43#19265
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1670

Complements

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

NH ≅ G/Ntype
4. #19134024C2semidirect
5. #19134023C2semidirect
6. #19133990C2semidirect
7. #19133989C2semidirect
8. #19133962C2semidirect
11. C43×#1670C2semidirect
216. #1670D43semidirect
258. C43#19265semidirect

Maximal subgroups

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

subgroupindex
#191451792
#191447272
C8×Q8×D432
#191340242
#191340232
#191339902
#191339892
#191339622
#191333572
#191332942
C43×#16702
#1926543