Finite Group Databasebeta

← #24997045

Subgroups — #24997045

Order 11008.

636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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#19145343C211yesmaximal, characteristic
2C2×#14583217C211yesmaximal, characteristic, complemented
3#19135431C211yesmaximal, characteristic, complemented
4#19134685C211yesmaximal, characteristic, complemented
5#19133163C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7C43×#2504C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583217—22no—
10#14583217—22no—
11#14583212—21no—
12#14583210—21no—
13#14583133—22no—
14#14583033—21no—
15#14583032—21no—
16C2×#13063256—21no—
17C2×#13063245—21no—
18C2×#13063239—22no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20C2×C22⋊(C43⋊C8)C2211yescharacteristic
21#14582759C2211yescharacteristic
22#14582661—22no—
23#14582633—22no—
24C2×#121×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#397—22no—
27C43×#390—21no—
28C43×#386—22no—
29C43×#382—21no—
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C2×#10621882—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8D412yes—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43D411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44#13063258—22no—
45#13063256—24no—
46#13063246—22no—
47#13063245—22no—
48#13063245—24no—
49#13063239—44no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yes—
54C43⋊#95—21no—
55C22×D4×C43—21no—
56C22×D4×C43D411yescharacteristic
57C23×C4×C43—21no—
58C23×C4×C43C2311yescharacteristic
59#121×C43—21no—
60#121×C43—21no—
61#121×C43—21no—
62#121×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43D412yes—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—24no—
72C2×C22⋊C4×C43D412yes—
73C2×C42×C43—21no—
74#95×C43—24no—
75#95×C43—21no—
76C24×C43—21no—
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—42no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—42no—
85C2×D4×C43—42no—
86C22×C4×C43—21no—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—42no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—82no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C2×C22⋊D43—41no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43—42no—
102C2×C22⋊D43—42no—
103C22×Dic43—21no—
104C22×Dic43—41no—
105C2×D172—21no—
106C2×D172—21no—
107C2×D172—42no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C22⋊C4×C43—22no—
115C22⋊C4×C43—22no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—84no—
119C42×C43—42no—
120C22⋊Dic43—42no—
121#10621882—82no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—42no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—42no—
130C2×C43⋊C8—42no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—42no—
134C23×C43—42no—
135C23×C43—41no—
136C23×C43—42no—
137C23×C43#12011yescharacteristic
138C23×C43#12111yescharacteristic
139C23×C43#12711yescharacteristic
140C23×C43#13512yes—
141C23×C43AGL(1,ℤ/8)12yes—
142C22×D43—41no—
143C22×D43—42no—
144C22×D43—81no—
145C22×D43—81no—
146D4×C43—42no—
147D4×C43—81no—
148D4×C43—82no—
149D4×C43—81no—
150D4×C43—81no—
151C2×C4×C43—22no—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—42no—
159C2×C4×C43—44no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—82no—
165C2×C4×C43—82no—
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C22⋊D43—82no—
171C22⋊D43—81no—
172C22⋊D43—81no—
173C2×Dic43—41no—
174C2×Dic43—42no—
175C2×Dic43—81no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178D172—42no—
179D172—42no—
180C43⋊C8—42no—
181C43⋊C8—42no—
182#9950—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—42no—
190C22×C43—42no—
191C22×C43—84no—
192C22×C43—81no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43#39211yescharacteristic
196C22×C43#44912yes—
197C22×C43#46312yes—
198C22×C43#49511yescharacteristic
199C22×C43#49611yescharacteristic
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—162no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—82no—
208C4×C43—82no—
209C4×C43—81no—
210C4×C43#45812yes—
211Dic43—81no—
212Dic43—161no—
213#3186—431no—
214C2×#481—431no—
215#2504D4311yescharacteristic, complemented
216#1964—431no—
217#1824—431no—
218#1519—431no—
219#1282—431no—
220C2×C43—21no—
221C2×C43—22no—
222C2×C43—22no—
223C2×C43—21no—
224C2×C43—161no—
225C2×C43#200811yescharacteristic
226C2×C43#201211yescharacteristic
227C2×C43#202211yescharacteristic
228D43—161no—
229C2×#121—431no—
230C2×#121C2×D4311yescharacteristic
231C22×C4⋊C4C2×D4311yescharacteristic
232#481—862no—
233#481—862no—
234#480—861no—
235#480—861no—
236#466—862no—
237#447—861no—
238#447—861no—
239C2×#106—861no—
240C2×#102—861no—
241C2×#99—862no—
242C2×C22⋊C8—431no—
243C2×C22⋊C8—431no—
244#397—22no—
245#390—21no—
246#386—22no—
247#382—21no—
248#380—431no—
249C4×C22⋊C4C2×D4311yescharacteristic
250#340—862no—
251#327—862no—
252C43#995011yescharacteristic, complemented, Sylow
253C22×D4—21no—
254C22×D4—431no—
255C22×D4—861no—
256C22×D4C22⋊D4311yescharacteristic
257C23×C4—21no—
258C23×C4C22×D4311yescharacteristic
259C2×D8—862no—
260C22×C8—432no—
261C22×C8—861no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266#121—861no—
267#121—861no—
268#121—861no—
269#121—861no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4C22⋊D4312yes—
278C2×C4⋊C4C22⋊D4311yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4C22⋊D4312yes—
284C2×C42—21no—
285#107—862no—
286#106—864no—
287#102—864no—
288#102—862no—
289#102—862no—
290#99—1724no—
291C22⋊C8—432no—
292C22⋊C8—861no—
293C22⋊C8—861no—
294C22⋊C8—861no—
295#95—24no—
296#95—21no—
297#95—861no—
298C24—21no—
299C24—861no—
300C24C2×C22⋊D4311yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—42no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—861no—
309C2×D4—861no—
310C2×D4—1722no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1722no—
314C2×D4—1722no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—42no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—82no—
322C22×C4—861no—
323C22×C4—1721no—
324C22×C4D4×D4311yescharacteristic
325C22×C4D4×D4311yescharacteristic
326C22×C4D4×D4311yescharacteristic
327C22×C4#1062190011yescharacteristic
328C22×C4C2×C22⋊D4311yescharacteristic
329C22×C4C2×C22⋊D4311yescharacteristic
330D8—3442no—
331C2×C8—862no—
332C2×C8—862no—
333C2×C8—1722no—
334C2×C8—1722no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—22no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—861no—
342C4⋊C4—861no—
343C4⋊C4—1722no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—84no—
349C22⋊C4—1722no—
350C22⋊C4—1721no—
351C22⋊C4—1721no—
352C42—42no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—41no—
359C23—3441no—
360C23—3441no—
361C23—1721no—
362C23—1722no—
363C23#1306329411yescharacteristic
364C23#1306329611yescharacteristic
365C23#1306332111yescharacteristic
366C23#1306334512yes—
367C23#1306335012yes—
368D4—42no—
369D4—81no—
370D4—82no—
371D4—81no—
372D4—81no—
373D4—3442no—
374D4—3441no—
375D4—3441no—
376D4—1722no—
377D4—1722no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—82no—
392C2×C4—82no—
393C2×C4—3441no—
394C2×C4—3441no—
395C2×C4—3441no—
396C2×C4—1721no—
397C2×C4—1722no—
398C2×C4#1306329311yescharacteristic
399C2×C4#1306329311yescharacteristic
400C2×C4#1306329711yescharacteristic
401C2×C4#1306329711yescharacteristic
402C8—1722no—
403C8—1722no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—3441no—
417C22—3441no—
418C22—3441no—
419C22—6882no—
420C22#1458280711yescharacteristic
421C22#1458304412yes—
422C22#1458311112yes—
423C22#1458328111yescharacteristic
424C22#1458328911yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—82no—
429C4—82no—
430C4—81no—
431C4—3441no—
432C4—6881no—
433C4#1458308812yes—
434C2—22no—
435C2—21no—
436C2—22no—
437C2—21no—
438C2—161no—
439C2—6881no—
440C2#1913564811yescharacteristic
441C2#1913567211yescharacteristic
442C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2504C2
socleC22×C43#392
prime radical#19145343C2
hypercenter#2504D43
hypocenterC43#9950
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2504

Complements

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

NH ≅ G/Ntype
2. C2×#14583217C2semidirect
3. #19135431C2semidirect
4. #19134685C2semidirect
5. #19133163C2semidirect
6. #19132443C2semidirect
7. C43×#2504C2semidirect
215. #2504D43semidirect
252. C43#9950semidirect

Maximal subgroups

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

subgroupindex
#191453432
C2×#145832172
#191354312
#191346852
#191331632
#191324432
C43×#25042
#995043