Finite Group Databasebeta

← #25138085

Subgroups — #25138085

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144411C211yesmaximal, characteristic
2C2×#14583185C211yesmaximal, characteristic, complemented
3C4×#13063358C211yesmaximal, characteristic
4#19143260C211yesmaximal, characteristic
5#19136042C212yesmaximal
6#19135896C212yesmaximal
7#19135584C211yesmaximal, characteristic, complemented
8#19135376C212yesmaximal, complemented
9#19135251C212yesmaximal, complemented
10#19134588C211yesmaximal, characteristic, complemented
11C43×#1950C211yesmaximal, characteristic, complemented
12C2×#13063358C2211yescharacteristic
13C2×#13063325C2211yescharacteristic
14C4×#10621898C2211yescharacteristic
15C2×C4×Dic86C2211yescharacteristic
16#14583195—21no—
17#14583190—21no—
18#14583185—21no—
19#14583185—21no—
20#14583185—21no—
21#14583185—22no—
22#14583180—21no—
23#14583007—21no—
24#14583001—21no—
25C4×Dic172—21no—
26C4×#10621873—21no—
27#14582959—22no—
28#14582955—21no—
29#14582951—21no—
30#14582941C2212yes—
31#14582941C2211yescharacteristic
32C2×#13063257C2212yes—
33#14582923C2211yescharacteristic
34#14582909C2211yescharacteristic
35#14582901C2211yescharacteristic
36#14582901C2212yes—
37C2×#13063250C2212yes—
38C2×#13063243C2212yes—
39#14582865C2212yes—
40#14582854C2212yes—
41#14582667C2212yes—
42#14582667C2212yes—
43#14582667C2212yes—
44C2×#108×C43C2212yes—
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×#341C2212yes—
49C2×#10621898C2311yescharacteristic
50C22×Dic86—21no—
51C22×Dic86C2311yescharacteristic
52#13063358—22no—
53#13063358—22no—
54C2×Dic172—21no—
55C2×#10621873—21no—
56C2×#10621877C2312yes—
57#13063325—21no—
58#13063325—21no—
59#13063325—21no—
60#13063325—21no—
61C4×Dic86—21no—
62C4×Dic86—21no—
63C4×Dic86—21no—
64C4×Dic86—21no—
65C4×Dic86D411yescharacteristic
66C4×Dic86D411yescharacteristic
67C4×D172D411yescharacteristic
68C4×D172D411yescharacteristic
69C4×C22⋊D43—21no—
70C4×C22⋊D43—21no—
71#13063284C2311yescharacteristic
72#13063282—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2312yes—
76C2×Dic43⋊C4—21no—
77C2×C4×Dic43—21no—
78C42×D43—21no—
79#13063259—22no—
80#13063259—21no—
81#13063257—22no—
82#13063257—22no—
83#13063257—22no—
84#13063257—21no—
85C4⋊(C43⋊C8)—21no—
86C4⋊(C43⋊C8)—21no—
87#13063250—22no—
88#13063250—21no—
89#13063250—22no—
90#13063250—22no—
91#13063250—21no—
92#13063250—21no—
93#13063247—22no—
94#13063247—21no—
95#13063243—24no—
96(C2×D43)⋊C8—22no—
97(C2×D43)⋊C8—22no—
98#13063235—22no—
99C8×Dic43—22no—
100C2×M16×C43C2312yes—
101C2×M16×C43C2311yescharacteristic
102C2×M16×C43C2311yescharacteristic
103C22×C8×C43C2312yes—
104C2×C42×C43C2311yescharacteristic
105#108×C43—24no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43D411yescharacteristic
109C4⋊C8×C43D411yescharacteristic
110C4⋊C8×C43D412yes—
111#97×C43—21no—
112C4×C8×C43—21no—
113C22×C4×C43#4111yescharacteristic
114C22×C4×C43#4111yescharacteristic
115C22×C4×C43C2411yescharacteristic
116C2×C22⋊D43—21no—
117C22×Dic43—21no—
118C22×Dic43—21no—
119C22×Dic43—22no—
120#10621898—21no—
121#10621898—21no—
122#10621898—21no—
123#10621898—21no—
124C2×D172C2×D411yescharacteristic
125C2×C4×D43—21no—
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×Dic86—21no—
129C2×Dic86—21no—
130C2×Dic86—21no—
131C2×Dic86—21no—
132C2×Dic86—21no—
133C2×Dic86—41no—
134C2×Dic86—41no—
135C2×Dic86—82no—
136C2×Dic86C2×D411yescharacteristic
137C2×Dic86#4112yes—
138M16×C43—21no—
139M16×C43—22no—
140M16×C43—22no—
141M16×C43—21no—
142M16×C43—21no—
143M16×C43#4112yes—
144C2×C8×C43—21no—
145C2×C8×C43—22no—
146C2×C8×C43—22no—
147C2×C8×C43—21no—
148C2×C8×C43—22no—
149C2×C8×C43C2×D412yes—
150C2×C8×C43C2×D412yes—
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C22⋊Dic43—21no—
156(C2×D43)⋊C4—21no—
157(C2×D43)⋊C4—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—22no—
160C4⋊Dic43—22no—
161C4⋊Dic43—21no—
162C4⋊Dic43—41no—
163C4⋊Dic43—41no—
164C4⋊Dic43C2×D411yescharacteristic
165C4⋊Dic43C2×D411yescharacteristic
166Dic43⋊C4—21no—
167Dic43⋊C4—21no—
168Dic43⋊C4—41no—
169Dic43⋊C4—41no—
170C4×Dic43—21no—
171C4×Dic43—21no—
172C4×Dic43—21no—
173C4×Dic43—41no—
174C4×Dic43—41no—
175#10621877—22no—
176#10621877—22no—
177C2×C43⋊C8—22no—
178Dic172—24no—
179#10621873—24no—
180C23×C43C2×#4111yescharacteristic
181C22×D43—21no—
182C2×C4×C43—22no—
183C2×C4×C43—41no—
184C2×C4×C43#12111yescharacteristic
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43C22×D411yescharacteristic
189C2×C4×C43C22×D411yescharacteristic
190C2×C4×C43C2×#4111yescharacteristic
191C2×C4×C43C2×#4111yescharacteristic
192C2×C4×C432−1+411yescharacteristic
193C2×C4×C432−1+411yescharacteristic
194C22⋊D43—41no—
195C22⋊D43—41no—
196C2×Dic43—21no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—22no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—41no—
203C2×Dic43—42no—
204C2×Dic43—82no—
205C2×Dic43—81no—
206D172—21no—
207D172—21no—
208C4×D43—41no—
209C4×D43—41no—
210C4×D43—42no—
211C4×D43—81no—
212Dic86—22no—
213Dic86—21no—
214Dic86—21no—
215Dic86—22no—
216Dic86—41no—
217Dic86—41no—
218Dic86—82no—
219Dic86—82no—
220C8×C43—22no—
221C8×C43—22no—
222C8×C43—22no—
223C8×C43—42no—
224C8×C43—41no—
225C43⋊C8—42no—
226#24723—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43C2×#12111yescharacteristic
230C22×C43#55211yescharacteristic
231C22×C43#55611yescharacteristic
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—41no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43#47112yes—
239C4×C43#52511yescharacteristic
240C4×C43#53611yescharacteristic
241C4×C43#54711yescharacteristic
242C4×C43#54811yescharacteristic
243Dic43—42no—
244Dic43—41no—
245Dic43—41no—
246Dic43—41no—
247Dic43—82no—
248Dic43—81no—
249#3079—431no—
250C2×#475—431no—
251C4×#137—431no—
252#2925—431no—
253#2079—432no—
254#2052—432no—
255#1997—431no—
256#1951—432no—
257#1950D4311yescharacteristic, complemented
258#1930—432no—
259#1801—431no—
260C2×C43—21no—
261C2×C43—21no—
262C2×C43#241511yescharacteristic
263C2×C43C2×#47111yescharacteristic
264C2×C43#306911yescharacteristic
265D43—81no—
266C2×#137—431no—
267C2×C4⋊Q8—431no—
268C4×#41—431no—
269C2×C4×Q8—431no—
270#477—861no—
271#476—861no—
272#475—861no—
273#475—861no—
274#475—861no—
275#475—862no—
276#474—861no—
277#441—861no—
278#440—861no—
279C4×Q16—861no—
280C4×SD16—861no—
281#433—862no—
282#432—861no—
283#431—861no—
284C2×#108C2×D4312yes—
285#428—432no—
286#428—431no—
287C2×#106—432no—
288#423—431no—
289#423C2×D4311yescharacteristic
290C2×C4⋊C8C2×D4311yescharacteristic
291#419—431no—
292#417—432no—
293#417—431no—
294C2×#103—432no—
295C2×#101—432no—
296#408—432no—
297#405—432no—
298C4×M16C2×D4311yescharacteristic
299#343—432no—
300#343—432no—
301#343—432no—
302#341C2×D4312yes—
303C43#2472311yescharacteristic, complemented, Sylow
304C2×#41—431no—
305C22×Q8—431no—
306C22×Q8—861no—
307#137—862no—
308#137—862no—
309C2×Q16—861no—
310C2×SD16—861no—
311C2×M16—432no—
312C2×M16C22×D4311yescharacteristic
313C2×M16C22×D4312yes—
314C2×M16C22×D4311yescharacteristic
315C22×C8C22×D4312yes—
316C4⋊Q8—861no—
317C4⋊Q8—861no—
318C4⋊Q8—861no—
319C4⋊Q8—861no—
320C4×Q8—431no—
321C4×Q8—431no—
322C4×Q8—861no—
323C4×Q8—861no—
324C4×Q8—861no—
325C4×Q8—861no—
326C4×D4—431no—
327C4×D4—431no—
328C4×D4—861no—
329C4×D4—861no—
330#117—431no—
331#117—861no—
332C2×C4⋊C4—431no—
333C2×C4⋊C4—432no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4—861no—
336C2×C42—861no—
337C2×C42—861no—
338C2×C42C22×D4311yescharacteristic
339#108—24no—
340#107—861no—
341#107—862no—
342#106—861no—
343#106—862no—
344#106—862no—
345#106—862no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—861no—
349C4⋊C8—861no—
350C4⋊C8D17211yescharacteristic
351C4⋊C8D17211yescharacteristic
352C4⋊C8D17212yes—
353#103—861no—
354#103—861no—
355#103—861no—
356#103—862no—
357#103—862no—
358#103—862no—
359#102—861no—
360#102—862no—
361#101—864no—
362C22⋊C8—862no—
363C22⋊C8—862no—
364#97—21no—
365#97—862no—
366C4×C8—21no—
367C4×C8—862no—
368#41—861no—
369#41—861no—
370#41—861no—
371#41—861no—
372C2×Q8—431no—
373C2×Q8—432no—
374C2×Q8—861no—
375C2×Q8—861no—
376C2×Q8—861no—
377C2×Q8—861no—
378C2×Q8—861no—
379C2×Q8—3442no—
380C2×Q8—1721no—
381C2×Q8—1721no—
382C2×D4—431no—
383C2×D4—861no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—862no—
390C22×C4#1062190211yescharacteristic
391C22×C4#1062190211yescharacteristic
392C22×C4C23×D4311yescharacteristic
393Q16—864no—
394SD16—864no—
395M16—21no—
396M16—22no—
397M16—22no—
398M16—21no—
399M16—21no—
400M16—862no—
401M16—862no—
402M16#1062190012yes—
403C2×C8—21no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—21no—
407C2×C8—22no—
408C2×C8—862no—
409C2×C8C2×D17212yes—
410C2×C8C2×D17212yes—
411C4⋊C4—431no—
412C4⋊C4—431no—
413C4⋊C4—861no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—862no—
417C4⋊C4—862no—
418C4⋊C4—861no—
419C4⋊C4—1721no—
420C4⋊C4—1721no—
421C4⋊C4—1721no—
422C4⋊C4—1721no—
423C22⋊C4—861no—
424C22⋊C4—861no—
425C22⋊C4—861no—
426C42—861no—
427C42—861no—
428C42—861no—
429C42—1721no—
430C42—1721no—
431C42C2×D17211yescharacteristic
432C42C2×D17211yescharacteristic
433C42D4×D4311yescharacteristic
434C42D4×D4311yescharacteristic
435C23—861no—
436C23C2×#1062190211yescharacteristic
437Q8—862no—
438Q8—862no—
439Q8—861no—
440Q8—861no—
441Q8—3442no—
442Q8—3442no—
443Q8—1721no—
444Q8—1721no—
445D4—861no—
446D4—861no—
447D4—1721no—
448D4—1721no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—862no—
452C2×C4—861no—
453C2×C4—861no—
454C2×C4—861no—
455C2×C4—3441no—
456C2×C4—3442no—
457C2×C4—3441no—
458C2×C4—1721no—
459C2×C4—1722no—
460C2×C4—1721no—
461C2×C4—1721no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1722no—
465C2×C4#1306330011yescharacteristic
466C2×C4#1306330011yescharacteristic
467C2×C4#1306330011yescharacteristic
468C2×C4#1306330011yescharacteristic
469C2×C4C2×D4×D4311yescharacteristic
470C2×C4C22×D17211yescharacteristic
471C2×C4#41×D4311yescharacteristic
472C2×C4C2×#1062190011yescharacteristic
473C2×C4#1306337211yescharacteristic
474C2×C4#1306337311yescharacteristic
475C8—22no—
476C8—22no—
477C8—22no—
478C8—42no—
479C8—41no—
480C8—1722no—
481C22—21no—
482C22—21no—
483C22—1721no—
484C22—1721no—
485C22—1721no—
486C22C2×#1306330011yescharacteristic
487C22#1458358711yescharacteristic
488C22#1458362311yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—3442no—
493C4—3441no—
494C4—1721no—
495C4—1721no—
496C4—1721no—
497C4—1722no—
498C4#1458316312yes—
499C4#1458340911yescharacteristic
500C4#1458347211yescharacteristic
501C4#1458355311yescharacteristic
502C4#1458356111yescharacteristic
503C2—21no—
504C2—21no—
505C2—3441no—
506C2#1913802211yescharacteristic
507C2C2×#1458316311yescharacteristic
508C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1950C2
socleC22×C43C2×#121
prime radicalC2×#10621898C23
hypercenter#1950D43
hypocenterC43#24723
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. C2×#14583185C2semidirect
7. #19135584C2semidirect
8. #19135376C2semidirect
9. #19135251C2semidirect
10. #19134588C2semidirect
11. C43×#1950C2semidirect
257. #1950D43semidirect
303. C43#24723semidirect

Maximal subgroups

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

subgroupindex
#191444112
C2×#145831852
C4×#130633582
#191432602
#191360422
#191358962
#191355842
#191353762
#191352512
#191345882
C43×#19502
#2472343