Finite Group Databasebeta

← #11787397

Subgroups — #11787397

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic, complemented
5#10591071C211yesmaximal, characteristic, complemented
6#10589166C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72087—31nomaximal
9#70377—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12#64157—22no—
13#64157—22no—
14C2×#3748—21no—
15C2×#3748C2211yescharacteristic
16C22×C3⋊(C3⋊C8)—21no—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#950—22no—
19C3×#950—22no—
20C2×C3×#216C411yescharacteristic, complemented
21C2×C3×#215C411yescharacteristic, complemented
22C2×C3×#214C411yescharacteristic, complemented
23C2×C3×#213C411yescharacteristic, complemented
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#837—22no—
28#63569—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×#135—31no—
32C2×#950D311yescharacteristic
33C2×#948—31no—
34C2×#948—31no—
35C2×#948—61no—
36C2×C3×#104—31no—
37C2×#837—31no—
38C2×#837D311yescharacteristic, complemented
39#5234—31no—
40#5129—31no—
41C2×#805—31no—
42#4558—31no—
43#4552—31no—
44#4550—31no—
45#4524—31no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41D412yes—
49C32×#41D412yes—
50C2×C32×Q8C2×C411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4C2×C411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12C2×C411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6C2×C411yescharacteristic
64#3748—24no—
65#3748—21no—
66#3748D412yes—
67C2×C3⋊(C3⋊C8)—24no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)D411yescharacteristic
72C2×C3⋊(C3⋊C8)D411yescharacteristic
73C3×#216—22no—
74C3×#215—22no—
75C3×#214—22no—
76C3×#213—22no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C3×#208—21no—
80C3×#208—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84C2×C3×C3⋊C8C2×C411yescharacteristic
85C2×C3×C3⋊C8C2×C411yescharacteristic
86#1876—91noSylow
87C2×C3×#41—21no—
88C2×C3×#41—31no—
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×#41C2×D311yescharacteristic
91C2×#235C2×D311yescharacteristic
92C3×#135—62no—
93C3×#135—62no—
94C2×C3×Q16—31no—
95C2×C3×SD16—31no—
96C2×C3×SD16—31no—
97C2×C3×D8—31no—
98C2×C3×M16—31no—
99C22×C3×C8—31no—
100C2×C3×C42—31no—
101#950—22no—
102#950—22no—
103#948—62no—
104#948—62no—
105#948—64no—
106#948—64no—
107#948—62no—
108#948—62no—
109C2×#216Dic311yescharacteristic, complemented
110C2×#215Dic311yescharacteristic, complemented
111C2×#214Dic311yescharacteristic, complemented
112C2×#213Dic311yescharacteristic, complemented
113C2×C4×Dic3C2×D311yescharacteristic
114C2×#208—31no—
115C2×#208—31no—
116C2×#208—61no—
117C2×#208—61no—
118C2×#208—61no—
119C2×#208—62no—
120C2×#208C2×D311yescharacteristic
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8—61no—
126C22×C3⋊C8—62no—
127C22×C3⋊C8C2×D311yescharacteristic
128C3×#104—62no—
129#837—22no—
130#837—62no—
131#830—61no—
132#830—61no—
133(C2×D3)⋊C8—61no—
134(C2×D3)⋊C8—61no—
135#805—62no—
136C23×C32—21no—
137C23×C32#4111yescharacteristic
138C22×C3×D3—21no—
139C32×Q8—21no—
140C32×Q8C22⋊C412yes—
141C32×D4—22no—
142C32×D4—22no—
143C32×D4—21no—
144C32×D4C22⋊C412yes—
145C2×C32×C4—21no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4C22×C411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4#4111yescharacteristic
154C3×#67—41no—
155C3×#67—41no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C3×D12—21no—
161C3×D12—21no—
162C3×C4×D3—41no—
163C3×C4×D3—41no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166C3⋊(C3⋊C8)—21no—
167C3⋊(C3⋊C8)—22no—
168C3⋊(C3⋊C8)—21no—
169C3×C3⋊C8—21no—
170C3×C3⋊C8—21no—
171C3×C3⋊C8—41no—
172C2×#135—31no—
173C2×#131—91no—
174C2×#104—31no—
175C2×#104—91no—
176#408—91no—
177#341—91no—
178#336—91no—
179C3×#41—22no—
180C3×#41—22no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—22no—
186C3×#41—22no—
187C3×#41—61no—
188C3×#41—61no—
189C3×#41—61no—
190C3×#41—61no—
191C3×#41D1212yes—
192C3×#41#6712yes—
193C3×#41#6712yes—
194C3×#41#6712yes—
195C2×C3×Q8—21no—
196C2×C3×Q8—31no—
197C2×C3×Q8C4×D311yescharacteristic
198C2×C3×Q8C2×Dic311yescharacteristic
199C2×C3×D4—22no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—31no—
204C2×C3×D4—61no—
205C2×C3×D4C4×D311yescharacteristic
206C2×C3×D4C2×Dic311yescharacteristic
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—61no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—21no—
216C22×Dic3—21no—
217#235—21no—
218#235—21no—
219#235—21no—
220#235—21no—
221C2×D12C2×Dic311yescharacteristic
222C2×C4×D3—21no—
223C2×Dic6C2×Dic311yescharacteristic
224C3×Q16—62no—
225C3×SD16—62no—
226C3×SD16—62no—
227C3×D8—62no—
228C3×M16—61no—
229C3×M16—61no—
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C3×C42—61no—
236C3×C42—61no—
237#216—22no—
238#215—22no—
239#214—22no—
240#213—22no—
241C4×Dic3—21no—
242C4×Dic3—21no—
243#208—21no—
244#208—21no—
245#208—32no—
246#208—32no—
247#208—62no—
248#208—68no—
249#208—64no—
250#208—64no—
251#208—62no—
252#208—61no—
253#208—61no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—31no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8—68no—
265C2×C3⋊C8—64no—
266C2×C3⋊C8—64no—
267C2×C3⋊C8—62no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8C2×Dic311yescharacteristic
276C2×C3⋊C8C2×Dic311yescharacteristic
277C22×C32—22no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32C4×D411yescharacteristic
283C22×C32#12111yescharacteristic
284C22×C32#12311yescharacteristic
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—22no—
289C32×C4C2×C22⋊C411yescharacteristic
290C32×C4C4×D411yescharacteristic
291C32×C4#12011yescharacteristic
292C32×C4#12111yescharacteristic
293C3×Dic3—42no—
294C3×Dic3—41no—
295C2×#41—31no—
296C2×#41D3211yescharacteristic
297#135—62no—
298#135—62no—
299C2×Q16—31no—
300C2×SD16—31no—
301C2×SD16—31no—
302C2×D8—31no—
303#131—182no—
304#131—182no—
305C2×M16—31no—
306C2×M16—91no—
307C2×M16—181no—
308C22×C8—31no—
309C22×C8—91no—
310C22×C8—181no—
311C2×C42—31no—
312#104—62no—
313#104—182no—
314C22⋊C8—181no—
315C22⋊C8—181no—
316C23×C3—22no—
317C23×C3—21no—
318C23×C3—21no—
319C23×C3—21no—
320C23×C3—61no—
321C23×C3#23711yescharacteristic
322C23×C3#23711yescharacteristic
323C22×D3—21no—
324C3×Q8—22no—
325C3×Q8—21no—
326C3×Q8—21no—
327C3×Q8—22no—
328C3×Q8—61no—
329C3×Q8—61no—
330C3×Q8(C2×D3)⋊C412yes—
331C3×Q8#21712yes—
332C3×D4—24no—
333C3×D4—24no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—21no—
340C3×D4—21no—
341C3×D4—22no—
342C3×D4—61no—
343C3×D4—61no—
344C3×D4—121no—
345C3×D4—121no—
346C3×D4(C2×D3)⋊C412yes—
347C3×D4#21712yes—
348C2×C3×C4—24no—
349C2×C3×C4—22no—
350C2×C3×C4—24no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—62no—
364C2×C3×C4—61no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4—121no—
368C2×C3×C4—121no—
369C2×C3×C4C2×C4×D311yescharacteristic
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4#23711yescharacteristic
376C2×C3×C4#23711yescharacteristic
377C2×C3×C4C22×Dic311yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381#67—41no—
382#67—41no—
383C2×Dic3—22no—
384C2×Dic3—21no—
385C2×Dic3—41no—
386C2×Dic3—41no—
387D12—21no—
388D12—21no—
389C4×D3—41no—
390C4×D3—41no—
391Dic6—21no—
392Dic6—21no—
393C3×C8—61no—
394C3×C8—61no—
395C3×C8—121no—
396C3⋊C8—21no—
397C3⋊C8—21no—
398C3⋊C8—41no—
399C3⋊C8—62no—
400C3⋊C8—62no—
401C3⋊C8—64no—
402C3⋊C8—61no—
403C3⋊C8—61no—
404C3⋊C8—62no—
405C3⋊C8—61no—
406C3⋊C8—61no—
407C3⋊C8—62no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32—42no—
411C2×C32#38611yescharacteristic
412C2×C32#44311yescharacteristic
413C2×C32#44411yescharacteristic
414C3×D3—81no—
415#41—21no—
416#41—21no—
417#41—61no—
418#41—61no—
419#41—61no—
420#41—61no—
421#41#62512yes—
422#41#62612yes—
423C2×Q8—31no—
424C2×Q8D3×Dic311yescharacteristic
425C2×D4—21no—
426C2×D4—31no—
427C2×D4—61no—
428C2×D4D3×Dic311yescharacteristic
429C22×C4—21no—
430C22×C4—61no—
431C22×C4—61no—
432C22×C4C2×D3211yescharacteristic
433Q16—62no—
434SD16—62no—
435SD16—62no—
436D8—62no—
437M16—61no—
438M16—61no—
439M16—92no—
440M16—184no—
441M16—181no—
442C2×C8—31no—
443C2×C8—31no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8—61no—
447C2×C8—91no—
448C2×C8—91no—
449C2×C8—184no—
450C2×C8—181no—
451C2×C8—181no—
452C2×C8—181no—
453C42—61no—
454C42—61no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—24no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—121no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3#67⋊C411yescharacteristic
477C22×C3#88611yescharacteristic
478C22×C3D4×Dic311yescharacteristic
479C22×C3#93511yescharacteristic
480C22×C3#93911yescharacteristic
481C22×C3#93911yescharacteristic
482C2×D3—41no—
483C2×D3—41no—
484C2×D3—41no—
485C3×C4—24no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—122no—
493C3×C4—121no—
494C3×C4#67⋊C411yescharacteristic
495C3×C4#88211yescharacteristic
496C3×C4C2×(C2×D3)⋊C411yescharacteristic
497C3×C4D4×Dic311yescharacteristic
498C3×C4#93711yescharacteristic
499C3×C4#93911yescharacteristic
500C3×C4#93911yescharacteristic
501C3×C4C2×#21711yescharacteristic
502Dic3—42no—
503Dic3—41no—
504C32#187611yescharacteristic, complemented, Sylow
505C23—21no—
506C23—61no—
507C23#380511yescharacteristic
508Q8—21no—
509Q8—61no—
510Q8—61no—
511Q8(C2×D3)⋊Dic312yes—
512D4—22no—
513D4—22no—
514D4—21no—
515D4—61no—
516D4—61no—
517D4—121no—
518D4—121no—
519D4(C2×D3)⋊Dic312yes—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—62no—
524C2×C4—61no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4C2×D3×Dic311yescharacteristic
530C2×C4#380511yescharacteristic
531C2×C4C2×#62511yescharacteristic
532C2×C4C2×#62611yescharacteristic
533C2×C4#381111yescharacteristic
534C2×C4#381111yescharacteristic
535C8—61no—
536C8—61no—
537C8—121no—
538C8—181no—
539C8—181no—
540C8—182no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—41no—
549C2×C3—41no—
550C2×C3—44no—
551C2×C3—42no—
552C2×C3—42no—
553C2×C3—241no—
554C2×C3#482311yescharacteristic
555C2×C3#482411yescharacteristic
556C2×C3#495811yescharacteristic
557C2×C3#519611yescharacteristic
558C2×C3#519711yescharacteristic
559C2×C3#522011yescharacteristic
560D3—81no—
561C22—21no—
562C22—21no—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—121no—
567C22—121no—
568C22—121no—
569C22#6396211yescharacteristic
570C22#67⋊Dic311yescharacteristic
571C22#6398011yescharacteristic
572C4—22no—
573C4—122no—
574C4—121no—
575C4C2×(C2×D3)⋊Dic311yescharacteristic
576C4#67⋊Dic311yescharacteristic
577C4#6398011yescharacteristic
578C4#6398111yescharacteristic
579C3—21no—
580C3#7037711yescharacteristic, complemented
581C3#7208711yescharacteristic, complemented
582C2—21no—
583C2—21no—
584C2—42no—
585C2—241no—
586C2#1059167511yescharacteristic
587C2#1059167611yescharacteristic
588C2#1059171311yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C4×D4
prime radicalC2×C3×#950C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1876
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64157C2semidirect
3. C2×C3×#837C2semidirect
4. C2×#63569C2semidirect
5. #10591071C2semidirect
6. #10589166C2semidirect
7. #10589155C2semidirect
20. C2×C3×#216C4semidirect
21. C2×C3×#215C4semidirect
22. C2×C3×#214C4semidirect
23. C2×C3×#213C4semidirect
38. C2×#837D3semidirect
109. C2×#216Dic3semidirect
110. C2×#215Dic3semidirect
111. C2×#214Dic3semidirect
112. C2×#213Dic3semidirect
504. C32#1876semidirect
580. C3#70377semidirect
581. C3#72087semidirect

Maximal subgroups

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

subgroupindex
C2×#641572
C2×C3×#9502
C2×C3×#8372
C2×#635692
#105910712
#105891662
#105891552
#720873
#703773