Finite Group Databasebeta

← #25004861

Subgroups — #25004861

Order 11008.

798 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
1C2×#14582765C211yesmaximal, characteristic
2C2×#14582662C212yesmaximal
3C2×#14582662C212yesmaximal
4#19132825C211yesmaximal, characteristic
5C2×C43×#336C211yesmaximal, characteristic
6C22×C4⋊Dic43C2211yescharacteristic
7C22×C4⋊Dic43C2212yes—
8C22×C4⋊Dic43C2211yescharacteristic
9#14582765—24no—
10C2×C43⋊#95—22no—
11C2×C43⋊#95—22no—
12#14582662—24no—
13#14582662—24no—
14C23×C8×C43C2212yes—
15C22×C42×C43C2211yescharacteristic
16C43×#336C414yescomplemented
17C23×Dic43—22no—
18C23×Dic43—21no—
19C23×Dic43—21no—
20C2×C4⋊Dic43—22no—
21C2×C4⋊Dic43—22no—
22C2×C4⋊Dic43—22no—
23C2×C4⋊Dic43—22no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43—22no—
26C2×C4⋊Dic43—22no—
27C2×C4⋊Dic43—22no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43D412yes—
32C2×C4⋊Dic43D414yes—
33C2×C4⋊Dic43Q812yes—
34C43⋊#95—28no—
35C43⋊#95—44no—
36C23×C4×C43D412yes—
37C23×C4×C43C2311yescharacteristic
38C22×C8×C43—22no—
39C22×C8×C43—22no—
40C22×C8×C43—22no—
41C22×C8×C43—22no—
42C22×C8×C43—22no—
43C22×C8×C43—22no—
44C22×C8×C43C2×C414yes—
45C2×C42×C43—22no—
46C2×C42×C43—22no—
47C2×C42×C43C2×C412yes—
48C2×C42×C43Q812yes—
49C24×C43C2×D411yescharacteristic
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—22no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43C4⋊C414yes—
57C22×C4×C43C22×C411yescharacteristic
58C22×C4×C43C2×D412yes—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×Q811yescharacteristic
61C22×C4×C43C2×Q811yescharacteristic
62C22×C4×C43#4111yescharacteristic
63C22×C4×C43#4111yescharacteristic
64C22×C4×C43#4112yes—
65C22×C4×C43#4112yes—
66C22×C4×C43#4112yes—
67C22×Dic43—24no—
68C22×Dic43—22no—
69C22×Dic43—22no—
70C22×Dic43—41no—
71C22×Dic43—42no—
72C22×Dic43—41no—
73C22×Dic43—41no—
74C22×Dic43—41no—
75C22×Dic43—42no—
76C22×Dic43—42no—
77C22×Dic43—42no—
78C22×Dic43—42no—
79C22×Dic43—42no—
80C22×Dic43—42no—
81C22×Dic43—42no—
82C22×Dic43—42no—
83C22×Dic43—42no—
84C2×C8×C43—24no—
85C2×C8×C43—24no—
86C2×C8×C43—24no—
87C2×C8×C43—42no—
88C2×C8×C43—42no—
89C2×C8×C43—42no—
90C2×C8×C43—42no—
91C42×C43—24no—
92C42×C43—24no—
93C4⋊Dic43—24no—
94C4⋊Dic43—24no—
95C4⋊Dic43—24no—
96C4⋊Dic43—24no—
97C4⋊Dic43—42no—
98C4⋊Dic43—42no—
99C4⋊Dic43—42no—
100C4⋊Dic43—42no—
101C23×C43C2×C4⋊C411yescharacteristic
102C23×C43#12011yescharacteristic
103C23×C43#12111yescharacteristic
104C23×C43C22⋊Q811yescharacteristic
105C23×C43#12311yescharacteristic
106C23×C43#12411yescharacteristic
107C23×C43#12411yescharacteristic
108C23×C43#13512yes—
109C23×C43#13512yes—
110C23×C43AGL(1,ℤ/8)12yes—
111C23×C43#13712yes—
112C2×C4×C43—24no—
113C2×C4×C43—24no—
114C2×C4×C43—24no—
115C2×C4×C43—42no—
116C2×C4×C43—42no—
117C2×C4×C43—42no—
118C2×C4×C43—42no—
119C2×C4×C43#11712yes—
120C2×C4×C43C4×D412yes—
121C2×C4×C43C4×D411yescharacteristic
122C2×C4×C43C4×Q811yescharacteristic
123C2×C4×C43#12112yes—
124C2×C4×C43C22⋊Q812yes—
125C2×C4×C43C22⋊Q812yes—
126C2×C4×C43#12312yes—
127C2×C4×C43#12312yes—
128C2×C4×C43#12412yes—
129C2×C4×C43#12512yes—
130C2×C4×C43#12511yescharacteristic
131C2×C4×C43#12512yes—
132C2×C4×C43#12612yes—
133C2×C4×C43#12612yes—
134C2×C4×C43C4⋊Q811yescharacteristic
135C2×Dic43—42no—
136C2×Dic43—44no—
137C2×Dic43—42no—
138C2×Dic43—44no—
139C2×Dic43—44no—
140C2×Dic43—44no—
141C2×Dic43—44no—
142C2×Dic43—82no—
143C2×Dic43—82no—
144C2×Dic43—82no—
145C2×Dic43—82no—
146C2×Dic43—81no—
147C2×Dic43—81no—
148C2×Dic43—82no—
149C2×Dic43—82no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C8×C43—44no—
153#11268—431nomaximal, Sylow
154C22×C43#38211yescharacteristic
155C22×C43#38511yescharacteristic
156C22×C43#38911yescharacteristic
157C22×C43#39311yescharacteristic
158C22×C43#39411yescharacteristic
159C22×C43#39711yescharacteristic
160C22×C43#40011yescharacteristic
161C22×C43#42712yes—
162C22×C43#42812yes—
163C22×C43#44912yes—
164C22×C43#45212yes—
165C22×C43#46312yes—
166C22×C43#46412yes—
167C22×C43#47812yes—
168C22×C43#47912yes—
169C22×C43#48212yes—
170C22×C43#48512yes—
171C22×C43#48811yescharacteristic
172C22×C43#48811yescharacteristic
173C22×C43#48812yes—
174C22×C43#48912yes—
175C22×C43#49011yescharacteristic
176C22×C43#49111yescharacteristic
177C4×C43—44no—
178C4×C43#38712yes—
179C4×C43#38812yes—
180C4×C43#39812yes—
181C4×C43#40012yes—
182Dic43—82no—
183Dic43—82no—
184Dic43—84no—
185C2×#382—431no—
186C2×#340—432no—
187C2×#340—432no—
188C2×#336D4311yescharacteristic
189C4⋊#95—431no—
190C2×C43#144211yescharacteristic
191C2×C43#183511yescharacteristic
192C2×C43#183611yescharacteristic
193C2×C43#185412yes—
194C2×C43#194912yes—
195C2×C43#202511yescharacteristic
196C2×C43#202611yescharacteristic
197C2×C43#204212yes—
198C2×C43#207311yescharacteristic
199C2×C43#207411yescharacteristic
200C2×C43#210112yes—
201C23×C8C2×D4312yes—
202C22×C4⋊C4—431no—
203C22×C4⋊C4—431no—
204C22×C4⋊C4—432no—
205C22×C42C2×D4311yescharacteristic
206#382—864no—
207C2×#95—862no—
208C2×#95—862no—
209#340—864no—
210#340—864no—
211#336Dic4314yescomplemented
212C43#1126811yescharacteristic, complemented, Sylow
213C23×C4—862no—
214C23×C4—861no—
215C23×C4—861no—
216C23×C4D17212yes—
217C23×C4C22×D4311yescharacteristic
218C22×C8—22no—
219C22×C8—22no—
220C22×C8—22no—
221C22×C8—22no—
222C22×C8—22no—
223C22×C8—22no—
224C22×C8C2×Dic4314yes—
225C2×C4⋊C4—432no—
226C2×C4⋊C4—434no—
227C2×C4⋊C4—432no—
228C2×C4⋊C4—862no—
229C2×C4⋊C4—862no—
230C2×C4⋊C4—862no—
231C2×C4⋊C4—862no—
232C2×C4⋊C4—862no—
233C2×C4⋊C4—862no—
234C2×C4⋊C4—862no—
235C2×C4⋊C4—862no—
236C2×C4⋊C4—862no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C42—22no—
240C2×C42—22no—
241C2×C42Dic8612yes—
242C2×C42C2×Dic4312yes—
243#95—868no—
244#95—1724no—
245C24C2×D17211yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—864no—
253C22×C4—862no—
254C22×C4—862no—
255C22×C4—1721no—
256C22×C4—1722no—
257C22×C4—1721no—
258C22×C4—1722no—
259C22×C4—1721no—
260C22×C4—1721no—
261C22×C4—1722no—
262C22×C4—1722no—
263C22×C4—1722no—
264C22×C4—1722no—
265C22×C4—1722no—
266C22×C4—1722no—
267C22×C4—1722no—
268C22×C4—1722no—
269C22×C4C4⋊Dic4314yes—
270C22×C4C2×Dic8611yescharacteristic
271C22×C4#1062189812yes—
272C22×C4#1062189812yes—
273C22×C4D4×D4311yescharacteristic
274C22×C4D4×D4312yes—
275C22×C4#1062190012yes—
276C22×C4#1062190011yescharacteristic
277C22×C4Q8×D4311yescharacteristic
278C22×C4#1062190211yescharacteristic
279C22×C4C22×Dic4311yescharacteristic
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—24no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C4⋊C4—864no—
288C4⋊C4—864no—
289C4⋊C4—864no—
290C4⋊C4—864no—
291C4⋊C4—1722no—
292C4⋊C4—1722no—
293C4⋊C4—1722no—
294C4⋊C4—1722no—
295C42—24no—
296C42—24no—
297C23C2×C4⋊Dic4311yescharacteristic
298C23#1306329511yescharacteristic
299C23#1306330011yescharacteristic
300C23#1306330511yescharacteristic
301C23#1306330911yescharacteristic
302C23#1306331311yescharacteristic
303C23#1306331311yescharacteristic
304C23#1306334712yes—
305C23#1306334712yes—
306C23#1306335312yes—
307C23#1306335812yes—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—3442no—
316C2×C4—3442no—
317C2×C4—3442no—
318C2×C4—3442no—
319C2×C4—3441no—
320C2×C4—3442no—
321C2×C4—3441no—
322C2×C4—3442no—
323C2×C4—3441no—
324C2×C4—3441no—
325C2×C4—1724no—
326C2×C4—1724no—
327C2×C4—1722no—
328C2×C4—1724no—
329C2×C4—1722no—
330C2×C4—1724no—
331C2×C4—1724no—
332C2×C4#1306328412yes—
333C2×C4D4×Dic4312yes—
334C2×C4D4×Dic4311yescharacteristic
335C2×C4Q8×Dic4311yescharacteristic
336C2×C4#1306329812yes—
337C2×C4#1306330212yes—
338C2×C4#1306330312yes—
339C2×C4#1306330712yes—
340C2×C4#1306331012yes—
341C2×C4#1306331112yes—
342C2×C4#1306331512yes—
343C2×C4#1306331611yescharacteristic
344C2×C4#1306331712yes—
345C2×C4#1306331812yes—
346C2×C4#1306332012yes—
347C2×C4#1306332411yescharacteristic
348C8—44no—
349C22#1458276511yescharacteristic
350C22#1458277411yescharacteristic
351C22#1458279811yescharacteristic
352C22#1458281211yescharacteristic
353C22#1458281711yescharacteristic
354C22#1458282611yescharacteristic
355C22#1458283911yescharacteristic
356C22#1458293712yes—
357C22#1458294112yes—
358C22#1458304612yes—
359C22#1458306312yes—
360C22#1458311512yes—
361C22#1458312212yes—
362C22#1458320012yes—
363C22#1458320712yes—
364C22#1458322412yes—
365C22#1458324112yes—
366C22#1458325411yescharacteristic
367C22#1458325411yescharacteristic
368C22#1458325412yes—
369C22#1458325912yes—
370C22#1458326411yescharacteristic
371C22#1458326811yescharacteristic
372C4—44no—
373C4—3442no—
374C4—3444no—
375C4—3442no—
376C4#1458278512yes—
377C4#1458279212yes—
378C4#1458283312yes—
379C4#1458284112yes—
380C2#1913285211yescharacteristic
381C2#1913472611yescharacteristic
382C2#1913472911yescharacteristic
383C2#1913479612yes—
384C2#1913536512yes—
385C2#1913574211yescharacteristic
386C2#1913574711yescharacteristic
387C2#1913583712yes—
388C2#1913601011yescharacteristic
389C2#1913601511yescharacteristic
390C2#1913616412yes—
subgroupG/H
centerC24C2×D172
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#336C2
socle, prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenterC2×#336D43
hypocenterC43#11268
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
16. C43×#336C4semidirect
211. #336Dic43semidirect
212. C43#11268semidirect

Maximal subgroups

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

subgroupindex
C2×#145827652
C2×#145826622
#191328252
C2×C43×#3362
#1126843