Finite Group Databasebeta

← #25000013

Subgroups — #25000013

Order 11008.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139590C211yesmaximal, characteristic
2#19135555C211yesmaximal, characteristic, complemented
3#19134592C211yesmaximal, characteristic
4C2×#14582644C211yesmaximal, characteristic, complemented
5C2×#14582626C211yesmaximal, characteristic
6#19132436C211yesmaximal, characteristic, complemented
7C43×#1947C211yesmaximal, characteristic, complemented
8C2×#13063325C2211yescharacteristic
9C2×#13063313—21no—
10C2×C4×D172C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063245—21no—
13C2×C4×C43⋊C8C2211yescharacteristic
14#14582826—22no—
15#14582805—21no—
16#14582756—21no—
17#14582756—21no—
18#14582661—22no—
19#14582661—21no—
20#14582644—22no—
21#14582626—22no—
22C2×#107×C43—21no—
23C2×C4⋊C8×C43C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C4×C4⋊C4×C43C2211yescharacteristic
26C43×#340—21no—
27C22×Dic86—21no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063325—21no—
33#13063325—21no—
34#13063325—21no—
35#13063325—21no—
36#13063313—42no—
37#13063313—42no—
38C4×D172—21no—
39C4×D172—21no—
40C4×D172—21no—
41C4×D172—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×C4⋊Dic43D412yes—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50#13063245—42no—
51C4×C43⋊C8—21no—
52C4×C43⋊C8—21no—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43D411yescharacteristic
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C42×C43—21no—
62C2×C42×C43C2311yescharacteristic
63#107×C43—42no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43D412yes—
66#95×C43—21no—
67C23×D43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—41no—
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—21no—
75C22×Dic43—22no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—21no—
80C2×D172—21no—
81C2×D172D812yes—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×C4×D43—41no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C2×C4×D43—41no—
88C2×Dic86—41no—
89C2×Dic86—41no—
90C2×Dic86—41no—
91C2×Dic86—41no—
92C2×Dic86—41no—
93C2×Dic86—41no—
94C2×C8×C43—22no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C42×C43—41no—
107C42×C43—41no—
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110C42×C43#4111yescharacteristic
111C42×C43#4111yescharacteristic
112(C2×D43)⋊C4—44no—
113(C2×D43)⋊C4—44no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116C4⋊Dic43—21no—
117C4⋊Dic43—22no—
118C4⋊Dic43—21no—
119C4⋊Dic43—22no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C23×C43#12011yescharacteristic
129C22×D43—22no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—81no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12311yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×C4×C43#12411yescharacteristic
153C2×C4×C43C2×D811yescharacteristic
154C2×C4×C43#13511yescharacteristic
155C2×C4×C43#13511yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C43#13711yescharacteristic
160C2×C4×C43#13711yescharacteristic
161C2×Dic43—42no—
162C2×Dic43—41no—
163C2×Dic43—42no—
164C2×Dic43—41no—
165C2×Dic43—42no—
166C2×Dic43—41no—
167D172—22no—
168D172—22no—
169D172—41no—
170D172—41no—
171C4×D43—81no—
172C4×D43—81no—
173C4×D43—81no—
174C4×D43—81no—
175Dic86—81no—
176Dic86—81no—
177Dic86—81no—
178Dic86—81no—
179C8×C43—42no—
180C43⋊C8—42no—
181C43⋊C8—81no—
182#10416—431nomaximal, Sylow
183C22×C43#39411yescharacteristic
184C22×C43#44711yescharacteristic
185C22×C43#44911yescharacteristic
186C22×C43#45211yescharacteristic
187C22×C43#45211yescharacteristic
188C22×C43#45411yescharacteristic
189C22×C43#45611yescharacteristic
190C2×D43—42no—
191C2×D43—42no—
192C2×D43—42no—
193C2×D43—81no—
194C2×D43—81no—
195C2×D43—81no—
196C2×D43—81no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—81no—
200C4×C43—81no—
201C4×C43—161no—
202C4×C43#46311yescharacteristic
203C4×C43#46411yescharacteristic
204C4×C43#46611yescharacteristic
205C4×C43#46811yescharacteristic
206C4×C43#48011yescharacteristic
207C4×C43#48211yescharacteristic
208C4×C43#48811yescharacteristic
209C4×C43#48911yescharacteristic
210Dic43—82no—
211Dic43—81no—
212#2547—431no—
213#1990—431no—
214#1947D4311yescharacteristic, complemented
215#1802—431no—
216C2×#332—431no—
217C2×D4⋊C8—431no—
218#1279—431no—
219C2×C43#162511yescharacteristic
220C2×C43#163811yescharacteristic
221C2×C43#164711yescharacteristic
222C2×C43#165211yescharacteristic
223C2×C43#203311yescharacteristic
224C2×C43#203811yescharacteristic
225C2×C43#204211yescharacteristic
226D43—82no—
227C2×C4⋊Q8—431no—
228C2×#124—861no—
229C2×C4×D4—431no—
230C2×#107—21no—
231C2×C4⋊C8—431no—
232C2×C4⋊C8C2×D4311yescharacteristic
233C2×#102—861no—
234C2×C4×C8—431no—
235#397—862no—
236#391—861no—
237#384C2×D4311yescharacteristic
238#380—861no—
239#380—861no—
240C4×C4⋊C4C2×D4311yescharacteristic
241#340—21no—
242#340—861no—
243#340—862no—
244#332—862no—
245D4⋊C8—862no—
246C43#1041611yescharacteristic, complemented, Sylow
247C22×Q8—861no—
248C22×D4—431no—
249C23×C4—861no—
250C22×C8—21no—
251C22×C8—861no—
252C22×C8—861no—
253C4⋊Q8—861no—
254C4⋊Q8—861no—
255C4⋊Q8—861no—
256C4⋊Q8—861no—
257#124—1722no—
258#124—1722no—
259C4×D4—861no—
260C4×D4—861no—
261C4×D4—861no—
262C4×D4—861no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—432no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4C22⋊D4311yescharacteristic
270C2×C4⋊C4C22⋊D4311yescharacteristic
271C2×C22⋊C4—862no—
272C2×C22⋊C4—862no—
273C2×C22⋊C4—861no—
274C2×C42—21no—
275C2×C42C22×D4311yescharacteristic
276#107—42no—
277C4⋊C8—21no—
278C4⋊C8—861no—
279C4⋊C8—861no—
280C4⋊C8D17212yes—
281#102—1722no—
282C4×C8—861no—
283C4×C8—861no—
284#95—21no—
285#95—862no—
286#95—862no—
287C24—861no—
288C2×Q8—1721no—
289C2×Q8—1721no—
290C2×Q8—1721no—
291C2×Q8—1721no—
292C2×Q8—1721no—
293C2×Q8—1721no—
294C2×D4—432no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4—861no—
299C2×D4—861no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—861no—
304C22×C4—862no—
305C22×C4—1721no—
306C22×C4—1721no—
307C22×C4—1721no—
308C22×C4—1721no—
309C22×C4—1721no—
310C22×C4—1721no—
311C22×C4D4×D4311yescharacteristic
312C22×C4D4×D4311yescharacteristic
313C22×C4C2×C22⋊D4311yescharacteristic
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—862no—
318C2×C8—1721no—
319C2×C8—1721no—
320C2×C8—1721no—
321C2×C8—1721no—
322C2×C8—1721no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—861no—
333C4⋊C4—862no—
334C4⋊C4—861no—
335C4⋊C4—862no—
336C4⋊C4—1721no—
337C4⋊C4—1721no—
338C22⋊C4—1724no—
339C22⋊C4—1724no—
340C22⋊C4—1721no—
341C22⋊C4—1721no—
342C42—41no—
343C42—41no—
344C42C2×D17211yescharacteristic
345C42#1062189811yescharacteristic
346C42#1062190211yescharacteristic
347C42#1062190211yescharacteristic
348C23—862no—
349C23—1721no—
350C23—1721no—
351C23—1721no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23#1306329311yescharacteristic
356Q8—3441no—
357Q8—3441no—
358Q8—3441no—
359Q8—3441no—
360D4—862no—
361D4—862no—
362D4—1721no—
363D4—1721no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—3441no—
376C2×C4—3441no—
377C2×C4—3441no—
378C2×C4—3441no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1722no—
382C2×C4—1721no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4#1306329911yescharacteristic
386C2×C4#1306330011yescharacteristic
387C2×C4#1306330011yescharacteristic
388C2×C4#1306331011yescharacteristic
389C2×C4#1306331011yescharacteristic
390C2×C4#1306331411yescharacteristic
391C2×C4D8×D4311yescharacteristic
392C2×C4#1306334511yescharacteristic
393C2×C4#1306334511yescharacteristic
394C2×C4#1306334811yescharacteristic
395C2×C4#1306334911yescharacteristic
396C2×C4#1306335111yescharacteristic
397C2×C4#1306335611yescharacteristic
398C2×C4#1306335711yescharacteristic
399C8—42no—
400C8—3441no—
401C8—1722no—
402C22—3441no—
403C22—3441no—
404C22—3441no—
405C22—3441no—
406C22—1722no—
407C22—1722no—
408C22—1722no—
409C22#1458281611yescharacteristic
410C22#1458303111yescharacteristic
411C22#1458304211yescharacteristic
412C22#1458305911yescharacteristic
413C22#1458306011yescharacteristic
414C22#1458307011yescharacteristic
415C22#1458308011yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—161no—
421C4—3442no—
422C4—3441no—
423C4#1458311411yescharacteristic
424C4#1458312111yescharacteristic
425C4#1458313611yescharacteristic
426C4#1458314611yescharacteristic
427C4#1458321411yescharacteristic
428C4#1458322611yescharacteristic
429C4#1458325611yescharacteristic
430C4#1458326111yescharacteristic
431C2—3442no—
432C2#1913368311yescharacteristic
433C2#1913376611yescharacteristic
434C2#1913382911yescharacteristic
435C2#1913386311yescharacteristic
436C2#1913577911yescharacteristic
437C2#1913581411yescharacteristic
438C2#1913583611yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1947C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#1947D43
hypocenterC43#10416
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
2. #19135555C2semidirect
4. C2×#14582644C2semidirect
6. #19132436C2semidirect
7. C43×#1947C2semidirect
214. #1947D43semidirect
246. C43#10416semidirect

Maximal subgroups

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

subgroupindex
#191395902
#191355552
#191345922
C2×#145826442
C2×#145826262
#191324362
C43×#19472
#1041643