Finite Group Databasebeta

← #25081882

Subgroups — #25081882

Order 11008.

656 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145522C211yesmaximal, characteristic
2C2×#14583184C211yesmaximal, characteristic, complemented
3#19144067C211yesmaximal, characteristic
4#19134025C214yesmaximal, complemented
5#19133943C214yesmaximal, complemented
6#19133366C211yesmaximal, characteristic, complemented
7#19133279C211yesmaximal, characteristic, complemented
8#19133242C211yesmaximal, characteristic
9C43×#2982C211yesmaximal, characteristic, complemented
10C2×#13063356—21no—
11#14583449C2211yescharacteristic
12C2×#13063325C2211yescharacteristic
13#14583272C2212yes—
14#14583250C2212yes—
15#14583184—22no—
16#14583184C2214yes—
17#14583121—22no—
18#14583109C2212yes—
19#14583105—22no—
20#14583099C2212yes—
21#14583040—22no—
22C2×#13063256—21no—
23#14582923C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25#14582898—21no—
26C2×#13063249—21no—
27#14582650C2214yes—
28#14582646C2214yes—
29#14582644C2212yes—
30#14582642C2212yes—
31C2×C4×Q8×C43C2211yescharacteristic
32C8×Q8×C43—22no—
33C8×Q8×C43C2214yes—
34C43×#431—22no—
35C43×#431C2211yescharacteristic
36C43×#431C2211yescharacteristic
37C2×#10621898—21no—
38C22×Dic86—21no—
39#13063356—44no—
40C2×#10621885—22no—
41C2×#10621873—24no—
42C2×#10621884—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#13063256—24no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)C2312yes—
62C4⋊(C43⋊C8)C2312yes—
63#13063250—24no—
64#13063249—24no—
65#13063248—22no—
66#13063245—22no—
67C22×Q8×C43D411yescharacteristic
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43D412yes—
71C4×Q8×C43C2312yes—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—24no—
77C4⋊C8×C43D412yes—
78C4⋊C8×C43C2312yes—
79C22⋊C8×C43—21no—
80C22⋊C8×C43D412yes—
81C4×C8×C43—24no—
82C4×C8×C43—21no—
83C4×C8×C43C2312yes—
84C2×Q8×C43—21no—
85C2×Q8×C43—22no—
86C2×Q8×C43SD1614yescomplemented
87C2×Q8×C43C2×D412yes—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C2×C22⋊D43—41no—
94C22×Dic43—41no—
95#10621898—42no—
96#10621898—42no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—21no—
100C2×C4×D43—41no—
101C2×Dic86—21no—
102C2×Dic86—22no—
103C2×Dic86—41no—
104C2×Dic86—82no—
105C2×C8×C43—22no—
106C2×C8×C43C2×D414yes—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43C2×D412yes—
111C42×C43—22no—
112C42×C43—22no—
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43#4111yescharacteristic
116C42×C43C2411yescharacteristic
117#10621885—44no—
118#10621884—44no—
119(C2×D43)⋊C4—41no—
120(C2×D43)⋊C4—41no—
121C4⋊Dic43—22no—
122C4⋊Dic43—21no—
123C4⋊Dic43—22no—
124C4⋊Dic43—21no—
125C4⋊Dic43—41no—
126C4⋊Dic43—41no—
127#10621877—42no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—42no—
131#10621873—84no—
132C23×C43#12111yescharacteristic
133C22×D43—41no—
134Q8×C43—22no—
135Q8×C43—24no—
136Q8×C43C2×SD1614yes—
137C2×C4×C43—22no—
138C2×C4×C43—24no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—81no—
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43C2×SD1612yes—
147C2×C4×C43#13512yes—
148C2×C4×C43C22×D411yescharacteristic
149C2×C4×C43C22×D411yescharacteristic
150C2×C4×C43C2×#4111yescharacteristic
151C22⋊D43—82no—
152C2×Dic43—42no—
153C2×Dic43—41no—
154C2×Dic43—82no—
155D172—41no—
156D172—41no—
157D172—42no—
158D172—81no—
159C4×D43—82no—
160Dic86—41no—
161Dic86—41no—
162Dic86—44no—
163Dic86—82no—
164C8×C43—24no—
165C8×C43—42no—
166C43⋊C8—42no—
167C43⋊C8—42no—
168#19397—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43#46512yes—
172C22×C43C2×#12111yescharacteristic
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C4×C43—21no—
177C4×C43—24no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—42no—
181C4×C43#46512yes—
182C4×C43C22×SD1611yescharacteristic
183C4×C43C2×#13511yescharacteristic
184C4×C43#57712yes—
185Dic43—82no—
186Dic43—81no—
187#3206—431no—
188C2×#475—431no—
189#3037—431no—
190#2982D4311yescharacteristic, complemented
191#1680—434no—
192#1666—434no—
193#1570—431no—
194#1549—431no—
195#1540—431no—
196C2×C43—22no—
197C2×C43#304311yescharacteristic
198C2×C43C2×#46511yescharacteristic
199C2×C43#306911yescharacteristic
200D43—161no—
201C2×#137—861no—
202#532—431no—
203C2×C4⋊Q8—431no—
204C2×C4×Q8C2×D4311yescharacteristic
205#492—432no—
206#487—432no—
207#475—434no—
208#475—862no—
209#464—862no—
210#462—432no—
211#461—862no—
212#460—432no—
213#448—862no—
214C8×Q8—22no—
215C8×Q8C2×D4314yes—
216#431—22no—
217#431C2×D4311yescharacteristic
218#431C2×D4311yescharacteristic
219C2×#106—861no—
220#423—431no—
221C2×C4⋊C8—431no—
222#417—861no—
223C2×#103—861no—
224#334—434no—
225#332—432no—
226#332—434no—
227#331—432no—
228C43#1939711yescharacteristic, complemented, Sylow
229C2×#41—861no—
230C22×Q8—861no—
231C22×Q8D17211yescharacteristic
232#137—1724no—
233C2×Q16—862no—
234C2×SD16—862no—
235C2×SD16—864no—
236C2×M16—861no—
237C22×C8—861no—
238C4⋊Q8—432no—
239C4⋊Q8—431no—
240C4⋊Q8—861no—
241C4⋊Q8—861no—
242C4⋊Q8—861no—
243#127—431no—
244#124—861no—
245#121—861no—
246#121—861no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8D17212yes—
250C4×Q8C22×D4312yes—
251C4×D4—861no—
252C4×D4—861no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4D17211yescharacteristic
257C2×C42—21no—
258C2×C42C22×D4311yescharacteristic
259#106—864no—
260C4⋊C8—24no—
261C4⋊C8—432no—
262C4⋊C8—432no—
263C4⋊C8—861no—
264C4⋊C8—861no—
265C4⋊C8C22⋊D4312yes—
266C4⋊C8C22×D4312yes—
267#103—864no—
268#103—864no—
269#103—862no—
270#102—862no—
271C22⋊C8—21no—
272C22⋊C8C22⋊D4312yes—
273C4×C8—24no—
274C4×C8—21no—
275C4×C8C22×D4312yes—
276#41—1722no—
277#41—1722no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—862no—
281C2×Q8—861no—
282C2×Q8—3442no—
283C2×Q8—1721no—
284C2×Q8#1062187314yescomplemented
285C2×Q8C2×D17212yes—
286C2×D4—861no—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—1721no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—1721no—
293C22×C4—1721no—
294C22×C4C2×D17211yescharacteristic
295C22×C4#1062189811yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297Q16—1724no—
298SD16—3444no—
299SD16—1724no—
300M16—1722no—
301C2×C8—22no—
302C2×C8—862no—
303C2×C8—862no—
304C2×C8—1722no—
305C2×C8C2×C22⋊D4314yes—
306C4⋊C4—22no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—861no—
310C4⋊C4—862no—
311C4⋊C4—862no—
312C4⋊C4—861no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C4⋊C4C2×D17212yes—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C42—22no—
319C42—22no—
320C42C2×D17211yescharacteristic
321C42#1062189811yescharacteristic
322C42C2×C22⋊D4311yescharacteristic
323C42C23×D4311yescharacteristic
324C23—1721no—
325C23#1306329911yescharacteristic
326Q8—24no—
327Q8—22no—
328Q8—3442no—
329Q8—1721no—
330Q8—1721no—
331Q8—1724no—
332Q8C2×#1062187314yes—
333D4—3441no—
334D4—3442no—
335D4—1721no—
336D4—1721no—
337D4—1722no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—3442no—
345C2×C4—3442no—
346C2×C4—1721no—
347C2×C4—1722no—
348C2×C4#1306329911yescharacteristic
349C2×C4#1306329911yescharacteristic
350C2×C4#1306329911yescharacteristic
351C2×C4C2×#1062187312yes—
352C2×C4#1306334712yes—
353C2×C4C22×C22⋊D4311yescharacteristic
354C2×C4C22×D17211yescharacteristic
355C2×C4C2×#1062189811yescharacteristic
356C8—24no—
357C8—42no—
358C8—1722no—
359C8—1722no—
360C22—21no—
361C22—21no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22#1458312812yes—
366C22C2×#1306329911yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—24no—
371C4—42no—
372C4—3442no—
373C4—3441no—
374C4#1458312812yes—
375C4C22×#1062187311yescharacteristic
376C4C2×#1306334711yescharacteristic
377C4#1458370712yes—
378C2—22no—
379C2—6881no—
380C2#1914411611yescharacteristic
381C2C2×#1458312811yescharacteristic
382C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2982C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenter#2982D43
hypocenterC43#19397
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. C2×#14583184C2semidirect
4. #19134025C2semidirect
5. #19133943C2semidirect
6. #19133366C2semidirect
7. #19133279C2semidirect
9. C43×#2982C2semidirect
86. C2×Q8×C43SD16semidirect
190. #2982D43semidirect
228. C43#19397semidirect
284. C2×Q8#10621873semidirect

Maximal subgroups

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

subgroupindex
#191455222
C2×#145831842
#191440672
#191340252
#191339432
#191333662
#191332792
#191332422
C43×#29822
#1939743