Finite Group Databasebeta

← #11882274

Subgroups — #11882274

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic, complemented
2#10593970C211yesmaximal, characteristic
3#10592726C211yesmaximal, characteristic, complemented
4C3×#5020C211yesmaximal, characteristic, complemented
5#10591585C212yesmaximal, complemented
6#10591565C212yesmaximal, complemented
7#10590577C212yesmaximal, complemented
8#10590466C212yesmaximal, complemented
9#10590367C211yesmaximal, characteristic, complemented
10D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12#83363—31nomaximal
13#81002—31nomaximal
14C2×#3799—21no—
15C32×C4×Q8C2211yescharacteristic
16C2×#3755C2212yes—
17#64083C2211yescharacteristic
18C3×#946C2211yescharacteristic
19C3×#944C2211yescharacteristic
20C3×#897C2211yescharacteristic
21C3×#896—21no—
22C3×#889—21no—
23C3×#888C2211yescharacteristic
24C3×#872—21no—
25C3×C42×D3C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×C4×Dic6—21no—
28C3×C4×Dic6C2211yescharacteristic
29#63909—21no—
30#63909C2212yes—
31#63894—21no—
32#63894C2212yes—
33#63864—21no—
34C2×#3717C2212yes—
35C2×D3×C3⋊C8C2212yes—
36#63636C2212yes—
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C3×#835C2212yes—
39C3×#808C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63574C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63565C2212yes—
44#63564C2212yes—
45C3×#533—31no—
46#5725—31no—
47#5578D311yescharacteristic, complemented
48#5477—31no—
49C3×#475—31no—
50#5094—31no—
51#5084—32no—
52#5083—32no—
53#5048—32no—
54#5048—32no—
55#5027—31no—
56#5027—31no—
57#5027—31no—
58#5027—61no—
59#5020—31no—
60#5020D311yescharacteristic, complemented
61C2×C4⋊(C3⋊C8)—31no—
62#4870—32no—
63#4864—32no—
64#4848—31no—
65D3×C4⋊C8—31no—
66#4818—32no—
67#4807—32no—
68C2×C32×Q8C2311yescharacteristic
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)C2312yes—
72C2×C3×C4×D3D411yescharacteristic
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3C2311yescharacteristic
75C2×C3×Dic6—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2311yescharacteristic
78C2×#626—22no—
79C2×#624—22no—
80#3799—44no—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C42—21no—
84C32×C42C2311yescharacteristic
85#3755—42no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103#3722—22no—
104#3722—22no—
105#3717—42no—
106D3×C3⋊C8—42no—
107#3246—91noSylow
108C2×#239—61no—
109C2×#235—61no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8—31no—
112C3×C4⋊Q8—31no—
113C3×#125—61no—
114C3×C22⋊Q8—31no—
115C3×C22⋊Q8—31no—
116C3×C22⋊Q8—61no—
117C3×C4×Q8—21no—
118C3×C4×Q8—31no—
119C3×C4×Q8—61no—
120C3×C4×Q8C2×D311yescharacteristic
121C3×C4×Q8C2×D311yescharacteristic
122C3×#117—61no—
123C2×C3×C42—31no—
124#947—61no—
125#946C2×D311yescharacteristic
126#944C2×D311yescharacteristic
127C2×#215—32no—
128C2×#215—32no—
129C2×#215—32no—
130C2×#215—62no—
131#930—32no—
132#930—61no—
133C22×C3⋊C8—32no—
134C2×#204—32no—
135C2×D3×C8—32no—
136#897C2×D311yescharacteristic
137#896—21no—
138#895—32no—
139#895—61no—
140#893—32no—
141#893—61no—
142#889—21no—
143#888C2×D311yescharacteristic
144#875—61no—
145#874—31no—
146#874—31no—
147#874—61no—
148C4×D12—32no—
149C4×D12—61no—
150#872—21no—
151C42×D3C2×D311yescharacteristic
152#869C2×D311yescharacteristic
153C4×Dic6—21no—
154C4×Dic6C2×D311yescharacteristic
155C3×#106—32no—
156C3×C4⋊C8—31no—
157C3×#103—32no—
158#835—32no—
159#835C2×D312yes—
160#821—32no—
161Dic3⋊C8—32no—
162#810—32no—
163#809—32no—
164#809—32no—
165#809—32no—
166#809—62no—
167#808—32no—
168#808—32no—
169#808C2×D312yes—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C22×C3⋊D3—22no—
176C22×C3×D3C2×D411yescharacteristic
177C32×Q8—21no—
178C32×Q8—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—22no—
186C4⋊(C3⋊D3)—42no—
187C4⋊(C3⋊D3)—42no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C3×C4×D3—21no—
195C3×C4×D3—21no—
196C3×C4×D3—41no—
197C3×C4×D3SD1614yescomplemented
198C3×Dic6—21no—
199C3×Dic6—21no—
200C3×Dic6—42no—
201C3×Dic6—42no—
202#626—44no—
203#624—44no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—31no—
207#532—91no—
208#476—92no—
209#475—31no—
210#475—91no—
211#465—92no—
212#465—92no—
213#461—92no—
214#460—91no—
215#460—91no—
216C2×C4⋊C8—91no—
217C2×C3×Q8—21no—
218C2×C3×Q8—31no—
219C2×C3×Q8—61no—
220C2×C3×Q8—61no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C22×D311yescharacteristic
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C2×#67—62no—
227#239—124no—
228#235—124no—
229C2×D12—32no—
230C2×D12—32no—
231C2×D12—62no—
232C2×D12—62no—
233C2×D12—61no—
234C2×D12—61no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—121no—
238C2×D12—121no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3#6711yescharacteristic
242C2×C4×D3#6711yescharacteristic
243C2×C4×D3C22×D311yescharacteristic
244C2×Dic6—21no—
245C2×Dic6—21no—
246C2×Dic6C22×D311yescharacteristic
247C2×C3×C8—32no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—32no—
253C3×C4⋊C4—41no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C22⋊C4—61no—
264C3×C22⋊C4—61no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—31no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—41no—
272C3×C42—61no—
273C3×C42C22×D311yescharacteristic
274C3×C42C22×D311yescharacteristic
275#215—122no—
276#215—122no—
277#215—122no—
278#215—124no—
279(C2×D3)⋊C4—21no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—62no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284(C2×D3)⋊C4—62no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289Dic3⋊C4—21no—
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294C4×Dic3—21no—
295C4×Dic3#6711yescharacteristic
296C4×Dic3#6711yescharacteristic
297C4×Dic3C22×D311yescharacteristic
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8—122no—
302C2×C3⋊C8C22×D312yes—
303#204—122no—
304D3×C8—122no—
305C22×C32C22×D411yescharacteristic
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—42no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3C2×SD1612yes—
312C32×C4—21no—
313C32×C4—41no—
314C32×C4—41no—
315C32×C4C2×SD1612yes—
316C32×C4H(5,𝔽2)11yescharacteristic
317C32×C42−1+411yescharacteristic
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3C2×SD1612yes—
324C2×#41—181no—
325C2×SD16—92no—
326C2×SD16—92no—
327C22×C8—92no—
328C4⋊Q8—31no—
329C4⋊Q8—31no—
330C4⋊Q8—31no—
331#127—91no—
332#125—61no—
333#124—181no—
334C22⋊Q8—31no—
335C22⋊Q8—31no—
336C22⋊Q8—61no—
337#121—92no—
338#121—181no—
339C4×Q8—31no—
340C4×Q8—61no—
341C4×Q8D3211yescharacteristic
342C4×D4—92no—
343C4×D4—181no—
344#117—61no—
345C2×C42—31no—
346#106—32no—
347#106—92no—
348C4⋊C8—31no—
349C4⋊C8—92no—
350C4⋊C8—91no—
351#103—32no—
352#103—92no—
353#102—92no—
354#102—92no—
355C23×C3—31no—
356C22×D3—62no—
357C22×D3—62no—
358C22×D3—122no—
359C22×D3C2×#6711yescharacteristic
360C3×Q8—22no—
361C3×Q8—21no—
362C3×Q8—21no—
363C3×Q8—21no—
364C3×Q8—21no—
365C3×Q8—41no—
366C3×Q8—61no—
367C3×Q8—61no—
368C3×Q8—122no—
369C3×Q8—122no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—31no—
378C2×C3×C4—34no—
379C2×C3×C4—31no—
380C2×C3×C4—31no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—62no—
388C2×C3×C4—121no—
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4C2×#6711yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—124no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3C2×#6711yescharacteristic
400C2×Dic3C2×#6711yescharacteristic
401C2×Dic3C2×#6711yescharacteristic
402D12—62no—
403D12—62no—
404D12—62no—
405D12—62no—
406D12—122no—
407D12—122no—
408D12—122no—
409D12—122no—
410D12—124no—
411D12—122no—
412D12—122no—
413D12—242no—
414D12—242no—
415C4×D3—21no—
416C4×D3—21no—
417C4×D3—41no—
418C4×D3—124no—
419C4×D3—124no—
420C4×D3#21514yescomplemented
421Dic6—21no—
422Dic6—21no—
423Dic6—42no—
424Dic6—42no—
425C3×C8—62no—
426C3⋊C8—22no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—122no—
430C2×C32#53711yescharacteristic
431C2×C32C22×SD1611yescharacteristic
432C2×C32#57511yescharacteristic
433C3⋊D3—82no—
434C3×D3—22no—
435#41—364no—
436C2×Q8—31no—
437C2×Q8—61no—
438C2×Q8—61no—
439C2×Q8C2×D3211yescharacteristic
440C2×D4—92no—
441C2×D4—182no—
442C2×D4—181no—
443C2×D4—181no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—182no—
448SD16—362no—
449SD16—362no—
450C2×C8—32no—
451C2×C8—92no—
452C2×C8—362no—
453C4⋊C4—21no—
454C4⋊C4—31no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C4⋊C4—61no—
462C4⋊C4—61no—
463C4⋊C4C2×D3211yescharacteristic
464C22⋊C4—61no—
465C22⋊C4—61no—
466C22⋊C4—182no—
467C22⋊C4—182no—
468C42—21no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—61no—
473C42C2×D3211yescharacteristic
474C22×C3—21no—
475C22×C3—32no—
476C22×C3—61no—
477C22×C3—61no—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C22×#6711yescharacteristic
480C2×D3—21no—
481C2×D3—21no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—242no—
489C2×D3—242no—
490C2×D3—242no—
491C2×D3C2×#21512yes—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—22no—
497C3×C4—32no—
498C3×C4—41no—
499C3×C4—42no—
500C3×C4—41no—
501C3×C4—41no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—61no—
505C3×C4—61no—
506C3×C4—81no—
507C3×C4—121no—
508C3×C4—122no—
509C3×C4—121no—
510C3×C4D3×SD1612yes—
511C3×C4C2×#21512yes—
512C3×C4#100711yescharacteristic
513C3×C4#100911yescharacteristic
514C3×C4#100911yescharacteristic
515C3×C4#101011yescharacteristic
516Dic3—21no—
517Dic3—21no—
518Dic3—42no—
519Dic3—41no—
520Dic3—41no—
521Dic3C2×#21512yes—
522C32#324611yescharacteristic, complemented, Sylow
523C23—31no—
524C23—182no—
525Q8—21no—
526Q8—21no—
527Q8—61no—
528Q8—61no—
529Q8—122no—
530Q8—122no—
531D4—182no—
532D4—182no—
533D4—362no—
534D4—364no—
535D4—362no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—31no—
539C2×C4—34no—
540C2×C4—31no—
541C2×C4—31no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—62no—
547C2×C4—121no—
548C2×C4—364no—
549C2×C4D3×#6711yescharacteristic
550C2×C4D3×#6711yescharacteristic
551C2×C4C22×D3211yescharacteristic
552C8—62no—
553C8—182no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—62no—
558C2×C3#562911yescharacteristic
559C2×C3C2×D3×SD1611yescharacteristic
560C2×C3#577711yescharacteristic
561C2×C3C22×#21511yescharacteristic
562C2×C3#582211yescharacteristic
563C2×C3#583311yescharacteristic
564D3—22no—
565D3—242no—
566D3—242no—
567D3—482no—
568C22—32no—
569C22—61no—
570C22—61no—
571C22—362no—
572C22—362no—
573C22—362no—
574C22C2×D3×#6711yescharacteristic
575C4—21no—
576C4—32no—
577C4—41no—
578C4—41no—
579C4—61no—
580C4—61no—
581C4—121no—
582C4—121no—
583C4—122no—
584C4D3×#21512yes—
585C4#6429711yescharacteristic
586C4#6430811yescharacteristic
587C3—21no—
588C3#8100211yescharacteristic, complemented
589C3#8336311yescharacteristic, complemented
590C2—62no—
591C2—722no—
592C2#1059489411yescharacteristic
593C2C2×D3×#21511yescharacteristic
594C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10593970C2
hypercenterC4×Q8D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5578C2semidirect
3. #10592726C2semidirect
4. C3×#5020C2semidirect
5. #10591585C2semidirect
6. #10591565C2semidirect
7. #10590577C2semidirect
8. #10590466C2semidirect
9. #10590367C2semidirect
10. D3×C4⋊(C3⋊C8)C2semidirect
11. #10590285C2semidirect
47. #5578D3semidirect
60. #5020D3semidirect
197. C3×C4×D3SD16semidirect
420. C4×D3#215semidirect
522. C32#3246semidirect
588. C3#81002semidirect
589. C3#83363semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
#105939702
#105927262
C3×#50202
#105915852
#105915652
#105905772
#105904662
#105903672
D3×C4⋊(C3⋊C8)2
#105902852
#833633
#810023