Finite Group Databasebeta

← #25003924

Subgroups — #25003924

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582948C211yesmaximal, characteristic, complemented
2C2×#14582916C212yesmaximal
3C2×#14582656C211yesmaximal, characteristic, complemented
4#19134291C212yesmaximal, complemented
5C2×C43×#408C211yesmaximal, characteristic
6C22×#10621877C2212yes—
7C2×#13063284C2212yes—
8#14582948—24no—
9C2×#13063261—22no—
10#14582916—24no—
11#14582916—24no—
12C2×#13063252—24no—
13#14582656—22no—
14#14582653—24no—
15C22×#41×C43C2211yescharacteristic
16C22×M16×C43C2211yescharacteristic
17C23×C8×C43C2211yescharacteristic
18C43×#408—22no—
19C43×#408C414yescomplemented
20C2×C22⋊C8×C43—22no—
21C2×#10621877—22no—
22C2×#10621877—22no—
23C2×#10621877—22no—
24C2×#10621877—22no—
25C2×#10621877—22no—
26C2×#10621877D414yes—
27C22×C43⋊C8—22no—
28#13063284—22no—
29#13063284—22no—
30#13063284—22no—
31#13063284—22no—
32C2×C4⋊Dic43—22no—
33C2×C22⋊Dic43—22no—
34C2×C4×Dic43D414yes—
35#13063261—28no—
36#13063252—216no—
37C2×#41×C43—21no—
38C2×#41×C43—21no—
39C2×#41×C43—22no—
40C2×#41×C43—22no—
41C2×#41×C43—22no—
42C2×#41×C43—22no—
43C2×#41×C43C2×C412yes—
44C2×#41×C43D412yes—
45C22×Q8×C43Q811yescharacteristic
46C22×D4×C43—21no—
47C22×D4×C43Q811yescharacteristic
48C23×C4×C43—21no—
49C23×C4×C43C2311yescharacteristic
50C2×M16×C43—22no—
51C2×M16×C43—22no—
52C2×M16×C43C2×C412yes—
53C2×M16×C43D412yes—
54C22×C8×C43—22no—
55C22×C8×C43—21no—
56C22×C8×C43—21no—
57C22×C8×C43—22no—
58C22×C8×C43C2×C412yes—
59C22×C8×C43D412yes—
60C22⋊C8×C43—28no—
61C24×C43—21no—
62C24×C43#4111yescharacteristic
63#41×C43—24no—
64#41×C43—24no—
65#41×C43—24no—
66#41×C43—24no—
67#41×C43—42no—
68#41×C43—42no—
69#41×C43—42no—
70#41×C43—42no—
71C2×Q8×C43—21no—
72C2×Q8×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43C4⋊C412yes—
75C2×D4×C43—21no—
76C2×D4×C43—22no—
77C2×D4×C43—22no—
78C2×D4×C43—22no—
79C2×D4×C43—22no—
80C2×D4×C43—42no—
81C2×D4×C43—42no—
82C2×D4×C43C4⋊C412yes—
83C22×C4×C43—22no—
84C22×C4×C43—22no—
85C22×C4×C43—21no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D412yes—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×Q811yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C22×C4×C43#4112yes—
99C22×C4×C43#4112yes—
100C22×Dic43—24no—
101M16×C43—24no—
102M16×C43—24no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C2×C8×C43—22no—
106C2×C8×C43—24no—
107C2×C8×C43—42no—
108C2×C8×C43—41no—
109C2×C8×C43—41no—
110C2×C8×C43C22⋊C414yes—
111C22⋊Dic43—42no—
112C22⋊Dic43—42no—
113C4⋊Dic43—42no—
114C4⋊Dic43—42no—
115C4×Dic43—24no—
116C4×Dic43—24no—
117#10621877—24no—
118#10621877—24no—
119#10621877—42no—
120#10621877—42no—
121C2×C43⋊C8—24no—
122C2×C43⋊C8—42no—
123C2×C43⋊C8—42no—
124C23×C43—22no—
125C23×C43—42no—
126C23×C43—44no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43#11711yescharacteristic
130C23×C43#12111yescharacteristic
131C23×C43C22⋊Q811yescharacteristic
132C23×C43#12312yes—
133C23×C43#12412yes—
134Q8×C43—24no—
135Q8×C43—42no—
136D4×C43—24no—
137D4×C43—44no—
138D4×C43—44no—
139D4×C43—42no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43C2×C22⋊C411yescharacteristic
148C2×C4×C43C2×C4⋊C411yescharacteristic
149C2×C4×C43C4×D412yes—
150C2×C4×C43C4×D412yes—
151C2×C4×C43#12011yescharacteristic
152C2×C4×C43#12012yes—
153C2×C4×C43#12112yes—
154C2×C4×C43#12112yes—
155C2×C4×C43#12112yes—
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43C22⋊Q812yes—
158C2×C4×C43C22⋊Q812yes—
159C2×C4×C43C22⋊Q811yescharacteristic
160C2×C4×C43#12311yescharacteristic
161C2×C4×C43#12312yes—
162C2×C4×C43#12411yescharacteristic
163C2×C4×C43#12612yes—
164C2×C4×C43#12711yescharacteristic
165C2×Dic43—48no—
166C2×Dic43—44no—
167C8×C43—24no—
168C8×C43—42no—
169C43⋊C8—44no—
170#11112—431nomaximal, Sylow
171C22×C43—22no—
172C22×C43—24no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—42no—
176C22×C43—44no—
177C22×C43—42no—
178C22×C43—82no—
179C22×C43—82no—
180C22×C43#38011yescharacteristic
181C22×C43#38812yes—
182C22×C43#39311yescharacteristic
183C22×C43#39412yes—
184C22×C43#39911yescharacteristic
185C4×C43—42no—
186C4×C43#38512yes—
187C4×C43#38611yescharacteristic
188C4×C43#39011yescharacteristic
189C4×C43#39211yescharacteristic
190C4×C43#39612yes—
191C4×C43#39711yescharacteristic
192Dic43—84no—
193C2×#430—431no—
194C2×#421—432no—
195C2×#408D4311yescharacteristic
196C2×H(3,ℤ/4)—431no—
197#1729—432no—
198C2×C43—22no—
199C2×C43—21no—
200C2×C43—21no—
201C2×C43—22no—
202C2×C43—82no—
203C2×C43#143911yescharacteristic
204C2×C43#209812yes—
205C22×#41C2×D4311yescharacteristic
206C22×M16—432no—
207C22×M16C2×D4311yescharacteristic
208C23×C8C2×D4311yescharacteristic
209C2×#117—432no—
210#430—864no—
211C2×#108—862no—
212#421—864no—
213#421—864no—
214C2×#104—864no—
215#408—22no—
216#408Dic4314yescomplemented
217C2×C22⋊C8—22no—
218H(3,ℤ/4)—862no—
219#336—864no—
220C43#1111211yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C2×#41—21no—
223C2×#41—22no—
224C2×#41—22no—
225C2×#41—22no—
226C2×#41—22no—
227C2×#41D17212yes—
228C2×#41C2×Dic4312yes—
229C22×Q8Dic8611yescharacteristic
230C22×D4—21no—
231C22×D4Dic8611yescharacteristic
232C23×C4—21no—
233C23×C4C22×D4311yescharacteristic
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—434no—
237C2×M16—862no—
238C2×M16—862no—
239C2×M16—862no—
240C2×M16—862no—
241C2×M16—862no—
242C2×M16C2×Dic4312yes—
243C2×M16C22⋊D4312yes—
244C22×C8—22no—
245C22×C8—22no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—862no—
249C22×C8C2×Dic4312yes—
250C22×C8C22⋊D4312yes—
251#117—862no—
252#117—862no—
253#117—862no—
254#117—862no—
255C2×C4⋊C4—862no—
256C2×C22⋊C4—862no—
257C2×C42—434no—
258#108—868no—
259#104—8616no—
260C22⋊C8—28no—
261C24—21no—
262C24#1062189811yescharacteristic
263#41—24no—
264#41—24no—
265#41—24no—
266#41—24no—
267#41—42no—
268#41—42no—
269#41—42no—
270#41—42no—
271C2×Q8—21no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8C4⋊Dic4312yes—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—21no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4C4⋊Dic4312yes—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—864no—
291C22×C4C2×Dic8611yescharacteristic
292C22×C4C2×D17211yescharacteristic
293C22×C4#1062189811yescharacteristic
294C22×C4D4×D4312yes—
295C22×C4D4×D4312yes—
296C22×C4#1062190012yes—
297C22×C4#1062190012yes—
298C22×C4C22×Dic4311yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300C22×C4C2×C22⋊D4311yescharacteristic
301M16—24no—
302M16—24no—
303M16—864no—
304M16—864no—
305M16—1722no—
306M16—1722no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—24no—
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—864no—
315C2×C8—1722no—
316C2×C8—1722no—
317C2×C8C22⋊Dic4314yes—
318C4⋊C4—1722no—
319C4⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4—1722no—
322C42—864no—
323C42—864no—
324C23—22no—
325C23—42no—
326C23—44no—
327C23—41no—
328C23—41no—
329C23#1306328411yescharacteristic
330C23#1306329911yescharacteristic
331C23#1306330411yescharacteristic
332C23#1306330712yes—
333C23#1306331112yes—
334Q8—24no—
335Q8—42no—
336D4—24no—
337D4—44no—
338D4—44no—
339D4—42no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—1728no—
348C2×C4—1724no—
349C2×C4C2×C22⋊Dic4311yescharacteristic
350C2×C4C2×C4⋊Dic4311yescharacteristic
351C2×C4D4×Dic4312yes—
352C2×C4D4×Dic4312yes—
353C2×C4#1306329311yescharacteristic
354C2×C4#1306329512yes—
355C2×C4#1306329612yes—
356C2×C4#1306329712yes—
357C2×C4#1306329812yes—
358C2×C4#1306329911yescharacteristic
359C2×C4#1306330212yes—
360C2×C4#1306330212yes—
361C2×C4#1306330411yescharacteristic
362C2×C4#1306330611yescharacteristic
363C2×C4#1306330912yes—
364C2×C4#1306331211yescharacteristic
365C2×C4#1306331812yes—
366C2×C4#1306332111yescharacteristic
367C8—24no—
368C8—42no—
369C8—1724no—
370C22—24no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—44no—
376C22—42no—
377C22—82no—
378C22—82no—
379C22#1458275911yescharacteristic
380C22#1458279212yes—
381C22#1458281111yescharacteristic
382C22#1458281512yes—
383C22#1458283511yescharacteristic
384C4—42no—
385C4—3444no—
386C4#1458277412yes—
387C4#1458277911yescharacteristic
388C4#1458280211yescharacteristic
389C4#1458280811yescharacteristic
390C4#1458282212yes—
391C4#1458282411yescharacteristic
392C2—22no—
393C2—21no—
394C2—21no—
395C2—22no—
396C2—82no—
397C2#1913284011yescharacteristic
398C2#1913614812yes—
subgroupG/H
centerC2×C4#13063321
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#408C2
socleC22×C43#399
prime radicalC22×#41×C43C22
cosocleC23×C4×C43C23
hypercenterC2×#408D43
hypocenterC43#11112
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#14582948C2semidirect
3. C2×#14582656C2semidirect
4. #19134291C2semidirect
19. C43×#408C4semidirect
216. #408Dic43semidirect
220. C43#11112semidirect

Maximal subgroups

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

subgroupindex
C2×#145829482
C2×#145829162
C2×#145826562
#191342912
C2×C43×#4082
#1111243