Finite Group Databasebeta

← #25152751

Subgroups — #25152751

Order 11008.

1094 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic
2#19139073C212yesmaximal, complemented
3#19138912C211yesmaximal, characteristic
4#19135949C214yesmaximal, complemented
5#19135580C212yesmaximal, complemented
6#19134878C214yesmaximal
7C4×#99×C43C211yesmaximal, characteristic
8#14583608—24no—
9#14583606—22no—
10D4×Dic86—22no—
11#14583530—21no—
12#14583525—21no—
13#14583525C2212yes—
14#14583456—21no—
15C2×#13063304—21no—
16C2×#13063304C2212yes—
17#14583374C2212yes—
18C22×C4⋊Dic43C2211yescharacteristic
19#14582838—21no—
20#14582835—21no—
21#14582831—24no—
22#14582805—22no—
23#14582797—21no—
24#14582779C2212yes—
25#14582774C2218yes—
26#14582771C2212yes—
27#14582769—22no—
28#14582759—21no—
29#14582759C2211yescharacteristic
30#14582665C2218yes—
31C2×C4×D4×C43C2211yescharacteristic
32C2×#99×C43C2212yes—
33C4×C22⋊C4×C43C2212yes—
34C43×#342C2212yes—
35C22×Dic86—21no—
36C22×Dic86D412yes—
37C23×Dic43C2312yes—
38#13063325—21no—
39#13063325—21no—
40#13063324—24no—
41#13063317—22no—
42#13063316—24no—
43#13063304—22no—
44#13063304—22no—
45#13063304—22no—
46#13063304—22no—
47#13063304—22no—
48#13063304—22no—
49#13063304—22no—
50#13063304—22no—
51#13063302—24no—
52#13063302—24no—
53#13063302—24no—
54#13063302—24no—
55C4×Dic86—22no—
56C4×Dic86—22no—
57D4×Dic43—24no—
58D4×Dic43—24no—
59#13063284—22no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—22no—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—28no—
67C2×C4⋊Dic43D412yes—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4D414yes—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—22no—
73C2×C22⋊Dic43C2312yes—
74C2×C22⋊Dic43C2314yes—
75C43⋊#95—22no—
76C43⋊#95—21no—
77C43⋊#95—22no—
78C43⋊#95—28no—
79C22×D4×C43C2311yescharacteristic
80C23×C4×C43D411yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C4×D4×C43—22no—
83C4×D4×C43—22no—
84C2×C4⋊C4×C43D411yescharacteristic
85C2×C22⋊C4×C43D411yescharacteristic
86C2×C22⋊C4×C43C2311yescharacteristic
87C2×C22⋊C4×C43C2314yes—
88C2×C42×C43—22no—
89C2×C42×C43D411yescharacteristic
90#99×C43Q818yescomplemented
91#95×C43—22no—
92C24×C43C2×D411yescharacteristic
93C24×C43C2411yescharacteristic
94C2×D4×C43—22no—
95C2×D4×C43—22no—
96C2×D4×C43C2×Q814yes—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—24no—
100C22×C4×C43—42no—
101C22×C4×C43—42no—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D412yes—
108C22×C4×C43C2×D412yes—
109C22×Dic43—22no—
110C22×Dic43—22no—
111C22×Dic43—22no—
112C22×Dic43—22no—
113C22×Dic43—24no—
114C22×Dic43—82no—
115C22×Dic43C2×D414yes—
116C22×Dic43C2×D414yes—
117C2×Dic86—22no—
118C2×Dic86—22no—
119C2×Dic86—22no—
120C2×Dic86—22no—
121C2×Dic86—44no—
122C2×Dic86—82no—
123C4⋊C4×C43—22no—
124C22⋊C4×C43—22no—
125C22⋊C4×C43—22no—
126C22⋊C4×C43—24no—
127C22⋊C4×C43C2×Q818yescomplemented
128C42×C43—21no—
129C42×C43—21no—
130C42×C43—44no—
131C22⋊Dic43—24no—
132C22⋊Dic43—24no—
133C22⋊Dic43—24no—
134C22⋊Dic43—24no—
135C22⋊Dic43—82no—
136C4⋊Dic43—22no—
137C4⋊Dic43—22no—
138C4⋊Dic43—22no—
139C4⋊Dic43—22no—
140C4⋊Dic43—22no—
141C4⋊Dic43—22no—
142C4⋊Dic43—42no—
143C4⋊Dic43—41no—
144C4⋊Dic43—42no—
145C4⋊Dic43—41no—
146C4⋊Dic43—88no—
147Dic43⋊C4—24no—
148Dic43⋊C4—24no—
149Dic43⋊C4—24no—
150Dic43⋊C4—24no—
151Dic43⋊C4—82no—
152C4×Dic43—24no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—41no—
156C23×C43—41no—
157C23×C43—41no—
158C23×C43—41no—
159C23×C43C4⋊Q812yes—
160C23×C43C22×D412yes—
161C23×C43C22×D411yescharacteristic
162C23×C43C22×Q812yes—
163C23×C432−1+412yes—
164D4×C43—28no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—22no—
168C2×C4×C43—24no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—28no—
172C2×C4×C43—41no—
173C2×C4×C43—42no—
174C2×C4×C43—44no—
175C2×C4×C43—44no—
176C2×C4×C43—42no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—81no—
180C2×C4×C43#12011yescharacteristic
181C2×C4×C43#12012yes—
182C2×C4×C43#12011yescharacteristic
183C2×C4×C43C4⋊Q812yes—
184C2×Dic43—24no—
185C2×Dic43—24no—
186C2×Dic43—44no—
187C2×Dic43—44no—
188C2×Dic43—42no—
189C2×Dic43—42no—
190C2×Dic43—42no—
191C2×Dic43—48no—
192C2×Dic43—42no—
193C2×Dic43—42no—
194C2×Dic43—42no—
195C2×Dic43—82no—
196C2×Dic43—82no—
197Dic86—44no—
198Dic86—82no—
199Dic86—82no—
200Dic86—82no—
201#25853—431nomaximal, Sylow
202C22×C43—21no—
203C22×C43—22no—
204C22×C43—21no—
205C22×C43—22no—
206C22×C43—22no—
207C22×C43—42no—
208C22×C43—42no—
209C22×C43—42no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—81no—
213C22×C43C2×#12011yescharacteristic
214C22×C43C2×C4⋊Q811yescharacteristic
215C22×C43#53611yescharacteristic
216C22×C43D4×Q814yes—
217C4×C43—22no—
218C4×C43—22no—
219C4×C43—21no—
220C4×C43—48no—
221C4×C43—41no—
222C4×C43—41no—
223C4×C43#45812yes—
224Dic43—44no—
225Dic43—44no—
226Dic43—82no—
227Dic43—82no—
228#3501—431no—
229#2502—432no—
230#2487—431no—
231#2062—434no—
232#1996—432no—
233#1867—434no—
234C4×#99D4311yescharacteristic
235C2×C43—21no—
236C2×C43—24no—
237C2×C43—21no—
238C2×C43—42no—
239C2×C43#243411yescharacteristic
240C2×C43C2×#45811yescharacteristic
241C2×C43#302711yescharacteristic
242#554—862no—
243#554—864no—
244D4×Q8—862no—
245#544—861no—
246#543—432no—
247#543—861no—
248#533—861no—
249C2×C22⋊Q8—432no—
250C2×C22⋊Q8—861no—
251#518—432no—
252C2×C4×D4C2×D4311yescharacteristic
253C22×C4⋊C4—431no—
254C2×#99C2×D4312yes—
255#400—861no—
256#399—861no—
257#398—864no—
258#391—862no—
259#389—861no—
260#386—432no—
261#385—432no—
262#385—438no—
263#384—862no—
264#380—431no—
265#380—861no—
266C4×C22⋊C4C2×D4312yes—
267#342—438no—
268#342C2×D4312yes—
269C43#2585311yescharacteristic, complemented, Sylow
270C22×Q8—432no—
271C22×Q8—861no—
272C22×D4C22×D4311yescharacteristic
273C23×C4—432no—
274C23×C4D17211yescharacteristic
275C23×C4C22×D4311yescharacteristic
276C4⋊Q8—861no—
277C4⋊Q8—861no—
278C4⋊Q8—864no—
279#125—862no—
280#125—864no—
281C22⋊Q8—864no—
282C22⋊Q8—864no—
283C22⋊Q8—864no—
284C22⋊Q8—864no—
285C22⋊Q8—862no—
286C22⋊Q8—862no—
287C22⋊Q8—862no—
288C22⋊Q8—862no—
289C22⋊Q8—862no—
290C22⋊Q8—862no—
291C22⋊Q8—862no—
292C22⋊Q8—862no—
293C4×Q8—862no—
294C4×Q8—862no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4—864no—
298C4×D4—864no—
299#117—862no—
300C2×C4⋊C4—434no—
301C2×C4⋊C4—432no—
302C2×C4⋊C4—862no—
303C2×C4⋊C4—861no—
304C2×C4⋊C4—868no—
305C2×C4⋊C4—862no—
306C2×C4⋊C4—861no—
307C2×C4⋊C4—861no—
308C2×C4⋊C4—861no—
309C2×C4⋊C4—862no—
310C2×C4⋊C4—862no—
311C2×C4⋊C4D17211yescharacteristic
312C2×C22⋊C4—434no—
313C2×C22⋊C4—432no—
314C2×C22⋊C4—862no—
315C2×C22⋊C4—862no—
316C2×C22⋊C4D17211yescharacteristic
317C2×C22⋊C4C22×D4311yescharacteristic
318C2×C22⋊C4C22×D4314yes—
319C2×C42—22no—
320C2×C42D17211yescharacteristic
321#99Dic8618yescomplemented
322#95—22no—
323#95—868no—
324#95—861no—
325#95—862no—
326#95—862no—
327C24C2×D17211yescharacteristic
328C24C23×D4311yescharacteristic
329C2×Q8—862no—
330C2×Q8—862no—
331C2×Q8—862no—
332C2×Q8—862no—
333C2×Q8—3442no—
334C2×Q8—1724no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4C2×Dic8614yes—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—434no—
344C22×C4—434no—
345C22×C4—862no—
346C22×C4—862no—
347C22×C4—864no—
348C22×C4—862no—
349C22×C4—862no—
350C22×C4—3442no—
351C22×C4C2×D17211yescharacteristic
352C22×C4C2×D17211yescharacteristic
353C22×C4C2×D17211yescharacteristic
354C22×C4C2×D17211yescharacteristic
355C22×C4C2×D17211yescharacteristic
356C22×C4D4×D4312yes—
357C22×C4D4×D4312yes—
358C4⋊C4—22no—
359C4⋊C4—862no—
360C4⋊C4—864no—
361C4⋊C4—862no—
362C4⋊C4—862no—
363C4⋊C4—864no—
364C4⋊C4—862no—
365C4⋊C4—864no—
366C4⋊C4—862no—
367C4⋊C4—862no—
368C4⋊C4—864no—
369C4⋊C4—3442no—
370C4⋊C4—3448no—
371C4⋊C4—1722no—
372C4⋊C4—1721no—
373C4⋊C4—1722no—
374C4⋊C4—1721no—
375C22⋊C4—22no—
376C22⋊C4—24no—
377C22⋊C4—22no—
378C22⋊C4—864no—
379C22⋊C4—864no—
380C22⋊C4—864no—
381C22⋊C4—864no—
382C22⋊C4—3442no—
383C22⋊C4C2×Dic8618yescomplemented
384C42—21no—
385C42—21no—
386C42—44no—
387C42—864no—
388C23—21no—
389C23—21no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23#1306332512yes—
395C23C2×D4×D4312yes—
396C23C22×D17211yescharacteristic
397C23C22×Dic8612yes—
398C23#1306337212yes—
399Q8—3442no—
400Q8—3442no—
401Q8—3442no—
402Q8—1724no—
403D4—28no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—28no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—81no—
419C2×C4—864no—
420C2×C4—864no—
421C2×C4—3442no—
422C2×C4—3442no—
423C2×C4—1722no—
424C2×C4—1722no—
425C2×C4—1728no—
426C2×C4—1722no—
427C2×C4—1722no—
428C2×C4—1722no—
429C2×C4—1722no—
430C2×C4—1724no—
431C2×C4—1724no—
432C2×C4#1306329511yescharacteristic
433C2×C4#1306329512yes—
434C2×C4#1306329511yescharacteristic
435C2×C4#1306332512yes—
436C22—22no—
437C22—21no—
438C22—22no—
439C22—21no—
440C22—22no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—41no—
445C22—41no—
446C22—81no—
447C22C2×#1306329511yescharacteristic
448C22C2×#1306332511yescharacteristic
449C22#1458347511yescharacteristic
450C22D4×Dic8614yes—
451C4—21no—
452C4—22no—
453C4—22no—
454C4—48no—
455C4—41no—
456C4—41no—
457C4—3442no—
458C4—3442no—
459C4—1724no—
460C4—1724no—
461C4#1458309012yes—
462C2—24no—
463C2—21no—
464C2—21no—
465C2—42no—
466C2#1913823911yescharacteristic
467C2C2×#1458309011yescharacteristic
468C2#1914399811yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC24×C43C24
FrattiniC24C23×D43
FittingC4×#99×C43C2
socleC22×C43C2×#120
prime radicalC22×D4×C43C23
hypercenterC4×#99D43
hypocenterC43#25853
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #19139073C2semidirect
4. #19135949C2semidirect
5. #19135580C2semidirect
90. #99×C43Q8semidirect
127. C22⋊C4×C43C2×Q8semidirect
269. C43#25853semidirect
321. #99Dic86semidirect
383. C22⋊C4C2×Dic86semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191390732
#191389122
#191359492
#191355802
#191348782
C4×#99×C432
#2585343