Finite Group Databasebeta

← #24997225

Subgroups — #24997225

Order 11008.

492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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#19145367C211yesmaximal, characteristic
2#19144544C211yesmaximal, characteristic
3#19144539C211yesmaximal, characteristic
4#19134664C211yesmaximal, characteristic
5#19132958C211yesmaximal, characteristic
6#19132471C211yesmaximal, characteristic
7C43×#1472C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10#14583241—22no—
11#14583237—22no—
12#14583235—21no—
13#14583234—21no—
14#14583232—21no—
15#14583232—21no—
16#14583230—21no—
17#14583227—21no—
18#14583138—22no—
19#14583055—21no—
20#14583054—21no—
21#14582941—21no—
22#14582939—21no—
23#14582909—21no—
24#14582908—21no—
25#14582863C2211yescharacteristic
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27#14582653—22no—
28#14582624—22no—
29C2×C22⋊Q8×C43C2211yescharacteristic
30C43×#407C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C43×#324—22no—
33C22×Dic86D411yescharacteristic
34C2×#10621885—22no—
35C2×#10621877—21no—
36C22×C43⋊C8D412yes—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—21no—
41#13063284—21no—
42#13063284—21no—
43#13063284—21no—
44#13063284—21no—
45C2×C4⋊Dic43D411yescharacteristic
46C2×C4⋊Dic43D411yescharacteristic
47C2×C4⋊Dic43D411yescharacteristic
48C2×Dic43⋊C4—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C4×Dic43—21no—
52#13063259—22no—
53#13063258—22no—
54#13063258—22no—
55#13063257—22no—
56#13063256—22no—
57#13063250—22no—
58#13063250—22no—
59#13063249—22no—
60#13063249—22no—
61#13063249—22no—
62#13063248—22no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)—21no—
66C22⋊(C43⋊C8)D412yes—
67C22×Q8×C43D411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C2×M16×C43—21no—
70C22×C8×C43—21no—
71C22⋊Q8×C43—21no—
72C22⋊Q8×C43—21no—
73C22⋊Q8×C43—21no—
74C22⋊Q8×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43D411yescharacteristic
77C2×C22⋊C4×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43D412yes—
82C24×C43#4111yescharacteristic
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—42no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—42no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C2×Dic86—21no—
100C2×Dic86—21no—
101C2×Dic86—42no—
102M16×C43—42no—
103C2×C8×C43—22no—
104C2×C8×C43—42no—
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—41no—
113C22⋊Dic43—41no—
114C22⋊Dic43—41no—
115C22⋊Dic43—41no—
116#10621885—82no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125C4×Dic43—41no—
126C4×Dic43—41no—
127#10621877—42no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—42no—
131C23×C43—22no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43#12111yescharacteristic
135C23×C43#12111yescharacteristic
136C23×C43#12111yescharacteristic
137Q8×C43—42no—
138Q8×C43—42no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—81no—
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12011yescharacteristic
151C2×C4×C43#12011yescharacteristic
152C2×C4×C43#12711yescharacteristic
153C2×Dic43—42no—
154C2×Dic43—42no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—42no—
160C2×Dic43—81no—
161Dic86—42no—
162Dic86—42no—
163C8×C43—42no—
164C8×C43—81no—
165C43⋊C8—42no—
166C43⋊C8—42no—
167#9979—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—82no—
177C22×C43#39211yescharacteristic
178C22×C43#47312yes—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43#45812yes—
185Dic43—81no—
186Dic43—81no—
187Dic43—81no—
188Dic43—81no—
189#3189—431no—
190#3095—431no—
191#3095—431no—
192#1818—431no—
193#1472—431no—
194#1472D4311yescharacteristic
195#1293—431no—
196C2×C43—22no—
197C2×C43—41no—
198C2×C43—41no—
199C2×C43#201711yescharacteristic
200C2×C43#202011yescharacteristic
201C2×C43#202211yescharacteristic
202C2×C22⋊Q8—431no—
203C2×C22⋊Q8C2×D4311yescharacteristic
204C2×#117—431no—
205#485—862no—
206#485—862no—
207#484—861no—
208#484—861no—
209#484—861no—
210#484—861no—
211#483—861no—
212#483—861no—
213#467—862no—
214#451—861no—
215#451—861no—
216#428—861no—
217#428—861no—
218#419—861no—
219#419—861no—
220#407—431no—
221#407C2×D4311yescharacteristic
222C2×C22⋊C8—431no—
223C2×C22⋊C8C2×D4311yescharacteristic
224#336—862no—
225#324—22no—
226#324—862no—
227C43#997911yescharacteristic, complemented, Sylow
228C22×Q8—431no—
229C22×Q8D17211yescharacteristic
230C23×C4C22×D4311yescharacteristic
231C2×Q16—862no—
232C2×M16—21no—
233C2×M16—861no—
234C22×C8—21no—
235C22×C8—432no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—861no—
241C22⋊Q8—861no—
242C22⋊Q8—861no—
243C22⋊Q8—861no—
244#117—861no—
245#117—861no—
246#117—861no—
247#117—861no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—431no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4D17211yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—861no—
256C2×C22⋊C4—861no—
257C2×C42—861no—
258#107—862no—
259#107—862no—
260#107—862no—
261#106—862no—
262#106—862no—
263#103—862no—
264#103—862no—
265#103—862no—
266#103—862no—
267#103—862no—
268#103—862no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—21no—
272C22⋊C8—432no—
273C22⋊C8—861no—
274C22⋊C8—861no—
275C22⋊C8—861no—
276C22⋊C8C22⋊D4312yes—
277C24#1062189811yescharacteristic
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—42no—
281C2×Q8—861no—
282C2×Q8—861no—
283C2×Q8—1722no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—42no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4C2×D17211yescharacteristic
292C22×C4D4×D4311yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4D4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297Q16—3442no—
298M16—42no—
299M16—1722no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—41no—
303C2×C8—862no—
304C2×C8—862no—
305C2×C8—1722no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—861no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—1721no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C22⋊C4—1721no—
324C42—1721no—
325C42—1721no—
326C23—22no—
327C23—41no—
328C23—41no—
329C23#1306329811yescharacteristic
330C23#1306329811yescharacteristic
331C23#1306329911yescharacteristic
332Q8—42no—
333Q8—42no—
334Q8—1722no—
335Q8—1722no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—3441no—
347C2×C4—1722no—
348C2×C4—1722no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1722no—
354C2×C4#1306329311yescharacteristic
355C2×C4#1306329511yescharacteristic
356C2×C4#1306329511yescharacteristic
357C2×C4#1306332111yescharacteristic
358C8—42no—
359C8—81no—
360C8—1722no—
361C8—1722no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—82no—
371C22#1458280811yescharacteristic
372C22#1458317312yes—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—3441no—
379C4—3441no—
380C4—3441no—
381C4—3441no—
382C4#1458309012yes—
383C2—22no—
384C2—41no—
385C2—41no—
386C2#1913569911yescharacteristic
387C2#1913571511yescharacteristic
388C2#1913572511yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1472C2
socleC22×C43#392
prime radicalC24×C43#41
hypercenter#1472D43
hypocenterC43#9979
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
227. C43#9979semidirect

Maximal subgroups

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

subgroupindex
#191453672
#191445442
#191445392
#191346642
#191329582
#191324712
C43×#14722
#997943