Finite Group Databasebeta

← #25080469

Subgroups — #25080469

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145174C211yesmaximal, characteristic
2#19144718C212yesmaximal, complemented
3C2×C8×Dic86C211yesmaximal, characteristic, complemented
4#19134012C214yesmaximal, complemented
5#19134000C212yesmaximal, complemented
6#19133956C212yesmaximal, complemented
7#19133291C212yesmaximal, complemented
8C43×#1568C211yesmaximal, characteristic, complemented
9#14583449C2212yes—
10C2×C4×Dic86C2211yescharacteristic
11#14583304C2211yescharacteristic
12#14583276C2211yescharacteristic
13#14583246C2212yes—
14#14583213—22no—
15#14583195C2214yes—
16#14583135—21no—
17#14583135—21no—
18#14583100C2214yes—
19#14583040—22no—
20C8×Dic86—21no—
21C8×Dic86—21no—
22C8×Dic86C2212yes—
23C8×Dic86C2212yes—
24#14583001—24no—
25C4×D344—21no—
26C4×D344—21no—
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×Dic43⋊C8—21no—
29C2×C8×Dic43—21no—
30#14582647C2214yes—
31#14582642C2214yes—
32C43×#432C2212yes—
33C2×C4×C8×C43C2211yescharacteristic
34C43×#335C2212yes—
35C43×#334C2212yes—
36C2×#10621898—22no—
37C22×Dic86D411yescharacteristic
38C2×#10621873—24no—
39C2×D344—21no—
40C2×D344—21no—
41C22×C43⋊C8—21no—
42#13063325C2312yes—
43#13063322C2312yes—
44#13063313—22no—
45#13063299—22no—
46#13063299—22no—
47C4×Dic86—21no—
48C4×Dic86—21no—
49C4×Dic86D412yes—
50C4×Dic86C2312yes—
51C4×D172—22no—
52C4×D172—22no—
53C2×C4⋊Dic43D411yescharacteristic
54C2×Dic43⋊C4—21no—
55C2×C4×Dic43—21no—
56#13063259—21no—
57#13063259—21no—
58#13063259—24no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)C2312yes—
61Dic43⋊C8—22no—
62Dic43⋊C8—22no—
63#13063250—24no—
64#13063247—22no—
65#13063247—22no—
66#13063247—24no—
67C8×Dic43—22no—
68C8×Dic43—22no—
69C22×C8×C43D411yescharacteristic
70C22×C8×C43D411yescharacteristic
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43C2314yes—
73C22⋊C8×C43—22no—
74#97×C43—22no—
75C4×C8×C43D411yescharacteristic
76C4×C8×C43D411yescharacteristic
77C4×C8×C43C2311yescharacteristic
78C4×C8×C43C2311yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C2×C22⋊D43—42no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85#10621898—84no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—22no—
89C2×C4×D43—42no—
90C2×Dic86—21no—
91C2×Dic86—24no—
92C2×Dic86—22no—
93C2×Dic86C2×D412yes—
94C2×C8×C43—22no—
95C2×C8×C43—24no—
96C2×C8×C43—41no—
97C2×C8×C43C2×D411yescharacteristic
98C2×C8×C43C2×D411yescharacteristic
99C2×C8×C43C2×D411yescharacteristic
100C2×C8×C43C2×D411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43#4111yescharacteristic
104C42×C43C2411yescharacteristic
105(C2×D43)⋊C4—42no—
106(C2×D43)⋊C4—42no—
107C4⋊Dic43—21no—
108C4⋊Dic43—22no—
109C4⋊Dic43—22no—
110C4⋊Dic43C2×D412yes—
111Dic43⋊C4—22no—
112Dic43⋊C4—22no—
113C4×Dic43—22no—
114C4×Dic43—22no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—42no—
117D344—42no—
118D344—42no—
119#10621873—48no—
120C23×C43#12111yescharacteristic
121C22×D43—42no—
122C2×C4×C43—22no—
123C2×C4×C43—22no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12111yescharacteristic
129C2×C4×C43C22×D411yescharacteristic
130C2×C4×C43C22×D411yescharacteristic
131C2×C4×C43C2×#4111yescharacteristic
132C22⋊D43—84no—
133C2×Dic43—24no—
134C2×Dic43—22no—
135C2×Dic43—22no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138D172—44no—
139D172—42no—
140D172—42no—
141D172—82no—
142C4×D43—84no—
143Dic86—24no—
144Dic86—22no—
145Dic86—82no—
146Dic86#13514yes—
147C8×C43—21no—
148C8×C43—21no—
149C8×C43—21no—
150C8×C43—44no—
151C8×C43#13712yes—
152C43⋊C8—42no—
153#19264—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#47212yes—
157C22×C43C2×#12111yescharacteristic
158C2×D43—82no—
159C2×D43—82no—
160C2×D43—82no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43C2×#13512yes—
166C4×C43C2×#13711yescharacteristic
167C4×C43#57511yescharacteristic
168Dic43—24no—
169Dic43—42no—
170Dic43—82no—
171#3169—431no—
172#3112—432no—
173C2×C8×Q8—431no—
174#1678—434no—
175#1676—432no—
176#1668—432no—
177#1568D4311yescharacteristic, complemented
178#1551—432no—
179C2×C43—22no—
180C2×C43#303711yescharacteristic
181C2×C43#305011yescharacteristic
182C2×C43C2×#47211yescharacteristic
183D43—162no—
184#532—432no—
185C2×C4×Q8—431no—
186#500—431no—
187#493—431no—
188#486—432no—
189#480—862no—
190#477—434no—
191#466—861no—
192#466—861no—
193#460—434no—
194#448—862no—
195C8×Q8—432no—
196C8×Q8—432no—
197C8×Q8—861no—
198C8×Q8—861no—
199#440—864no—
200C4×D8—861no—
201C4×D8—861no—
202#432C2×D4312yes—
203C2×C4⋊C8—431no—
204C2×C4⋊C8—861no—
205C2×C4×C8—861no—
206C2×C4×C8C2×D4311yescharacteristic
207#335C2×D4312yes—
208#334C2×D4312yes—
209#333—434no—
210#331—434no—
211C43#1926411yescharacteristic, complemented, Sylow
212C2×#41—862no—
213C22×Q8—431no—
214C2×SD16—864no—
215C2×D8—861no—
216C2×D8—861no—
217C22×C8—861no—
218C22×C8D17211yescharacteristic
219C22×C8D17211yescharacteristic
220C4⋊Q8—432no—
221#127—432no—
222#124—862no—
223#121—862no—
224#121—862no—
225C4×Q8—432no—
226C4×Q8—432no—
227C4×Q8—861no—
228C4×Q8—861no—
229C4×D4—862no—
230C4×D4—862no—
231C2×C4⋊C4—431no—
232C2×C4⋊C4—861no—
233C2×C42—861no—
234C2×C42C22×D4311yescharacteristic
235#107—864no—
236#107—861no—
237#107—861no—
238C4⋊C8—432no—
239C4⋊C8—862no—
240C4⋊C8—862no—
241C4⋊C8—861no—
242C4⋊C8C22×D4314yes—
243#103—864no—
244#102—864no—
245#102—862no—
246#102—862no—
247C22⋊C8—22no—
248#97—22no—
249C4×C8—862no—
250C4×C8—862no—
251C4×C8D17211yescharacteristic
252C4×C8D17211yescharacteristic
253C4×C8C22×D4311yescharacteristic
254C4×C8C22×D4311yescharacteristic
255#41—3444no—
256C2×Q8—432no—
257C2×Q8—864no—
258C2×Q8—861no—
259C2×Q8—862no—
260C2×D4—862no—
261C2×D4—862no—
262C2×D4—862no—
263C2×D4—1722no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—1722no—
267C22×C4C2×D17211yescharacteristic
268C22×C4D4×D4311yescharacteristic
269C22×C4#1062190211yescharacteristic
270SD16—1728no—
271D8—1722no—
272D8—1722no—
273C2×C8—22no—
274C2×C8—24no—
275C2×C8—41no—
276C2×C8—862no—
277C2×C8—1722no—
278C2×C8C2×D17211yescharacteristic
279C2×C8C2×D17211yescharacteristic
280C2×C8C2×D17211yescharacteristic
281C2×C8C2×D17211yescharacteristic
282C4⋊C4—432no—
283C4⋊C4—861no—
284C4⋊C4—862no—
285C4⋊C4—862no—
286C4⋊C4—862no—
287C4⋊C4—862no—
288C22⋊C4—1722no—
289C22⋊C4—1722no—
290C42—862no—
291C42—862no—
292C42C2×D17211yescharacteristic
293C42D4×D4311yescharacteristic
294C42#1062190211yescharacteristic
295C42C23×D4311yescharacteristic
296C23—1722no—
297C23#1306330011yescharacteristic
298Q8—434no—
299Q8—864no—
300Q8—862no—
301Q8—3442no—
302D4—3442no—
303D4—3444no—
304D4—1724no—
305D4—1722no—
306D4—1722no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—864no—
312C2×C4—862no—
313C2×C4—862no—
314C2×C4—3444no—
315C2×C4—1722no—
316C2×C4—1722no—
317C2×C4#1306330011yescharacteristic
318C2×C4#1306330011yescharacteristic
319C2×C4#1306330011yescharacteristic
320C2×C4C2×D4×D4311yescharacteristic
321C2×C4C22×D17211yescharacteristic
322C2×C4C2×#1062190211yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—44no—
327C8—1722no—
328C8#1306335812yes—
329C22—21no—
330C22—21no—
331C22—3442no—
332C22—3442no—
333C22—3442no—
334C22#1458317012yes—
335C22C2×#1306330011yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—864no—
341C4—3442no—
342C4—1722no—
343C4#135×D4312yes—
344C4C2×#1306335811yescharacteristic
345C4#1458369911yescharacteristic
346C2—22no—
347C2—6882no—
348C2#1914406911yescharacteristic
349C2#1914417711yescharacteristic
350C2C2×#1458317011yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1568C2
socleC22×C43C2×#121
prime radical#19145174C2
hypercenter#1568D43
hypocenterC43#19264
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
2. #19144718C2semidirect
3. C2×C8×Dic86C2semidirect
4. #19134012C2semidirect
5. #19134000C2semidirect
6. #19133956C2semidirect
7. #19133291C2semidirect
8. C43×#1568C2semidirect
177. #1568D43semidirect
211. C43#19264semidirect

Maximal subgroups

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

subgroupindex
#191451742
#191447182
C2×C8×Dic862
#191340122
#191340002
#191339562
#191332912
C43×#15682
#1926443