Finite Group Databasebeta

← #25125667

Subgroups — #25125667

Order 11008.

874 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×#13063258C211yesmaximal, characteristic
2C2×#14582927C211yesmaximal, characteristic
3#19137219C211yesmaximal, characteristic
4#19137218C211yesmaximal, characteristic
5#19136092C214yesmaximal, complemented
6#19136087C214yesmaximal, complemented
7#19134315C211yesmaximal, characteristic
8#19134311C211yesmaximal, characteristic
9C43×#1736C211yesmaximal, characteristic
10C23×C43⋊C8C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12C2×#13063284C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C2×#13063258—24no—
15C2×#13063258C2212yes—
16C2×#13063258C2212yes—
17#14582927—24no—
18C2×Dic43⋊C8C2212yes—
19C2×Dic43⋊C8C2212yes—
20#14582798C2214yes—
21#14582795C2214yes—
22#14582774—22no—
23#14582772—22no—
24#14582769—21no—
25#14582768—21no—
26#14582765—21no—
27#14582764—21no—
28#14582662C2214yes—
29#14582661C2212yes—
30#14582661C2212yes—
31C22×M16×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C43×#340C2214yes—
35C23×Dic43—21no—
36C22×C43⋊C8—22no—
37C22×C43⋊C8—22no—
38C22×C43⋊C8D414yes—
39C22×C43⋊C8C2311yescharacteristic
40C22×C43⋊C8C2311yescharacteristic
41#13063284—22no—
42#13063284—22no—
43#13063284—22no—
44#13063284Q814yes—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—24no—
49C2×C4⋊Dic43D411yescharacteristic
50C2×C4⋊Dic43D411yescharacteristic
51C2×C4⋊Dic43C2312yes—
52C2×C4⋊Dic43C2312yes—
53C2×Dic43⋊C4—24no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43D412yes—
56C2×C4×Dic43—21no—
57C2×C4×Dic43C2312yes—
58#13063258—24no—
59#13063258—24no—
60Dic43⋊C8—24no—
61Dic43⋊C8—24no—
62C43⋊#95—24no—
63C43⋊#95—24no—
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C2×M16×C43—22no—
67C2×M16×C43—22no—
68C2×M16×C43—22no—
69C22×C8×C43C2312yes—
70#117×C43—22no—
71#117×C43Q814yes—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43—22no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43C2312yes—
76C2×C4⋊C4×C43C2312yes—
77C2×C22⋊C4×C43—21no—
78C2×C42×C43—21no—
79C24×C43C2×D411yescharacteristic
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—42no—
83C22×C4×C43—82no—
84C22×C4×C43C2×D412yes—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×Q812yes—
87C22×C4×C43C2×Q812yes—
88C22×C4×C43#4112yes—
89C22×C4×C43#4112yes—
90C22×C4×C43#4112yes—
91C22×C4×C43C2411yescharacteristic
92C22×Dic43—22no—
93C22×Dic43—22no—
94C22×Dic43—42no—
95C22×Dic43—82no—
96C22×Dic43C2×D412yes—
97C22×Dic43C2×D412yes—
98M16×C43—44no—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—42no—
106C4⋊C4×C43C2×Q814yes—
107C22⋊C4×C43—24no—
108C42×C43—24no—
109C22⋊Dic43—24no—
110C22⋊Dic43—24no—
111C4⋊Dic43—22no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—42no—
117C4⋊Dic43—84no—
118C4⋊Dic43C2×Q814yes—
119Dic43⋊C4—84no—
120C4×Dic43—24no—
121C4×Dic43—22no—
122C4×Dic43—22no—
123C2×C43⋊C8—28no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8C2×D412yes—
129C2×C43⋊C8C2×D412yes—
130C23×C43—22no—
131C23×C43—22no—
132C23×C43#12112yes—
133C23×C43C22⋊Q812yes—
134C23×C43C22⋊Q812yes—
135C23×C43C22×D411yescharacteristic
136C2×C4×C43—24no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—44no—
141C2×C4×C43—84no—
142C2×C4×C43#12112yes—
143C2×C4×C43C22⋊Q812yes—
144C2×C4×C43C22⋊Q812yes—
145C2×C4×C43#12314yes—
146C2×C4×C43#12514yes—
147C2×C4×C43#12514yes—
148C2×C4×C43C4⋊Q814yes—
149C2×C4×C43C22×D411yescharacteristic
150C2×C4×C43C22×Q811yescharacteristic
151C2×C4×C43C22×Q811yescharacteristic
152C2×C4×C43C2×#4111yescharacteristic
153C2×C4×C43C2×#4111yescharacteristic
154C2×C4×C43C2×#4111yescharacteristic
155C2×Dic43—22no—
156C2×Dic43—22no—
157C2×Dic43—24no—
158C2×Dic43—24no—
159C2×Dic43—24no—
160C2×Dic43—42no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—44no—
164C2×Dic43—84no—
165C8×C43—42no—
166C43⋊C8—22no—
167C43⋊C8—22no—
168#23667—431nomaximal, Sylow
169C22×C43—24no—
170C22×C43—24no—
171C22×C43—22no—
172C22×C43—22no—
173C22×C43#39814yes—
174C22×C43C2×#12111yescharacteristic
175C22×C43C2×C22⋊Q811yescharacteristic
176C22×C43C2×C22⋊Q811yescharacteristic
177C22×C43#57612yes—
178C22×C43#57812yes—
179C4×C43—44no—
180C4×C43—82no—
181C4×C43#39814yes—
182C4×C43C2×#12311yescharacteristic
183C4×C43C2×#12511yescharacteristic
184C4×C43C2×#12511yescharacteristic
185C4×C43C2×C4⋊Q811yescharacteristic
186Dic43—44no—
187Dic43—42no—
188Dic43—42no—
189Dic43—82no—
190C22×#107—431no—
191C2×#424—431no—
192#2317—431no—
193#2317—431no—
194#2087—434no—
195#2086—434no—
196#1736—431no—
197#1736D4311yescharacteristic
198#1735—431no—
199C2×C43—24no—
200C2×C43C2×#39811yescharacteristic
201C2×C43#305811yescharacteristic
202C2×C43#305911yescharacteristic
203C2×C43#308312yes—
204C2×C43#308312yes—
205C22×M16C2×D4311yescharacteristic
206C23×C8—431no—
207C2×#117—431no—
208C2×#117—431no—
209C2×#117C2×D4311yescharacteristic
210C22×C4⋊C4—431no—
211C22×C4⋊C4C2×D4311yescharacteristic
212C2×#107—432no—
213C2×#107—432no—
214C2×#107—864no—
215#424—864no—
216C2×C4⋊C8—432no—
217C2×C4⋊C8—432no—
218#389—434no—
219#389—434no—
220#385—862no—
221#385—862no—
222#384—861no—
223#384—861no—
224#382—861no—
225#382—861no—
226#340—434no—
227#340—432no—
228#340—432no—
229#340C2×D4314yes—
230C43#2366711yescharacteristic, complemented, Sylow
231C23×C4—21no—
232C23×C4—861no—
233C23×C4C22×D4311yescharacteristic
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C22×C8—434no—
238C22×C8—431no—
239C22×C8—431no—
240C22×C8—862no—
241C22×C8—862no—
242C22×C8C22×D4312yes—
243#117—22no—
244#117—434no—
245#117—862no—
246#117—862no—
247#117—862no—
248#117Dic8614yes—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—432no—
253C2×C4⋊C4—431no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—432no—
256C2×C4⋊C4—862no—
257C2×C4⋊C4—862no—
258C2×C4⋊C4—864no—
259C2×C4⋊C4—864no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4C22×D4312yes—
262C2×C4⋊C4C22×D4312yes—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—432no—
265C2×C22⋊C4—861no—
266C2×C42—21no—
267C2×C42—432no—
268C2×C42—861no—
269#107—864no—
270#107—864no—
271C4⋊C8—864no—
272C4⋊C8—864no—
273#95—864no—
274#95—864no—
275C24D4×D4311yescharacteristic
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—42no—
279C22×C4—82no—
280C22×C4—432no—
281C22×C4—432no—
282C22×C4—862no—
283C22×C4—862no—
284C22×C4—3442no—
285C22×C4—1722no—
286C22×C4C2×Dic8612yes—
287C22×C4#1062189812yes—
288C22×C4#1062189812yes—
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4312yes—
291C22×C4#1062190012yes—
292C22×C4Q8×D4312yes—
293C22×C4C23×D4311yescharacteristic
294M16—44no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—432no—
299C2×C8—432no—
300C2×C8—868no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8—861no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—42no—
309C4⋊C4—434no—
310C4⋊C4—862no—
311C4⋊C4—862no—
312C4⋊C4—862no—
313C4⋊C4—862no—
314C4⋊C4—862no—
315C4⋊C4—3444no—
316C4⋊C4—3444no—
317C4⋊C4—1722no—
318C4⋊C4C2×Dic8614yes—
319C22⋊C4—24no—
320C22⋊C4—864no—
321C22⋊C4—864no—
322C42—24no—
323C42—864no—
324C42—862no—
325C42—862no—
326C23—22no—
327C23—22no—
328C23#1306329812yes—
329C23#1306330212yes—
330C23#1306330312yes—
331C23C2×D4×D4311yescharacteristic
332C2×C4—24no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—84no—
338C2×C4—862no—
339C2×C4—862no—
340C2×C4—864no—
341C2×C4—864no—
342C2×C4—864no—
343C2×C4—3444no—
344C2×C4—1722no—
345C2×C4—1724no—
346C2×C4—1722no—
347C2×C4—1722no—
348C2×C4#1306329812yes—
349C2×C4#1306330212yes—
350C2×C4#1306330312yes—
351C2×C4#1306330714yes—
352C2×C4#1306331514yes—
353C2×C4#1306331714yes—
354C2×C4#1306332414yes—
355C2×C4C2×D4×D4311yescharacteristic
356C2×C4C2×Q8×D4311yescharacteristic
357C2×C4C22×Dic8611yescharacteristic
358C2×C4C2×#1062190011yescharacteristic
359C2×C4C2×#1062189811yescharacteristic
360C2×C4C2×#1062189811yescharacteristic
361C8—42no—
362C8—862no—
363C8—862no—
364C22—24no—
365C22—22no—
366C22—22no—
367C22—24no—
368C22#1458283314yes—
369C22C2×#1306329811yescharacteristic
370C22C2×#1306330211yescharacteristic
371C22C2×#1306330311yescharacteristic
372C22#1458370312yes—
373C22#1458371512yes—
374C4—44no—
375C4—82no—
376C4—3442no—
377C4—1722no—
378C4—1722no—
379C4—1724no—
380C4#1458283314yes—
381C4C2×#1306330711yescharacteristic
382C4C2×#1306331511yescharacteristic
383C4C2×#1306331711yescharacteristic
384C4C2×#1306332411yescharacteristic
385C2—24no—
386C2C2×#1458283311yescharacteristic
387C2#1914424211yescharacteristic
388C2#1914424911yescharacteristic
389C2#1914444512yes—
390C2#1914445012yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#1736D43
hypocenterC43#23667
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
5. #19136092C2semidirect
6. #19136087C2semidirect
230. C43#23667semidirect

Maximal subgroups

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

subgroupindex
C22×#130632582
C2×#145829272
#191372192
#191372182
#191360922
#191360872
#191343152
#191343112
C43×#17362
#2366743