Finite Group Databasebeta

← #24992989

Subgroups — #24992989

Order 11008.

528 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583180C211yesmaximal, characteristic
2#19143330C211yesmaximal, characteristic
3#19135438C211yesmaximal, characteristic, complemented
4#19133268C211yesmaximal, characteristic, complemented
5#19133019C211yesmaximal, characteristic
6#19132445C211yesmaximal, characteristic, complemented
7C43×#1292C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×#13063325C2211yescharacteristic
10C2×C4×D172C2211yescharacteristic
11#14583180—21no—
12#14583180—21no—
13#14583180—21no—
14#14583180—21no—
15#14582976—21no—
16#14582969—22no—
17#14582964—21no—
18#14582952C2211yescharacteristic
19C2×#13063259C412yes—
20C2×#13063247C412yes—
21C2×#13063243—21no—
22C2×#13063243—21no—
23#14582862—21no—
24C4×#10621877C2211yescharacteristic
25#14582646—22no—
26#14582626—21no—
27#14582626—21no—
28C43×#423C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C22×Dic86—21no—
32C22×D172C2×C411yescharacteristic
33C22×C4×D43—21no—
34C2×#10621877D411yescharacteristic
35C2×#10621877D411yescharacteristic
36C2×#10621872—22no—
37M16×D43—42no—
38M16×D43—42no—
39C2×C8×D43—22no—
40#13063325—21no—
41#13063325—21no—
42#13063325—21no—
43#13063325—21no—
44C4×D172—21no—
45C4×D172—21no—
46C4×D172D411yescharacteristic
47C4×D172D411yescharacteristic
48C4×D172D411yescharacteristic
49C4×D172D411yescharacteristic
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43C2×C412yes—
52C2×C4⋊Dic43C2×C411yescharacteristic
53C2×(C2×D43)⋊C4—21no—
54#13063259—22no—
55#13063259—22no—
56C4⋊(C43⋊C8)—21no—
57#13063247—22no—
58#13063247—22no—
59#13063243—42no—
60#13063243—42no—
61C22⋊(C43⋊C8)—21no—
62(C2×D43)⋊C8—22no—
63(C2×D43)⋊C8—22no—
64#13063236—21no—
65C4×C43⋊C8—21no—
66C4×C43⋊C8—21no—
67C2×M16×C43—21no—
68C2×M16×C43—21no—
69C22×C8×C43C2×C412yes—
70C2×C42×C43C2311yescharacteristic
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43D412yes—
77C23×D43—21no—
78C22×C4×C43C22×C411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43#4111yescharacteristic
81C22×Dic43—21no—
82C22×Dic43—22no—
83C2×D172—21no—
84C2×D172—22no—
85C2×D172—41no—
86C2×D172C22⋊C411yescharacteristic
87C2×D172C22⋊C411yescharacteristic
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43—21no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C4×D43—41no—
95C2×C4×D43—41no—
96C2×Dic86—41no—
97C2×Dic86—41no—
98C2×Dic86—41no—
99C2×Dic86—41no—
100C2×Dic86—41no—
101C2×Dic86—41no—
102M16×C43—41no—
103M16×C43—41no—
104M16×C43—41no—
105M16×C43—41no—
106C2×C8×C43—22no—
107C2×C8×C43—22no—
108C2×C8×C43—42no—
109C2×C8×C43—41no—
110C42×C43C2×D411yescharacteristic
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114(C2×D43)⋊C4—21no—
115(C2×D43)⋊C4—21no—
116(C2×D43)⋊C4—21no—
117(C2×D43)⋊C4—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—22no—
120C4⋊Dic43—22no—
121C4⋊Dic43—41no—
122C4⋊Dic43—41no—
123C4⋊Dic43C22⋊C411yescharacteristic
124C4⋊Dic43C22⋊C411yescharacteristic
125#10621877—21no—
126#10621877—21no—
127#10621877—21no—
128#10621877D812yes—
129C2×C43⋊C8—21no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—41no—
132#10621872—44no—
133C8×D43—44no—
134C23×C43C4×D411yescharacteristic
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—42no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—81no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—41no—
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43#12011yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12311yescharacteristic
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43#13511yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—42no—
161D172—21no—
162D172—21no—
163D172—21no—
164D172—42no—
165D172#10112yescomplemented
166C4×D43—41no—
167C4×D43—41no—
168C4×D43—41no—
169C4×D43—41no—
170C4×D43—41no—
171C4×D43—41no—
172C4×D43—41no—
173C4×D43—41no—
174Dic86—81no—
175Dic86—81no—
176Dic86—81no—
177Dic86—81no—
178C8×C43—42no—
179C8×C43—42no—
180C8×C43—81no—
181C43⋊C8—22no—
182C43⋊C8—41no—
183C43⋊C8—81no—
184#9251—431nomaximal, Sylow
185C22×C43—21no—
186C22×C43—21no—
187C22×C43#38611yescharacteristic
188C22×C43C4×D811yescharacteristic
189C22×C43#44211yescharacteristic
190C2×D43—22no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—82no—
197C2×D43—82no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43C2×#10111yescharacteristic
202C4×C43#41311yescharacteristic
203C4×C43#44711yescharacteristic
204C4×C43#44911yescharacteristic
205C4×C43#45911yescharacteristic
206C4×C43#46311yescharacteristic
207Dic43—41no—
208Dic43—41no—
209Dic43—82no—
210C2×#474—431no—
211D4×M16—431no—
212#1966—431no—
213#1546—431no—
214#1486—431no—
215#1292D4311yescharacteristic, complemented
216#1283—431no—
217C2×C43—21no—
218C2×C43—21no—
219C2×C43#187911yescharacteristic
220C2×C43#190111yescharacteristic
221C2×C43#190211yescharacteristic
222D43—42no—
223D43—81no—
224C22×M16—861no—
225C2×C4⋊Q8—431no—
226C2×C4×D4—431no—
227#474—861no—
228#474—861no—
229#474—861no—
230#474—861no—
231#436—861no—
232#435—862no—
233C8×D4—861no—
234#431—431no—
235C2×#107—432no—
236#423C2×D4311yescharacteristic
237#423C2×D4311yescharacteristic
238C2×C4⋊C8C2×D4311yescharacteristic
239C2×#102—432no—
240C2×#101—861no—
241C2×#101—861no—
242#407—861no—
243C4×M16—431no—
244#332—862no—
245D4⋊C8—861no—
246D4⋊C8—861no—
247C43#925111yescharacteristic, complemented, Sylow
248C22×Q8—861no—
249C22×D4—431no—
250C23×C4—861no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—431no—
254C2×M16—431no—
255C2×M16—862no—
256C2×M16—1722no—
257C2×M16—1722no—
258C22×C8—862no—
259C22×C8C4×D4312yes—
260C4⋊Q8—861no—
261C4⋊Q8—861no—
262C4⋊Q8—861no—
263C4⋊Q8—861no—
264C4×D4—431no—
265C4×D4—431no—
266C4×D4—431no—
267C4×D4—431no—
268C4×D4—861no—
269C4×D4—861no—
270C2×C4⋊C4—431no—
271C2×C4⋊C4—432no—
272C2×C4⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C42C22×D4311yescharacteristic
275#107—862no—
276#107—862no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—861no—
283C4⋊C8D17212yes—
284#102—862no—
285#102—862no—
286#101—1722no—
287#101—1722no—
288C22⋊C8—862no—
289C22⋊C8—862no—
290C22⋊C8—861no—
291#97—861no—
292C4×C8—861no—
293C4×C8—861no—
294C24—861no—
295C2×Q8—1721no—
296C2×Q8—1721no—
297C2×Q8—1721no—
298C2×Q8—1721no—
299C2×Q8—1721no—
300C2×Q8—1721no—
301C2×D4—431no—
302C2×D4—431no—
303C2×D4—862no—
304C2×D4—861no—
305C2×D4—1721no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—862no—
312C22×C4—1721no—
313C22×C4—1721no—
314C22×C4—1721no—
315C22×C4—1721no—
316C22×C4C2×C4×D4311yescharacteristic
317C22×C4D4×D4311yescharacteristic
318C22×C4#1062190211yescharacteristic
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—432no—
324M16—861no—
325M16—861no—
326M16—861no—
327M16—1724no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—42no—
331C2×C8—41no—
332C2×C8—861no—
333C2×C8—861no—
334C2×C8—1724no—
335C2×C8—1721no—
336C4⋊C4—431no—
337C4⋊C4—431no—
338C4⋊C4—861no—
339C4⋊C4—862no—
340C4⋊C4—862no—
341C4⋊C4—1721no—
342C4⋊C4—1721no—
343C22⋊C4—861no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C42C2×D17211yescharacteristic
348C42#1062189811yescharacteristic
349C42D4×D4311yescharacteristic
350C42D4×D4311yescharacteristic
351C23—861no—
352C23—861no—
353C23—3441no—
354C23—1722no—
355C23—1721no—
356C23—1721no—
357C23#1306328711yescharacteristic
358Q8—3441no—
359Q8—3441no—
360Q8—3441no—
361Q8—3441no—
362D4—432no—
363D4—861no—
364D4—861no—
365D4—861no—
366D4—1722no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—1722no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4C22⋊C4×D4311yescharacteristic
386C2×C4C4×D17211yescharacteristic
387C2×C4#1306329511yescharacteristic
388C2×C4#1306329811yescharacteristic
389C2×C4#1306330011yescharacteristic
390C2×C4#1306331011yescharacteristic
391C2×C4D8×D4311yescharacteristic
392C2×C4#1306334811yescharacteristic
393C2×C4#1306335211yescharacteristic
394C2×C4#1306335211yescharacteristic
395C8—42no—
396C8—42no—
397C8—81no—
398C8—862no—
399C8—3441no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—862no—
404C22—3442no—
405C22—3442no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22—1721no—
410C22—1721no—
411C22#1458277711yescharacteristic
412C22#1458298111yescharacteristic
413C22#1458301011yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—3442no—
418C4—1721no—
419C4—1721no—
420C4#101×D4311yescharacteristic
421C4#1458288011yescharacteristic
422C4#1458303411yescharacteristic
423C4#1458304711yescharacteristic
424C4#1458309311yescharacteristic
425C4#1458311711yescharacteristic
426C2—21no—
427C2—21no—
428C2—3441no—
429C2—1722no—
430C2#1913494411yescharacteristic
431C2#1913506211yescharacteristic
432C2#1913506911yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1292C2
socleC22×C43#386
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenter#1292D43
hypocenterC43#9251
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #19135438C2semidirect
4. #19133268C2semidirect
6. #19132445C2semidirect
7. C43×#1292C2semidirect
165. D172#101semidirect
215. #1292D43semidirect
247. C43#9251semidirect

Maximal subgroups

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

subgroupindex
C2×#145831802
#191433302
#191354382
#191332682
#191330192
#191324452
C43×#12922
#925143