Finite Group Databasebeta

← #25079838

Subgroups — #25079838

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#19145542C212yesmaximal
2#500×D43C211yesmaximal, characteristic
3#19143524C211yesmaximal, characteristic
4#19134112C212yesmaximal, complemented
5#19134111C212yesmaximal, complemented
6#19133990C211yesmaximal, characteristic, complemented
7#19133989C211yesmaximal, characteristic, complemented
8#19133986C211yesmaximal, characteristic, complemented
9#19133342C211yesmaximal, characteristic
10#19133278C212yesmaximal
11C43×#1674C211yesmaximal, characteristic, complemented
12#14583453C2211yescharacteristic
13C4⋊Q8×D43C2212yes—
14#14583304C2211yescharacteristic
15#14583303—21no—
16#14583303—21no—
17#14583302C2212yes—
18#14583277—22no—
19#14583248—22no—
20#14583110C2212yes—
21#14583109C2212yes—
22#14583106C2212yes—
23#14583056—22no—
24#14583053—22no—
25#14583030C2211yescharacteristic
26#14583028—21no—
27#14583026C2211yescharacteristic
28C8×Dic86—21no—
29C8×Dic86C2211yescharacteristic
30#14582951C2212yes—
31#107×D43—21no—
32#107×D43—21no—
33#14582924—21no—
34#14582921C2211yescharacteristic
35#14582853—21no—
36C4×C8×D43C2211yescharacteristic
37#14582652C2211yescharacteristic
38#14582649C2212yes—
39#14582646C2212yes—
40#14582645C2212yes—
41#14582644C2212yes—
42C43×#500C2211yescharacteristic
43C43×#462C2212yes—
44C8×Q8×C43C2211yescharacteristic
45C43×#335C2211yescharacteristic
46C43×#332C2212yes—
47C2×Q8×D43—22no—
48C2×Dic172—22no—
49C2×#10621885—22no—
50C2×#10621885—22no—
51C2×#10621872—21no—
52C2×C8×D43D411yescharacteristic
53C2×C8×D43D411yescharacteristic
54#13063325C2312yes—
55#13063324—22no—
56#13063324—22no—
57#13063324D411yescharacteristic
58#13063323—22no—
59#13063323D411yescharacteristic
60#13063315—21no—
61#13063305D411yescharacteristic
62#13063303—21no—
63#13063301D411yescharacteristic
64C4×Dic86—21no—
65C4×Dic86C2311yescharacteristic
66#13063282—21no—
67C4⋊C4×D43—22no—
68C4⋊C4×D43—22no—
69C42×D43C2311yescharacteristic
70#13063259—21no—
71#13063259—21no—
72#13063258—22no—
73#13063258—22no—
74C4⋊(C43⋊C8)—21no—
75C4⋊(C43⋊C8)C2312yes—
76C4⋊(C43⋊C8)C2311yescharacteristic
77Dic43⋊C8—21no—
78Dic43⋊C8—21no—
79Dic43⋊C8—21no—
80#13063250—22no—
81#13063249—22no—
82#13063248—22no—
83(C2×D43)⋊C8—22no—
84#13063236—21no—
85#13063235—21no—
86C4×C43⋊C8C2311yescharacteristic
87C8×Dic43—21no—
88C8×Dic43—22no—
89C8×Dic43D411yescharacteristic
90C8×Dic43D411yescharacteristic
91C2×Q16×C43—22no—
92C4⋊Q8×C43C2312yes—
93C4×Q8×C43C2311yescharacteristic
94#107×C43—21no—
95#107×C43—21no—
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—82no—
105Q8×D43—82no—
106C2×C4×D43—42no—
107C2×C4×D43C2×D411yescharacteristic
108C2×C4×D43C2×D411yescharacteristic
109C2×C4×D43#4111yescharacteristic
110C2×Dic86—21no—
111C2×Dic86—22no—
112C2×Dic86—42no—
113C2×Dic86C2×D411yescharacteristic
114Q16×C43—82no—
115C2×C8×C43—21no—
116C2×C8×C43—22no—
117C2×C8×C43C2×D411yescharacteristic
118C2×C8×C43C2×D411yescharacteristic
119C4⋊C4×C43—21no—
120C4⋊C4×C43—22no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43C2×D411yescharacteristic
123C42×C43—21no—
124C42×C43C2411yescharacteristic
125#10621885—82no—
126#10621885—82no—
127(C2×D43)⋊C4—21no—
128(C2×D43)⋊C4—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—22no—
131C4⋊Dic43—22no—
132C4⋊Dic43C2×D411yescharacteristic
133Dic43⋊C4—21no—
134Dic43⋊C4—21no—
135Dic43⋊C4—21no—
136Dic43⋊C4—21no—
137Dic43⋊C4—21no—
138Dic43⋊C4—42no—
139Dic43⋊C4—42no—
140C4×Dic43—21no—
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—82no—
149#10621872—42no—
150C8×D43—22no—
151C8×D43Q1614yescomplemented
152C22×D43#12111yescharacteristic
153Q8×C43—21no—
154Q8×C43—21no—
155Q8×C43—42no—
156Q8×C43—42no—
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—21no—
170C4×D43—21no—
171C4×D43—22no—
172C4×D43—84no—
173C4×D43C2×Q1612yes—
174C4×D43#13712yes—
175Dic86—21no—
176Dic86—21no—
177Dic86—42no—
178Dic86—42no—
179Dic86—42no—
180Dic86—84no—
181C8×C43—21no—
182C8×C43—41no—
183C8×C43—42no—
184C8×C43C2×Q1612yes—
185C43⋊C8—21no—
186C43⋊C8—41no—
187C43⋊C8—42no—
188C43⋊C8C2×Q1612yes—
189#19208—431nomaximal, Sylow
190C22×C43C2×#12111yescharacteristic
191C2×D43—21no—
192C2×D43—21no—
193C2×D43#46212yes—
194C4×C43—21no—
195C4×C43—41no—
196C4×C43—41no—
197C4×C43—82no—
198C4×C43C22×Q1611yescharacteristic
199C4×C43C2×#13711yescharacteristic
200C4×C43#57611yescharacteristic
201C4×C43#57611yescharacteristic
202Dic43—21no—
203Dic43—41no—
204Dic43—41no—
205Dic43—82no—
206Dic43#46212yes—
207Dic43#47312yes—
208#3209—432no—
209C2×#500—431no—
210#2960—431no—
211#1694—432no—
212#1694—432no—
213#1674—431no—
214#1674—431no—
215#1674—431no—
216#1674D4311yescharacteristic, complemented
217#1564—431no—
218#1549—432no—
219C2×C43C2×#46211yescharacteristic
220C2×C43#305811yescharacteristic
221C2×C43C2×#47311yescharacteristic
222D43—22no—
223#533—431no—
224C2×C4⋊Q8—432no—
225#500—432no—
226#500—431no—
227#500—861no—
228#500—861no—
229#500C2×D4311yescharacteristic
230#494—862no—
231#487—862no—
232#462—432no—
233#462—432no—
234#462—432no—
235#462C2×D4312yes—
236#451—862no—
237#451—862no—
238#446—431no—
239#446—431no—
240#446—861no—
241C8×Q8—431no—
242C8×Q8—861no—
243C8×Q8C2×D4311yescharacteristic
244#431—432no—
245C2×#107—861no—
246C2×#107—861no—
247#424—861no—
248#423—431no—
249#405—861no—
250C2×C4×C8—431no—
251#335—431no—
252#335C2×D4311yescharacteristic
253#334—432no—
254#332—432no—
255#332—432no—
256#332—432no—
257#332C2×D4312yes—
258C43#1920811yescharacteristic, complemented, Sylow
259C22×Q8—862no—
260C2×Q16—22no—
261C2×Q16—862no—
262C2×Q16—862no—
263C2×Q16—862no—
264C2×M16—861no—
265C22×C8—431no—
266C22×C8—431no—
267C4⋊Q8—431no—
268C4⋊Q8—431no—
269C4⋊Q8—432no—
270C4⋊Q8—862no—
271C4⋊Q8—862no—
272C4⋊Q8—862no—
273C4⋊Q8C22×D4312yes—
274#125—861no—
275C22⋊Q8—431no—
276C22⋊Q8—431no—
277C22⋊Q8—861no—
278C4×Q8—431no—
279C4×Q8—861no—
280C4×Q8C22×D4311yescharacteristic
281#117—861no—
282C2×C4⋊C4—862no—
283C2×C4⋊C4—862no—
284C2×C42—431no—
285#107—21no—
286#107—21no—
287#107—862no—
288#107—862no—
289#107—861no—
290#107—861no—
291C4⋊C8—21no—
292C4⋊C8—431no—
293C4⋊C8—432no—
294C4⋊C8—861no—
295C4⋊C8—861no—
296C4⋊C8—861no—
297C4⋊C8—861no—
298C4⋊C8C22×D4311yescharacteristic
299C4⋊C8C22×D4312yes—
300#103—22no—
301#103—862no—
302#103—862no—
303#103—862no—
304C22⋊C8—862no—
305#97—861no—
306#97—861no—
307C4×C8—21no—
308C4×C8—431no—
309C4×C8—431no—
310C4×C8—431no—
311C4×C8—862no—
312C4×C8—861no—
313C4×C8C22×D4311yescharacteristic
314C2×Q8—22no—
315C2×Q8—431no—
316C2×Q8—861no—
317C2×Q8—862no—
318C2×Q8—3442no—
319C2×Q8—3442no—
320C2×Q8—1722no—
321C2×Q8D4×D4311yescharacteristic
322C22×C4—431no—
323C22×C4—431no—
324C22×C4—431no—
325C22×C4—1722no—
326Q16—82no—
327Q16—3442no—
328Q16—3442no—
329Q16—3442no—
330M16—1722no—
331C2×C8—21no—
332C2×C8—22no—
333C2×C8—431no—
334C2×C8—434no—
335C2×C8—431no—
336C2×C8—862no—
337C2×C8—861no—
338C2×C8—862no—
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—861no—
350C4⋊C4—861no—
351C4⋊C4—862no—
352C4⋊C4—862no—
353C4⋊C4—1722no—
354C4⋊C4—1722no—
355C4⋊C4D4×D4311yescharacteristic
356C22⋊C4—861no—
357C22⋊C4—861no—
358C42—21no—
359C42—431no—
360C42—431no—
361C42—431no—
362C42—861no—
363C42C23×D4311yescharacteristic
364C23—431no—
365Q8—21no—
366Q8—21no—
367Q8—42no—
368Q8—42no—
369Q8—861no—
370Q8—861no—
371Q8—3444no—
372Q8—1722no—
373Q8—1722no—
374Q8—1722no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—42no—
378C2×C4—431no—
379C2×C4—431no—
380C2×C4—432no—
381C2×C4—432no—
382C2×C4—431no—
383C2×C4—862no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—3444no—
389C2×C4—1722no—
390C2×C4C2×D4×D4311yescharacteristic
391C2×C4C2×D4×D4311yescharacteristic
392C2×C4#41×D4311yescharacteristic
393C8—21no—
394C8—41no—
395C8—42no—
396C8—432no—
397C8—861no—
398C8—1721no—
399C8—1722no—
400C8Q16×D4312yes—
401C22—432no—
402C22—861no—
403C22—861no—
404C22#121×D4311yescharacteristic
405C4—21no—
406C4—41no—
407C4—41no—
408C4—82no—
409C4—432no—
410C4—432no—
411C4—861no—
412C4—3442no—
413C4—1721no—
414C4—1721no—
415C4C2×Q16×D4311yescharacteristic
416C4#137×D4311yescharacteristic
417C4#1458370011yescharacteristic
418C4#1458370111yescharacteristic
419C2—862no—
420C2#462×D4311yescharacteristic
421C2#1914423811yescharacteristic
422C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1674C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1674D43
hypocenterC43#19208
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1674

Complements

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

NH ≅ G/Ntype
4. #19134112C2semidirect
5. #19134111C2semidirect
6. #19133990C2semidirect
7. #19133989C2semidirect
8. #19133986C2semidirect
11. C43×#1674C2semidirect
151. C8×D43Q16semidirect
216. #1674D43semidirect
258. C43#19208semidirect

Maximal subgroups

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

subgroupindex
#191455422
#500×D432
#191435242
#191341122
#191341112
#191339902
#191339892
#191339862
#191333422
#191332782
C43×#16742
#1920843