Finite Group Databasebeta

← #24989571

Subgroups — #24989571

Order 11008.

456 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143289C211yesmaximal, characteristic
2#19134633C211yesmaximal, characteristic, complemented
3#19133136C212yesmaximal
4#19132501C212yesmaximal, complemented
5C43×#1808C211yesmaximal, characteristic, complemented
6C2×#13063331C411yescharacteristic, complemented
7#14583410C2211yescharacteristic
8#14582970—21no—
9#14582970—21no—
10C8×C22⋊D43—21no—
11C8×C22⋊D43—21no—
12C2×#13063261—21no—
13#14582925C411yescharacteristic, complemented
14#14582865C411yescharacteristic, complemented
15#14582863C2212yes—
16#14582863C2211yescharacteristic
17#14582854C411yescharacteristic, complemented
18#14582664—21no—
19#14582635—22no—
20#14582632—22no—
21C23×C8×C43C2211yescharacteristic
22C2×#107×C43—21no—
23C43×#380C2212yes—
24C43×#340—21no—
25C2×#10621898C2×C411yescharacteristic
26#13063331—42no—
27C2×#10621877—22no—
28C2×#10621877C2×C411yescharacteristic
29C2×#10621877C2×C411yescharacteristic
30C2×#10621872—21no—
31C2×C8×D43—21no—
32#13063308—21no—
33#13063304D411yescharacteristic
34#13063304Q811yescharacteristic
35#13063299D411yescharacteristic
36#13063299Q811yescharacteristic
37#13063294—21no—
38C4×C22⋊D43—21no—
39C4×C22⋊D43—21no—
40#13063284C2×C411yescharacteristic
41#13063261—42no—
42Dic43⋊C8—21no—
43Dic43⋊C8—21no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—22no—
47C22⋊(C43⋊C8)—22no—
48(C2×D43)⋊C8—21no—
49(C2×D43)⋊C8—21no—
50#13063235—21no—
51C8×Dic43—21no—
52C23×C4×C43C2311yescharacteristic
53C22×C8×C43—42no—
54C22×C8×C43C2×C411yescharacteristic
55C22×C8×C43C2×C411yescharacteristic
56C22×C8×C43D411yescharacteristic
57C22×C8×C43D411yescharacteristic
58C22×C8×C43D411yescharacteristic
59C22×C8×C43D411yescharacteristic
60C2×C4⋊C4×C43—22no—
61C2×C22⋊C4×C43—22no—
62#107×C43—42no—
63#95×C43—22no—
64C24×C43#4111yescharacteristic
65C22×C4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43—42no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×Q811yescharacteristic
73C22×C4×C43#4111yescharacteristic
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C2×C22⋊D43—21no—
77#10621898—41no—
78#10621898—41no—
79C2×D172C4⋊C411yescharacteristic
80C2×C4×D43—21no—
81C2×Dic86C4⋊C411yescharacteristic
82C2×C8×C43—22no—
83C2×C8×C43—22no—
84C2×C8×C43—22no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43C22⋊C411yescharacteristic
89C2×C8×C43C22⋊C411yescharacteristic
90C2×C8×C43C22⋊C411yescharacteristic
91C2×C8×C43C22⋊C411yescharacteristic
92C4⋊C4×C43—42no—
93C4⋊C4×C43—42no—
94C22⋊C4×C43—82no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100C4⋊Dic43C4⋊C411yescharacteristic
101C4⋊Dic43C4⋊C411yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105#10621877—41no—
106#10621877—41no—
107#10621877—42no—
108#10621877—42no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—42no—
112#10621872—42no—
113C8×D43—42no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43#11711yescharacteristic
119C23×C43#12111yescharacteristic
120C23×C43C22⋊Q811yescharacteristic
121C22×D43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—82no—
132C2×C4×C43—82no—
133C2×C4×C43—82no—
134C2×C4×C43C2×C22⋊C411yescharacteristic
135C2×C4×C43C2×C4⋊C411yescharacteristic
136C2×C4×C43#12111yescharacteristic
137C2×C4×C43C22⋊Q811yescharacteristic
138C22⋊D43—42no—
139C22⋊D43—42no—
140C22⋊D43—41no—
141C22⋊D43—41no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145D172—41no—
146C4×D43—41no—
147C4×D43—41no—
148Dic86—41no—
149C8×C43—21no—
150C8×C43—21no—
151C8×C43—21no—
152C8×C43#9912yes—
153C43⋊C8—41no—
154C43⋊C8—41no—
155C43⋊C8—82no—
156#8627—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—42no—
166C22×C43—42no—
167C22×C43#38011yescharacteristic
168C22×C43#47211yescharacteristic
169C22×C43#47311yescharacteristic
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—162no—
177C4×C43C2×#9911yescharacteristic
178C4×C43#41011yescharacteristic
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182#2929—431no—
183#1810—431no—
184#1808D4311yescharacteristic, complemented
185#1513—432no—
186#1305—432no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—41no—
190C2×C43—41no—
191C2×C43#179911yescharacteristic
192C2×C43#181411yescharacteristic
193C2×C43#181611yescharacteristic
194D43—81no—
195C2×#131—431no—
196C23×C8C2×D4311yescharacteristic
197#525—431no—
198#435—861no—
199#435—861no—
200C8×D4—861no—
201C8×D4—861no—
202C2×#108—861no—
203C2×#107—21no—
204#424—431no—
205#408—431no—
206#407—431no—
207#407—432no—
208#405—431no—
209#380C2×D4312yes—
210#341—861no—
211#340—21no—
212#328—862no—
213#327—862no—
214C43#862711yescharacteristic, complemented, Sylow
215C2×#41—431no—
216C23×C4C22×D4311yescharacteristic
217#131—1722no—
218C2×M16—431no—
219C2×M16—431no—
220C2×M16—861no—
221C2×M16—862no—
222C22×C8—42no—
223C22×C8—861no—
224C22×C8C4×D4311yescharacteristic
225C22×C8C4×D4311yescharacteristic
226C22×C8D17211yescharacteristic
227C22×C8D17211yescharacteristic
228C22×C8C22⋊D4311yescharacteristic
229C22×C8C22⋊D4311yescharacteristic
230#123—861no—
231C22⋊Q8—431no—
232C22⋊Q8—431no—
233#121—431no—
234#121—431no—
235#120—861no—
236C4×D4—861no—
237C4×D4—861no—
238#117—431no—
239C2×C4⋊C4—22no—
240C2×C22⋊C4—22no—
241#108—1722no—
242#107—42no—
243C4⋊C8—861no—
244C4⋊C8—861no—
245C22⋊C8—861no—
246C22⋊C8—861no—
247C22⋊C8—861no—
248C22⋊C8—861no—
249C22⋊C8—862no—
250C22⋊C8—862no—
251#97—861no—
252C4×C8—861no—
253#95—22no—
254C24#1062190011yescharacteristic
255#41—1721no—
256#41—1721no—
257C2×Q8—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—42no—
265C22×C4—861no—
266C22×C4C2×C4×D4311yescharacteristic
267C22×C4C2×D17211yescharacteristic
268C22×C4D4×D4311yescharacteristic
269C22×C4Q8×D4311yescharacteristic
270C22×C4#1062190211yescharacteristic
271C22×C4C2×C22⋊D4311yescharacteristic
272M16—1722no—
273M16—1722no—
274M16—1722no—
275M16—1721no—
276M16—1721no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—861no—
284C2×C8—861no—
285C2×C8—1722no—
286C2×C8—1722no—
287C2×C8(C2×D43)⋊C411yescharacteristic
288C2×C8(C2×D43)⋊C411yescharacteristic
289C2×C8(C2×D43)⋊C411yescharacteristic
290C2×C8(C2×D43)⋊C411yescharacteristic
291C4⋊C4—42no—
292C4⋊C4—42no—
293C4⋊C4—431no—
294C4⋊C4—431no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C22⋊C4—82no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C42—861no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—41no—
308C23—861no—
309C23#1306328311yescharacteristic
310C23#1306329611yescharacteristic
311C23#1306330511yescharacteristic
312Q8—1721no—
313D4—1721no—
314D4—1722no—
315D4—1722no—
316D4—1721no—
317D4—1721no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4C2×(C2×D43)⋊C411yescharacteristic
336C2×C4C4⋊C4×D4311yescharacteristic
337C2×C4#1306330011yescharacteristic
338C2×C4#1306330111yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—3442no—
343C8—1721no—
344C8—1721no—
345C8#1306323912yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—42no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22#1458275611yescharacteristic
360C22#1458316611yescharacteristic
361C22#1458317111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—162no—
366C4—1721no—
367C4—1721no—
368C4—1721no—
369C4C2×#1306323911yescharacteristic
370C4#1458287211yescharacteristic
371C2—21no—
372C2—21no—
373C2—41no—
374C2—41no—
375C2—3441no—
376C2#1913458011yescharacteristic
377C2#1913464611yescharacteristic
378C2#1913466011yescharacteristic
subgroupG/H
centerC22#14582756
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1808C2
socleC22×C43#380
prime radical#14583410C22
cosocleC23×C4×C43C23
hypercenter#1808D43
hypocenterC43#8627
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. #19134633C2semidirect
4. #19132501C2semidirect
5. C43×#1808C2semidirect
6. C2×#13063331C4semidirect
13. #14582925C4semidirect
14. #14582865C4semidirect
17. #14582854C4semidirect
184. #1808D43semidirect
214. C43#8627semidirect

Maximal subgroups

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

subgroupindex
#191432892
#191346332
#191331362
#191325012
C43×#18082
#862743