Finite Group Databasebeta

← #11868661

Subgroups — #11868661

Order 1152.

934 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×D12C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic, complemented
3#10592545C211yesmaximal, characteristic, complemented
4C3×#4842C211yesmaximal, characteristic, complemented
5C3×#4837C211yesmaximal, characteristic, complemented
6#10590939C212yesmaximal
7#10590769C212yesmaximal, complemented
8#10590767C212yesmaximal, complemented
9#10590681C212yesmaximal, complemented
10#10590300C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#81060—31nomaximal
13#79059—31nomaximal
14C2×D3×D12C2211yescharacteristic
15C2×C4×D32—21no—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C2×C3×ΓL(1,𝔽25)C2212yes—
19C3×C4×D12C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#869C2211yescharacteristic, complemented
22D3×(C2×D3)⋊C4—21no—
23C4×#626—21no—
24#63894C2211yescharacteristic
25Dic3×D12C2211yescharacteristic
26D3×C4⋊Dic3C2211yescharacteristic
27#63880—21no—
28#63869C2212yescomplemented
29#63857—21no—
30#63856—21no—
31#63844—21no—
32Dic3×Dic6—21no—
33#63841C2212yes—
34C32×C4⋊C8C2211yescharacteristic, complemented
35#63648C2212yes—
36#63645C2212yescomplemented
37C3×#821C2212yes—
38C3×#817C2212yescomplemented
39C3×Dic3⋊C8C2212yescomplemented
40C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
41#63575C2212yescomplemented
42#63573C2212yescomplemented
43#63564C2212yes—
44#63563C2212yes—
45#5728—31no—
46C4×D3×D4—31no—
47C2×C4×D12—31no—
48#5470—31no—
49C3×#476—31no—
50C3×#423—31no—
51#5131—32no—
52#5121—32no—
53#5084—31no—
54#5007—31no—
55#4871—32no—
56#4861—32no—
57#4847—32no—
58#4847—32no—
59#4846—31no—
60#4846—31no—
61#4846—31no—
62#4846—61no—
63#4842—31no—
64#4842D311yescharacteristic, complemented
65#4837D311yescharacteristic, complemented
66#4770—32no—
67#4766—32no—
68C22×D32—21no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×#634—21no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×#626—21no—
79C2×#624—21no—
80C2×D3×Dic3—21no—
81C2×D3×Dic3—21no—
82D3×D12—22no—
83D3×D12Q814yescomplemented
84C4×D32—44no—
85C2×C32×C8C2312yes—
86C32×C42C2311yescharacteristic
87#3752—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4×Dic3D411yescharacteristic
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99C3×ΓL(1,𝔽25)—24no—
100#3724—22no—
101Dic3⋊Dic3—22no—
102Dic3⋊Dic3—21no—
103#3722—21no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—21no—
106Dic32—22no—
107#3077—91noSylow
108C2×D3×D4—31no—
109C22×D12—31no—
110C22×C4×D3—61no—
111C22×C4×D3—61no—
112C2×C3×M16—32no—
113C3×C4⋊Q8—31no—
114C3×C4×D4—31no—
115C2×C3×C42—31no—
116#946—61no—
117Q8×Dic3—61no—
118D4×Dic3—31no—
119C4×#67—61no—
120C2×(C2×D3)⋊C4—61no—
121#926—32no—
122C2×C4⋊Dic3—31no—
123#924—61no—
124#924—61no—
125C2×ΓL(1,𝔽25)C2×D312yes—
126#897—61no—
127#893—31no—
128#892—32no—
129D3×C4⋊C4—31no—
130#890—32no—
131#887—61no—
132#67⋊C4—61no—
133D3×C22⋊C4—61no—
134C4×D12—31no—
135C4×D12—31no—
136C4×D12—31no—
137C4×D12—31no—
138C4×D12—61no—
139C4×D12—61no—
140C4×D12—61no—
141C4×D12C2×D311yescharacteristic
142C42×D3C2×D311yescharacteristic
143#870—32no—
144#869—31no—
145#869—31no—
146#869—61no—
147#869C2×D311yescharacteristic, complemented
148C4×Dic6—61no—
149C4×Dic6—61no—
150C3×#106—32no—
151C3×C4⋊C8—21no—
152C3×C4⋊C8—32no—
153C3×C4⋊C8—31no—
154C3×C4⋊C8C2×D311yescharacteristic, complemented
155C3×C4⋊C8C2×D311yescharacteristic, complemented
156C3×#102—32no—
157#832—32no—
158#821—32no—
159#821—32no—
160#821—32no—
161#821—32no—
162#821—62no—
163#821C2×D312yes—
164#818—32no—
165#818—32no—
166#818—32no—
167#818—62no—
168#817—32no—
169#817C2×D312yescomplemented
170Dic3⋊C8C2×D312yescomplemented
171#809—32no—
172#808—32no—
173#807—32no—
174C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
175C22×C3⋊D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C2×D32—24no—
179C2×D32—42no—
180C2×D32—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—21no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)C2×Q812yes—
188C4×C3⋊D3—42no—
189#634—42no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×D12—21no—
196C3×D12C2×Q812yes—
197C3×C4×D3—22no—
198C3×C4×D3—41no—
199C3×C4×D3—42no—
200C3×C4×D3C2×Q812yes—
201C3×C4×D3#4112yes—
202C3×Dic6—42no—
203#626—24no—
204#624—42no—
205D3×Dic3—42no—
206D3×Dic3—42no—
207C32×C8—22no—
208C3×C3⋊C8—22no—
209#533—91no—
210C2×C4×D4—91no—
211#478—92no—
212#478—92no—
213#476—31no—
214#476—91no—
215#474—91no—
216#474—91no—
217#428—92no—
218#423—31no—
219#418—92no—
220C23×D3—61no—
221C23×D3—61no—
222C2×C3×Q8—61no—
223C2×C3×D4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—61no—
228C2×#67—61no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231D3×D4—34no—
232D3×D4—62no—
233C2×D12—31no—
234C2×D12—31no—
235C2×D12—34no—
236C2×D12—61no—
237C2×D12—62no—
238C2×D12—61no—
239C2×D12C22×D311yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×C4×D3—61no—
247C2×C4×D3—121no—
248C2×C4×D3—124no—
249C2×C4×D3—124no—
250C2×C4×D3D1211yescharacteristic
251C2×C4×D3D1211yescharacteristic
252C2×C4×D3C22×D311yescharacteristic
253C2×Dic6—21no—
254C2×Dic6—61no—
255C2×Dic6—61no—
256C2×Dic6—121no—
257C3×M16—64no—
258C2×C3×C8—22no—
259C2×C3×C8—32no—
260C2×C3×C8C22×D312yes—
261C2×C3×C8C22×D312yes—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—61no—
265C3×C22⋊C4—61no—
266C3×C42—21no—
267C3×C42—31no—
268C3×C42—31no—
269C3×C42—31no—
270C3×C42C22×D311yescharacteristic
271C3×C42C22×D311yescharacteristic
272#217—62no—
273#217—61no—
274(C2×D3)⋊C4—21no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—61no—
279(C2×D3)⋊C4—61no—
280(C2×D3)⋊C4—61no—
281(C2×D3)⋊C4—121no—
282C4⋊Dic3—21no—
283C4⋊Dic3—32no—
284C4⋊Dic3—31no—
285C4⋊Dic3—31no—
286C4⋊Dic3—32no—
287C4⋊Dic3—61no—
288C4⋊Dic3—62no—
289C4⋊Dic3—61no—
290C4⋊Dic3—61no—
291C4⋊Dic3—61no—
292C4⋊Dic3—62no—
293C4⋊Dic3—121no—
294C4⋊Dic3C22×D312yes—
295C4⋊Dic3C22×D311yescharacteristic
296Dic3⋊C4—62no—
297Dic3⋊C4—62no—
298Dic3⋊C4—61no—
299Dic3⋊C4—62no—
300C4×Dic3—62no—
301C4×Dic3—62no—
302C4×Dic3D1211yescharacteristic
303C4×Dic3D1211yescharacteristic
304C4×Dic3C22×D311yescharacteristic
305C2×C3⋊C8C22×D312yes—
306ΓL(1,𝔽25)—24no—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—22no—
309C2×C3⋊D3—41no—
310C2×C3⋊D3—41no—
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—22no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3C22⋊Q812yes—
317D32—48no—
318C32×C4—21no—
319C32×C4AGL(1,ℤ/8)12yes—
320C32×C4C22×Q811yescharacteristic
321C32×C4C2×#4111yescharacteristic
322C3⋊Dic3—41no—
323C3⋊Dic3—42no—
324C3×Dic3—21no—
325C3×Dic3—21no—
326C3×Dic3—41no—
327C3×Dic3—42no—
328C3×Dic3C22⋊Q812yes—
329C22×D4—91no—
330C23×C4—181no—
331C2×M16—32no—
332C4⋊Q8—31no—
333C4⋊Q8—91no—
334#125—92no—
335C22⋊Q8—181no—
336C22⋊Q8—181no—
337C4×Q8—181no—
338C4×Q8—181no—
339C4×D4—31no—
340C4×D4—91no—
341C4×D4—91no—
342C4×D4—91no—
343C4×D4—181no—
344C4×D4—181no—
345#117—92no—
346C2×C4⋊C4—91no—
347C2×C22⋊C4—181no—
348C2×C42—31no—
349#107—92no—
350#107—92no—
351#106—32no—
352#106—92no—
353C4⋊C8—32no—
354C4⋊C8—31no—
355C4⋊C8D3211yescharacteristic, complemented
356#102—32no—
357#102—92no—
358#102—92no—
359#102—92no—
360C23×C3—31no—
361C23×C3—61no—
362C22×D3—21no—
363C22×D3—64no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—64no—
367C22×D3—121no—
368C22×D3—122no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3C2×D1211yescharacteristic
373C3×Q8—122no—
374C3×D4—32no—
375C3×D4—61no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—31no—
380C2×C3×C4—32no—
381C2×C3×C4—32no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—121no—
388C2×C3×C4—122no—
389C2×C3×C4C2×D1211yescharacteristic
390C2×C3×C4C2×D1211yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—64no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—62no—
399C2×Dic3—61no—
400C2×Dic3—62no—
401C2×Dic3—61no—
402C2×Dic3—122no—
403C2×Dic3—121no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3C2×D1211yescharacteristic
407C2×Dic3C2×D1211yescharacteristic
408C2×Dic3C2×D1211yescharacteristic
409D12—21no—
410D12—32no—
411D12—32no—
412D12—62no—
413D12—64no—
414D12—61no—
415D12—61no—
416D12—121no—
417D12D3×Q812yes—
418C4×D3—22no—
419C4×D3—41no—
420C4×D3—42no—
421C4×D3—122no—
422C4×D3—122no—
423C4×D3—122no—
424C4×D3—122no—
425C4×D3—122no—
426C4×D3—122no—
427C4×D3—242no—
428C4×D3#23712yes—
429C4×D3D3×Q812yes—
430Dic6—42no—
431Dic6—122no—
432Dic6—122no—
433Dic6—242no—
434C3×C8—22no—
435C3×C8—22no—
436C3×C8—42no—
437C3×C8—62no—
438C3⋊C8—22no—
439C2×C32C2×C22⋊Q811yescharacteristic
440C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
441C2×C32#57511yescharacteristic
442C3⋊D3—42no—
443C3×D3—22no—
444C3×D3—42no—
445C24—181no—
446C2×Q8—61no—
447C2×Q8—181no—
448C2×D4—31no—
449C2×D4—94no—
450C2×D4—91no—
451C2×D4—182no—
452C2×D4—181no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—61no—
457C22×C4—181no—
458C22×C4—181no—
459C22×C4—181no—
460C22×C4—181no—
461C22×C4—364no—
462M16—64no—
463C2×C8—32no—
464C2×C8C2×D3212yes—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—61no—
468C4⋊C4—92no—
469C4⋊C4—91no—
470C4⋊C4—181no—
471C4⋊C4—182no—
472C4⋊C4—182no—
473C4⋊C4—181no—
474C22⋊C4—61no—
475C22⋊C4—181no—
476C22⋊C4—181no—
477C22⋊C4—182no—
478C22⋊C4—181no—
479C42—31no—
480C42—31no—
481C42—31no—
482C42—182no—
483C42C2×D3211yescharacteristic
484C22×C3—21no—
485C22×C3—32no—
486C22×C3—61no—
487C22×C3—61no—
488C22×C3—62no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3C22×D1211yescharacteristic
492C22×C3C2×D3×D411yescharacteristic
493C2×D3—21no—
494C2×D3—21no—
495C2×D3—22no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—122no—
501C2×D3—128no—
502C2×D3—128no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—241no—
508C2×D3—241no—
509C2×D3#89712yes—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—32no—
516C3×C4—41no—
517C3×C4—61no—
518C3×C4—61no—
519C3×C4—121no—
520C3×C4—122no—
521C3×C4#90812yes—
522C3×C4#91412yes—
523C3×C4C2×#23711yescharacteristic
524C3×C4C2×D3×Q811yescharacteristic
525C3×C4C2×D3×Q811yescharacteristic
526C3×C4D3×#4111yescharacteristic
527Dic3—21no—
528Dic3—21no—
529Dic3—41no—
530Dic3—42no—
531Dic3—122no—
532Dic3—121no—
533Dic3—122no—
534Dic3—121no—
535Dic3—242no—
536Dic3—241no—
537Dic3#89712yes—
538C32#307711yescharacteristic, complemented, Sylow
539C23—31no—
540C23—61no—
541C23—184no—
542C23—181no—
543C23—362no—
544C23—362no—
545Q8—122no—
546Q8—362no—
547D4—32no—
548D4—61no—
549D4—92no—
550D4—184no—
551D4—181no—
552C2×C4—31no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—61no—
560C2×C4—121no—
561C2×C4—122no—
562C2×C4—182no—
563C2×C4—181no—
564C2×C4—362no—
565C2×C4—362no—
566C2×C4—362no—
567C2×C4—362no—
568C2×C4D3×D1211yescharacteristic
569C2×C4D3×D1211yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—22no—
572C8—62no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—62no—
577C2×C3—122no—
578C2×C3C2×#89711yescharacteristic
579C2×C3D3×C22⋊Q811yescharacteristic
580C2×C3C2×#90811yescharacteristic
581C2×C3#574811yescharacteristic
582C2×C3C2×#91411yescharacteristic
583C2×C3#577311yescharacteristic
584D3—22no—
585D3—42no—
586D3—122no—
587D3—122no—
588D3—242no—
589C22—32no—
590C22—61no—
591C22—61no—
592C22—62no—
593C22—121no—
594C22—121no—
595C22—182no—
596C22—368no—
597C22—361no—
598C22—361no—
599C22C2×D3×D1211yescharacteristic
600C4—21no—
601C4—32no—
602C4—61no—
603C4—61no—
604C4—121no—
605C4—122no—
606C4—361no—
607C4—362no—
608C4#6379412yes—
609C4D3×#23711yescharacteristic
610C4D32×Q811yescharacteristic
611C3—21no—
612C3#7905911yescharacteristic, complemented
613C3#8106011yescharacteristic, complemented
614C2—62no—
615C2—122no—
616C2—362no—
617C2D3×#89711yescharacteristic
618C2C2×#6379411yescharacteristic
619C2#1059471211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenterC4⋊C8D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593859C2semidirect
3. #10592545C2semidirect
4. C3×#4842C2semidirect
5. C3×#4837C2semidirect
7. #10590769C2semidirect
8. #10590767C2semidirect
9. #10590681C2semidirect
10. #10590300C2semidirect
11. #10590272C2semidirect
17. #64078C22semidirect
21. C3×#869C22semidirect
28. #63869C22semidirect
34. C32×C4⋊C8C22semidirect
36. #63645C22semidirect
38. C3×#817C22semidirect
39. C3×Dic3⋊C8C22semidirect
40. C3×C4⋊(C3⋊C8)C22semidirect
41. #63575C22semidirect
42. #63573C22semidirect
64. #4842D3semidirect
65. #4837D3semidirect
83. D3×D12Q8semidirect
147. #869C2×D3semidirect
154. C3×C4⋊C8C2×D3semidirect
155. C3×C4⋊C8C2×D3semidirect
169. #817C2×D3semidirect
170. Dic3⋊C8C2×D3semidirect
174. C4⋊(C3⋊C8)C2×D3semidirect
355. C4⋊C8D32semidirect
538. C32#3077semidirect
612. C3#79059semidirect
613. C3#81060semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
#105938592
#105925452
C3×#48422
C3×#48372
#105909392
#105907692
#105907672
#105906812
#105903002
#105902722
#810603
#790593