Finite Group Databasebeta

← #25015297

Subgroups — #25015297

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063268C211yesmaximal, characteristic, complemented
2C2×#14583135C211yesmaximal, characteristic
3C2×#14582703C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic, complemented
5C2×C22⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C2×C43×#467C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063299—21no—
10C2×#13063268—22no—
11C2×#13063268—22no—
12C2×#13063268—22no—
13C22×C43⋊C16C2211yescharacteristic
14C22×C43⋊C16C2211yescharacteristic
15#14583135—22no—
16#14583135—22no—
17C2×#13063259C2211yescharacteristic
18C2×#13063247—21no—
19#14582703—22no—
20#14582699—22no—
21C22⋊(C43⋊C16)—22no—
22C22×Q16×C43C2211yescharacteristic
23C23×C8×C43C2211yescharacteristic
24C2×C22⋊Q8×C43—21no—
25C43×#467—22no—
26C43×#467—22no—
27C2×#107×C43C2211yescharacteristic
28C2×#103×C43—21no—
29C22×D172—21no—
30C22×C22⋊D43—41no—
31C2×D344—21no—
32C2×D344—21no—
33C2×D344—21no—
34C2×D344—21no—
35C2×D344—21no—
36C2×D344D412yes—
37#13063299—24no—
38#13063299—42no—
39C2×C4⋊Dic43—21no—
40C2×(C2×D43)⋊C4—41no—
41#13063268—28no—
42C2×C43⋊C16—21no—
43C2×C43⋊C16—21no—
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47C2×C43⋊C16D412yescomplemented
48#13063259—21no—
49#13063259D412yes—
50#13063247—24no—
51C22×Q8×C43—21no—
52C23×C4×C43D411yescharacteristic
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×Q16×C43—21no—
56C2×Q16×C43—21no—
57C2×Q16×C43—21no—
58C2×Q16×C43D412yescomplemented
59C22×C8×C43—21no—
60C22×C8×C43—21no—
61C22×C8×C43—21no—
62C22×C8×C43—21no—
63C22×C8×C43—21no—
64C22×C8×C43—21no—
65C22×C8×C43D411yescharacteristic
66C22×C8×C43C2311yescharacteristic
67C22⋊Q8×C43—24no—
68C22⋊Q8×C43—42no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—41no—
71C2×C22⋊C4×C43—41no—
72#107×C43—21no—
73#107×C43D412yescomplemented
74#103×C43—24no—
75C24×C43D811yescharacteristic
76C23×D43—41no—
77C2×Q8×C43—22no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C2×Q8×C43—41no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43D811yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C2×C22⋊D43—44no—
94C2×C22⋊D43—82no—
95C2×C22⋊D43—82no—
96C22×Dic43—41no—
97C2×D172—22no—
98C2×D172—41no—
99C2×D172—41no—
100C2×D172—41no—
101C2×D172—41no—
102C2×D172—41no—
103Q16×C43—22no—
104Q16×C43—22no—
105Q16×C43—41no—
106Q16×C43—41no—
107C2×C8×C43—21no—
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—41no—
111C2×C8×C43—41no—
112C2×C8×C43—41no—
113C2×C8×C43—41no—
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43C2×D411yescharacteristic
117C2×C8×C43C2×D411yescharacteristic
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43#4111yescharacteristic
120C4⋊C4×C43—22no—
121C4⋊C4×C43—44no—
122C4⋊C4×C43—41no—
123C22⋊C4×C43—44no—
124(C2×D43)⋊C4—44no—
125C4⋊Dic43—22no—
126C4⋊Dic43—41no—
127D344—22no—
128D344—22no—
129D344—41no—
130D344—41no—
131C43⋊C16—22no—
132C43⋊C16—41no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43—21no—
139C23×C43SD3212yescomplemented
140C23×C43C2×D811yescharacteristic
141C22×D43—42no—
142C22×D43—81no—
143C22×D43—81no—
144C22×D43—81no—
145C22×D43—81no—
146C22×D43—81no—
147C22×D43—81no—
148Q8×C43—42no—
149Q8×C43—42no—
150Q8×C43—81no—
151Q8×C43—81no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43#12011yescharacteristic
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#13511yescharacteristic
169C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
171C22⋊D43—88no—
172C2×Dic43—42no—
173C2×Dic43—81no—
174C2×Dic43—81no—
175D172—42no—
176D172—42no—
177D172—81no—
178D172—81no—
179C8×C43—41no—
180C8×C43#12011yescharacteristic
181C8×C43#12111yescharacteristic
182C8×C43#12111yescharacteristic
183C8×C43#12711yescharacteristic
184#13305—431nomaximal, Sylow
185C22×C43—22no—
186C22×C43—22no—
187C22×C43—22no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43#44711yescharacteristic
193C22×C43#44711yescharacteristic
194C22×C43#46611yescharacteristic
195C22×C43C2×SD3211yescharacteristic
196C22×C43#50811yescharacteristic
197C22×C43#50911yescharacteristic
198C22×C43#51011yescharacteristic
199C2×D43—82no—
200C2×D43—82no—
201C2×D43—82no—
202C2×D43—161no—
203C2×D43—161no—
204C2×D43—161no—
205C2×D43—161no—
206C4×C43—41no—
207C4×C43—82no—
208C4×C43—82no—
209C4×C43#39211yescharacteristic
210C4×C43#44911yescharacteristic
211C4×C43#44911yescharacteristic
212C4×C43#46911yescharacteristic
213Dic43—82no—
214C22×SD32—431no—
215C2×#467D4311yescharacteristic, complemented
216C2×#466—431no—
217C2×#358—431no—
218C2×#357—431no—
219C2×C22⋊C16—431no—
220#1380—431no—
221C2×C43—42no—
222C2×C43#199911yescharacteristic
223C2×C43#218511yescharacteristic
224C2×C43#218611yescharacteristic
225C2×C43#218711yescharacteristic
226C2×C43#218911yescharacteristic
227C2×C43#221711yescharacteristic
228C2×C43#222011yescharacteristic
229D43—162no—
230C22×Q16C2×D4311yescharacteristic
231C22×D8—431no—
232C23×C8C2×D4311yescharacteristic
233C2×C22⋊Q8—21no—
234C2×#121—861no—
235C2×SD32—862no—
236C2×SD32—862no—
237C2×SD32—862no—
238C22×C16—431no—
239C22×C16—431no—
240#467—22no—
241#467—22no—
242#466—862no—
243#466—862no—
244C2×#107—431no—
245C2×#107C2×D4311yescharacteristic
246C2×#103—21no—
247C2×#102—861no—
248#358—862no—
249#357—862no—
250C22⋊C16—862no—
251C43#1330511yescharacteristic, complemented, Sylow
252C22×Q8—21no—
253C22×D4—861no—
254C22×D4—1721no—
255C23×C4C22⋊D4311yescharacteristic
256C2×Q16—21no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16—21no—
260C2×Q16—21no—
261C2×Q16C22⋊D4312yescomplemented
262C2×D8—432no—
263C2×D8—861no—
264C2×D8—861no—
265C2×D8—861no—
266C2×D8—861no—
267C2×D8—861no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8C22⋊D4311yescharacteristic
275C22×C8C22×D4311yescharacteristic
276C22⋊Q8—24no—
277C22⋊Q8—42no—
278#121—864no—
279#121—1722no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—861no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4—1721no—
285SD32—868no—
286C2×C16—432no—
287C2×C16—861no—
288C2×C16—861no—
289C2×C16—861no—
290C2×C16—861no—
291C2×C16—861no—
292#107—21no—
293#107—432no—
294#107—861no—
295#107C22⋊D4312yescomplemented
296#103—24no—
297#102—864no—
298C24—1721no—
299C24#1062188211yescharacteristic
300C2×Q8—22no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×D4—862no—
307C2×D4—3442no—
308C2×D4—3442no—
309C2×D4—1724no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—1721no—
324C22×C4#1062188211yescharacteristic
325C22×C4C2×C22⋊D4311yescharacteristic
326Q16—22no—
327Q16—22no—
328Q16—41no—
329Q16—41no—
330D8—862no—
331D8—862no—
332D8—1721no—
333D8—1721no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8D4×D4311yescharacteristic
342C2×C8D4×D4311yescharacteristic
343C2×C8D4×D4311yescharacteristic
344C2×C8#1062190011yescharacteristic
345C2×C8C2×C22⋊D4311yescharacteristic
346C2×C8C2×C22⋊D4311yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—44no—
349C4⋊C4—41no—
350C4⋊C4—862no—
351C4⋊C4—1721no—
352C22⋊C4—44no—
353C22⋊C4—1724no—
354C16—862no—
355C16—1721no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—3441no—
363C23—3441no—
364C23—3441no—
365C23—3441no—
366C23—3441no—
367C23—3441no—
368C23—1722no—
369C23#1306326812yescomplemented
370C23C2×#1062188211yescharacteristic
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375D4—3448no—
376D4—3441no—
377D4—3441no—
378D4—1722no—
379D4—1722no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—3441no—
394C2×C4—3441no—
395C2×C4—1722no—
396C2×C4#1306329311yescharacteristic
397C2×C4#1306329411yescharacteristic
398C2×C4#1306329711yescharacteristic
399C2×C4#1306334511yescharacteristic
400C2×C4#1306335011yescharacteristic
401C2×C4#1306335111yescharacteristic
402C8—41no—
403C8#1306329311yescharacteristic
404C8#1306329611yescharacteristic
405C8#1306329711yescharacteristic
406C8#1306332111yescharacteristic
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—3442no—
415C22—3442no—
416C22—3442no—
417C22—6881no—
418C22—6881no—
419C22—6881no—
420C22—6881no—
421C22#1458303211yescharacteristic
422C22#1458303311yescharacteristic
423C22#1458313311yescharacteristic
424C22C2×#1306326811yescharacteristic
425C22#1458332911yescharacteristic
426C22#1458333411yescharacteristic
427C22#1458334011yescharacteristic
428C4—41no—
429C4—82no—
430C4—82no—
431C4—3442no—
432C4#1458280711yescharacteristic
433C4#1458304211yescharacteristic
434C4#1458304411yescharacteristic
435C4#1458315011yescharacteristic
436C2—42no—
437C2—6882no—
438C2#1913559111yescharacteristic
439C2#1913651211yescharacteristic
440C2#1913651811yescharacteristic
441C2#1913652311yescharacteristic
442C2#1913653311yescharacteristic
443C2#1913669311yescharacteristic
444C2#1913671011yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC2×C43×#467C2
socleC23×C43C2×D8
prime radicalC2×#14583135C2
hypercenterC2×#467D43
hypocenterC43#13305
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#13063268C2semidirect
3. C2×#14582703C2semidirect
4. C2×#14582699C2semidirect
5. C2×C22⋊(C43⋊C16)C2semidirect
6. #19132686C2semidirect
7. C2×C43×#467C2semidirect
47. C2×C43⋊C16D4semidirect
58. C2×Q16×C43D4semidirect
73. #107×C43D4semidirect
139. C23×C43SD32semidirect
215. C2×#467D43semidirect
251. C43#13305semidirect
261. C2×Q16C22⋊D43semidirect
295. #107C22⋊D43semidirect
369. C23#13063268semidirect

Maximal subgroups

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

subgroupindex
C22×#130632682
C2×#145831352
C2×#145827032
C2×#145826992
C2×C22⋊(C43⋊C16)2
#191326862
C2×C43×#4672
#1330543