Finite Group Databasebeta

← #13170624

Subgroups — #13170624

Order 1728.

1242 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724619C211yesmaximal, characteristic, complemented
2C3×#64297C211yesmaximal, characteristic, complemented
3#11723375C211yesmaximal, characteristic, complemented
4#11723365C211yesmaximal, characteristic, complemented
5#11723352C211yesmaximal, characteristic, complemented
6C2×C3×#3717C211yesmaximal, characteristic, complemented
7C3×#63829C211yesmaximal, characteristic, complemented
8#11722892C212yesmaximal, complemented
9#11722876C212yesmaximal, complemented
10#11722859C212yesmaximal, complemented
11#11722840C212yesmaximal, complemented
12#10595457—31nomaximal
13#10595318—31nomaximal
14#10594686—31nomaximal
15C3×#3828C2211yescharacteristic
16C3×#3828C2211yescharacteristic
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C32×#235C2211yescharacteristic, complemented
19C2×C32×Dic6C2211yescharacteristic, complemented
20#89049—22no—
21C4⋊#1113—21no—
22C4⋊#1113C2212yes—
23#89041—21no—
24#89041C2212yes—
25C3×#3804—22no—
26C3×#3799—21no—
27C3×#3797C2212yescomplemented
28C3×#3796C2212yescomplemented
29C3×D3×Dic6—21no—
30#88855C2211yescharacteristic, complemented
31C2×C32×C3⋊C8C2211yescharacteristic, complemented
32#88798C2212yescomplemented
33#88793C2212yescomplemented
34#88793C2212yescomplemented
35#88789C2212yescomplemented
36#88787C2212yescomplemented
37C3⋊D3×C3⋊C8C2212yescomplemented
38C3×#3719C2211yescharacteristic, complemented
39C3×#3717C2211yescharacteristic, complemented
40C3×#3717C2212yescomplemented
41C3×#3717C2212yescomplemented
42C3×#3716C2211yescharacteristic, complemented
43C3×#3714C2211yescharacteristic, complemented
44C3×#1010—31no—
45C3×#1007—31no—
46#64308—31no—
47#64307—31no—
48#64307—31no—
49#64297D311yescharacteristic, complemented
50#64158—31no—
51#64151—31no—
52#64110—31no—
53C3×#950—31no—
54C2×C3×#215—31no—
55C3×#904—31no—
56C2×C3×#204—31no—
57#63948—32no—
58#63947—32no—
59#63946—32no—
60#63939—32no—
61D3×#215—32no—
62D3×#215—32no—
63#63935—32no—
64#63925—32no—
65C2×#3717D311yescharacteristic, complemented
66#63829D311yescharacteristic, complemented
67#63827—31no—
68#63827—31no—
69#63827—61no—
70#63823—31no—
71#63823—31no—
72#63823—61no—
73#63814—31no—
74#63814—31no—
75#63814—61no—
76#63811—32no—
77#63809—32no—
78#63798—32no—
79#63796—32no—
80C22×C3×C3⋊D3—21no—
81C2×#1113—22no—
82C2×C33×C4C2311yescharacteristic
83C3×#638—21no—
84C3×#638D412yes—
85C3×C4⋊(C3⋊D3)—21no—
86C3×C4⋊(C3⋊D3)D411yescharacteristic
87C3×C4⋊(C3⋊D3)C2311yescharacteristic
88C3×C4⋊(C3⋊D3)C2312yes—
89C3×C4×C3⋊D3—21no—
90C3×C4×C3⋊D3C2312yes—
91C3×#634D411yescharacteristic
92C3×#634C2311yescharacteristic
93C32×#67—21no—
94C2×C32×Dic3—21no—
95C32×D12C2311yescharacteristic
96C32×C4×D3—21no—
97C32×Dic6—21no—
98C32×Dic6C2312yes—
99C32×Dic6C2311yescharacteristic
100#6295—22no—
101#6295—22no—
102#6294—22no—
103C3×#627—22no—
104C3×#626—22no—
105C3×#624—22no—
106C3×D3×Dic3—22no—
107C3⋊(C3⋊(C3⋊C8))C2312yes—
108C32×C3⋊C8C2311yescharacteristic
109C32×C3⋊C8C2311yescharacteristic
110#5837—91no—
111#5770—91no—
112#5762—91no—
113C32×#41—31no—
114C2×C32×Q8—31no—
115#3828C2×D311yescharacteristic
116#3828C2×D311yescharacteristic
117C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
118C3×#239—32no—
119C3×#239—61no—
120C3×D3×Q8—32no—
121C3×D3×Q8—32no—
122C3×D3×Q8—61no—
123C3×#237—32no—
124C3×#237—62no—
125C3×#235—21no—
126C3×#235—31no—
127C3×#235—31no—
128C3×#235—31no—
129C3×#235—31no—
130C3×#235—61no—
131C3×#235—62no—
132C3×#235—61no—
133C3×#235—61no—
134C3×#235C2×D311yescharacteristic, complemented
135C3×#235C2×D311yescharacteristic, complemented
136C2×C3×D12—31no—
137C2×C3×D12—31no—
138C2×C3×D12—61no—
139C2×C3×Dic6—21no—
140C2×C3×Dic6—61no—
141C2×C3×Dic6C2×D311yescharacteristic, complemented
142C2×C3×Dic6C2×D311yescharacteristic, complemented
143#3811—62no—
144D3×#67—62no—
145D3×#67—62no—
146#3804—22no—
147#3802—32no—
148#3802—61no—
149D3×D12—32no—
150D3×D12—32no—
151D3×D12—61no—
152D3×D12—61no—
153#3799—21no—
154#3799—32no—
155#3799—61no—
156#3797C2×D312yescomplemented
157#3796—32no—
158#3796—61no—
159#3796C2×D312yescomplemented
160#3795—32no—
161#3795—61no—
162D3×Dic6—21no—
163C2×C32×C8—31no—
164#3756—32no—
165#3755—32no—
166#3755—32no—
167#3753—32no—
168#3748—31no—
169#3748—31no—
170#3748—31no—
171#3748—61no—
172#3748—61no—
173#3748—61no—
174#3748—121no—
175#3743—32no—
176C8×C3⋊D3—32no—
177C3×#216—31no—
178C3×#215—32no—
179C3×#215—32no—
180C3×#215—31no—
181C3×#214—31no—
182C3×#213—31no—
183C2×C3×C3⋊C8—21no—
184C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
185C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
186C3×Dic12—31no—
187C3×D24—31no—
188C3×#204—31no—
189C3×#204—32no—
190C3×#204—32no—
191C3×#204—31no—
192#3719C2×D311yescharacteristic, complemented
193#3718—32no—
194#3718—32no—
195#3718—62no—
196#3717C2×D311yescharacteristic, complemented
197#3717C2×D312yescomplemented
198#3717C2×D312yescomplemented
199#3716C2×D311yescharacteristic, complemented
200#3715—32no—
201#3715—32no—
202#3715—32no—
203#3715—32no—
204#3715—62no—
205#3715—62no—
206#3714C2×D311yescharacteristic, complemented
207#3713—32no—
208#3713—32no—
209#3713—62no—
210#3711—32no—
211#3711—32no—
212#3711—62no—
213D3×C3⋊C8—32no—
214D3×C3⋊C8—32no—
215D3×C3⋊C8—62no—
216C22×C33C2×D411yescharacteristic
217C2×C3×C3⋊D3—22no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—81no—
220C2×C3×C3⋊D3C2×D412yes—
221C2×C32×D3—21no—
222#1113—82no—
223C33×C4C2×D411yescharacteristic
224C33×C4C2411yescharacteristic
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3C2×D412yes—
227C32×Dic3—22no—
228C32×Dic3—21no—
229C3×2−1+4—91no—
230#1010—31no—
231#1009—91no—
232#1009—91no—
233#1007—31no—
234#1004—91no—
235C3×#135—91no—
236C2×C3×SD16—91no—
237#951—91no—
238#950—31no—
239#950—92no—
240#949—92no—
241#949—91no—
242#949—91no—
243#949—181no—
244#948—91no—
245#942—92no—
246#942—91no—
247#942—91no—
248#942—181no—
249C2×#215—31no—
250C2×#215—92no—
251#932—91no—
252#918—92no—
253#916—92no—
254#916—92no—
255#915—92no—
256#914—92no—
257D3×SD16—92no—
258D3×SD16—92no—
259#911—92no—
260#904—31no—
261C2×#204—31no—
262#901—91no—
263#901—91no—
264#901—181no—
265C22×C3⋊D3—21no—
266C22×C3×D3—61no—
267C22×C3×D3—61no—
268C22×C3×D3—121no—
269C2×D32—62no—
270C2×D32—62no—
271C2×D32—62no—
272C32×Q8—32no—
273C32×Q8—31no—
274C32×Q8—61no—
275C32×D4—31no—
276C32×D4—61no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—41no—
281C2×C32×C4—61no—
282C2×C32×C4—61no—
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286#638—21no—
287#638#6712yes—
288C4⋊(C3⋊D3)—21no—
289C4⋊(C3⋊D3)#6711yescharacteristic
290C4⋊(C3⋊D3)C22×D311yescharacteristic
291C4⋊(C3⋊D3)C22×D312yes—
292C4×C3⋊D3—21no—
293C4×C3⋊D3C22×D312yes—
294#634#6711yescharacteristic
295#634C22×D311yescharacteristic
296C3×#67—21no—
297C3×#67—21no—
298C3×#67—32no—
299C3×#67—32no—
300C3×#67—41no—
301C3×#67—62no—
302C3×#67—62no—
303C3×#67—61no—
304C3×#67—61no—
305C3×#67—121no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—41no—
309C2×C3×Dic3—62no—
310C3×D12—21no—
311C3×D12—31no—
312C3×D12—31no—
313C3×D12—32no—
314C3×D12—32no—
315C3×D12—31no—
316C3×D12—31no—
317C3×D12—61no—
318C3×D12—62no—
319C3×D12—61no—
320C3×D12—62no—
321C3×D12—61no—
322C3×D12—61no—
323C3×D12—121no—
324C3×D12C22×D311yescharacteristic
325C3×D12C22×D311yescharacteristic
326C3×C4×D3—21no—
327C3×C4×D3—21no—
328C3×C4×D3—32no—
329C3×C4×D3—32no—
330C3×C4×D3—41no—
331C3×C4×D3—62no—
332C3×C4×D3—62no—
333C3×C4×D3—62no—
334C3×C4×D3—62no—
335C3×C4×D3—61no—
336C3×C4×D3—61no—
337C3×C4×D3—121no—
338C3×Dic6—21no—
339C3×Dic6—21no—
340C3×Dic6—21no—
341C3×Dic6—22no—
342C3×Dic6—31no—
343C3×Dic6—31no—
344C3×Dic6—31no—
345C3×Dic6—31no—
346C3×Dic6—41no—
347C3×Dic6—61no—
348C3×Dic6—61no—
349C3×Dic6—62no—
350C3×Dic6—62no—
351C3×Dic6C22×D311yescharacteristic
352C3×Dic6C22×D311yescharacteristic
353C3×Dic6C22×D312yes—
354C3×Dic6C22×D312yes—
355#627—22no—
356#626—22no—
357#626—62no—
358#626—62no—
359#626—62no—
360#626—62no—
361#625—62no—
362#625—62no—
363#624—22no—
364#624—62no—
365D3×Dic3—22no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368C32×C8—31no—
369C32×C8—31no—
370C3⋊(C3⋊C8)—32no—
371C3⋊(C3⋊C8)—32no—
372C3⋊(C3⋊C8)—32no—
373C3⋊(C3⋊C8)—62no—
374C3⋊(C3⋊C8)—62no—
375C3⋊(C3⋊C8)—62no—
376C3⋊(C3⋊C8)—122no—
377C3×C3⋊C8—21no—
378C3×C3⋊C8—21no—
379C3×C3⋊C8C22×D311yescharacteristic
380C3×C3⋊C8C22×D311yescharacteristic
381C3×C3⋊C8C22×D311yescharacteristic
382C3×C3⋊C8C22×D311yescharacteristic
383#577—271noSylow
384C2×C33—21no—
385C2×C33C22×D411yescharacteristic
386C3×C3⋊D3—22no—
387C3×C3⋊D3—41no—
388C3×C3⋊D3—42no—
389C32×D3—41no—
390C3×#41—31no—
391C3×#41—31no—
392C3×#41—61no—
393C3×#41—91no—
394C3×#41—92no—
395C3×#41—91no—
396C3×#41—182no—
397C3×#41—181no—
398C2×C3×Q8—31no—
399C2×C3×Q8—31no—
400C2×C3×Q8—61no—
401C2×C3×Q8—92no—
402C2×C3×Q8—181no—
403C2×C3×D4—91no—
404C2×#67—182no—
405#239—32no—
406#239—61no—
407#239—92no—
408#239—181no—
409D3×Q8—32no—
410D3×Q8—32no—
411D3×Q8—61no—
412#237—32no—
413#237—62no—
414#237—92no—
415#237—181no—
416D3×D4—92no—
417D3×D4—92no—
418D3×D4—181no—
419D3×D4—181no—
420D3×D4—182no—
421D3×D4—182no—
422#235—31no—
423#235—31no—
424#235—31no—
425#235—31no—
426#235—61no—
427#235—61no—
428#235—61no—
429#235—62no—
430#235—92no—
431#235—181no—
432#235D3211yescharacteristic, complemented
433C2×D12—31no—
434C2×D12—31no—
435C2×D12—61no—
436C2×D12—92no—
437C2×D12—181no—
438C2×Dic6—61no—
439C2×Dic6D3211yescharacteristic, complemented
440C3×Q16—91no—
441C3×SD16—91no—
442C3×SD16—91no—
443C3×SD16—92no—
444C3×SD16—92no—
445C3×D8—91no—
446C2×C3×C8—31no—
447C2×C3×C8—31no—
448C2×C3×C8—61no—
449#216—31no—
450#216—92no—
451#216—92no—
452#216—92no—
453#216—182no—
454#215—32no—
455#215—32no—
456#215—31no—
457#215—92no—
458#215—92no—
459#215—92no—
460#215—92no—
461#215—182no—
462#215—182no—
463#214—31no—
464#214—92no—
465#214—92no—
466#213—31no—
467#213—92no—
468#213—92no—
469#213—92no—
470#213—182no—
471#208—91no—
472#208—91no—
473#208—91no—
474#208—92no—
475#208—181no—
476#208—181no—
477#208—181no—
478#208—361no—
479C2×C3⋊C8—92no—
480C2×C3⋊C8D3211yescharacteristic, complemented
481Dic12—31no—
482D24—31no—
483#204—31no—
484#204—32no—
485#204—32no—
486#204—31no—
487ΓL(1,𝔽25)—92no—
488ΓL(1,𝔽25)—92no—
489ΓL(1,𝔽25)—182no—
490D3×C8—92no—
491D3×C8—92no—
492D3×C8—182no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—41no—
497C22×C32—61no—
498C22×C32D3×D411yescharacteristic
499C22×C32D3×D411yescharacteristic
500C22×C32C2×#6711yescharacteristic
501C2×C3⋊D3—22no—
502C2×C3⋊D3—21no—
503C2×C3⋊D3—81no—
504C2×C3⋊D3C2×#6712yes—
505C2×C3×D3—21no—
506C2×C3×D3—21no—
507C2×C3×D3—32no—
508C2×C3×D3—32no—
509C2×C3×D3—41no—
510C2×C3×D3—62no—
511C2×C3×D3—62no—
512C2×C3×D3—61no—
513C2×C3×D3—62no—
514C2×C3×D3—61no—
515C2×C3×D3—121no—
516C2×C3×D3—122no—
517C2×C3×D3—241no—
518C2×C3×D3—241no—
519C2×C3×D3—242no—
520D32—242no—
521D32—242no—
522D32—242no—
523C32×C4—21no—
524C32×C4—21no—
525C32×C4—21no—
526C32×C4—21no—
527C32×C4—21no—
528C32×C4—21no—
529C32×C4—41no—
530C32×C4—41no—
531C32×C4—61no—
532C32×C4—62no—
533C32×C4D3×D411yescharacteristic
534C32×C4D3×D411yescharacteristic
535C32×C4C2×#6711yescharacteristic
536C32×C4C23×D311yescharacteristic
537C32×C4C23×D311yescharacteristic
538C32×C4C23×D311yescharacteristic
539C3⋊Dic3—21no—
540C3⋊Dic3C2×#6712yes—
541C3×Dic3—22no—
542C3×Dic3—21no—
543C3×Dic3—22no—
544C3×Dic3—21no—
545C3×Dic3—32no—
546C3×Dic3—32no—
547C3×Dic3—42no—
548C3×Dic3—41no—
549C3×Dic3—62no—
550C3×Dic3—61no—
551C3×Dic3—61no—
552C3×Dic3—121no—
5532−1+4—91no—
554H(5,𝔽2)—271no—
555#137—272no—
556#137—271no—
557AGL(1,ℤ/8)—272no—
558AGL(1,ℤ/8)—271no—
559#135—91no—
560#135—272no—
561C2×SD16—91no—
562C2×SD16—272no—
563#131—271no—
564C33#57711yescharacteristic, complemented, Sylow
565C23×C3—181no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—121no—
569C22×D3—182no—
570C22×D3—182no—
571C22×D3—182no—
572C3×Q8—32no—
573C3×Q8—31no—
574C3×Q8—31no—
575C3×Q8—32no—
576C3×Q8—61no—
577C3×Q8—62no—
578C3×Q8—61no—
579C3×Q8—61no—
580C3×Q8—91no—
581C3×Q8—91no—
582C3×Q8—121no—
583C3×Q8—182no—
584C3×D4—31no—
585C3×D4—31no—
586C3×D4—61no—
587C3×D4—61no—
588C3×D4—61no—
589C3×D4—92no—
590C3×D4—92no—
591C3×D4—91no—
592C3×D4—91no—
593C3×D4—121no—
594C3×D4—182no—
595C3×D4—181no—
596C3×D4—181no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—41no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—92no—
606C2×C3×C4—121no—
607C2×C3×C4—121no—
608C2×C3×C4—182no—
609C2×C3×C4—182no—
610C2×C3×C4—181no—
611C2×C3×C4C2×D3211yescharacteristic
612C2×C3×C4C2×D3211yescharacteristic
613C2×C3×C4C2×D3211yescharacteristic
614#67—21no—
615#67—32no—
616#67—32no—
617#67—62no—
618#67—62no—
619#67—61no—
620#67—61no—
621#67—121no—
622#67—182no—
623#67—182no—
624#67—182no—
625#67—182no—
626C2×Dic3—21no—
627C2×Dic3—62no—
628C2×Dic3—182no—
629D12—32no—
630D12—31no—
631D12—31no—
632D12—32no—
633D12—31no—
634D12—31no—
635D12—61no—
636D12—62no—
637D12—61no—
638D12—62no—
639D12—61no—
640D12—61no—
641D12—121no—
642D12—182no—
643D12—182no—
644D12C2×D3211yescharacteristic
645C4×D3—21no—
646C4×D3—32no—
647C4×D3—32no—
648C4×D3—62no—
649C4×D3—62no—
650C4×D3—62no—
651C4×D3—62no—
652C4×D3—61no—
653C4×D3—61no—
654C4×D3—121no—
655C4×D3—182no—
656C4×D3—182no—
657Dic6—21no—
658Dic6—31no—
659Dic6—31no—
660Dic6—31no—
661Dic6—31no—
662Dic6—61no—
663Dic6—61no—
664Dic6—62no—
665Dic6—62no—
666Dic6C2×D3212yes—
667Dic6C2×D3211yescharacteristic
668C3×C8—31no—
669C3×C8—31no—
670C3×C8—31no—
671C3×C8—31no—
672C3×C8—61no—
673C3×C8—61no—
674C3⋊C8—92no—
675C3⋊C8—92no—
676C3⋊C8—92no—
677C3⋊C8—182no—
678C3⋊C8—182no—
679C3⋊C8—182no—
680C3⋊C8—362no—
681C3⋊C8C2×D3211yescharacteristic
682C3⋊C8C2×D3211yescharacteristic
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—41no—
690C2×C32—41no—
691C2×C32—41no—
692C2×C32—41no—
693C2×C32—81no—
694C2×C32—121no—
695C2×C32C2×D3×D411yescharacteristic
696C2×C32C2×D3×D411yescharacteristic
697C2×C32C22×#6711yescharacteristic
698C3⋊D3—22no—
699C3⋊D3—42no—
700C3⋊D3—41no—
701C3×D3—41no—
702C3×D3—41no—
703C3×D3—62no—
704C3×D3—62no—
705C3×D3—81no—
706C3×D3—122no—
707C3×D3—121no—
708C3×D3—122no—
709C3×D3—121no—
710C3×D3—122no—
711C3×D3—241no—
712C3×D3—242no—
713#41—31no—
714#41—91no—
715#41—92no—
716#41—91no—
717#41—182no—
718#41—181no—
719#41—272no—
720#41—541no—
721C2×Q8—31no—
722C2×Q8—92no—
723C2×Q8—181no—
724C2×D4—91no—
725C2×D4—272no—
726C2×D4—541no—
727C2×D4—542no—
728Q16—91no—
729Q16—272no—
730SD16—91no—
731SD16—92no—
732SD16—92no—
733SD16—91no—
734SD16—272no—
735SD16—272no—
736D8—91no—
737D8—272no—
738M16—272no—
739M16—271no—
740C2×C8—31no—
741C2×C8—272no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—41no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—92no—
749C22×C3—121no—
750C22×C3—182no—
751C22×C3—181no—
752C22×C3—721no—
753C22×C3#380211yescharacteristic
754C22×C3D3×#6711yescharacteristic
755C22×C3D3×#6711yescharacteristic
756C2×D3—21no—
757C2×D3—32no—
758C2×D3—32no—
759C2×D3—62no—
760C2×D3—61no—
761C2×D3—62no—
762C2×D3—61no—
763C2×D3—62no—
764C2×D3—121no—
765C2×D3—122no—
766C2×D3—241no—
767C2×D3—241no—
768C2×D3—242no—
769C2×D3—722no—
770C2×D3—722no—
771C2×D3—722no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—61no—
781C3×C4—62no—
782C3×C4—61no—
783C3×C4—62no—
784C3×C4—92no—
785C3×C4—121no—
786C3×C4—122no—
787C3×C4—181no—
788C3×C4#380211yescharacteristic
789C3×C4D3×#6711yescharacteristic
790C3×C4D3×#6711yescharacteristic
791C3×C4C22×D3211yescharacteristic
792C3×C4C22×D3211yescharacteristic
793C3×C4C22×D3211yescharacteristic
794Dic3—22no—
795Dic3—21no—
796Dic3—32no—
797Dic3—32no—
798Dic3—62no—
799Dic3—61no—
800Dic3—61no—
801Dic3—121no—
802C32—21no—
803C32—21no—
804C32—21no—
805C32—41no—
806C32#576211yescharacteristic, complemented
807C32#577011yescharacteristic, complemented
808C32#583711yescharacteristic, complemented
809C23—181no—
810C23—542no—
811Q8—32no—
812Q8—31no—
813Q8—61no—
814Q8—91no—
815Q8—91no—
816Q8—182no—
817D4—31no—
818D4—61no—
819D4—92no—
820D4—91no—
821D4—92no—
822D4—91no—
823D4—182no—
824D4—181no—
825D4—181no—
826D4—542no—
827D4—542no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—92no—
831C2×C4—182no—
832C2×C4—182no—
833C2×C4—181no—
834C2×C4—542no—
835C2×C4D3311yescharacteristic
836C8—31no—
837C8—31no—
838C8—272no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—41no—
846C2×C3—41no—
847C2×C3—41no—
848C2×C3—41no—
849C2×C3—81no—
850C2×C3—121no—
851C2×C3—121no—
852C2×C3—182no—
853C2×C3—241no—
854C2×C3—362no—
855C2×C3—361no—
856C2×C3C2×#380211yescharacteristic
857C2×C3C2×D3×#6711yescharacteristic
858C2×C3C2×D3×#6711yescharacteristic
859D3—41no—
860D3—62no—
861D3—62no—
862D3—122no—
863D3—122no—
864D3—121no—
865D3—121no—
866D3—122no—
867D3—242no—
868D3—241no—
869C22—61no—
870C22—92no—
871C22—181no—
872C22—182no—
873C22—721no—
874C22—2162no—
875C22#8895311yescharacteristic
876C4—61no—
877C4—62no—
878C4—92no—
879C4—181no—
880C4#8895311yescharacteristic
881C4C2×D3311yescharacteristic
882C3—21no—
883C3—21no—
884C3—21no—
885C3—41no—
886C3#1059468611yescharacteristic, complemented
887C3#1059531811yescharacteristic, complemented
888C3#1059545711yescharacteristic, complemented
889C2—21no—
890C2—121no—
891C2—182no—
892C2—362no—
893C2—361no—
894C2C2×#8895311yescharacteristic
subgroupG/H
centerC2C2×#88953
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC2×C33C22×D4
hypercenterC2×C4D33
hypocenterC33#577
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. #11724619C2semidirect
2. C3×#64297C2semidirect
3. #11723375C2semidirect
4. #11723365C2semidirect
5. #11723352C2semidirect
6. C2×C3×#3717C2semidirect
7. C3×#63829C2semidirect
8. #11722892C2semidirect
9. #11722876C2semidirect
10. #11722859C2semidirect
11. #11722840C2semidirect
18. C32×#235C22semidirect
19. C2×C32×Dic6C22semidirect
27. C3×#3797C22semidirect
28. C3×#3796C22semidirect
30. #88855C22semidirect
31. C2×C32×C3⋊C8C22semidirect
32. #88798C22semidirect
33. #88793C22semidirect
34. #88793C22semidirect
35. #88789C22semidirect
36. #88787C22semidirect
37. C3⋊D3×C3⋊C8C22semidirect
38. C3×#3719C22semidirect
39. C3×#3717C22semidirect
40. C3×#3717C22semidirect
41. C3×#3717C22semidirect
42. C3×#3716C22semidirect
43. C3×#3714C22semidirect
49. #64297D3semidirect
65. C2×#3717D3semidirect
66. #63829D3semidirect
134. C3×#235C2×D3semidirect
135. C3×#235C2×D3semidirect
141. C2×C3×Dic6C2×D3semidirect
142. C2×C3×Dic6C2×D3semidirect
156. #3797C2×D3semidirect
159. #3796C2×D3semidirect
184. C2×C3×C3⋊C8C2×D3semidirect
185. C2×C3×C3⋊C8C2×D3semidirect
192. #3719C2×D3semidirect
196. #3717C2×D3semidirect
197. #3717C2×D3semidirect
198. #3717C2×D3semidirect
199. #3716C2×D3semidirect
206. #3714C2×D3semidirect
432. #235D32semidirect
439. C2×Dic6D32semidirect
480. C2×C3⋊C8D32semidirect
564. C33#577semidirect
806. C32#5762semidirect
807. C32#5770semidirect
808. C32#5837semidirect
886. C3#10594686semidirect
887. C3#10595318semidirect
888. C3#10595457semidirect

Maximal subgroups

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

subgroupindex
#117246192
C3×#642972
#117233752
#117233652
#117233522
C2×C3×#37172
C3×#638292
#117228922
#117228762
#117228592
#117228402
#105954573
#105953183
#105946863