Finite Group Databasebeta

← #25007216

Subgroups — #25007216

Order 11008.

516 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 73 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#19139543C211yesmaximal, characteristic
2#19134382C211yesmaximal, characteristic
3#19132930C211yesmaximal, characteristic
4#19132620C211yesmaximal, characteristic, complemented
5#19132619C211yesmaximal, characteristic, complemented
6#19132618C211yesmaximal, characteristic, complemented
7C43×#1352C211yesmaximal, characteristic, complemented
8C2×#13063324C411yescharacteristic, complemented
9C2×#13063303—21no—
10C2×#13063302—21no—
11C2×(C22⋊D43)⋊C4C2211yescharacteristic
12C2×#13063239—21no—
13#14582861—21no—
14#14582836C411yescharacteristic, complemented
15#14582835C2211yescharacteristic
16#14582834C411yescharacteristic, complemented
17#14582799—21no—
18#14582768—21no—
19#14582750C411yescharacteristic, complemented
20C22⋊C4×Dic43—21no—
21#14582666C2211yescharacteristic
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#399C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Dic86—21no—
28C22×C22⋊D43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621872—41no—
32#13063324—41no—
33#13063324—41no—
34#13063303—44no—
35#13063302—44no—
36(C22⋊D43)⋊C4—41no—
37(C22⋊D43)⋊C4—41no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2×C411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4D411yescharacteristic
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4C2×C411yescharacteristic
50C2×C4×Dic43—21no—
51C2×C4×Dic43—41no—
52C2×C4×Dic43C2×C411yescharacteristic
53#13063239—24no—
54C22⋊(C43⋊C8)—21no—
55(C2×D43)⋊C8—41no—
56C43⋊#95—41no—
57C43⋊#95C2×C411yescharacteristic
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43—21no—
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43C2311yescharacteristic
63C22⋊C8×C43—21no—
64#95×C43C2×C411yescharacteristic
65C24×C43C2×D411yescharacteristic
66C23×D43C22⋊C411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—22no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43—21no—
75C2×C22⋊D43—41no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—41no—
81C22×Dic43—42no—
82C22×Dic43C22⋊C411yescharacteristic
83C22×Dic43C22⋊C411yescharacteristic
84C22×Dic43C22⋊C411yescharacteristic
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43—42no—
88C2×Dic86—42no—
89C2×Dic86—42no—
90C2×Dic86—41no—
91C2×Dic86—41no—
92C2×C8×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—42no—
95C22⋊C4×C43—22no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—42no—
98C22⋊C4×C43—41no—
99C22⋊Dic43—22no—
100C22⋊Dic43—42no—
101C22⋊Dic43—41no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—42no—
104(C2×D43)⋊C4—42no—
105C4⋊Dic43—42no—
106C4⋊Dic43—41no—
107Dic43⋊C4—24no—
108Dic43⋊C4—41no—
109Dic43⋊C4—42no—
110Dic43⋊C4—42no—
111Dic43⋊C4—42no—
112C4×Dic43—21no—
113C4×Dic43—21no—
114C4×Dic43—42no—
115C4×Dic43—82no—
116C2×C43⋊C8—41no—
117#10621872—82no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43C2×C22⋊C411yescharacteristic
123C23×C43#13711yescharacteristic
124C23×C43#13711yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—41no—
129C22×D43—41no—
130C2×C4×C43—22no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—41no—
141C2×C4×C43—81no—
142C2×C4×C43—81no—
143C22⋊D43—42no—
144C22⋊D43—42no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—22no—
148C2×Dic43—22no—
149C2×Dic43—21no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—42no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—81no—
159C2×Dic43—81no—
160C2×Dic43—81no—
161C2×Dic43#9911yescharacteristic
162C2×Dic43#9911yescharacteristic
163C2×Dic43#10412yes—
164C4×D43—42no—
165C4×D43—81no—
166Dic86—82no—
167Dic86—82no—
168C8×C43—81no—
169C43⋊C8—81no—
170#11788—431nomaximal, Sylow
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—81no—
180C22×C43C2×#9911yescharacteristic
181C22×C43#41911yescharacteristic
182C22×C43C2×#10411yescharacteristic
183C2×D43—42no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—81no—
188C4×C43—42no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—82no—
192C4×C43—81no—
193Dic43—21no—
194Dic43—22no—
195Dic43—42no—
196Dic43—41no—
197Dic43—82no—
198Dic43—81no—
199Dic43#35312yes—
200#2542—431no—
201C4×#99—431no—
202#1465—431no—
203#1352—431no—
204#1352—431no—
205#1352—431no—
206#1352D4311yescharacteristic, complemented
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—41no—
210C2×C43—41no—
211C2×C43#150811yescharacteristic
212C2×C43#212311yescharacteristic
213C2×C43C2×#35311yescharacteristic
214D43—81no—
215C2×C4⋊Q8—431no—
216C2×C22⋊Q8—861no—
217C2×C22⋊Q8—861no—
218C2×C4×D4—431no—
219C2×#99—861no—
220#407—861no—
221#399—431no—
222#399—431no—
223#399—431no—
224#399C2×D4311yescharacteristic
225#390—861no—
226#384—861no—
227C4×C4⋊C4—431no—
228C4×C22⋊C4—861no—
229#342—431no—
230#342C2×D4311yescharacteristic
231#324—861no—
232#323—431no—
233#323C2×D4311yescharacteristic
234C43#1178811yescharacteristic, complemented, Sylow
235C22×Q8—861no—
236C22×D4—431no—
237C23×C4—431no—
238C23×C4—431no—
239C2×M16—1721no—
240C4⋊Q8—1721no—
241C4⋊Q8—1721no—
242C22⋊Q8—1724no—
243C22⋊Q8—1724no—
244C4×D4—1721no—
245C4×D4—1721no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4C4×D4311yescharacteristic
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—431no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C22⋊C4—861no—
262C2×C22⋊C4C22×D4311yescharacteristic
263C2×C42—431no—
264C2×C42—861no—
265C2×C42—1721no—
266#99—864no—
267C22⋊C8—21no—
268C22⋊C8—861no—
269C22⋊C8—1721no—
270#95—431no—
271#95—1721no—
272#95C4×D4311yescharacteristic
273C24—431no—
274C24D4×D4311yescharacteristic
275C2×Q8—1721no—
276C2×Q8—1721no—
277C2×Q8—1722no—
278C2×Q8—1722no—
279C2×D4—862no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—1721no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—431no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—1722no—
296C22×C4—1722no—
297C22×C4—1721no—
298C22×C4C2×C4×D4311yescharacteristic
299C22×C4D4×D4311yescharacteristic
300M16—3442no—
301C2×C8—41no—
302C2×C8—1721no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—864no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C4⋊C4—1722no—
309C4⋊C4—1722no—
310C4⋊C4—1722no—
311C4⋊C4—1722no—
312C22⋊C4—22no—
313C22⋊C4—41no—
314C22⋊C4—42no—
315C22⋊C4—41no—
316C22⋊C4—862no—
317C22⋊C4—1721no—
318C22⋊C4—1722no—
319C22⋊C4—1722no—
320C22⋊C4—1722no—
321C22⋊C4—1721no—
322C42—861no—
323C42—861no—
324C42—3442no—
325C42—1722no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23—861no—
331C23—861no—
332C23—861no—
333C23—1721no—
334C23—1721no—
335C23C22⋊C4×D4311yescharacteristic
336C23#1306335411yescharacteristic
337C23#1306335711yescharacteristic
338Q8—3442no—
339Q8—3442no—
340D4—1722no—
341D4—1722no—
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—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—431no—
356C2×C4—431no—
357C2×C4—432no—
358C2×C4—862no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—862no—
362C2×C4—861no—
363C2×C4—3441no—
364C2×C4—3441no—
365C2×C4—3441no—
366C2×C4—3441no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4—1722no—
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—3441no—
388C22—1722no—
389C22—1721no—
390C22—1721no—
391C22—1721no—
392C22#99×D4311yescharacteristic
393C22#1458290611yescharacteristic
394C22#104×D4311yescharacteristic
395C4—42no—
396C4—41no—
397C4—41no—
398C4—82no—
399C4—81no—
400C4—432no—
401C4—862no—
402C4—861no—
403C4—3442no—
404C4—3441no—
405C4—1722no—
406C4—1721no—
407C2—21no—
408C2—21no—
409C2—41no—
410C2—41no—
411C2—3441no—
412C2#1913311311yescharacteristic
413C2#1913624711yescharacteristic
414C2#353×D4311yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1352C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1352D43
hypocenterC43#11788
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #19132620C2semidirect
5. #19132619C2semidirect
6. #19132618C2semidirect
7. C43×#1352C2semidirect
8. C2×#13063324C4semidirect
14. #14582836C4semidirect
16. #14582834C4semidirect
19. #14582750C4semidirect
206. #1352D43semidirect
234. C43#11788semidirect

Maximal subgroups

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

subgroupindex
#191395432
#191343822
#191329302
#191326202
#191326192
#191326182
C43×#13522
#1178843