Finite Group Databasebeta

← #24991653

Subgroups — #24991653

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582830C211yesmaximal, characteristic
2#19137212C211yesmaximal, characteristic
3#19134681C211yesmaximal, characteristic
4C2×#14582624C211yesmaximal, characteristic
5#19132475C211yesmaximal, characteristic
6#19132473C211yesmaximal, characteristic
7C43×#1823C211yesmaximal, characteristic
8C2×#13063281—21no—
9C22×Dic43⋊C4—21no—
10C22×Dic43⋊C4C2211yescharacteristic
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12#14582830—22no—
13#14582830C414yescomplemented
14#14582796—22no—
15#14582794—22no—
16#14582759C2211yescharacteristic
17#14582757—21no—
18C2×C43⋊#95—21no—
19C2×C43⋊#95C2211yescharacteristic
20#14582661—22no—
21#14582624—22no—
22C22×C4⋊C4×C43C2211yescharacteristic
23C2×C22⋊C8×C43C2211yescharacteristic
24C43×#380C2211yescharacteristic
25C43×#340—22no—
26C23×Dic43—21no—
27C23×Dic43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C22×C43⋊C8—21no—
30#13063281—42no—
31#13063281—42no—
32C2×C4⋊Dic43D412yes—
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—22no—
38C2×Dic43⋊C4—24no—
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4—42no—
41C2×Dic43⋊C4—42no—
42C2×Dic43⋊C4C2×C412yes—
43C2×Dic43⋊C4D412yes—
44C2×C22⋊Dic43—21no—
45C2×C4×Dic43—22no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C43⋊#95—22no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—24no—
52C43⋊#95C2×C412yes—
53C23×C4×C43—21no—
54C23×C4×C43C2311yescharacteristic
55C22×C8×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43C2×C412yes—
62C2×C4⋊C4×C43D412yes—
63C2×C22⋊C4×C43—21no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43—21no—
66#95×C43—21no—
67C24×C43C2×D411yescharacteristic
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—42no—
71C22×C4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43—41no—
75C22×C4×C43—41no—
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
83C22×Dic43—24no—
84C22×Dic43—22no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—22no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—42no—
93C22×Dic43—42no—
94C22×Dic43—41no—
95C22×Dic43—41no—
96C22×Dic43C22⋊C412yes—
97C22×Dic43C22⋊C412yes—
98C22×Dic43D812yes—
99C22×Dic43SD1612yes—
100C2×C8×C43—42no—
101C2×C8×C43—41no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—42no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊Dic43—41no—
110C22⋊Dic43—41no—
111C4⋊Dic43—42no—
112Dic43⋊C4—22no—
113Dic43⋊C4—22no—
114Dic43⋊C4—22no—
115Dic43⋊C4—22no—
116Dic43⋊C4—44no—
117Dic43⋊C4—48no—
118Dic43⋊C4—82no—
119C4×Dic43—44no—
120C2×C43⋊C8—42no—
121C2×C43⋊C8—41no—
122C23×C43—22no—
123C23×C43—22no—
124C23×C43C2×C22⋊C411yescharacteristic
125C23×C43#12011yescharacteristic
126C23×C43#12311yescharacteristic
127C23×C43C2×D811yescharacteristic
128C23×C43C2×SD1611yescharacteristic
129C23×C43AGL(1,ℤ/8)11yescharacteristic
130C23×C43#13711yescharacteristic
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—81no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43C4×D411yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×Dic43—22no—
152C2×Dic43—22no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—22no—
156C2×Dic43—22no—
157C2×Dic43—24no—
158C2×Dic43—22no—
159C2×Dic43—44no—
160C2×Dic43—44no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—81no—
169C2×Dic43#10214yes—
170C8×C43—81no—
171C43⋊C8—81no—
172#9027—431nomaximal, Sylow
173C22×C43—22no—
174C22×C43—22no—
175C22×C43—22no—
176C22×C43—22no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43#38611yescharacteristic
182C22×C43C2×#10211yescharacteristic
183C22×C43#41711yescharacteristic
184C22×C43#44711yescharacteristic
185C22×C43#44811yescharacteristic
186C22×C43#45612yes—
187C22×C43#45812yes—
188C22×C43#48011yescharacteristic
189C22×C43#48111yescharacteristic
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—82no—
195C4×C43—82no—
196Dic43—24no—
197Dic43—44no—
198Dic43—42no—
199Dic43—82no—
200C2×#398—431no—
201#2316—431no—
202#1823—431no—
203#1823D4311yescharacteristic
204C2×#324—431no—
205#1294—431no—
206#1294—431no—
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—21no—
210C2×C43—21no—
211C2×C43#161012yes—
212C2×C43#161112yes—
213C2×C43#187411yescharacteristic
214C2×C43#188611yescharacteristic
215C2×C43#189011yescharacteristic
216C2×#117—861no—
217C22×C4⋊C4—431no—
218C22×C4⋊C4—861no—
219C22×C4⋊C4C2×D4311yescharacteristic
220C2×C22⋊C8—431no—
221C2×C22⋊C8C2×D4311yescharacteristic
222#398—434no—
223#398—862no—
224#389—862no—
225#389—862no—
226#380—431no—
227#380—861no—
228#380C2×D4311yescharacteristic
229C2×#95—431no—
230C2×#95—861no—
231#340—22no—
232#340—862no—
233#324—862no—
234C43#902711yescharacteristic, complemented, Sylow
235C23×C4—21no—
236C23×C4—431no—
237C23×C4—431no—
238C23×C4—861no—
239C23×C4C22×D4311yescharacteristic
240C22×C8—21no—
241C22×C8—861no—
242#117—1722no—
243#117—1722no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—432no—
250C2×C4⋊C4—432no—
251C2×C4⋊C4—432no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—862no—
257C2×C4⋊C4—864no—
258C2×C4⋊C4—862no—
259C2×C4⋊C4—1722no—
260C2×C4⋊C4—1722no—
261C2×C4⋊C4C4×D4312yes—
262C2×C4⋊C4C22⋊D4312yes—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—861no—
265C2×C42—862no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C22⋊C8—861no—
269C22⋊C8—861no—
270#95—21no—
271#95—432no—
272#95—864no—
273#95—862no—
274#95—861no—
275#95—861no—
276C24D4×D4311yescharacteristic
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—432no—
287C22×C4—432no—
288C22×C4—432no—
289C22×C4—432no—
290C22×C4—861no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—864no—
296C22×C4—862no—
297C22×C4—861no—
298C22×C4—862no—
299C22×C4—1722no—
300C22×C4—1722no—
301C22×C4—1721no—
302C22×C4—1721no—
303C22×C4C2×C4×D4311yescharacteristic
304C22×C4#1062189811yescharacteristic
305C22×C4D4×D4311yescharacteristic
306C22×C4D4×D4311yescharacteristic
307C22×C4#1062190011yescharacteristic
308C22×C4C2×C22⋊D4311yescharacteristic
309C2×C8—42no—
310C2×C8—41no—
311C2×C8—1722no—
312C2×C8—1721no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—862no—
319C4⋊C4—862no—
320C4⋊C4—862no—
321C4⋊C4—862no—
322C4⋊C4—3442no—
323C4⋊C4—1722no—
324C4⋊C4—1728no—
325C4⋊C4—1724no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—1721no—
329C22⋊C4—1721no—
330C42—1724no—
331C23—22no—
332C23—22no—
333C23C22⋊C4×D4311yescharacteristic
334C23#1306329311yescharacteristic
335C23#1306330711yescharacteristic
336C23D8×D4311yescharacteristic
337C23SD16×D4311yescharacteristic
338C23#1306334911yescharacteristic
339C23#1306335411yescharacteristic
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—434no—
357C2×C4—862no—
358C2×C4—862no—
359C2×C4—862no—
360C2×C4—862no—
361C2×C4—862no—
362C2×C4—862no—
363C2×C4—864no—
364C2×C4—862no—
365C2×C4—3441no—
366C2×C4—1722no—
367C2×C4—1722no—
368C2×C4—1722no—
369C2×C4—1722no—
370C2×C4—1724no—
371C2×C4—1724no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4(C22⋊D43)⋊C411yescharacteristic
376C2×C4C4×C22⋊D4311yescharacteristic
377C2×C4#1306329611yescharacteristic
378C2×C4#1306329811yescharacteristic
379C8—81no—
380C8—3441no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22#1458277511yescharacteristic
390C22#102×D4311yescharacteristic
391C22#1458289711yescharacteristic
392C22#1458303111yescharacteristic
393C22#1458303611yescharacteristic
394C22#1458308012yes—
395C22#1458308812yes—
396C22#1458321111yescharacteristic
397C22#1458321611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—864no—
405C4—3442no—
406C4—1724no—
407C4—1722no—
408C2—21no—
409C2—21no—
410C2—21no—
411C2—21no—
412C2#1913359612yes—
413C2#1913360112yes—
414C2#1913490911yescharacteristic
415C2#1913498511yescharacteristic
416C2#1913500511yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1823C2
socleC23×C43#120
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1823D43
hypocenterC43#9027
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
13. #14582830C4semidirect
234. C43#9027semidirect

Maximal subgroups

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

subgroupindex
C2×#145828302
#191372122
#191346812
C2×#145826242
#191324752
#191324732
C43×#18232
#902743