Finite Group Databasebeta

← #11884392

Subgroups — #11884392

Order 1152.

1530 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic, complemented
2C2×#64113C211yesmaximal, characteristic, complemented
3#10596024C211yesmaximal, characteristic, complemented
4#10596021C211yesmaximal, characteristic, complemented
5C32×#435C211yesmaximal, characteristic, complemented
6#10592833C211yesmaximal, characteristic, complemented
7#10592814C211yesmaximal, characteristic, complemented
8#10592544C211yesmaximal, characteristic, complemented
9#10592542C211yesmaximal, characteristic, complemented
10#10592433C211yesmaximal, characteristic, complemented
11#10592433C211yesmaximal, characteristic, complemented
12#10592432C211yesmaximal, characteristic, complemented
13#10592431C211yesmaximal, characteristic, complemented
14#10592411C211yesmaximal, characteristic, complemented
15#10592409C211yesmaximal, characteristic, complemented
16#79497—34nomaximal
17C2×#3828C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C2×#3828C2211yescharacteristic, complemented
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×M16C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24#64149—21no—
25#64146—21no—
26#64139C2211yescharacteristic
27#64139C2211yescharacteristic
28#64139C2211yescharacteristic, complemented
29#64133C2211yescharacteristic
30#64117—24no—
31C2×#3746C2211yescharacteristic, complemented
32#64113—24no—
33C2×#3745C2211yescharacteristic
34C2×#3745C2211yescharacteristic
35C2×#3745C2211yescharacteristic
36C2×#3745C2211yescharacteristic
37C2×#3744C2211yescharacteristic
38C2×#3744C2211yescharacteristic
39C2×#3744C2211yescharacteristic, complemented
40C2×#3744C2211yescharacteristic, complemented
41#64103—21no—
42#64102—21no—
43#64093—21no—
44#64093—21no—
45#64093—21no—
46C22⋊C4×C3⋊D3—21no—
47#64084C2211yescharacteristic
48#64083C2211yescharacteristic, complemented
49C4×C4⋊(C3⋊D3)C2211yescharacteristic
50C4×#634C2211yescharacteristic, complemented
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×C22⋊C8C2211yescharacteristic
53C32×C22⋊C8C2211yescharacteristic, complemented
54C32×#97C2211yescharacteristic, complemented
55#63648C2211yescharacteristic
56#63648C2211yescharacteristic
57#63648C2211yescharacteristic, complemented
58#63648C2211yescharacteristic, complemented
59#63645C2211yescharacteristic, complemented
60#63643C2211yescharacteristic, complemented
61#63643C2211yescharacteristic, complemented
62C2×#908—34no—
63C2×#904—34no—
64#5553—34no—
65#5550—34no—
66C3×#435D314yescomplemented
67#5134—34no—
68#5115—34no—
69#4845—34no—
70#4843—34no—
71#4734—34no—
72#4734—34no—
73#4733—34no—
74#4732—34no—
75#4712—34no—
76#4710—34no—
77C23×C3⋊D3—21no—
78C2×C32×D4D411yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C2×#638—21no—
82C2×#638—21no—
83C2×#638—21no—
84C2×#638—21no—
85C2×#638—21no—
86C2×#638—21no—
87#3828—22no—
88#3828—22no—
89#3828—22no—
90#3828—41no—
91#3828—41no—
92#3828—41no—
93C2×C4⋊(C3⋊D3)—22no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C32×M16—22no—
109C2×C32×C8—22no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4D411yescharacteristic
115C32×C22⋊C4D411yescharacteristic
116C32×C22⋊C4D411yescharacteristic
117C32×C42C2311yescharacteristic
118#3757—21no—
119#3752—21no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123#3752—21no—
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128#3750—21no—
129C4×C3⋊Dic3—21no—
130#3746—22no—
131#3745—22no—
132#3745—22no—
133#3745—22no—
134#3745—41no—
135#3744—22no—
136#3744—22no—
137#3744—41no—
138#3744D414yescomplemented
139#3268—91noSylow
140C2×#235—34no—
141C2×#235—34no—
142C2×#235—34no—
143C22×D12—34no—
144C2×C3×M16C2×D314yes—
145C22×C3×C8C2×D314yescomplemented
146C3×C4×D4C2×D314yes—
147#940—64no—
148#937—64no—
149#930—34no—
150#930—34no—
151#930—34no—
152#924—34no—
153#908—616no—
154C2×Dic12—34no—
155#904—616no—
156C2×D24—34no—
157C2×D24—34no—
158C2×D24—34no—
159C2×D24—34no—
160C2×#204—34no—
161C2×#204—34no—
162C2×#204—34no—
163C2×#204—34no—
164#894—64no—
165#893—64no—
166#884—64no—
167#884—64no—
168#884—64no—
169D3×C22⋊C4—64no—
170#875—34no—
171#874—34no—
172C4×D12—34no—
173C4×Dic6—34no—
174C3×C4⋊C8C2×D314yescomplemented
175C3×C22⋊C8C2×D314yes—
176C3×C22⋊C8C2×D314yescomplemented
177C3×#97C2×D314yescomplemented
178#821—34no—
179#821—34no—
180#821—34no—
181#821—34no—
182#818—34no—
183#816—34no—
184#816—34no—
185C23×C32C2×D411yescharacteristic
186C23×C32C2×D411yescharacteristic
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
189C22×C3⋊D3—21no—
190C22×C3⋊D3—21no—
191C22×C3⋊D3—42no—
192C22×C3⋊D3—42no—
193C22×C3⋊D3—81no—
194C32×D4—41no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4C2×D411yescharacteristic
203C2×C32×C4C2411yescharacteristic
204#638—42no—
205#638—42no—
206#638—42no—
207#638—81no—
208#638—81no—
209#638—81no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)—21no—
216C4⋊(C3⋊D3)—21no—
217C4⋊(C3⋊D3)—21no—
218C4⋊(C3⋊D3)—21no—
219C4⋊(C3⋊D3)—21no—
220C4⋊(C3⋊D3)—21no—
221C4⋊(C3⋊D3)—42no—
222C4⋊(C3⋊D3)—42no—
223C4⋊(C3⋊D3)—81no—
224C4⋊(C3⋊D3)C2×D412yes—
225C4×C3⋊D3—42no—
226C4×C3⋊D3—42no—
227C4×C3⋊D3—42no—
228C4×C3⋊D3—81no—
229#634—21no—
230#634—21no—
231#634—21no—
232#634C2×D412yes—
233C32×C8—21no—
234C32×C8—21no—
235C32×C8—21no—
236C32×C8C2×D412yes—
237C2×AGL(1,ℤ/8)—91no—
238C2×#135—91no—
239#550—91no—
240#546—91no—
241#496—91no—
242#468—91no—
243#466—91no—
244#464—91no—
245#459—91no—
246#452—91no—
247#449—91no—
248#449—91no—
249#447—91no—
250#440—91no—
251#435C3⋊D311yescharacteristic, complemented
252C23×D3—64no—
253C2×C3×D4D1214yes—
254C22×C3×C4C22×D314yes—
255C22×C3×C4C22×D314yes—
256C2×#67—64no—
257C2×#67—64no—
258C2×#67—64no—
259C2×#67—64no—
260C2×#67—64no—
261C2×#67—64no—
262#235—68no—
263#235—68no—
264#235—68no—
265#235—124no—
266#235—124no—
267#235—124no—
268C2×D12—34no—
269C2×D12—34no—
270C2×D12—34no—
271C2×D12—34no—
272C2×D12—68no—
273C2×D12—64no—
274C2×D12—64no—
275C2×D12—64no—
276C2×D12—124no—
277C2×C4×D3—64no—
278C2×C4×D3—64no—
279C2×C4×D3—64no—
280C2×C4×D3—64no—
281C2×Dic6—34no—
282C2×Dic6—34no—
283C3×M16—28no—
284C2×C3×C8—28no—
285C2×C3×C8C22×D314yes—
286C2×C3×C8C22×D314yes—
287C2×C3×C8C22×D314yes—
288C2×C3×C8C22×D314yes—
289C3×C4⋊C4D1214yes—
290C3×C22⋊C4D1214yes—
291C3×C22⋊C4D1214yes—
292C3×C42C22×D314yes—
293#217—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4—64no—
298(C2×D3)⋊C4—64no—
299(C2×D3)⋊C4—64no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302Dic3⋊C4—64no—
303Dic3⋊C4—64no—
304C4×Dic3—64no—
305Dic12—68no—
306D24—68no—
307D24—68no—
308D24—68no—
309D24—124no—
310#204—316no—
311#204—68no—
312#204—68no—
313#204—124no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32C22×D411yescharacteristic
321C2×C3⋊D3—22no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3—41no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—41no—
330C2×C3⋊D3—41no—
331C2×C3⋊D3—41no—
332C2×C3⋊D3—41no—
333C2×C3⋊D3—84no—
334C32×C4—21no—
335C32×C4—21no—
336C32×C4—21no—
337C32×C4—21no—
338C32×C4C22×D411yescharacteristic
339C32×C4H(5,𝔽2)11yescharacteristic
340C3⋊Dic3—22no—
341C3⋊Dic3—41no—
342C3⋊Dic3—41no—
343C3⋊Dic3—41no—
344C2×#41—91no—
345C2×#41—91no—
346C2×#41—91no—
347C22×D4—91no—
348AGL(1,ℤ/8)—184no—
349#135—184no—
350C2×Q16—91no—
351C2×SD16—91no—
352C2×SD16—91no—
353C2×SD16—91no—
354C2×SD16—91no—
355C2×D8—91no—
356C2×D8—91no—
357C2×D8—91no—
358C2×D8—91no—
359C2×M16C2×C3⋊D311yescharacteristic
360C22×C8C2×C3⋊D311yescharacteristic, complemented
361#127—91no—
362#127—181no—
363#124—91no—
364#123—181no—
365C22⋊Q8—91no—
366#121—91no—
367#121—91no—
368#121—91no—
369#121—181no—
370#121—181no—
371#121—181no—
372#120—181no—
373C4×Q8—91no—
374C4×D4—91no—
375C4×D4—181no—
376C4×D4C2×C3⋊D311yescharacteristic
377C2×C22⋊C4—181no—
378#107—91no—
379C4⋊C8C2×C3⋊D311yescharacteristic, complemented
380#103—91no—
381#103—91no—
382#102—91no—
383#102—91no—
384#102—91no—
385#102—91no—
386C22⋊C8C2×C3⋊D311yescharacteristic
387C22⋊C8C2×C3⋊D311yescharacteristic, complemented
388#97C2×C3⋊D311yescharacteristic, complemented
389C23×C3C2×D1214yes—
390C23×C3C2×D1214yes—
391C22×D3—64no—
392C22×D3—64no—
393C22×D3—64no—
394C22×D3—64no—
395C22×D3—128no—
396C22×D3—128no—
397C22×D3—244no—
398C3×D4—44no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4C2×D1214yes—
404C2×C3×C4C2×D1214yes—
405C2×C3×C4C2×D1214yes—
406C2×C3×C4C2×D1214yes—
407C2×C3×C4C23×D314yes—
408#67—128no—
409#67—128no—
410#67—128no—
411#67—244no—
412#67—244no—
413#67—244no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418D12—38no—
419D12—64no—
420D12—64no—
421D12—64no—
422D12—64no—
423D12—64no—
424D12—64no—
425D12—64no—
426D12—128no—
427D12—128no—
428D12—244no—
429C4×D3—128no—
430C4×D3—128no—
431C4×D3—128no—
432C4×D3—244no—
433Dic6—38no—
434Dic6—64no—
435Dic6—64no—
436Dic6—64no—
437C3×C8—24no—
438C3×C8—24no—
439C3×C8—24no—
440C3×C8D3×D418yes—
441C2×C32—41no—
442C2×C32—41no—
443C2×C32D4211yescharacteristic
444C2×C32#57511yescharacteristic
445C2×C32#57611yescharacteristic
446C3⋊D3—42no—
447C3⋊D3—81no—
448C3⋊D3—81no—
449C3⋊D3—81no—
450C24—181no—
451#41—182no—
452#41—182no—
453#41—182no—
454#41—361no—
455#41—361no—
456#41—361no—
457C2×Q8—91no—
458C2×Q8—91no—
459C2×D4—91no—
460C2×D4—91no—
461C2×D4—91no—
462C2×D4—91no—
463C2×D4—182no—
464C2×D4—181no—
465C2×D4—181no—
466C2×D4—181no—
467C2×D4—181no—
468C2×D4—181no—
469C2×D4—181no—
470C2×D4—181no—
471C2×D4—181no—
472C2×D4—181no—
473C2×D4—361no—
474C2×D4C4⋊(C3⋊D3)11yescharacteristic
475C22×C4—181no—
476C22×C4—181no—
477C22×C4—181no—
478C22×C4—181no—
479C22×C4C22×C3⋊D311yescharacteristic
480C22×C4C22×C3⋊D311yescharacteristic
481Q16—182no—
482SD16—94no—
483SD16—182no—
484SD16—182no—
485SD16—361no—
486D8—182no—
487D8—182no—
488D8—182no—
489D8—361no—
490M16—22no—
491C2×C8—22no—
492C2×C8C22×C3⋊D311yescharacteristic
493C2×C8C22×C3⋊D311yescharacteristic
494C2×C8C22×C3⋊D311yescharacteristic
495C2×C8C22×C3⋊D311yescharacteristic
496C4⋊C4—91no—
497C4⋊C4—91no—
498C4⋊C4—181no—
499C4⋊C4—181no—
500C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
501C22⋊C4—181no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C22⋊C4—181no—
507C22⋊C4—181no—
508C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
509C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
510C42—181no—
511C42C22×C3⋊D311yescharacteristic
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3C22×D1214yes—
519C2×D3—68no—
520C2×D3—124no—
521C2×D3—124no—
522C2×D3—124no—
523C2×D3—124no—
524C2×D3—124no—
525C2×D3—124no—
526C2×D3—124no—
527C2×D3—124no—
528C2×D3—124no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3—2416no—
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4C2×D3×D414yes—
537C3×C4#100914yes—
538Dic3—68no—
539Dic3—124no—
540Dic3—124no—
541Dic3—124no—
542C32#326811yescharacteristic, complemented, Sylow
543C23—181no—
544C23—181no—
545C23—181no—
546C23—181no—
547C23—362no—
548C23—362no—
549C23—721no—
550C23C2×C4⋊(C3⋊D3)11yescharacteristic
551C23C2×C4⋊(C3⋊D3)11yescharacteristic
552Q8—92no—
553Q8—181no—
554Q8—181no—
555Q8—181no—
556D4—41no—
557D4—92no—
558D4—181no—
559D4—181no—
560D4—181no—
561D4—181no—
562D4—181no—
563D4—181no—
564D4—181no—
565D4—362no—
566D4—362no—
567D4—362no—
568D4—362no—
569D4—362no—
570D4—721no—
571D4—721no—
572D4—721no—
573D4—721no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—362no—
583C2×C4—362no—
584C2×C4—362no—
585C2×C4—721no—
586C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
587C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
588C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
589C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
590C2×C4C23×C3⋊D311yescharacteristic
591C8—21no—
592C8—21no—
593C8—21no—
594C8D4×C3⋊D312yes—
595C2×C3—44no—
596C2×C3—44no—
597C2×C3D4×D1214yes—
598C2×C3#574814yes—
599C2×C3#575214yes—
600D3—128no—
601D3—244no—
602D3—244no—
603D3—244no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—182no—
611C22—361no—
612C22—361no—
613C22—361no—
614C22—361no—
615C22—361no—
616C22—361no—
617C22—361no—
618C22—361no—
619C22—361no—
620C22—361no—
621C22—361no—
622C22—724no—
623C22C22×C4⋊(C3⋊D3)11yescharacteristic
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—182no—
629C4—361no—
630C4—361no—
631C4—361no—
632C4C2×D4×C3⋊D311yescharacteristic
633C4#6436611yescharacteristic
634C3#7949714yescomplemented
635C2—41no—
636C2—41no—
637C2—362no—
638C2—721no—
639C2—721no—
640C2—721no—
641C2D4×C4⋊(C3⋊D3)11yescharacteristic
642C2#1059621911yescharacteristic
643C2#1059622311yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#435C2
socleC22×C32C22×D4
hypercenter#435C3⋊D3
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#64117C2semidirect
2. C2×#64113C2semidirect
3. #10596024C2semidirect
4. #10596021C2semidirect
5. C32×#435C2semidirect
6. #10592833C2semidirect
7. #10592814C2semidirect
8. #10592544C2semidirect
9. #10592542C2semidirect
10. #10592433C2semidirect
11. #10592433C2semidirect
12. #10592432C2semidirect
13. #10592431C2semidirect
14. #10592411C2semidirect
15. #10592409C2semidirect
19. C2×#3828C22semidirect
22. C22×C32×C8C22semidirect
28. #64139C22semidirect
31. C2×#3746C22semidirect
39. C2×#3744C22semidirect
40. C2×#3744C22semidirect
48. #64083C22semidirect
50. C4×#634C22semidirect
51. C32×C4⋊C8C22semidirect
53. C32×C22⋊C8C22semidirect
54. C32×#97C22semidirect
57. #63648C22semidirect
58. #63648C22semidirect
59. #63645C22semidirect
60. #63643C22semidirect
61. #63643C22semidirect
66. C3×#435D3semidirect
138. #3744D4semidirect
145. C22×C3×C8C2×D3semidirect
174. C3×C4⋊C8C2×D3semidirect
176. C3×C22⋊C8C2×D3semidirect
177. C3×#97C2×D3semidirect
251. #435C3⋊D3semidirect
360. C22×C8C2×C3⋊D3semidirect
379. C4⋊C8C2×C3⋊D3semidirect
387. C22⋊C8C2×C3⋊D3semidirect
388. #97C2×C3⋊D3semidirect
542. C32#3268semidirect
634. C3#79497semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
C2×#641132
#105960242
#105960212
C32×#4352
#105928332
#105928142
#105925442
#105925422
#105924332
#105924322
#105924312
#105924112
#105924092
#794973