Finite Group Databasebeta

← #25016191

Subgroups — #25016191

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063266C211yesmaximal, characteristic
2C2×C4⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
3C2×#14582700C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5#19135461C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C43×#1970C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063266—22no—
10C2×#13063266—22no—
11C2×#13063266—22no—
12C22×C43⋊C16C2211yescharacteristic
13C22×C43⋊C16C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063247—21no—
16#14582801—21no—
17C4⋊(C43⋊C16)—22no—
18#14582700—22no—
19#14582699—22no—
20C22×D8×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C2×#102×C43—21no—
23C2×C4×C8×C43C2211yescharacteristic
24C43×#390—21no—
25C22×D172—21no—
26C2×D344—21no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344D412yes—
32C2×C4⋊Dic43—21no—
33C2×(C2×D43)⋊C4—41no—
34C2×(C2×D43)⋊C4—41no—
35#13063266—28no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16—21no—
39C2×C43⋊C16—21no—
40C2×C43⋊C16—21no—
41C2×C43⋊C16D412yes—
42#13063259—21no—
43#13063259—21no—
44#13063247—42no—
45C22×D4×C43—21no—
46C2×D8×C43—21no—
47C2×D8×C43—21no—
48C2×D8×C43—21no—
49C2×D8×C43—21no—
50C2×D8×C43—21no—
51C2×D8×C43D412yes—
52C22×C8×C43D411yescharacteristic
53C22×C8×C43C2311yescharacteristic
54C2×C4⋊C4×C43—21no—
55C2×C22⋊C4×C43—41no—
56C2×C22⋊C4×C43—41no—
57C2×C42×C43D411yescharacteristic
58#107×C43—21no—
59#107×C43—21no—
60#102×C43—42no—
61C4×C8×C43—21no—
62C4×C8×C43—21no—
63C24×C43—41no—
64C23×D43—41no—
65C2×D4×C43—22no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C22×C4×C43—41no—
72C22×C4×C43D811yescharacteristic
73C22×C4×C43D811yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—41no—
76C2×D172—22no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82D8×C43—22no—
83D8×C43—22no—
84D8×C43—41no—
85D8×C43—41no—
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C2×C8×C43#4111yescharacteristic
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C22⋊C4×C43—82no—
98C22⋊C4×C43—82no—
99C42×C43—21no—
100C42×C43—21no—
101(C2×D43)⋊C4—82no—
102(C2×D43)⋊C4—82no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105D344—22no—
106D344—22no—
107D344—41no—
108D344—41no—
109C43⋊C16—22no—
110C43⋊C16—41no—
111C23×C43—42no—
112C23×C43—81no—
113C23×C43—81no—
114C23×C43—81no—
115C23×C43—81no—
116C23×C43—81no—
117C23×C43—81no—
118C23×C43C2×D811yescharacteristic
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C22×D43—81no—
123C22×D43—81no—
124C22×D43—81no—
125C22×D43—81no—
126D4×C43—42no—
127D4×C43—42no—
128D4×C43—81no—
129D4×C43—81no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43—81no—
138C2×C4×C43D1612yescomplemented
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12111yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#13511yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
145C2×Dic43—81no—
146C2×Dic43—81no—
147C2×Dic43—81no—
148D172—42no—
149D172—42no—
150D172—81no—
151D172—81no—
152C8×C43—41no—
153C8×C43#12011yescharacteristic
154C8×C43#12311yescharacteristic
155C8×C43#12311yescharacteristic
156C8×C43#12411yescharacteristic
157#13448—431nomaximal, Sylow
158C22×C43—82no—
159C22×C43—82no—
160C22×C43—82no—
161C22×C43—161no—
162C22×C43—161no—
163C22×C43—161no—
164C22×C43—161no—
165C22×C43#45911yescharacteristic
166C22×C43#45911yescharacteristic
167C22×C43#46611yescharacteristic
168C22×C43C2×D1611yescharacteristic
169C22×C43#50811yescharacteristic
170C22×C43#50911yescharacteristic
171C22×C43#50911yescharacteristic
172C2×D43—82no—
173C2×D43—82no—
174C2×D43—82no—
175C2×D43—161no—
176C2×D43—161no—
177C2×D43—161no—
178C2×D43—161no—
179C4×C43—22no—
180C4×C43—41no—
181C4×C43—161no—
182C4×C43#39411yescharacteristic
183C4×C43#46311yescharacteristic
184C4×C43#46311yescharacteristic
185C4×C43#46911yescharacteristic
186Dic43—161no—
187C22×D16—431no—
188C2×C4⋊C16—431no—
189C2×#357—431no—
190C2×#357—431no—
191#1970—431no—
192#1970D4311yescharacteristic, complemented
193#1380—431no—
194C2×C43—162no—
195C2×C43#205411yescharacteristic
196C2×C43#220611yescharacteristic
197C2×C43#220611yescharacteristic
198C2×C43#221011yescharacteristic
199C2×C43#221011yescharacteristic
200C2×C43#221511yescharacteristic
201C2×C43#221811yescharacteristic
202D43—162no—
203C22×D8—431no—
204C22×D8C2×D4311yescharacteristic
205C2×D16—862no—
206C2×D16—862no—
207C2×D16—862no—
208C22×C16—431no—
209C22×C16—431no—
210C2×#107—431no—
211C2×#107C2×D4311yescharacteristic
212C2×#102—21no—
213C2×#102—861no—
214C2×C4×C8C2×D4311yescharacteristic
215#390—21no—
216#390—861no—
217C4⋊C16—862no—
218#357—862no—
219#357—862no—
220C43#1344811yescharacteristic, complemented, Sylow
221C22×D4—21no—
222C22×D4—861no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—432no—
229C2×D8—861no—
230C2×D8—861no—
231C2×D8—861no—
232C2×D8—861no—
233C2×D8—861no—
234C2×D8D17212yes—
235C22×C8C22⋊D4311yescharacteristic
236C22×C8C22×D4311yescharacteristic
237C2×C4⋊C4—21no—
238C2×C4⋊C4—861no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—1721no—
242C2×C22⋊C4—1721no—
243C2×C42C22⋊D4311yescharacteristic
244D16—868no—
245C2×C16—432no—
246C2×C16—861no—
247C2×C16—861no—
248C2×C16—861no—
249C2×C16—861no—
250C2×C16—861no—
251#107—21no—
252#107—21no—
253#107—861no—
254#107—861no—
255#102—42no—
256#102—1722no—
257C4×C8—21no—
258C4×C8—21no—
259C24—41no—
260C24—1721no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—862no—
268C2×D4—1721no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1721no—
272C2×D4—1721no—
273C22×C4—41no—
274C22×C4—1721no—
275C22×C4#1062188211yescharacteristic
276C22×C4#1062188211yescharacteristic
277C22×C4C2×C22⋊D4311yescharacteristic
278D8—22no—
279D8—22no—
280D8—41no—
281D8—41no—
282D8—862no—
283D8—862no—
284D8—1721no—
285D8—1721no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8C2×D17211yescharacteristic
290C2×C8#1062189811yescharacteristic
291C2×C8D4×D4311yescharacteristic
292C2×C8D4×D4311yescharacteristic
293C2×C8#1062190011yescharacteristic
294C2×C8#1062190011yescharacteristic
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C22⋊C4—82no—
300C22⋊C4—82no—
301C22⋊C4—3442no—
302C22⋊C4—3442no—
303C42—21no—
304C42—21no—
305C16—862no—
306C16—1721no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—3441no—
315C23—3441no—
316C23—3441no—
317C23—3441no—
318C23—3441no—
319C23—3441no—
320C23—1722no—
321C23C2×#1062188211yescharacteristic
322D4—42no—
323D4—42no—
324D4—81no—
325D4—81no—
326D4—3441no—
327D4—3441no—
328D4—1722no—
329D4—1722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4#1306326612yescomplemented
342C2×C4#1306329611yescharacteristic
343C2×C4#1306329711yescharacteristic
344C2×C4#1306329911yescharacteristic
345C2×C4#1306334511yescharacteristic
346C2×C4#1306335011yescharacteristic
347C2×C4#1306335111yescharacteristic
348C8—41no—
349C8#1306329511yescharacteristic
350C8#1306330711yescharacteristic
351C8#1306330911yescharacteristic
352C8#1306331111yescharacteristic
353C22—82no—
354C22—82no—
355C22—82no—
356C22—161no—
357C22—161no—
358C22—161no—
359C22—161no—
360C22—3442no—
361C22—3442no—
362C22—3442no—
363C22—6881no—
364C22—6881no—
365C22—6881no—
366C22—6881no—
367C22#1458309111yescharacteristic
368C22#1458309411yescharacteristic
369C22#1458313311yescharacteristic
370C22C2×#1306326611yescharacteristic
371C22#1458332911yescharacteristic
372C22#1458333411yescharacteristic
373C22#1458333511yescharacteristic
374C4—22no—
375C4—41no—
376C4—161no—
377C4—6881no—
378C4#1458281511yescharacteristic
379C4#1458311111yescharacteristic
380C4#1458311411yescharacteristic
381C4#1458315011yescharacteristic
382C2—162no—
383C2—6882no—
384C2#1913590511yescharacteristic
385C2#1913662711yescharacteristic
386C2#1913663011yescharacteristic
387C2#1913664711yescharacteristic
388C2#1913665011yescharacteristic
389C2#1913667911yescharacteristic
390C2#1913669611yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1970C2
socleC23×C43C2×D8
prime radicalC22×#13063266C2
hypercenter#1970D43
hypocenterC43#13448
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C43⋊C16)C2semidirect
3. C2×#14582700C2semidirect
4. C2×#14582699C2semidirect
5. #19135461C2semidirect
6. #19132686C2semidirect
7. C43×#1970C2semidirect
138. C2×C4×C43D16semidirect
192. #1970D43semidirect
220. C43#13448semidirect
341. C2×C4#13063266semidirect

Maximal subgroups

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

subgroupindex
C22×#130632662
C2×C4⋊(C43⋊C16)2
C2×#145827002
C2×#145826992
#191354612
#191326862
C43×#19702
#1344843