Finite Group Databasebeta

← #25007498

Subgroups — #25007498

Order 11008.

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

normal subgroups only

This group has 572 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#19137930C211yesmaximal, characteristic
2C2×#14582625C211yesmaximal, characteristic, complemented
3#19132624C212yesmaximal, complemented
4#19132597C212yesmaximal, complemented
5C43×#1821C211yesmaximal, characteristic, complemented
6C22×#10621898C411yescharacteristic
7C2×#13063308—21no—
8C2×C22⋊(C43⋊C8)—21no—
9#14582819C411yescharacteristic
10#14582819C2211yescharacteristic
11#14582816C411yescharacteristic
12#14582816C2211yescharacteristic
13#14582778—21no—
14#14582770—21no—
15#14582770—21no—
16#14582762C411yescharacteristic
17#14582625—21no—
18#14582625C2212yes—
19C22×C4⋊C4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#343—21no—
22C43×#343C2212yes—
23C2×#10621898—41no—
24C2×#10621898—41no—
25C2×#10621898—44no—
26C22×Dic86C2×C411yescharacteristic
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C22×C4×D43—21no—
30C22×C43⋊C8—41no—
31#13063308—44no—
32C2×Dic43⋊C4—21no—
33C2×Dic43⋊C4—21no—
34C2×C22⋊Dic43—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C22⋊(C43⋊C8)—22no—
40C22⋊(C43⋊C8)—41no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95C2×C411yescharacteristic
45C43⋊#95C2×C411yescharacteristic
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C2×M16×C43—22no—
50C2×C4⋊C4×C43—41no—
51C2×C4⋊C4×C43—41no—
52C2×C4⋊C4×C43C2×C411yescharacteristic
53C2×C4⋊C4×C43D411yescharacteristic
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C4⋊C4×C43C2311yescharacteristic
56C22⋊C8×C43—41no—
57C22⋊C8×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C23×D43—21no—
60C22×C4×C43—22no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43—42no—
69C22×C4×C43—42no—
70C22×C4×C43C22⋊C411yescharacteristic
71C22×C4×C43C22⋊C411yescharacteristic
72C22×C4×C43C22⋊C411yescharacteristic
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—24no—
77C2×C22⋊D43—42no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83#10621898—44no—
84#10621898—44no—
85#10621898—44no—
86#10621898—44no—
87C2×D172—42no—
88C2×D172—41no—
89C2×C4×D43—42no—
90C2×C4×D43—42no—
91C2×C4×D43—42no—
92C2×Dic86—41no—
93C2×Dic86—42no—
94M16×C43—42no—
95M16×C43—42no—
96C2×C8×C43—42no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C22⋊Dic43—42no—
102(C2×D43)⋊C4—42no—
103(C2×D43)⋊C4—42no—
104(C2×D43)⋊C4—42no—
105(C2×D43)⋊C4—42no—
106Dic43⋊C4—42no—
107Dic43⋊C4—42no—
108C2×C43⋊C8—42no—
109C2×C43⋊C8—82no—
110C23×C43—22no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—41no—
114C23×C43#9911yescharacteristic
115C23×C43#9911yescharacteristic
116C23×C43C2×C22⋊C411yescharacteristic
117C22×D43—22no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—42no—
137C2×C4×C43—42no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—81no—
143C2×C4×C43#13512yes—
144C22⋊D43—44no—
145C22⋊D43—44no—
146C2×Dic43—22no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155D172—42no—
156D172—42no—
157C4×D43—48no—
158Dic86—42no—
159Dic86—42no—
160C8×C43—82no—
161C43⋊C8—82no—
162#11848—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—42no—
171C22×C43—42no—
172C22×C43AΣL(1,𝔽16)12yes—
173C22×C43C2×#9911yescharacteristic
174C22×C43#41611yescharacteristic
175C22×C43#42111yescharacteristic
176C2×D43—42no—
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C2×D43—81no—
183C4×C43—22no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43—41no—
189Dic43—42no—
190Dic43—81no—
191Dic43—81no—
192#2406—431no—
193#1821D4311yescharacteristic, complemented
194C2×#324—431no—
195#1354—432no—
196#1345—432no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—22no—
200C2×C43—41no—
201C2×C43#151611yescharacteristic
202C2×C43C2×AΣL(1,𝔽16)11yescharacteristic
203C2×C43#213311yescharacteristic
204D43—82no—
205C22×#41—431no—
206C2×#123—861no—
207C22×C4⋊C4C2×D4311yescharacteristic
208#407—21no—
209C2×C22⋊C8—861no—
210#395—431no—
211#395—431no—
212#394—431no—
213#394—431no—
214#386—861no—
215#385—861no—
216#385—861no—
217#381—431no—
218#343—21no—
219#343C2×D4312yes—
220#324—432no—
221#324—861no—
222C43#1184811yescharacteristic, complemented, Sylow
223C2×#41—1721no—
224C2×#41—1721no—
225C2×#41—1724no—
226C22×Q8—431no—
227C22×D4—431no—
228C22×D4—861no—
229C23×C4—861no—
230C23×C4C4×D4311yescharacteristic
231C23×C4D17211yescharacteristic
232C23×C4C22⋊D4311yescharacteristic
233C2×M16—22no—
234C22×C8—1721no—
235#123—1724no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4C4×D4311yescharacteristic
241C2×C4⋊C4D17211yescharacteristic
242C2×C4⋊C4C22⋊D4311yescharacteristic
243C2×C4⋊C4C22×D4311yescharacteristic
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C22⋊C8—41no—
250C22⋊C8—41no—
251C22⋊C8—862no—
252C22⋊C8—1721no—
253#95—431no—
254#95—431no—
255#95—861no—
256#95—861no—
257#95—861no—
258C24—861no—
259C24(C2×D43)⋊C411yescharacteristic
260#41—1724no—
261#41—1724no—
262#41—1724no—
263#41—1724no—
264C2×Q8—1721no—
265C2×Q8—1722no—
266C2×D4—864no—
267C2×D4—1721no—
268C2×D4—1722no—
269C2×D4—1722no—
270C2×D4—1721no—
271C2×D4—1721no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—1722no—
286C22×C4—1722no—
287C22×C4—1722no—
288C22×C4(C2×D43)⋊C411yescharacteristic
289C22×C4(C2×D43)⋊C411yescharacteristic
290C22×C4(C2×D43)⋊C411yescharacteristic
291C22×C4C2×C4×D4311yescharacteristic
292C22×C4C2×D17211yescharacteristic
293C22×C4C2×C22⋊D4311yescharacteristic
294M16—42no—
295M16—42no—
296C2×C8—42no—
297C2×C8—3442no—
298C2×C8—1722no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—1722no—
304C4⋊C4—1722no—
305C22⋊C4—1722no—
306C22⋊C4—1722no—
307C22⋊C4—1722no—
308C22⋊C4—1722no—
309C22⋊C4—1722no—
310C23—21no—
311C23—21no—
312C23—22no—
313C23—41no—
314C23—862no—
315C23—1721no—
316C23—1721no—
317C23—1721no—
318C23—1721no—
319C23—1721no—
320C23—1721no—
321C23#1306323911yescharacteristic
322C23#1306323911yescharacteristic
323C23C2×(C2×D43)⋊C411yescharacteristic
324Q8—1722no—
325Q8—1722no—
326D4—1722no—
327D4—1722no—
328D4—1724no—
329D4—1724no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—862no—
350C2×C4—1728no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4#1306334512yes—
360C8—82no—
361C8—3442no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—3441no—
372C22—3441no—
373C22—3441no—
374C22—3441no—
375C22—1722no—
376C22—1722no—
377C22—1722no—
378C22#1458268712yes—
379C22C2×#1306323911yescharacteristic
380C22#1458289311yescharacteristic
381C22#1458291711yescharacteristic
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—3441no—
389C4—3441no—
390C4—1722no—
391C2—21no—
392C2—21no—
393C2—22no—
394C2—41no—
395C2—3442no—
396C2#1913314911yescharacteristic
397C2C2×#1458268711yescharacteristic
398C2#1913628211yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1821C2
socleC22×C43C2×#99
prime radicalC22×#10621898C4
cosocleC2×C4⋊C4×C43C23
hypercenter#1821D43
hypocenterC43#11848
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. C2×#14582625C2semidirect
3. #19132624C2semidirect
4. #19132597C2semidirect
5. C43×#1821C2semidirect
193. #1821D43semidirect
222. C43#11848semidirect

Maximal subgroups

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

subgroupindex
#191379302
C2×#145826252
#191326242
#191325972
C43×#18212
#1184843