Finite Group Databasebeta

← #24994666

Subgroups — #24994666

Order 11008.

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

normal subgroups only

This group has 482 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#19144544C211yesmaximal, characteristic
2#19137351C211yesmaximal, characteristic
3#19134695C211yesmaximal, characteristic
4#19134670C211yesmaximal, characteristic
5#19133127C211yesmaximal, characteristic
6#19132504C211yesmaximal, characteristic
7C43×#1284C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10#14583241—22no—
11#14583235C412yescomplemented
12#14583230C412yescomplemented
13#14582941—21no—
14#14582909—21no—
15#14582863C2211yescharacteristic
16#14582803—21no—
17#14582793—21no—
18#14582787—21no—
19#14582784—21no—
20#14582783—21no—
21#14582762C2211yescharacteristic
22C4×Dic43⋊C4—21no—
23#14582665—21no—
24#14582665—21no—
25#14582659—21no—
26#14582659—21no—
27#14582635—22no—
28C43×#407C2211yescharacteristic
29C43×#381C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C2×#10621877—21no—
33#13063304—21no—
34#13063304—21no—
35#13063304C2×C412yes—
36#13063304D412yes—
37#13063284—21no—
38#13063284—21no—
39#13063284—21no—
40#13063284—21no—
41C2×C4⋊Dic43C2×C411yescharacteristic
42C2×C4⋊Dic43C2×C411yescharacteristic
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43D411yescharacteristic
50C2×C22⋊Dic43D411yescharacteristic
51C2×C4×Dic43—21no—
52C2×C4×Dic43—21no—
53C2×C4×Dic43—21no—
54#13063259—22no—
55#13063257—22no—
56#13063250—22no—
57#13063250—22no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C23×C4×C43C2311yescharacteristic
67C2×M16×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C42×C43D411yescharacteristic
71C2×C42×C43D411yescharacteristic
72C22⋊C8×C43—21no—
73C22⋊C8×C43C2×C412yes—
74#95×C43—21no—
75#95×C43—21no—
76#95×C43—21no—
77C24×C43C2×D411yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C2×Dic86—21no—
96C2×Dic86—41no—
97C2×Dic86—41no—
98C2×Dic86C22⋊C412yes—
99M16×C43—41no—
100M16×C43—41no—
101C2×C8×C43—22no—
102C22⋊C4×C43—41no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—42no—
105C42×C43—41no—
106C42×C43—41no—
107C22⋊Dic43—22no—
108C22⋊Dic43—22no—
109C22⋊Dic43—41no—
110C22⋊Dic43—41no—
111C22⋊Dic43—41no—
112C22⋊Dic43—41no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43C22⋊C412yes—
119Dic43⋊C4—22no—
120Dic43⋊C4—22no—
121Dic43⋊C4—42no—
122Dic43⋊C4—81no—
123C4×Dic43—42no—
124C4×Dic43—41no—
125C4×Dic43—41no—
126C4×Dic43—81no—
127#10621877—41no—
128#10621877—41no—
129C2×C43⋊C8—41no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43C4×D411yescharacteristic
135C23×C43#12011yescharacteristic
136C23×C43#12111yescharacteristic
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43C2×C22⋊C411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×Dic43—22no—
159C2×Dic43—22no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—81no—
173C2×Dic43—81no—
174Dic86—42no—
175Dic86—81no—
176C8×C43—42no—
177C43⋊C8—81no—
178#9526—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43#38611yescharacteristic
190C22×C43#45811yescharacteristic
191C22×C43#45811yescharacteristic
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—42no—
197C4×C43—81no—
198C4×C43—161no—
199Dic43—42no—
200Dic43—42no—
201Dic43—81no—
202Dic43—81no—
203Dic43—81no—
204Dic43—81no—
205#3095—431no—
206#2332—431no—
207#1826—431no—
208#1820—431no—
209#1511—431no—
210#1306—431no—
211#1284D4311yescharacteristic
212C2×C43—21no—
213C2×C43—21no—
214C2×C43—41no—
215C2×C43—41no—
216C2×C43#189011yescharacteristic
217C2×C43#190511yescharacteristic
218C2×C43#190611yescharacteristic
219C2×C22⋊Q8—431no—
220C2×#117—431no—
221#485—862no—
222#484—432no—
223#483—432no—
224#428—861no—
225#419—861no—
226#407—431no—
227#407C2×D4311yescharacteristic
228#391—861no—
229#388—861no—
230#388—861no—
231#387—861no—
232#387—861no—
233#381—431no—
234#381C2×D4311yescharacteristic
235C4×C4⋊C4—861no—
236C4×C22⋊C4C2×D4311yescharacteristic
237#342—861no—
238#342—861no—
239#339—861no—
240#339—861no—
241#328—862no—
242C43#952611yescharacteristic, complemented, Sylow
243C22×Q8—431no—
244C23×C4C22×D4311yescharacteristic
245C2×M16—21no—
246C2×M16—861no—
247C22⋊Q8—432no—
248C22⋊Q8—432no—
249C22⋊Q8—861no—
250C22⋊Q8—861no—
251#117—861no—
252#117—861no—
253#117—861no—
254#117—861no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4—861no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—431no—
264C2×C22⋊C4—431no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C42—861no—
268C2×C42—861no—
269C2×C42—861no—
270C2×C42D17211yescharacteristic
271C2×C42D17211yescharacteristic
272#107—862no—
273#106—862no—
274#103—862no—
275#103—862no—
276C22⋊C8—21no—
277C22⋊C8—861no—
278C22⋊C8—861no—
279C22⋊C8C4×D4312yes—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—861no—
284#95—861no—
285#95—861no—
286#95—861no—
287#95—861no—
288#95—861no—
289C24D4×D4311yescharacteristic
290C2×Q8—432no—
291C2×Q8—861no—
292C2×Q8—1721no—
293C2×Q8—1721no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—861no—
300C22×C4—861no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4C2×C4×D4311yescharacteristic
306C22×C4C2×D17211yescharacteristic
307C22×C4#1062189811yescharacteristic
308C22×C4D4×D4311yescharacteristic
309C22×C4D4×D4311yescharacteristic
310C22×C4#1062190211yescharacteristic
311M16—41no—
312M16—41no—
313M16—1721no—
314M16—1721no—
315C2×C8—22no—
316C2×C8—1721no—
317C4⋊C4—432no—
318C4⋊C4—862no—
319C4⋊C4—862no—
320C4⋊C4—861no—
321C4⋊C4—861no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—3441no—
326C4⋊C4—1722no—
327C22⋊C4—42no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C22⋊C4—1721no—
336C42—41no—
337C42—41no—
338C42—3441no—
339C42—1722no—
340C42—1721no—
341C42—1721no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23#1306328711yescharacteristic
347C23#1306329511yescharacteristic
348C23#1306329811yescharacteristic
349Q8—3441no—
350Q8—1722no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—862no—
369C2×C4—862no—
370C2×C4—3441no—
371C2×C4—3441no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4C22⋊C4×D4311yescharacteristic
385C2×C4C4×D17211yescharacteristic
386C2×C4#1306330011yescharacteristic
387C2×C4#1306331011yescharacteristic
388C8—42no—
389C8—3441no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#1458277711yescharacteristic
401C22#1458309011yescharacteristic
402C22#1458309011yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—81no—
409C4—161no—
410C4—3441no—
411C4—3441no—
412C4—3441no—
413C4—3441no—
414C4—1722no—
415C4—1722no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2#1913500711yescharacteristic
421C2#1913509011yescharacteristic
422C2#1913509511yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#9526
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
11. #14583235C4semidirect
12. #14583230C4semidirect
242. C43#9526semidirect

Maximal subgroups

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

subgroupindex
#191445442
#191373512
#191346952
#191346702
#191331272
#191325042
C43×#12842
#952643