Finite Group Databasebeta

← #24985115

Subgroups — #24985115

Order 11008.

494 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 95 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#19142933C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic
3#19134287C211yesmaximal, characteristic
4#19132420C211yesmaximal, characteristic, complemented
5#19132420C211yesmaximal, characteristic, complemented
6#19132418C211yesmaximal, characteristic, complemented
7C43×#1271C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×#13063305C411yescharacteristic
10C2×C42×D43C2211yescharacteristic
11C2×(C2×D43)⋊C8—21no—
12#14582805C2211yescharacteristic
13#14582804C411yescharacteristic
14#14582795C411yescharacteristic
15#14582786—21no—
16#14582785—21no—
17#14582770—21no—
18#14582761—21no—
19#14582756C411yescharacteristic
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22#14582653—21no—
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621872—24no—
32C2×#10621872—42no—
33C2×#10621872—42no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063305—42no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43D411yescharacteristic
44C2×C4×Dic43D411yescharacteristic
45C42×D43—42no—
46(C2×D43)⋊C8—42no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C22×C8×C43—21no—
54C22×C8×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#95×C43—21no—
60C23×D43C22⋊C411yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68C22×Dic43C22⋊C411yescharacteristic
69C22×Dic43C22⋊C411yescharacteristic
70C22×Dic43C22⋊C411yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43—22no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—22no—
79C2×C4×D43—22no—
80C2×C4×D43—22no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×Dic86—21no—
84C2×Dic86—21no—
85C2×Dic86—41no—
86C2×Dic86—41no—
87C2×C8×C43—22no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C42×C43—41no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101C4⋊Dic43—42no—
102C4⋊Dic43—41no—
103Dic43⋊C4—42no—
104C4×Dic43—41no—
105C4×Dic43—41no—
106C4×Dic43—41no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113#10621872—48no—
114C23×C43C2×C22⋊C411yescharacteristic
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43#9912yes—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43#13111yescharacteristic
135C2×C4×C43#13111yescharacteristic
136C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C43#13711yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43#10412yes—
155C4×D43—24no—
156C4×D43—24no—
157C4×D43—42no—
158C4×D43—42no—
159C4×D43—42no—
160C4×D43—42no—
161Dic86—81no—
162Dic86—81no—
163C8×C43—42no—
164C8×C43—81no—
165C43⋊C8—42no—
166C43⋊C8—81no—
167#7695—431nomaximal, Sylow
168C22×C43#40811yescharacteristic
169C22×C43C2×#9911yescharacteristic
170C22×C43#41311yescharacteristic
171C22×C43#41711yescharacteristic
172C22×C43#41911yescharacteristic
173C22×C43C2×#10411yescharacteristic
174C22×C43#42111yescharacteristic
175C2×D43—22no—
176C2×D43—22no—
177C2×D43—22no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—81no—
189C4×C43—81no—
190Dic43—22no—
191Dic43—41no—
192Dic43—41no—
193Dic43—81no—
194Dic43—81no—
195#2855—431no—
196#1817—431no—
197#1728—431no—
198#1272—431no—
199#1272—431no—
200#1271—431no—
201#1271D4311yescharacteristic, complemented
202C2×C43#146811yescharacteristic
203C2×C43#148511yescharacteristic
204C2×C43#149511yescharacteristic
205C2×C43#150411yescharacteristic
206C2×C43#151111yescharacteristic
207C2×C43#152911yescharacteristic
208C2×C43#155911yescharacteristic
209D43—42no—
210C22×M16—861no—
211C2×C22⋊Q8—431no—
212C22×C42—431no—
213C2×C22⋊C8—861no—
214#391—431no—
215#391—431no—
216#389—431no—
217#389C2×D4311yescharacteristic
218#387—861no—
219#387—861no—
220#385—861no—
221#381—861no—
222#380—431no—
223#336—431no—
224#336—431no—
225#336—861no—
226#336—861no—
227#336C2×D4311yescharacteristic
228#336C2×D4311yescharacteristic
229C43#769511yescharacteristic, complemented, Sylow
230C22×Q8—431no—
231C23×C4—431no—
232C23×C4—431no—
233C23×C4—431no—
234C2×M16—864no—
235C2×M16—1722no—
236C2×M16—1722no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—861no—
240C22×C8—861no—
241C22⋊Q8—1722no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—431no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4—861no—
246C2×C4⋊C4C4×D4311yescharacteristic
247C2×C4⋊C4C4×D4311yescharacteristic
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C42—431no—
251C2×C42—431no—
252C2×C42—431no—
253C2×C42—1722no—
254C2×C42C22×D4311yescharacteristic
255C22⋊C8—1722no—
256#95—21no—
257#95—861no—
258#95—861no—
259#95—861no—
260#95—861no—
261#95—861no—
262#95—861no—
263C24—431no—
264C2×Q8—861no—
265C2×Q8—861no—
266C2×Q8—1721no—
267C2×Q8—1721no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—431no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—862no—
274C22×C4—862no—
275C22×C4—862no—
276C22×C4—862no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—1721no—
286C22×C4—1721no—
287C22×C4C2×C4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C22×C4D4×D4311yescharacteristic
290M16—1728no—
291C2×C8—22no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—862no—
298C2×C8—1721no—
299C2×C8—1721no—
300C2×C8—1721no—
301C2×C8—1721no—
302C2×C8—1721no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—1721no—
309C4⋊C4—1722no—
310C4⋊C4—1722no—
311C22⋊C4—1722no—
312C22⋊C4—1722no—
313C42—41no—
314C42—1721no—
315C42—1721no—
316C42—1721no—
317C23—432no—
318C23—861no—
319C23—861no—
320C23—861no—
321C23—861no—
322C23—861no—
323C23—861no—
324C23C22⋊C4×D4311yescharacteristic
325Q8—3441no—
326Q8—3441no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—432no—
340C2×C4—864no—
341C2×C4—864no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4—1722no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4#1306333111yescharacteristic
361C2×C4#1306333311yescharacteristic
362C2×C4#1306334911yescharacteristic
363C2×C4#1306335411yescharacteristic
364C2×C4#1306335411yescharacteristic
365C2×C4#1306335711yescharacteristic
366C8—42no—
367C8—81no—
368C8—3441no—
369C8—1722no—
370C22—862no—
371C22—862no—
372C22—862no—
373C22—1721no—
374C22—1721no—
375C22—1721no—
376C22—1721no—
377C22#1458286411yescharacteristic
378C22#99×D4311yescharacteristic
379C22#1458288211yescharacteristic
380C22#1458289711yescharacteristic
381C22#1458290611yescharacteristic
382C22#104×D4311yescharacteristic
383C22#1458291411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—81no—
391C4—81no—
392C4—862no—
393C4—3441no—
394C4—3441no—
395C4—1721no—
396C4—1721no—
397C2—1722no—
398C2#1913294211yescharacteristic
399C2#1913301411yescharacteristic
400C2#1913305711yescharacteristic
401C2#1913309611yescharacteristic
402C2#1913312611yescharacteristic
403C2#1913320111yescharacteristic
404C2#1913332411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1271D43
hypocenterC43#7695
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #19132420C2semidirect
5. #19132420C2semidirect
6. #19132418C2semidirect
7. C43×#1271C2semidirect
201. #1271D43semidirect
229. C43#7695semidirect

Maximal subgroups

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

subgroupindex
#191429332
#191346622
#191342872
#191324202
#191324182
C43×#12712
#769543