Finite Group Databasebeta

← #24990899

Subgroups — #24990899

Order 11008.

438 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#19143163C211yesmaximal, characteristic
2#19134615C211yesmaximal, characteristic
3#19133370C211yesmaximal, characteristic, complemented
4#19133354C211yesmaximal, characteristic, complemented
5#19132497C211yesmaximal, characteristic, complemented
6#19132435C211yesmaximal, characteristic, complemented
7C43×#1476C211yesmaximal, characteristic
8C2×#13063332—21no—
9#14582926—22no—
10#14582926—21no—
11#14582923—21no—
12#14582923C2211yescharacteristic
13#14582923C2211yescharacteristic
14C2×C4⋊(C43⋊C8)—21no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×#13063252—21no—
17C4×C4⋊Dic43C2211yescharacteristic
18#14582658—21no—
19#14582652—22no—
20#14582652—21no—
21#14582652—21no—
22C4×#41×C43C2211yescharacteristic
23C43×#431C2211yescharacteristic
24C2×C4×C8×C43C2211yescharacteristic
25C43×Q8⋊C8C411yescharacteristic, complemented
26C43×Q8⋊C8C411yescharacteristic, complemented
27C43×D4⋊C8C411yescharacteristic, complemented
28C43×D4⋊C8C411yescharacteristic, complemented
29#13063332—42no—
30#13063332—42no—
31C2×#10621877—22no—
32C2×#10621877—21no—
33C2×#10621877—21no—
34C22×C43⋊C8—22no—
35C22×C43⋊C8—21no—
36C2×C4⋊Dic43—21no—
37C2×C4×Dic43—21no—
38C4⋊(C43⋊C8)—22no—
39C4⋊(C43⋊C8)—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)D411yescharacteristic
45C4⋊(C43⋊C8)D411yescharacteristic
46C4⋊(C43⋊C8)D412yes—
47#13063252—42no—
48C43⋊#95—21no—
49C2×#41×C43D411yescharacteristic
50C22×C8×C43—21no—
51C4×Q8×C43C2×C411yescharacteristic
52C4×Q8×C43Q811yescharacteristic
53C4×D4×C43—21no—
54C4×D4×C43—21no—
55C4×D4×C43C2×C411yescharacteristic
56C4×D4×C43Q811yescharacteristic
57#117×C43—21no—
58#117×C43D411yescharacteristic
59C2×C42×C43—21no—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43C2×C411yescharacteristic
62C4⋊C8×C43C2×C411yescharacteristic
63C22⋊C8×C43—21no—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C4×C8×C43C2×C411yescharacteristic
67C4×C8×C43C2×C411yescharacteristic
68#41×C43—21no—
69#41×C43—21no—
70#41×C43D812yes—
71#41×C43Q1612yes—
72C2×Q8×C43C4⋊C411yescharacteristic
73C2×D4×C43—21no—
74C2×D4×C43C4⋊C411yescharacteristic
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×Dic43—41no—
82C2×C8×C43—21no—
83C2×C8×C43—21no—
84C2×C8×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43—42no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43C4⋊C411yescharacteristic
90C4⋊C4×C43C4⋊C411yescharacteristic
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43—21no—
94C42×C43—21no—
95C42×C43—21no—
96C42×C43—21no—
97C42×C43C22×C411yescharacteristic
98C42×C43C2×D411yescharacteristic
99C42×C43C2×D411yescharacteristic
100C42×C43C2×Q811yescharacteristic
101C4⋊Dic43—22no—
102C4⋊Dic43—41no—
103C4×Dic43—41no—
104C4×Dic43—41no—
105#10621877—44no—
106#10621877—41no—
107#10621877—41no—
108#10621877—41no—
109#10621877—41no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—22no—
112C2×C43⋊C8—21no—
113C2×C43⋊C8—44no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C23×C43—21no—
118C23×C43#12311yescharacteristic
119Q8×C43—21no—
120Q8×C43#10712yes—
121D4×C43—22no—
122D4×C43—22no—
123D4×C43—21no—
124D4×C43#10712yes—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—81no—
136C2×C4×C43C2×C4⋊C411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43#12011yescharacteristic
140C2×C4×C43C22⋊Q811yescharacteristic
141C2×C4×C43C22⋊Q811yescharacteristic
142C2×C4×C43C2×D811yescharacteristic
143C2×C4×C43C2×Q1611yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C43#13711yescharacteristic
146C2×Dic43—42no—
147C2×Dic43—81no—
148C2×Dic43—81no—
149C8×C43—22no—
150C8×C43—41no—
151C8×C43—41no—
152C8×C43—41no—
153C43⋊C8—41no—
154C43⋊C8—42no—
155C43⋊C8—41no—
156C43⋊C8—81no—
157#8902—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—22no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43#38511yescharacteristic
164C22×C43#48011yescharacteristic
165C22×C43#48411yescharacteristic
166C4×C43—22no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#10711yescharacteristic
173C4×C43#42811yescharacteristic
174C4×C43#44311yescharacteristic
175C4×C43#44411yescharacteristic
176C4×C43#44711yescharacteristic
177C4×C43#45111yescharacteristic
178Dic43—82no—
179#2906—431no—
180#1806—431no—
181#1571—431no—
182#1567—431no—
183#1476D4311yescharacteristic
184#1303—431no—
185#1279—431no—
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—42no—
189C2×C43#185211yescharacteristic
190C2×C43#186111yescharacteristic
191C2×C43#186611yescharacteristic
192C2×#131—861no—
193C4×#41C2×D4311yescharacteristic
194#431C2×D4311yescharacteristic
195#424—862no—
196#424—861no—
197#423—431no—
198#423—431no—
199#423—861no—
200C2×C4⋊C8—431no—
201C2×C4⋊C8—861no—
202C2×#104—861no—
203C2×C4×C8C2×D4311yescharacteristic
204C4×C4⋊C4—431no—
205#339—861no—
206#335—862no—
207#335—861no—
208#335—861no—
209Q8⋊C8Dic4311yescharacteristic, complemented
210Q8⋊C8Dic4311yescharacteristic, complemented
211D4⋊C8Dic4311yescharacteristic, complemented
212D4⋊C8Dic4311yescharacteristic, complemented
213C43#890211yescharacteristic, complemented, Sylow
214C2×#41D17211yescharacteristic
215#131—1722no—
216#131—1722no—
217C2×M16—862no—
218C2×M16—861no—
219C2×M16—861no—
220C22×C8—21no—
221C22×C8—862no—
222C22×C8—861no—
223C4×Q8Dic8611yescharacteristic
224C4×Q8C2×Dic4311yescharacteristic
225C4×D4—21no—
226C4×D4—21no—
227C4×D4Dic8611yescharacteristic
228C4×D4C2×Dic4311yescharacteristic
229#117—21no—
230#117D17211yescharacteristic
231C2×C4⋊C4—861no—
232C2×C42—21no—
233C2×C42—861no—
234C2×C42C22×D4311yescharacteristic
235C4⋊C8—431no—
236C4⋊C8—431no—
237C4⋊C8—432no—
238C4⋊C8—862no—
239C4⋊C8—862no—
240C4⋊C8—861no—
241C4⋊C8—861no—
242C4⋊C8—861no—
243C4⋊C8—861no—
244C4⋊C8C2×Dic4311yescharacteristic
245C4⋊C8C2×Dic4311yescharacteristic
246#104—1722no—
247C22⋊C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8C2×Dic4311yescharacteristic
251C4×C8C2×Dic4311yescharacteristic
252#95—861no—
253#41—21no—
254#41—21no—
255#41D34412yes—
256#41Dic17212yes—
257C2×Q8C4⋊Dic4311yescharacteristic
258C2×D4—21no—
259C2×D4C4⋊Dic4311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1721no—
264C22×C4C2×D17211yescharacteristic
265C22×C4#1062190011yescharacteristic
266C22×C4#1062190011yescharacteristic
267M16—1721no—
268M16—1721no—
269M16—1724no—
270M16—1721no—
271M16—1721no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—42no—
277C2×C8—861no—
278C2×C8—861no—
279C2×C8—862no—
280C2×C8—1721no—
281C2×C8—1724no—
282C2×C8—1721no—
283C2×C8—1721no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—862no—
287C4⋊C4—1721no—
288C4⋊C4C4⋊Dic4311yescharacteristic
289C4⋊C4C4⋊Dic4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—1721no—
297C42—1721no—
298C42C2×Dic8611yescharacteristic
299C42D4×D4311yescharacteristic
300C42D4×D4311yescharacteristic
301C42C22×Dic4311yescharacteristic
302C23—21no—
303C23#1306330911yescharacteristic
304Q8—21no—
305Q8#1306325912yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4#1306325912yes—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—1722no—
324C2×C4C2×C4⋊Dic4311yescharacteristic
325C2×C4D4×Dic4311yescharacteristic
326C2×C4D4×Dic4311yescharacteristic
327C2×C4#1306329511yescharacteristic
328C2×C4#1306330211yescharacteristic
329C2×C4#1306330211yescharacteristic
330C2×C4C2×D34411yescharacteristic
331C2×C4C2×Dic17211yescharacteristic
332C2×C4#1306335311yescharacteristic
333C2×C4#1306335811yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—3441no—
339C8—1721no—
340C8—1722no—
341C8—1721no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22#1458277411yescharacteristic
348C22#1458321311yescharacteristic
349C22#1458323511yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—3442no—
357C4C2×#1306325911yescharacteristic
358C4#1458294111yescharacteristic
359C4#1458301611yescharacteristic
360C4#1458302111yescharacteristic
361C4#1458303511yescharacteristic
362C4#1458305711yescharacteristic
363C2—21no—
364C2—21no—
365C2—42no—
366C2#1913478511yescharacteristic
367C2#1913483711yescharacteristic
368C2#1913487211yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1476C2
socleC22×C43#385
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenter#1476D43
hypocenterC43#8902
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
3. #19133370C2semidirect
4. #19133354C2semidirect
5. #19132497C2semidirect
6. #19132435C2semidirect
25. C43×Q8⋊C8C4semidirect
26. C43×Q8⋊C8C4semidirect
27. C43×D4⋊C8C4semidirect
28. C43×D4⋊C8C4semidirect
209. Q8⋊C8Dic43semidirect
210. Q8⋊C8Dic43semidirect
211. D4⋊C8Dic43semidirect
212. D4⋊C8Dic43semidirect
213. C43#8902semidirect

Maximal subgroups

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

subgroupindex
#191431632
#191346152
#191333702
#191333542
#191324972
#191324352
C43×#14762
#890243