Finite Group Databasebeta

← #11869671

Subgroups — #11869671

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2#10594922C211yesmaximal, characteristic
3C3×#4971C211yesmaximal, characteristic, complemented
4C3×#4967C211yesmaximal, characteristic, complemented
5#10591152C211yesmaximal, characteristic, complemented
6#10591103C211yesmaximal, characteristic, complemented
7#10591092C211yesmaximal, characteristic, complemented
8#10590611C212yesmaximal, complemented
9#10590574C212yesmaximal, complemented
10#10590526C212yesmaximal, complemented
11#10590513C212yesmaximal, complemented
12#81426—31nomaximal
13#81281—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×#3796C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3—21no—
20#64101—21no—
21#64101—21no—
22#64101C2212yes—
23#64101C2212yes—
24C3×#930C2211yescharacteristic
25C3×#924C2211yescharacteristic
26#63981—21no—
27#67⋊Dic3—21no—
28#63916C2211yescharacteristic
29#63881—21no—
30#63871C2211yescharacteristic
31#63853—21no—
32#63849C2211yescharacteristic
33C2×#3710C2212yes—
34C3×#830C2211yescharacteristic
35C3×#830C2211yescharacteristic
36C3×#810C2212yescomplemented
37C3×#809C2212yescomplemented
38C3×#808C2212yescomplemented
39C3×#807C2212yescomplemented
40#63575C2212yescomplemented
41#63573C2212yescomplemented
42#63566C2212yescomplemented
43#63563C2212yescomplemented
44#63557C2212yes—
45#5627—31no—
46#5606—31no—
47C2×#892—31no—
48C2×#892—31no—
49C2×#892—61no—
50C3×#483—31no—
51C3×#480—31no—
52#5044—31no—
53#5034—31no—
54#4971D311yescharacteristic, complemented
55#4967D311yescharacteristic, complemented
56#4888—32no—
57#4880—32no—
58#4866—32no—
59#4860—32no—
60#4815—32no—
61#4804—32no—
62#4784—32no—
63#4772—32no—
64#4735—31no—
65D3×C22⋊C8—31no—
66D3×C22⋊C8—31no—
67#4722—31no—
68C23×C3⋊D3D411yescharacteristic
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C22×C3⋊Dic3D411yescharacteristic
73C2×C4×C3⋊D3—24no—
74C2×C4×C3⋊D3D411yescharacteristic
75C2×C4×C3⋊D3D411yescharacteristic
76C2×C4×C3⋊D3C2311yescharacteristic
77C2×C4×C3⋊D3C2311yescharacteristic
78C2×C3×#67—21no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×Dic6C2311yescharacteristic
81C2×#626—21no—
82C2×#626—21no—
83C2×D3×Dic3—21no—
84#3796—24no—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2312yes—
87#3752—22no—
88#3752—22no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)C2312yes—
91C4×C3⋊Dic3—22no—
92C4×C3⋊Dic3—22no—
93C3×#217—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2311yescharacteristic
97C3×Dic3⋊C4—21no—
98C2×C3×C3⋊C8C2312yes—
99C2×C3×C3⋊C8C2312yes—
100Dic3⋊Dic3—21no—
101#3722—21no—
102#3722—21no—
103(C2×D3)⋊Dic3—21no—
104Dic32—21no—
105#3710—24no—
106#3091—91noSylow
107C2×#239—31no—
108C2×#237—31no—
109C22×C4×D3—31no—
110C22×C4×D3—31no—
111C22×C4×D3—61no—
112C3×C22⋊Q8—31no—
113C3×#121—31no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4C2×D311yescharacteristic
116C2×C3×C4⋊C4C2×D311yescharacteristic
117#946—31no—
118#938—31no—
119#937—61no—
120D4×Dic3—61no—
121#930C2×D311yescharacteristic
122C2×(C2×D3)⋊C4—61no—
123C2×(C2×D3)⋊C4—61no—
124C2×(C2×D3)⋊C4—62no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—61no—
128#924C2×D311yescharacteristic
129C2×C4×Dic3—61no—
130C2×C4×Dic3—61no—
131C2×C4×Dic3—62no—
132C2×D3×C8—32no—
133C2×D3×C8—32no—
134#897—31no—
135#895—31no—
136#894—61no—
137#893—61no—
138#892—32no—
139#892—32no—
140#892—32no—
141#892—32no—
142#892—31no—
143#892—31no—
144#892—62no—
145#892—62no—
146#892—61no—
147#892—61no—
148#892—61no—
149#892—61no—
150#892—62no—
151#892—62no—
152#883—61no—
153#882—61no—
154#67⋊C4—61no—
155#67⋊C4—61no—
156C3×#107—32no—
157C3×#106—32no—
158C3×#103—32no—
159C3×#102—32no—
160C3×C22⋊C8—31no—
161C3×C22⋊C8—31no—
162#835—32no—
163#832—32no—
164#830C2×D311yescharacteristic
165#830C2×D311yescharacteristic
166#821—32no—
167(C2×D3)⋊C8—32no—
168(C2×D3)⋊C8—32no—
169#818—32no—
170#817—32no—
171#816—32no—
172#810C2×D312yescomplemented
173#809C2×D312yescomplemented
174#808—32no—
175#808C2×D312yescomplemented
176#807—32no—
177#807C2×D312yescomplemented
178C23×C32C2×D411yescharacteristic
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—41no—
182C22×C3⋊D3C2×D411yescharacteristic
183C22×C3⋊D3C2×D411yescharacteristic
184C22×C3×D3—21no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—42no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—42no—
193C2×C3⋊Dic3C2×D411yescharacteristic
194C2×C3⋊Dic3C2×D411yescharacteristic
195C4×C3⋊D3—22no—
196C4×C3⋊D3—22no—
197C4×C3⋊D3—22no—
198C4×C3⋊D3#4114yes—
199C3×#67—42no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C3×D12—22no—
204C3×Dic6—22no—
205#626—42no—
206#626—42no—
207D3×Dic3—42no—
208C3×C3⋊C8—22no—
209C3×C3⋊C8—22no—
210#525—91no—
211C2×#117—91no—
212#485—92no—
213#484—91no—
214#483—31no—
215#482—92no—
216#481—91no—
217#480—31no—
218#427—92no—
219#416—92no—
220C2×C22⋊C8—91no—
221C23×D3—31no—
222C23×D3—31no—
223C23×D3—61no—
224C2×C3×Q8—31no—
225C2×C3×D4—31no—
226C2×C3×D4—61no—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C2×#67—61no—
235C2×#67—61no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—62no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243#239—64no—
244#237—64no—
245C2×D12—61no—
246C2×D12—61no—
247C2×D12C22×D311yescharacteristic
248C2×C4×D3—31no—
249C2×C4×D3—31no—
250C2×C4×D3—31no—
251C2×C4×D3—31no—
252C2×C4×D3—31no—
253C2×C4×D3—31no—
254C2×C4×D3—31no—
255C2×C4×D3—31no—
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×C4×D3—61no—
259C2×C4×D3—61no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—68no—
263C2×C4×D3—61no—
264C2×Dic6C22×D311yescharacteristic
265C2×C3×C8—32no—
266C2×C3×C8—32no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—31no—
272C3×C4⋊C4—31no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4C22×D312yes—
275C3×C4⋊C4C22×D312yes—
276C3×C22⋊C4—61no—
277C3×C22⋊C4—61no—
278#217—21no—
279#217—61no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290(C2×D3)⋊C4—64no—
291(C2×D3)⋊C4—64no—
292C4⋊Dic3—32no—
293C4⋊Dic3—32no—
294C4⋊Dic3—62no—
295C4⋊Dic3—61no—
296C4⋊Dic3—62no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3C22×D311yescharacteristic
300C4⋊Dic3C22×D311yescharacteristic
301Dic3⋊C4—21no—
302Dic3⋊C4—61no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—62no—
306C4×Dic3—62no—
307C4×Dic3—62no—
308C4×Dic3—62no—
309C4×Dic3—64no—
310C4×Dic3—64no—
311C2×C3⋊C8C22×D312yes—
312C2×C3⋊C8C22×D312yes—
313D3×C8—64no—
314D3×C8—64no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32#13512yes—
318C22×C32C22×D411yescharacteristic
319C2×C3⋊D3—21no—
320C2×C3⋊D3—21no—
321C2×C3⋊D3—21no—
322C2×C3⋊D3—21no—
323C2×C3⋊D3—21no—
324C2×C3⋊D3—44no—
325C2×C3⋊D3#12312yes—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C32×C4—21no—
330C32×C4—42no—
331C32×C4C2×#4112yes—
332C3⋊Dic3—21no—
333C3⋊Dic3—42no—
334C3⋊Dic3#12312yes—
335C3×Dic3—41no—
336C3×Dic3—41no—
337C3×Dic3—41no—
338C2×#41—91no—
339C23×C4—91no—
340C22×C8—92no—
341#123—181no—
342C22⋊Q8—31no—
343C22⋊Q8—91no—
344#121—31no—
345#121—91no—
346#120—181no—
347C4×D4—181no—
348C4×D4—181no—
349#117—91no—
350#117—92no—
351#117—92no—
352#117—181no—
353#117—181no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4D3211yescharacteristic
356C2×C22⋊C4—181no—
357C2×C42—181no—
358#107—32no—
359#107—92no—
360#106—32no—
361#106—92no—
362#103—32no—
363#103—92no—
364#102—32no—
365#102—92no—
366C22⋊C8—31no—
367C22⋊C8—31no—
368C22⋊C8—92no—
369C23×C3—21no—
370C23×C3—61no—
371C23×C3D3×D411yescharacteristic
372C23×C3D3×D411yescharacteristic
373C22×D3—21no—
374C22×D3—31no—
375C22×D3—31no—
376C22×D3—31no—
377C22×D3—31no—
378C22×D3—61no—
379C22×D3—61no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—64no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—122no—
386C22×D3—121no—
387C22×D3—121no—
388C22×D3—122no—
389C3×Q8—62no—
390C3×D4—62no—
391C3×D4—122no—
392C2×C3×C4—24no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—44no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—42no—
411#67—122no—
412#67—122no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—31no—
417C2×Dic3—31no—
418C2×Dic3—31no—
419C2×Dic3—31no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—122no—
429C2×Dic3—124no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432D12—22no—
433D12—122no—
434D12—122no—
435C4×D3—34no—
436C4×D3—34no—
437C4×D3—64no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—62no—
442C4×D3—64no—
443C4×D3—64no—
444C4×D3—64no—
445C4×D3—62no—
446C4×D3—62no—
447C4×D3—122no—
448Dic6—22no—
449C3×C8—62no—
450C3×C8—62no—
451C3⋊C8—22no—
452C3⋊C8—22no—
453C2×C32—22no—
454C2×C32C2×#12311yescharacteristic
455C2×C32C2×#13511yescharacteristic
456C2×C32#57511yescharacteristic
457C3⋊D3—22no—
458C3⋊D3—41no—
459C3×D3—81no—
460C24—91no—
461#41—184no—
462C2×Q8—31no—
463C2×D4—31no—
464C2×D4—61no—
465C2×D4—181no—
466C2×D4—181no—
467C22×C4—21no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—91no—
471C22×C4—91no—
472C22×C4—91no—
473C22×C4—184no—
474C22×C4—181no—
475C22×C4—181no—
476C22×C4C2×D3211yescharacteristic
477C2×C8—32no—
478C2×C8—32no—
479C2×C8—184no—
480C4⋊C4—21no—
481C4⋊C4—31no—
482C4⋊C4—31no—
483C4⋊C4—61no—
484C4⋊C4—92no—
485C4⋊C4—181no—
486C4⋊C4—181no—
487C4⋊C4C2×D3212yes—
488C22⋊C4—61no—
489C22⋊C4—61no—
490C22⋊C4—182no—
491C22⋊C4—182no—
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C42—182no—
496C42—182no—
497C42—181no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—22no—
506C22×C3—121no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3#91212yes—
510C22×C3#91612yes—
511C22×C3C2×D3×D411yescharacteristic
512C22×C3C2×D3×D411yescharacteristic
513C2×D3—32no—
514C2×D3—32no—
515C2×D3—41no—
516C2×D3—41no—
517C2×D3—41no—
518C2×D3—62no—
519C2×D3—61no—
520C2×D3—61no—
521C2×D3—61no—
522C2×D3—61no—
523C2×D3—62no—
524C2×D3—61no—
525C2×D3—61no—
526C2×D3—61no—
527C2×D3—61no—
528C2×D3—61no—
529C2×D3—61no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—121no—
534C2×D3—124no—
535C2×D3—124no—
536C2×D3—128no—
537C3×C4—22no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—44no—
542C3×C4—42no—
543C3×C4—42no—
544C3×C4—121no—
545C3×C4—121no—
546C3×C4—121no—
547C3×C4D3×#4112yes—
548C3×C4D3×#4112yes—
549Dic3—32no—
550Dic3—32no—
551Dic3—41no—
552Dic3—41no—
553Dic3—41no—
554Dic3—62no—
555Dic3—62no—
556Dic3—61no—
557Dic3—61no—
558Dic3—124no—
559Dic3—122no—
560Dic3—122no—
561C32#309111yescharacteristic, complemented, Sylow
562C23—61no—
563C23—91no—
564C23—91no—
565C23—182no—
566C23—182no—
567C23—361no—
568C23#381111yescharacteristic
569Q8—62no—
570D4—62no—
571D4—122no—
572D4—362no—
573D4—362no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—42no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—91no—
581C2×C4—94no—
582C2×C4—91no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—362no—
589C2×C4—362no—
590C2×C4#381111yescharacteristic
591C2×C4C22×D3211yescharacteristic
592C8—62no—
593C8—62no—
594C2×C3—24no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—241no—
601C2×C3D3×#12311yescharacteristic
602C2×C3D3×#12311yescharacteristic
603C2×C3C2×#91211yescharacteristic
604C2×C3C2×#91611yescharacteristic
605C2×C3#577711yescharacteristic
606C2×C3#577711yescharacteristic
607D3—62no—
608D3—62no—
609D3—81no—
610D3—122no—
611D3—122no—
612D3—121no—
613D3—121no—
614C22—21no—
615C22—21no—
616C22—92no—
617C22—121no—
618C22—121no—
619C22—121no—
620C22—181no—
621C22—181no—
622C22—181no—
623C22—181no—
624C22—181no—
625C22—364no—
626C22#6393612yes—
627C22C2×#381111yescharacteristic
628C4—21no—
629C4—42no—
630C4—92no—
631C4—121no—
632C4—121no—
633C4—121no—
634C4—181no—
635C4—362no—
636C4#6430612yes—
637C3—21no—
638C3#8128111yescharacteristic, complemented
639C3#8142611yescharacteristic, complemented
640C2—22no—
641C2—182no—
642C2—241no—
643C2—361no—
644C2#1059507911yescharacteristic
645C2C2×#6393611yescharacteristic
646C2#1059532311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10594922C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64101C2semidirect
3. C3×#4971C2semidirect
4. C3×#4967C2semidirect
5. #10591152C2semidirect
6. #10591103C2semidirect
7. #10591092C2semidirect
8. #10590611C2semidirect
9. #10590574C2semidirect
10. #10590526C2semidirect
11. #10590513C2semidirect
36. C3×#810C22semidirect
37. C3×#809C22semidirect
38. C3×#808C22semidirect
39. C3×#807C22semidirect
40. #63575C22semidirect
41. #63573C22semidirect
42. #63566C22semidirect
43. #63563C22semidirect
54. #4971D3semidirect
55. #4967D3semidirect
172. #810C2×D3semidirect
173. #809C2×D3semidirect
175. #808C2×D3semidirect
177. #807C2×D3semidirect
561. C32#3091semidirect
638. C3#81281semidirect
639. C3#81426semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
#105949222
C3×#49712
C3×#49672
#105911522
#105911032
#105910922
#105906112
#105905742
#105905262
#105905132
#814263
#812813