Finite Group Databasebeta

← #24994423

Subgroups — #24994423

Order 11008.

614 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 93 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#19138865C211yesmaximal, characteristic
2#19137190C211yesmaximal, characteristic
3#19134694C211yesmaximal, characteristic, complemented
4#19132921C211yesmaximal, characteristic
5#19132449C211yesmaximal, characteristic, complemented
6#19132448C211yesmaximal, characteristic, complemented
7C43×#1826C211yesmaximal, characteristic, complemented
8C22×(C2×D43)⋊C4C2211yescharacteristic
9#14582863C2211yescharacteristic
10#14582834C412yescomplemented
11#14582825C412yescomplemented
12#14582790—22no—
13#14582790—22no—
14#14582788—22no—
15#14582771—21no—
16#14582762C2211yescharacteristic
17#14582757—21no—
18#14582754—21no—
19#14582754—21no—
20C4×C22⋊Dic43C2211yescharacteristic
21#14582658—22no—
22#14582622—22no—
23C2×#117×C43C2211yescharacteristic
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C43×#339—22no—
27C24×D43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C2×#10621877—21no—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—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—22no—
39C2×(C2×D43)⋊C4—22no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4—22no—
42C2×(C2×D43)⋊C4C2×C412yes—
43C2×(C2×D43)⋊C4D412yes—
44C2×C4×Dic43D412yes—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47C43⋊#95—22no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—22no—
51C43⋊#95C2×C412yes—
52C23×C4×C43C2311yescharacteristic
53C2×M16×C43—21no—
54#117×C43—21no—
55#117×C43—21no—
56#117×C43—21no—
57#117×C43—21no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C42×C43—21no—
63C2×C42×C43D412yes—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43—21no—
67C24×C43C2×D411yescharacteristic
68C23×D43—21no—
69C23×D43—21no—
70C23×D43—42no—
71C23×D43—42no—
72C23×D43—81no—
73C23×D43C22⋊C412yes—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—22no—
77C22×C4×C43—42no—
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×Dic43—22no—
85C22×Dic43—21no—
86C22×Dic43—22no—
87C22×Dic43—21no—
88C22×Dic43—81no—
89C22×Dic43C22⋊C412yes—
90M16×C43—42no—
91C2×C8×C43—41no—
92C4⋊C4×C43—21no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—21no—
96C22⋊C4×C43—42no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C42×C43—42no—
100C42×C43—41no—
101C42×C43—41no—
102C22⋊Dic43—42no—
103C22⋊Dic43—42no—
104(C2×D43)⋊C4—22no—
105(C2×D43)⋊C4—22no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—44no—
109(C2×D43)⋊C4—82no—
110(C2×D43)⋊C4—82no—
111(C2×D43)⋊C4—82no—
112Dic43⋊C4—82no—
113Dic43⋊C4—82no—
114C4×Dic43—42no—
115#10621877—42no—
116C2×C43⋊C8—41no—
117C23×C43—22no—
118C23×C43—22no—
119C23×C43—41no—
120C23×C43C2×C22⋊C411yescharacteristic
121C23×C43#12011yescharacteristic
122C23×C43#12311yescharacteristic
123C22×D43—22no—
124C22×D43—22no—
125C22×D43—22no—
126C22×D43—42no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—42no—
130C22×D43—42no—
131C22×D43—42no—
132C22×D43—81no—
133C22×D43—81no—
134C22×D43—88no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C4×D411yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×Dic43—22no—
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—42no—
161C2×Dic43—81no—
162C8×C43—81no—
163C43⋊C8—81no—
164#9481—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—44no—
173C22×C43#38611yescharacteristic
174C22×C43#42112yes—
175C22×C43#45812yes—
176C2×D43—44no—
177C2×D43—42no—
178C2×D43—42no—
179C2×D43—42no—
180C2×D43—84no—
181C2×D43—84no—
182C2×D43—82no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—82no—
188C4×C43—81no—
189C4×C43—81no—
190Dic43—42no—
191Dic43—82no—
192Dic43—82no—
193#2482—431no—
194#2312—431no—
195#1826—431no—
196#1826D4311yescharacteristic, complemented
197#1462—431no—
198#1284—431no—
199#1284—431no—
200C2×C43—22no—
201C2×C43—22no—
202C2×C43—41no—
203C2×C43#189011yescharacteristic
204C2×C43#189711yescharacteristic
205C2×C43#191111yescharacteristic
206D43—82no—
207C2×#117C2×D4311yescharacteristic
208C22×C22⋊C4—431no—
209#407—431no—
210#407C2×D4311yescharacteristic
211#399—432no—
212#397—432no—
213#388—862no—
214#388—862no—
215#388—862no—
216#385—861no—
217#381—431no—
218#380—861no—
219#379—861no—
220#379—861no—
221C4×C22⋊C4—431no—
222C4×C22⋊C4C2×D4311yescharacteristic
223#339—22no—
224#339—862no—
225#323—862no—
226C43#948111yescharacteristic, complemented, Sylow
227C25—431no—
228C23×C4—431no—
229C23×C4C22×D4311yescharacteristic
230C2×M16—21no—
231C2×M16—861no—
232#117—21no—
233#117—21no—
234#117—21no—
235#117—21no—
236C2×C4⋊C4—862no—
237C2×C4⋊C4—862no—
238C2×C4⋊C4C4×D4311yescharacteristic
239C2×C4⋊C4C4×D4311yescharacteristic
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—432no—
243C2×C22⋊C4—432no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—862no—
249C2×C22⋊C4—862no—
250C2×C22⋊C4—862no—
251C2×C22⋊C4—862no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C42—21no—
255C2×C42—432no—
256C2×C42C22⋊D4312yes—
257C22⋊C8—21no—
258C22⋊C8—21no—
259C22⋊C8—861no—
260C22⋊C8—861no—
261#95—21no—
262#95—432no—
263#95—862no—
264#95—862no—
265#95—861no—
266#95—861no—
267C24—432no—
268C24—861no—
269C24—861no—
270C24—3441no—
271C24—1722no—
272C24—1722no—
273C24D4×D4311yescharacteristic
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—432no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—862no—
282C22×C4—862no—
283C22×C4—3441no—
284C22×C4C2×C4×D4311yescharacteristic
285C22×C4#1062189811yescharacteristic
286C22×C4D4×D4311yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4#1062190011yescharacteristic
289C22×C4C2×C22⋊D4311yescharacteristic
290M16—42no—
291M16—1722no—
292C2×C8—41no—
293C2×C8—1721no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—3442no—
299C4⋊C4—3442no—
300C22⋊C4—42no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—862no—
304C22⋊C4—862no—
305C22⋊C4—862no—
306C22⋊C4—862no—
307C22⋊C4—3442no—
308C22⋊C4—3442no—
309C22⋊C4—3442no—
310C22⋊C4—1724no—
311C22⋊C4—1722no—
312C22⋊C4—1722no—
313C42—42no—
314C42—41no—
315C42—41no—
316C42—1722no—
317C23—22no—
318C23—22no—
319C23—41no—
320C23—862no—
321C23—862no—
322C23—862no—
323C23—3441no—
324C23—3441no—
325C23—3448no—
326C23—1722no—
327C23—1722no—
328C23—1722no—
329C23—1722no—
330C23—1722no—
331C23—1722no—
332C23C22⋊C4×D4311yescharacteristic
333C23#1306329311yescharacteristic
334C23#1306330711yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—862no—
349C2×C4—3441no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4(C22⋊D43)⋊C411yescharacteristic
359C2×C4C4×C22⋊D4311yescharacteristic
360C2×C4#1306329611yescharacteristic
361C2×C4#1306329811yescharacteristic
362C8—81no—
363C8—3441no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—44no—
372C22—3442no—
373C22—3444no—
374C22—3444no—
375C22—1724no—
376C22—1722no—
377C22—1722no—
378C22—1722no—
379C22#1458277511yescharacteristic
380C22#1458291412yes—
381C22#1458308812yes—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—82no—
387C4—81no—
388C4—81no—
389C4—3442no—
390C4—3442no—
391C4—1722no—
392C2—22no—
393C2—22no—
394C2—41no—
395C2—3442no—
396C2#1913500511yescharacteristic
397C2#1913504011yescharacteristic
398C2#1913512411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1826C2
socleC22×C43#386
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenter#1826D43
hypocenterC43#9481
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #19134694C2semidirect
5. #19132449C2semidirect
6. #19132448C2semidirect
7. C43×#1826C2semidirect
10. #14582834C4semidirect
11. #14582825C4semidirect
196. #1826D43semidirect
226. C43#9481semidirect

Maximal subgroups

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

subgroupindex
#191388652
#191371902
#191346942
#191329212
#191324492
#191324482
C43×#18262
#948143