Finite Group Databasebeta

← #25007363

Subgroups — #25007363

Order 11008.

582 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134583C211yesmaximal, characteristic, complemented
2#19132933C211yesmaximal, characteristic, complemented
3#19132619C212yesmaximal, complemented
4#19132592C212yesmaximal, complemented
5C43×#2397C211yesmaximal, characteristic
6C2×#13063240—21no—
7#14582863—21no—
8#14582759—21no—
9#14582666C2212yes—
10#14582625—21no—
11#14582623C2212yes—
12C2×C4×D4×C43—21no—
13C2×C4×D4×C43—21no—
14C2×C4×D4×C43C411yescharacteristic, complemented
15C2×C4×D4×C43C2211yescharacteristic
16C43×#399—21no—
17C43×#399C411yescharacteristic, complemented
18C43×#399C2211yescharacteristic
19C43×#392—21no—
20C43×#392C411yescharacteristic, complemented
21C43×#392C2211yescharacteristic
22C43×#376C411yescharacteristic, complemented
23C2×#10621877—41no—
24C2×C4⋊Dic43—41no—
25C2×C22⋊Dic43—22no—
26#13063240—42no—
27C22⋊(C43⋊C8)—22no—
28C22⋊(C43⋊C8)—41no—
29C43⋊#95—41no—
30C22×D4×C43—21no—
31C22×D4×C43—21no—
32C22×D4×C43C2×C411yescharacteristic
33C22×D4×C43D411yescharacteristic
34C23×C4×C43—21no—
35C23×C4×C43D411yescharacteristic
36C23×C4×C43D411yescharacteristic
37C4×D4×C43—41no—
38C4×D4×C43—41no—
39C4×D4×C43—44no—
40C4×D4×C43—44no—
41C4×D4×C43—41no—
42C4×D4×C43—41no—
43C2×C4⋊C4×C43—21no—
44C2×C4⋊C4×C43—21no—
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C22⋊C4×C43—21no—
48C2×C22⋊C4×C43—21no—
49C2×C22⋊C4×C43—21no—
50C2×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43C2×C411yescharacteristic
53C2×C22⋊C4×C43C2311yescharacteristic
54C2×C42×C43—21no—
55C2×C42×C43C2×C411yescharacteristic
56#95×C43—21no—
57#95×C43C2×C411yescharacteristic
58#95×C43C2×C411yescharacteristic
59C24×C43—21no—
60C24×C43C22⋊C411yescharacteristic
61C24×C43C2×D411yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43—41no—
65C2×D4×C43—41no—
66C2×D4×C43—42no—
67C2×D4×C43—42no—
68C2×D4×C43—42no—
69C2×D4×C43—42no—
70C2×D4×C43—42no—
71C2×D4×C43—42no—
72C2×D4×C43—41no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—42no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43—42no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C22⋊C411yescharacteristic
89C22×C4×C43C22⋊C411yescharacteristic
90C22×C4×C43C22⋊C411yescharacteristic
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×Dic43—42no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—42no—
97C4⋊C4×C43—42no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—42no—
101C22⋊C4×C43—42no—
102C22⋊C4×C43—42no—
103C22⋊C4×C43—42no—
104C22⋊C4×C43—42no—
105C42×C43—24no—
106C42×C43—21no—
107C42×C43—21no—
108C22⋊Dic43—42no—
109C22⋊Dic43—42no—
110C4⋊Dic43—82no—
111#10621877—82no—
112C2×C43⋊C8—42no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—22no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43—41no—
129C23×C43C2×C22⋊C411yescharacteristic
130C23×C43AGL(1,ℤ/8)11yescharacteristic
131C23×C43#13711yescharacteristic
132D4×C43—42no—
133D4×C43—42no—
134D4×C43—42no—
135D4×C43—44no—
136D4×C43—44no—
137D4×C43—48no—
138D4×C43—42no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43—82no—
163C2×C4×C43—82no—
164C2×C4×C43#9911yescharacteristic
165C2×C4×C43#9911yescharacteristic
166C2×Dic43—82no—
167C2×Dic43—82no—
168C2×Dic43—82no—
169C43⋊C8—82no—
170#11821—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—42no—
178C22×C43—42no—
179C22×C43—42no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—42no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—81no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43C2×#9911yescharacteristic
193C22×C43#41711yescharacteristic
194C22×C43#42111yescharacteristic
195C4×C43—21no—
196C4×C43—42no—
197C4×C43—42no—
198C4×C43—41no—
199C4×C43—41no—
200C4×C43—41no—
201C4×C43—41no—
202C4×C43—81no—
203C4×C43#35312yes—
204Dic43—162no—
205#2397D4311yescharacteristic
206#1799—431no—
207#1465—431no—
208#1352—432no—
209#1343—432no—
210C2×C43—21no—
211C2×C43—21no—
212C2×C43—41no—
213C2×C43—41no—
214C2×C43—81no—
215C2×C43—82no—
216C2×C43#151311yescharacteristic
217C2×C43#212011yescharacteristic
218C2×C43C2×#35311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4—21no—
221C2×C4×D4Dic4311yescharacteristic, complemented
222C2×C4×D4C2×D4311yescharacteristic
223C2×#99—861no—
224#407—861no—
225#399—21no—
226#399Dic4311yescharacteristic, complemented
227#399C2×D4311yescharacteristic
228#392—21no—
229#392Dic4311yescharacteristic, complemented
230#392C2×D4311yescharacteristic
231#380—861no—
232#376Dic4311yescharacteristic, complemented
233#342—432no—
234#324—861no—
235#323—432no—
236C43#1182111yescharacteristic, complemented, Sylow
237C22×D4—21no—
238C22×D4—21no—
239C22×D4C2×Dic4311yescharacteristic
240C22×D4C22⋊D4311yescharacteristic
241C23×C4—21no—
242C23×C4C22⋊D4311yescharacteristic
243C23×C4C22⋊D4311yescharacteristic
244C2×M16—1721no—
245C4×D4—41no—
246C4×D4—41no—
247C4×D4—44no—
248C4×D4—44no—
249C4×D4—41no—
250C4×D4—41no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—1721no—
254C2×C4⋊C4C2×Dic4311yescharacteristic
255C2×C4⋊C4C22⋊D4311yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—862no—
262C2×C22⋊C4C2×Dic4311yescharacteristic
263C2×C22⋊C4C22×D4311yescharacteristic
264C2×C42—21no—
265C2×C42C2×Dic4311yescharacteristic
266#99—1722no—
267C22⋊C8—862no—
268C22⋊C8—1721no—
269#95—21no—
270#95—1721no—
271#95C2×Dic4311yescharacteristic
272#95C2×Dic4311yescharacteristic
273C24—21no—
274C24C22⋊Dic4311yescharacteristic
275C24C2×C22⋊D4311yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—42no—
285C2×D4—42no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—42no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—1722no—
303C22×C4C22⋊Dic4311yescharacteristic
304C22×C4C22⋊Dic4311yescharacteristic
305C22×C4C22⋊Dic4311yescharacteristic
306C22×C4C22×Dic4311yescharacteristic
307C22×C4C2×C22⋊D4311yescharacteristic
308M16—3442no—
309C2×C8—1722no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—3442no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—42no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—1722no—
323C22⋊C4—1722no—
324C42—24no—
325C42—21no—
326C42—21no—
327C23—21no—
328C23—21no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23C2×C22⋊Dic4311yescharacteristic
344C23#1306335011yescharacteristic
345C23#1306335511yescharacteristic
346D4—42no—
347D4—42no—
348D4—42no—
349D4—44no—
350D4—44no—
351D4—48no—
352D4—42no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—3442no—
379C2×C4—3442no—
380C2×C4—3442no—
381C2×C4#1306324011yescharacteristic
382C2×C4#1306324011yescharacteristic
383C8—3442no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—42no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22C2×#1306324011yescharacteristic
406C22#1458290011yescharacteristic
407C22#1458291611yescharacteristic
408C4—21no—
409C4—42no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—6882no—
417C4#1458269212yes—
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—81no—
423C2—82no—
424C2#1913313811yescharacteristic
425C2#1913623611yescharacteristic
426C2C2×#1458269211yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
Fitting, prime radicalC43×#2397C2
socleC22×C43C2×#99
cosocleC2×C22⋊C4×C43C23
hypercenter#2397D43
hypocenterC43#11821
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #19134583C2semidirect
2. #19132933C2semidirect
3. #19132619C2semidirect
4. #19132592C2semidirect
14. C2×C4×D4×C43C4semidirect
17. C43×#399C4semidirect
20. C43×#392C4semidirect
22. C43×#376C4semidirect
221. C2×C4×D4Dic43semidirect
226. #399Dic43semidirect
229. #392Dic43semidirect
232. #376Dic43semidirect
236. C43#11821semidirect

Maximal subgroups

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

subgroupindex
#191345832
#191329332
#191326192
#191325922
C43×#23972
#1182143