Finite Group Databasebeta

← #25006281

Subgroups — #25006281

Order 11008.

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

normal subgroups only

This group has 426 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#19139947C211yesmaximal, characteristic
2#19132934C211yesmaximal, characteristic
3#19132910C211yesmaximal, characteristic
4#19132544C211yesmaximal, characteristic, complemented
5#19132543C211yesmaximal, characteristic, complemented
6#19132542C211yesmaximal, characteristic, complemented
7C43×#1326C211yesmaximal, characteristic, complemented
8C2×(C22⋊D43)⋊C4C2211yescharacteristic
9C22×Dic43⋊C4C411yescharacteristic
10#14582953—21no—
11C22⋊C8×D43—21no—
12#14582830—21no—
13#14582823—21no—
14#14582781—21no—
15#14582778C411yescharacteristic
16#14582776C411yescharacteristic
17#14582771C2211yescharacteristic
18#14582770—21no—
19#14582757C411yescharacteristic
20#14582624—21no—
21#14582623C2211yescharacteristic
22#14582623C2211yescharacteristic
23#14582622—21no—
24C43×#385C2211yescharacteristic
25C43×#323C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×C22⋊D43C2×C411yescharacteristic
28C23×Dic43C2×C411yescharacteristic
29C23×Dic43C2×C411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×C8×D43—41no—
32(C22⋊D43)⋊C4—41no—
33(C22⋊D43)⋊C4—41no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—41no—
39C2×Dic43⋊C4—41no—
40C2×Dic43⋊C4D411yescharacteristic
41C2×C22⋊Dic43C2×C411yescharacteristic
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4D411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46Dic43⋊C8—41no—
47C22⋊(C43⋊C8)—21no—
48C22⋊(C43⋊C8)—21no—
49(C2×D43)⋊C8—41no—
50#13063235—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C23×C4×C43C2×C411yescharacteristic
56C2×C4⋊C4×C43—21no—
57C2×C22⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43C2311yescharacteristic
59C22⋊C8×C43—21no—
60C22⋊C8×C43—21no—
61#95×C43—21no—
62C24×C43C22×C411yescharacteristic
63C23×D43C22⋊C411yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—41no—
67C22×C4×C43—81no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—22no—
73C2×C22⋊D43—41no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—41no—
79C22×Dic43—42no—
80C22×Dic43—81no—
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—81no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C4⋊C4×C43—81no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊C4×C43—41no—
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—42no—
97(C2×D43)⋊C4—81no—
98Dic43⋊C4—41no—
99Dic43⋊C4—42no—
100Dic43⋊C4—42no—
101Dic43⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—81no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C8×D43—82no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43C2×C22⋊C411yescharacteristic
114C23×C43#13111yescharacteristic
115C23×C43#13111yescharacteristic
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43#10112yes—
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×C43—82no—
132C22⋊D43—42no—
133C22⋊D43—42no—
134C2×Dic43—22no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150C2×Dic43#9911yescharacteristic
151C2×Dic43#9911yescharacteristic
152C4×D43—42no—
153C4×D43—81no—
154C8×C43—81no—
155C8×C43—81no—
156C43⋊C8—81no—
157C43⋊C8—81no—
158#11578—431nomaximal, Sylow
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—42no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43#40811yescharacteristic
169C22×C43C2×#9911yescharacteristic
170C22×C43C2×#10111yescharacteristic
171C2×D43—22no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—42no—
175C2×D43—81no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—81no—
179C4×C43—81no—
180Dic43—21no—
181Dic43—21no—
182Dic43—42no—
183Dic43—41no—
184Dic43—41no—
185Dic43—81no—
186#2579—431no—
187#1466—431no—
188#1459—431no—
189#1326—431no—
190#1326—431no—
191#1326—431no—
192#1326D4311yescharacteristic, complemented
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—41no—
196C2×C43—41no—
197C2×C43#147211yescharacteristic
198C2×C43#212011yescharacteristic
199C2×C43#212111yescharacteristic
200D43—42no—
201C2×C4×D4—431no—
202C22×C4⋊C4—431no—
203#432—861no—
204C2×C22⋊C8—861no—
205#398—861no—
206#396—861no—
207#387—861no—
208#386—431no—
209#386—431no—
210#385—431no—
211#385—861no—
212#385C2×D4311yescharacteristic
213#380—431no—
214#324—861no—
215#323—431no—
216#323—431no—
217#323—861no—
218#323C2×D4311yescharacteristic
219#323C2×D4311yescharacteristic
220C43#1157811yescharacteristic, complemented, Sylow
221C22×D4—431no—
222C23×C4—431no—
223C23×C4—431no—
224C23×C4—431no—
225C23×C4C4×D4311yescharacteristic
226C22×C8—1721no—
227C4×D4—1721no—
228C4×D4—1721no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—431no—
231C2×C4⋊C4—861no—
232C2×C4⋊C4—861no—
233C2×C4⋊C4—861no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—1721no—
236C2×C4⋊C4—1721no—
237C2×C22⋊C4—431no—
238C2×C22⋊C4—431no—
239C2×C22⋊C4—861no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4C4×D4311yescharacteristic
242C2×C22⋊C4C22×D4311yescharacteristic
243C2×C42—431no—
244C4⋊C8—1721no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—861no—
248C22⋊C8—861no—
249C22⋊C8—1721no—
250#97—1721no—
251#95—21no—
252#95—861no—
253#95—861no—
254#95—861no—
255#95—861no—
256C24—431no—
257C24C2×C4×D4311yescharacteristic
258C2×D4—862no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—1721no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—81no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—431no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—3441no—
276C22×C4—3441no—
277C22×C4—1722no—
278C22×C4—1721no—
279C22×C4D4×D4311yescharacteristic
280C22×C4D4×D4311yescharacteristic
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—3442no—
284C2×C8—1721no—
285C2×C8—1721no—
286C4⋊C4—81no—
287C4⋊C4—3441no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4—1722no—
292C4⋊C4—1722no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—41no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—3441no—
299C22⋊C4—1721no—
300C22⋊C4—1722no—
301C42—861no—
302C42—861no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—432no—
308C23—861no—
309C23—861no—
310C23—1721no—
311C23—1721no—
312C23C22⋊C4×D4311yescharacteristic
313C23#1306333111yescharacteristic
314C23#1306333311yescharacteristic
315D4—1722no—
316D4—1722no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—82no—
328C2×C4—431no—
329C2×C4—431no—
330C2×C4—862no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4—3441no—
338C2×C4—1722no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1722no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4—1722no—
348C8—81no—
349C8—81no—
350C8—3441no—
351C8—3441no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—41no—
360C22—41no—
361C22—862no—
362C22—3441no—
363C22—1722no—
364C22—1721no—
365C22—1721no—
366C22#1458286411yescharacteristic
367C22#99×D4311yescharacteristic
368C22#101×D4311yescharacteristic
369C4—41no—
370C4—41no—
371C4—81no—
372C4—81no—
373C4—861no—
374C4—861no—
375C4—3441no—
376C4—1721no—
377C4—1722no—
378C4—1721no—
379C2—21no—
380C2—21no—
381C2—41no—
382C2—41no—
383C2—1722no—
384C2#1913295711yescharacteristic
385C2#1913623511yescharacteristic
386C2#1913623811yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1326C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43C2×C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1326D43
hypocenterC43#11578
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1326

Complements

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

NH ≅ G/Ntype
4. #19132544C2semidirect
5. #19132543C2semidirect
6. #19132542C2semidirect
7. C43×#1326C2semidirect
192. #1326D43semidirect
220. C43#11578semidirect

Maximal subgroups

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

subgroupindex
#191399472
#191329342
#191329102
#191325442
#191325432
#191325422
C43×#13262
#1157843