Finite Group Databasebeta

← #25069327

Subgroups — #25069327

Order 11008.

962 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148398C211yesmaximal, characteristic
2#19144543C212yesmaximal, complemented
3#19133636C212yesmaximal, complemented
4#19133619C212yesmaximal, complemented
5#19133602C212yesmaximal, complemented
6#19133585C212yesmaximal, complemented
7#19133114C212yesmaximal, complemented
8#19132933C211yesmaximal, characteristic
9C43×#2395C211yesmaximal, characteristic
10#14583608—24no—
11#14583606—22no—
12D4×Dic86—22no—
13#14583530C2212yes—
14#14583525—21no—
15#14583525C2212yes—
16#14583456—21no—
17C2×#13063304—21no—
18C2×#13063304C2212yes—
19#14583374—21no—
20#14583240—24no—
21#14583234C2214yes—
22#14583229C2214yes—
23#14582942—22no—
24#14582907—22no—
25#14582863C2212yes—
26#14582635C2214yes—
27#14582635C2214yes—
28#14582625C2212yes—
29#14582623C2212yes—
30C2×C4×D4×C43C2211yescharacteristic
31C2×#117×C43C2211yescharacteristic
32C43×#400C2211yescharacteristic
33C43×#399C2211yescharacteristic
34C43×#398C2211yescharacteristic
35C43×#397—21no—
36C43×#397C2211yescharacteristic
37C43×#394—21no—
38C4×C4⋊C4×C43—21no—
39C4×C22⋊C4×C43—21no—
40C4×C22⋊C4×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86D412yes—
43C2×#10621877—22no—
44#13063325—21no—
45#13063325—21no—
46#13063324—24no—
47#13063317—22no—
48#13063316—24no—
49#13063304—22no—
50#13063304—22no—
51#13063304—22no—
52#13063304—22no—
53#13063304—22no—
54#13063304—22no—
55#13063304D414yes—
56#13063304C2314yes—
57#13063302—24no—
58#13063302—24no—
59#13063302—24no—
60#13063302—24no—
61C4×Dic86—22no—
62C4×Dic86—22no—
63D4×Dic43—24no—
64D4×Dic43—24no—
65#13063284—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43D412yes—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—22no—
70C2×C22⋊Dic43—22no—
71C2×C22⋊Dic43—22no—
72#13063258—24no—
73#13063256—24no—
74#13063248—24no—
75#13063248—24no—
76C22⋊(C43⋊C8)—22no—
77C22⋊(C43⋊C8)C2314yes—
78C22×D4×C43D411yescharacteristic
79C23×C4×C43D411yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C4×D4×C43—22no—
82C4×D4×C43—22no—
83#117×C43—22no—
84#117×C43—22no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C4⋊C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43C2311yescharacteristic
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43D411yescharacteristic
95C2×C22⋊C4×C43C2311yescharacteristic
96C2×C42×C43—21no—
97C2×C42×C43—21no—
98C2×C42×C43D411yescharacteristic
99#95×C43—21no—
100#95×C43—21no—
101#95×C43—21no—
102#95×C43—21no—
103#95×C43C2311yescharacteristic
104#95×C43C2311yescharacteristic
105C24×C43C2×D411yescharacteristic
106C24×C43C2×D411yescharacteristic
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—42no—
117C22×C4×C43—42no—
118C22×C4×C43C2×D412yes—
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2411yescharacteristic
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C2×Dic86—22no—
130C2×Dic86—22no—
131C2×Dic86—22no—
132C2×Dic86—44no—
133C2×Dic86—82no—
134C2×Dic86C2×D414yes—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—42no—
139C4⋊C4×C43—42no—
140C22⋊C4×C43—22no—
141C22⋊C4×C43—22no—
142C22⋊C4×C43—42no—
143C22⋊C4×C43—42no—
144C22⋊C4×C43—42no—
145C22⋊C4×C43—42no—
146C42×C43—21no—
147C42×C43—21no—
148C42×C43—42no—
149C42×C43—41no—
150C42×C43—41no—
151C22⋊Dic43—24no—
152C22⋊Dic43—24no—
153C22⋊Dic43—24no—
154C4⋊Dic43—22no—
155C4⋊Dic43—22no—
156C4⋊Dic43—22no—
157C4⋊Dic43—22no—
158C4⋊Dic43—22no—
159C4⋊Dic43C2×D414yes—
160Dic43⋊C4—24no—
161Dic43⋊C4—24no—
162Dic43⋊C4—24no—
163Dic43⋊C4—24no—
164C4×Dic43—24no—
165#10621877—44no—
166C2×C43⋊C8—24no—
167C23×C43—21no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—21no—
171C23×C43—41no—
172C23×C43—41no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43#12012yes—
176C23×C43#13712yes—
177C23×C43C22×D411yescharacteristic
178D4×C43—28no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—24no—
182C2×C4×C43—22no—
183C2×C4×C43—22no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—42no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—42no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—81no—
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C2×C4×C43#13712yes—
206C2×C4×C43C22×D412yes—
207C2×Dic43—24no—
208C2×Dic43—24no—
209C2×Dic43—82no—
210C2×Dic43—82no—
211C2×Dic43—82no—
212C2×Dic43—82no—
213Dic86—44no—
214Dic86—44no—
215Dic86—82no—
216Dic86—82no—
217C43⋊C8—44no—
218#18174—431nomaximal, Sylow
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—22no—
222C22×C43—22no—
223C22×C43—22no—
224C22×C43—22no—
225C22×C43—42no—
226C22×C43—41no—
227C22×C43—41no—
228C22×C43—81no—
229C22×C43—81no—
230C22×C43—81no—
231C22×C43C2×#12011yescharacteristic
232C22×C43C2×#13711yescharacteristic
233C22×C43C2×#13711yescharacteristic
234C4×C43—22no—
235C4×C43—22no—
236C4×C43—21no—
237C4×C43—42no—
238C4×C43—41no—
239C4×C43—41no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43#45812yes—
244Dic43—44no—
245Dic43—44no—
246#3501—431no—
247#3095—432no—
248#2395D4311yescharacteristic
249#1617—432no—
250#1614—432no—
251#1611—432no—
252#1608—432no—
253#1508—432no—
254#1465—431no—
255C2×C43—21no—
256C2×C43—21no—
257C2×C43—42no—
258C2×C43—42no—
259C2×C43#300411yescharacteristic
260C2×C43#301811yescharacteristic
261C2×C43C2×#45811yescharacteristic
262#554—862no—
263#554—864no—
264D4×Q8—862no—
265#544—432no—
266#543—432no—
267#543—861no—
268#533—861no—
269C2×C22⋊Q8—432no—
270C2×C22⋊Q8—861no—
271#518—861no—
272C2×C4×D4C2×D4311yescharacteristic
273C2×#117C2×D4311yescharacteristic
274#485—864no—
275#484—434no—
276#483—434no—
277#428—862no—
278#419—862no—
279#407—432no—
280#400C2×D4311yescharacteristic
281#399C2×D4311yescharacteristic
282#398C2×D4311yescharacteristic
283#397—21no—
284#397C2×D4311yescharacteristic
285#394—21no—
286C4×C4⋊C4—21no—
287C4×C22⋊C4—21no—
288C4×C22⋊C4C2×D4311yescharacteristic
289#328—434no—
290#328—434no—
291#324—432no—
292#323—432no—
293C43#1817411yescharacteristic, complemented, Sylow
294C22×Q8—432no—
295C22×Q8—861no—
296C22×D4C22⋊D4311yescharacteristic
297C23×C4C22⋊D4311yescharacteristic
298C23×C4C22×D4311yescharacteristic
299C2×M16—862no—
300C4⋊Q8—861no—
301C4⋊Q8—861no—
302C4⋊Q8—864no—
303#125—862no—
304#125—864no—
305C22⋊Q8—434no—
306C22⋊Q8—434no—
307C22⋊Q8—864no—
308C22⋊Q8—864no—
309C22⋊Q8—864no—
310C22⋊Q8—864no—
311C22⋊Q8—862no—
312C22⋊Q8—862no—
313C22⋊Q8—862no—
314C22⋊Q8—862no—
315C22⋊Q8—862no—
316C22⋊Q8—862no—
317C4×Q8—862no—
318C4×Q8—862no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—864no—
322C4×D4—864no—
323#117—22no—
324#117—22no—
325#117—862no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—432no—
329C2×C4⋊C4—862no—
330C2×C4⋊C4—861no—
331C2×C4⋊C4—862no—
332C2×C4⋊C4C22×D4311yescharacteristic
333C2×C4⋊C4C22×D4311yescharacteristic
334C2×C4⋊C4C22×D4311yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—862no—
340C2×C22⋊C4—862no—
341C2×C22⋊C4C22⋊D4311yescharacteristic
342C2×C22⋊C4C22×D4311yescharacteristic
343C2×C42—21no—
344C2×C42—21no—
345C2×C42C22⋊D4311yescharacteristic
346#107—864no—
347#106—864no—
348#103—864no—
349#103—864no—
350C22⋊C8—434no—
351C22⋊C8—862no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95C22×D4311yescharacteristic
357#95C22×D4311yescharacteristic
358C24C2×C22⋊D4311yescharacteristic
359C24C2×C22⋊D4311yescharacteristic
360C2×Q8—434no—
361C2×Q8—862no—
362C2×Q8—862no—
363C2×Q8—862no—
364C2×Q8—3442no—
365C2×Q8—1724no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—862no—
378C22×C4—862no—
379C22×C4—862no—
380C22×C4—862no—
381C22×C4D4×D4312yes—
382C22×C4D4×D4312yes—
383C22×C4C2×C22⋊D4311yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385C22×C4C2×C22⋊D4311yescharacteristic
386C22×C4C2×C22⋊D4311yescharacteristic
387C22×C4C23×D4311yescharacteristic
388M16—1724no—
389C2×C8—864no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4—434no—
396C4⋊C4—862no—
397C4⋊C4—864no—
398C4⋊C4—862no—
399C4⋊C4—862no—
400C4⋊C4—864no—
401C4⋊C4—862no—
402C4⋊C4—862no—
403C4⋊C4—864no—
404C4⋊C4—864no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C22⋊C4—864no—
412C22⋊C4—864no—
413C22⋊C4—864no—
414C42—21no—
415C42—21no—
416C42—42no—
417C42—41no—
418C42—41no—
419C42—864no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23#1306329312yes—
429C23#1306335512yes—
430C23C22×C22⋊D4311yescharacteristic
431Q8—3442no—
432Q8—3442no—
433Q8—1724no—
434Q8—1724no—
435D4—28no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—81no—
460C2×C4—864no—
461C2×C4—864no—
462C2×C4—3442no—
463C2×C4—3442no—
464C2×C4—3442no—
465C2×C4—3442no—
466C2×C4#1306329311yescharacteristic
467C2×C4#1306329311yescharacteristic
468C2×C4#1306335512yes—
469C2×C4C2×D4×D4312yes—
470C8—1724no—
471C22—21no—
472C22—21no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—42no—
478C22—41no—
479C22—41no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C2×#1306329311yescharacteristic
484C22C2×#1306335511yescharacteristic
485C22C2×#1306335511yescharacteristic
486C4—22no—
487C4—21no—
488C4—22no—
489C4—42no—
490C4—41no—
491C4—41no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—1724no—
496C4—1724no—
497C4#1458308812yes—
498C2—21no—
499C2—21no—
500C2—42no—
501C2—42no—
502C2#1914382811yescharacteristic
503C2#1914394311yescharacteristic
504C2C2×#1458308811yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2395C2
socleC22×C43C2×#120
prime radicalC22×D4×C43D4
hypercenter#2395D43
hypocenterC43#18174
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
2. #19144543C2semidirect
3. #19133636C2semidirect
4. #19133619C2semidirect
5. #19133602C2semidirect
6. #19133585C2semidirect
7. #19133114C2semidirect
293. C43#18174semidirect

Maximal subgroups

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

subgroupindex
#191483982
#191445432
#191336362
#191336192
#191336022
#191335852
#191331142
#191329332
C43×#23952
#1817443