Finite Group Databasebeta

← #24993791

Subgroups — #24993791

Order 11008.

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

normal subgroups only

This group has 542 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
1#19144535C211yesmaximal, characteristic
2#19137488C211yesmaximal, characteristic, complemented
3#19135431C211yesmaximal, characteristic
4#19133112C211yesmaximal, characteristic
5#19132502C211yesmaximal, characteristic, complemented
6#19132481C211yesmaximal, characteristic, complemented
7C43×#1826C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583223—22no—
10#14583217—21no—
11#14583212—21no—
12#14582942C412yescomplemented
13#14582903C412yescomplemented
14C2×#13063239—22no—
15#14582863C2211yescharacteristic
16#14582798—21no—
17#14582792—22no—
18#14582767—21no—
19#14582759C2211yescharacteristic
20C4⋊C4×Dic43—21no—
21C4×C4⋊Dic43—21no—
22C4×C22⋊Dic43C2211yescharacteristic
23#14582634—21no—
24#14582634—21no—
25C2×#117×C43C2211yescharacteristic
26C43×#407C2211yescharacteristic
27C4×C22⋊C4×C43C2211yescharacteristic
28C43×#339—22no—
29C22×D172C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C2×#10621877C2×C412yes—
32#13063299—21no—
33#13063299—21no—
34#13063299—21no—
35#13063299—21no—
36C2×C4⋊Dic43—22no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43C2×C411yescharacteristic
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43D412yes—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—22no—
44#13063258—22no—
45#13063256—22no—
46#13063245—22no—
47#13063245—22no—
48#13063239—44no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C43⋊#95—22no—
52C43⋊#95—22no—
53C43⋊#95—21no—
54C43⋊#95D411yescharacteristic
55C43⋊#95D411yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C2×M16×C43—21no—
58#117×C43—21no—
59#117×C43—21no—
60#117×C43C2×C412yes—
61#117×C43D412yes—
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C4⋊C4×C43D411yescharacteristic
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C42×C43—21no—
67C2×C42×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70#95×C43—21no—
71C24×C43C2×D411yescharacteristic
72C23×D43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—42no—
76C22×C4×C43—41no—
77C22×C4×C43C22×C411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C22×C4×C43#4111yescharacteristic
83C2×C22⋊D43—42no—
84C2×C22⋊D43—42no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—22no—
91C2×D172—21no—
92C2×D172—21no—
93C2×D172—42no—
94M16×C43—42no—
95C2×C8×C43—41no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43C22⋊C412yes—
99C4⋊C4×C43C22⋊C412yes—
100C22⋊C4×C43—22no—
101C22⋊C4×C43—22no—
102C22⋊C4×C43—22no—
103C22⋊C4×C43—41no—
104C42×C43—22no—
105C42×C43—22no—
106C42×C43—42no—
107C22⋊Dic43—42no—
108C22⋊Dic43—42no—
109(C2×D43)⋊C4—41no—
110(C2×D43)⋊C4—41no—
111C4⋊Dic43—21no—
112C4⋊Dic43—21no—
113C4⋊Dic43—44no—
114C4⋊Dic43—42no—
115C4×Dic43—42no—
116C4×Dic43—82no—
117#10621877—42no—
118C2×C43⋊C8—22no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43C4×D411yescharacteristic
124C23×C43#12011yescharacteristic
125C23×C43#12111yescharacteristic
126C22×D43—41no—
127C22×D43—42no—
128C22×D43—81no—
129C22×D43—81no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—81no—
143C2×C4×C43—81no—
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12311yescharacteristic
148C22⋊D43—82no—
149C22⋊D43—81no—
150C22⋊D43—81no—
151C2×Dic43—22no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—42no—
159C2×Dic43—41no—
160C2×Dic43—42no—
161C2×Dic43—41no—
162D172—42no—
163D172—81no—
164C8×C43—81no—
165C43⋊C8—42no—
166#9366—431nomaximal, Sylow
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43#38611yescharacteristic
178C22×C43#45311yescharacteristic
179C22×C43#45411yescharacteristic
180C2×D43—81no—
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—162no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—42no—
188C4×C43—42no—
189C4×C43—82no—
190C4×C43#41012yes—
191Dic43—42no—
192Dic43—82no—
193Dic43—81no—
194Dic43—81no—
195#3094—431no—
196#2347—431no—
197#1964—431no—
198#1826D4311yescharacteristic, complemented
199#1507—431no—
200#1305—431no—
201#1297—431no—
202C2×C43—21no—
203C2×C43—21no—
204C2×C43—41no—
205C2×C43—41no—
206C2×C43#188311yescharacteristic
207C2×C43#189911yescharacteristic
208C2×C43#190611yescharacteristic
209D43—161no—
210C2×#121—431no—
211C2×#117C2×D4311yescharacteristic
212#482—862no—
213#481—861no—
214#480—861no—
215#428—432no—
216#418—432no—
217C2×#99—862no—
218#407—431no—
219#407C2×D4311yescharacteristic
220#389—861no—
221#388—862no—
222#383—861no—
223#380—431no—
224C4×C4⋊C4—861no—
225C4×C4⋊C4—861no—
226C4×C22⋊C4—431no—
227C4×C22⋊C4C2×D4311yescharacteristic
228#339—22no—
229#327—861no—
230#327—861no—
231C43#936611yescharacteristic, complemented, Sylow
232C22×D4—431no—
233C22×D4—861no—
234C23×C4C22×D4311yescharacteristic
235C2×M16—21no—
236C2×M16—432no—
237#121—861no—
238#121—861no—
239#121—861no—
240#121—861no—
241#117—21no—
242#117—21no—
243#117C4×D4312yes—
244#117C22⋊D4312yes—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—862no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4D17211yescharacteristic
249C2×C4⋊C4D17211yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—432no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C42—21no—
256C2×C42—21no—
257C2×C42—862no—
258C2×C42—861no—
259#107—862no—
260#106—862no—
261#102—862no—
262#102—862no—
263#99—1724no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C22⋊C8—861no—
267C22⋊C8—861no—
268#95—21no—
269#95—431no—
270#95—431no—
271#95—862no—
272#95—862no—
273#95—861no—
274C24—861no—
275C24D4×D4311yescharacteristic
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—1722no—
279C2×D4—1722no—
280C2×D4—1722no—
281C2×D4—1721no—
282C2×D4—1721no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—862no—
291C22×C4C2×C4×D4311yescharacteristic
292C22×C4C2×D17211yescharacteristic
293C22×C4D4×D4311yescharacteristic
294C22×C4#1062190011yescharacteristic
295C22×C4#1062190011yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297M16—42no—
298M16—1722no—
299C2×C8—41no—
300C2×C8—862no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4—1722no—
306C4⋊C4—1724no—
307C4⋊C4(C2×D43)⋊C412yes—
308C4⋊C4(C2×D43)⋊C412yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—41no—
313C22⋊C4—1722no—
314C22⋊C4—1721no—
315C22⋊C4—1721no—
316C22⋊C4—1722no—
317C42—22no—
318C42—22no—
319C42—42no—
320C42—3442no—
321C42—1722no—
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23—3441no—
327C23—3441no—
328C23—1722no—
329C23—1721no—
330C23(C22⋊D43)⋊C411yescharacteristic
331C23#1306329511yescharacteristic
332C23#1306329711yescharacteristic
333D4—3441no—
334D4—3442no—
335D4—3441no—
336D4—3441no—
337D4—1722no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—862no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4C2×(C2×D43)⋊C411yescharacteristic
364C2×C4(C22⋊D43)⋊C411yescharacteristic
365C2×C4#1306329711yescharacteristic
366C2×C4#1306330911yescharacteristic
367C8—81no—
368C8—1722no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—81no—
378C22—81no—
379C22—3441no—
380C22—3441no—
381C22—3441no—
382C22—6882no—
383C22#1458277611yescharacteristic
384C22#1458306811yescharacteristic
385C22#1458307311yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—42no—
391C4—82no—
392C4—3442no—
393C4—3441no—
394C4—3441no—
395C4—1722no—
396C4#1458287212yes—
397C2—21no—
398C2—21no—
399C2—41no—
400C2—41no—
401C2—6881no—
402C2#1913496911yescharacteristic
403C2#1913505111yescharacteristic
404C2#1913509411yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1826C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1826D43
hypocenterC43#9366
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
2. #19137488C2semidirect
5. #19132502C2semidirect
6. #19132481C2semidirect
7. C43×#1826C2semidirect
12. #14582942C4semidirect
13. #14582903C4semidirect
198. #1826D43semidirect
231. C43#9366semidirect

Maximal subgroups

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

subgroupindex
#191445352
#191374882
#191354312
#191331122
#191325022
#191324812
C43×#18262
#936643