Finite Group Databasebeta

← #11874312

Subgroups — #11874312

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic, complemented
2#10595153C212yesmaximal, complemented
3C2×#63935C212yesmaximal, complemented
4C2×#63808C211yesmaximal, characteristic, complemented
5#10592850C211yesmaximal, characteristic, complemented
6C3×#5155C211yesmaximal, characteristic, complemented
7#10591492C212yesmaximal, complemented
8#10591473C212yesmaximal, complemented
9#10590905C211yesmaximal, characteristic, complemented
10#10590865C211yesmaximal, characteristic, complemented
11D3×C8×Dic3C211yesmaximal, characteristic, complemented
12#83903—31nomaximal
13#81820—31nomaximal
14C2×C3×#237C2212yes—
15C2×#3799C2212yes—
16C2×C32×D8C2211yescharacteristic
17#64149C2212yes—
18C2×#3753C2212yes—
19C2×#3745C2211yescharacteristic
20C3×#936C2212yes—
21C2×C3×#214C2212yes—
22C2×C3×#214C2212yes—
23C3×#912—24no—
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27#63971—24no—
28#63952—24no—
29#63935—28no—
30C4×D3×Dic3C2211yescharacteristic
31#63873C2212yes—
32#63864C2212yes—
33C2×#3718C2212yes—
34C2×#3717C2212yes—
35C2×#3717C2212yes—
36C2×D3×C3⋊C8C2211yescharacteristic
37#63808—24no—
38C8×C3⋊Dic3C2211yescharacteristic
39C3×C8×Dic3C2211yescharacteristic
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C2×C3×#135—31no—
43#5832—32no—
44C2×#950—32no—
45C2×#919—31no—
46C2×#916—32no—
47C2×#912D311yescharacteristic, complemented
48C2×#904—31no—
49#5668—32no—
50C3×#495—31no—
51#5191—31no—
52#5183—31no—
53#5183—31no—
54#5175—32no—
55#5175—32no—
56#5168—32no—
57#5155D311yescharacteristic, complemented
58#5151—31no—
59#5151—31no—
60#5151—61no—
61C2×C8×Dic3—31no—
62#5059—32no—
63#4696—31no—
64C4×D3×C8—31no—
65C2×C32×D4C2312yes—
66C2×#638—24no—
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C3×#67—22no—
69C22×C3×Dic3—22no—
70C3×#237—24no—
71C3×#237—24no—
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2312yes—
75C2×#626—22no—
76C2×#624—22no—
77C2×D3×Dic3D412yes—
78#3799—24no—
79#3799—24no—
80C32×D8—22no—
81C2×C32×C8C2311yescharacteristic
82#3753—24no—
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3745—22no—
86C3×#217—24no—
87C3×#214—24no—
88C3×#214—24no—
89C3×C4×Dic3C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C3×Dic12—22no—
93C3×Dic12—22no—
94C3×D3×C8D414yescomplemented
95#3724—24no—
96#3722—24no—
97Dic32D412yes—
98#3718—24no—
99#3717—24no—
100#3717—24no—
101D3×C3⋊C8D414yescomplemented
102#3147—91noSylow
103C2×C3×#41—32no—
104C2×#239—32no—
105C2×#237C2×D312yes—
106C2×#235—32no—
107C3×#135—64no—
108C2×C3×Q16—31no—
109C2×C3×Q16—31no—
110C2×C3×SD16—32no—
111C2×C3×SD16—32no—
112C2×C3×D8—21no—
113C2×C3×D8C2×D311yescharacteristic
114C2×C3×D8C2×D311yescharacteristic
115C22×C3×C8—31no—
116C3×#124—32no—
117#950—68no—
118#947—32no—
119#944—32no—
120#944—32no—
121C2×#216—32no—
122C2×#216—32no—
123C2×#215—32no—
124C2×#215—32no—
125#940—32no—
126#940—32no—
127#940—62no—
128#939—64no—
129#936C2×D312yes—
130C2×#214C2×D312yes—
131C2×#214C2×D312yes—
132C2×#213—32no—
133C2×#213—32no—
134C2×#213—62no—
135C4×#67—64no—
136C2×C4×Dic3—31no—
137C22×C3⋊C8—31no—
138#919—64no—
139#916—68no—
140#912—24no—
141C2×Dic12C2×D311yescharacteristic
142C2×Dic12C2×D311yescharacteristic
143#904—64no—
144C2×D24—31no—
145C2×D24—31no—
146C2×D24—61no—
147C2×#204—32no—
148C2×#204—32no—
149C2×D3×C8—31no—
150C2×D3×C8C2×D311yescharacteristic
151#884—64no—
152#67⋊C4—64no—
153#875—32no—
154C42×D3—31no—
155C3×C4×C8—31no—
156C8×Dic3—31no—
157C8×Dic3—31no—
158C8×Dic3—31no—
159C8×Dic3—31no—
160C8×Dic3—31no—
161C8×Dic3—61no—
162C8×Dic3C2×D311yescharacteristic
163C4×C3⋊C8—31no—
164C23×C32—22no—
165C22×C3⋊D3—22no—
166C22×C3×D3C2×D411yescharacteristic
167C32×D4—22no—
168C32×D4—22no—
169C2×C32×C4C2411yescharacteristic
170#638—48no—
171C2×C3⋊Dic3C2×D412yes—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—22no—
174C3×#67—44no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—44no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D411yescharacteristic
180C3×C4×D3C2×D412yes—
181C3×C4×D3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186#626—44no—
187#624—44no—
188D3×Dic3—24no—
189C32×C8C2×D412yes—
190C3⋊(C3⋊C8)C2×D412yes—
191C3×C3⋊C8C2×D412yes—
192C3×C3⋊C8C2×D412yes—
193C2×#135—31no—
194C2×#135—91no—
195C2×#135—92no—
196#532—92no—
197#495—31no—
198#495—91no—
199#495—92no—
200#494—91no—
201#493—91no—
202#492—92no—
203C2×C4×C8—91no—
204C3×#41—64no—
205C3×#41—64no—
206C2×C3×Q8—32no—
207C2×C3×Q8—32no—
208C2×C3×D4—22no—
209C2×C3×D4—62no—
210C2×C3×D4C22×D312yes—
211C2×C3×D4C22×D312yes—
212C22×C3×C4—31no—
213C22×C3×C4—62no—
214C2×#67—22no—
215C2×#67—62no—
216C2×#67—64no—
217C2×#67—64no—
218C2×#67—124no—
219C22×Dic3—22no—
220C22×Dic3—32no—
221#239—64no—
222#239—64no—
223#237—24no—
224#237—24no—
225#235—64no—
226#235—64no—
227C2×D12—32no—
228C2×D12—32no—
229C2×D12—62no—
230C2×D12—62no—
231C2×C4×D3—32no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3C22×D311yescharacteristic
235C2×Dic6C22×D312yes—
236C2×Dic6C22×D312yes—
237C3×Q16—62no—
238C3×Q16—62no—
239C3×SD16—64no—
240C3×SD16—64no—
241C3×D8—22no—
242C3×D8—22no—
243C3×D8—42no—
244C2×C3×C8—21no—
245C2×C3×C8—31no—
246C2×C3×C8—31no—
247C2×C3×C8—34no—
248C2×C3×C8C22×D311yescharacteristic
249C2×C3×C8C22×D311yescharacteristic
250C3×C22⋊C4—64no—
251C3×C42—31no—
252#217—24no—
253#216—64no—
254#216—64no—
255#215—64no—
256#215—64no—
257#214—24no—
258#214—24no—
259#213—64no—
260#213—64no—
261#213—124no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266C4×Dic3—31no—
267C4×Dic3—31no—
268C4×Dic3—32no—
269C4×Dic3—32no—
270C4×Dic3—61no—
271C4×Dic3C22×D311yescharacteristic
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—34no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278Dic12—22no—
279Dic12—22no—
280D24—62no—
281D24—62no—
282D24—122no—
283#204—64no—
284#204—64no—
285D3×C8—34no—
286D3×C8#6714yescomplemented
287C22×C32—42no—
288C22×C32—44no—
289C22×C32C22×D411yescharacteristic
290C2×C3⋊D3—42no—
291C2×C3⋊D3—44no—
292C2×C3×D3—22no—
293C2×C3×D3#12712yes—
294C32×C4C22×D411yescharacteristic
295C32×C4C22×D411yescharacteristic
296C3⋊Dic3#13514yescomplemented
297C3×Dic3—22no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C3×Dic3#12712yes—
301C2×#41—32no—
302C2×#41—92no—
303#135—64no—
304#135—184no—
305#135—188no—
306C2×Q16—31no—
307C2×Q16—31no—
308C2×Q16—92no—
309C2×SD16—32no—
310C2×SD16—32no—
311C2×SD16—92no—
312C2×SD16—92no—
313C2×D8—92no—
314C2×D8—91no—
315C2×D8D3211yescharacteristic
316C22×C8—31no—
317C22×C8—91no—
318C4⋊Q8—92no—
319#127—92no—
320#124—32no—
321#124—92no—
322#121—184no—
323C4×D4—184no—
324C2×C42—91no—
325C4×C8—31no—
326C4×C8—91no—
327C4×C8—91no—
328C4×C8—91no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—31no—
332C23×C3—42no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—122no—
336C22×D3D3×D411yescharacteristic
337C3×Q8—62no—
338C3×Q8—62no—
339C3×Q8—62no—
340C3×Q8—62no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—42no—
346C3×D4—42no—
347C3×D4—124no—
348C2×C3×C4—21no—
349C2×C3×C4—31no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—124no—
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—44no—
359#67—128no—
360#67—128no—
361#67—124no—
362#67—248no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—44no—
368C2×Dic3—62no—
369C2×Dic3—64no—
370C2×Dic3D3×D412yes—
371C2×Dic3D3×D411yescharacteristic
372D12—62no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—122no—
377D12—122no—
378D12—124no—
379C4×D3—64no—
380C4×D3—124no—
381C4×D3—124no—
382C4×D3D3×D412yes—
383C4×D3C2×#6712yes—
384Dic6—22no—
385Dic6—22no—
386Dic6—22no—
387Dic6—22no—
388C3×C8—22no—
389C3×C8—32no—
390C3×C8—32no—
391C3×C8D3×D412yes—
392C3×C8C2×#6712yes—
393C3⋊C8—32no—
394C3⋊C8—32no—
395C3⋊C8—62no—
396C3⋊C8D3×D412yes—
397C3⋊C8C2×#6712yes—
398C2×C32—82no—
399C2×C32C2×#12711yescharacteristic
400C2×C32C2×#13512yes—
401C3⋊D3—82no—
402C3×D3—22no—
403#41—64no—
404#41—64no—
405#41—184no—
406#41—184no—
407C2×Q8—32no—
408C2×Q8—32no—
409C2×D4—62no—
410C2×D4—92no—
411C2×D4—182no—
412C2×D4—184no—
413C2×D4C2×D3212yes—
414C22×C4—31no—
415C22×C4—62no—
416C22×C4—92no—
417C22×C4—182no—
418Q16—62no—
419Q16—62no—
420Q16—184no—
421SD16—64no—
422SD16—64no—
423SD16—184no—
424SD16—184no—
425D8—22no—
426D8—184no—
427D8—182no—
428C2×C8—31no—
429C2×C8—31no—
430C2×C8—34no—
431C2×C8—94no—
432C2×C8—91no—
433C2×C8C2×D3211yescharacteristic
434C4⋊C4—184no—
435C22⋊C4—64no—
436C22⋊C4—184no—
437C42—31no—
438C42—92no—
439C42—91no—
440C22×C3—21no—
441C22×C3—32no—
442C22×C3—42no—
443C22×C3—44no—
444C22×C3—44no—
445C22×C3—42no—
446C22×C3—62no—
447C22×C3—84no—
448C22×C3—82no—
449C22×C3C2×D3×D411yescharacteristic
450C22×C3C2×D3×D411yescharacteristic
451C2×D3—22no—
452C2×D3—122no—
453C2×D3—124no—
454C2×D3—124no—
455C2×D3—122no—
456C2×D3—242no—
457C2×D3—244no—
458C2×D3#94012yes—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—32no—
462C3×C4—62no—
463C3×C4—122no—
464C3×C4—122no—
465C3×C4C2×D3×D411yescharacteristic
466C3×C4C2×D3×D411yescharacteristic
467C3×C4C2×D3×D411yescharacteristic
468C3×C4C22×#6711yescharacteristic
469Dic3—22no—
470Dic3—34no—
471Dic3—34no—
472Dic3—42no—
473Dic3—42no—
474Dic3—64no—
475Dic3#94012yes—
476C32#314711yescharacteristic, complemented, Sylow
477C23—22no—
478C23—31no—
479C23—182no—
480Q8—62no—
481Q8—62no—
482Q8—62no—
483Q8—62no—
484D4—22no—
485D4—22no—
486D4—124no—
487D4—182no—
488D4—182no—
489D4—368no—
490D4—364no—
491C2×C4—31no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—92no—
498C2×C4—124no—
499C2×C4—184no—
500C2×C4—364no—
501C2×C4C22×D3211yescharacteristic
502C8—32no—
503C8—32no—
504C8—92no—
505C8D3×#6712yes—
506C2×C3—22no—
507C2×C3—21no—
508C2×C3—62no—
509C2×C3—82no—
510C2×C3—82no—
511C2×C3—162no—
512C2×C3D3×#12711yescharacteristic
513C2×C3D3×#13512yes—
514C2×C3D3×#13512yes—
515C2×C3C2×#94011yescharacteristic
516D3—22no—
517D3—242no—
518D3—242no—
519D3—482no—
520C22—32no—
521C22—44no—
522C22—42no—
523C22—62no—
524C22—364no—
525C22—362no—
526C22D32×D411yescharacteristic
527C4—32no—
528C4—62no—
529C4—94no—
530C4—122no—
531C4—122no—
532C4D32×D411yescharacteristic
533C4C2×D3×#6711yescharacteristic
534C3—21no—
535C3#8182011yescharacteristic, complemented
536C3#8390311yescharacteristic, complemented
537C2—62no—
538C2—82no—
539C2—722no—
540C2#1059473012yes—
541C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3147
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#912C2semidirect
2. #10595153C2semidirect
3. C2×#63935C2semidirect
4. C2×#63808C2semidirect
5. #10592850C2semidirect
6. C3×#5155C2semidirect
7. #10591492C2semidirect
8. #10591473C2semidirect
9. #10590905C2semidirect
10. #10590865C2semidirect
11. D3×C8×Dic3C2semidirect
47. C2×#912D3semidirect
57. #5155D3semidirect
94. C3×D3×C8D4semidirect
101. D3×C3⋊C8D4semidirect
286. D3×C8#67semidirect
296. C3⋊Dic3#135semidirect
476. C32#3147semidirect
535. C3#81820semidirect
536. C3#83903semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
#105951532
C2×#639352
C2×#638082
#105928502
C3×#51552
#105914922
#105914732
#105909052
#105908652
D3×C8×Dic32
#839033
#818203