Finite Group Databasebeta

← #24989914

Subgroups — #24989914

Order 11008.

384 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143571C211yesmaximal, characteristic
2C4×#13063258C211yesmaximal, characteristic, complemented
3#19133356C211yesmaximal, characteristic, complemented
4#19133120C211yesmaximal, characteristic
5#19132451C211yesmaximal, characteristic, complemented
6#19132450C211yesmaximal, characteristic, complemented
7C43×#1509C211yesmaximal, characteristic
8#14583030C411yescharacteristic, complemented
9Q8×C43⋊C8C411yescharacteristic, complemented
10#14582977C411yescharacteristic, complemented
11#14582971—21no—
12D4×C43⋊C8—21no—
13D4×C43⋊C8C411yescharacteristic, complemented
14#14582960—21no—
15#14582956C2211yescharacteristic
16#14582956C2211yescharacteristic
17C2×#13063258—21no—
18#14582855—21no—
19C2×C4×C43⋊C8C2211yescharacteristic
20C4×C4⋊Dic43C2211yescharacteristic
21#14582661—21no—
22#14582651—21no—
23#14582649—21no—
24#14582636—21no—
25#14582633—21no—
26C43×#529C2211yescharacteristic
27C43×#432C2211yescharacteristic
28C4×C4⋊C4×C43C2211yescharacteristic
29C43×#328—21no—
30C43×#327—21no—
31C2×#10621877—21no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8D411yescharacteristic
34C22×C43⋊C8D411yescharacteristic
35C2×C4⋊Dic43—21no—
36C2×C4×Dic43—21no—
37#13063258—24no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)C2×C411yescharacteristic
42C4⋊(C43⋊C8)C2×C411yescharacteristic
43C22⋊(C43⋊C8)—21no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47#13063236—21no—
48#13063236—21no—
49#13063236—21no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8C2×C411yescharacteristic
52C4×C43⋊C8C2×C411yescharacteristic
53C4×C43⋊C8D411yescharacteristic
54C4×C43⋊C8D411yescharacteristic
55C43⋊#95—21no—
56#126×C43—21no—
57#125×C43Q811yescharacteristic
58#124×C43Q811yescharacteristic
59#123×C43—21no—
60C22⋊Q8×C43D411yescharacteristic
61#121×C43D411yescharacteristic
62C4×Q8×C43C2×C411yescharacteristic
63C4×D4×C43—21no—
64C4×D4×C43C2×C411yescharacteristic
65#117×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C42×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71#97×C43—21no—
72#95×C43—21no—
73C2×Q8×C43C4⋊C411yescharacteristic
74C2×D4×C43—21no—
75C2×D4×C43C4⋊C411yescharacteristic
76C22×C4×C43—21no—
77C22×C4×C43—41no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×Dic43—41no—
82C2×C8×C43—41no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—22no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43C4⋊C411yescharacteristic
90C4⋊C4×C43C4⋊C411yescharacteristic
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C42×C43—21no—
97C42×C43—81no—
98C42×C43C22×C411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×Q811yescharacteristic
101C42×C43#4111yescharacteristic
102C4⋊Dic43—22no—
103C4⋊Dic43—41no—
104C4×Dic43—81no—
105#10621877—42no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—21no—
108C2×C43⋊C8—21no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—42no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8C22⋊C411yescharacteristic
113C2×C43⋊C8C22⋊C411yescharacteristic
114C2×C43⋊C8C22⋊C411yescharacteristic
115C2×C43⋊C8C22⋊C411yescharacteristic
116C23×C43—21no—
117C23×C43#12111yescharacteristic
118Q8×C43—41no—
119D4×C43—41no—
120D4×C43—41no—
121D4×C43—41no—
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—21no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—42no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43C2×C4⋊C411yescharacteristic
137C2×C4×C43#11711yescharacteristic
138C2×C4×C43#12111yescharacteristic
139C2×C4×C43C22⋊Q811yescharacteristic
140C2×C4×C43C22⋊Q811yescharacteristic
141C2×Dic43—42no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144C8×C43—81no—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C43⋊C8—41no—
149C43⋊C8—41no—
150C43⋊C8—81no—
151C43⋊C8#10412yes—
152#8697—431nomaximal, Sylow
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43#38011yescharacteristic
159C22×C43#47211yescharacteristic
160C22×C43#47311yescharacteristic
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—82no—
170C4×C43C2×#10411yescharacteristic
171C4×C43#42111yescharacteristic
172Dic43—82no—
173#2966—431no—
174C4×#107—431no—
175#1568—431no—
176#1509—431no—
177#1509D4311yescharacteristic
178#1285—431no—
179#1285—431no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—81no—
183C2×C43#180611yescharacteristic
184C2×C43#181211yescharacteristic
185C2×C43#181611yescharacteristic
186#529C2×D4311yescharacteristic
187#446—431no—
188C8×Q8—431no—
189#436—431no—
190#435—861no—
191C8×D4—431no—
192C8×D4—861no—
193#433—861no—
194#432—431no—
195#432—431no—
196#432C2×D4311yescharacteristic
197C2×#107—861no—
198#405—861no—
199C2×C4×C8—431no—
200C4×C4⋊C4—431no—
201C4×C4⋊C4C2×D4311yescharacteristic
202#340—861no—
203#335—861no—
204#334—861no—
205#328—21no—
206#328—861no—
207#327—21no—
208#327—861no—
209C43#869711yescharacteristic, complemented, Sylow
210C2×M16—861no—
211C22×C8—431no—
212C22×C8—431no—
213C22×C8—861no—
214#126—21no—
215#125Dic8611yescharacteristic
216#124Dic8611yescharacteristic
217#123—21no—
218C22⋊Q8C22⋊D4311yescharacteristic
219#121C22⋊D4311yescharacteristic
220C4×Q8C4×D4311yescharacteristic
221C4×D4—21no—
222C4×D4C4×D4311yescharacteristic
223#117—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—861no—
226C2×C42—21no—
227C2×C42—861no—
228C2×C42C22×D4311yescharacteristic
229#107—864no—
230C4⋊C8—21no—
231C4⋊C8—431no—
232C4⋊C8—431no—
233C4⋊C8—861no—
234C4⋊C8—861no—
235C4⋊C8—861no—
236C22⋊C8—21no—
237C22⋊C8—861no—
238C22⋊C8—861no—
239C22⋊C8—861no—
240C22⋊C8—861no—
241#97—21no—
242#97—861no—
243#97—861no—
244#97—861no—
245C4×C8—431no—
246C4×C8—431no—
247C4×C8—431no—
248C4×C8—431no—
249C4×C8—861no—
250#95—21no—
251#95—861no—
252C2×Q8Dic43⋊C411yescharacteristic
253C2×D4—21no—
254C2×D4Dic43⋊C411yescharacteristic
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—1721no—
258C22×C4D4×D4311yescharacteristic
259C22×C4#1062190011yescharacteristic
260C22×C4C2×C22⋊D4311yescharacteristic
261M16—1722no—
262C2×C8—41no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—431no—
266C2×C8—431no—
267C2×C8—862no—
268C2×C8—861no—
269C2×C8—861no—
270C2×C8—1721no—
271C2×C8—1722no—
272C2×C8—1721no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—862no—
280C4⋊C4—1721no—
281C4⋊C4Dic43⋊C411yescharacteristic
282C4⋊C4Dic43⋊C411yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C42—21no—
289C42—81no—
290C42—3441no—
291C42C2×Dic8611yescharacteristic
292C42C2×C4×D4311yescharacteristic
293C42D4×D4311yescharacteristic
294C42#1062190011yescharacteristic
295C23—21no—
296C23#1306329711yescharacteristic
297Q8—41no—
298D4—41no—
299D4—41no—
300D4—41no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—3441no—
315C2×C4—3441no—
316C2×C4—1722no—
317C2×C4C22⋊C4×D4311yescharacteristic
318C2×C4C2×Dic43⋊C411yescharacteristic
319C2×C4#1306328111yescharacteristic
320C2×C4#1306329711yescharacteristic
321C2×C4#1306330211yescharacteristic
322C2×C4#1306330211yescharacteristic
323C8—81no—
324C8—432no—
325C8—861no—
326C8—861no—
327C8—861no—
328C8—3441no—
329C8—1721no—
330C8—1721no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22#1458275711yescharacteristic
337C22#1458316711yescharacteristic
338C22#1458317211yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—82no—
348C4—3442no—
349C4#104×D4311yescharacteristic
350C4#1458291411yescharacteristic
351C2—21no—
352C2—21no—
353C2—81no—
354C2#1913461311yescharacteristic
355C2#1913463911yescharacteristic
356C2#1913465711yescharacteristic
subgroupG/H
centerC22#14582757
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1509C2
socleC22×C43#380
prime radical#121×C43D4
cosocleC2×C42×C43C23
hypercenter#1509D43
hypocenterC43#8697
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. C4×#13063258C2semidirect
3. #19133356C2semidirect
5. #19132451C2semidirect
6. #19132450C2semidirect
8. #14583030C4semidirect
9. Q8×C43⋊C8C4semidirect
10. #14582977C4semidirect
13. D4×C43⋊C8C4semidirect
209. C43#8697semidirect

Maximal subgroups

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

subgroupindex
#191435712
C4×#130632582
#191333562
#191331202
#191324512
#191324502
C43×#15092
#869743