Finite Group Databasebeta

← #24995638

Subgroups — #24995638

Order 11008.

570 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142991C211yesmaximal, characteristic
2#19134746C211yesmaximal, characteristic
3C4⋊C8×Dic43C211yesmaximal, characteristic
4C2×#14582646C211yesmaximal, characteristic
5C2×#14582645C211yesmaximal, characteristic
6C2×#14582644C211yesmaximal, characteristic
7C2×C43×#332C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063323—21no—
10C2×#13063323—21no—
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×Dic43⋊C8—22no—
14C2×C8×Dic43—21no—
15#14582768—22no—
16#14582768C414yes—
17C42×Dic43C2211yescharacteristic
18#14582653—21no—
19#14582646—22no—
20#14582645—22no—
21#14582644—22no—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C43×#332—22no—
26C22×Dic86—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29#13063325—21no—
30#13063325—21no—
31#13063325—21no—
32#13063325—21no—
33#13063323—42no—
34#13063323—42no—
35#13063323—42no—
36#13063323—42no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C412yes—
39C2×Dic43⋊C4—24no—
40C2×Dic43⋊C4—24no—
41C2×C4×Dic43C2×C412yes—
42C2×C4×Dic43D411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44C2×C4×Dic43D412yes—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)D412yes—
49Dic43⋊C8—44no—
50C8×Dic43—42no—
51C22×Q8×C43—21no—
52C22×C8×C43—21no—
53C22×C8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C412yes—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C4⋊C8×C43D412yes—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C22×C4×C43—22no—
72C22×C4×C43C22×C411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—22no—
76C22×Dic43C22⋊C412yes—
77C22×Dic43C22⋊C412yes—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×C8×C43—22no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43—42no—
89C4⋊C4×C43—22no—
90C4⋊C4×C43—22no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C42×C43C2×D411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43#4111yescharacteristic
96C42×C43#4111yescharacteristic
97C4⋊Dic43—22no—
98C4⋊Dic43—22no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101Dic43⋊C4—48no—
102Dic43⋊C4—48no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—24no—
106C4×Dic43D812yes—
107C4×Dic43SD1612yes—
108C4×Dic43SD1614yes—
109C4×Dic43Q1614yes—
110C2×C43⋊C8—22no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—42no—
115C23×C43C2×C22⋊C411yescharacteristic
116Q8×C43—81no—
117Q8×C43—81no—
118Q8×C43—81no—
119Q8×C43—81no—
120C2×C4×C43—22no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43C4×D411yescharacteristic
125C2×C4×C43C4×D411yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43#12411yescharacteristic
129C2×C4×C43#12711yescharacteristic
130C2×C4×C43C2×D811yescharacteristic
131C2×C4×C43C2×SD1611yescharacteristic
132C2×C4×C43C2×SD1612yes—
133C2×C4×C43C2×Q1612yes—
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43#10114yes—
142C2×Dic43#10214yes—
143C2×Dic43#10314yes—
144C2×Dic43#10314yes—
145Dic86—81no—
146Dic86—81no—
147Dic86—81no—
148Dic86—81no—
149C8×C43—42no—
150C8×C43—81no—
151C43⋊C8—42no—
152C43⋊C8—81no—
153#9694—431nomaximal, Sylow
154C22×C43#39011yescharacteristic
155C22×C43C2×#10112yes—
156C22×C43C2×#10211yescharacteristic
157C22×C43C2×#10312yes—
158C22×C43#41811yescharacteristic
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—82no—
162C4×C43#45911yescharacteristic
163C4×C43#45911yescharacteristic
164C4×C43#46011yescharacteristic
165C4×C43#46011yescharacteristic
166C4×C43#48712yes—
167C4×C43#49211yescharacteristic
168C4×C43#49411yescharacteristic
169Dic43—24no—
170Dic43—82no—
171Dic43#33218yescomplemented
172#2868—431no—
173#1842—431no—
174C4×C4⋊C8—431no—
175C2×#332—431no—
176C2×#332—431no—
177C2×#332—431no—
178C2×#332D4311yescharacteristic
179C2×C43C2×#33212yes—
180C2×C43#154912yes—
181C2×C43#195611yescharacteristic
182C2×C43#196611yescharacteristic
183C2×C43#198211yescharacteristic
184C2×C4⋊Q8—431no—
185C2×C4⋊Q8—861no—
186C2×C4⋊Q8—861no—
187C2×C4⋊Q8C2×D4311yescharacteristic
188C2×C4⋊C8—431no—
189C2×C4⋊C8—431no—
190C2×C4⋊C8—862no—
191C2×C4⋊C8C2×D4311yescharacteristic
192C2×C4⋊C8C2×D4311yescharacteristic
193C2×C4×C8—861no—
194#384—434no—
195#384—862no—
196C43—431no—
197#336—861no—
198#332—22no—
199#332—862no—
200#332—862no—
201#332—862no—
202C43#969411yescharacteristic, complemented, Sylow
203C22×Q8—21no—
204C22×Q8—861no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—861no—
208C22×C8—861no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—861no—
214C4⋊Q8—861no—
215C4⋊Q8—861no—
216C4⋊Q8—861no—
217C4⋊Q8—1722no—
218C4⋊Q8—1722no—
219C4⋊Q8—1722no—
220C4⋊Q8—1722no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—432no—
223C2×C4⋊C4—864no—
224C2×C4⋊C4—864no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4C4×D4312yes—
227C2×C42—431no—
228C2×C42—432no—
229C2×C42—432no—
230C2×C42—431no—
231C2×C42C22×D4311yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—432no—
236C4⋊C8—861no—
237C4⋊C8—861no—
238C4⋊C8—861no—
239C4⋊C8—1724no—
240C4⋊C8C22⋊D4312yes—
241C4×C8—1722no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—1721no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C2×Q8—1721no—
254C22×C4—22no—
255C22×C4—432no—
256C22×C4—432no—
257C22×C4—862no—
258C22×C4C2×C4×D4311yescharacteristic
259C22×C4D4×D4311yescharacteristic
260C22×C4D4×D4311yescharacteristic
261C2×C8—22no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—42no—
266C2×C8—862no—
267C2×C8—1721no—
268C2×C8—1722no—
269C2×C8—1721no—
270C2×C8—1721no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—862no—
276C4⋊C4—862no—
277C4⋊C4—1728no—
278C4⋊C4—1728no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C42—432no—
282C42—434no—
283C42—432no—
284C42—434no—
285C42—864no—
286C42—861no—
287C42—861no—
288C42#1062189811yescharacteristic
289C42D4×D4311yescharacteristic
290C42#1062190011yescharacteristic
291C42C2×C22⋊D4311yescharacteristic
292C23C22⋊C4×D4311yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—81no—
296Q8—81no—
297Q8—3441no—
298Q8—3441no—
299Q8—3441no—
300Q8—3441no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—434no—
306C2×C4—434no—
307C2×C4—434no—
308C2×C4—434no—
309C2×C4—862no—
310C2×C4—862no—
311C2×C4—1722no—
312C2×C4—1722no—
313C2×C4—1722no—
314C2×C4(C22⋊D43)⋊C411yescharacteristic
315C2×C4C4×C22⋊D4311yescharacteristic
316C2×C4#1306329711yescharacteristic
317C2×C4#1306329811yescharacteristic
318C2×C4#1306331111yescharacteristic
319C2×C4#1306332111yescharacteristic
320C2×C4D8×D4311yescharacteristic
321C2×C4SD16×D4311yescharacteristic
322C2×C4SD16×D4312yes—
323C2×C4Q16×D4312yes—
324C2×C4#1306334911yescharacteristic
325C2×C4#1306335211yescharacteristic
326C8—42no—
327C8—81no—
328C8—3441no—
329C8—1722no—
330C22#1458279911yescharacteristic
331C22#101×D4312yes—
332C22#102×D4311yescharacteristic
333C22#103×D4312yes—
334C22#1458290211yescharacteristic
335C4—21no—
336C4—21no—
337C4—82no—
338C4—438no—
339C4—864no—
340C4—3442no—
341C4#1458309211yescharacteristic
342C4#1458309311yescharacteristic
343C4#1458309711yescharacteristic
344C4#1458309811yescharacteristic
345C4#1458324812yes—
346C4#1458327011yescharacteristic
347C4#1458327711yescharacteristic
348C2#332×D4312yes—
349C2#1913327812yes—
350C2#1913539511yescharacteristic
351C2#1913543711yescharacteristic
352C2#1913552011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socle, prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenterC2×#332D43
hypocenterC43#9694
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
171. Dic43#332semidirect
202. C43#9694semidirect

Maximal subgroups

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

subgroupindex
#191429912
#191347462
C4⋊C8×Dic432
C2×#145826462
C2×#145826452
C2×#145826442
C2×C43×#3322
#969443