Finite Group Databasebeta

← #24989137

Subgroups — #24989137

Order 11008.

656 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583511C211yesmaximal, characteristic
2#19133320C212yesmaximal, complemented
3#19133221C212yesmaximal, complemented
4#19132929C211yesmaximal, characteristic
5C43×#1464C211yesmaximal, characteristic
6#14583511—24no—
7#14583511—24no—
8C2×#13063325C2211yescharacteristic
9C2×#13063318—21no—
10C2×#13063318—21no—
11C2×#13063317C2211yescharacteristic
12C2×#13063315—21no—
13C2×#13063315—21no—
14C2×#13063304C411yescharacteristic
15C2×#13063304C411yescharacteristic
16C2×C4×Dic86C411yescharacteristic
17C2×C4×Dic86C411yescharacteristic
18#14582956C2212yes—
19#14582647—24no—
20#14582640—24no—
21#14582625—21no—
22#14582623—21no—
23C2×#117×C43C2211yescharacteristic
24C43×#432C2212yes—
25C43×#324—21no—
26C43×#323—21no—
27C22×Dic86C2×C411yescharacteristic
28C22×Dic86C2×C411yescharacteristic
29#13063325—22no—
30#13063325D414yes—
31#13063318—28no—
32#13063318—28no—
33#13063317—22no—
34#13063317D414yes—
35#13063315—28no—
36#13063315—28no—
37#13063304—22no—
38#13063304—22no—
39#13063304—22no—
40#13063304—22no—
41C4×Dic86—22no—
42C4×Dic86—22no—
43C4×Dic86—22no—
44C4×Dic86—22no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C4×Dic43—21no—
58C2×C4×Dic43—21no—
59C4⋊(C43⋊C8)—22no—
60C22⋊(C43⋊C8)—22no—
61#13063236—22no—
62C23×C4×C43C2×C411yescharacteristic
63#117×C43—22no—
64#117×C43—22no—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C4⋊C4×C43D411yescharacteristic
67C2×C22⋊C4×C43D411yescharacteristic
68C2×C22⋊C4×C43D411yescharacteristic
69C2×C42×C43C2×C411yescharacteristic
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—22no—
72C22⋊C8×C43—22no—
73#97×C43—22no—
74C24×C43C22⋊C411yescharacteristic
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—42no—
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C22⋊C411yescharacteristic
81C22×C4×C43C22×C411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C2×Dic86—21no—
89C2×Dic86—21no—
90C2×Dic86—42no—
91C2×Dic86—42no—
92C2×Dic86C22⋊C412yes—
93C2×Dic86C22⋊C412yes—
94C2×C8×C43—42no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C42×C43—21no—
100C42×C43—21no—
101C42×C43C2×D412yes—
102C42×C43C2×D412yes—
103C22⋊Dic43—24no—
104C22⋊Dic43—24no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C4⋊Dic43—24no—
108C4⋊Dic43—24no—
109C4⋊Dic43C22⋊C412yes—
110C4⋊Dic43C22⋊C412yes—
111Dic43⋊C4—24no—
112Dic43⋊C4—24no—
113Dic43⋊C4—24no—
114Dic43⋊C4—24no—
115Dic43⋊C4—24no—
116Dic43⋊C4—24no—
117C4×Dic43—24no—
118C4×Dic43—24no—
119C2×C43⋊C8—42no—
120C23×C43—21no—
121C23×C43—22no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43C2×C22⋊C411yescharacteristic
125C2×C4×C43—22no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—22no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—42no—
133C2×C4×C43—42no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43C2×C22⋊C411yescharacteristic
137C2×C4×C43C2×C22⋊C411yescharacteristic
138C2×C4×C43#12012yes—
139C2×C4×C43#12012yes—
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147C2×Dic43—42no—
148Dic86—42no—
149Dic86—42no—
150Dic86—42no—
151Dic86—42no—
152C8×C43—82no—
153C43⋊C8—82no—
154#8527—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—82no—
161C22×C43#37911yescharacteristic
162C22×C43#41312yes—
163C4×C43—22no—
164C4×C43—22no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170Dic43—42no—
171Dic43—42no—
172Dic43—42no—
173Dic43—42no—
174C2×#541—431no—
175#1558—432no—
176#1534—432no—
177#1464—431no—
178#1464D4311yescharacteristic
179C2×C43—22no—
180C2×C43—81no—
181C2×C43#178511yescharacteristic
182C2×C43#179611yescharacteristic
183C2×C43#179611yescharacteristic
184#541—864no—
185#541—864no—
186C2×C4⋊Q8—431no—
187C2×#126—861no—
188C2×#126—861no—
189C2×#125—431no—
190C2×#125—861no—
191C2×#125—861no—
192C2×C22⋊Q8—431no—
193C2×C22⋊Q8—431no—
194C2×C4×Q8—431no—
195C2×C4×Q8—431no—
196C2×#117C2×D4311yescharacteristic
197#432—432no—
198#432C2×D4312yes—
199#333—864no—
200#330—864no—
201#324—21no—
202#324—861no—
203#323—21no—
204#323—861no—
205C43#852711yescharacteristic, complemented, Sylow
206C22×Q8—431no—
207C22×Q8—431no—
208C23×C4C4×D4311yescharacteristic
209C4⋊Q8—434no—
210C4⋊Q8—862no—
211#126—868no—
212#126—868no—
213#125—434no—
214#125—868no—
215#125—868no—
216#125—862no—
217C22⋊Q8—862no—
218C22⋊Q8—862no—
219C22⋊Q8—862no—
220C22⋊Q8—862no—
221C4×Q8—862no—
222C4×Q8—862no—
223C4×Q8—862no—
224C4×Q8—862no—
225#117—22no—
226#117—22no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4D17211yescharacteristic
238C2×C4⋊C4C22⋊D4311yescharacteristic
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4D17211yescharacteristic
242C2×C22⋊C4C22⋊D4311yescharacteristic
243C2×C42—861no—
244C2×C42—861no—
245C2×C42C4×D4311yescharacteristic
246C2×C42C22×D4311yescharacteristic
247C4⋊C8—22no—
248C4⋊C8—862no—
249C22⋊C8—22no—
250C22⋊C8—862no—
251#97—22no—
252#97—862no—
253C24(C2×D43)⋊C411yescharacteristic
254C2×Q8—432no—
255C2×Q8—432no—
256C2×Q8—861no—
257C2×Q8—861no—
258C2×Q8—1722no—
259C2×Q8—1722no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4(C2×D43)⋊C411yescharacteristic
268C22×C4(C2×D43)⋊C411yescharacteristic
269C22×C4(C2×D43)⋊C411yescharacteristic
270C22×C4C2×C4×D4311yescharacteristic
271C22×C4C2×D17211yescharacteristic
272C22×C4C2×C22⋊D4311yescharacteristic
273C2×C8—42no—
274C2×C8—1722no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—432no—
278C4⋊C4—432no—
279C4⋊C4—864no—
280C4⋊C4—864no—
281C4⋊C4—864no—
282C4⋊C4—864no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—864no—
286C4⋊C4—864no—
287C4⋊C4—864no—
288C4⋊C4—864no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—864no—
292C22⋊C4—864no—
293C42—21no—
294C42—21no—
295C42—864no—
296C42—864no—
297C42D4×D4312yes—
298C42D4×D4312yes—
299C23—21no—
300C23—22no—
301C23—41no—
302C23—41no—
303C23C2×(C2×D43)⋊C411yescharacteristic
304Q8—1722no—
305Q8—1722no—
306Q8—1722no—
307Q8—1722no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—862no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—862no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4—1722no—
326C2×C4—1722no—
327C2×C4C22⋊C4×D4311yescharacteristic
328C2×C4C22⋊C4×D4311yescharacteristic
329C2×C4#1306329312yes—
330C2×C4#1306329512yes—
331C8—82no—
332C8—3442no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—82no—
339C22#1458275411yescharacteristic
340C22#1458288112yes—
341C4—21no—
342C4—21no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—1722no—
349C4—1722no—
350C4—1722no—
351C4—1722no—
352C2—22no—
353C2—81no—
354C2#1913452111yescharacteristic
355C2#1913456811yescharacteristic
356C2#1913457111yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1464C2
socleC22×C43#379
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1464D43
hypocenterC43#8527
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #19133320C2semidirect
3. #19133221C2semidirect
205. C43#8527semidirect

Maximal subgroups

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

subgroupindex
C2×#145835112
#191333202
#191332212
#191329292
C43×#14642
#852743