Finite Group Databasebeta

← #25069328

Subgroups — #25069328

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#19144539C212yesmaximal, complemented
2#19137854C211yesmaximal, characteristic
3#19133637C212yesmaximal, complemented
4#19133620C212yesmaximal, complemented
5#19133603C212yesmaximal, complemented
6#19133586C212yesmaximal, complemented
7#19133115C212yesmaximal, complemented
8#19132933C211yesmaximal, characteristic
9C43×#3501C211yesmaximal, characteristic
10C2×#13063284C2211yescharacteristic
11#14583237—24no—
12#14583232C2214yes—
13#14583227C2214yes—
14#14582939—22no—
15#14582908—22no—
16#14582863C2212yes—
17#14582838C2211yescharacteristic
18#14582835C2211yescharacteristic
19#14582829C2211yescharacteristic
20#14582827—21no—
21#14582824C2211yescharacteristic
22#14582813—21no—
23C4×Dic43⋊C4—21no—
24C4×C22⋊Dic43—21no—
25C4×C22⋊Dic43C2211yescharacteristic
26#14582636C2214yes—
27#14582636C2214yes—
28#14582625C2212yes—
29#14582623C2212yes—
30C43×#554—24no—
31C43×#554—22no—
32D4×Q8×C43—22no—
33C43×#544C2212yes—
34C43×#543—21no—
35C43×#543C2212yes—
36C43×#533—21no—
37C2×C22⋊Q8×C43—21no—
38C2×C22⋊Q8×C43C2212yes—
39C43×#518—21no—
40C2×C4×D4×C43C2211yescharacteristic
41C2×#10621877—22no—
42#13063284—22no—
43#13063284—22no—
44C2×C4⋊Dic43C2311yescharacteristic
45C2×C4⋊Dic43C2311yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C4×Dic43—21no—
53C2×C4×Dic43—21no—
54#13063258—24no—
55#13063256—24no—
56#13063249—24no—
57#13063249—24no—
58C22⋊(C43⋊C8)—22no—
59C22⋊(C43⋊C8)C2314yes—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95C2311yescharacteristic
65C43⋊#95C2311yescharacteristic
66C22×Q8×C43—21no—
67C22×Q8×C43D412yes—
68C22×D4×C43D411yescharacteristic
69C23×C4×C43D411yescharacteristic
70C23×C4×C43C2311yescharacteristic
71C4⋊Q8×C43—21no—
72C4⋊Q8×C43—21no—
73C4⋊Q8×C43—24no—
74#125×C43—22no—
75#125×C43—24no—
76C22⋊Q8×C43—22no—
77C22⋊Q8×C43—22no—
78C22⋊Q8×C43—24no—
79C22⋊Q8×C43—24no—
80C22⋊Q8×C43—24no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43—24no—
86C22⋊Q8×C43D414yes—
87C22⋊Q8×C43C2314yes—
88C4×Q8×C43—22no—
89C4×Q8×C43—22no—
90C4×D4×C43—24no—
91C4×D4×C43—24no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94#117×C43—22no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43D412yes—
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43D411yescharacteristic
103C2×C22⋊C4×C43C2311yescharacteristic
104C2×C42×C43D411yescharacteristic
105C24×C43C2×D411yescharacteristic
106C24×C43C2×D411yescharacteristic
107C2×Q8×C43—22no—
108C2×Q8×C43—22no—
109C2×Q8×C43—22no—
110C2×Q8×C43—44no—
111C2×Q8×C43—82no—
112C2×Q8×C43C2×D414yes—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C2×D412yes—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—24no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—24no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—24no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—24no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43C2×D414yes—
146C22⋊C4×C43—24no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—24no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—24no—
151C42×C43—24no—
152C42×C43—21no—
153C42×C43—21no—
154C22⋊Dic43—42no—
155C22⋊Dic43—42no—
156C22⋊Dic43—42no—
157C22⋊Dic43—42no—
158C4⋊Dic43—22no—
159C4⋊Dic43—22no—
160Dic43⋊C4—42no—
161Dic43⋊C4—42no—
162C4×Dic43—42no—
163C4×Dic43—41no—
164C4×Dic43—41no—
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
178Q8×C43—44no—
179Q8×C43—44no—
180Q8×C43—82no—
181Q8×C43—82no—
182D4×C43—28no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—24no—
186C2×C4×C43—22no—
187C2×C4×C43—21no—
188C2×C4×C43—24no—
189C2×C4×C43—24no—
190C2×C4×C43—21no—
191C2×C4×C43—42no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—81no—
197C2×C4×C43—82no—
198C2×C4×C43—82no—
199C2×C4×C43—82no—
200C2×C4×C43—82no—
201C2×C4×C43#12011yescharacteristic
202C2×C4×C43#12011yescharacteristic
203C2×C4×C43#13712yes—
204C2×C4×C43C22×D412yes—
205C2×Dic43—22no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216C2×Dic43—41no—
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—41no—
238C4×C43—44no—
239C4×C43—41no—
240C4×C43—44no—
241C4×C43#45812yes—
242Dic43—42no—
243Dic43—81no—
244Dic43—81no—
245Dic43—81no—
246#3501D4311yescharacteristic
247#3095—432no—
248#2395—431no—
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—24no—
263#554—22no—
264D4×Q8—22no—
265#544C2×D4312yes—
266#543—21no—
267#543C2×D4312yes—
268#533—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8C2×D4312yes—
271#518—21no—
272C2×C4×D4C2×D4311yescharacteristic
273C2×#117—431no—
274#485—864no—
275#484—434no—
276#483—434no—
277#428—862no—
278#419—862no—
279#407—432no—
280#400—431no—
281#399—431no—
282#398—431no—
283#397—431no—
284#397—861no—
285#394—861no—
286C4×C4⋊C4—861no—
287C4×C22⋊C4—431no—
288C4×C22⋊C4—861no—
289#328—434no—
290#328—434no—
291#324—432no—
292#323—432no—
293C43#1817411yescharacteristic, complemented, Sylow
294C22×Q8—21no—
295C22×Q8C22⋊D4312yes—
296C22×D4C22⋊D4311yescharacteristic
297C23×C4C22⋊D4311yescharacteristic
298C23×C4C22×D4311yescharacteristic
299C2×M16—862no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—24no—
303#125—22no—
304#125—24no—
305C22⋊Q8—22no—
306C22⋊Q8—22no—
307C22⋊Q8—24no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—24no—
315C22⋊Q8C22⋊D4314yes—
316C22⋊Q8C22×D4314yes—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×D4—24no—
320C4×D4—24no—
321C4×D4—22no—
322C4×D4—22no—
323#117—22no—
324#117—862no—
325#117—862no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—431no—
330C2×C4⋊C4—431no—
331C2×C4⋊C4—861no—
332C2×C4⋊C4—861no—
333C2×C4⋊C4C22⋊D4312yes—
334C2×C4⋊C4C22×D4311yescharacteristic
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—861no—
341C2×C22⋊C4C22⋊D4311yescharacteristic
342C2×C22⋊C4C22×D4311yescharacteristic
343C2×C42—861no—
344C2×C42—861no—
345C2×C42C22⋊D4311yescharacteristic
346#107—864no—
347#106—864no—
348#103—864no—
349#103—864no—
350C22⋊C8—434no—
351C22⋊C8—862no—
352#95—431no—
353#95—431no—
354#95—861no—
355#95—861no—
356#95—861no—
357#95—861no—
358C24C2×C22⋊D4311yescharacteristic
359C24C2×C22⋊D4311yescharacteristic
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—44no—
364C2×Q8—82no—
365C2×Q8C2×C22⋊D4314yes—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—861no—
380C22×C4—861no—
381C22×C4C2×C22⋊D4311yescharacteristic
382C22×C4C2×C22⋊D4312yes—
383C22×C4C2×C22⋊D4311yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385C22×C4C2×C22⋊D4311yescharacteristic
386C22×C4C2×C22⋊D4312yes—
387C22×C4C23×D4311yescharacteristic
388M16—1724no—
389C2×C8—864no—
390C4⋊C4—22no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—24no—
399C4⋊C4—22no—
400C4⋊C4—862no—
401C4⋊C4—862no—
402C4⋊C4—1722no—
403C4⋊C4—1722no—
404C4⋊C4C2×C22⋊D4314yes—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—24no—
409C22⋊C4—22no—
410C22⋊C4—1722no—
411C22⋊C4—1722no—
412C22⋊C4—1722no—
413C22⋊C4—1722no—
414C42—24no—
415C42—21no—
416C42—21no—
417C42—1722no—
418C42—1721no—
419C42—1721no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23#1306329412yes—
429C23#1306335612yes—
430C23C22×C22⋊D4311yescharacteristic
431Q8—44no—
432Q8—44no—
433Q8—82no—
434Q8—82no—
435D4—28no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—21no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—81no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—862no—
455C2×C4—1721no—
456C2×C4—1721no—
457C2×C4—1721no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4#1306329411yescharacteristic
467C2×C4#1306329411yescharacteristic
468C2×C4#1306335612yes—
469C2×C4C22×C22⋊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×#1306329411yescharacteristic
484C22C2×#1306335611yescharacteristic
485C22C2×#1306335611yescharacteristic
486C4—22no—
487C4—21no—
488C4—22no—
489C4—41no—
490C4—44no—
491C4—41no—
492C4—44no—
493C4—3441no—
494C4—3441no—
495C4—3441no—
496C4—1722no—
497C4#1458308912yes—
498C2—21no—
499C2—21no—
500C2—42no—
501C2—42no—
502C2#1914382911yescharacteristic
503C2#1914394411yescharacteristic
504C2C2×#1458308911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3501C2
socleC22×C43C2×#120
prime radicalC22×D4×C43D4
hypercenter#3501D43
hypocenterC43#18174
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #19144539C2semidirect
3. #19133637C2semidirect
4. #19133620C2semidirect
5. #19133603C2semidirect
6. #19133586C2semidirect
7. #19133115C2semidirect
293. C43#18174semidirect

Maximal subgroups

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

subgroupindex
#191445392
#191378542
#191336372
#191336202
#191336032
#191335862
#191331152
#191329332
C43×#35012
#1817443