Finite Group Databasebeta

← #25081766

Subgroups — #25081766

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145522C211yesmaximal, characteristic, complemented
2C2×#14583179C211yesmaximal, characteristic, complemented
3#19144059C211yesmaximal, characteristic
4#19134018C214yesmaximal, complemented
5#19133936C214yesmaximal, complemented
6#19133366C211yesmaximal, characteristic, complemented
7#19133279C211yesmaximal, characteristic, complemented
8#19133242C211yesmaximal, characteristic, complemented
9C43×#2972C211yesmaximal, characteristic, complemented
10C2×#13063351—21no—
11#14583449C2211yescharacteristic
12C2×#13063325C2211yescharacteristic
13#14583272C2212yescomplemented
14#14583250C2212yescomplemented
15#14583179—22no—
16#14583179C2214yes—
17#14583114—22no—
18#14583105—22no—
19#14583104C2212yes—
20#14583094C2212yes—
21#14583040—22no—
22C2×#13063258—21no—
23#14582923C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25#14582898—21no—
26C2×#13063246—21no—
27#14582650C2214yescomplemented
28#14582646C2214yescomplemented
29#14582644C2212yescomplemented
30#14582642C2212yescomplemented
31C2×C4×D4×C43C2211yescharacteristic
32C8×D4×C43—22no—
33C8×D4×C43C2214yes—
34C43×#431C2211yescharacteristic
35C43×#431C2211yescharacteristic
36C2×C22⋊C8×C43—22no—
37C2×#10621898—21no—
38C22×Dic86—21no—
39#13063351—44no—
40C2×#10621873—24no—
41C2×#10621883—22no—
42C2×#10621882—22no—
43C2×#10621877—21no—
44C22×C43⋊C8—21no—
45#13063325—21no—
46#13063325—21no—
47#13063325—21no—
48#13063325C2311yescharacteristic
49#13063325C2312yes—
50#13063322C2311yescharacteristic
51#13063313—21no—
52#13063299—21no—
53#13063299—21no—
54C4×D172—21no—
55C4×D172—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58#13063258—24no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)C2312yes—
62C4⋊(C43⋊C8)C2312yes—
63#13063250—24no—
64#13063248—22no—
65#13063246—24no—
66#13063245—22no—
67C22×D4×C43D411yescharacteristic
68C23×C4×C43—21no—
69C22×C8×C43—24no—
70C4×D4×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43D412yes—
73C4×D4×C43C2312yes—
74C2×C4⋊C4×C43D411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43D412yes—
78C4⋊C8×C43C2312yes—
79C22⋊C8×C43—21no—
80C22⋊C8×C43—24no—
81C22⋊C8×C43D412yes—
82C4×C8×C43—21no—
83C4×C8×C43C2312yes—
84C24×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—22no—
87C2×D4×C43SD1614yescomplemented
88C2×D4×C43C2×D412yes—
89C22×C4×C43—22no—
90C22×C4×C43—22no—
91C22×C4×C43—21no—
92C22×C4×C43—82no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C2×C22⋊D43—41no—
97C22×Dic43—41no—
98#10621898—42no—
99#10621898—42no—
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—21no—
103C2×C4×D43—41no—
104C2×Dic86—21no—
105C2×Dic86—22no—
106C2×Dic86—41no—
107C2×Dic86—82no—
108C2×C8×C43—22no—
109C2×C8×C43—84no—
110C2×C8×C43C2×D414yes—
111C4⋊C4×C43—21no—
112C4⋊C4×C43C2×D412yes—
113C22⋊C4×C43—22no—
114C22⋊C4×C43—22no—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118C42×C43C2411yescharacteristic
119#10621883—44no—
120#10621882—44no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—41no—
123C4⋊Dic43—22no—
124C4⋊Dic43—21no—
125C4⋊Dic43—22no—
126C4⋊Dic43—21no—
127C4⋊Dic43—41no—
128C4⋊Dic43—41no—
129#10621877—42no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8—42no—
133#10621873—84no—
134C23×C43—22no—
135C23×C43—24no—
136C23×C43—81no—
137C23×C43—81no—
138C23×C43#12111yescharacteristic
139C22×D43—41no—
140D4×C43—22no—
141D4×C43—24no—
142D4×C43C2×SD1614yes—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—44no—
147C2×C4×C43—82no—
148C2×C4×C43—81no—
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43C2×SD1612yes—
153C2×C4×C43#13512yes—
154C2×C4×C43C22×D411yescharacteristic
155C2×C4×C43C22×D411yescharacteristic
156C2×C4×C43C2×#4111yescharacteristic
157C22⋊D43—82no—
158C2×Dic43—42no—
159C2×Dic43—41no—
160C2×Dic43—82no—
161D172—41no—
162D172—41no—
163D172—42no—
164D172—81no—
165C4×D43—82no—
166Dic86—41no—
167Dic86—41no—
168Dic86—44no—
169Dic86—82no—
170C8×C43—24no—
171C8×C43—42no—
172C43⋊C8—42no—
173C43⋊C8—42no—
174#19385—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—24no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—84no—
181C22×C43#46512yes—
182C22×C43C2×#12111yescharacteristic
183C2×D43—81no—
184C2×D43—81no—
185C2×D43—81no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—42no—
190C4×C43#46512yes—
191C4×C43C22×SD1611yescharacteristic
192C4×C43C2×#13511yescharacteristic
193C4×C43#57612yes—
194Dic43—82no—
195Dic43—81no—
196#3206—431no—
197C2×#474—431no—
198#3036—431no—
199#2972D4311yescharacteristic, complemented
200#1679—434no—
201#1665—434no—
202#1570—431no—
203#1549—431no—
204#1540—431no—
205C2×C43—22no—
206C2×C43—44no—
207C2×C43#304111yescharacteristic
208C2×C43C2×#46511yescharacteristic
209C2×C43#306911yescharacteristic
210D43—161no—
211C2×AGL(1,ℤ/8)—861no—
212#532—431no—
213C2×C4⋊Q8—431no—
214C2×C4×D4C2×D4311yescharacteristic
215#492—432no—
216#487—432no—
217#474—434no—
218#474—862no—
219#463—862no—
220#461—432no—
221#461—862no—
222#459—432no—
223#448—862no—
224C8×D4—22no—
225C8×D4C2×D4314yes—
226#431C2×D4311yescharacteristic
227#431C2×D4311yescharacteristic
228C2×#107—861no—
229#423—431no—
230C2×C4⋊C8—431no—
231#417—861no—
232C2×#102—861no—
233C2×C22⋊C8—22no—
234#334—434no—
235#332—432no—
236#332—434no—
237#331—432no—
238C43#1938511yescharacteristic, complemented, Sylow
239C2×#41—861no—
240C22×Q8—861no—
241C22×D4D17211yescharacteristic
242C23×C4—21no—
243AGL(1,ℤ/8)—1724no—
244C2×SD16—862no—
245C2×SD16—864no—
246C2×D8—862no—
247C2×M16—861no—
248C22×C8—24no—
249C22×C8—861no—
250C4⋊Q8—432no—
251C4⋊Q8—431no—
252C4⋊Q8—861no—
253C4⋊Q8—861no—
254C4⋊Q8—861no—
255#127—431no—
256#124—861no—
257#121—861no—
258#121—861no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—861no—
262C4×D4—861no—
263C4×D4D17212yes—
264C4×D4C22×D4312yes—
265C2×C4⋊C4—861no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4D17211yescharacteristic
268C2×C22⋊C4—21no—
269C2×C42C22×D4311yescharacteristic
270#107—864no—
271C4⋊C8—432no—
272C4⋊C8—432no—
273C4⋊C8—861no—
274C4⋊C8—861no—
275C4⋊C8C22⋊D4312yes—
276C4⋊C8C22×D4312yes—
277#103—864no—
278#103—862no—
279#102—864no—
280#102—862no—
281C22⋊C8—21no—
282C22⋊C8—24no—
283C22⋊C8C22⋊D4312yes—
284C4×C8—21no—
285C4×C8C22×D4312yes—
286C24—21no—
287#41—1722no—
288#41—1722no—
289C2×Q8—862no—
290C2×Q8—861no—
291C2×Q8—3442no—
292C2×Q8—1721no—
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4—1721no—
299C2×D4#1062187314yescomplemented
300C2×D4C2×D17212yes—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—82no—
305C22×C4—1721no—
306C22×C4—1721no—
307C22×C4C2×D17211yescharacteristic
308C22×C4#1062189811yescharacteristic
309C22×C4C2×C22⋊D4311yescharacteristic
310SD16—3444no—
311SD16—1724no—
312D8—1724no—
313M16—1722no—
314C2×C8—22no—
315C2×C8—84no—
316C2×C8—862no—
317C2×C8—862no—
318C2×C8—1722no—
319C2×C8C2×C22⋊D4314yes—
320C4⋊C4—21no—
321C4⋊C4—861no—
322C4⋊C4—862no—
323C4⋊C4—862no—
324C4⋊C4—861no—
325C4⋊C4—1721no—
326C4⋊C4—1721no—
327C4⋊C4C2×D17212yes—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—1721no—
331C22⋊C4—1721no—
332C42C2×D17211yescharacteristic
333C42#1062189811yescharacteristic
334C42C2×C22⋊D4311yescharacteristic
335C42C23×D4311yescharacteristic
336C23—22no—
337C23—24no—
338C23—81no—
339C23—81no—
340C23—1721no—
341C23#1306329911yescharacteristic
342Q8—3442no—
343Q8—1721no—
344Q8—1721no—
345Q8—1724no—
346D4—24no—
347D4—22no—
348D4—3441no—
349D4—3442no—
350D4—1721no—
351D4—1721no—
352D4—1722no—
353D4C2×#1062187314yes—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—44no—
358C2×C4—82no—
359C2×C4—81no—
360C2×C4—3442no—
361C2×C4—3442no—
362C2×C4—1721no—
363C2×C4—1722no—
364C2×C4#1306329911yescharacteristic
365C2×C4#1306329911yescharacteristic
366C2×C4#1306329911yescharacteristic
367C2×C4C2×#1062187312yes—
368C2×C4#1306334712yes—
369C2×C4C22×C22⋊D4311yescharacteristic
370C2×C4C22×D17211yescharacteristic
371C2×C4C2×#1062189811yescharacteristic
372C8—24no—
373C8—42no—
374C8—1722no—
375C8—1722no—
376C22—21no—
377C22—21no—
378C22—24no—
379C22—42no—
380C22—42no—
381C22—84no—
382C22—3441no—
383C22—3441no—
384C22—3441no—
385C22#1458312812yes—
386C22C2×#1306329911yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—3442no—
392C4—3441no—
393C4#1458312812yes—
394C4C22×#1062187311yescharacteristic
395C4C2×#1306334711yescharacteristic
396C4#1458370212yes—
397C2—22no—
398C2—44no—
399C2—6881no—
400C2#1914409811yescharacteristic
401C2C2×#1458312811yescharacteristic
402C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2972C2
socleC22×C43C2×#121
prime radical#19144059C2
hypercenter#2972D43
hypocenterC43#19385
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #19145522C2semidirect
2. C2×#14583179C2semidirect
4. #19134018C2semidirect
5. #19133936C2semidirect
6. #19133366C2semidirect
7. #19133279C2semidirect
8. #19133242C2semidirect
9. C43×#2972C2semidirect
13. #14583272C22semidirect
14. #14583250C22semidirect
27. #14582650C22semidirect
28. #14582646C22semidirect
29. #14582644C22semidirect
30. #14582642C22semidirect
87. C2×D4×C43SD16semidirect
199. #2972D43semidirect
238. C43#19385semidirect
299. C2×D4#10621873semidirect

Maximal subgroups

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

subgroupindex
#191455222
C2×#145831792
#191440592
#191340182
#191339362
#191333662
#191332792
#191332422
C43×#29722
#1938543