Finite Group Databasebeta

← #25006180

Subgroups — #25006180

Order 11008.

414 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 71 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#19139072C211yesmaximal, characteristic
2#19132923C211yesmaximal, characteristic
3#324×D43C211yesmaximal, characteristic
4#19132540C211yesmaximal, characteristic, complemented
5#19132540C211yesmaximal, characteristic, complemented
6#19132529C211yesmaximal, characteristic, complemented
7C43×#1319C211yesmaximal, characteristic, complemented
8C2×#13063301C411yescharacteristic
9C2×C4⋊C4×D43C2211yescharacteristic
10#14582861—21no—
11C22⋊C8×D43—21no—
12#14582833—21no—
13#14582833—21no—
14#14582806C411yescharacteristic
15#14582773—21no—
16#14582773—21no—
17#14582769C411yescharacteristic
18#14582768C2211yescharacteristic
19C4×(C2×D43)⋊C4C411yescharacteristic
20#14582625C2211yescharacteristic
21#14582625C2211yescharacteristic
22#14582624—21no—
23#14582624—21no—
24C43×#391C2211yescharacteristic
25C43×#324C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621872—41no—
31C2×C8×D43—41no—
32#13063301—41no—
33#13063301—41no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4D411yescharacteristic
42C2×Dic43⋊C4D411yescharacteristic
43C4⋊C4×D43—41no—
44C4⋊C4×D43—41no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×C4×Dic43C2×C411yescharacteristic
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50(C2×D43)⋊C8—41no—
51(C2×D43)⋊C8—41no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C22×Q8×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C42×C43C2×C411yescharacteristic
58C22⋊C8×C43—21no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62C23×D43C22⋊C411yescharacteristic
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C22×Dic43C22⋊C411yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—41no—
86C2×C4×D43—81no—
87C2×C4×D43—81no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C42×C43—41no—
92(C2×D43)⋊C4—24no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97C4⋊Dic43—81no—
98C4⋊Dic43—81no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—42no—
102Dic43⋊C4—81no—
103Dic43⋊C4—81no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108#10621872—82no—
109C8×D43—82no—
110C23×C43C2×C22⋊C411yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—22no—
114C22×D43—41no—
115C22×D43#9911yescharacteristic
116C22×D43#9911yescharacteristic
117Q8×C43—81no—
118Q8×C43—81no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—22no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43#13111yescharacteristic
132C2×C4×C43#13111yescharacteristic
133C2×Dic43—22no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C4×D43—41no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—41no—
150C4×D43—42no—
151C4×D43—42no—
152C4×D43—81no—
153C4×D43—81no—
154C8×C43—81no—
155C8×C43—81no—
156C43⋊C8—81no—
157C43⋊C8—81no—
158#11555—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43#40811yescharacteristic
162C22×C43C2×#9911yescharacteristic
163C22×C43#41311yescharacteristic
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—42no—
170C2×D43—42no—
171C2×D43#35612yes—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—42no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—81no—
178Dic43—42no—
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182Dic43—81no—
183#2502—431no—
184#1463—431no—
185C2×#324—431no—
186#1325—431no—
187#1325—431no—
188#1319—431no—
189#1319D4311yescharacteristic, complemented
190C2×C43—21no—
191C2×C43—21no—
192C2×C43#146811yescharacteristic
193C2×C43#212711yescharacteristic
194C2×C43C2×#35611yescharacteristic
195D43—22no—
196D43—41no—
197C2×C22⋊Q8—431no—
198C22×C4⋊C4—431no—
199#407—861no—
200C2×C22⋊C8—861no—
201#398—861no—
202#398—861no—
203#391—431no—
204#391C2×D4311yescharacteristic
205#385—861no—
206#385—861no—
207#384—431no—
208#384—431no—
209C4×C22⋊C4—431no—
210#324—431no—
211#324—431no—
212#324—861no—
213#324—861no—
214#324C2×D4311yescharacteristic
215#324C2×D4311yescharacteristic
216C43#1155511yescharacteristic, complemented, Sylow
217C22×Q8C4×D4311yescharacteristic
218C23×C4—431no—
219C23×C4—431no—
220C23×C4—431no—
221C2×M16—1721no—
222C22×C8—1721no—
223C22⋊Q8—1721no—
224C22⋊Q8—1721no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—861no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—1721no—
235C2×C4⋊C4—1721no—
236C2×C4⋊C4C22×D4311yescharacteristic
237C2×C22⋊C4—861no—
238C2×C22⋊C4—861no—
239C2×C42—431no—
240C2×C42C4×D4311yescharacteristic
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—861no—
244C22⋊C8—861no—
245C22⋊C8—1721no—
246C22⋊C8—1721no—
247#95—21no—
248#95—21no—
249#95—861no—
250#95—861no—
251#95—861no—
252C24—431no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—3441no—
273C22×C4—3441no—
274C22×C4—1721no—
275C22×C4C2×C4×D4311yescharacteristic
276C22×C4D4×D4311yescharacteristic
277C22×C4D4×D4311yescharacteristic
278M16—3442no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—3442no—
282C2×C8—1721no—
283C2×C8—1721no—
284C4⋊C4—41no—
285C4⋊C4—3441no—
286C4⋊C4—3441no—
287C4⋊C4—3441no—
288C4⋊C4—3441no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4—1721no—
292C4⋊C4—1721no—
293C4⋊C4—1722no—
294C22⋊C4—864no—
295C22⋊C4—1721no—
296C22⋊C4—1721no—
297C42—41no—
298C42—861no—
299C42—861no—
300C23—431no—
301C23—431no—
302C23—862no—
303C23—861no—
304C23—861no—
305C23—1721no—
306C23C22⋊C4×D4311yescharacteristic
307Q8—81no—
308Q8—81no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—862no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—3441no—
328C2×C4—3441no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4—1721no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4—1721no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4#1306333111yescharacteristic
343C2×C4#1306333311yescharacteristic
344C8—81no—
345C8—81no—
346C8—3441no—
347C8—3441no—
348C22—21no—
349C22—21no—
350C22—432no—
351C22—861no—
352C22—861no—
353C22—861no—
354C22—861no—
355C22—861no—
356C22—1722no—
357C22—1722no—
358C22#1458286411yescharacteristic
359C22#99×D4311yescharacteristic
360C22#1458288011yescharacteristic
361C4—21no—
362C4—21no—
363C4—42no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—3441no—
368C4—1722no—
369C4—1721no—
370C4—1721no—
371C4—1721no—
372C2—21no—
373C2—21no—
374C2—862no—
375C2—1721no—
376C2#1913294011yescharacteristic
377C2#1913626311yescharacteristic
378C2#356×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1319C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1319D43
hypocenterC43#11555
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
4. #19132540C2semidirect
5. #19132540C2semidirect
6. #19132529C2semidirect
7. C43×#1319C2semidirect
189. #1319D43semidirect
216. C43#11555semidirect

Maximal subgroups

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

subgroupindex
#191390722
#191329232
#324×D432
#191325402
#191325292
C43×#13192
#1155543