Finite Group Databasebeta

← #25006204

Subgroups — #25006204

Order 11008.

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

normal subgroups only

This group has 534 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#19139481C211yesmaximal, characteristic
2#19132936C211yesmaximal, characteristic, complemented
3#19132524C212yesmaximal, complemented
4#19132522C212yesmaximal, complemented
5C43×#1459C211yesmaximal, characteristic, complemented
6C2×#13063306C411yescharacteristic
7C2×#13063293C411yescharacteristic
8C22×(C2×D43)⋊C4C411yescharacteristic
9#14582956—21no—
10#14582821—21no—
11#14582815—21no—
12#14582790—21no—
13#14582778—21no—
14#14582760C2211yescharacteristic
15#14582759C411yescharacteristic
16#14582754C2211yescharacteristic
17#14582623—21no—
18#14582623C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C2×C22⋊C8×C43—21no—
21C43×#324—21no—
22C43×#323C2212yes—
23C24×D43C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C23×Dic43C2×C411yescharacteristic
26#13063306—42no—
27#13063293—42no—
28C2×C4⋊Dic43—21no—
29C2×Dic43⋊C4—21no—
30C2×C22⋊Dic43—21no—
31C2×C22⋊Dic43C2×C411yescharacteristic
32C2×C22⋊Dic43C2×C411yescharacteristic
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—41no—
39C2×(C2×D43)⋊C4—41no—
40C4⋊(C43⋊C8)—41no—
41C22⋊(C43⋊C8)—22no—
42#13063236—41no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C22×D4×C43C2×C411yescharacteristic
47C23×C4×C43C2×C411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C22×C8×C43—41no—
50C4×D4×C43—41no—
51C4×D4×C43—41no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43C2311yescharacteristic
55C2×C42×C43D411yescharacteristic
56C22⋊C8×C43—22no—
57C22⋊C8×C43—41no—
58C24×C43C22⋊C411yescharacteristic
59C24×C43C22×C411yescharacteristic
60C23×D43—21no—
61C23×D43—22no—
62C23×D43—42no—
63C23×D43—41no—
64C23×D43—41no—
65C23×D43—81no—
66C2×D4×C43—22no—
67C2×D4×C43—22no—
68C2×D4×C43—41no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—81no—
74C22×C4×C43—81no—
75C22×C4×C43C22⋊C411yescharacteristic
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C2×C22⋊D43—42no—
81C2×C22⋊D43—42no—
82C2×C22⋊D43—81no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—22no—
87C22×Dic43—41no—
88C22×Dic43—41no—
89C2×C8×C43—42no—
90C2×C8×C43—82no—
91C4⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C42×C43—21no—
95C42×C43—21no—
96C22⋊Dic43—41no—
97C22⋊Dic43—41no—
98C22⋊Dic43—42no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101(C2×D43)⋊C4—42no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—81no—
105C4⋊Dic43—81no—
106Dic43⋊C4—42no—
107C2×C43⋊C8—42no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43#10012yes—
117C23×C43C2×C22⋊C411yescharacteristic
118C23×C43#13112yes—
119C22×D43—22no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—42no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—42no—
128C22×D43—84no—
129C22×D43—84no—
130C22×D43—82no—
131C22×D43—82no—
132D4×C43—44no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43#9911yescharacteristic
148C2×C4×C43#9911yescharacteristic
149C22⋊D43—84no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—82no—
160C8×C43—82no—
161C43⋊C8—82no—
162#11560—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—22no—
166C22×C43—22no—
167C22×C43—42no—
168C22×C43—42no—
169C22×C43—42no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—81no—
175C22×C43#40811yescharacteristic
176C22×C43C2×#9911yescharacteristic
177C22×C43C2×#10011yescharacteristic
178C2×D43—42no—
179C2×D43—42no—
180C2×D43—42no—
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—84no—
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—84no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—41no—
193Dic43—81no—
194Dic43—81no—
195Dic43—81no—
196#2534—431no—
197#1466—431no—
198#1459D4311yescharacteristic, complemented
199#1317—432no—
200#1316—432no—
201C2×C43—21no—
202C2×C43—21no—
203C2×C43—42no—
204C2×C43—42no—
205C2×C43#147111yescharacteristic
206C2×C43#212011yescharacteristic
207C2×C43#212111yescharacteristic
208D43—82no—
209C2×#123—431no—
210C2×#120—431no—
211C2×C4×D4C2×D4311yescharacteristic
212C22×C22⋊C4—431no—
213#432—861no—
214C2×C22⋊C8—21no—
215#396—861no—
216#394—861no—
217#388—861no—
218#386—861no—
219#381—431no—
220#380—431no—
221#379—431no—
222#324—21no—
223#323—432no—
224#323—861no—
225#323C2×D4312yes—
226C43#1156011yescharacteristic, complemented, Sylow
227C25—431no—
228C22×D4—861no—
229C22×D4C4×D4311yescharacteristic
230C23×C4—431no—
231C23×C4C4×D4311yescharacteristic
232C23×C4C22⋊D4311yescharacteristic
233C22×C8—41no—
234#123—1722no—
235#120—1722no—
236C4×D4—41no—
237C4×D4—41no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4C22⋊D4311yescharacteristic
241C2×C22⋊C4—431no—
242C2×C22⋊C4—431no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—1721no—
250C2×C22⋊C4—1721no—
251C2×C22⋊C4D17211yescharacteristic
252C2×C22⋊C4C22×D4311yescharacteristic
253C2×C42D17211yescharacteristic
254C4⋊C8—1721no—
255C22⋊C8—22no—
256C22⋊C8—41no—
257C22⋊C8—862no—
258#97—1721no—
259#95—861no—
260#95—861no—
261#95—861no—
262C24—861no—
263C24—862no—
264C24—3441no—
265C24—1721no—
266C24—1721no—
267C24—1722no—
268C24(C2×D43)⋊C411yescharacteristic
269C24C2×C4×D4311yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—3441no—
274C2×D4—1722no—
275C2×D4—1722no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—81no—
281C22×C4—81no—
282C22×C4—862no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—1721no—
287C22×C4—1721no—
288C22×C4(C2×D43)⋊C411yescharacteristic
289C22×C4(C2×D43)⋊C411yescharacteristic
290C22×C4(C2×D43)⋊C411yescharacteristic
291C22×C4C2×D17211yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293C2×C8—42no—
294C2×C8—82no—
295C2×C8—1722no—
296C4⋊C4—41no—
297C4⋊C4—3441no—
298C4⋊C4—1722no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—3441no—
302C22⋊C4—1722no—
303C22⋊C4—1722no—
304C22⋊C4—1722no—
305C22⋊C4—1722no—
306C22⋊C4—1721no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C22⋊C4—1721no—
310C42—21no—
311C42—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—862no—
321C23—3442no—
322C23—3442no—
323C23—3444no—
324C23—3444no—
325C23—1721no—
326C23—1721no—
327C23—1721no—
328C23—1722no—
329C23—1722no—
330C23—1721no—
331C23—1721no—
332C23—1721no—
333C23#1306324112yes—
334C23C2×(C2×D43)⋊C411yescharacteristic
335C23#1306333112yes—
336D4—44no—
337D4—3444no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—3442no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4#1306323911yescharacteristic
363C2×C4#1306323911yescharacteristic
364C8—82no—
365C8—3442no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—22no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—81no—
378C22—3441no—
379C22—3441no—
380C22—3444no—
381C22—3444no—
382C22—3441no—
383C22—3441no—
384C22—1722no—
385C22—1722no—
386C22—1722no—
387C22#1458286511yescharacteristic
388C22C2×#1306323911yescharacteristic
389C22C2×#1306324111yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—3441no—
397C4—3441no—
398C4—3441no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—3442no—
404C2#1913295411yescharacteristic
405C2#1913623711yescharacteristic
406C2#1913623911yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1459C2
socleC22×C43C2×#99
prime radicalC2×#13063293C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1459D43
hypocenterC43#11560
LCSG ▷ C24×C43 ▷ C22×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. #19132936C2semidirect
3. #19132524C2semidirect
4. #19132522C2semidirect
5. C43×#1459C2semidirect
198. #1459D43semidirect
226. C43#11560semidirect

Maximal subgroups

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

subgroupindex
#191394812
#191329362
#191325242
#191325222
C43×#14592
#1156043