Finite Group Databasebeta

← #25251392

Subgroups — #25251392

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
1C2×#14582937C211yesmaximal, characteristic, complemented
2#19136800C212yesmaximal, complemented
3#19136795C211yesmaximal, characteristic, complemented
4#19136790C211yesmaximal, characteristic, complemented
5#19136783C212yesmaximal, complemented
6#19136778C211yesmaximal, characteristic, complemented
7#19136773C211yesmaximal, characteristic, complemented
8#19136377C212yesmaximal, complemented
9#19136302C212yesmaximal, complemented
10C2×C22⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
11C43×#3050C211yesmaximal, characteristic
12C2×#13063284—21no—
13C22×C43⋊C16C2212yes—
14#14582937—21no—
15#14582937—21no—
16#14582937C2212yes—
17#14582937C2212yes—
18C2×#13063259C2211yescharacteristic
19C2×#13063259C2211yescharacteristic
20C2×#13063257—21no—
21#14582726C2212yescomplemented
22#14582726C2212yescomplemented
23#14582724C2212yescomplemented
24#14582724C2212yescomplemented
25#14582703C2212yescomplemented
26#14582703C2212yescomplemented
27#14582700C2212yescomplemented
28#14582700C2212yescomplemented
29C22⋊(C43⋊C16)C2211yescharacteristic
30C22⋊(C43⋊C16)C2211yescharacteristic
31C22⋊(C43⋊C16)C2212yes—
32C2×#135×C43C2211yescharacteristic
33C23×C8×C43C2211yescharacteristic
34C43×#525—21no—
35C43×#467C2211yescharacteristic
36C43×#467C2211yescharacteristic
37C43×#466C2211yescharacteristic
38C43×#466C2211yescharacteristic
39C43×#465—21no—
40C43×#465—21no—
41C43×#427C2211yescharacteristic
42C43×#416—21no—
43#13063284—22no—
44#13063284—22no—
45#13063284—41no—
46#13063284—41no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C2×C22⋊Dic43—41no—
50C2×C4×Dic43—41no—
51C2×C43⋊C16—24no—
52C2×C43⋊C16C2312yes—
53C2×C43⋊C16C2312yes—
54#13063259—21no—
55#13063259—21no—
56#13063259C2312yes—
57#13063259C2312yes—
58#13063257—22no—
59#13063257—22no—
60C2×#41×C43—21no—
61C23×C4×C43D411yescharacteristic
62#135×C43—24no—
63C2×Q16×C43C2311yescharacteristic
64C2×SD16×C43—21no—
65C2×D8×C43C2311yescharacteristic
66C22×C8×C43—24no—
67C22×C8×C43D411yescharacteristic
68C22×C8×C43D411yescharacteristic
69C22×C8×C43D411yescharacteristic
70C22×C8×C43C2311yescharacteristic
71C22×C8×C43C2311yescharacteristic
72C22×C8×C43C2311yescharacteristic
73#123×C43—41no—
74C22⋊Q8×C43—21no—
75C22⋊Q8×C43—21no—
76#121×C43—21no—
77#121×C43—21no—
78#120×C43—41no—
79C4×D4×C43—41no—
80C4×D4×C43—41no—
81#117×C43—21no—
82#107×C43C2311yescharacteristic
83#107×C43C2311yescharacteristic
84#106×C43—21no—
85#103×C43—21no—
86#103×C43—21no—
87#102×C43—21no—
88#102×C43—21no—
89C24×C43D811yescharacteristic
90#41×C43—42no—
91#41×C43—42no—
92C2×Q8×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C22×C4×C43—22no—
98C22×C4×C43—22no—
99C22×C4×C43—41no—
100C22×C4×C43D811yescharacteristic
101C22×C4×C43D811yescharacteristic
102C22×C4×C43D811yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×Dic43—41no—
107C22×Dic43—41no—
108Q16×C43—22no—
109SD16×C43—42no—
110D8×C43—22no—
111C2×C8×C43—22no—
112C2×C8×C43—22no—
113C2×C8×C43—22no—
114C2×C8×C43—22no—
115C2×C8×C43—22no—
116C2×C8×C43C2×D411yescharacteristic
117C2×C8×C43C2×D411yescharacteristic
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43#4114yes—
120C2×C8×C43C2411yescharacteristic
121C4⋊C4×C43—21no—
122C4⋊C4×C43—21no—
123C4⋊C4×C43—41no—
124C4⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—41no—
127C22⋊C4×C43—41no—
128C22⋊C4×C43—41no—
129C22⋊C4×C43—41no—
130C42×C43—41no—
131C22⋊Dic43—42no—
132C22⋊Dic43—42no—
133C4⋊Dic43—22no—
134C4⋊Dic43—22no—
135C4⋊Dic43—41no—
136C4⋊Dic43—41no—
137C4×Dic43—42no—
138C4×Dic43—42no—
139C43⋊C16—22no—
140C43⋊C16—22no—
141C23×C43—22no—
142C23×C43—22no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43C2×D811yescharacteristic
146C23×C43C2×D811yescharacteristic
147C23×C43C2×D811yescharacteristic
148Q8×C43—41no—
149Q8×C43—41no—
150D4×C43—41no—
151D4×C43—41no—
152D4×C43—82no—
153D4×C43—82no—
154D4×C43—82no—
155C2×C4×C43—22no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—22no—
161C2×C4×C43—22no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—82no—
166C2×C4×C43#12312yes—
167C2×C4×C43C2×D811yescharacteristic
168C2×C4×C43C2×D811yescharacteristic
169C2×C4×C43C2×D811yescharacteristic
170C2×C4×C43#13712yes—
171C2×C4×C43C22×D411yescharacteristic
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—82no—
175C2×Dic43—82no—
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—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43#48012yes—
193C22×C43#50812yes—
194C22×C43C22×D811yescharacteristic
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—81no—
198C4×C43—81no—
199C4×C43—81no—
200C4×C43#48012yes—
201C4×C43C2×#12311yescharacteristic
202C4×C43C2×#13711yescharacteristic
203Dic43—82no—
204Dic43—82no—
205#3050D4311yescharacteristic
206C2×#427—431no—
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×C43—161no—
220C2×C43C2×#48011yescharacteristic
221C2×C43C2×#50811yescharacteristic
222C2×C43#341411yescharacteristic
223C2×#135C2×D4311yescharacteristic
224C23×C8C2×D4311yescharacteristic
225#525—21no—
226C2×#117—861no—
227C22×C16—432no—
228#467C2×D4311yescharacteristic
229#467C2×D4311yescharacteristic
230#466C2×D4311yescharacteristic
231#466C2×D4311yescharacteristic
232#465—21no—
233#465—21no—
234#427—432no—
235#427—432no—
236#427—861no—
237#427—861no—
238#427C2×D4311yescharacteristic
239C2×#107—431no—
240C2×#107—431no—
241C2×#106—861no—
242#416—21no—
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—21no—
256C23×C4C22⋊D4311yescharacteristic
257#135—24no—
258C2×Q16C22×D4311yescharacteristic
259C2×SD16—21no—
260C2×D8C22×D4311yescharacteristic
261C22×C8—24no—
262C22×C8C22⋊D4311yescharacteristic
263C22×C8C22⋊D4311yescharacteristic
264C22×C8C22⋊D4311yescharacteristic
265C22×C8C22×D4311yescharacteristic
266C22×C8C22×D4311yescharacteristic
267C22×C8C22×D4311yescharacteristic
268#123—41no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271#121—21no—
272#121—21no—
273#120—41no—
274C4×D4—41no—
275C4×D4—41no—
276#117—21no—
277#117—862no—
278#117—862no—
279#117—1721no—
280#117—1721no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—861no—
283C2×C22⋊C4—1721no—
284C2×C42—1721no—
285C2×C16—432no—
286C2×C16—432no—
287C2×C16—864no—
288#107—432no—
289#107—432no—
290#107—861no—
291#107—861no—
292#107C22×D4311yescharacteristic
293#107C22×D4311yescharacteristic
294#106—21no—
295#106—862no—
296#106—862no—
297#103—21no—
298#103—21no—
299#102—21no—
300#102—21no—
301C24#1062188211yescharacteristic
302#41—42no—
303#41—42no—
304C2×Q8—21no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—1721no—
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—22no—
321SD16—42no—
322D8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8#1062190014yes—
329C2×C8C2×C22⋊D4311yescharacteristic
330C2×C8C2×C22⋊D4311yescharacteristic
331C2×C8C2×C22⋊D4311yescharacteristic
332C2×C8C23×D4311yescharacteristic
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—862no—
338C4⋊C4—862no—
339C4⋊C4—1721no—
340C4⋊C4—1721no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—1722no—
347C22⋊C4—1722no—
348C42—41no—
349C42—1722no—
350C42—1722no—
351C16—862no—
352C16—862no—
353C23—22no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23C2×#1062188211yescharacteristic
358C23C2×#1062188211yescharacteristic
359C23C2×#1062188211yescharacteristic
360Q8—41no—
361Q8—41no—
362D4—41no—
363D4—41no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—82no—
378C2×C4—3442no—
379C2×C4—3442no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4#1306330612yes—
383C2×C4C2×#1062188211yescharacteristic
384C2×C4C2×#1062188211yescharacteristic
385C2×C4C2×#1062188211yescharacteristic
386C2×C4#1306335512yes—
387C2×C4C22×C22⋊D4311yescharacteristic
388C8—21no—
389C8—21no—
390C8#1306330612yes—
391C8C2×#1062190012yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22#1458321012yes—
404C22#1458332912yes—
405C22C22×#1062188211yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—3442no—
412C4—3442no—
413C4#1458321012yes—
414C4C2×#1306330611yescharacteristic
415C4C2×#1306335511yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—161no—
420C2C2×#1458321011yescharacteristic
421C2C2×#1458332911yescharacteristic
422C2#1914772911yescharacteristic
subgroupG/H
centerC2×C4C2×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
Fitting, prime radicalC43×#3050C2
socleC22×C43C22×D8
hypercenter#3050D43
hypocenterC43#33645
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#14582937C2semidirect
2. #19136800C2semidirect
3. #19136795C2semidirect
4. #19136790C2semidirect
5. #19136783C2semidirect
6. #19136778C2semidirect
7. #19136773C2semidirect
8. #19136377C2semidirect
9. #19136302C2semidirect
10. C2×C22⋊(C43⋊C16)C2semidirect
21. #14582726C22semidirect
22. #14582726C22semidirect
23. #14582724C22semidirect
24. #14582724C22semidirect
25. #14582703C22semidirect
26. #14582703C22semidirect
27. #14582700C22semidirect
28. #14582700C22semidirect
254. C43#33645semidirect

Maximal subgroups

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

subgroupindex
C2×#145829372
#191368002
#191367952
#191367902
#191367832
#191367782
#191367732
#191363772
#191363022
C2×C22⋊(C43⋊C16)2
C43×#30502
#3364543