Finite Group Databasebeta

← #25006053

Subgroups — #25006053

Order 11008.

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

normal subgroups only

This group has 530 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#19137249C211yesmaximal, characteristic
2#19132936C211yesmaximal, characteristic, complemented
3#19132544C212yesmaximal, complemented
4#19132522C212yesmaximal, complemented
5C43×#1465C211yesmaximal, characteristic, complemented
6C2×#13063293C411yescharacteristic
7C22×(C2×D43)⋊C4C411yescharacteristic
8#14582956—21no—
9#14582799—21no—
10#14582790—21no—
11#14582789—21no—
12#14582779C411yescharacteristic
13#14582778—21no—
14#14582771C2211yescharacteristic
15#14582754C2211yescharacteristic
16C4×C22⋊Dic43C411yescharacteristic
17#14582623—21no—
18#14582623C2212yes—
19C2×C4×D4×C43C2211yescharacteristic
20C43×#407—21no—
21C43×#324—21no—
22C43×#323C2212yes—
23C24×D43C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C23×Dic43C2×C411yescharacteristic
26#13063293—22no—
27#13063293—22no—
28C2×Dic43⋊C4—21no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43C2×C411yescharacteristic
31C2×C22⋊Dic43C2×C411yescharacteristic
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C2×(C2×D43)⋊C4—21no—
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—41no—
38C2×(C2×D43)⋊C4—41no—
39C2×C4×Dic43—21no—
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
49C2×M16×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—21no—
62C23×D43—41no—
63C23×D43—41no—
64C23×D43—81no—
65C23×D43—81no—
66C23×D43M1612yescomplemented
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—81no—
76C22×C4×C43—81no—
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C2×C22⋊D43—24no—
83C2×C22⋊D43—81no—
84C2×C22⋊D43—81no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—41no—
89C22×Dic43—81no—
90M16×C43—82no—
91C2×C8×C43—42no—
92C4⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C42×C43—21no—
96C42×C43—21no—
97C22⋊Dic43—21no—
98C22⋊Dic43—41no—
99C22⋊Dic43—81no—
100C22⋊Dic43M1612yescomplemented
101(C2×D43)⋊C4—24no—
102(C2×D43)⋊C4—42no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—81no—
106(C2×D43)⋊C4—81no—
107Dic43⋊C4—81no—
108C4×Dic43—81no—
109C2×C43⋊C8—42no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—41no—
116C23×C43—41no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43C2×C22⋊C411yescharacteristic
120C23×C43C2×M1611yescharacteristic
121C23×C43C2×M1611yescharacteristic
122C22×D43—22no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126C22×D43—41no—
127C22×D43—42no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—42no—
131C22×D43—82no—
132C22×D43—82no—
133C22×D43—84no—
134C22×D43—82no—
135C22×D43—82no—
136D4×C43—42no—
137D4×C43—42no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43#9911yescharacteristic
153C2×C4×C43#9911yescharacteristic
154C22⋊D43—84no—
155C2×Dic43—22no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—82no—
165C8×C43—82no—
166C43⋊C8—82no—
167#11527—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43—81no—
182C22×C43#40711yescharacteristic
183C22×C43C2×#9911yescharacteristic
184C22×C43#41311yescharacteristic
185C2×D43—42no—
186C2×D43—42no—
187C2×D43—42no—
188C2×D43—81no—
189C2×D43—81no—
190C2×D43—84no—
191C2×D43—81no—
192C2×D43—81no—
193C2×D43—84no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—41no—
197C4×C43—41no—
198C4×C43—41no—
199C4×C43—41no—
200Dic43—42no—
201Dic43—81no—
202Dic43—81no—
203#2321—431no—
204#1466—431no—
205#1465D4311yescharacteristic, complemented
206#1326—432no—
207#1316—432no—
208C2×C43—21no—
209C2×C43—21no—
210C2×C43—41no—
211C2×C43—41no—
212C2×C43—81no—
213C2×C43#146511yescharacteristic
214C2×C43#212111yescharacteristic
215C2×C43#212211yescharacteristic
216D43—82no—
217C2×#120—431no—
218C2×C4×D4C2×D4311yescharacteristic
219C22×C22⋊C4—431no—
220#432—861no—
221#407—21no—
222#390—861no—
223#388—861no—
224#388—861no—
225#386—431no—
226#386—861no—
227#385—431no—
228#379—431no—
229C4×C22⋊C4—431no—
230#324—21no—
231#323—432no—
232#323—861no—
233#323C2×D4312yes—
234C43#1152711yescharacteristic, complemented, Sylow
235C25—431no—
236C22×D4—861no—
237C22×D4C4×D4311yescharacteristic
238C23×C4—431no—
239C23×C4C4×D4311yescharacteristic
240C23×C4C22⋊D4311yescharacteristic
241C2×M16—41no—
242#120—862no—
243#120—862no—
244C4×D4—41no—
245C4×D4—41no—
246C2×C4⋊C4—861no—
247C2×C4⋊C4C22⋊D4311yescharacteristic
248C2×C22⋊C4—431no—
249C2×C22⋊C4—431no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—1721no—
257C2×C22⋊C4—1721no—
258C2×C22⋊C4D17211yescharacteristic
259C2×C22⋊C4C22×D4311yescharacteristic
260C2×C42—861no—
261C2×C42D17211yescharacteristic
262C4⋊C8—1721no—
263C22⋊C8—22no—
264C22⋊C8—41no—
265C22⋊C8—862no—
266#97—1721no—
267#95—861no—
268#95—861no—
269#95—861no—
270C24—432no—
271C24—861no—
272C24—861no—
273C24—3441no—
274C24—3441no—
275C24—1721no—
276C24—1721no—
277C24(C2×D43)⋊C411yescharacteristic
278C24C2×C4×D4311yescharacteristic
279C2×D4—21no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—864no—
284C2×D4—3441no—
285C2×D4—3441no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—3441no—
296C22×C4—1721no—
297C22×C4(C2×D43)⋊C411yescharacteristic
298C22×C4(C2×D43)⋊C411yescharacteristic
299C22×C4(C2×D43)⋊C411yescharacteristic
300C22×C4C2×D17211yescharacteristic
301C22×C4C2×C22⋊D4311yescharacteristic
302M16—82no—
303C2×C8—42no—
304C2×C8—1722no—
305C4⋊C4—41no—
306C4⋊C4—3441no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—432no—
310C22⋊C4—864no—
311C22⋊C4—861no—
312C22⋊C4—3441no—
313C22⋊C4—3441no—
314C22⋊C4—3441no—
315C22⋊C4—1722no—
316C22⋊C4—1721no—
317C22⋊C4—1721no—
318C22⋊C4—1721no—
319C42—21no—
320C42—21no—
321C42—3441no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—862no—
332C23—3442no—
333C23—3442no—
334C23—3444no—
335C23—3442no—
336C23—3442no—
337C23—1722no—
338C23—1721no—
339C23—1721no—
340C23—1721no—
341C23—1721no—
342C23—1722no—
343C23—1721no—
344C23—1721no—
345C23C2×(C2×D43)⋊C411yescharacteristic
346C23M16×D4311yescharacteristic
347C23M16×D4311yescharacteristic
348D4—42no—
349D4—42no—
350D4—3444no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—862no—
366C2×C4—3442no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4#1306323911yescharacteristic
376C2×C4#1306323911yescharacteristic
377C8—82no—
378C8—3442no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—42no—
386C22—42no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—3441no—
394C22—3441no—
395C22—3444no—
396C22—3444no—
397C22—3441no—
398C22—3441no—
399C22—1722no—
400C22—1722no—
401C22—1722no—
402C22#1458286211yescharacteristic
403C22C2×#1306323911yescharacteristic
404C22#1458288111yescharacteristic
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—3441no—
412C4—3441no—
413C4—1722no—
414C2—21no—
415C2—21no—
416C2—41no—
417C2—41no—
418C2—81no—
419C2—3442no—
420C2#1913293111yescharacteristic
421C2#1913623911yescharacteristic
422C2#1913624611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC24×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1465C2
socleC22×C43C2×#99
prime radicalC2×#13063293C4
cosocleC2×C22⋊C4×C43C23
hypercenter#1465D43
hypocenterC43#11527
LCSG ▷ C24×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #19132936C2semidirect
3. #19132544C2semidirect
4. #19132522C2semidirect
5. C43×#1465C2semidirect
66. C23×D43M16semidirect
100. C22⋊Dic43M16semidirect
205. #1465D43semidirect
234. C43#11527semidirect

Maximal subgroups

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

subgroupindex
#191372492
#191329362
#191325442
#191325222
C43×#14652
#1152743