Finite Group Databasebeta

← #25006907

Subgroups — #25006907

Order 11008.

452 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140407C211yesmaximal, characteristic
2#343×D43C211yesmaximal, characteristic
3#324×D43C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic, complemented
5#19132623C211yesmaximal, characteristic, complemented
6#19132621C211yesmaximal, characteristic, complemented
7C43×#1354C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063301C411yescharacteristic
10C2×C4⋊C4×D43C2211yescharacteristic
11C22⋊C8×D43—21no—
12#14582839C411yescharacteristic
13#14582838C2211yescharacteristic
14#14582833—21no—
15#14582830—21no—
16#14582818C411yescharacteristic
17#14582770—21no—
18#14582761—21no—
19#14582758C411yescharacteristic
20#14582668C2211yescharacteristic
21#14582667—21no—
22#14582625C2211yescharacteristic
23#14582624—21no—
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C2×#10621877—21no—
31C2×#10621872—41no—
32M16×D43—24no—
33M16×D43—42no—
34C2×C8×D43—41no—
35C2×C8×D43—41no—
36#13063301—41no—
37#13063301—41no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4C2×C411yescharacteristic
44C2×Dic43⋊C4D411yescharacteristic
45C4⋊C4×D43—41no—
46C4⋊C4×D43—41no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C22⋊(C43⋊C8)—21no—
50(C2×D43)⋊C8—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C22×Q8×C43C2×C411yescharacteristic
58C2×M16×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43C2×C411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C2×Q8×C43—41no—
66C2×Q8×C43—81no—
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—22no—
84C2×C4×D43—81no—
85C2×C4×D43—81no—
86C2×C4×D43SD1612yes—
87C2×C4×D43Q1612yes—
88M16×C43—22no—
89M16×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—81no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—42no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—42no—
102Dic43⋊C4—81no—
103Dic43⋊C4—81no—
104#10621877—22no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108#10621872—44no—
109C8×D43—44no—
110C8×D43—82no—
111C23×C43C2×C22⋊C411yescharacteristic
112C22×D43—41no—
113C22×D43—41no—
114C22×D43#9911yescharacteristic
115C22×D43#9911yescharacteristic
116C22×D43#10312yes—
117C22×D43#10412yes—
118Q8×C43—82no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—41no—
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×C43C2×SD1611yescharacteristic
132C2×C4×C43C2×Q1611yescharacteristic
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43#10312yes—
145C4×D43—22no—
146C4×D43—22no—
147C4×D43—22no—
148C4×D43—22no—
149C4×D43—42no—
150C4×D43—81no—
151C4×D43—81no—
152C4×D43—81no—
153C8×C43—42no—
154C8×C43—81no—
155C43⋊C8—42no—
156C43⋊C8—81no—
157#11722—431nomaximal, Sylow
158C22×C43—21no—
159C22×C43—21no—
160C22×C43C2×#9911yescharacteristic
161C22×C43C2×#10311yescharacteristic
162C22×C43C2×#10411yescharacteristic
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—42no—
168C2×D43—42no—
169C2×D43#32812yes—
170C2×D43#32812yes—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43—81no—
176C4×C43—81no—
177Dic43—22no—
178Dic43—41no—
179Dic43—41no—
180Dic43—81no—
181Dic43—81no—
182#2627—431no—
183C2×#343—431no—
184C2×#324—431no—
185#1354—431no—
186#1354D4311yescharacteristic, complemented
187#1353—431no—
188#1353—431no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43C2×#32811yescharacteristic
192C2×C43#212111yescharacteristic
193C2×C43#213311yescharacteristic
194D43—22no—
195D43—22no—
196C22×M16—861no—
197C2×C22⋊Q8—431no—
198C22×C4⋊C4—431no—
199C2×C22⋊C8—861no—
200#400—431no—
201#400—431no—
202#398—861no—
203#398—861no—
204#395—431no—
205#395C2×D4311yescharacteristic
206#385—861no—
207#381—861no—
208#380—431no—
209#343—431no—
210#343—861no—
211#343C2×D4311yescharacteristic
212#324—431no—
213#324—861no—
214#324C2×D4311yescharacteristic
215C43#1172211yescharacteristic, complemented, Sylow
216C22×Q8C4×D4311yescharacteristic
217C23×C4—431no—
218C23×C4—431no—
219C23×C4—431no—
220C2×M16—21no—
221C2×M16—864no—
222C2×M16—861no—
223C2×M16—1721no—
224C2×M16—1722no—
225C22×C8—1721no—
226C22×C8—1721no—
227C22⋊Q8—1721no—
228C22⋊Q8—1721no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—431no—
231C2×C4⋊C4—431no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—1721no—
238C2×C4⋊C4—1721no—
239C2×C4⋊C4C22×D4311yescharacteristic
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C22⋊C8—21no—
243C22⋊C8—861no—
244C22⋊C8—1721no—
245#95—21no—
246#95—431no—
247#95—861no—
248#95—861no—
249#95—861no—
250#95—861no—
251#95—861no—
252#95C4×D4311yescharacteristic
253C24—431no—
254C2×Q8—41no—
255C2×Q8—81no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—431no—
259C22×C4—432no—
260C22×C4—432no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—862no—
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×C4C2×C4×D4311yescharacteristic
275C22×C4D4×D4311yescharacteristic
276C22×C4D4×D4311yescharacteristic
277M16—22no—
278M16—41no—
279M16—862no—
280M16—1724no—
281M16—1721no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—3442no—
285C2×C8—1724no—
286C2×C8—1721no—
287C2×C8—1721no—
288C4⋊C4—41no—
289C4⋊C4—81no—
290C4⋊C4—3441no—
291C4⋊C4—3441no—
292C4⋊C4—1721no—
293C4⋊C4—1721no—
294C4⋊C4—1721no—
295C4⋊C4—1721no—
296C4⋊C4—1722no—
297C22⋊C4—1721no—
298C22⋊C4—1721no—
299C22⋊C4—1722no—
300C23—431no—
301C23—431no—
302C23—432no—
303C23—432no—
304C23—1721no—
305C23—1721no—
306C23C22⋊C4×D4311yescharacteristic
307Q8—82no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—432no—
321C2×C4—862no—
322C2×C4—862no—
323C2×C4—862no—
324C2×C4—862no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—1722no—
333C2×C4—1721no—
334C2×C4—1721no—
335C2×C4—1722no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4SD16×D4311yescharacteristic
341C2×C4Q16×D4311yescharacteristic
342C8—42no—
343C8—81no—
344C8—3441no—
345C8—1722no—
346C22—21no—
347C22—21no—
348C22—432no—
349C22—432no—
350C22—861no—
351C22—861no—
352C22—861no—
353C22—861no—
354C22—1722no—
355C22—1722no—
356C22#99×D4311yescharacteristic
357C22#103×D4311yescharacteristic
358C22#104×D4311yescharacteristic
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—81no—
364C4—81no—
365C4—862no—
366C4—3441no—
367C4—3441no—
368C4—1721no—
369C4—1721no—
370C2—21no—
371C2—21no—
372C2—862no—
373C2—862no—
374C2#328×D4311yescharacteristic
375C2#1913623811yescharacteristic
376C2#1913628311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43C2×#99
prime radicalC23×D43C22⋊C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1354D43
hypocenterC43#11722
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
4. #19132625C2semidirect
5. #19132623C2semidirect
6. #19132621C2semidirect
7. C43×#1354C2semidirect
186. #1354D43semidirect
215. C43#11722semidirect

Maximal subgroups

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

subgroupindex
#191404072
#343×D432
#324×D432
#191326252
#191326232
#191326212
C43×#13542
#1172243