Finite Group Databasebeta

← #25015302

Subgroups — #25015302

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×#13063270C211yesmaximal, characteristic, complemented
2C2×#14583141C211yesmaximal, characteristic, complemented
3C2×#14583136C211yesmaximal, characteristic
4C2×#14582702C211yesmaximal, characteristic, complemented
5C2×#14582699C211yesmaximal, characteristic, complemented
6C2×(C2×D43)⋊C16C211yesmaximal, characteristic, complemented
7C43×#1380C211yesmaximal, characteristic, complemented
8C22×Dic172C2211yescharacteristic
9C22×D344C2211yescharacteristic
10C22×C8×D43C2211yescharacteristic
11C2×#13063305—21no—
12C2×#13063300—21no—
13C2×#13063270—22no—
14C2×#13063270—22no—
15C2×#13063270—22no—
16C22×C43⋊C16C2211yescharacteristic
17#14583141—22no—
18#14583141—22no—
19#14583136—22no—
20#14583136—22no—
21C2×#13063248—21no—
22C2×#13063245—21no—
23#14582702—22no—
24#14582699—22no—
25(C2×D43)⋊C16—22no—
26C22×C16×C43C2211yescharacteristic
27C2×#107×C43C2211yescharacteristic
28C2×#107×C43C2211yescharacteristic
29C22×Dic86—21no—
30C22×D172—21no—
31C22×D172—41no—
32C22×C4×D43D411yescharacteristic
33C2×Dic172—21no—
34C2×Dic172—21no—
35C2×Dic172—21no—
36C2×Dic172—21no—
37C2×Dic172—21no—
38C2×Dic172D412yescomplemented
39C2×D344—21no—
40C2×D344—21no—
41C2×D344—21no—
42C2×D344—21no—
43C2×D344—21no—
44C2×D344D412yes—
45C22×C43⋊C8D411yescharacteristic
46C2×C8×D43—21no—
47C2×C8×D43—21no—
48C2×C8×D43—21no—
49C2×C8×D43—21no—
50C2×C8×D43—21no—
51C2×C8×D43—21no—
52#13063305—24no—
53#13063305—42no—
54#13063300—24no—
55#13063300—42no—
56C2×C4⋊Dic43—41no—
57C2×(C2×D43)⋊C4—41no—
58C2×(C2×D43)⋊C4—41no—
59#13063270—28no—
60C2×C43⋊C16—21no—
61C2×C43⋊C16—21no—
62C2×C43⋊C16—21no—
63#13063248—24no—
64#13063245—24no—
65C22×C8×C43C2311yescharacteristic
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C16×C43—21no—
69C2×C16×C43—21no—
70C2×C16×C43D412yescomplemented
71#107×C43—21no—
72#107×C43—21no—
73#107×C43D412yes—
74#107×C43D412yescomplemented
75C23×D43—41no—
76C23×D43D811yescharacteristic
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—41no—
81C22×Dic43D811yescharacteristic
82C2×D172—22no—
83C2×D172—44no—
84C2×D172—41no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—82no—
90C2×D172—82no—
91C2×C4×D43—21no—
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×Dic86—22no—
98C2×Dic86—41no—
99C2×Dic86—41no—
100C2×Dic86—41no—
101C2×Dic86—41no—
102C2×Dic86—41no—
103C2×C8×C43C2×D411yescharacteristic
104C2×C8×C43C2×D411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43#4111yescharacteristic
109C4⋊C4×C43—22no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113(C2×D43)⋊C4—44no—
114(C2×D43)⋊C4—44no—
115C4⋊Dic43—44no—
116C2×C43⋊C8—21no—
117C2×C43⋊C8—21no—
118C2×C43⋊C8—21no—
119Dic172—22no—
120Dic172—22no—
121Dic172—41no—
122Dic172—41no—
123D344—22no—
124D344—22no—
125D344—41no—
126D344—41no—
127C8×D43—41no—
128C8×D43—41no—
129C8×D43—41no—
130C8×D43—41no—
131C16×C43—22no—
132C43⋊C16—41no—
133C23×C43C2×D811yescharacteristic
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—21no—
138C22×D43—21no—
139C22×D43—21no—
140C22×D43—42no—
141C22×D43—81no—
142C22×D43—81no—
143C22×D43—81no—
144C22×D43—81no—
145C22×D43—81no—
146C22×D43—81no—
147C22×D43SD3212yescomplemented
148C2×C4×C43—42no—
149C2×C4×C43—42no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#13511yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—42no—
164C2×Dic43—81no—
165C2×Dic43—81no—
166D172—42no—
167D172—42no—
168D172—88no—
169D172—81no—
170D172—81no—
171C4×D43—41no—
172C4×D43—41no—
173C4×D43—41no—
174C4×D43—41no—
175Dic86—42no—
176Dic86—42no—
177Dic86—81no—
178Dic86—81no—
179C8×C43#12011yescharacteristic
180C8×C43#12111yescharacteristic
181C8×C43#12111yescharacteristic
182C8×C43#12711yescharacteristic
183C43⋊C8—41no—
184#13305—431nomaximal, Sylow
185C22×C43#44711yescharacteristic
186C22×C43#44711yescharacteristic
187C22×C43#46611yescharacteristic
188C22×C43C2×SD3211yescharacteristic
189C22×C43#50811yescharacteristic
190C22×C43#50911yescharacteristic
191C22×C43#51011yescharacteristic
192C2×D43—22no—
193C2×D43—22no—
194C2×D43—22no—
195C2×D43—41no—
196C2×D43—41no—
197C2×D43—41no—
198C2×D43—41no—
199C2×D43—82no—
200C2×D43—82no—
201C2×D43—82no—
202C2×D43—161no—
203C2×D43—161no—
204C2×D43—161no—
205C2×D43—161no—
206C4×C43—82no—
207C4×C43—82no—
208C4×C43#39211yescharacteristic
209C4×C43#44911yescharacteristic
210C4×C43#44911yescharacteristic
211C4×C43#46911yescharacteristic
212Dic43—41no—
213Dic43—82no—
214C22×SD32—431no—
215C2×#467—431no—
216C2×#466—431no—
217C2×#358—431no—
218C2×#357—431no—
219C2×C22⋊C16—431no—
220#1380D4311yescharacteristic, complemented
221C2×C43#199911yescharacteristic
222C2×C43#218511yescharacteristic
223C2×C43#218611yescharacteristic
224C2×C43#218711yescharacteristic
225C2×C43#218911yescharacteristic
226C2×C43#221711yescharacteristic
227C2×C43#222011yescharacteristic
228D43—42no—
229D43—162no—
230C22×Q16—431no—
231C22×D8—431no—
232C23×C8—431no—
233C2×C22⋊Q8—861no—
234C2×#121—861no—
235C2×SD32—862no—
236C2×SD32—862no—
237C2×SD32—862no—
238C22×C16—431no—
239C22×C16C2×D4311yescharacteristic
240#467—862no—
241#467—862no—
242#466—862no—
243#466—862no—
244C2×#107C2×D4311yescharacteristic
245C2×#107C2×D4311yescharacteristic
246C2×#103—861no—
247C2×#102—861no—
248#358—862no—
249#357—862no—
250C22⋊C16—862no—
251C43#1330511yescharacteristic, complemented, Sylow
252C22×Q8—861no—
253C22×D4—861no—
254C22×D4—1721no—
255C23×C4—431no—
256C2×Q16—432no—
257C2×Q16—861no—
258C2×Q16—861no—
259C2×Q16—861no—
260C2×Q16—861no—
261C2×Q16—861no—
262C2×D8—432no—
263C2×D8—861no—
264C2×D8—861no—
265C2×D8—861no—
266C2×D8—861no—
267C2×D8—861no—
268C22×C8—431no—
269C22×C8—861no—
270C22×C8—861no—
271C22×C8—861no—
272C22×C8—861no—
273C22×C8—861no—
274C22×C8—861no—
275C22×C8C22×D4311yescharacteristic
276C22⋊Q8—864no—
277C22⋊Q8—1722no—
278#121—864no—
279#121—1722no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—1721no—
283C2×C22⋊C4—1721no—
284C2×C22⋊C4—1721no—
285SD32—868no—
286C2×C16—21no—
287C2×C16—21no—
288C2×C16—861no—
289C2×C16—861no—
290C2×C16—861no—
291C2×C16D17212yescomplemented
292#107—21no—
293#107—21no—
294#107D17212yes—
295#107D17212yescomplemented
296#103—864no—
297#102—864no—
298C24—431no—
299C24—1721no—
300C2×Q8—862no—
301C2×Q8—1721no—
302C2×Q8—1721no—
303C2×Q8—1721no—
304C2×Q8—1721no—
305C2×Q8—1721no—
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—41no—
316C22×C4—41no—
317C22×C4—431no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—861no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—1721no—
325C22×C4D4×D4311yescharacteristic
326Q16—862no—
327Q16—862no—
328Q16—1721no—
329Q16—1721no—
330D8—862no—
331D8—862no—
332D8—1721no—
333D8—1721no—
334C2×C8—861no—
335C2×C8—861no—
336C2×C8—861no—
337C2×C8—1721no—
338C2×C8—1721no—
339C2×C8—1721no—
340C2×C8—1721no—
341C2×C8C2×D17211yescharacteristic
342C2×C8C2×D17211yescharacteristic
343C2×C8C2×D17211yescharacteristic
344C2×C8D4×D4311yescharacteristic
345C2×C8D4×D4311yescharacteristic
346C2×C8#1062190211yescharacteristic
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—1724no—
352C22⋊C4—1724no—
353C22⋊C4—1724no—
354C16—22no—
355C16—1721no—
356C23—432no—
357C23—861no—
358C23—861no—
359C23—861no—
360C23—861no—
361C23—861no—
362C23—861no—
363C23—3441no—
364C23—3441no—
365C23—3441no—
366C23—3441no—
367C23—3441no—
368C23—3441no—
369C23—1722no—
370C23D8×D4311yescharacteristic
371Q8—3441no—
372Q8—3441no—
373Q8—1722no—
374Q8—1722no—
375D4—3448no—
376D4—3441no—
377D4—3441no—
378D4—1722no—
379D4—1722no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—3441no—
390C2×C4—3441no—
391C2×C4—1722no—
392C2×C4—1721no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4#1306329511yescharacteristic
397C2×C4#1306329511yescharacteristic
398C2×C4#1306330011yescharacteristic
399C2×C4#1306334811yescharacteristic
400C2×C4#1306335211yescharacteristic
401C2×C4#1306335211yescharacteristic
402C8—1721no—
403C8#1306329511yescharacteristic
404C8#1306330011yescharacteristic
405C8#1306330011yescharacteristic
406C8#1306332211yescharacteristic
407C22—862no—
408C22—862no—
409C22—862no—
410C22—3442no—
411C22—3442no—
412C22—3442no—
413C22—1721no—
414C22—1721no—
415C22—1721no—
416C22—1721no—
417C22—6881no—
418C22—6881no—
419C22—6881no—
420C22—6881no—
421C22#1458303411yescharacteristic
422C22#1458303411yescharacteristic
423C22#1458313611yescharacteristic
424C22SD32×D4311yescharacteristic
425C22#1458333011yescharacteristic
426C22#1458333311yescharacteristic
427C22#1458334111yescharacteristic
428C4—82no—
429C4—82no—
430C4—3442no—
431C4—1721no—
432C4#1458280911yescharacteristic
433C4#1458304711yescharacteristic
434C4#1458304711yescharacteristic
435C4#1458315311yescharacteristic
436C2—1722no—
437C2—6882no—
438C2#1913559411yescharacteristic
439C2#1913651311yescharacteristic
440C2#1913651911yescharacteristic
441C2#1913652511yescharacteristic
442C2#1913653811yescharacteristic
443C2#1913669211yescharacteristic
444C2#1913670911yescharacteristic
subgroupG/H
centerC23D8×D43
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#1380C2
socleC23×C43C2×D8
prime radicalC2×#14583136C2
hypercenter#1380D43
hypocenterC43#13305
LCSG ▷ C22×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C22×#13063270C2semidirect
2. C2×#14583141C2semidirect
4. C2×#14582702C2semidirect
5. C2×#14582699C2semidirect
6. C2×(C2×D43)⋊C16C2semidirect
7. C43×#1380C2semidirect
38. C2×Dic172D4semidirect
70. C2×C16×C43D4semidirect
74. #107×C43D4semidirect
147. C22×D43SD32semidirect
220. #1380D43semidirect
251. C43#13305semidirect
291. C2×C16D172semidirect
295. #107D172semidirect

Maximal subgroups

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

subgroupindex
C22×#130632702
C2×#145831412
C2×#145831362
C2×#145827022
C2×#145826992
C2×(C2×D43)⋊C162
C43×#13802
#1330543