Finite Group Databasebeta

← #13170649

Subgroups — #13170649

Order 1728.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89022C211yesmaximal, characteristic, complemented
2C3×D3×#235C211yesmaximal, characteristic, complemented
3#11723663C211yesmaximal, characteristic, complemented
4#11723371C211yesmaximal, characteristic, complemented
5#11723367C211yesmaximal, characteristic, complemented
6C3×#63831C211yesmaximal, characteristic, complemented
7C3×D3×#208C211yesmaximal, characteristic, complemented
8#11722885C212yesmaximal, complemented
9#11722868C212yesmaximal, complemented
10#11722856C212yesmaximal, complemented
11#11722853C212yesmaximal, complemented
12#10595470—31nomaximal
13#10594795—31nomaximal
14#10594711—31nomaximal
15C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
16C3×#3828C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic, complemented
18C32×#235C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×#6291—21no—
21C2×#6289—21no—
22#89022—21no—
23#89022—21no—
24#89022C2212yes—
25#89022C2212yescomplemented
26C3×D3×#67—21no—
27C3×#3804—21no—
28C3×D3×D12C2211yescharacteristic, complemented
29C3×C4×D32—21no—
30C3×#3799C2211yescharacteristic, complemented
31C3×#3798—21no—
32C3×#3795C2211yescharacteristic, complemented
33C3×D3×Dic6C2211yescharacteristic, complemented
34C3×#3748C2211yescharacteristic, complemented
35C32×#208C2211yescharacteristic, complemented
36#88812C2212yescomplemented
37#88811C2212yescomplemented
38#88797C2212yescomplemented
39#88795C2212yescomplemented
40#88791C2212yescomplemented
41#88790C2212yescomplemented
42C3×#3719C2212yescomplemented
43C3×#3716C2212yescomplemented
44C3×#3711C2212yescomplemented
45C3×D3×C3⋊C8C2212yescomplemented
46C2×#3828—31no—
47C3×D3×#41—31no—
48C2×C3×#235—31no—
49D3×#235D311yescharacteristic, complemented
50C2×#3799—31no—
51C2×#3799—31no—
52C2×#3799—61no—
53#64158—31no—
54#64117—31no—
55C3×#951—31no—
56C2×C3×#208—31no—
57C3×#909—31no—
58C3×D3×M16—31no—
59#63949—32no—
60#63948—32no—
61#63935—32no—
62#63934—32no—
63#63833—31no—
64#63833—32no—
65#63831—31no—
66#63831D311yescharacteristic, complemented
67#63830—32no—
68#63829—32no—
69#63829—32no—
70#63827—31no—
71#63825—31no—
72#63825—31no—
73#63825—31no—
74#63825—31no—
75#63825—61no—
76#63825—61no—
77D3×#208D311yescharacteristic, complemented
78#63808—32no—
79#63806—32no—
80#63801—32no—
81#63794—32no—
82C22×C3⋊(C3⋊D3)—21no—
83C22×C32×D3D411yescharacteristic
84C2×C3×D32—21no—
85C2×C33×C4C2311yescharacteristic
86C4⋊(C3⋊(C3⋊D3))—21no—
87C4⋊(C3⋊(C3⋊D3))C2312yes—
88C3×#638—21no—
89C2×C3×C3⋊Dic3—21no—
90C3×C4⋊(C3⋊D3)C2311yescharacteristic
91C3×C4×C3⋊D3—21no—
92C3×#634—21no—
93C3×#634C2311yescharacteristic
94C3×#634C2312yes—
95C32×#67—21no—
96C2×C32×Dic3D411yescharacteristic
97C32×D12C2311yescharacteristic
98C32×C4×D3—21no—
99C32×C4×D3D411yescharacteristic
100C32×C4×D3D411yescharacteristic
101C32×C4×D3C2311yescharacteristic
102C32×C4×D3C2311yescharacteristic
103C32×Dic6C2311yescharacteristic
104#6291—22no—
105#6291—22no—
106#6289—22no—
107#6289—22no—
108C3×#627—21no—
109C3×#626—21no—
110C3×#626—21no—
111C3×#625—21no—
112C3×#624—21no—
113C3×D3×Dic3—21no—
114C3×D3×Dic3—21no—
115C3×C3⋊(C3⋊C8)C2312yes—
116C32×C3⋊C8C2312yes—
117#5822—91no—
118#5777—91no—
119#5748—91no—
120C32×#41—31no—
121C22×C32×C4—31no—
122C2×#638—61no—
123#3828—32no—
124#3828—32no—
125#3828—61no—
126#3828—61no—
127#3828C2×D311yescharacteristic
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—61no—
132C2×C4⋊(C3⋊D3)—61no—
133C2×C4⋊(C3⋊D3)—61no—
134C2×C4⋊(C3⋊D3)—121no—
135C2×C4×C3⋊D3—61no—
136C2×#634C2×D311yescharacteristic, complemented
137C2×C3×#67—61no—
138C3×#239—31no—
139C3×D3×Q8—31no—
140C3×#237—31no—
141C3×#237—61no—
142C3×D3×D4—31no—
143C3×D3×D4—61no—
144C3×#235—21no—
145C3×#235—31no—
146C3×#235—31no—
147C3×#235—31no—
148C3×#235—31no—
149C3×#235—61no—
150C3×#235—61no—
151C3×#235—61no—
152C3×#235—61no—
153C3×#235C2×D311yescharacteristic
154C3×#235C2×D311yescharacteristic
155C2×C3×D12—31no—
156C2×C3×C4×D3—21no—
157C2×C3×C4×D3—61no—
158C2×C3×C4×D3—61no—
159C2×C3×C4×D3C2×D311yescharacteristic
160C2×C3×C4×D3C2×D311yescharacteristic
161C2×C3×Dic6—31no—
162C2×C3×Dic6—31no—
163C2×C3×Dic6—31no—
164C2×C3×Dic6—61no—
165D3×#67—21no—
166C2×#626—62no—
167C2×#626—61no—
168C2×#626—61no—
169C2×#624—62no—
170C2×#624—61no—
171C2×#624—61no—
172#3804—21no—
173D3×D12C2×D311yescharacteristic, complemented
174C4×D32—21no—
175#3799—32no—
176#3799—32no—
177#3799—32no—
178#3799—32no—
179#3799—62no—
180#3799—62no—
181#3799—62no—
182#3799—62no—
183#3799—61no—
184#3799—61no—
185#3799—61no—
186#3799—61no—
187#3799C2×D311yescharacteristic, complemented
188#3798—21no—
189#3795C2×D311yescharacteristic, complemented
190D3×Dic6C2×D311yescharacteristic, complemented
191C32×M16—31no—
192#3755—32no—
193#3753—32no—
194#3748C2×D311yescharacteristic, complemented
195#3745—32no—
196#3744—32no—
197C3×#216—32no—
198C3×#214—32no—
199C3×#208—21no—
200C3×#208—31no—
201C3×#208—31no—
202C3×#208—32no—
203C3×#208—61no—
204C3×#208C2×D311yescharacteristic, complemented
205C3×#208C2×D311yescharacteristic, complemented
206C2×C3×C3⋊C8—32no—
207C3×Dic12—32no—
208C3×#204—32no—
209C3×ΓL(1,𝔽25)—32no—
210C3×D3×C8—32no—
211#3719—32no—
212#3719—32no—
213#3719C2×D312yescomplemented
214#3718—32no—
215#3717—32no—
216#3717—32no—
217#3717—32no—
218#3717—32no—
219#3717—32no—
220#3717—62no—
221#3717—62no—
222#3716—32no—
223#3716C2×D312yescomplemented
224#3715—32no—
225#3714—32no—
226#3714—32no—
227#3714—32no—
228#3714—32no—
229#3714—62no—
230#3714—62no—
231#3711C2×D312yescomplemented
232D3×C3⋊C8C2×D312yescomplemented
233C22×C33C2×D411yescharacteristic
234C2×C3⋊(C3⋊D3)—22no—
235C2×C3⋊(C3⋊D3)—42no—
236C2×C3×C3⋊D3—21no—
237C2×C32×D3—21no—
238C2×C32×D3—41no—
239C2×C32×D3C2×D411yescharacteristic
240C2×C32×D3C2×D411yescharacteristic
241C3×D32—42no—
242C33×C4C2×D411yescharacteristic
243C33×C4C2411yescharacteristic
244C3×C3⋊Dic3—22no—
245C3×C3⋊Dic3—21no—
246C32×Dic3—21no—
247C32×Dic3C2×D411yescharacteristic
248C32×Dic3C2×D411yescharacteristic
249C2×C3×#41—91no—
250D3×#41—31no—
251C2×#239—91no—
252C2×#235—31no—
253C2×#235—91no—
254C2×#235—91no—
255C2×#235—181no—
256C3×#137—91no—
257C2×C3×M16—91no—
258#951—31no—
259#951—91no—
260#950—92no—
261#950—92no—
262#949—91no—
263#949—91no—
264#949—91no—
265#949—181no—
266#942—92no—
267#942—91no—
268#932—92no—
269C2×#208—31no—
270#919—92no—
271#918—92no—
272#916—92no—
273#914—92no—
274#909—31no—
275#909—92no—
276#909—91no—
277#908—92no—
278#908—91no—
279#908—91no—
280#908—91no—
281#908—181no—
282D3×M16—31no—
283#904—92no—
284#904—92no—
285C23×C32—31no—
286C22×C3⋊D3—61no—
287C22×C3⋊D3—62no—
288C22×C3⋊D3—61no—
289C22×C3⋊D3—61no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3—122no—
293C22×C3×D3—21no—
294C22×C3×D3—61no—
295C22×C3×D3—61no—
296C22×C3×D3D1211yescharacteristic
297C22×C3×D3#6711yescharacteristic
298C2×D32—21no—
299C32×Q8—31no—
300C32×D4—31no—
301C32×D4—61no—
302C2×C32×C4—21no—
303C2×C32×C4—21no—
304C2×C32×C4—21no—
305C2×C32×C4—31no—
306C2×C32×C4—31no—
307C2×C32×C4—31no—
308C2×C32×C4—31no—
309C2×C32×C4—31no—
310C2×C32×C4—41no—
311C2×C32×C4—61no—
312C2×C32×C4C22×D311yescharacteristic
313C2×C32×C4C22×D311yescharacteristic
314C2×C32×C4C22×D311yescharacteristic
315#638—21no—
316#638—62no—
317#638—62no—
318C2×C3⋊Dic3—21no—
319C4⋊(C3⋊D3)—32no—
320C4⋊(C3⋊D3)—32no—
321C4⋊(C3⋊D3)—32no—
322C4⋊(C3⋊D3)—62no—
323C4⋊(C3⋊D3)—62no—
324C4⋊(C3⋊D3)—62no—
325C4⋊(C3⋊D3)—61no—
326C4⋊(C3⋊D3)—62no—
327C4⋊(C3⋊D3)—61no—
328C4⋊(C3⋊D3)—61no—
329C4⋊(C3⋊D3)—122no—
330C4⋊(C3⋊D3)—121no—
331C4⋊(C3⋊D3)—121no—
332C4⋊(C3⋊D3)—122no—
333C4⋊(C3⋊D3)C22×D311yescharacteristic
334C4×C3⋊D3—21no—
335C4×C3⋊D3—62no—
336C4×C3⋊D3—62no—
337#634—21no—
338#634C22×D312yes—
339#634C22×D311yescharacteristic
340C3×#67—21no—
341C3×#67—21no—
342C3×#67—41no—
343C3×#67—61no—
344C3×#67—61no—
345C3×#67—61no—
346C3×#67—61no—
347C3×#67—61no—
348C3×#67—61no—
349C3×#67—121no—
350C2×C3×Dic3—21no—
351C2×C3×Dic3—61no—
352C2×C3×Dic3—62no—
353C2×C3×Dic3—61no—
354C2×C3×Dic3—61no—
355C2×C3×Dic3—61no—
356C2×C3×Dic3D1211yescharacteristic
357C2×C3×Dic3#6711yescharacteristic
358C3×D12—21no—
359C3×D12—31no—
360C3×D12—31no—
361C3×D12—61no—
362C3×D12—61no—
363C3×D12—61no—
364C3×D12C22×D311yescharacteristic
365C3×D12C22×D311yescharacteristic
366C3×C4×D3—21no—
367C3×C4×D3—21no—
368C3×C4×D3—21no—
369C3×C4×D3—21no—
370C3×C4×D3—21no—
371C3×C4×D3—21no—
372C3×C4×D3—41no—
373C3×C4×D3—61no—
374C3×C4×D3—61no—
375C3×C4×D3—61no—
376C3×C4×D3—61no—
377C3×C4×D3—61no—
378C3×C4×D3—61no—
379C3×C4×D3—121no—
380C3×C4×D3D1211yescharacteristic
381C3×C4×D3D1211yescharacteristic
382C3×C4×D3#6711yescharacteristic
383C3×C4×D3#6711yescharacteristic
384C3×C4×D3C22×D311yescharacteristic
385C3×C4×D3C22×D311yescharacteristic
386C3×C4×D3C22×D311yescharacteristic
387C3×C4×D3C22×D311yescharacteristic
388C3×Dic6—21no—
389C3×Dic6—32no—
390C3×Dic6—31no—
391C3×Dic6—31no—
392C3×Dic6—32no—
393C3×Dic6—62no—
394C3×Dic6—61no—
395C3×Dic6—61no—
396C3×Dic6—62no—
397C3×Dic6—61no—
398C3×Dic6—61no—
399C3×Dic6—61no—
400C3×Dic6C22×D311yescharacteristic
401C3×Dic6C22×D311yescharacteristic
402#627—21no—
403#626—21no—
404#626—21no—
405#626—64no—
406#626—64no—
407#626—62no—
408#626—62no—
409#626—62no—
410#626—62no—
411#625—21no—
412#624—21no—
413#624—64no—
414#624—64no—
415#624—62no—
416#624—62no—
417#624—62no—
418#624—62no—
419D3×Dic3—21no—
420D3×Dic3—21no—
421C32×C8—32no—
422C3⋊(C3⋊C8)C22×D312yes—
423C3×C3⋊C8—22no—
424C3×C3⋊C8—32no—
425C3×C3⋊C8—32no—
426C3×C3⋊C8—62no—
427C3×C3⋊C8C22×D312yes—
428C3×C3⋊C8C22×D312yes—
429#575—271noSylow
430C2×C33—21no—
431C2×C33C22×D411yescharacteristic
432C3⋊(C3⋊D3)—42no—
433C3×C3⋊D3—41no—
434C32×D3—21no—
435C32×D3—21no—
436C32×D3—41no—
437C3×#41—31no—
438C3×#41—31no—
439C3×#41—61no—
440C3×#41—91no—
441C3×#41—91no—
442C3×#41—91no—
443C3×#41—181no—
444C3×#41—181no—
445C2×C3×Q8—91no—
446C2×C3×Q8—91no—
447C2×C3×D4—91no—
448C2×C3×D4—181no—
449C22×C3×C4—31no—
450C22×C3×C4—31no—
451C22×C3×C4—61no—
452C22×C3×C4—181no—
453C2×#67—61no—
454C2×#67—181no—
455C2×#67—181no—
456C2×#67—182no—
457#239—31no—
458#239—92no—
459#239—92no—
460#239—181no—
461#239—181no—
462D3×Q8—31no—
463#237—31no—
464#237—61no—
465D3×D4—31no—
466D3×D4—61no—
467#235—31no—
468#235—31no—
469#235—31no—
470#235—31no—
471#235—61no—
472#235—61no—
473#235—61no—
474#235—61no—
475#235—92no—
476#235—92no—
477#235—92no—
478#235—92no—
479#235—182no—
480#235—182no—
481#235—181no—
482#235—181no—
483#235—181no—
484#235—181no—
485#235—182no—
486#235—182no—
487#235D3211yescharacteristic
488C2×D12—31no—
489C2×D12—91no—
490C2×D12—91no—
491C2×D12—91no—
492C2×D12—181no—
493C2×D12—181no—
494C2×D12—181no—
495C2×D12—181no—
496C2×D12—361no—
497C2×C4×D3—61no—
498C2×C4×D3—61no—
499C2×C4×D3—181no—
500C2×C4×D3—181no—
501C2×C4×D3—182no—
502C2×C4×D3—181no—
503C2×C4×D3D3211yescharacteristic
504C2×Dic6—31no—
505C2×Dic6—31no—
506C2×Dic6—31no—
507C2×Dic6—61no—
508C3×Q16—92no—
509C3×SD16—92no—
510C3×M16—31no—
511C3×M16—31no—
512C3×M16—61no—
513C3×M16—92no—
514C3×M16—91no—
515C2×C3×C8—92no—
516#216—32no—
517#216—92no—
518#216—92no—
519#215—92no—
520#215—92no—
521#215—92no—
522#215—92no—
523#215—182no—
524#214—32no—
525#214—92no—
526#213—92no—
527#213—92no—
528#213—92no—
529#213—182no—
530#208—31no—
531#208—31no—
532#208—32no—
533#208—61no—
534#208D3211yescharacteristic, complemented
535C2×C3⋊C8—32no—
536Dic12—32no—
537Dic12—92no—
538D24—92no—
539D24—92no—
540D24—92no—
541D24—182no—
542#204—32no—
543#204—92no—
544#204—92no—
545#204—92no—
546#204—92no—
547#204—182no—
548ΓL(1,𝔽25)—32no—
549D3×C8—32no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—31no—
554C22×C32—31no—
555C22×C32—41no—
556C22×C32—61no—
557C22×C32—121no—
558C22×C32C2×D1211yescharacteristic
559C22×C32D3×D411yescharacteristic
560C22×C32C2×#6711yescharacteristic
561C2×C3⋊D3—21no—
562C2×C3⋊D3—62no—
563C2×C3⋊D3—64no—
564C2×C3⋊D3—62no—
565C2×C3⋊D3—62no—
566C2×C3⋊D3—122no—
567C2×C3⋊D3—122no—
568C2×C3⋊D3—124no—
569C2×C3⋊D3—122no—
570C2×C3⋊D3—124no—
571C2×C3⋊D3—122no—
572C2×C3⋊D3—122no—
573C2×C3⋊D3—242no—
574C2×C3⋊D3—242no—
575C2×C3⋊D3—244no—
576C2×C3×D3—21no—
577C2×C3×D3—21no—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—41no—
581C2×C3×D3—41no—
582C2×C3×D3—41no—
583C2×C3×D3—42no—
584C2×C3×D3—61no—
585C2×C3×D3—61no—
586C2×C3×D3—121no—
587C2×C3×D3—122no—
588C2×C3×D3—122no—
589C2×C3×D3C2×D1211yescharacteristic
590C2×C3×D3C2×D1211yescharacteristic
591C2×C3×D3C2×#6711yescharacteristic
592C2×C3×D3C2×#6711yescharacteristic
593D32—42no—
594C32×C4—21no—
595C32×C4—21no—
596C32×C4—21no—
597C32×C4—21no—
598C32×C4—21no—
599C32×C4—21no—
600C32×C4—31no—
601C32×C4—31no—
602C32×C4—41no—
603C32×C4—41no—
604C32×C4—61no—
605C32×C4C2×D1211yescharacteristic
606C32×C4D3×D411yescharacteristic
607C32×C4C2×#6711yescharacteristic
608C32×C4C23×D311yescharacteristic
609C32×C4C23×D311yescharacteristic
610C32×C4C23×D311yescharacteristic
611C3⋊Dic3—22no—
612C3⋊Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—41no—
618C3×Dic3—64no—
619C3×Dic3—62no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—62no—
623C3×Dic3—121no—
624C3×Dic3C2×D1211yescharacteristic
625C3×Dic3C2×D1211yescharacteristic
626C3×Dic3C2×#6711yescharacteristic
627C3×Dic3C2×#6711yescharacteristic
628C2×#41—91no—
629C2×#41—271no—
630#137—91no—
631#137—272no—
632#137—271no—
633AGL(1,ℤ/8)—271no—
634AGL(1,ℤ/8)—272no—
635AGL(1,ℤ/8)—271no—
636#135—272no—
637#135—272no—
638C2×M16—91no—
639C33#57511yescharacteristic, complemented, Sylow
640C23×C3—31no—
641C23×C3—31no—
642C23×C3—61no—
643C23×C3—181no—
644C22×D3—61no—
645C22×D3—61no—
646C22×D3—182no—
647C22×D3—181no—
648C22×D3—181no—
649C22×D3—181no—
650C22×D3—361no—
651C22×D3—361no—
652C22×D3—362no—
653C22×D3#62611yescharacteristic
654C3×Q8—31no—
655C3×Q8—31no—
656C3×Q8—61no—
657C3×Q8—91no—
658C3×Q8—92no—
659C3×Q8—181no—
660C3×Q8—181no—
661C3×D4—31no—
662C3×D4—31no—
663C3×D4—61no—
664C3×D4—61no—
665C3×D4—61no—
666C3×D4—91no—
667C3×D4—121no—
668C3×D4—181no—
669C3×D4—181no—
670C3×D4—181no—
671C3×D4—181no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—31no—
684C2×C3×C4—31no—
685C2×C3×C4—41no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—121no—
694C2×C3×C4—181no—
695C2×C3×C4—181no—
696C2×C3×C4—181no—
697C2×C3×C4—181no—
698C2×C3×C4—181no—
699C2×C3×C4C2×D3211yescharacteristic
700C2×C3×C4C2×D3211yescharacteristic
701C2×C3×C4C2×D3211yescharacteristic
702#67—21no—
703#67—61no—
704#67—61no—
705#67—61no—
706#67—61no—
707#67—61no—
708#67—61no—
709#67—121no—
710#67—182no—
711#67—182no—
712#67—182no—
713#67—182no—
714#67—184no—
715#67—184no—
716C2×Dic3—61no—
717C2×Dic3—62no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3#62611yescharacteristic
722D12—31no—
723D12—31no—
724D12—61no—
725D12—61no—
726D12—61no—
727D12—92no—
728D12—92no—
729D12—92no—
730D12—182no—
731D12—182no—
732D12—182no—
733D12—182no—
734D12—182no—
735D12—182no—
736D12—181no—
737D12—181no—
738D12—181no—
739D12—362no—
740D12—361no—
741D12—361no—
742D12—362no—
743D12C2×D3211yescharacteristic
744C4×D3—21no—
745C4×D3—61no—
746C4×D3—61no—
747C4×D3—61no—
748C4×D3—61no—
749C4×D3—61no—
750C4×D3—61no—
751C4×D3—121no—
752C4×D3—182no—
753C4×D3—182no—
754C4×D3—182no—
755C4×D3—182no—
756C4×D3—184no—
757C4×D3—184no—
758C4×D3—182no—
759C4×D3—182no—
760C4×D3#62611yescharacteristic
761C4×D3#62611yescharacteristic
762C4×D3C2×D3211yescharacteristic
763C4×D3C2×D3211yescharacteristic
764Dic6—32no—
765Dic6—31no—
766Dic6—31no—
767Dic6—32no—
768Dic6—62no—
769Dic6—61no—
770Dic6—61no—
771Dic6—62no—
772Dic6—61no—
773Dic6—61no—
774Dic6—61no—
775Dic6C2×D3211yescharacteristic
776C3×C8—32no—
777C3×C8—32no—
778C3×C8—62no—
779C3×C8—92no—
780C3⋊C8—32no—
781C3⋊C8—32no—
782C3⋊C8—62no—
783C3⋊C8C2×D3212yes—
784C2×C32—21no—
785C2×C32—22no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—41no—
792C2×C32—41no—
793C2×C32—41no—
794C2×C32—42no—
795C2×C32—61no—
796C2×C32—61no—
797C2×C32—121no—
798C2×C32C22×D1211yescharacteristic
799C2×C32C2×D3×D411yescharacteristic
800C2×C32C22×#6711yescharacteristic
801C3⋊D3—41no—
802C3⋊D3—122no—
803C3⋊D3—124no—
804C3⋊D3—122no—
805C3⋊D3—122no—
806C3⋊D3—242no—
807C3⋊D3—242no—
808C3⋊D3—244no—
809C3×D3—21no—
810C3×D3—21no—
811C3×D3—21no—
812C3×D3—21no—
813C3×D3—41no—
814C3×D3—41no—
815C3×D3—41no—
816C3×D3—41no—
817C3×D3—81no—
818C3×D3—121no—
819C3×D3—121no—
820C3×D3—241no—
821#41—31no—
822#41—91no—
823#41—91no—
824#41—91no—
825#41—181no—
826#41—181no—
827#41—272no—
828#41—272no—
829#41—541no—
830#41—541no—
831C2×Q8—91no—
832C2×Q8—91no—
833C2×D4—91no—
834C2×D4—181no—
835C2×D4—271no—
836C2×D4—541no—
837C22×C4—31no—
838C22×C4—181no—
839C22×C4—541no—
840Q16—92no—
841Q16—272no—
842SD16—92no—
843SD16—272no—
844SD16—272no—
845SD16—272no—
846D8—272no—
847D8—272no—
848M16—31no—
849M16—92no—
850M16—91no—
851C2×C8—92no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—31no—
856C22×C3—31no—
857C22×C3—31no—
858C22×C3—31no—
859C22×C3—41no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—122no—
868C22×C3—181no—
869C22×C3—362no—
870C22×C3D3×D1211yescharacteristic
871C22×C3C2×#62611yescharacteristic
872C22×C3D3×#6711yescharacteristic
873C2×D3—21no—
874C2×D3—41no—
875C2×D3—61no—
876C2×D3—61no—
877C2×D3—121no—
878C2×D3—122no—
879C2×D3—122no—
880C2×D3—184no—
881C2×D3—182no—
882C2×D3—182no—
883C2×D3—182no—
884C2×D3—362no—
885C2×D3—362no—
886C2×D3—364no—
887C2×D3—362no—
888C2×D3—364no—
889C2×D3—362no—
890C2×D3—362no—
891C2×D3—722no—
892C2×D3—722no—
893C2×D3—724no—
894C2×D3C2×#62611yescharacteristic
895C2×D3C2×#62611yescharacteristic
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—21no—
900C3×C4—21no—
901C3×C4—21no—
902C3×C4—31no—
903C3×C4—31no—
904C3×C4—31no—
905C3×C4—31no—
906C3×C4—41no—
907C3×C4—41no—
908C3×C4—61no—
909C3×C4—61no—
910C3×C4—61no—
911C3×C4—61no—
912C3×C4—121no—
913C3×C4—181no—
914C3×C4—182no—
915C3×C4D3×D1211yescharacteristic
916C3×C4C2×#62611yescharacteristic
917C3×C4D3×#6711yescharacteristic
918C3×C4C22×D3211yescharacteristic
919C3×C4C22×D3211yescharacteristic
920C3×C4C22×D3211yescharacteristic
921Dic3—21no—
922Dic3—64no—
923Dic3—62no—
924Dic3—61no—
925Dic3—61no—
926Dic3—62no—
927Dic3—121no—
928Dic3C2×#62611yescharacteristic
929Dic3C2×#62611yescharacteristic
930C32—21no—
931C32—21no—
932C32—21no—
933C32—41no—
934C32#574811yescharacteristic, complemented
935C32#577711yescharacteristic, complemented
936C32#582211yescharacteristic, complemented
937C23—31no—
938C23—181no—
939C23—541no—
940Q8—31no—
941Q8—92no—
942Q8—91no—
943Q8—181no—
944Q8—181no—
945D4—31no—
946D4—61no—
947D4—91no—
948D4—181no—
949D4—181no—
950D4—181no—
951D4—181no—
952D4—272no—
953D4—542no—
954D4—542no—
955D4—541no—
956C2×C4—31no—
957C2×C4—31no—
958C2×C4—31no—
959C2×C4—31no—
960C2×C4—31no—
961C2×C4—61no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—181no—
966C2×C4—181no—
967C2×C4—542no—
968C2×C4—542no—
969C2×C4D3311yescharacteristic
970C8—32no—
971C8—92no—
972C2×C3—22no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—41no—
980C2×C3—41no—
981C2×C3—42no—
982C2×C3—41no—
983C2×C3—61no—
984C2×C3—61no—
985C2×C3—61no—
986C2×C3—61no—
987C2×C3—121no—
988C2×C3—121no—
989C2×C3—121no—
990C2×C3—121no—
991C2×C3—241no—
992C2×C3—361no—
993C2×C3C2×D3×D1211yescharacteristic
994C2×C3C22×#62611yescharacteristic
995C2×C3C2×D3×#6711yescharacteristic
996D3—21no—
997D3—21no—
998D3—41no—
999D3—121no—
1000D3—121no—
1001D3—241no—
1002D3—364no—
1003D3—362no—
1004D3—362no—
1005D3—362no—
1006D3—722no—
1007D3—722no—
1008D3—724no—
1009C22—31no—
1010C22—31no—
1011C22—61no—
1012C22—121no—
1013C22—181no—
1014C22—362no—
1015C22—542no—
1016C22—1082no—
1017C22D3×#62611yescharacteristic
1018C4—31no—
1019C4—31no—
1020C4—61no—
1021C4—181no—
1022C4—182no—
1023C4D3×#62611yescharacteristic
1024C4C2×D3311yescharacteristic
1025C3—21no—
1026C3—21no—
1027C3—21no—
1028C3—41no—
1029C3#1059471111yescharacteristic, complemented
1030C3#1059479511yescharacteristic, complemented
1031C3#1059547011yescharacteristic, complemented
1032C2—21no—
1033C2—61no—
1034C2—61no—
1035C2—121no—
1036C2—361no—
1037C2—1082no—
1038C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC2C2×D3×#626
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC2×C33C22×D4
hypercenterC2×C4D33
hypocenterC33#575
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89022C2semidirect
2. C3×D3×#235C2semidirect
3. #11723663C2semidirect
4. #11723371C2semidirect
5. #11723367C2semidirect
6. C3×#63831C2semidirect
7. C3×D3×#208C2semidirect
8. #11722885C2semidirect
9. #11722868C2semidirect
10. #11722856C2semidirect
11. #11722853C2semidirect
15. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
17. C2×C3×#634C22semidirect
25. #89022C22semidirect
28. C3×D3×D12C22semidirect
30. C3×#3799C22semidirect
32. C3×#3795C22semidirect
33. C3×D3×Dic6C22semidirect
34. C3×#3748C22semidirect
35. C32×#208C22semidirect
36. #88812C22semidirect
37. #88811C22semidirect
38. #88797C22semidirect
39. #88795C22semidirect
40. #88791C22semidirect
41. #88790C22semidirect
42. C3×#3719C22semidirect
43. C3×#3716C22semidirect
44. C3×#3711C22semidirect
45. C3×D3×C3⋊C8C22semidirect
49. D3×#235D3semidirect
66. #63831D3semidirect
77. D3×#208D3semidirect
136. C2×#634C2×D3semidirect
173. D3×D12C2×D3semidirect
187. #3799C2×D3semidirect
189. #3795C2×D3semidirect
190. D3×Dic6C2×D3semidirect
194. #3748C2×D3semidirect
204. C3×#208C2×D3semidirect
205. C3×#208C2×D3semidirect
213. #3719C2×D3semidirect
223. #3716C2×D3semidirect
231. #3711C2×D3semidirect
232. D3×C3⋊C8C2×D3semidirect
534. #208D32semidirect
639. C33#575semidirect
934. C32#5748semidirect
935. C32#5777semidirect
936. C32#5822semidirect
1029. C3#10594711semidirect
1030. C3#10594795semidirect
1031. C3#10595470semidirect

Maximal subgroups

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

subgroupindex
C2×#890222
C3×D3×#2352
#117236632
#117233712
#117233672
C3×#638312
C3×D3×#2082
#117228852
#117228682
#117228562
#117228532
#105954703
#105947953
#105947113