Finite Group Databasebeta

← #25007631

Subgroups — #25007631

Order 11008.

644 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 99 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#19139541C211yesmaximal, characteristic
2#19134583C211yesmaximal, characteristic, complemented
3#19132593C214yesmaximal, complemented
4C43×#1459C211yesmaximal, characteristic, complemented
5C2×#13063322C411yescharacteristic, complemented
6C2×#13063321—21no—
7C2×#13063299—21no—
8C2×#13063299—21no—
9C2×#13063240—21no—
10#14582808C412yescomplemented
11#14582808C2212yes—
12#14582800—21no—
13#14582759—21no—
14C4×C4⋊Dic43C411yescharacteristic, complemented
15#14582666C2212yes—
16C2×C4×D4×C43C2211yescharacteristic
17C2×C22⋊C8×C43—21no—
18C43×#324—21no—
19C43×#323C2212yes—
20C22×D172—21no—
21C22×D172—21no—
22C22×D172C2×C412yes—
23C22×C22⋊D43—22no—
24C22×C22⋊D43—22no—
25#13063322—41no—
26#13063322—41no—
27#13063321—42no—
28#13063321—42no—
29#13063299—44no—
30#13063299—44no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—41no—
33C2×C22⋊Dic43—22no—
34C2×(C2×D43)⋊C4—22no—
35C2×(C2×D43)⋊C4—22no—
36C2×C4×Dic43—21no—
37#13063240—42no—
38C43⋊#95—41no—
39C43⋊#95C2×C412yes—
40C22×D4×C43D411yescharacteristic
41C23×C4×C43D411yescharacteristic
42C23×C4×C43D411yescharacteristic
43C22×C8×C43—41no—
44C4×D4×C43—41no—
45C4×D4×C43—41no—
46C2×C4⋊C4×C43D411yescharacteristic
47C2×C22⋊C4×C43C2×C411yescharacteristic
48C2×C22⋊C4×C43C2311yescharacteristic
49C2×C42×C43C2×C411yescharacteristic
50C22⋊C8×C43—22no—
51C22⋊C8×C43—41no—
52C24×C43C22⋊C411yescharacteristic
53C24×C43C2×D411yescharacteristic
54C23×D43—22no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C2×D4×C43D812yes—
58C2×D4×C43SD1612yes—
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—42no—
64C22×C4×C43—42no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C2×C22⋊D43—44no—
71C2×C22⋊D43—44no—
72C2×C22⋊D43—44no—
73C2×C22⋊D43—42no—
74C2×C22⋊D43—42no—
75C2×C22⋊D43—82no—
76C2×C22⋊D43—82no—
77C22×Dic43—22no—
78C22×Dic43—42no—
79C2×D172—42no—
80C2×D172—42no—
81C2×D172—42no—
82C2×D172—42no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—42no—
86C2×D172—42no—
87C2×D172—82no—
88C2×C8×C43—42no—
89C2×C8×C43—82no—
90C4⋊C4×C43—41no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C42×C43—21no—
94C42×C43—21no—
95C22⋊Dic43—42no—
96C22⋊Dic43—42no—
97(C2×D43)⋊C4—44no—
98(C2×D43)⋊C4—44no—
99C4⋊Dic43—24no—
100C4⋊Dic43—82no—
101C4×Dic43—42no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43#10212yes—
111C23×C43C2×C22⋊C411yescharacteristic
112C23×C43C2×D811yescharacteristic
113C23×C43C2×SD1611yescharacteristic
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—42no—
121D4×C43—42no—
122D4×C43—42no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—22no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43#9911yescharacteristic
137C2×C4×C43#9911yescharacteristic
138C2×C4×C43#10212yes—
139C22⋊D43—88no—
140C22⋊D43—84no—
141C22⋊D43—84no—
142C2×Dic43—24no—
143C2×Dic43—42no—
144C2×Dic43—42no—
145C2×Dic43—82no—
146C2×Dic43—82no—
147C2×Dic43—82no—
148D172—82no—
149D172—84no—
150D172—84no—
151D172—82no—
152C8×C43—82no—
153#11877—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—22no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—42no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—81no—
167C22×C43—81no—
168C22×C43C2×#9911yescharacteristic
169C22×C43C2×#10211yescharacteristic
170C22×C43#42111yescharacteristic
171C2×D43—82no—
172C2×D43—82no—
173C2×D43—82no—
174C2×D43—82no—
175C2×D43—82no—
176C2×D43—82no—
177C2×D43—82no—
178C4×C43—21no—
179C4×C43—22no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43#35312yes—
184Dic43—44no—
185Dic43—162no—
186#2541—431no—
187#1799—431no—
188#1459D4311yescharacteristic, complemented
189#1343—434no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43—41no—
193C2×C43—42no—
194C2×C43—41no—
195C2×C43#151911yescharacteristic
196C2×C43#212211yescharacteristic
197C2×C43C2×#35311yescharacteristic
198D43—162no—
199C2×#127—431no—
200C2×#127—861no—
201C2×#121—861no—
202C2×#121—861no—
203C2×C4×D4C2×D4311yescharacteristic
204C2×#99—861no—
205C2×C22⋊C8—21no—
206#392—432no—
207#392—432no—
208#390—861no—
209#380—861no—
210C4×C4⋊C4—431no—
211#342—432no—
212#324—21no—
213#323C2×D4312yes—
214C43#1187711yescharacteristic, complemented, Sylow
215C22×D4—432no—
216C22×D4—862no—
217C22×D4—862no—
218C22×D4—861no—
219C22×D4—861no—
220C22×D4D17211yescharacteristic
221C23×C4D17211yescharacteristic
222C23×C4C22⋊D4311yescharacteristic
223C22×C8—41no—
224#127—1721no—
225#127—1721no—
226#127—1722no—
227#127—1722no—
228#121—1724no—
229#121—1724no—
230C4×D4—41no—
231C4×D4—41no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—1721no—
234C2×C4⋊C4C22⋊D4311yescharacteristic
235C2×C22⋊C4—862no—
236C2×C22⋊C4—862no—
237C2×C22⋊C4—862no—
238C2×C22⋊C4C4×D4311yescharacteristic
239C2×C22⋊C4C22×D4311yescharacteristic
240C2×C42—861no—
241C2×C42C4×D4311yescharacteristic
242#99—1722no—
243C22⋊C8—22no—
244C22⋊C8—41no—
245#95—432no—
246#95—1721no—
247C24—862no—
248C24(C2×D43)⋊C411yescharacteristic
249C24C2×D17211yescharacteristic
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—3442no—
253C2×D4—3442no—
254C2×D4—3442no—
255C2×D4—1722no—
256C2×D4—1722no—
257C2×D4—1722no—
258C2×D4—1722no—
259C2×D4—1722no—
260C2×D4—1724no—
261C2×D4—1724no—
262C2×D4—1724no—
263C2×D4—1722no—
264C2×D4—1722no—
265C2×D4—1721no—
266C2×D4—1721no—
267C2×D4—1722no—
268C2×D4#1062187312yes—
269C2×D4D34412yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—862no—
277C22×C4—1722no—
278C22×C4(C2×D43)⋊C411yescharacteristic
279C22×C4(C2×D43)⋊C411yescharacteristic
280C22×C4(C2×D43)⋊C411yescharacteristic
281C22×C4C2×C4×D4311yescharacteristic
282C22×C4C2×C22⋊D4311yescharacteristic
283C2×C8—42no—
284C2×C8—82no—
285C4⋊C4—41no—
286C4⋊C4—864no—
287C4⋊C4—3442no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—1724no—
291C22⋊C4—1724no—
292C22⋊C4—1722no—
293C22⋊C4—1722no—
294C42—21no—
295C42—21no—
296C42—1722no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—1722no—
306C23—1722no—
307C23—1722no—
308C23—1722no—
309C23—1722no—
310C23—1722no—
311C23—1722no—
312C23#1306324712yes—
313C23C2×(C2×D43)⋊C411yescharacteristic
314C23C2×D34411yescharacteristic
315C23C2×#1062187311yescharacteristic
316D4—42no—
317D4—42no—
318D4—3444no—
319D4—3442no—
320D4—3444no—
321D4—3448no—
322D4—3444no—
323D4—3444no—
324D4—3442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—864no—
339C2×C4—3442no—
340C2×C4—3442no—
341C2×C4—3442no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4#1306323911yescharacteristic
345C2×C4#1306323911yescharacteristic
346C2×C4#1306324712yes—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—21no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—3442no—
363C22—3442no—
364C22—3442no—
365C22—3442no—
366C22—3442no—
367C22—3442no—
368C22—3442no—
369C22C2×#1306323911yescharacteristic
370C22C2×#1306324711yescharacteristic
371C22#1458291511yescharacteristic
372C4—22no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—1724no—
378C4—6882no—
379C4#1458269112yes—
380C2—21no—
381C2—21no—
382C2—41no—
383C2—42no—
384C2—41no—
385C2—6882no—
386C2#1913316411yescharacteristic
387C2#1913624611yescharacteristic
388C2C2×#1458269111yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1459C2
socleC22×C43C2×#99
prime radical#19139541C2
cosocleC2×C22⋊C4×C43C23
hypercenter#1459D43
hypocenterC43#11877
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #19134583C2semidirect
3. #19132593C2semidirect
4. C43×#1459C2semidirect
5. C2×#13063322C4semidirect
10. #14582808C4semidirect
14. C4×C4⋊Dic43C4semidirect
188. #1459D43semidirect
214. C43#11877semidirect

Maximal subgroups

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

subgroupindex
#191395412
#191345832
#191325932
C43×#14592
#1187743