Finite Group Databasebeta

← #25000010

Subgroups — #25000010

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#19139591C211yesmaximal, characteristic
2#19135557C211yesmaximal, characteristic, complemented
3#19135354C211yesmaximal, characteristic, complemented
4#19134596C211yesmaximal, characteristic
5C2×#14582626C211yesmaximal, characteristic
6#19132434C211yesmaximal, characteristic, complemented
7C2×C43×#332C211yesmaximal, characteristic, complemented
8C2×#13063314—21no—
9C2×C4×D172C2211yescharacteristic
10C2×#13063259—21no—
11C2×#13063247—21no—
12C2×C4×C43⋊C8C2211yescharacteristic
13#14582825—22no—
14#14582806—21no—
15#14582769C2211yescharacteristic
16#14582756—21no—
17#14582756—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582662—21no—
20#14582662—21no—
21#14582661—22no—
22#14582626—22no—
23C2×C4⋊Q8×C43C2211yescharacteristic
24C2×C4⋊C8×C43C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C43×#332—22no—
27C22×D172D411yescharacteristic
28C22×C4×D43—21no—
29C22×C43⋊C8—21no—
30#13063314—42no—
31#13063314—42no—
32C4×D172—21no—
33C4×D172—21no—
34C4×D172—21no—
35C4×D172—21no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×C4⋊Dic43D411yescharacteristic
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43—21no—
46#13063259—42no—
47#13063247—42no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C43⋊#95—22no—
51C43⋊#95—22no—
52C43⋊#95—21no—
53C22×Q8×C43—21no—
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43—21no—
59C4⋊Q8×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43D412yes—
62C2×C42×C43C2311yescharacteristic
63C4⋊C8×C43—21no—
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66C4⋊C8×C43D412yes—
67C23×D43—21no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C2×Q8×C43—41no—
73C2×Q8×C43—41no—
74C22×C4×C43—22no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C22×Dic43—41no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172D812yes—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C4×D43—41no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C8×C43—22no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C2×C8×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43—41no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C42×C43C2×D411yescharacteristic
105C42×C43#4111yescharacteristic
106C42×C43#4111yescharacteristic
107C42×C43#4111yescharacteristic
108(C2×D43)⋊C4—44no—
109(C2×D43)⋊C4—44no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112C4⋊Dic43—21no—
113C4⋊Dic43—21no—
114C4⋊Dic43—21no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—42no—
119C4⋊Dic43—41no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122C4⋊Dic43—41no—
123C4×Dic43—41no—
124C4×Dic43—41no—
125C2×C43⋊C8—22no—
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—
136Q8×C43—81no—
137Q8×C43—81no—
138Q8×C43—81no—
139Q8×C43—81no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12311yescharacteristic
149C2×C4×C43#12311yescharacteristic
150C2×C4×C43#12411yescharacteristic
151C2×C4×C43C2×D811yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43#13511yescharacteristic
154C2×C4×C43#13511yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C43#13711yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—81no—
169C2×Dic43—81no—
170C2×Dic43—81no—
171D172—22no—
172D172—22no—
173D172—41no—
174D172—41no—
175C4×D43—81no—
176C4×D43—81no—
177C4×D43—81no—
178C4×D43—81no—
179C8×C43—42no—
180C8×C43—81no—
181C43⋊C8—42no—
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—82no—
200C4×C43#46311yescharacteristic
201C4×C43#46411yescharacteristic
202C4×C43#46611yescharacteristic
203C4×C43#46811yescharacteristic
204C4×C43#48011yescharacteristic
205C4×C43#48211yescharacteristic
206C4×C43#48811yescharacteristic
207C4×C43#48911yescharacteristic
208Dic43—81no—
209Dic43—81no—
210Dic43—81no—
211Dic43—161no—
212#2547—431no—
213#1990—431no—
214#1947—431no—
215#1802—431no—
216C2×#332D4311yescharacteristic, complemented
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⋊Q8C2×D4311yescharacteristic
228C2×#124—861no—
229C2×C4×D4—431no—
230C2×#107—861no—
231C2×C4⋊C8C2×D4311yescharacteristic
232C2×C4⋊C8C2×D4311yescharacteristic
233C2×#102—861no—
234C2×C4×C8—431no—
235#397—862no—
236#391—861no—
237#384—431no—
238#380—861no—
239#380—861no—
240C4×C4⋊C4—431no—
241#340—861no—
242#340—861no—
243#340—862no—
244#332—22no—
245D4⋊C8—862no—
246C43#1041611yescharacteristic, complemented, Sylow
247C22×Q8—21no—
248C22×D4—431no—
249C23×C4—861no—
250C22×C8—21no—
251C22×C8—21no—
252C22×C8—861no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
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—431no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—861no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—861no—
270C2×C4⋊C4D17212yes—
271C2×C22⋊C4—862no—
272C2×C22⋊C4—862no—
273C2×C22⋊C4—861no—
274C2×C42—861no—
275C2×C42C22×D4311yescharacteristic
276#107—1722no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8C22⋊D4312yes—
281#102—1722no—
282C4×C8—861no—
283C4×C8—861no—
284#95—862no—
285#95—862no—
286#95—861no—
287C24—861no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—432no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—861no—
298C2×D4—861no—
299C2×D4—861no—
300C22×C4—22no—
301C22×C4—861no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4—1721no—
305C22×C4—1721no—
306C22×C4—1721no—
307C22×C4—1721no—
308C22×C4—1721no—
309C22×C4—1721no—
310C22×C4—1721no—
311C22×C4C2×D17211yescharacteristic
312C22×C4D4×D4311yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C2×C8—22no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—862no—
321C2×C8—1721no—
322C2×C8—1721no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—861no—
330C4⋊C4—861no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4—1722no—
334C4⋊C4—1721no—
335C4⋊C4—1721no—
336C4⋊C4—1721no—
337C4⋊C4—1721no—
338C22⋊C4—1724no—
339C22⋊C4—1724no—
340C22⋊C4—1721no—
341C22⋊C4—1721no—
342C42—1721no—
343C42—1721no—
344C42#1062189811yescharacteristic
345C42#1062190011yescharacteristic
346C42#1062190011yescharacteristic
347C42C2×C22⋊D4311yescharacteristic
348C23—862no—
349C23—1721no—
350C23—1721no—
351C23—1721no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23#1306329511yescharacteristic
356Q8—81no—
357Q8—81no—
358Q8—81no—
359Q8—81no—
360D4—862no—
361D4—862no—
362D4—1721no—
363D4—1721no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—3441no—
370C2×C4—3441no—
371C2×C4—3441no—
372C2×C4—3441no—
373C2×C4—3441no—
374C2×C4—3441no—
375C2×C4—3441no—
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×C4#1306329611yescharacteristic
386C2×C4#1306329711yescharacteristic
387C2×C4#1306329911yescharacteristic
388C2×C4#1306330711yescharacteristic
389C2×C4#1306330911yescharacteristic
390C2×C4#1306331111yescharacteristic
391C2×C4D8×D4311yescharacteristic
392C2×C4#1306334411yescharacteristic
393C2×C4#1306334611yescharacteristic
394C2×C4#1306334811yescharacteristic
395C2×C4#1306335211yescharacteristic
396C2×C4#1306335211yescharacteristic
397C2×C4#1306335411yescharacteristic
398C2×C4#1306335711yescharacteristic
399C8—42no—
400C8—81no—
401C8—1722no—
402C22—3441no—
403C22—3441no—
404C22—3441no—
405C22—3441no—
406C22—1722no—
407C22—1722no—
408C22—1722no—
409C22#1458281511yescharacteristic
410C22#1458303411yescharacteristic
411C22#1458304711yescharacteristic
412C22#1458306211yescharacteristic
413C22#1458306411yescharacteristic
414C22#1458307411yescharacteristic
415C22#1458308411yescharacteristic
416C4—21no—
417C4—21no—
418C4—82no—
419C4—3441no—
420C4—3441no—
421C4—3441no—
422C4—6881no—
423C4#1458311611yescharacteristic
424C4#1458312311yescharacteristic
425C4#1458313211yescharacteristic
426C4#1458314211yescharacteristic
427C4#1458321111yescharacteristic
428C4#1458322111yescharacteristic
429C4#1458325511yescharacteristic
430C4#1458326011yescharacteristic
431C2—3442no—
432C2#1913368511yescharacteristic
433C2#1913376811yescharacteristic
434C2#1913383111yescharacteristic
435C2#1913386611yescharacteristic
436C2#1913577611yescharacteristic
437C2#1913581311yescharacteristic
438C2#1913583311yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#332C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenterC2×#332D43
hypocenterC43#10416
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #19135557C2semidirect
3. #19135354C2semidirect
6. #19132434C2semidirect
7. C2×C43×#332C2semidirect
216. C2×#332D43semidirect
246. C43#10416semidirect

Maximal subgroups

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

subgroupindex
#191395912
#191355572
#191353542
#191345962
C2×#145826262
#191324342
C2×C43×#3322
#1041643