Finite Group Databasebeta

← #24997111

Subgroups — #24997111

Order 11008.

568 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 109 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#19145370C211yesmaximal, characteristic
2C2×#14583235C211yesmaximal, characteristic
3#19139073C211yesmaximal, characteristic
4#19135580C211yesmaximal, characteristic
5#19134686C211yesmaximal, characteristic
6#19133168C211yesmaximal, characteristic
7C43×#1282C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063304C2211yescharacteristic
10C22×C4⋊Dic43C2211yescharacteristic
11#14583235—22no—
12#14583235—21no—
13#14583235—21no—
14#14583235—22no—
15#14583140—22no—
16#14583057—21no—
17#14583057—21no—
18C2×#13063259—21no—
19C2×#13063250—21no—
20#14582831—22no—
21#14582805—21no—
22#14582774—22no—
23#14582769—21no—
24#14582759C2211yescharacteristic
25#14582665—22no—
26#14582662—22no—
27#14582637—22no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×C22⋊C8×C43C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C22×Dic86D411yescharacteristic
33C23×Dic43—21no—
34C2×Dic172—22no—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—21no—
41#13063304—21no—
42#13063304—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43—24no—
50C2×C4⋊Dic43D412yes—
51C2×C4⋊Dic43D411yescharacteristic
52C2×C4⋊Dic43D411yescharacteristic
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58#13063259—22no—
59#13063259—24no—
60#13063250—22no—
61#13063250—22no—
62#13063250—24no—
63C43⋊#95—24no—
64C43⋊#95—21no—
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—21no—
67C22×C8×C43D412yes—
68C2×C22⋊C4×C43D412yes—
69C2×C42×C43—21no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72C22⋊C8×C43—21no—
73C22⋊C8×C43D412yes—
74#95×C43—21no—
75C24×C43C2×D411yescharacteristic
76C22×C4×C43—22no—
77C22×C4×C43—42no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43#4111yescharacteristic
84C22×Dic43—21no—
85C22×Dic43—22no—
86C22×Dic43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—41no—
90C22×Dic43—41no—
91C22×Dic43—41no—
92C22×Dic43—82no—
93C2×Dic86—21no—
94C2×Dic86—21no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86—42no—
98C2×Dic86—42no—
99C2×C8×C43—22no—
100C2×C8×C43—22no—
101C2×C8×C43—42no—
102C2×C8×C43—42no—
103C22⋊C4×C43—22no—
104C22⋊C4×C43Q1614yescomplemented
105C42×C43—42no—
106C22⋊Dic43—41no—
107C22⋊Dic43—41no—
108C22⋊Dic43—41no—
109C22⋊Dic43—41no—
110C22⋊Dic43—42no—
111C4⋊Dic43—22no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—22no—
116C4⋊Dic43—21no—
117C4⋊Dic43—41no—
118C4⋊Dic43—41no—
119C4⋊Dic43—42no—
120C4⋊Dic43—84no—
121Dic43⋊C4—41no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125Dic172—82no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43#12011yescharacteristic
129C23×C43#12111yescharacteristic
130C23×C43#12711yescharacteristic
131C23×C43C2×Q1612yes—
132C23×C43#13712yes—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—24no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43#12011yescharacteristic
143C2×C4×C43#12011yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×Dic43—42no—
147C2×Dic43—44no—
148C2×Dic43—42no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—42no—
154C2×Dic43—82no—
155C2×Dic43—82no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158C2×Dic43—81no—
159C2×Dic43—81no—
160C2×Dic43—81no—
161Dic86—42no—
162Dic86—42no—
163Dic86—42no—
164Dic86—81no—
165C8×C43—42no—
166C8×C43—42no—
167#9959—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—42no—
175C22×C43—42no—
176C22×C43#39211yescharacteristic
177C22×C43#45112yes—
178C22×C43#46212yes—
179C22×C43#49411yescharacteristic
180C22×C43#49711yescharacteristic
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—44no—
185C4×C43#45812yes—
186Dic43—81no—
187Dic43—82no—
188Dic43—81no—
189Dic43—81no—
190Dic43—81no—
191Dic43—161no—
192#3189—431no—
193C2×#484—431no—
194#2502—431no—
195#1996—431no—
196#1824—431no—
197#1520—431no—
198#1282D4311yescharacteristic
199C2×C43—21no—
200C2×C43—22no—
201C2×C43—22no—
202C2×C43—21no—
203C2×C43#200811yescharacteristic
204C2×C43#201611yescharacteristic
205C2×C43#202211yescharacteristic
206C2×C22⋊Q8—431no—
207C2×C22⋊Q8—431no—
208C22×C4⋊C4—431no—
209#484—862no—
210#484—861no—
211#484—861no—
212#484—862no—
213#467—862no—
214#451—861no—
215#451—861no—
216C2×#107—861no—
217C2×#103—861no—
218C2×C22⋊C8C2×D4311yescharacteristic
219C2×C22⋊C8C2×D4311yescharacteristic
220#398—862no—
221#391—861no—
222#385—862no—
223#384—861no—
224#380—431no—
225C4×C22⋊C4C2×D4311yescharacteristic
226#342—862no—
227#340—862no—
228#328—862no—
229C43#995911yescharacteristic, complemented, Sylow
230C22×Q8—431no—
231C22×Q8—431no—
232C23×C4—861no—
233C23×C4C22×D4311yescharacteristic
234C2×Q16—862no—
235C22×C8—21no—
236C22×C8D17212yes—
237C22⋊Q8—861no—
238C22⋊Q8—861no—
239C22⋊Q8—861no—
240C22⋊Q8—861no—
241C22⋊Q8—861no—
242C22⋊Q8—861no—
243C22⋊Q8—861no—
244C22⋊Q8—861no—
245C2×C4⋊C4—432no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—864no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—861no—
257C2×C22⋊C4—861no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4D17212yes—
261C2×C42—21no—
262#107—864no—
263#107—862no—
264#103—864no—
265#103—862no—
266#103—862no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269C22⋊C8—21no—
270C22⋊C8D17212yes—
271#95—21no—
272#95—864no—
273#95—861no—
274C24C2×D17211yescharacteristic
275C2×Q8—861no—
276C2×Q8—861no—
277C2×Q8—861no—
278C2×Q8—861no—
279C2×Q8—1722no—
280C2×Q8—1722no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—862no—
287C22×C4—861no—
288C22×C4—3442no—
289C22×C4—1721no—
290C22×C4—1721no—
291C22×C4—1721no—
292C22×C4C2×D17211yescharacteristic
293C22×C4C2×D17211yescharacteristic
294C22×C4D4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4D4×D4311yescharacteristic
297C22×C4#1062190211yescharacteristic
298Q16—3442no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—42no—
303C4⋊C4—862no—
304C4⋊C4—861no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4—862no—
308C4⋊C4—861no—
309C4⋊C4—3444no—
310C4⋊C4—1722no—
311C4⋊C4—1721no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C22⋊C4—22no—
318C22⋊C4—1722no—
319C22⋊C4—1721no—
320C22⋊C4—1721no—
321C22⋊C4—1721no—
322C22⋊C4—1721no—
323C22⋊C4Dic17214yescomplemented
324C42—42no—
325C23—41no—
326C23—41no—
327C23#1306329511yescharacteristic
328C23#1306330011yescharacteristic
329C23#1306332211yescharacteristic
330C23C2×Dic17212yes—
331C23#1306335812yes—
332Q8—3441no—
333Q8—1722no—
334Q8—1722no—
335Q8—1722no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—3442no—
346C2×C4—3442no—
347C2×C4—3441no—
348C2×C4—3441no—
349C2×C4—3441no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—1722no—
353C2×C4—1724no—
354C2×C4—1722no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1722no—
360C2×C4#1306329511yescharacteristic
361C2×C4#1306329511yescharacteristic
362C2×C4#1306330011yescharacteristic
363C2×C4#1306330011yescharacteristic
364C8—42no—
365C8—42no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22#1458280911yescharacteristic
375C22#1458305712yes—
376C22#1458311012yes—
377C22#1458327911yescharacteristic
378C22#1458329311yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—3442no—
384C4—3441no—
385C4—3441no—
386C4—3441no—
387C4—3441no—
388C4—6881no—
389C4#1458309012yes—
390C2—22no—
391C2—21no—
392C2—22no—
393C2—21no—
394C2#1913565111yescharacteristic
395C2#1913569711yescharacteristic
396C2#1913572711yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1282C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#1282D43
hypocenterC43#9959
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1282

Complements

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

NH ≅ G/Ntype
104. C22⋊C4×C43Q16semidirect
229. C43#9959semidirect
323. C22⋊C4Dic172semidirect

Maximal subgroups

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

subgroupindex
#191453702
C2×#145832352
#191390732
#191355802
#191346862
#191331682
C43×#12822
#995943