Finite Group Databasebeta

← #25013434

Subgroups — #25013434

Order 11008.

460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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#19137683C211yesmaximal, characteristic
2C2×#14582697C211yesmaximal, characteristic
3#19134988C211yesmaximal, characteristic
4#19134810C211yesmaximal, characteristic
5#19132722C211yesmaximal, characteristic
6#19132721C211yesmaximal, characteristic
7C43×#1857C211yesmaximal, characteristic
8C2×#13063323C2211yescharacteristic
9#14582942—21no—
10#14582907—21no—
11C2×#13063244C2211yescharacteristic
12C2×#13063244C2211yescharacteristic
13#14582806C2211yescharacteristic
14#14582803—21no—
15#14582796—21no—
16#14582794—21no—
17C4×Dic43⋊C4—21no—
18#14582750—21no—
19#14582750—21no—
20#14582697C414yescomplemented
21#14582658—21no—
22#14582658—21no—
23C43×#519C2211yescharacteristic
24C43×#428—21no—
25C2×#101×C43C2211yescharacteristic
26C43×#391C2211yescharacteristic
27C43×#339—21no—
28C22×Dic86D411yescharacteristic
29C2×#10621877—21no—
30C2×#10621877—21no—
31#13063323—21no—
32#13063323—21no—
33#13063323C2×C412yes—
34#13063323Q812yes—
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43D411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46#13063258—41no—
47#13063256—41no—
48#13063248—41no—
49#13063248—41no—
50#13063244—21no—
51#13063244—21no—
52#13063244—21no—
53#13063244C2×C412yes—
54C43⋊#95—21no—
55C43⋊#95—21no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C22×Q8×C43C2311yescharacteristic
59C2×M16×C43—21no—
60C4×Q8×C43—41no—
61C4×Q8×C43—41no—
62#117×C43—21no—
63#117×C43—21no—
64#117×C43—21no—
65C2×C4⋊C4×C43D411yescharacteristic
66C2×C42×C43D411yescharacteristic
67#107×C43—41no—
68#106×C43—41no—
69#101×C43—21no—
70#101×C43C2×C412yes—
71#95×C43—21no—
72#95×C43—21no—
73C2×Q8×C43—41no—
74C2×Q8×C43—41no—
75C2×Q8×C43C22×C411yescharacteristic
76C2×Q8×C43C2×Q811yescharacteristic
77C2×Q8×C43#4111yescharacteristic
78C2×Q8×C43#4111yescharacteristic
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C2×Dic86—21no—
89C2×Dic86—41no—
90C2×Dic86—41no—
91C2×Dic86C4⋊C412yes—
92M16×C43—22no—
93M16×C43—41no—
94C2×C8×C43—41no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—41no—
103C42×C43—41no—
104C42×C43—41no—
105C42×C43—41no—
106C42×C43—41no—
107C4⋊Dic43—41no—
108Dic43⋊C4—24no—
109Dic43⋊C4—22no—
110Dic43⋊C4—22no—
111Dic43⋊C4—22no—
112Dic43⋊C4—22no—
113Dic43⋊C4—42no—
114Dic43⋊C4—81no—
115C4×Dic43—21no—
116C4×Dic43—42no—
117C4×Dic43—42no—
118C4×Dic43—41no—
119C4×Dic43—81no—
120C4×Dic43C4⋊C412yes—
121#10621877—22no—
122#10621877—41no—
123#10621877—41no—
124#10621877—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C23×C43#12011yescharacteristic
128Q8×C43—41no—
129Q8×C43—41no—
130Q8×C43—41no—
131Q8×C43—41no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—22no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43C2×C4⋊C411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43C22⋊Q811yescharacteristic
150C2×C4×C43C22⋊Q811yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×Dic43—22no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—22no—
156C2×Dic43—22no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164Dic86—42no—
165Dic86—81no—
166C8×C43—42no—
167C43⋊C8—42no—
168C43⋊C8—81no—
169#12973—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38511yescharacteristic
173C22×C43B(4,𝔽2)11yescharacteristic
174C22×C43#45811yescharacteristic
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43—81no—
185Dic43—24no—
186Dic43—42no—
187Dic43—42no—
188Dic43—81no—
189#2369—431no—
190C2×#356—431no—
191#1886—431no—
192#1857—431no—
193#1857D4311yescharacteristic
194#1394—431no—
195#1394—431no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43#186711yescharacteristic
199C2×C43#220411yescharacteristic
200C2×C43#220511yescharacteristic
201C2×C4⋊Q8—431no—
202#519C2×D4311yescharacteristic
203#428—21no—
204#428—861no—
205#419—861no—
206C2×#101—431no—
207C2×#101—431no—
208C2×#101C2×D4311yescharacteristic
209#391—431no—
210#391—861no—
211#391C2×D4311yescharacteristic
212#389—861no—
213#389—861no—
214C4×C4⋊C4—861no—
215C4×C4⋊C4—861no—
216C4×C4⋊C4—861no—
217#356—434no—
218#339—21no—
219#339—861no—
220#339—861no—
221C43#1297311yescharacteristic, complemented, Sylow
222C22×Q8—431no—
223C22×Q8C22×D4311yescharacteristic
224C2×M16—21no—
225C2×M16—861no—
226C2×M16—861no—
227C4⋊Q8—432no—
228C4⋊Q8—432no—
229C4⋊Q8—861no—
230C4⋊Q8—861no—
231C4×Q8—41no—
232C4×Q8—41no—
233#117—21no—
234#117—21no—
235#117—21no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4C22⋊D4311yescharacteristic
243C2×C42—431no—
244C2×C42—431no—
245C2×C42—861no—
246C2×C42—861no—
247C2×C42—861no—
248C2×C42C22⋊D4311yescharacteristic
249#107—41no—
250#107—1721no—
251#106—41no—
252#106—1721no—
253#103—1721no—
254#103—1721no—
255#101—21no—
256#101—432no—
257#101—861no—
258#101—861no—
259#101—861no—
260#101C4×D4312yes—
261#95—21no—
262#95—21no—
263#95—861no—
264#95—861no—
265#95—861no—
266#95—861no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—432no—
270C2×Q8—861no—
271C2×Q8—1721no—
272C2×Q8—1721no—
273C2×Q8C2×C4×D4311yescharacteristic
274C2×Q8#1062189811yescharacteristic
275C2×Q8Q8×D4311yescharacteristic
276C2×Q8#1062190211yescharacteristic
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4D4×D4311yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C22×C4C2×C22⋊D4311yescharacteristic
286M16—22no—
287M16—41no—
288M16—862no—
289M16—1721no—
290M16—1721no—
291M16—1721no—
292C2×C8—41no—
293C2×C8—1721no—
294C2×C8—1721no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—864no—
303C4⋊C4—862no—
304C4⋊C4—862no—
305C4⋊C4—862no—
306C4⋊C4—862no—
307C4⋊C4—3441no—
308C4⋊C4—1721no—
309C4⋊C4—1722no—
310C22⋊C4—41no—
311C42—41no—
312C42—41no—
313C42—41no—
314C42—41no—
315C42—432no—
316C42—861no—
317C42—3441no—
318C42—1721no—
319C42—1722no—
320C42—1722no—
321C23#1306329311yescharacteristic
322Q8—41no—
323Q8—41no—
324Q8—41no—
325Q8—41no—
326Q8—3441no—
327Q8—1722no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—862no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4C4⋊C4×D4311yescharacteristic
355C2×C4C4×C22⋊D4311yescharacteristic
356C2×C4#1306328711yescharacteristic
357C2×C4#1306330111yescharacteristic
358C2×C4#1306330311yescharacteristic
359C2×C4#1306331011yescharacteristic
360C8—42no—
361C8—3441no—
362C8—1722no—
363C22—21no—
364C22—21no—
365C22#1458277011yescharacteristic
366C22#1458308511yescharacteristic
367C22#1458308811yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4—864no—
379C4—3441no—
380C4—1722no—
381C4—1722no—
382C2—21no—
383C2—21no—
384C2#1913487411yescharacteristic
385C2#1913661911yescharacteristic
386C2#1913662411yescharacteristic
subgroupG/H
centerC22#14583085
commutatorC2×Q8×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC43×#1857C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
cosocleC22×Q8×C43C23
hypercenter#1857D43
hypocenterC43#12973
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
20. #14582697C4semidirect
221. C43#12973semidirect

Maximal subgroups

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

subgroupindex
#191376832
C2×#145826972
#191349882
#191348102
#191327222
#191327212
C43×#18572
#1297343