Finite Group Databasebeta

← #11865735

Subgroups — #11865735

Order 1152.

1488 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#135C211yesmaximal, characteristic, complemented
2#10596303C211yesmaximal, characteristic, complemented
3#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#64159C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10592884C211yesmaximal, characteristic, complemented
7#10592881C211yesmaximal, characteristic, complemented
8#10592865C211yesmaximal, characteristic, complemented
9#10592864C211yesmaximal, characteristic, complemented
10#10592862C211yesmaximal, characteristic, complemented
11#10592861C211yesmaximal, characteristic, complemented
12#10592852C211yesmaximal, characteristic, complemented
13#10592849C211yesmaximal, characteristic, complemented
14#10592812C211yesmaximal, characteristic, complemented
15C2×#63641C211yesmaximal, characteristic, complemented
16#83900—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C32×#135—24no—
21C2×C32×Q16C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic
24C2×C32×D8C2211yescharacteristic
25C22×C32×C8C2211yescharacteristic
26#64159—24no—
27#64156C2211yescharacteristic
28Q8×C3⋊Dic3C2211yescharacteristic
29Q8×C3⋊Dic3C2211yescharacteristic
30#64153C2211yescharacteristic
31C2×#3756C2211yescharacteristic
32C2×#3755C2211yescharacteristic
33#64149C2211yescharacteristic
34#64148—21no—
35#64148—21no—
36#64145C2211yescharacteristic
37D4×C3⋊Dic3—21no—
38D4×C3⋊Dic3—21no—
39D4×C3⋊Dic3C2211yescharacteristic
40D4×C3⋊Dic3C2211yescharacteristic
41C2×#3754C2211yescharacteristic
42C2×#3753C2211yescharacteristic
43C4×#638—21no—
44C4×#638—21no—
45#64135—21no—
46#64135C2211yescharacteristic
47C2×C4×C3⋊Dic3—21no—
48C2×C4×C3⋊Dic3C2211yescharacteristic
49C22×C3⋊(C3⋊C8)C2211yescharacteristic
50#63662C2211yescharacteristic
51#63662C2211yescharacteristic
52#63659C2211yescharacteristic
53#63659C2211yescharacteristic
54#63648C2211yescharacteristic
55#63648C2211yescharacteristic
56#63643C2211yescharacteristic
57#63643C2211yescharacteristic
58#63641C2211yescharacteristic
59#63641C2211yescharacteristic
60#63641C2211yescharacteristic
61#63641C2211yescharacteristic
62C2×C3×#135D314yescomplemented
63#5832—34no—
64Dic3×#41—34no—
65C2×#950—34no—
66#5233—34no—
67#5185—34no—
68#5182—34no—
69#5166—34no—
70#5165—34no—
71#5163—34no—
72#5162—34no—
73#5153—34no—
74#5150—34no—
75#5113—34no—
76C2×Dic3⋊C8—34no—
77C32×#41—22no—
78C32×#41—22no—
79C32×#41—22no—
80C32×#41D414yescomplemented
81C2×C32×Q8C2311yescharacteristic
82C2×C32×Q8C2311yescharacteristic
83C2×C32×D4—21no—
84C2×C32×D4—21no—
85C2×C32×D4C2311yescharacteristic
86C2×C32×D4C2311yescharacteristic
87C22×C32×C4—21no—
88C22×C32×C4—21no—
89C22×C32×C4C2311yescharacteristic
90C2×#638—21no—
91C2×#638—21no—
92C2×#638—21no—
93C22×C3⋊Dic3—21no—
94C22×C3⋊Dic3—21no—
95C22×C3⋊Dic3D411yescharacteristic
96C22×C3⋊Dic3D411yescharacteristic
97#3828—22no—
98#3828—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C32×Q16—22no—
103C32×SD16—22no—
104C32×SD16—22no—
105C32×D8—22no—
106C2×C32×C8—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109#3757—21no—
110#3757—21no—
111#3757—21no—
112#3757—21no—
113#3757—21no—
114#3756—22no—
115#3755—22no—
116#3754—22no—
117#3753—22no—
118#3752—21no—
119#3752—21no—
120C4⋊(C3⋊Dic3)—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3750—21no—
125#3750—21no—
126C4×C3⋊Dic3—21no—
127C4×C3⋊Dic3—21no—
128C4×C3⋊Dic3—21no—
129C4×C3⋊Dic3D411yescharacteristic
130C4×C3⋊Dic3D411yescharacteristic
131C4×C3⋊Dic3C2311yescharacteristic
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)—22no—
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136#3035—91noSylow
137C2×C3×#41C2×D314yes—
138C2×C3×#41C2×D314yes—
139C2×#235—34no—
140C3×#135—216no—
141C2×C3×Q16C2×D314yes—
142C2×C3×SD16C2×D314yes—
143C2×C3×SD16C2×D314yes—
144C2×C3×D8C2×D314yes—
145C22×C3×C8C2×D314yes—
146#950—616no—
147#947—34no—
148Q8×Dic3—34no—
149Q8×Dic3—34no—
150#944—34no—
151C2×#216—34no—
152C2×#215—34no—
153#940—34no—
154#939—64no—
155#939—64no—
156#936—34no—
157D4×Dic3—34no—
158D4×Dic3—34no—
159D4×Dic3—64no—
160D4×Dic3—64no—
161C2×#214—34no—
162C2×#213—34no—
163C4×#67—64no—
164C4×#67—64no—
165#926—34no—
166#926—64no—
167C2×C4×Dic3—34no—
168C2×C4×Dic3—64no—
169C22×C3⋊C8—34no—
170#835—34no—
171#835—34no—
172#832—34no—
173#832—34no—
174#821—34no—
175#821—34no—
176#816—34no—
177#816—34no—
178Dic3⋊C8—34no—
179Dic3⋊C8—34no—
180Dic3⋊C8—34no—
181Dic3⋊C8—34no—
182C23×C32—21no—
183C23×C32—21no—
184C23×C32C2×D411yescharacteristic
185C22×C3⋊D3—21no—
186C32×Q8—21no—
187C32×Q8—21no—
188C32×Q8—21no—
189C32×Q8C2×D412yes—
190C32×D4—24no—
191C32×D4—21no—
192C32×D4—21no—
193C32×D4—21no—
194C32×D4—42no—
195C32×D4C2×D412yes—
196C2×C32×C4—21no—
197C2×C32×C4—24no—
198C2×C32×C4—21no—
199C2×C32×C4—42no—
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2×D412yes—
202C2×C32×C4#4112yes—
203C2×C32×C4C2411yescharacteristic
204#638—42no—
205#638—42no—
206#638—42no—
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—41no—
212C2×C3⋊Dic3—42no—
213C2×C3⋊Dic3—42no—
214C2×C3⋊Dic3C2×D411yescharacteristic
215C2×C3⋊Dic3C2×D411yescharacteristic
216C2×C3⋊Dic3C2×D411yescharacteristic
217C2×C3⋊Dic3C2×D411yescharacteristic
218C4⋊(C3⋊D3)—21no—
219C4⋊(C3⋊D3)—21no—
220C4×C3⋊D3—42no—
221#634—21no—
222#634—21no—
223C32×C8—21no—
224C32×C8—21no—
225C3⋊(C3⋊C8)—21no—
226C3⋊(C3⋊C8)—21no—
227C2×#135—91no—
228C2×#135C3⋊D311yescharacteristic, complemented
229#532—91no—
230C4×#41—91no—
231#464—91no—
232#464—91no—
233#463—91no—
234#463—91no—
235#462—91no—
236#461—91no—
237#460—91no—
238#459—91no—
239C2×C4⋊C8—91no—
240#416—91no—
241#416—91no—
242C3×#41—28no—
243C3×#41—28no—
244C3×#41—28no—
245C3×#41#67116yescomplemented
246C2×C3×Q8C22×D314yes—
247C2×C3×Q8C22×D314yes—
248C2×C3×D4—24no—
249C2×C3×D4—24no—
250C2×C3×D4C22×D314yes—
251C2×C3×D4C22×D314yes—
252C22×C3×C4—24no—
253C22×C3×C4—24no—
254C22×C3×C4C22×D314yes—
255C2×#67—64no—
256C2×#67—64no—
257C2×#67—64no—
258C22×Dic3—34no—
259C22×Dic3—34no—
260C22×Dic3—64no—
261C22×Dic3—64no—
262#235—68no—
263#235—68no—
264C2×D12—34no—
265C2×C4×D3—64no—
266C2×Dic6—34no—
267C3×Q16—28no—
268C3×SD16—28no—
269C3×SD16—28no—
270C3×D8—28no—
271C2×C3×C8—28no—
272C2×C3×C8C22×D314yes—
273C2×C3×C8C22×D314yes—
274#217—64no—
275#217—64no—
276#217—64no—
277#217—64no—
278#217—64no—
279#216—68no—
280#215—68no—
281#214—68no—
282#213—68no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285C4⋊Dic3—34no—
286C4⋊Dic3—34no—
287C4⋊Dic3—64no—
288C4⋊Dic3—64no—
289Dic3⋊C4—64no—
290Dic3⋊C4—64no—
291C4×Dic3—34no—
292C4×Dic3—34no—
293C4×Dic3—34no—
294C4×Dic3—34no—
295C4×Dic3—64no—
296C4×Dic3—64no—
297C4×Dic3—64no—
298C2×C3⋊C8—34no—
299C2×C3⋊C8—34no—
300C2×C3⋊C8—68no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—22no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32#12112yes—
310C22×C32C22×D411yescharacteristic
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C32×C4—22no—
315C32×C4—41no—
316C32×C4#12112yes—
317C32×C4C22×D411yescharacteristic
318C32×C4C2×#4111yescharacteristic
319C3⋊Dic3—21no—
320C3⋊Dic3—21no—
321C3⋊Dic3—21no—
322C3⋊Dic3—41no—
323C3⋊Dic3—41no—
324C3⋊Dic3—41no—
325C3⋊Dic3#13512yescomplemented
326C2×#41—91no—
327C2×#41C2×C3⋊D311yescharacteristic
328C2×#41C2×C3⋊D311yescharacteristic
329#135—24no—
330#135—184no—
331C2×Q16—91no—
332C2×Q16C2×C3⋊D311yescharacteristic
333C2×SD16—91no—
334C2×SD16—91no—
335C2×SD16C2×C3⋊D311yescharacteristic
336C2×SD16C2×C3⋊D311yescharacteristic
337C2×D8—91no—
338C2×D8C2×C3⋊D311yescharacteristic
339C22×C8—91no—
340C22×C8C2×C3⋊D311yescharacteristic
341C4⋊Q8—91no—
342#127—91no—
343#124—91no—
344#124—91no—
345#121—181no—
346#121—181no—
347C4×Q8—91no—
348C4×Q8—91no—
349C4×D4—91no—
350C4×D4—91no—
351C4×D4—181no—
352C4×D4—181no—
353C4×D4—181no—
354C4×D4—181no—
355#117—91no—
356#117—181no—
357C2×C42—91no—
358C2×C42—181no—
359C4⋊C8—91no—
360C4⋊C8—91no—
361C4⋊C8—91no—
362C4⋊C8—91no—
363#103—91no—
364#103—91no—
365#103—91no—
366#103—91no—
367#102—91no—
368#102—91no—
369#102—91no—
370#102—91no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3D3×D414yes—
374C22×D3—64no—
375C3×Q8—24no—
376C3×Q8—24no—
377C3×Q8—24no—
378C3×Q8C2×#6718yes—
379C3×D4—216no—
380C3×D4—24no—
381C3×D4—24no—
382C3×D4—24no—
383C3×D4—48no—
384C3×D4C2×#6718yes—
385C2×C3×C4—24no—
386C2×C3×C4—216no—
387C2×C3×C4—24no—
388C2×C3×C4—48no—
389C2×C3×C4D3×D414yes—
390C2×C3×C4#23718yes—
391C2×C3×C4C2×#6718yes—
392C2×C3×C4C23×D314yes—
393#67—128no—
394#67—128no—
395#67—128no—
396C2×Dic3—34no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—68no—
401C2×Dic3—64no—
402C2×Dic3—64no—
403C2×Dic3—64no—
404C2×Dic3—128no—
405C2×Dic3—124no—
406C2×Dic3—128no—
407D12—64no—
408D12—64no—
409C4×D3—128no—
410Dic6—64no—
411Dic6—64no—
412C3×C8—24no—
413C3×C8—24no—
414C3⋊C8—64no—
415C3⋊C8—64no—
416C2×C32—22no—
417C2×C32—42no—
418C2×C32—81no—
419C2×C32C2×#12111yescharacteristic
420C2×C32C2×#13511yescharacteristic
421C2×C32#57511yescharacteristic
422C3⋊D3—81no—
423#41—22no—
424#41—22no—
425#41—22no—
426#41—182no—
427#41—182no—
428#41#63814yescomplemented
429C2×Q8—91no—
430C2×Q8C22×C3⋊D311yescharacteristic
431C2×Q8C22×C3⋊D311yescharacteristic
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—91no—
435C2×D4—181no—
436C2×D4—181no—
437C2×D4—181no—
438C2×D4C22×C3⋊D311yescharacteristic
439C2×D4C22×C3⋊D311yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—181no—
445C22×C4—181no—
446C22×C4—181no—
447C22×C4C22×C3⋊D311yescharacteristic
448Q16—22no—
449Q16—182no—
450SD16—22no—
451SD16—22no—
452SD16—182no—
453SD16—182no—
454D8—22no—
455D8—182no—
456C2×C8—22no—
457C2×C8—91no—
458C2×C8—91no—
459C2×C8—182no—
460C2×C8C22×C3⋊D311yescharacteristic
461C2×C8C22×C3⋊D311yescharacteristic
462C4⋊C4—91no—
463C4⋊C4—91no—
464C4⋊C4—181no—
465C4⋊C4—181no—
466C4⋊C4—181no—
467C4⋊C4—181no—
468C22⋊C4—181no—
469C22⋊C4—181no—
470C22⋊C4—181no—
471C22⋊C4—181no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C42—91no—
476C42—91no—
477C42—91no—
478C42—91no—
479C42—181no—
480C42—181no—
481C42—181no—
482C22×C3—24no—
483C22×C3—24no—
484C22×C3—28no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3—44no—
488C22×C3—44no—
489C22×C3—44no—
490C22×C3#93918yes—
491C22×C3C2×D3×D414yes—
492C2×D3—124no—
493C2×D3—124no—
494C2×D3—124no—
495C3×C4—28no—
496C3×C4—44no—
497C3×C4#93918yes—
498C3×C4C2×#23714yes—
499C3×C4C22×#6714yes—
500Dic3—38no—
501Dic3—64no—
502Dic3—64no—
503Dic3—64no—
504Dic3—124no—
505Dic3—124no—
506Dic3—124no—
507C32#303511yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—181no—
511C23D4×C3⋊D311yescharacteristic
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—181no—
516Q8—181no—
517Q8C2×#63812yes—
518D4—24no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—42no—
523D4—181no—
524D4—181no—
525D4—362no—
526D4—362no—
527D4—362no—
528D4C2×#63812yes—
529C2×C4—21no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—42no—
533C2×C4—91no—
534C2×C4—91no—
535C2×C4—91no—
536C2×C4—91no—
537C2×C4—182no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—362no—
542C2×C4—361no—
543C2×C4—362no—
544C2×C4—362no—
545C2×C4D4×C3⋊D311yescharacteristic
546C2×C4#383012yes—
547C2×C4C2×#63812yes—
548C2×C4C23×C3⋊D311yescharacteristic
549C8—21no—
550C8—21no—
551C8—181no—
552C8—181no—
553C2×C3—28no—
554C2×C3—48no—
555C2×C3—84no—
556C2×C3D3×#13514yes—
557C2×C3#576814yes—
558C2×C3C2×#93914yes—
559D3—244no—
560C22—21no—
561C22—21no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—361no—
569C22—361no—
570C22—361no—
571C22#6414812yes—
572C22C2×D4×C3⋊D311yescharacteristic
573C4—22no—
574C4—41no—
575C4—92no—
576C4—181no—
577C4—181no—
578C4—181no—
579C4—361no—
580C4—361no—
581C4—361no—
582C4#6414812yes—
583C4C2×#383011yescharacteristic
584C4C22×#63811yescharacteristic
585C3#8390014yescomplemented
586C2—22no—
587C2—42no—
588C2—81no—
589C2—721no—
590C2C3⋊D3×#13511yescharacteristic
591C2#1059623911yescharacteristic
592C2C2×#6414811yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#135C2
socleC22×C32C22×D4
hypercenterC2×#135C3⋊D3
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C32×#135C2semidirect
2. #10596303C2semidirect
3. #41×C3⋊Dic3C2semidirect
4. C2×#64159C2semidirect
5. #10592932C2semidirect
6. #10592884C2semidirect
7. #10592881C2semidirect
8. #10592865C2semidirect
9. #10592864C2semidirect
10. #10592862C2semidirect
11. #10592861C2semidirect
12. #10592852C2semidirect
13. #10592849C2semidirect
14. #10592812C2semidirect
15. C2×#63641C2semidirect
62. C2×C3×#135D3semidirect
80. C32×#41D4semidirect
228. C2×#135C3⋊D3semidirect
245. C3×#41#67semidirect
325. C3⋊Dic3#135semidirect
428. #41#638semidirect
507. C32#3035semidirect
585. C3#83900semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1352
#105963032
#41×C3⋊Dic32
C2×#641592
#105929322
#105928842
#105928812
#105928652
#105928642
#105928622
#105928612
#105928522
#105928492
#105928122
C2×#636412
#839003