Finite Group Databasebeta

← #25251396

Subgroups — #25251396

Order 11008.

590 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#19144176C211yesmaximal, characteristic
2#19136803C212yesmaximal, complemented
3#19136797C211yesmaximal, characteristic, complemented
4#19136792C211yesmaximal, characteristic, complemented
5#19136786C212yesmaximal, complemented
6#19136780C211yesmaximal, characteristic, complemented
7#19136775C211yesmaximal, characteristic, complemented
8#19136377C212yesmaximal, complemented
9#19136300C212yesmaximal, complemented
10C2×C22⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
11C2×C43×#427C211yesmaximal, characteristic, complemented
12C2×#13063347C2211yescharacteristic
13#14583410—21no—
14C22×C43⋊C16C2212yes—
15#14583140C2211yescharacteristic
16#14583140C2211yescharacteristic
17#14583135C2211yescharacteristic
18#14583135C2211yescharacteristic
19#14583128—21no—
20#14583128—21no—
21#14582937C2211yescharacteristic
22#14582896—21no—
23#14582726C2212yescomplemented
24#14582726C2212yescomplemented
25#14582724C2212yescomplemented
26#14582724C2212yescomplemented
27#14582702C2212yescomplemented
28#14582702C2212yescomplemented
29#14582699C2212yescomplemented
30#14582699C2212yescomplemented
31C22⋊(C43⋊C16)C2211yescharacteristic
32C22⋊(C43⋊C16)C2211yescharacteristic
33C22⋊(C43⋊C16)C2212yes—
34C23×C8×C43C2211yescharacteristic
35C2×#117×C43—21no—
36C43×#427—21no—
37C43×#427—21no—
38C43×#427C2212yes—
39C43×#427C2212yes—
40C2×#107×C43C2211yescharacteristic
41C2×#107×C43C2211yescharacteristic
42C2×#106×C43—21no—
43C2×#10621898—21no—
44#13063347—24no—
45C2×Dic172C2311yescharacteristic
46C2×#10621873—21no—
47C2×D344C2311yescharacteristic
48#13063308—41no—
49#13063304—21no—
50#13063304—21no—
51#13063299—21no—
52#13063299—21no—
53#13063294—41no—
54C4×C22⋊D43—41no—
55C4×C22⋊D43—41no—
56#13063284—21no—
57C2×C43⋊C16—24no—
58C2×C43⋊C16C2312yes—
59C2×C43⋊C16C2312yes—
60#13063259C2311yescharacteristic
61#13063259C2311yescharacteristic
62#13063257—21no—
63#13063250—21no—
64#13063250—21no—
65#13063247—21no—
66#13063247—21no—
67C23×C4×C43D411yescharacteristic
68C22×C8×C43—24no—
69C22×C8×C43D411yescharacteristic
70C22×C8×C43D411yescharacteristic
71C22×C8×C43D411yescharacteristic
72C22×C8×C43C2311yescharacteristic
73C22×C8×C43C2311yescharacteristic
74C22×C8×C43C2311yescharacteristic
75#117×C43—22no—
76#117×C43—22no—
77#117×C43—41no—
78#117×C43—41no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C22⋊C4×C43—41no—
82C2×C42×C43—41no—
83#107×C43—21no—
84#107×C43—21no—
85#107×C43C2312yes—
86#107×C43C2312yes—
87#106×C43—22no—
88#106×C43—22no—
89C24×C43D811yescharacteristic
90C22×C4×C43—22no—
91C22×C4×C43—22no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43D811yescharacteristic
95C22×C4×C43D811yescharacteristic
96C22×C4×C43D811yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103#10621898—42no—
104#10621898—42no—
105C2×D172—21no—
106C2×C4×D43—41no—
107C2×Dic86—21no—
108C2×C8×C43—22no—
109C2×C8×C43—22no—
110C2×C8×C43—22no—
111C2×C8×C43—22no—
112C2×C8×C43—22no—
113C2×C8×C43C2×D411yescharacteristic
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43#4114yes—
117C2×C8×C43C2411yescharacteristic
118C4⋊C4×C43—22no—
119C4⋊C4×C43—22no—
120C4⋊C4×C43—41no—
121C4⋊C4×C43—41no—
122C22⋊C4×C43—42no—
123C22⋊C4×C43—42no—
124C42×C43—42no—
125C42×C43—42no—
126C22⋊Dic43—41no—
127C22⋊Dic43—41no—
128C22⋊Dic43—41no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133Dic43⋊C4—41no—
134Dic43⋊C4—41no—
135C4×Dic43—41no—
136Dic172—22no—
137D344—22no—
138#10621873—42no—
139C43⋊C16—22no—
140C43⋊C16—22no—
141C23×C43—22no—
142C23×C43—22no—
143C23×C43—41no—
144C23×C43C2×D811yescharacteristic
145C23×C43C2×D811yescharacteristic
146C23×C43C2×D811yescharacteristic
147C22×D43—41no—
148C2×C4×C43—22no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—22no—
154C2×C4×C43—22no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43—82no—
158C2×C4×C43—82no—
159C2×C4×C43#12312yes—
160C2×C4×C43C2×D811yescharacteristic
161C2×C4×C43C2×D811yescharacteristic
162C2×C4×C43C2×D811yescharacteristic
163C2×C4×C43#13712yes—
164C2×C4×C43C22×D411yescharacteristic
165C22⋊D43—82no—
166C22⋊D43—82no—
167C22⋊D43—82no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171D172—41no—
172D172—41no—
173C4×D43—82no—
174Dic86—41no—
175Dic86—41no—
176C8×C43—21no—
177C8×C43—21no—
178C8×C43#12312yes—
179C8×C43C2×#4112yes—
180#33645—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—44no—
189C22×C43#48012yes—
190C22×C43#50812yes—
191C22×C43C22×D811yescharacteristic
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—81no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—82no—
198C4×C43—82no—
199C4×C43#48012yes—
200C4×C43C2×#12311yescharacteristic
201C4×C43C2×#13711yescharacteristic
202Dic43—81no—
203Dic43—81no—
204Dic43—81no—
205#3050—431no—
206C2×#427D4311yescharacteristic, complemented
207#2237—432no—
208#2236—431no—
209#2235—431no—
210#2234—432no—
211#2233—431no—
212#2232—431no—
213#2158—432no—
214#2138—432no—
215C2×C22⋊C16—431no—
216C2×C43—22no—
217C2×C43—22no—
218C2×C43—41no—
219C2×C43C2×#48011yescharacteristic
220C2×C43C2×#50811yescharacteristic
221C2×C43#341411yescharacteristic
222D43—161no—
223C2×#135—431no—
224C23×C8C2×D4311yescharacteristic
225#525—861no—
226C2×#117—21no—
227C22×C16—432no—
228#467—431no—
229#467—431no—
230#466—431no—
231#466—431no—
232#465—861no—
233#465—861no—
234#427—21no—
235#427—21no—
236#427—431no—
237#427C2×D4312yes—
238#427C2×D4312yes—
239C2×#107C2×D4311yescharacteristic
240C2×#107C2×D4311yescharacteristic
241C2×#106—21no—
242#416—861no—
243#367—432no—
244#367—432no—
245#366—432no—
246#366—432no—
247#358—432no—
248#358—432no—
249#357—432no—
250#357—432no—
251C22⋊C16—431no—
252C22⋊C16—431no—
253C22⋊C16—432no—
254C43#3364511yescharacteristic, complemented, Sylow
255C2×#41—861no—
256C23×C4C22⋊D4311yescharacteristic
257#135—864no—
258C2×Q16—431no—
259C2×SD16—861no—
260C2×D8—431no—
261C22×C8—24no—
262C22×C8C22⋊D4311yescharacteristic
263C22×C8C22⋊D4311yescharacteristic
264C22×C8C22⋊D4311yescharacteristic
265C22×C8C22×D4311yescharacteristic
266C22×C8C22×D4311yescharacteristic
267C22×C8C22×D4311yescharacteristic
268#123—1721no—
269C22⋊Q8—861no—
270C22⋊Q8—861no—
271#121—861no—
272#121—861no—
273#120—1721no—
274C4×D4—1721no—
275C4×D4—1721no—
276#117—22no—
277#117—22no—
278#117—41no—
279#117—41no—
280#117—861no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C22⋊C4—41no—
284C2×C42—41no—
285C2×C16—432no—
286C2×C16—432no—
287C2×C16—864no—
288#107—21no—
289#107—21no—
290#107—431no—
291#107—431no—
292#107C22×D4312yes—
293#107C22×D4312yes—
294#106—22no—
295#106—22no—
296#106—861no—
297#103—861no—
298#103—861no—
299#102—861no—
300#102—861no—
301C24#1062188211yescharacteristic
302#41—1722no—
303#41—1722no—
304C2×Q8—861no—
305C2×D4—861no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—1721no—
314C22×C4#1062188211yescharacteristic
315C22×C4#1062188211yescharacteristic
316C22×C4#1062188211yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319C22×C4C2×C22⋊D4311yescharacteristic
320Q16—862no—
321SD16—1722no—
322D8—862no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8#1062189814yes—
329C2×C8C2×C22⋊D4311yescharacteristic
330C2×C8C2×C22⋊D4311yescharacteristic
331C2×C8C2×C22⋊D4311yescharacteristic
332C2×C8C23×D4311yescharacteristic
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—861no—
338C4⋊C4—861no—
339C4⋊C4—1721no—
340C4⋊C4—1721no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C42—42no—
349C42—42no—
350C42—1721no—
351C16—862no—
352C16—862no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—1721no—
357C23C2×#1062188211yescharacteristic
358C23C2×#1062188211yescharacteristic
359C23C2×#1062188211yescharacteristic
360Q8—1721no—
361Q8—1721no—
362D4—3442no—
363D4—3442no—
364D4—3442no—
365D4—1721no—
366D4—1721no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—3442no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4#1306330812yes—
383C2×C4C2×#1062188211yescharacteristic
384C2×C4C2×#1062188211yescharacteristic
385C2×C4C2×#1062188211yescharacteristic
386C2×C4#1306335612yes—
387C2×C4C22×C22⋊D4311yescharacteristic
388C8—21no—
389C8—21no—
390C8#1306330812yes—
391C8C2×#1062189812yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—3441no—
401C22—3441no—
402C22—3441no—
403C22#1458321212yes—
404C22#1458332912yes—
405C22C22×#1062188211yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—82no—
410C4—3441no—
411C4—3441no—
412C4—3441no—
413C4#1458321212yes—
414C4C2×#1306330811yescharacteristic
415C4C2×#1306335611yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—6881no—
420C2C2×#1458321211yescharacteristic
421C2C2×#1458332911yescharacteristic
422C2#1914772911yescharacteristic
subgroupG/H
centerC2×C4C2×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#427C2
socleC22×C43C22×D8
prime radical#19144176C2
hypercenterC2×#427D43
hypocenterC43#33645
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. #19136803C2semidirect
3. #19136797C2semidirect
4. #19136792C2semidirect
5. #19136786C2semidirect
6. #19136780C2semidirect
7. #19136775C2semidirect
8. #19136377C2semidirect
9. #19136300C2semidirect
10. C2×C22⋊(C43⋊C16)C2semidirect
11. C2×C43×#427C2semidirect
23. #14582726C22semidirect
24. #14582726C22semidirect
25. #14582724C22semidirect
26. #14582724C22semidirect
27. #14582702C22semidirect
28. #14582702C22semidirect
29. #14582699C22semidirect
30. #14582699C22semidirect
206. C2×#427D43semidirect
254. C43#33645semidirect

Maximal subgroups

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

subgroupindex
#191441762
#191368032
#191367972
#191367922
#191367862
#191367802
#191367752
#191363772
#191363002
C2×C22⋊(C43⋊C16)2
C2×C43×#4272
#3364543