Finite Group Databasebeta

← #11898263

Subgroups — #11898263

Order 1152.

990 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic, complemented
3#10592714C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591482C212yesmaximal, complemented
6#10591429C212yesmaximal, complemented
7#10590547C212yesmaximal, complemented
8#10590456C212yesmaximal, complemented
9#10590350C211yesmaximal, characteristic, complemented
10#10590347C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
12#83582—31nomaximal
13#79578—31nomaximal
14C2×C3×#235—21no—
15C2×#3799—21no—
16C32×C4×D4C2211yescharacteristic
17C2×#3753C2212yes—
18#64083C2211yescharacteristic
19C3×#940C2212yes—
20C2×C3×#213C2211yescharacteristic
21C3×#930—21no—
22C3×#893C2212yes—
23C3×#884—22no—
24C3×#874C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63911C2212yes—
28#63910—22no—
29#63909—21no—
30#63894C2212yes—
31C2×#3714C2212yes—
32C2×#3714C2212yes—
33C2×#3713C2212yes—
34#63636C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
36C3×#832C2211yescharacteristic
37C3×#809C2211yescharacteristic
38C3×#807C2211yescharacteristic
39C3×C4×C3⋊C8C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#550—31no—
44#5577—31no—
45#5553—31no—
46#5553D311yescharacteristic, complemented
47C3×C4×D8—31no—
48#5151—32no—
49#5073—32no—
50#5073—31no—
51#5072—31no—
52#5072—32no—
53Q8×C3⋊C8—31no—
54#5015—31no—
55#5015—31no—
56#5015—31no—
57#5015—32no—
58#5015—61no—
59C4×#213—32no—
60C4×#213D311yescharacteristic, complemented
61#4872—32no—
62#4786—32no—
63#4786—32no—
64#4695—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C3×#235—44no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6D411yescharacteristic
81C2×#626—22no—
82C2×#626—22no—
83C2×#624—22no—
84#3799—44no—
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42C2311yescharacteristic
88#3753—42no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#213—22no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—22no—
93C3×C4⋊Dic3D411yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4D412yes—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99#3722—22no—
100#3714—24no—
101#3714—42no—
102#3713—42no—
103#3391—91noSylow
104C2×C3×#41—61no—
105C2×#239—61no—
106C2×#235—21no—
107C2×#235—61no—
108C2×C3×D8—31no—
109C3×#127—32no—
110C3×#127—31no—
111C3×#121—62no—
112C3×#121—61no—
113C3×C4×Q8—31no—
114C3×C4×D4—21no—
115C3×C4×D4—32no—
116C3×C4×D4—31no—
117C3×C4×D4C2×D311yescharacteristic
118C3×C4×D4C2×D311yescharacteristic
119#940—32no—
120#940C2×D312yes—
121C2×#213—32no—
122C2×#213—32no—
123C2×#213—32no—
124C2×#213—32no—
125C2×#213—32no—
126C2×#213—32no—
127C2×#213—62no—
128C2×#213C2×D311yescharacteristic
129#930—21no—
130#930—61no—
131C2×D24—32no—
132C2×D24—32no—
133#895—62no—
134#895—61no—
135#893—32no—
136#893C2×D312yes—
137#884—22no—
138#884—62no—
139#874—32no—
140#874—31no—
141#874—31no—
142#874—61no—
143#874C2×D311yescharacteristic
144C4×D12—32no—
145C4×D12C2×D311yescharacteristic
146C4×Dic6C2×D311yescharacteristic
147C3×#107—31no—
148C3×#102—31no—
149C3×#102—31no—
150C3×C4×C8—31no—
151#832—32no—
152#832C2×D311yescharacteristic
153Dic3⋊C8—32no—
154C8×Dic3—32no—
155#809—32no—
156#809—32no—
157#809—32no—
158#809—62no—
159#809C2×D311yescharacteristic
160#807C2×D311yescharacteristic
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—31no—
163C4⋊(C3⋊C8)—32no—
164C4⋊(C3⋊C8)—61no—
165C4×C3⋊C8—32no—
166C4×C3⋊C8C2×D311yescharacteristic
167C23×C32—21no—
168C22×C3⋊D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3—22no—
171C32×D4—21no—
172C32×D4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—42no—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—42no—
181C4⋊(C3⋊D3)—81no—
182C3×#67—44no—
183C3×#67—82no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C3×D12—22no—
188C3×D12—21no—
189C3×D12—21no—
190C3×D12—22no—
191C3×D12—42no—
192C3×D12—81no—
193C3×C4×D3—42no—
194C3×C4×D3—44no—
195C3×Dic6D814yescomplemented
196#626—44no—
197#626—82no—
198#624—44no—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8#4112yescomplemented
202#550—31no—
203#550—91no—
204#493—91no—
205#493—92no—
206#459—92no—
207#459—92no—
208#459—91no—
209#459—91no—
210C8×Q8—91no—
211C4×D8—31no—
212C4×D8—92no—
213C3×#41—124no—
214C2×C3×Q8—31no—
215C2×C3×D4—21no—
216C2×C3×D4—32no—
217C2×C3×D4—31no—
218C2×C3×D4—62no—
219C2×C3×D4—62no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C2×C3×D4C22×D311yescharacteristic
223C2×C3×D4C22×D311yescharacteristic
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—41no—
227C22×C3×C4—62no—
228C22×C3×C4—61no—
229C2×#67—22no—
230C2×#67—22no—
231C2×#67—62no—
232C2×#67—62no—
233#239—124no—
234#235—44no—
235#235—124no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—32no—
239C2×D12—32no—
240C2×D12—62no—
241C2×D12—62no—
242C2×D12—61no—
243C2×D12—61no—
244C2×D12—62no—
245C2×D12—61no—
246C2×D12—61no—
247C2×D12—121no—
248C2×D12—121no—
249C2×D12C22×D312yes—
250C2×D12C22×D311yescharacteristic
251C2×C4×D3—21no—
252C2×C4×D3—22no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×Dic6#6711yescharacteristic
256C3×D8—62no—
257C2×C3×C8—31no—
258C2×C3×C8—31no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C22⋊C4—21no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—41no—
268C3×C22⋊C4—62no—
269C3×C22⋊C4—61no—
270C3×C42—21no—
271C3×C42—32no—
272C3×C42C22×D311yescharacteristic
273C3×C42C22×D311yescharacteristic
274#213—22no—
275#213—64no—
276#213—122no—
277#213—122no—
278#213—122no—
279#213—122no—
280#213—122no—
281#213—124no—
282(C2×D3)⋊C4—21no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286C4⋊Dic3#6711yescharacteristic
287C4⋊Dic3C22×D311yescharacteristic
288Dic3⋊C4#6712yes—
289C4×Dic3C22×D312yes—
290C2×C3⋊C8—32no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8C22×D311yescharacteristic
294C2×C3⋊C8C22×D311yescharacteristic
295D24—64no—
296D24—122no—
297C22×C32—41no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32C22×D411yescharacteristic
301C2×C3⋊D3—42no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—42no—
304C2×C3×D3—41no—
305C2×C3×D3—42no—
306C2×C3×D3—41no—
307C2×C3×D3—42no—
308C2×C3×D3—41no—
309C2×C3×D3—42no—
310C32×C4—21no—
311C32×C4—41no—
312C32×C4C2×D812yes—
313C32×C4C2×#4111yescharacteristic
314C32×C4H(5,𝔽2)11yescharacteristic
315C3×Dic3—22no—
316C3×Dic3—41no—
317C3×Dic3C2×D814yes—
318C2×#41—61no—
319C2×#41—181no—
320C2×D8—31no—
321C2×D8—92no—
322C2×D8—92no—
323C2×D8—92no—
324C2×D8—92no—
325#127—32no—
326#127—31no—
327#127—92no—
328#127—91no—
329#121—62no—
330#121—61no—
331#121—182no—
332#121—181no—
333C4×Q8—31no—
334C4×D4—32no—
335C4×D4—31no—
336C4×D4—92no—
337C4×D4D3211yescharacteristic
338#107—31no—
339C4⋊C8—92no—
340C4⋊C8—91no—
341#102—31no—
342#102—31no—
343#102—92no—
344#102—92no—
345C4×C8—31no—
346C4×C8—92no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—41no—
350C23×C3—62no—
351C23×C3—61no—
352C22×D3—21no—
353C22×D3—22no—
354C22×D3—62no—
355C22×D3—62no—
356C22×D3—122no—
357C3×Q8—34no—
358C3×D4—22no—
359C3×D4—21no—
360C3×D4—21no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4—41no—
364C3×D4—62no—
365C3×D4—61no—
366C3×D4—62no—
367C3×D4—61no—
368C3×D4—124no—
369C3×D4—122no—
370C3×D4—241no—
371C3×D4—242no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—32no—
378C2×C3×C4—32no—
379C2×C3×C4—41no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—61no—
383C2×C3×C4—82no—
384C2×C3×C4—124no—
385C2×C3×C4—122no—
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C2×#6711yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391C2×C3×C4C23×D311yescharacteristic
392#67—44no—
393#67—82no—
394#67—124no—
395#67—242no—
396C2×Dic3—21no—
397C2×Dic3C2×#6712yes—
398C2×Dic3C2×#6712yes—
399D12—21no—
400D12—22no—
401D12—22no—
402D12—21no—
403D12—42no—
404D12—62no—
405D12—62no—
406D12—62no—
407D12—62no—
408D12—81no—
409D12—122no—
410D12—122no—
411D12—124no—
412D12—122no—
413D12—122no—
414D12—242no—
415D12—241no—
416D12—241no—
417D12—242no—
418D12—242no—
419C4×D3—42no—
420C4×D3—44no—
421C4×D3—124no—
422C4×D3—124no—
423Dic6#21314yescomplemented
424C3×C8—32no—
425C3×C8—61no—
426C3⋊C8—21no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—122no—
430C3⋊C8#23512yescomplemented
431C2×C32—81no—
432C2×C32#55011yescharacteristic
433C2×C32C22×D811yescharacteristic
434C2×C32#57611yescharacteristic
435C3⋊D3—82no—
436C3×D3—82no—
437C3×D3—81no—
438#41—124no—
439#41—364no—
440C2×Q8—31no—
441C2×D4—31no—
442C2×D4—32no—
443C2×D4—62no—
444C2×D4—62no—
445C2×D4—61no—
446C2×D4—61no—
447C2×D4—92no—
448C2×D4—182no—
449C2×D4—182no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4C2×D3211yescharacteristic
453C22×C4—21no—
454C22×C4—62no—
455C22×C4—61no—
456C22×C4—182no—
457D8—62no—
458D8—184no—
459D8—362no—
460D8—362no—
461D8—362no—
462C2×C8—31no—
463C2×C8—31no—
464C2×C8—92no—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—31no—
468C4⋊C4C2×D3211yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—62no—
471C22⋊C4—61no—
472C22⋊C4—182no—
473C42—32no—
474C42C2×D3211yescharacteristic
475C22×C3—21no—
476C22×C3—42no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—121no—
488C22×C3—122no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3C2×D3×D411yescharacteristic
492C22×C3C22×#6711yescharacteristic
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—42no—
496C2×D3—41no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—242no—
506C2×D3—242no—
507C2×D3—242no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—34no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4—41no—
517C3×C4—62no—
518C3×C4—81no—
519C3×C4—121no—
520C3×C4D3×D812yes—
521C3×C4C2×#21312yes—
522C3×C4C2×#23511yescharacteristic
523C3×C4D3×#4111yescharacteristic
524C3×C4#100911yescharacteristic
525C3×C4#100911yescharacteristic
526Dic3—22no—
527Dic3—41no—
528Dic3C2×#21314yes—
529C32#339111yescharacteristic, complemented, Sylow
530C23—21no—
531C23—62no—
532C23—61no—
533C23—182no—
534Q8—34no—
535D4—21no—
536D4—21no—
537D4—61no—
538D4—62no—
539D4—62no—
540D4—61no—
541D4—124no—
542D4—122no—
543D4—182no—
544D4—182no—
545D4—241no—
546D4—242no—
547D4—364no—
548D4—362no—
549D4—721no—
550D4—722no—
551C2×C4—21no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—42no—
555C2×C4—61no—
556C2×C4—124no—
557C2×C4—122no—
558C2×C4—364no—
559C2×C4D3×#6711yescharacteristic
560C2×C4D3×#6711yescharacteristic
561C2×C4C22×D3211yescharacteristic
562C8—32no—
563C8—61no—
564C8—182no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—82no—
569C2×C3—81no—
570C2×C3—81no—
571C2×C3—241no—
572C2×C3—242no—
573C2×C3#555311yescharacteristic
574C2×C3C2×D3×D811yescharacteristic
575C2×C3#576911yescharacteristic
576C2×C3C22×#21311yescharacteristic
577C2×C3#583411yescharacteristic
578C2×C3#583511yescharacteristic
579D3—82no—
580D3—81no—
581D3—242no—
582D3—242no—
583D3—482no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—122no—
588C22—121no—
589C22—122no—
590C22—121no—
591C22—121no—
592C22—122no—
593C22—362no—
594C22—362no—
595C22—362no—
596C22C2×D3×#6711yescharacteristic
597C4—21no—
598C4—34no—
599C4—41no—
600C4—62no—
601C4—121no—
602C4D3×#21312yes—
603C4D3×#23511yescharacteristic
604C4#6430811yescharacteristic
605C3—21no—
606C3#7957811yescharacteristic, complemented
607C3#8358211yescharacteristic, complemented
608C2—81no—
609C2—242no—
610C2—241no—
611C2—722no—
612C2#1059500711yescharacteristic
613C2C2×D3×#21311yescharacteristic
614C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3391
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5553C2semidirect
2. #10593902C2semidirect
3. #10592714C2semidirect
4. C3×C4×#213C2semidirect
5. #10591482C2semidirect
6. #10591429C2semidirect
7. #10590547C2semidirect
8. #10590456C2semidirect
9. #10590350C2semidirect
10. #10590347C2semidirect
11. C3⋊C8×Dic6C2semidirect
46. #5553D3semidirect
60. C4×#213D3semidirect
195. C3×Dic6D8semidirect
201. C3×C3⋊C8#41semidirect
423. Dic6#213semidirect
430. C3⋊C8#235semidirect
529. C32#3391semidirect
606. C3#79578semidirect
607. C3#83582semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105939022
#105927142
C3×C4×#2132
#105914822
#105914292
#105905472
#105904562
#105903502
#105903472
C3⋊C8×Dic62
#835823
#795783