Finite Group Databasebeta

← #25007075

Subgroups — #25007075

Order 11008.

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

normal subgroups only

This group has 486 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#19140275C211yesmaximal, characteristic
2#19134326C211yesmaximal, characteristic, complemented
3#19132926C211yesmaximal, characteristic, complemented
4#19132617C211yesmaximal, characteristic, complemented
5#19132615C211yesmaximal, characteristic, complemented
6#19132592C211yesmaximal, characteristic
7C43×#1343C211yesmaximal, characteristic
8C2×#13063312C411yescharacteristic, complemented
9C2×#13063281—21no—
10C2×#13063281C2211yescharacteristic
11#14582953—21no—
12#14582820C411yescharacteristic, complemented
13#14582813C411yescharacteristic, complemented
14#14582811C2211yescharacteristic
15#14582802—21no—
16#14582792—21no—
17#14582787—21no—
18#14582779—21no—
19#14582744C411yescharacteristic, complemented
20#14582666C2211yescharacteristic
21#14582665—21no—
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#392C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C23×Dic43D411yescharacteristic
29#13063312—41no—
30#13063312—41no—
31#13063281—24no—
32#13063281—41no—
33#13063281—41no—
34#13063281—42no—
35C2×C4⋊Dic43—21no—
36C2×Dic43⋊C4—41no—
37C2×Dic43⋊C4C2×C411yescharacteristic
38C2×Dic43⋊C4D411yescharacteristic
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43D411yescharacteristic
46C2×C4×Dic43—21no—
47C2×C4×Dic43—41no—
48C2×C4×Dic43C2×C411yescharacteristic
49C2×C4×Dic43D411yescharacteristic
50Dic43⋊C8—41no—
51C22⋊(C43⋊C8)—21no—
52#13063235—41no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95C2×C411yescharacteristic
57C22×D4×C43—21no—
58C22×D4×C43C2×C411yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43C2311yescharacteristic
62C22⋊C8×C43—21no—
63#95×C43C2×C411yescharacteristic
64C24×C43—21no—
65C24×C43C2×D411yescharacteristic
66C2×D4×C43—42no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—81no—
71C2×D4×C43—81no—
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—22no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—41no—
84C22×Dic43C22⋊C411yescharacteristic
85C22×Dic43C22⋊C411yescharacteristic
86C22×Dic43C22⋊C411yescharacteristic
87C22×Dic43C22⋊C411yescharacteristic
88C2×Dic86—41no—
89C2×Dic86—81no—
90C2×C8×C43—41no—
91C22⋊C4×C43—22no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—42no—
94C22⋊C4×C43—41no—
95C22⋊Dic43—22no—
96C22⋊Dic43—41no—
97C22⋊Dic43—42no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C22⋊Dic43—42no—
101C22⋊Dic43—41no—
102C22⋊Dic43—81no—
103C22⋊Dic43—81no—
104C4⋊Dic43—81no—
105Dic43⋊C4—41no—
106Dic43⋊C4—41no—
107Dic43⋊C4—44no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C4×Dic43—44no—
113C4×Dic43—42no—
114C2×C43⋊C8—41no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43C2×C22⋊C411yescharacteristic
127C23×C43AGL(1,ℤ/8)11yescharacteristic
128C23×C43#13711yescharacteristic
129D4×C43—82no—
130D4×C43—82no—
131D4×C43—82no—
132C2×C4×C43—22no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—81no—
141C2×C4×C43—81no—
142C2×Dic43—22no—
143C2×Dic43—22no—
144C2×Dic43—22no—
145C2×Dic43—22no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—42no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—81no—
162C2×Dic43—81no—
163C2×Dic43#9911yescharacteristic
164C2×Dic43#9911yescharacteristic
165C2×Dic43#10412yes—
166Dic86—82no—
167C8×C43—81no—
168C43⋊C8—81no—
169#11758—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43—81no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43C2×#9911yescharacteristic
187C22×C43#41711yescharacteristic
188C22×C43C2×#10411yescharacteristic
189C4×C43—42no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—82no—
193Dic43—21no—
194Dic43—21no—
195Dic43—22no—
196Dic43—41no—
197Dic43—41no—
198Dic43—81no—
199Dic43—82no—
200Dic43—81no—
201#2610—431no—
202#1740—431no—
203#1464—431no—
204#1351—431no—
205#1351—431no—
206#1343—431no—
207#1343D4311yescharacteristic
208C2×C43—21no—
209C2×C43—21no—
210C2×C43—41no—
211C2×C43—41no—
212C2×C43—161no—
213C2×C43#150411yescharacteristic
214C2×C43#212211yescharacteristic
215C2×C43#212611yescharacteristic
216C2×#124—431no—
217C2×#117—431no—
218C2×#117—861no—
219#432—861no—
220#395—431no—
221#394—431no—
222#393—431no—
223#392C2×D4311yescharacteristic
224#390—861no—
225#388—861no—
226#388—861no—
227#386—861no—
228#376—431no—
229#342—431no—
230#342—861no—
231#342C2×D4311yescharacteristic
232#324—861no—
233#323—431no—
234#323C2×D4311yescharacteristic
235C43#1175811yescharacteristic, complemented, Sylow
236C22×Q8—431no—
237C22×D4—21no—
238C22×D4C4×D4311yescharacteristic
239C23×C4—431no—
240#124—1721no—
241#124—1721no—
242#117—864no—
243#117—1721no—
244#117—1721no—
245#117—1722no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—1721no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—431no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4C22×D4311yescharacteristic
260C2×C42—431no—
261C2×C42—431no—
262C2×C42—861no—
263C2×C42—1721no—
264C4⋊C8—1721no—
265C22⋊C8—21no—
266C22⋊C8—861no—
267#97—1721no—
268#95—431no—
269#95—861no—
270#95—861no—
271#95—861no—
272#95C4×D4311yescharacteristic
273C24—21no—
274C24D4×D4311yescharacteristic
275C2×Q8—3441no—
276C2×Q8—1721no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—81no—
282C2×D4—81no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—431no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—862no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—1721no—
297C22×C4C2×C4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C2×C8—41no—
300C2×C8—1721no—
301C4⋊C4—3441no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C4⋊C4—1724no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—862no—
310C22⋊C4—3441no—
311C22⋊C4—3441no—
312C22⋊C4—1721no—
313C22⋊C4—1721no—
314C22⋊C4—1722no—
315C22⋊C4—1721no—
316C22⋊C4—1722no—
317C22⋊C4—1721no—
318C42—861no—
319C42—861no—
320C42—861no—
321C42—861no—
322C42—1722no—
323C42—1724no—
324C23—21no—
325C23—21no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23C22⋊C4×D4311yescharacteristic
336C23#1306334911yescharacteristic
337C23#1306335411yescharacteristic
338Q8—3442no—
339D4—82no—
340D4—82no—
341D4—82no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—431no—
353C2×C4—431no—
354C2×C4—432no—
355C2×C4—862no—
356C2×C4—862no—
357C2×C4—862no—
358C2×C4—862no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—3441no—
366C2×C4—3441no—
367C2×C4—1722no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C8—81no—
377C8—3441no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22#99×D4311yescharacteristic
395C22#1458289711yescharacteristic
396C22#104×D4311yescharacteristic
397C4—42no—
398C4—41no—
399C4—41no—
400C4—82no—
401C4—861no—
402C4—861no—
403C4—862no—
404C4—3441no—
405C4—3442no—
406C4—3441no—
407C4—1721no—
408C4—1721no—
409C2—21no—
410C2—21no—
411C2—41no—
412C2—41no—
413C2—161no—
414C2#1913309611yescharacteristic
415C2#1913624311yescharacteristic
416C2#1913625711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1343C2
socleC22×C43C2×#99
prime radicalC43×#392C22
cosocleC2×C22⋊C4×C43C23
hypercenter#1343D43
hypocenterC43#11758
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #19134326C2semidirect
3. #19132926C2semidirect
4. #19132617C2semidirect
5. #19132615C2semidirect
8. C2×#13063312C4semidirect
12. #14582820C4semidirect
13. #14582813C4semidirect
19. #14582744C4semidirect
235. C43#11758semidirect

Maximal subgroups

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

subgroupindex
#191402752
#191343262
#191329262
#191326172
#191326152
#191325922
C43×#13432
#1175843