Finite Group Databasebeta

← #24996321

Subgroups — #24996321

Order 11008.

484 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#14583138C211yesmaximal, characteristic
2#19134631C211yesmaximal, characteristic
3#19134374C211yesmaximal, characteristic
4#19133116C211yesmaximal, characteristic
5#19133115C211yesmaximal, characteristic
6#19132958C211yesmaximal, characteristic
7C43×#1472C211yesmaximal, characteristic
8C22×#10621885C411yescharacteristic, complemented
9C23×C43⋊C8C2211yescharacteristic
10C2×#13063304C2211yescharacteristic
11#14583138—21no—
12#14583138—21no—
13#14583138—21no—
14#14583138—21no—
15C2×#13063260—21no—
16C2×#13063258C411yescharacteristic, complemented
17C2×#13063249C411yescharacteristic, complemented
18C2×#13063248C411yescharacteristic, complemented
19#14582863C2211yescharacteristic
20C2×#13063235—21no—
21C4×C22⋊Dic43C2211yescharacteristic
22#14582663—21no—
23#14582653—21no—
24#14582637—22no—
25#14582636—22no—
26#14582624—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C43×#324—22no—
31C22×Dic86C2×C411yescharacteristic
32C2×#10621885—21no—
33C2×#10621885—21no—
34C2×#10621885—42no—
35C2×#10621877—21no—
36C22×C43⋊C8—42no—
37C22×C43⋊C8C2×C411yescharacteristic
38C22×C43⋊C8C2×C411yescharacteristic
39C22×C43⋊C8D411yescharacteristic
40C22×C43⋊C8D411yescharacteristic
41C22×C43⋊C8D411yescharacteristic
42C22×C43⋊C8D411yescharacteristic
43#13063304—21no—
44#13063304—21no—
45#13063304—21no—
46#13063304—21no—
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×Dic43⋊C4—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C4×Dic43—21no—
52#13063260—42no—
53#13063258—21no—
54#13063258—21no—
55#13063249—21no—
56#13063249—21no—
57#13063248—21no—
58#13063248—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)—21no—
61#13063235—42no—
62C43⋊#95D412yes—
63C22×Q8×C43C2×C411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C2×M16×C43—21no—
66C22×C8×C43—21no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C22⋊C4×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43D412yes—
78C24×C43#4111yescharacteristic
79C2×Q8×C43—21no—
80C2×Q8×C43—21no—
81C2×Q8×C43—41no—
82C2×Q8×C43—41no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—22no—
96C2×Dic86—21no—
97C2×Dic86—21no—
98C2×Dic86—41no—
99C2×Dic86—41no—
100M16×C43—41no—
101M16×C43—41no—
102C2×C8×C43—22no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C2×C8×C43—41no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊Dic43—42no—
113C22⋊Dic43—41no—
114C22⋊Dic43—41no—
115#10621885—42no—
116#10621885—42no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119Dic43⋊C4—41no—
120Dic43⋊C4—41no—
121C4×Dic43—41no—
122C4×Dic43—41no—
123#10621877—41no—
124#10621877—41no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8C22⋊C411yescharacteristic
133C2×C43⋊C8C22⋊C411yescharacteristic
134C2×C43⋊C8C22⋊C411yescharacteristic
135C2×C43⋊C8C22⋊C411yescharacteristic
136C23×C43—22no—
137C23×C43—22no—
138C23×C43—41no—
139C23×C43C4×D411yescharacteristic
140C23×C43#12111yescharacteristic
141C23×C43#12411yescharacteristic
142Q8×C43—41no—
143Q8×C43—41no—
144Q8×C43—81no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—42no—
157C2×C4×C43—81no—
158C2×C4×C43C2×C22⋊C411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12711yescharacteristic
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—81no—
169Dic86—41no—
170Dic86—41no—
171Dic86—81no—
172C8×C43—42no—
173C8×C43—81no—
174C43⋊C8—21no—
175C43⋊C8—21no—
176C43⋊C8—21no—
177C43⋊C8—81no—
178C43⋊C8#9912yes—
179#9817—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—44no—
188C22×C43#39011yescharacteristic
189C22×C43#44412yes—
190C22×C43#47312yes—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—81no—
195C4×C43—81no—
196C4×C43C2×#9911yescharacteristic
197C4×C43#41011yescharacteristic
198Dic43—82no—
199Dic43—81no—
200Dic43—81no—
201C2×#467—431no—
202#1810—431no—
203#1752—431no—
204#1508—431no—
205#1508—431no—
206#1472—431no—
207#1472D4311yescharacteristic
208C2×C43—22no—
209C2×C43—22no—
210C2×C43—41no—
211C2×C43#196411yescharacteristic
212C2×C43#197511yescharacteristic
213C2×C43#197911yescharacteristic
214C22×Q16—431no—
215C23×C8—431no—
216C2×C22⋊Q8—431no—
217C2×C22⋊Q8C2×D4311yescharacteristic
218#467—861no—
219#467—861no—
220#467—861no—
221#467—861no—
222C2×#108—861no—
223C2×#107—431no—
224C2×#103—431no—
225C2×#103—431no—
226#407—431no—
227#407C2×D4311yescharacteristic
228C2×C22⋊C8C2×D4311yescharacteristic
229C2×#97—861no—
230C4×C22⋊C4—431no—
231#341—861no—
232#336—861no—
233#328—862no—
234#328—862no—
235#324—22no—
236#324—862no—
237C43#981711yescharacteristic, complemented, Sylow
238C22×Q8—431no—
239C22×Q8C4×D4311yescharacteristic
240C23×C4C22×D4311yescharacteristic
241C2×Q16—861no—
242C2×Q16—861no—
243C2×Q16—1722no—
244C2×M16—21no—
245C2×M16—861no—
246C22×C8—21no—
247C22×C8—431no—
248C22×C8—431no—
249C22×C8—431no—
250C22×C8—431no—
251C22×C8—431no—
252C22×C8—431no—
253C22×C8—1722no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258C22⋊Q8—861no—
259C22⋊Q8—861no—
260C22⋊Q8—861no—
261C22⋊Q8—861no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4C4×D4311yescharacteristic
266C2×C22⋊C4—21no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C42—861no—
270#108—1722no—
271#107—861no—
272#107—861no—
273#103—861no—
274#103—861no—
275#103—861no—
276#103—861no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8—21no—
280C22⋊C8—861no—
281C22⋊C8—861no—
282C22⋊C8C22⋊D4312yes—
283#97—1722no—
284#95—432no—
285C24#1062189811yescharacteristic
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—861no—
291C2×Q8—861no—
292C2×Q8—1721no—
293C2×Q8—1721no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—861no—
299C22×C4—861no—
300C22×C4—862no—
301C22×C4C2×C4×D4311yescharacteristic
302C22×C4D4×D4311yescharacteristic
303C22×C4D4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305C22×C4#1062190011yescharacteristic
306C22×C4C2×C22⋊D4311yescharacteristic
307Q16—1722no—
308Q16—1722no—
309M16—41no—
310M16—41no—
311M16—1721no—
312M16—1721no—
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—431no—
320C2×C8—431no—
321C2×C8—862no—
322C2×C8—862no—
323C2×C8—862no—
324C2×C8—1721no—
325C2×C8—1721no—
326C2×C8—1721no—
327C2×C8—1721no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—1721no—
335C4⋊C4—1721no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—1722no—
339C22⋊C4—1721no—
340C22⋊C4—1721no—
341C42—1721no—
342C42—1721no—
343C23—22no—
344C23—22no—
345C23—41no—
346C23C4×C22⋊D4311yescharacteristic
347C23#1306329811yescharacteristic
348C23#1306331111yescharacteristic
349Q8—41no—
350Q8—41no—
351Q8—81no—
352Q8—3441no—
353Q8—1721no—
354Q8—1721no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—81no—
368C2×C4—3441no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4C22⋊C4×D4311yescharacteristic
376C2×C4(C22⋊D43)⋊C411yescharacteristic
377C2×C4#1306329711yescharacteristic
378C2×C4#1306332111yescharacteristic
379C8—42no—
380C8—81no—
381C8—432no—
382C8—861no—
383C8—861no—
384C8—861no—
385C8—3441no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22#1458279911yescharacteristic
395C22#1458301912yes—
396C22#1458317312yes—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—81no—
401C4—81no—
402C4—3442no—
403C4—3441no—
404C4—3441no—
405C4#99×D4311yescharacteristic
406C4#1458287111yescharacteristic
407C2—22no—
408C2—22no—
409C2—41no—
410C2#1913542911yescharacteristic
411C2#1913548711yescharacteristic
412C2#1913550711yescharacteristic
subgroupG/H
centerC22#14582799
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1472C2
socleC22×C43#390
prime radicalC24×C43#41
cosocleC23×C4×C43C23
hypercenter#1472D43
hypocenterC43#9817
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
8. C22×#10621885C4semidirect
16. C2×#13063258C4semidirect
17. C2×#13063249C4semidirect
18. C2×#13063248C4semidirect
237. C43#9817semidirect

Maximal subgroups

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

subgroupindex
C2×#145831382
#191346312
#191343742
#191331162
#191331152
#191329582
C43×#14722
#981743