Finite Group Databasebeta

← #24989584

Subgroups — #24989584

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134633C211yesmaximal, characteristic, complemented
2#19134620C211yesmaximal, characteristic, complemented
3#19133138C212yesmaximal
4#19132500C212yesmaximal, complemented
5C43×#2929C211yesmaximal, characteristic
6C2×#13063261—21no—
7C2×#13063257—21no—
8#14582863C2212yes—
9#14582759C2212yes—
10#14582664—21no—
11#14582662—21no—
12#14582636—22no—
13#14582633—22no—
14C2×#131×C43C411yescharacteristic, complemented
15C23×C8×C43C2211yescharacteristic
16C43×#525C2211yescharacteristic
17C43×#435—21no—
18C43×#435—21no—
19C8×D4×C43—21no—
20C8×D4×C43—21no—
21C43×#424C411yescharacteristic, complemented
22C43×#408C411yescharacteristic, complemented
23C43×#407C2211yescharacteristic
24C43×#405C411yescharacteristic, complemented
25C2×#10621877—22no—
26C2×C4⋊Dic43—22no—
27C2×C22⋊Dic43—22no—
28#13063261—42no—
29#13063257—42no—
30C22⋊(C43⋊C8)—22no—
31C22⋊(C43⋊C8)—22no—
32C43⋊#95—22no—
33C2×#41×C43C2×C411yescharacteristic
34C23×C4×C43C2311yescharacteristic
35#131×C43—42no—
36C2×M16×C43—21no—
37C2×M16×C43C2×C411yescharacteristic
38C2×M16×C43C2×C411yescharacteristic
39C22×C8×C43—21no—
40C22×C8×C43—42no—
41C22×C8×C43C2×C411yescharacteristic
42C22×C8×C43C2×C411yescharacteristic
43C22×C8×C43D411yescharacteristic
44C22×C8×C43D411yescharacteristic
45C22×C8×C43D411yescharacteristic
46C22×C8×C43D411yescharacteristic
47#123×C43—21no—
48C22⋊Q8×C43D411yescharacteristic
49C22⋊Q8×C43Q811yescharacteristic
50#121×C43D411yescharacteristic
51#121×C43Q811yescharacteristic
52#120×C43—21no—
53C4×D4×C43—21no—
54C4×D4×C43—21no—
55#117×C43C2×C411yescharacteristic
56C4⋊C8×C43—21no—
57C4⋊C8×C43—21no—
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60C22⋊C8×C43—21no—
61C22⋊C8×C43—21no—
62#97×C43—21no—
63C4×C8×C43—21no—
64C24×C43#4111yescharacteristic
65#41×C43—41no—
66#41×C43—41no—
67C2×Q8×C43C4⋊C411yescharacteristic
68C2×D4×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43C4⋊C411yescharacteristic
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43C22×C411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×Q811yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×Dic43—42no—
82M16×C43—42no—
83M16×C43—41no—
84M16×C43—41no—
85C2×C8×C43—22no—
86C2×C8×C43—22no—
87C2×C8×C43—22no—
88C2×C8×C43—21no—
89C2×C8×C43—21no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C2×C8×C43—42no—
94C2×C8×C43C22⋊C411yescharacteristic
95C2×C8×C43C22⋊C411yescharacteristic
96C2×C8×C43C22⋊C411yescharacteristic
97C2×C8×C43C22⋊C411yescharacteristic
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43C4⋊C411yescharacteristic
101C4⋊C4×C43C4⋊C411yescharacteristic
102C22⋊C4×C43—21no—
103C22⋊C4×C43—21no—
104C22⋊C4×C43—21no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43—21no—
107C42×C43—21no—
108C22⋊Dic43—82no—
109C4⋊Dic43—42no—
110C4⋊Dic43—42no—
111#10621877—42no—
112#10621877—42no—
113C2×C43⋊C8—42no—
114C23×C43—22no—
115C23×C43—21no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43#11711yescharacteristic
119C23×C43#12111yescharacteristic
120C23×C43C22⋊Q811yescharacteristic
121Q8×C43—41no—
122D4×C43—41no—
123D4×C43—42no—
124D4×C43—42no—
125D4×C43—42no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43C2×C22⋊C411yescharacteristic
141C2×C4×C43C2×C4⋊C411yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43C22⋊Q811yescharacteristic
144C2×Dic43—82no—
145C2×Dic43—82no—
146C2×Dic43—82no—
147C8×C43—21no—
148C8×C43—21no—
149C8×C43—21no—
150C8×C43—41no—
151C8×C43—41no—
152C8×C43#9912yes—
153C43⋊C8—82no—
154#8629—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—44no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43#38011yescharacteristic
168C22×C43#47112yes—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43C2×#9911yescharacteristic
176C4×C43#41011yescharacteristic
177Dic43—162no—
178#2929D4311yescharacteristic
179#1810—431no—
180#1807—431no—
181#1513—432no—
182#1305—432no—
183C2×C43—22no—
184C2×C43—41no—
185C2×C43—41no—
186C2×C43—81no—
187C2×C43#179911yescharacteristic
188C2×C43#181411yescharacteristic
189C2×C43#181511yescharacteristic
190C2×#131Dic4311yescharacteristic, complemented
191C23×C8C2×D4311yescharacteristic
192#525C2×D4311yescharacteristic
193#435—21no—
194#435—21no—
195C8×D4—21no—
196C8×D4—21no—
197C2×#108—861no—
198C2×#106—861no—
199#424Dic4311yescharacteristic, complemented
200#408Dic4311yescharacteristic, complemented
201#407—432no—
202#407C2×D4311yescharacteristic
203#405Dic4311yescharacteristic, complemented
204#380—432no—
205#341—861no—
206#340—861no—
207#328—862no—
208#327—862no—
209C43#862911yescharacteristic, complemented, Sylow
210C2×#41C2×Dic4311yescharacteristic
211C23×C4C22×D4311yescharacteristic
212#131—42no—
213C2×M16—21no—
214C2×M16—862no—
215C2×M16C2×Dic4311yescharacteristic
216C2×M16C2×Dic4311yescharacteristic
217C22×C8—21no—
218C22×C8—42no—
219C22×C8C2×Dic4311yescharacteristic
220C22×C8C2×Dic4311yescharacteristic
221C22×C8C22⋊D4311yescharacteristic
222C22×C8C22⋊D4311yescharacteristic
223C22×C8C22⋊D4311yescharacteristic
224C22×C8C22⋊D4311yescharacteristic
225#123—21no—
226C22⋊Q8Dic8611yescharacteristic
227C22⋊Q8D17211yescharacteristic
228#121Dic8611yescharacteristic
229#121D17211yescharacteristic
230#120—21no—
231C4×D4—21no—
232C4×D4—21no—
233#117C2×Dic4311yescharacteristic
234C2×C4⋊C4—862no—
235C2×C22⋊C4—862no—
236#108—1722no—
237#106—1722no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—862no—
245C22⋊C8—862no—
246#97—21no—
247C4×C8—21no—
248#95—862no—
249C24#1062189811yescharacteristic
250#41—41no—
251#41—41no—
252C2×Q8C4⋊Dic4311yescharacteristic
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4C4⋊Dic4311yescharacteristic
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—1722no—
261C22×C4C2×Dic8611yescharacteristic
262C22×C4C2×D17211yescharacteristic
263C22×C4#1062189811yescharacteristic
264C22×C4C22×Dic4311yescharacteristic
265C22×C4C2×C22⋊D4311yescharacteristic
266C22×C4C2×C22⋊D4311yescharacteristic
267M16—42no—
268M16—41no—
269M16—41no—
270M16—1722no—
271M16—1722no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—42no—
281C2×C8—1722no—
282C2×C8C22⋊Dic4311yescharacteristic
283C2×C8C22⋊Dic4311yescharacteristic
284C2×C8C22⋊Dic4311yescharacteristic
285C2×C8C22⋊Dic4311yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—1722no—
289C4⋊C4—1722no—
290C4⋊C4C4⋊Dic4311yescharacteristic
291C4⋊C4C4⋊Dic4311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—3442no—
298C42—21no—
299C23—22no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23#1306328411yescharacteristic
304C23#1306329911yescharacteristic
305C23#1306330411yescharacteristic
306Q8—41no—
307D4—41no—
308D4—42no—
309D4—42no—
310D4—42no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—3442no—
326C2×C4—3442no—
327C2×C4—3442no—
328C2×C4C2×C22⋊Dic4311yescharacteristic
329C2×C4C2×C4⋊Dic4311yescharacteristic
330C2×C4#1306329911yescharacteristic
331C2×C4#1306330411yescharacteristic
332C8—21no—
333C8—21no—
334C8—21no—
335C8—41no—
336C8—41no—
337C8—3442no—
338C8#1306324012yes—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22#1458275911yescharacteristic
352C22#1458316212yes—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—6882no—
360C4C2×#1306324011yescharacteristic
361C4#1458287311yescharacteristic
362C2—22no—
363C2—41no—
364C2—41no—
365C2—81no—
366C2#1913458311yescharacteristic
367C2#1913464911yescharacteristic
368C2#1913465411yescharacteristic
subgroupG/H
centerC22#14582759
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2929C2
socleC22×C43#380
prime radicalC43×#525C22
cosocleC23×C4×C43C23
hypercenter#2929D43
hypocenterC43#8629
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #19134633C2semidirect
2. #19134620C2semidirect
4. #19132500C2semidirect
14. C2×#131×C43C4semidirect
21. C43×#424C4semidirect
22. C43×#408C4semidirect
24. C43×#405C4semidirect
190. C2×#131Dic43semidirect
199. #424Dic43semidirect
200. #408Dic43semidirect
203. #405Dic43semidirect
209. C43#8629semidirect

Maximal subgroups

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

subgroupindex
#191346332
#191346202
#191331382
#191325002
C43×#29292
#862943