Finite Group Databasebeta

← #11872846

Subgroups — #11872846

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593994C211yesmaximal, characteristic
2#10593881C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4840C211yesmaximal, characteristic, complemented
6#10590946C211yesmaximal, characteristic
7#10590946C211yesmaximal, characteristic
8#10590773C211yesmaximal, characteristic, complemented
9#10590758C211yesmaximal, characteristic, complemented
10#10590747C211yesmaximal, characteristic, complemented
11#10590744C211yesmaximal, characteristic, complemented
12#10590709C211yesmaximal, characteristic, complemented
13#10590708C211yesmaximal, characteristic, complemented
14#10590365C211yesmaximal, characteristic, complemented
15#10590308C211yesmaximal, characteristic, complemented
16#81147—31nomaximal
17#79387—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3744C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22#64078C2211yescharacteristic, complemented
23C3×C4×D12C2211yescharacteristic
24C3×#872C2211yescharacteristic
25C3×#870C2211yescharacteristic, complemented
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63904—21no—
29#63894C2211yescharacteristic
30Dic3×D12C2211yescharacteristic
31#63881—21no—
32#63861—21no—
33#63861—21no—
34#63857C2211yescharacteristic
35#63857C2211yescharacteristic
36#63845—21no—
37#63845—21no—
38#63844C2211yescharacteristic, complemented
39#63844C2211yescharacteristic, complemented
40#63841C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic, complemented
44#63643C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5698—31no—
62#5545—31no—
63#5521—31no—
64#5518—31no—
65C3×#478—31no—
66C3×#433—31no—
67#5066—31no—
68#5019—31no—
69#4889—31no—
70#4888—31no—
71#4868—31no—
72#4852—31no—
73#4847—31no—
74#4847D311yescharacteristic, complemented
75#4841—31no—
76#4841—31no—
77#4841—31no—
78#4841—61no—
79#4840D311yescharacteristic, complemented
80#4776—31no—
81#4776—31no—
82#4758—31no—
83#4757—31no—
84#4731—31no—
85#4731—31no—
86#4723—31no—
87#4723—31no—
88#4710—31no—
89#4710—31no—
90C4×#204—31no—
91C4×#204—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×#626—21no—
101C2×#624—21no—
102C2×D3×Dic3—21no—
103D3×D12—22no—
104D3×D12—22no—
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C42C2311yescharacteristic
108#3752—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3744—22no—
113#3744—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4D411yescharacteristic
116C3×(C2×D3)⋊C4D411yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4D411yescharacteristic
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3716—22no—
140#3716—22no—
141#3123—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C3×#125—31no—
145C3×C4×D4—31no—
146C3×#117—31no—
147D4×Dic3—31no—
148C2×#214—31no—
149C2×#214—31no—
150C4×#67—61no—
151C2×(C2×D3)⋊C4—61no—
152#926—31no—
153#924—31no—
154#924—31no—
155C2×#204—31no—
156C2×#204—31no—
157C2×#204—31no—
158C2×#204—31no—
159C2×#204—31no—
160C2×#204—31no—
161C2×#204—61no—
162C2×#204—61no—
163#898—61no—
164#898—61no—
165#897—31no—
166#897—31no—
167#893—31no—
168#893—61no—
169#893—61no—
170#892—31no—
171#890—61no—
172#890—61no—
173#889—61no—
174#889—61no—
175#887—31no—
176#887—31no—
177#67⋊C4—61no—
178D3×C22⋊C4—61no—
179D3×C22⋊C4—61no—
180D3×C22⋊C4—61no—
181#879—61no—
182#879—61no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—61no—
188C4×D12C2×D311yescharacteristic
189#872C2×D311yescharacteristic
190#870C2×D311yescharacteristic, complemented
191#869—31no—
192#869—31no—
193#869—61no—
194C4×Dic6—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic, complemented
201C3×C4⋊C8C2×D311yescharacteristic, complemented
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207C3×C4×C8—31no—
208#821—31no—
209#821—31no—
210#821C2×D311yescharacteristic
211#821C2×D311yescharacteristic
212(C2×D3)⋊C8C2×D311yescharacteristic
213(C2×D3)⋊C8C2×D311yescharacteristic
214#818—31no—
215#818C2×D311yescharacteristic, complemented
216#817—31no—
217#817C2×D311yescharacteristic, complemented
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#816—61no—
226#815C2×D311yescharacteristic, complemented
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C2×D32—24no—
239C2×D32—81no—
240C2×D32—81no—
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)#4112yes—
249C4×C3⋊D3—81no—
250#634—21no—
251#634—21no—
252#634—21no—
253#634—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265#626—24no—
266#624—81no—
267D3×Dic3—81no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—91no—
274#485—91no—
275#485—91no—
276#478—31no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—91no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—91no—
285C4×SD16—91no—
286#433—31no—
287C23×D3—61no—
288C23×D3—61no—
289C2×C3×D4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—61no—
292C2×#67—61no—
293C22×Dic3—61no—
294D3×D4—62no—
295D3×D4—62no—
296C2×D12—31no—
297C2×D12—31no—
298C2×D12—61no—
299C2×D12—62no—
300C2×D12—61no—
301C2×D12—62no—
302C2×D12C22×D311yescharacteristic
303C2×C4×D3—21no—
304C2×C4×D3—61no—
305C2×C4×D3—61no—
306C2×C4×D3—61no—
307C2×C4×D3—61no—
308C2×C4×D3—61no—
309C2×C4×D3—121no—
310C2×C4×D3C22×D311yescharacteristic
311C2×Dic6—31no—
312C2×Dic6—31no—
313C2×Dic6—31no—
314C2×Dic6—31no—
315C2×Dic6—61no—
316C2×Dic6—61no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—31no—
320C2×C3×C8—31no—
321C2×C3×C8C22×D311yescharacteristic
322C2×C3×C8C22×D311yescharacteristic
323C2×C3×C8C22×D311yescharacteristic
324C2×C3×C8C22×D311yescharacteristic
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C22⋊C4—31no—
333C3×C22⋊C4—31no—
334C3×C22⋊C4—61no—
335C3×C42—21no—
336C3×C42—31no—
337C3×C42C22×D311yescharacteristic
338C3×C42C22×D311yescharacteristic
339#217—61no—
340#217—61no—
341#217—61no—
342#217—61no—
343#214—62no—
344#214—62no—
345(C2×D3)⋊C4—21no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—121no—
355(C2×D3)⋊C4D1211yescharacteristic
356(C2×D3)⋊C4D1211yescharacteristic
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—121no—
367C4⋊Dic3—121no—
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4D1211yescharacteristic
380Dic3⋊C4D1211yescharacteristic
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390#204—62no—
391#204—62no—
392#204—62no—
393#204—62no—
394#204—62no—
395#204—62no—
396#204—122no—
397#204—122no—
398C22×C32C22×D411yescharacteristic
399C2×C3⋊D3—22no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C2×C3×D3—22no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408D32—84no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3⋊Dic3—41no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C22×D4—91no—
423C2×SD16—91no—
424C2×SD16—91no—
425C2×SD16—91no—
426C2×SD16—91no—
427C4⋊Q8—91no—
428#126—181no—
429#126—181no—
430#125—31no—
431#125—181no—
432#125—181no—
433C22⋊Q8—91no—
434C22⋊Q8—91no—
435C4×Q8—91no—
436C4×Q8—91no—
437C4×D4—31no—
438C4×D4—91no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—181no—
442C4×D4—181no—
443#117—31no—
444#117—91no—
445C2×C22⋊C4—181no—
446C2×C22⋊C4—181no—
447#107—31no—
448#107—91no—
449#106—31no—
450#106—91no—
451C4⋊C8—31no—
452C4⋊C8D3211yescharacteristic, complemented
453#103—91no—
454#103—91no—
455#103—91no—
456#103—91no—
457#102—31no—
458#102—31no—
459#102—91no—
460#102—91no—
461C22⋊C8—31no—
462C22⋊C8—31no—
463#97—31no—
464C4×C8—31no—
465C23×C3—31no—
466C23×C3—61no—
467C22×D3—21no—
468C22×D3—64no—
469C22×D3—64no—
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—121no—
473C22×D3—241no—
474C22×D3—241no—
475C22×D3—241no—
476C22×D3—241no—
477C22×D3C2×D1211yescharacteristic
478C3×D4—32no—
479C3×D4—61no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—241no—
492C2×C3×C4C2×D1211yescharacteristic
493C2×C3×C4C2×D1211yescharacteristic
494C2×C3×C4D3×D411yescharacteristic
495C2×C3×C4D3×D411yescharacteristic
496C2×C3×C4C23×D311yescharacteristic
497C2×C3×C4C23×D311yescharacteristic
498#67—64no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—121no—
509C2×Dic3—121no—
510C2×Dic3—121no—
511C2×Dic3—241no—
512C2×Dic3C2×D1211yescharacteristic
513C2×Dic3C2×D1211yescharacteristic
514C2×Dic3C2×D1211yescharacteristic
515D12—21no—
516D12—32no—
517D12—32no—
518D12—62no—
519D12—64no—
520D12—61no—
521D12—61no—
522D12—121no—
523D12#23912yes—
524C4×D3—21no—
525C4×D3—21no—
526C4×D3—81no—
527C4×D3—241no—
528C4×D3—241no—
529C4×D3—241no—
530C4×D3—241no—
531C4×D3—241no—
532C4×D3—242no—
533Dic6—61no—
534Dic6—61no—
535Dic6—61no—
536Dic6—61no—
537Dic6—61no—
538Dic6—61no—
539Dic6—61no—
540Dic6—61no—
541Dic6—121no—
542Dic6—121no—
543Dic6—121no—
544Dic6—121no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—41no—
550C3×C8—41no—
551C3×C8—61no—
552C3×C8—61no—
553C3⋊C8—21no—
554C3⋊C8—21no—
555C2×C32#52511yescharacteristic
556C2×C32#57711yescharacteristic
557C2×C32#57711yescharacteristic
558C3⋊D3—42no—
559C3×D3—41no—
560C3×D3—42no—
561C24—181no—
562C2×Q8—91no—
563C2×Q8—91no—
564C2×D4—31no—
565C2×D4—91no—
566C2×D4—181no—
567C2×D4—182no—
568C2×D4—182no—
569C22×C4—31no—
570C22×C4—61no—
571C22×C4—181no—
572C22×C4—181no—
573C22×C4—181no—
574SD16—182no—
575SD16—182no—
576SD16—182no—
577SD16—182no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8C2×D3211yescharacteristic
581C2×C8C2×D3211yescharacteristic
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—91no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4—181no—
594C4⋊C4—181no—
595C4⋊C4—181no—
596C22⋊C4—31no—
597C22⋊C4—31no—
598C22⋊C4—61no—
599C22⋊C4—181no—
600C22⋊C4—181no—
601C22⋊C4—181no—
602C22⋊C4—181no—
603C22⋊C4—181no—
604C22⋊C4—181no—
605C42—31no—
606C42—181no—
607C42—181no—
608C42—181no—
609C42C2×D3211yescharacteristic
610C22×C3—21no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—62no—
614C22×C3—61no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3C22×D1211yescharacteristic
618C22×C3C2×D3×D411yescharacteristic
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—122no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—241no—
633C2×D3—241no—
634C2×D3—244no—
635C2×D3—244no—
636C3×C4—22no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C2×#23911yescharacteristic
651C3×C4D3×#4111yescharacteristic
652C3×C4D3×#4111yescharacteristic
653C3×C4D3×#4111yescharacteristic
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—241no—
667Dic3—241no—
668Dic3—241no—
669C32#312311yescharacteristic, complemented, Sylow
670C23—31no—
671C23—61no—
672C23—184no—
673C23—181no—
674C23—721no—
675C23—721no—
676Q8—181no—
677Q8—181no—
678Q8—181no—
679Q8—181no—
680D4—32no—
681D4—61no—
682D4—92no—
683D4—184no—
684D4—181no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—241no—
697C2×C4—721no—
698C2×C4—721no—
699C2×C4—721no—
700C2×C4D3×D1211yescharacteristic
701C2×C4D3×D1211yescharacteristic
702C2×C4C22×D3211yescharacteristic
703C8—21no—
704C8—21no—
705C8—61no—
706C8—61no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—122no—
711C2×C3—121no—
712C2×C3#552411yescharacteristic
713C2×C3#562711yescharacteristic
714C2×C3#575111yescharacteristic
715C2×C3#575111yescharacteristic
716C2×C3#577011yescharacteristic
717C2×C3#577511yescharacteristic
718D3—41no—
719D3—42no—
720D3—122no—
721D3—122no—
722D3—242no—
723C22—61no—
724C22—62no—
725C22—61no—
726C22—61no—
727C22—121no—
728C22—121no—
729C22—182no—
730C22—361no—
731C22—361no—
732C22—724no—
733C22C2×D3×D1211yescharacteristic
734C4—21no—
735C4—21no—
736C4—61no—
737C4—61no—
738C4—61no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—361no—
743C4—361no—
744C4—361no—
745C4#6431211yescharacteristic
746C4D3×#23911yescharacteristic
747C3—21no—
748C3#7938711yescharacteristic, complemented
749C3#8114711yescharacteristic, complemented
750C2—121no—
751C2—122no—
752C2—362no—
753C2#1059462711yescharacteristic
754C2#1059467911yescharacteristic
755C2#1059471311yescharacteristic
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#3123
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. #10593881C2semidirect
3. #10592540C2semidirect
4. C3×#4847C2semidirect
5. C3×#4840C2semidirect
8. #10590773C2semidirect
9. #10590758C2semidirect
10. #10590747C2semidirect
11. #10590744C2semidirect
12. #10590709C2semidirect
13. #10590708C2semidirect
14. #10590365C2semidirect
15. #10590308C2semidirect
22. #64078C22semidirect
25. C3×#870C22semidirect
38. #63844C22semidirect
39. #63844C22semidirect
43. C32×C4⋊C8C22semidirect
44. #63643C22semidirect
45. #63643C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
74. #4847D3semidirect
79. #4840D3semidirect
190. #870C2×D3semidirect
200. C3×C4⋊C8C2×D3semidirect
201. C3×C4⋊C8C2×D3semidirect
215. #818C2×D3semidirect
217. #817C2×D3semidirect
226. #815C2×D3semidirect
227. C8×Dic3C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
452. C4⋊C8D32semidirect
669. C32#3123semidirect
748. C3#79387semidirect
749. C3#81147semidirect

Maximal subgroups

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

subgroupindex
#105939942
#105938812
#105925402
C3×#48472
C3×#48402
#105909462
#105907732
#105907582
#105907472
#105907442
#105907092
#105907082
#105903652
#105903082
#811473
#793873