Finite Group Databasebeta

← #24997216

Subgroups — #24997216

Order 11008.

518 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 85 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#19145348C211yesmaximal, characteristic
2#19144535C211yesmaximal, characteristic
3#19134666C211yesmaximal, characteristic, complemented
4#19132959C211yesmaximal, characteristic, complemented
5#19132956C211yesmaximal, characteristic
6#19132471C211yesmaximal, characteristic, complemented
7C43×#3095C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583227—21no—
10#14583223—22no—
11#14583217—21no—
12#14583217—21no—
13#14583212—21no—
14#14583130—22no—
15#14583049—21no—
16#14583038—21no—
17#14582942—21no—
18#14582903—21no—
19#14582863C2211yescharacteristic
20C2×C22⋊(C43⋊C8)C2211yescharacteristic
21C2×C22⋊(C43⋊C8)C2211yescharacteristic
22#14582654—22no—
23#14582625—22no—
24#14582622—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C43×#485—22no—
28C43×#484—21no—
29C43×#483—21no—
30C43×#428—21no—
31C43×#419—21no—
32C43×#407C2211yescharacteristic
33C22×D172D411yescharacteristic
34C22×C22⋊D43—21no—
35C2×#10621884—22no—
36C2×#10621877—21no—
37C22×C43⋊C8—21no—
38C22×C43⋊C8D412yes—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×(C2×D43)⋊C4—21no—
45#13063258—22no—
46#13063256—22no—
47#13063256—22no—
48#13063249—22no—
49#13063245—22no—
50#13063245—22no—
51#13063245—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)D412yes—
58C22×Q8×C43D411yescharacteristic
59C23×C4×C43C2311yescharacteristic
60C2×M16×C43—21no—
61C22⋊Q8×C43—21no—
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65#117×C43—21no—
66#117×C43—21no—
67#117×C43—21no—
68#117×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43D411yescharacteristic
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C42×C43—21no—
76#107×C43—22no—
77#106×C43—22no—
78#103×C43—22no—
79#103×C43—22no—
80C22⋊C8×C43—21no—
81C22⋊C8×C43D412yes—
82C24×C43#4111yescharacteristic
83C23×D43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—42no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—42no—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C2×C22⋊D43—41no—
99C2×C22⋊D43—41no—
100C2×C22⋊D43—82no—
101C22×Dic43—21no—
102C2×D172—21no—
103C2×D172—21no—
104C2×D172—42no—
105M16×C43—42no—
106C2×C8×C43—22no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C42×C43—41no—
120C42×C43—41no—
121#10621884—82no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126#10621877—42no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—42no—
130C2×C43⋊C8—42no—
131C2×C43⋊C8—41no—
132C23×C43—22no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43#12111yescharacteristic
136C23×C43#12111yescharacteristic
137C23×C43#12111yescharacteristic
138C22×D43—41no—
139C22×D43—42no—
140C22×D43—81no—
141C22×D43—81no—
142Q8×C43—42no—
143Q8×C43—42no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
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×C43#12011yescharacteristic
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12011yescharacteristic
161C2×C4×C43#12711yescharacteristic
162C22⋊D43—82no—
163C22⋊D43—82no—
164C2×Dic43—41no—
165C2×Dic43—81no—
166D172—42no—
167D172—42no—
168C8×C43—42no—
169C43⋊C8—42no—
170C43⋊C8—42no—
171C43⋊C8—81no—
172#9978—431nomaximal, Sylow
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—82no—
182C22×C43#39211yescharacteristic
183C22×C43#47112yes—
184C2×D43—81no—
185C2×D43—81no—
186C2×D43—81no—
187C2×D43—162no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—81no—
192C4×C43—81no—
193C4×C43—81no—
194C4×C43—81no—
195C4×C43#45812yes—
196Dic43—81no—
197#3187—431no—
198#3095D4311yescharacteristic, complemented
199#3094—431no—
200#1818—431no—
201#1472—431no—
202#1471—431no—
203#1293—431no—
204C2×C43—22no—
205C2×C43—41no—
206C2×C43—41no—
207C2×C43#201711yescharacteristic
208C2×C43#201911yescharacteristic
209C2×C43#202211yescharacteristic
210D43—161no—
211C2×C22⋊Q8C2×D4311yescharacteristic
212C2×#121—431no—
213C2×#117C2×D4311yescharacteristic
214#485—22no—
215#484—21no—
216#483—21no—
217#483—861no—
218#482—862no—
219#481—861no—
220#481—861no—
221#480—861no—
222#465—862no—
223#450—861no—
224#448—861no—
225#428—21no—
226#428—861no—
227#419—21no—
228#418—861no—
229#407—431no—
230#407C2×D4311yescharacteristic
231C2×C22⋊C8—431no—
232C2×C22⋊C8—431no—
233#336—862no—
234#324—862no—
235#323—862no—
236C43#997811yescharacteristic, complemented, Sylow
237C22×Q8C22⋊D4311yescharacteristic
238C22×D4—431no—
239C22×D4—861no—
240C23×C4C22×D4311yescharacteristic
241C2×SD16—862no—
242C2×M16—21no—
243C2×M16—861no—
244C22×C8—432no—
245C22×C8—861no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250#121—861no—
251#121—861no—
252#121—861no—
253#121—861no—
254#117—21no—
255#117—21no—
256#117—21no—
257#117—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4C22⋊D4311yescharacteristic
261C2×C4⋊C4C22⋊D4311yescharacteristic
262C2×C4⋊C4C22⋊D4311yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—861no—
266C2×C42—21no—
267#107—22no—
268#107—862no—
269#106—22no—
270#106—862no—
271#106—862no—
272#103—22no—
273#103—22no—
274#103—862no—
275#102—862no—
276#102—862no—
277#102—862no—
278C22⋊C8—21no—
279C22⋊C8—432no—
280C22⋊C8—861no—
281C22⋊C8—861no—
282C22⋊C8—861no—
283C22⋊C8—861no—
284C22⋊C8—861no—
285C22⋊C8C22⋊D4312yes—
286C24—861no—
287C24#1062190011yescharacteristic
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—42no—
291C2×D4—861no—
292C2×D4—861no—
293C2×D4—3442no—
294C2×D4—1722no—
295C2×D4—1721no—
296C2×D4—1721no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—861no—
303C22×C4D4×D4311yescharacteristic
304C22×C4D4×D4311yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4C2×C22⋊D4311yescharacteristic
307C22×C4C2×C22⋊D4311yescharacteristic
308C22×C4C2×C22⋊D4311yescharacteristic
309SD16—3442no—
310M16—42no—
311M16—1722no—
312C2×C8—22no—
313C2×C8—862no—
314C2×C8—862no—
315C2×C8—1722no—
316C2×C8—1721no—
317C2×C8—1722no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C42—41no—
335C42—41no—
336C23—22no—
337C23—41no—
338C23—41no—
339C23—3441no—
340C23—3441no—
341C23—1722no—
342C23—1721no—
343C23#1306329611yescharacteristic
344C23#1306329711yescharacteristic
345C23#1306329711yescharacteristic
346Q8—42no—
347Q8—42no—
348D4—3442no—
349D4—3442no—
350D4—1722no—
351D4—1722no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—3441no—
367C2×C4—1721no—
368C2×C4#1306329311yescharacteristic
369C2×C4#1306329311yescharacteristic
370C2×C4#1306329411yescharacteristic
371C2×C4#1306332111yescharacteristic
372C8—42no—
373C8—3441no—
374C8—1722no—
375C8—1722no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—82no—
385C22—3441no—
386C22—3441no—
387C22—3441no—
388C22—6882no—
389C22#1458280711yescharacteristic
390C22#1458316412yes—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—3441no—
399C4#1458308812yes—
400C2—22no—
401C2—41no—
402C2—41no—
403C2—6881no—
404C2#1913569811yescharacteristic
405C2#1913570611yescharacteristic
406C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#3095C2
socleC22×C43#392
prime radicalC2×#13063299C22
hypercenter#3095D43
hypocenterC43#9978
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
3. #19134666C2semidirect
4. #19132959C2semidirect
6. #19132471C2semidirect
7. C43×#3095C2semidirect
198. #3095D43semidirect
236. C43#9978semidirect

Maximal subgroups

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

subgroupindex
#191453482
#191445352
#191346662
#191329592
#191329562
#191324712
C43×#30952
#997843