Finite Group Databasebeta

← #24999219

Subgroups — #24999219

Order 11008.

510 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
1C2×#14583302C211yesmaximal, characteristic
2C2×#14583194C211yesmaximal, characteristic
3#19135532C211yesmaximal, characteristic
4C2×#14582648C211yesmaximal, characteristic
5C2×#14582647C211yesmaximal, characteristic
6#19132429C211yesmaximal, characteristic
7C2×C43×#477C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9#14583302—22no—
10#14583302—22no—
11#14583194—22no—
12#14583194—22no—
13C2×#13063258—22no—
14C2×#13063258—21no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×C4⋊(C43⋊C8)C2211yescharacteristic
17C2×#13063249—21no—
18C2×C4×C43⋊C8C2211yescharacteristic
19#14582654—22no—
20#14582648—22no—
21#14582647—22no—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#477—22no—
25C43×#477—22no—
26C2×#107×C43—21no—
27C2×C4⋊C8×C43C2211yescharacteristic
28C2×#103×C43—21no—
29C22×Dic86—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8D412yes—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063325D412yes—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39#13063258—28no—
40#13063258—24no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)D412yes—
45#13063249—24no—
46C4×C43⋊C8—21no—
47C4×C43⋊C8—21no—
48C22×Q8×C43—21no—
49C22×Q8×C43D411yescharacteristic
50C22×C8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43D412yes—
55C4×Q8×C43—21no—
56C4×Q8×C43—21no—
57C4×Q8×C43—21no—
58C4×Q8×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C42×C43—21no—
64C2×C42×C43C2311yescharacteristic
65#107×C43—24no—
66C4⋊C8×C43—21no—
67C4⋊C8×C43D412yes—
68#103×C43—24no—
69C2×Q8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—22no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43—41no—
76C2×Q8×C43—82no—
77C2×Q8×C43Q1612yes—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×Dic43—41no—
85C2×Dic86—22no—
86C2×Dic86—41no—
87C2×Dic86—82no—
88C2×C8×C43—22no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C4⋊C4×C43—22no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C42×C43—41no—
100C42×C43—41no—
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43C2×D411yescharacteristic
104C42×C43C2×D411yescharacteristic
105C4⋊Dic43—22no—
106C4⋊Dic43—22no—
107C4⋊Dic43—41no—
108C4⋊Dic43—41no—
109C2×C43⋊C8—22no—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—42no—
116C2×C43⋊C8Q1614yes—
117C23×C43#12111yescharacteristic
118Q8×C43—22no—
119Q8×C43—22no—
120Q8×C43—41no—
121Q8×C43—41no—
122Q8×C43—82no—
123Q8×C43—82no—
124C2×C4×C43—22no—
125C2×C4×C43—22no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—82no—
132C2×C4×C43#12011yescharacteristic
133C2×C4×C43#12011yescharacteristic
134C2×C4×C43#12011yescharacteristic
135C2×C4×C43#12111yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43#12711yescharacteristic
138C2×C4×C43C2×Q1612yes—
139C2×C4×C43C2×Q1611yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×C4×C43#13711yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×C4×C43#13712yes—
144C2×Dic43—42no—
145C2×Dic43—82no—
146Dic86—82no—
147Dic86—82no—
148C8×C43—42no—
149C43⋊C8—24no—
150C43⋊C8—42no—
151C43⋊C8—81no—
152#10279—431nomaximal, Sylow
153C22×C43#39211yescharacteristic
154C22×C43#46212yes—
155C22×C43#46711yescharacteristic
156C22×C43#47011yescharacteristic
157C22×C43#47212yes—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—42no—
161C4×C43—81no—
162C4×C43—82no—
163C4×C43#45112yes—
164C4×C43#45111yescharacteristic
165C4×C43#45111yescharacteristic
166C4×C43#45211yescharacteristic
167C4×C43#45211yescharacteristic
168C4×C43#49411yescharacteristic
169C4×C43#49711yescharacteristic
170Dic43—82no—
171C2×#500—431no—
172C2×#477—431no—
173C2×#477D4311yescharacteristic
174#1984—431no—
175C2×#333—431no—
176C2×#333—431no—
177#1277—431no—
178C2×C43#167612yes—
179C2×C43#169612yes—
180C2×C43#200111yescharacteristic
181C2×C43#201611yescharacteristic
182C2×C43#201811yescharacteristic
183C2×C4⋊Q8—431no—
184C2×C4⋊Q8C2×D4311yescharacteristic
185C2×C4×Q8C2×D4311yescharacteristic
186#500—862no—
187#500—862no—
188#477—22no—
189#477—22no—
190#477—862no—
191#477—862no—
192C2×#107—21no—
193C2×#107—862no—
194C2×#107—861no—
195C2×C4⋊C8—431no—
196C2×C4⋊C8—431no—
197C2×C4⋊C8C2×D4311yescharacteristic
198C2×#103—21no—
199C2×#103—861no—
200C2×C4×C8—431no—
201#336—862no—
202#333—862no—
203#333—862no—
204C43#1027911yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×Q8—861no—
207C22×Q8C22⋊D4311yescharacteristic
208C22×C8—21no—
209C22×C8—432no—
210C22×C8—861no—
211C22×C8—861no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—432no—
216C4⋊Q8—861no—
217C4⋊Q8—861no—
218C4⋊Q8—861no—
219C4⋊Q8C22⋊D4312yes—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C4⋊C4C22⋊D4311yescharacteristic
230C2×C42—21no—
231C2×C42C22×D4311yescharacteristic
232#107—24no—
233#107—864no—
234#107—868no—
235C4⋊C8—21no—
236C4⋊C8—432no—
237C4⋊C8—861no—
238C4⋊C8—861no—
239C4⋊C8—861no—
240C4⋊C8C22⋊D4312yes—
241#103—24no—
242#103—864no—
243C4×C8—861no—
244C4×C8—861no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—22no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—41no—
252C2×Q8—82no—
253C2×Q8—862no—
254C2×Q8—3442no—
255C2×Q8—1721no—
256C2×Q8#1062188512yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—1721no—
261C22×C4D4×D4311yescharacteristic
262C22×C4#1062190011yescharacteristic
263C22×C4C2×C22⋊D4311yescharacteristic
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—434no—
268C2×C8—862no—
269C2×C8—862no—
270C2×C8—862no—
271C2×C8—1721no—
272C2×C8—1722no—
273C2×C8—1721no—
274C2×C8—1721no—
275C4⋊C4—22no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—862no—
284C4⋊C4—862no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C42—41no—
288C42—41no—
289C42D4×D4311yescharacteristic
290C42D4×D4311yescharacteristic
291C42C2×C22⋊D4311yescharacteristic
292C42C2×C22⋊D4311yescharacteristic
293C23#1306329711yescharacteristic
294Q8—22no—
295Q8—22no—
296Q8—41no—
297Q8—41no—
298Q8—82no—
299Q8—82no—
300Q8—3442no—
301Q8—3442no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—3442no—
311C2×C4—1722no—
312C2×C4#1306329311yescharacteristic
313C2×C4#1306329311yescharacteristic
314C2×C4#1306329411yescharacteristic
315C2×C4#1306329611yescharacteristic
316C2×C4#1306329711yescharacteristic
317C2×C4#1306332111yescharacteristic
318C2×C4Q16×D4312yes—
319C2×C4C2×#1062188511yescharacteristic
320C2×C4#1306334511yescharacteristic
321C2×C4#1306335511yescharacteristic
322C2×C4#1306335611yescharacteristic
323C2×C4#1306335712yes—
324C8—42no—
325C8—864no—
326C8—3441no—
327C8—1722no—
328C22#1458280711yescharacteristic
329C22#1458310712yes—
330C22#1458313811yescharacteristic
331C22#1458315511yescharacteristic
332C22#1458316712yes—
333C4—21no—
334C4—21no—
335C4—42no—
336C4—81no—
337C4—82no—
338C4—3442no—
339C4#1458305312yes—
340C4#1458305411yescharacteristic
341C4#1458305511yescharacteristic
342C4#1458305911yescharacteristic
343C4#1458306111yescharacteristic
344C4#1458327711yescharacteristic
345C4#1458329211yescharacteristic
346C2#1913399712yes—
347C2#1913412112yes—
348C2#1913560311yescharacteristic
349C2#1913569311yescharacteristic
350C2#1913570111yescharacteristic
subgroupG/H
centerC23#13063297
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#477C2
socle, prime radicalC23×C43#121
hypercenterC2×#477D43
hypocenterC43#10279
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
204. C43#10279semidirect

Maximal subgroups

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

subgroupindex
C2×#145833022
C2×#145831942
#191355322
C2×#145826482
C2×#145826472
#191324292
C2×C43×#4772
#1027943