Finite Group Databasebeta

← #11884237

Subgroups — #11884237

Order 1152.

1500 conjugacy classes of subgroups.

The subgroup lattice has 627 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#10596022C211yesmaximal, characteristic, complemented
4#10596021C211yesmaximal, characteristic, complemented
5C32×#435C211yesmaximal, characteristic, complemented
6#10592836C211yesmaximal, characteristic, complemented
7#10592813C211yesmaximal, characteristic, complemented
8#10592543C211yesmaximal, characteristic, complemented
9#10592540C211yesmaximal, characteristic, complemented
10#10592433C211yesmaximal, characteristic, complemented
11#10592432C211yesmaximal, characteristic, complemented
12#10592432C211yesmaximal, characteristic, complemented
13#10592430C211yesmaximal, characteristic, complemented
14#10592414C211yesmaximal, characteristic, complemented
15#10592410C211yesmaximal, characteristic, complemented
16#79496—34nomaximal
17C2×#3828C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C2×#3828C2211yescharacteristic, complemented
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×M16C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24#64147—21no—
25#64146—21no—
26#64139C2211yescharacteristic
27#64133C2211yescharacteristic
28#64133C2211yescharacteristic
29#64133C2211yescharacteristic, complemented
30#64117—24no—
31C2×#3746C2211yescharacteristic, complemented
32C2×#3746C2211yescharacteristic, complemented
33#64113—24no—
34C2×#3745C2211yescharacteristic
35C2×#3745C2211yescharacteristic
36C2×#3744C2211yescharacteristic
37C2×#3744C2211yescharacteristic
38C2×#3744C2211yescharacteristic
39C2×#3744C2211yescharacteristic
40C2×#3744C2211yescharacteristic, complemented
41#64103—21no—
42C4⋊C4×C3⋊D3—21no—
43#64093—21no—
44#64092—21no—
45#64092—21no—
46C22⋊C4×C3⋊D3—21no—
47#64084C2211yescharacteristic
48C4×C4⋊(C3⋊D3)C2211yescharacteristic
49C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
50#64078C2211yescharacteristic, complemented
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×C22⋊C8C2211yescharacteristic
53C32×C22⋊C8C2211yescharacteristic, complemented
54C32×#97C2211yescharacteristic, complemented
55#63648C2211yescharacteristic
56#63648C2211yescharacteristic
57#63648C2211yescharacteristic, complemented
58#63644C2211yescharacteristic, complemented
59#63643C2211yescharacteristic, complemented
60#63643C2211yescharacteristic, complemented
61#63643C2211yescharacteristic, complemented
62C2×#908—34no—
63C2×#904—34no—
64#5551—34no—
65#5550—34no—
66C3×#435D314yescomplemented
67#5137—34no—
68#5114—34no—
69#4844—34no—
70#4841—34no—
71#4734—34no—
72#4733—34no—
73#4733—34no—
74#4731—34no—
75#4715—34no—
76#4711—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—
85#3828—22no—
86#3828—22no—
87#3828—22no—
88#3828—41no—
89#3828—41no—
90#3828—41no—
91C2×C4⋊(C3⋊D3)—22no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)—41no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×#634C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C32×M16—22no—
106C2×C32×C8—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4D411yescharacteristic
112C32×C22⋊C4D411yescharacteristic
113C32×C22⋊C4D411yescharacteristic
114C32×C42C2311yescharacteristic
115#3757—21no—
116#3757—21no—
117#3757—21no—
118#3752—21no—
119#3752—21no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123C4⋊(C3⋊Dic3)—21no—
124C4⋊(C3⋊Dic3)—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128#3750—21no—
129#3750—21no—
130#3746—22no—
131#3746—41no—
132#3745—22no—
133#3745D414yescomplemented
134#3744—22no—
135#3744—22no—
136#3744—22no—
137#3744—22no—
138#3744—41no—
139#3267—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#938—64no—
148#937—64no—
149#930—34no—
150#924—34no—
151#924—34no—
152#924—34no—
153#908—616no—
154C2×Dic12—34no—
155C2×Dic12—34no—
156#904—616no—
157C2×D24—34no—
158C2×D24—34no—
159C2×#204—34no—
160C2×#204—34no—
161C2×#204—34no—
162C2×#204—34no—
163C2×#204—34no—
164#894—64no—
165D3×C4⋊C4—64no—
166#884—64no—
167#883—64no—
168#883—64no—
169D3×C22⋊C4—64no—
170#875—34no—
171C4×D12—34no—
172C4×D12—34no—
173#869—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#817—34no—
182#816—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—42no—
191C22×C3⋊D3—42no—
192C22×C3⋊D3—81no—
193C32×D4—41no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2×D411yescharacteristic
200C2×C32×C4C2×D411yescharacteristic
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4C2411yescharacteristic
203#638—42no—
204#638—42no—
205#638—42no—
206#638—81no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—21no—
212C4⋊(C3⋊D3)—21no—
213C4⋊(C3⋊D3)—21no—
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)—21no—
216C4⋊(C3⋊D3)—42no—
217C4⋊(C3⋊D3)C2×D412yes—
218C4⋊(C3⋊D3)C2×D412yes—
219C4×C3⋊D3—42no—
220C4×C3⋊D3—42no—
221C4×C3⋊D3—42no—
222C4×C3⋊D3—42no—
223C4×C3⋊D3—81no—
224#634—21no—
225#634—21no—
226#634—21no—
227#634—21no—
228#634—21no—
229#634—21no—
230C32×C8—21no—
231C32×C8—21no—
232C32×C8—21no—
233C32×C8C2×D412yes—
234C2×AGL(1,ℤ/8)—91no—
235C2×#135—91no—
236#547—91no—
237#546—91no—
238#497—91no—
239#470—91no—
240#465—91no—
241#463—91no—
242#461—91no—
243#452—91no—
244#452—91no—
245#450—91no—
246#449—91no—
247#442—91no—
248#435C3⋊D311yescharacteristic, complemented
249C23×D3—64no—
250C2×C3×D4D1214yes—
251C22×C3×C4C22×D314yes—
252C22×C3×C4C22×D314yes—
253C2×#67—64no—
254C2×#67—64no—
255C2×#67—64no—
256C2×#67—64no—
257#235—68no—
258#235—68no—
259#235—68no—
260#235—124no—
261#235—124no—
262#235—124no—
263C2×D12—34no—
264C2×D12—34no—
265C2×D12—34no—
266C2×D12—68no—
267C2×D12—64no—
268C2×D12—124no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×Dic6—34no—
275C2×Dic6—34no—
276C2×Dic6—34no—
277C3×M16—28no—
278C2×C3×C8—28no—
279C2×C3×C8C22×D314yes—
280C2×C3×C8C22×D314yes—
281C2×C3×C8C22×D314yes—
282C2×C3×C8C22×D314yes—
283C3×C4⋊C4D1214yes—
284C3×C22⋊C4D1214yes—
285C3×C22⋊C4D1214yes—
286C3×C42C22×D314yes—
287#217—64no—
288#217—64no—
289#217—64no—
290(C2×D3)⋊C4—64no—
291(C2×D3)⋊C4—64no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295C4⋊Dic3—34no—
296C4⋊Dic3—34no—
297C4⋊Dic3—64no—
298C4⋊Dic3—64no—
299Dic3⋊C4—64no—
300Dic3⋊C4—64no—
301Dic3⋊C4—64no—
302Dic12—68no—
303Dic12—124no—
304D24—316no—
305D24—68no—
306#204—68no—
307#204—68no—
308#204—68no—
309#204—68no—
310#204—124no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32C22×D411yescharacteristic
318C2×C3⋊D3—22no—
319C2×C3⋊D3—22no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3—84no—
328C32×C4—21no—
329C32×C4—21no—
330C32×C4—21no—
331C32×C4—21no—
332C32×C4C22×D411yescharacteristic
333C32×C4H(5,𝔽2)11yescharacteristic
334C3⋊Dic3—41no—
335C3⋊Dic3—41no—
336C3⋊Dic3—41no—
337C3⋊Dic3—41no—
338C3⋊Dic3—41no—
339C2×#41—91no—
340C2×#41—91no—
341C2×#41—91no—
342C22×D4—91no—
343AGL(1,ℤ/8)—184no—
344#135—184no—
345C2×Q16—91no—
346C2×Q16—91no—
347C2×SD16—91no—
348C2×SD16—91no—
349C2×SD16—91no—
350C2×SD16—91no—
351C2×SD16—91no—
352C2×D8—91no—
353C2×D8—91no—
354C2×M16C2×C3⋊D311yescharacteristic
355C22×C8C2×C3⋊D311yescharacteristic, complemented
356C4⋊Q8—91no—
357#124—91no—
358#123—181no—
359#123—181no—
360#123—181no—
361C22⋊Q8—91no—
362C22⋊Q8—91no—
363C22⋊Q8—91no—
364#121—91no—
365#121—181no—
366#121—181no—
367#120—181no—
368C4×D4—91no—
369C4×D4—91no—
370C4×D4C2×C3⋊D311yescharacteristic
371C2×C4⋊C4—181no—
372C2×C22⋊C4—181no—
373#106—91no—
374C4⋊C8C2×C3⋊D311yescharacteristic, complemented
375#103—91no—
376#103—91no—
377#103—91no—
378#102—91no—
379#102—91no—
380#102—91no—
381C22⋊C8C2×C3⋊D311yescharacteristic
382C22⋊C8C2×C3⋊D311yescharacteristic, complemented
383#97C2×C3⋊D311yescharacteristic, complemented
384C23×C3C2×D1214yes—
385C23×C3C2×D1214yes—
386C22×D3—64no—
387C22×D3—64no—
388C22×D3—64no—
389C22×D3—128no—
390C22×D3—128no—
391C22×D3—244no—
392C3×D4—44no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4C2×D1214yes—
398C2×C3×C4C2×D1214yes—
399C2×C3×C4C2×D1214yes—
400C2×C3×C4C2×D1214yes—
401C2×C3×C4C23×D314yes—
402#67—128no—
403#67—128no—
404#67—128no—
405#67—244no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—64no—
411D12—38no—
412D12—38no—
413D12—64no—
414D12—64no—
415D12—64no—
416D12—64no—
417D12—128no—
418C4×D3—128no—
419C4×D3—128no—
420C4×D3—128no—
421C4×D3—128no—
422C4×D3—244no—
423Dic6—64no—
424Dic6—64no—
425Dic6—64no—
426Dic6—64no—
427Dic6—64no—
428Dic6—64no—
429C3×C8—24no—
430C3×C8—24no—
431C3×C8—24no—
432C3×C8D3×D418yes—
433C2×C32—41no—
434C2×C32—41no—
435C2×C32D4211yescharacteristic
436C2×C32#57511yescharacteristic
437C2×C32#57711yescharacteristic
438C3⋊D3—42no—
439C3⋊D3—42no—
440C3⋊D3—81no—
441C24—181no—
442#41—182no—
443#41—182no—
444#41—182no—
445#41—361no—
446#41—361no—
447#41—361no—
448C2×Q8—91no—
449C2×Q8—91no—
450C2×Q8—91no—
451C2×D4—91no—
452C2×D4—91no—
453C2×D4—91no—
454C2×D4—182no—
455C2×D4—181no—
456C2×D4—181no—
457C2×D4—181no—
458C2×D4—181no—
459C2×D4—181no—
460C2×D4—361no—
461C2×D4C4⋊(C3⋊D3)11yescharacteristic
462C22×C4—181no—
463C22×C4—181no—
464C22×C4—181no—
465C22×C4—181no—
466C22×C4—181no—
467C22×C4C22×C3⋊D311yescharacteristic
468C22×C4C22×C3⋊D311yescharacteristic
469Q16—182no—
470Q16—361no—
471SD16—182no—
472SD16—182no—
473SD16—182no—
474SD16—182no—
475SD16—361no—
476D8—94no—
477D8—182no—
478M16—22no—
479C2×C8—22no—
480C2×C8C22×C3⋊D311yescharacteristic
481C2×C8C22×C3⋊D311yescharacteristic
482C2×C8C22×C3⋊D311yescharacteristic
483C2×C8C22×C3⋊D311yescharacteristic
484C4⋊C4—91no—
485C4⋊C4—91no—
486C4⋊C4—181no—
487C4⋊C4—181no—
488C4⋊C4—181no—
489C4⋊C4—181no—
490C4⋊C4—181no—
491C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
492C22⋊C4—181no—
493C22⋊C4—181no—
494C22⋊C4—181no—
495C22⋊C4—181no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C22⋊C4—181no—
499C22⋊C4—181no—
500C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
501C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
502C42C22×C3⋊D311yescharacteristic
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3C22×D1214yes—
510C2×D3—68no—
511C2×D3—68no—
512C2×D3—124no—
513C2×D3—124no—
514C2×D3—124no—
515C2×D3—124no—
516C2×D3—124no—
517C2×D3—124no—
518C2×D3—124no—
519C2×D3—2416no—
520C3×C4—24no—
521C3×C4—24no—
522C3×C4—24no—
523C3×C4—24no—
524C3×C4C2×D3×D414yes—
525C3×C4#100914yes—
526Dic3—124no—
527Dic3—124no—
528Dic3—124no—
529Dic3—124no—
530Dic3—124no—
531C32#326711yescharacteristic, complemented, Sylow
532C23—181no—
533C23—181no—
534C23—181no—
535C23—362no—
536C23—362no—
537C23—721no—
538C23C2×C4⋊(C3⋊D3)11yescharacteristic
539C23C2×C4⋊(C3⋊D3)11yescharacteristic
540Q8—181no—
541Q8—181no—
542Q8—181no—
543Q8—181no—
544Q8—181no—
545Q8—181no—
546D4—41no—
547D4—92no—
548D4—92no—
549D4—181no—
550D4—181no—
551D4—181no—
552D4—181no—
553D4—362no—
554D4—362no—
555D4—362no—
556D4—362no—
557D4—721no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—362no—
568C2×C4—362no—
569C2×C4—362no—
570C2×C4—362no—
571C2×C4—721no—
572C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
573C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
574C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
575C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
576C2×C4C23×C3⋊D311yescharacteristic
577C8—21no—
578C8—21no—
579C8—21no—
580C8D4×C3⋊D312yes—
581C2×C3—44no—
582C2×C3—44no—
583C2×C3D4×D1214yes—
584C2×C3#574814yes—
585C2×C3#575114yes—
586D3—128no—
587D3—128no—
588D3—244no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—182no—
596C22—182no—
597C22—361no—
598C22—361no—
599C22—361no—
600C22—361no—
601C22—361no—
602C22—361no—
603C22—361no—
604C22—724no—
605C22C22×C4⋊(C3⋊D3)11yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—361no—
611C4—361no—
612C4—361no—
613C4—361no—
614C4—361no—
615C4C2×D4×C3⋊D311yescharacteristic
616C4#6436611yescharacteristic
617C3#7949614yescomplemented
618C2—41no—
619C2—41no—
620C2—362no—
621C2—362no—
622C2—721no—
623C2D4×C4⋊(C3⋊D3)11yescharacteristic
624C2#1059621911yescharacteristic
625C2#1059622211yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#435C2
socleC22×C32C22×D4
hypercenter#435C3⋊D3
hypocenterC32#3267
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. #10596022C2semidirect
4. #10596021C2semidirect
5. C32×#435C2semidirect
6. #10592836C2semidirect
7. #10592813C2semidirect
8. #10592543C2semidirect
9. #10592540C2semidirect
10. #10592433C2semidirect
11. #10592432C2semidirect
12. #10592432C2semidirect
13. #10592430C2semidirect
14. #10592414C2semidirect
15. #10592410C2semidirect
19. C2×#3828C22semidirect
22. C22×C32×C8C22semidirect
29. #64133C22semidirect
31. C2×#3746C22semidirect
32. C2×#3746C22semidirect
40. C2×#3744C22semidirect
49. C4×C4⋊(C3⋊D3)C22semidirect
50. #64078C22semidirect
51. C32×C4⋊C8C22semidirect
53. C32×C22⋊C8C22semidirect
54. C32×#97C22semidirect
57. #63648C22semidirect
58. #63644C22semidirect
59. #63643C22semidirect
60. #63643C22semidirect
61. #63643C22semidirect
66. C3×#435D3semidirect
133. #3745D4semidirect
145. C22×C3×C8C2×D3semidirect
174. C3×C4⋊C8C2×D3semidirect
176. C3×C22⋊C8C2×D3semidirect
177. C3×#97C2×D3semidirect
248. #435C3⋊D3semidirect
355. C22×C8C2×C3⋊D3semidirect
374. C4⋊C8C2×C3⋊D3semidirect
382. C22⋊C8C2×C3⋊D3semidirect
383. #97C2×C3⋊D3semidirect
531. C32#3267semidirect
617. C3#79496semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
C2×#641132
#105960222
#105960212
C32×#4352
#105928362
#105928132
#105925432
#105925402
#105924332
#105924322
#105924302
#105924142
#105924102
#794963