Finite Group Databasebeta

← #11882253

Subgroups — #11882253

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×#5716C211yesmaximal, characteristic
2#10593873C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic, complemented
4C3×#5075C211yesmaximal, characteristic, complemented
5#10591499C212yesmaximal, complemented
6#10591489C212yesmaximal, complemented
7#10591460C212yesmaximal, complemented
8#10591408C212yesmaximal, complemented
9D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10590307C211yesmaximal, characteristic, complemented
11#10590285C211yesmaximal, characteristic, complemented
12#83320—31nomaximal
13#80366—31nomaximal
14C2×C3×#237—21no—
15C32×#127C2211yescharacteristic
16C2×#3754C2212yes—
17C4×#634C2211yescharacteristic
18C3×#938—21no—
19C3×#938C2212yes—
20C3×#936—21no—
21C3×D4×Dic3—21no—
22C3×D4×Dic3C2212yes—
23C2×C3×#214C2212yes—
24C3×C42×D3C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63918C2211yescharacteristic
28C4×#627—21no—
29#63867—21no—
30#63866C2211yescharacteristic
31#63857C2211yescharacteristic
32#63856C2211yescharacteristic
33#63855—21no—
34#63851—21no—
35C2×D3×C3⋊C8C2212yes—
36#63659C2212yes—
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C3×#832C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63574C2212yes—
41#63573C2212yes—
42Dic3⋊(C3⋊C8)C2212yes—
43#63567C2212yes—
44#63565C2212yes—
45C3×#532—31no—
46#5716D311yescharacteristic
47#5578—31no—
48#5470—31no—
49C3×#460—31no—
50#5171—32no—
51#5162—32no—
52#5094—31no—
53#5094—31no—
54#5075—31no—
55#5075—31no—
56#5075—61no—
57#5075D311yescharacteristic, complemented
58#5041—32no—
59#5041—32no—
60#5020—31no—
61#5019—32no—
62#5008—32no—
63C2×C4⋊(C3⋊C8)—31no—
64#4851—31no—
65D3×C4⋊C8—31no—
66#4778—32no—
67#4761—32no—
68C2×C32×D4—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2312yes—
71C2×#634C2311yescharacteristic
72C2×C3×#67—22no—
73C22×C3×Dic3—22no—
74C3×#237—44no—
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3D411yescharacteristic
77C2×C3×C4×D3C2311yescharacteristic
78C2×C3×Dic6—21no—
79C2×C3×Dic6C2311yescharacteristic
80C2×#627—21no—
81C32×C42C2311yescharacteristic
82#3754—42no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3—21no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—22no—
88C3×#217—22no—
89C3×#214—42no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99#3724—21no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic3⋊Dic3—21no—
104(C2×D3)⋊Dic3—21no—
105(C2×D3)⋊Dic3—21no—
106D3×C3⋊C8—42no—
107#3246—91noSylow
108C2×C3×#41—61no—
109C2×#237—21no—
110C2×C3×SD16—32no—
111C3×C4⋊Q8—31no—
112C3×#127—21no—
113C3×#127C2×D311yescharacteristic
114C3×#127C2×D311yescharacteristic
115C3×#124—61no—
116C3×#121—32no—
117C3×#121—61no—
118C3×C4×Q8—31no—
119C3×C4×D4—32no—
120C3×C4×D4—61no—
121C2×C3×C42—31no—
122#946—31no—
123#944—31no—
124#938—21no—
125#938C2×D312yes—
126#936—21no—
127D4×Dic3—21no—
128D4×Dic3C2×D312yes—
129C2×#214—32no—
130C2×#214—32no—
131C2×#214—62no—
132C2×#214C2×D312yes—
133#926—61no—
134#924—31no—
135#924—31no—
136#924—61no—
137C22×C3⋊C8—32no—
138C2×D3×C8—32no—
139#897—31no—
140#896—61no—
141#889—61no—
142#888—31no—
143#872—61no—
144C42×D3C2×D311yescharacteristic
145#870—61no—
146#869—31no—
147#869—31no—
148#869C2×D311yescharacteristic
149C4×Dic6—31no—
150C4×Dic6—31no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C4×Dic6—61no—
154C4×Dic6C2×D311yescharacteristic
155C3×C4⋊C8—31no—
156C3×#102—32no—
157#835—32no—
158#832—32no—
159#832—32no—
160#832—62no—
161#832C2×D312yes—
162#817—32no—
163#816—32no—
164Dic3⋊C8—32no—
165#810—32no—
166#810—32no—
167#808—32no—
168#808—32no—
169#808—32no—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—32no—
173C4⋊(C3⋊C8)—61no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic
175C23×C32—22no—
176C22×C3×D3C2×D411yescharacteristic
177C32×D4—22no—
178C32×D4—22no—
179C32×D4—42no—
180C32×D4—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186#634—21no—
187#634—21no—
188C3×#67—44no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—44no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×C4×D3—21no—
197C3×C4×D3—21no—
198C3×C4×D3—41no—
199C3×C4×D3SD1614yescomplemented
200C3×Dic6—21no—
201C3×Dic6—21no—
202C3×Dic6—42no—
203#627—42no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—91no—
207#532—31no—
208#476—92no—
209#475—91no—
210#475—91no—
211#465—92no—
212#465—92no—
213#461—92no—
214#460—31no—
215#460—91no—
216C2×C4⋊C8—91no—
217C3×#41—124no—
218C2×C3×Q8—31no—
219C2×C3×Q8—61no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4—41no—
226C2×C3×D4—41no—
227C2×C3×D4—62no—
228C2×C3×D4C22×D312yes—
229C2×C3×D4C22×D312yes—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—62no—
234C2×#67—22no—
235C22×Dic3—22no—
236#237—44no—
237C2×C4×D3#6711yescharacteristic
238C2×C4×D3#6711yescharacteristic
239C2×C4×D3C22×D311yescharacteristic
240C2×Dic6—21no—
241C2×Dic6—31no—
242C2×Dic6—31no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—61no—
246C2×Dic6C22×D311yescharacteristic
247C3×SD16—122no—
248C2×C3×C8—32no—
249C3×C4⋊C4—32no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—61no—
253C3×C22⋊C4—62no—
254C3×C22⋊C4—62no—
255C3×C42—21no—
256C3×C42—31no—
257C3×C42—31no—
258C3×C42—31no—
259C3×C42—61no—
260C3×C42C22×D311yescharacteristic
261C3×C42C22×D311yescharacteristic
262#217—22no—
263#217—22no—
264#217—61no—
265#217—61no—
266#214—42no—
267#214—122no—
268#214—122no—
269#214—124no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272C4⋊Dic3—21no—
273C4⋊Dic3—31no—
274C4⋊Dic3—31no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—61no—
280C4⋊Dic3C22×D311yescharacteristic
281C4⋊Dic3C22×D312yes—
282Dic3⋊C4—21no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286Dic3⋊C4—61no—
287Dic3⋊C4—61no—
288Dic3⋊C4—61no—
289Dic3⋊C4—61no—
290Dic3⋊C4—61no—
291Dic3⋊C4—121no—
292C4×Dic3—21no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3—121no—
296C4×Dic3#6711yescharacteristic
297C4×Dic3#6711yescharacteristic
298C4×Dic3C22×D311yescharacteristic
299C2×C3⋊C8—32no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8—122no—
303C2×C3⋊C8C22×D312yes—
304D3×C8—122no—
305C22×C32—42no—
306C22×C32—42no—
307C22×C32—42no—
308C22×C32C22×D411yescharacteristic
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3C2×SD1612yes—
312C32×C4—21no—
313C32×C4C2×SD1612yes—
314C32×C4H(5,𝔽2)11yescharacteristic
315C32×C42−1+411yescharacteristic
316C3⋊Dic3—41no—
317C3⋊Dic3—41no—
318C3×Dic3—21no—
319C3×Dic3—21no—
320C3×Dic3—41no—
321C3×Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3C2×SD1612yes—
324C2×#41—61no—
325C2×SD16—32no—
326C2×SD16—92no—
327C22×C8—92no—
328C4⋊Q8—31no—
329C4⋊Q8—91no—
330C4⋊Q8—91no—
331#127D3211yescharacteristic
332#125—181no—
333#124—61no—
334C22⋊Q8—91no—
335C22⋊Q8—91no—
336C22⋊Q8—181no—
337#121—32no—
338#121—61no—
339C4×Q8—31no—
340C4×Q8—91no—
341C4×Q8—181no—
342C4×D4—32no—
343C4×D4—61no—
344#117—181no—
345C2×C42—31no—
346#106—92no—
347#106—92no—
348C4⋊C8—31no—
349C4⋊C8—92no—
350C4⋊C8—91no—
351#103—92no—
352#103—92no—
353#102—32no—
354#102—92no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—31no—
358C23×C3—42no—
359C22×D3C2×#6711yescharacteristic
360C3×Q8—61no—
361C3×Q8—61no—
362C3×Q8—122no—
363C3×D4—22no—
364C3×D4—22no—
365C3×D4—22no—
366C3×D4—22no—
367C3×D4—42no—
368C3×D4—42no—
369C3×D4—42no—
370C3×D4—42no—
371C3×D4—42no—
372C3×D4—42no—
373C3×D4—82no—
374C3×D4—82no—
375C3×D4—124no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—31no—
380C2×C3×C4—34no—
381C2×C3×C4—31no—
382C2×C3×C4—31no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—121no—
389C2×C3×C4—124no—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396#67—44no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—22no—
400C2×Dic3—44no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3C2×#6711yescharacteristic
408C2×Dic3C2×#6711yescharacteristic
409C2×Dic3C2×#6711yescharacteristic
410C4×D3—21no—
411C4×D3—21no—
412C4×D3—41no—
413C4×D3#21414yescomplemented
414Dic6—21no—
415Dic6—21no—
416Dic6—42no—
417Dic6—62no—
418Dic6—61no—
419Dic6—61no—
420Dic6—61no—
421Dic6—61no—
422Dic6—121no—
423Dic6—122no—
424Dic6—122no—
425C3×C8—62no—
426C3⋊C8—22no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—122no—
430C2×C32—82no—
431C2×C32#53711yescharacteristic
432C2×C32C22×SD1611yescharacteristic
433C2×C32#57511yescharacteristic
434C3×D3—22no—
435#41—124no—
436C2×Q8—31no—
437C2×Q8—61no—
438C2×Q8—91no—
439C2×Q8—181no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—62no—
443C2×D4C2×D3212yes—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—62no—
448SD16—122no—
449SD16—362no—
450C2×C8—32no—
451C2×C8—92no—
452C2×C8—362no—
453C4⋊C4—31no—
454C4⋊C4—32no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—91no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C4⋊C4—181no—
464C22⋊C4—62no—
465C22⋊C4—62no—
466C22⋊C4—181no—
467C22⋊C4—181no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—61no—
472C42—181no—
473C42C2×D3211yescharacteristic
474C22×C3—21no—
475C22×C3—32no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3—61no—
483C22×C3—61no—
484C22×C3—82no—
485C22×C3—82no—
486C22×C3—82no—
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C22×#6711yescharacteristic
489C2×D3—21no—
490C2×D3—21no—
491C2×D3C2×#21412yes—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—22no—
497C3×C4—32no—
498C3×C4—41no—
499C3×C4—61no—
500C3×C4—61no—
501C3×C4—122no—
502C3×C4—121no—
503C3×C4—121no—
504C3×C4D3×SD1612yes—
505C3×C4C2×#21412yes—
506C3×C4#100411yescharacteristic
507C3×C4#100911yescharacteristic
508C3×C4#101011yescharacteristic
509C3×C4#101011yescharacteristic
510Dic3—21no—
511Dic3—21no—
512Dic3—41no—
513Dic3—42no—
514Dic3—41no—
515Dic3—122no—
516Dic3—121no—
517Dic3—121no—
518Dic3—121no—
519Dic3—121no—
520Dic3—241no—
521Dic3C2×#21412yes—
522C32#324611yescharacteristic, complemented, Sylow
523C23—22no—
524C23—31no—
525Q8—61no—
526Q8—61no—
527Q8—122no—
528Q8—181no—
529Q8—181no—
530Q8—362no—
531D4—22no—
532D4—22no—
533D4—42no—
534D4—42no—
535D4—124no—
536C2×C4—31no—
537C2×C4—34no—
538C2×C4—31no—
539C2×C4—31no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—62no—
545C2×C4—121no—
546C2×C4—124no—
547C2×C4—181no—
548C2×C4—181no—
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—82no—
559C2×C3—82no—
560C2×C3—162no—
561C2×C3#560811yescharacteristic
562C2×C3C2×D3×SD1611yescharacteristic
563C2×C3#577311yescharacteristic
564C2×C3C22×#21411yescharacteristic
565C2×C3#582211yescharacteristic
566C2×C3#583311yescharacteristic
567D3—22no—
568C22—32no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—61no—
573C22—61no—
574C22C2×D3×#6711yescharacteristic
575C4—21no—
576C4—32no—
577C4—61no—
578C4—61no—
579C4—121no—
580C4—122no—
581C4—121no—
582C4—361no—
583C4—361no—
584C4D3×#21412yes—
585C4#6430911yescharacteristic
586C4#6431411yescharacteristic
587C3—21no—
588C3#8036611yescharacteristic, complemented
589C3#8332011yescharacteristic, complemented
590C2—62no—
591C2—82no—
592C2#1059509511yescharacteristic
593C2C2×D3×#21411yescharacteristic
594C2#1059523211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5716C2
hypercenter#127D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593873C2semidirect
3. #10592774C2semidirect
4. C3×#5075C2semidirect
5. #10591499C2semidirect
6. #10591489C2semidirect
7. #10591460C2semidirect
8. #10591408C2semidirect
9. D3×C4⋊(C3⋊C8)C2semidirect
10. #10590307C2semidirect
11. #10590285C2semidirect
57. #5075D3semidirect
199. C3×C4×D3SD16semidirect
413. C4×D3#214semidirect
522. C32#3246semidirect
588. C3#80366semidirect
589. C3#83320semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
#105938732
#105927742
C3×#50752
#105914992
#105914892
#105914602
#105914082
D3×C4⋊(C3⋊C8)2
#105903072
#105902852
#833203
#803663