Finite Group Databasebeta

← #11884430

Subgroups — #11884430

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic, complemented
2C3×#5806C211yesmaximal, characteristic, complemented
3C2×#63933C211yesmaximal, characteristic, complemented
4#10594919C211yesmaximal, characteristic, complemented
5C3×#5217C211yesmaximal, characteristic, complemented
6#10591519C211yesmaximal, characteristic, complemented
7#10591483C211yesmaximal, characteristic, complemented
8#10591481C211yesmaximal, characteristic, complemented
9#10591452C211yesmaximal, characteristic, complemented
10#10591449C211yesmaximal, characteristic, complemented
11#10591441C211yesmaximal, characteristic, complemented
12#10591405C211yesmaximal, characteristic, complemented
13#10591184C211yesmaximal, characteristic, complemented
14#10591180C211yesmaximal, characteristic, complemented
15#10591151C211yesmaximal, characteristic, complemented
16#83507—31nomaximal
17#80013—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×#3754C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24#64141—24no—
25C2×#3753C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28C3×#953—21no—
29C2×C3×#217—21no—
30C3×#939—21no—
31C3×#938C2211yescharacteristic
32C3×#936C2211yescharacteristic
33C3×#935—21no—
34C3×D4×Dic3C2211yescharacteristic
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×#930C2211yescharacteristic
38C3×C4×#67C2211yescharacteristic
39C3×#924C2211yescharacteristic
40#63979—21no—
41#63971—21no—
42#63933—24no—
43#63912—21no—
44#63911C2211yescharacteristic, complemented
45#63909C2211yescharacteristic, complemented
46#63881—21no—
47#63844C2211yescharacteristic, complemented
48C2×#3719C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic
53C3×#832C2211yescharacteristic
54C3×#830C2211yescharacteristic
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64C2×#950—31no—
65#5806D311yescharacteristic, complemented
66C2×#932—31no—
67C2×#932—31no—
68C2×#932—61no—
69C2×#912—31no—
70#5599—31no—
71#5553—31no—
72C3×#447—31no—
73#5238—31no—
74#5217D311yescharacteristic, complemented
75#5158—31no—
76#5154—31no—
77#5150—31no—
78#5058—31no—
79#5054—31no—
80#5049—31no—
81#5047—31no—
82#5042—31no—
83#5038—31no—
84#5037—31no—
85#5018—31no—
86#5015—31no—
87#5011—31no—
88#4781—31no—
89#4775—31no—
90#4767—31no—
91#4757—31no—
92#4733—31no—
93#4728—31no—
94C24×C32—21no—
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4—41no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102#3828—22no—
103#3828—41no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237—41no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#625—21no—
122C2×D3×Dic3—21no—
123#3795—22no—
124#3795—41no—
125#3754—22no—
126#3754D414yescomplemented
127#3753—22no—
128#3753—22no—
129#3748—22no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#217—21no—
137C3×#217D411yescharacteristic
138C3×#213—22no—
139C3×#213—41no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4D411yescharacteristic
146C3×C4×Dic3C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149#3724—21no—
150#3722—21no—
151Dic32—21no—
152#3719—22no—
153#3717—41no—
154#3715—22no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—21no—
159C22×C3×D4C2×D311yescharacteristic
160C22×C3×D4C2×D311yescharacteristic
161C2×#237—31no—
162C2×#237C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×#235—31no—
166C2×#235—61no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C3×#124—31no—
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×#121—31no—
174C3×#121—61no—
175C3×#120—61no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C22⋊C4—61no—
179#953—21no—
180C2×#217—21no—
181#950—64no—
182C2×#216—31no—
183C2×#215—31no—
184C2×#215—31no—
185#940—31no—
186#940—61no—
187#940—61no—
188#939—21no—
189#939—61no—
190#938C2×D311yescharacteristic
191#936C2×D311yescharacteristic
192#935—21no—
193D4×Dic3C2×D311yescharacteristic
194C2×#214—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—61no—
200C2×#214—61no—
201#932—64no—
202#932—64no—
203#932—68no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209C2×#213—61no—
210C2×#213C2×D311yescharacteristic
211C2×#213C2×D311yescharacteristic
212#930—31no—
213#930C2×D311yescharacteristic
214C4×#67C2×D311yescharacteristic
215#924C2×D311yescharacteristic
216C2×#208—31no—
217C2×#208—31no—
218C2×#208—61no—
219C22×C3⋊C8—31no—
220#912—64no—
221C2×Dic12—31no—
222C2×#204—31no—
223C2×D3×C8—31no—
224#895—31no—
225#893—61no—
226#887—31no—
227#884—61no—
228#884—61no—
229#884—61no—
230#67⋊C4—61no—
231#874—31no—
232C4×Dic6—31no—
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#832—31no—
238#832C2×D311yescharacteristic
239#832C2×D311yescharacteristic
240#830—31no—
241#830C2×D311yescharacteristic
242#821—31no—
243(C2×D3)⋊C8—31no—
244#816—31no—
245#815—31no—
246Dic3⋊C8—31no—
247#810—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#807—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—42no—
258C23×C32—42no—
259C23×C32—81no—
260C23×C32C2×D411yescharacteristic
261C22×C3⋊D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3C2×D411yescharacteristic
264C32×D4—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—42no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273#638—42no—
274C2×C3⋊Dic3—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4×C3⋊D3—42no—
278#634—21no—
279#634C2×D412yes—
280C3×#67—41no—
281C3×#67—42no—
282C3×#67—81no—
283C3×#67—81no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—42no—
288C2×C3×Dic3—81no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—42no—
299#626—81no—
300#626—81no—
301#625—42no—
302D3×Dic3—42no—
303C3⋊(C3⋊C8)—21no—
304C3⋊(C3⋊C8)C2×D412yes—
305C3×C3⋊C8—21no—
306C3×C3⋊C8—21no—
307C2×AGL(1,ℤ/8)—91no—
308C2×#135—91no—
309#550—91no—
310#546—31no—
311#496—91no—
312#468—91no—
313#466—91no—
314#464—91no—
315#459—91no—
316#452—91no—
317#449—91no—
318#449—91no—
319#447—31no—
320#440—91no—
321#435—91no—
322C24×C3—21no—
323C24×C3—21no—
324C24×C3—41no—
325C3×#41—62no—
326C3×#41—121no—
327C2×C3×Q8—31no—
328C2×C3×D4—24no—
329C2×C3×D4—22no—
330C2×C3×D4—22no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—41no—
338C2×C3×D4—41no—
339C2×C3×D4—41no—
340C2×C3×D4—42no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C2×C3×D4C22×D311yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—121no—
365C2×#67#6711yescharacteristic
366C22×Dic3—21no—
367C22×Dic3—21no—
368C22×Dic3—61no—
369#237—22no—
370#237—41no—
371#237—62no—
372#237—121no—
373#235—62no—
374#235—62no—
375#235—62no—
376#235—64no—
377#235—121no—
378#235—121no—
379#235—121no—
380#235—122no—
381C2×D12—31no—
382C2×D12—31no—
383C2×D12—61no—
384C2×D12—61no—
385C2×D12—61no—
386C2×D12—61no—
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—121no—
392C2×C4×D3C22×D311yescharacteristic
393C2×Dic6—31no—
394C2×Dic6—31no—
395C2×Dic6—61no—
396C2×Dic6C22×D311yescharacteristic
397C3×D8—62no—
398C3×D8—121no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—61no—
405C3×C22⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C42—31no—
414#217—21no—
415#217—21no—
416#217—21no—
417#217—21no—
418#217—21no—
419#217#6711yescharacteristic
420#216—62no—
421#215—62no—
422#215—121no—
423#214—34no—
424#214—34no—
425#214—64no—
426#214—62no—
427#214—62no—
428#214—62no—
429#214—64no—
430#213—22no—
431#213—41no—
432#213—62no—
433#213—62no—
434#213—64no—
435#213—64no—
436#213—62no—
437#213—62no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4#6711yescharacteristic
442C4⋊Dic3C22×D311yescharacteristic
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—21no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447Dic3⋊C4#6711yescharacteristic
448C4×Dic3—61no—
449C4×Dic3—61no—
450C4×Dic3C22×D311yescharacteristic
451#208—62no—
452#208—62no—
453#208—64no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—31no—
457C2×C3⋊C8—31no—
458C2×C3⋊C8—61no—
459C2×C3⋊C8—61no—
460C2×C3⋊C8—62no—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463Dic12—62no—
464#204—121no—
465D3×C8—62no—
466C22×C32—21no—
467C22×C32—22no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32—41no—
475C22×C32—84no—
476C22×C32C22×D411yescharacteristic
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C32×C4—21no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—22no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—31no—
497C2×#41—91no—
498C2×#41—91no—
499C22×D4D3211yescharacteristic
500AGL(1,ℤ/8)—184no—
501#135—184no—
502C2×Q16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×D8—31no—
508C2×D8—31no—
509C2×D8—91no—
510C2×D8—91no—
511C2×M16—91no—
512C22×C8—91no—
513#127—91no—
514#127—181no—
515#124—31no—
516#123—61no—
517C22⋊Q8—31no—
518#121—31no—
519#121—31no—
520#121—61no—
521#121—91no—
522#121—181no—
523#121—181no—
524#120—61no—
525C4×Q8—91no—
526C4×D4—31no—
527C4×D4—31no—
528C4×D4—181no—
529C2×C22⋊C4—61no—
530#107—91no—
531C4⋊C8—91no—
532#103—91no—
533#103—91no—
534#102—31no—
535#102—31no—
536#102—91no—
537#102—91no—
538C22⋊C8—31no—
539C22⋊C8—91no—
540#97—91no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—31no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—42no—
550C23×C3—42no—
551C23×C3—44no—
552C23×C3—42no—
553C23×C3—42no—
554C23×C3—61no—
555C23×C3—82no—
556C23×C3—81no—
557C23×C3—81no—
558C23×C3—82no—
559C23×C3D3×D411yescharacteristic
560C23×C3C2×#6711yescharacteristic
561C22×D3—21no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—121no—
565C22×D3C2×#6711yescharacteristic
566C3×Q8—61no—
567C3×Q8—61no—
568C3×D4—22no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—21no—
575C3×D4—22no—
576C3×D4—41no—
577C3×D4—41no—
578C3×D4—42no—
579C3×D4—42no—
580C3×D4—44no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—121no—
584C3×D4—122no—
585C3×D4—241no—
586C3×D4—241no—
587C3×D4D3×D412yes—
588C3×D4D3×D412yes—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—122no—
606C2×C3×C4—241no—
607C2×C3×C4D3×D411yescharacteristic
608C2×C3×C4C2×#6711yescharacteristic
609C2×C3×C4C23×D311yescharacteristic
610C2×C3×C4C23×D311yescharacteristic
611#67—41no—
612#67—42no—
613#67—81no—
614#67—81no—
615#67—122no—
616#67—122no—
617#67—122no—
618#67—122no—
619#67—122no—
620#67—124no—
621#67—241no—
622#67—241no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—42no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—81no—
630C2×Dic3—121no—
631C2×Dic3—122no—
632C2×Dic3C2×#6711yescharacteristic
633C2×Dic3C2×#6711yescharacteristic
634C2×Dic3C2×#6711yescharacteristic
635D12—21no—
636D12—21no—
637D12—62no—
638D12—61no—
639D12—61no—
640D12—61no—
641D12—61no—
642D12—121no—
643D12—122no—
644D12—241no—
645D12—241no—
646C4×D3—21no—
647C4×D3—21no—
648C4×D3—122no—
649C4×D3—122no—
650C4×D3—122no—
651C4×D3—124no—
652Dic6—21no—
653Dic6—21no—
654Dic6—32no—
655Dic6—32no—
656Dic6—62no—
657Dic6—61no—
658Dic6—61no—
659Dic6—121no—
660C3×C8—61no—
661C3×C8—61no—
662C3⋊C8—21no—
663C3⋊C8—21no—
664C3⋊C8—32no—
665C3⋊C8—32no—
666C3⋊C8—62no—
667C3⋊C8—62no—
668C3⋊C8—61no—
669C3⋊C8—61no—
670C2×C32—41no—
671C2×C32—42no—
672C2×C32—81no—
673C2×C32D4211yescharacteristic
674C2×C32#57511yescharacteristic
675C2×C32#57611yescharacteristic
676C3⋊D3—81no—
677C3×D3—41no—
678C3×D3—81no—
679C24—21no—
680#41—62no—
681#41—121no—
682#41—182no—
683#41—182no—
684#41—361no—
685#41—361no—
686C2×Q8—31no—
687C2×Q8—91no—
688C2×D4—22no—
689C2×D4—21no—
690C2×D4—31no—
691C2×D4—31no—
692C2×D4—41no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—91no—
697C2×D4—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4C2×D3211yescharacteristic
703C2×D4C2×D3211yescharacteristic
704C22×C4—31no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—181no—
708C22×C4—181no—
709C22×C4C2×D3211yescharacteristic
710Q16—182no—
711SD16—94no—
712SD16—182no—
713SD16—182no—
714SD16—361no—
715D8—62no—
716D8—121no—
717D8—182no—
718D8—182no—
719M16—182no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—91no—
723C2×C8—91no—
724C2×C8—182no—
725C4⋊C4—31no—
726C4⋊C4—31no—
727C4⋊C4—31no—
728C4⋊C4—61no—
729C4⋊C4—181no—
730C22⋊C4—31no—
731C22⋊C4—31no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—181no—
739C42—31no—
740C42—181no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—22no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—22no—
750C22×C3—21no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3—61no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—84no—
773C22×C3—84no—
774C22×C3—88no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C22×#6711yescharacteristic
780C2×D3—21no—
781C2×D3—21no—
782C2×D3—21no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—122no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—241no—
794C2×D3—241no—
795C3×C4—22no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—121no—
804C3×C4—121no—
805C3×C4—121no—
806C3×C4C2×D3×D411yescharacteristic
807C3×C4C2×D3×D411yescharacteristic
808C3×C4#100411yescharacteristic
809C3×C4#100411yescharacteristic
810Dic3—21no—
811Dic3—21no—
812Dic3—21no—
813Dic3—41no—
814Dic3—41no—
815Dic3—41no—
816Dic3—62no—
817Dic3—62no—
818Dic3—122no—
819C32#326811yescharacteristic, complemented, Sylow
820C23—21no—
821C23—21no—
822C23—31no—
823C23—42no—
824C23—42no—
825C23—61no—
826C23—81no—
827C23—181no—
828C23D3×#6711yescharacteristic
829Q8—61no—
830Q8—61no—
831Q8—92no—
832Q8—181no—
833D4—21no—
834D4—21no—
835D4—21no—
836D4—42no—
837D4—61no—
838D4—61no—
839D4—121no—
840D4—122no—
841D4—181no—
842D4—181no—
843D4—241no—
844D4—241no—
845D4—362no—
846D4—362no—
847D4—362no—
848D4—721no—
849D4—721no—
850D4#381112yes—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—122no—
862C2×C4—181no—
863C2×C4—241no—
864C2×C4—362no—
865C2×C4—362no—
866C2×C4D3×#6711yescharacteristic
867C2×C4C22×D3211yescharacteristic
868C8—61no—
869C8—61no—
870C8—92no—
871C8—181no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—42no—
876C2×C3—41no—
877C2×C3—42no—
878C2×C3—41no—
879C2×C3—42no—
880C2×C3—82no—
881C2×C3—82no—
882C2×C3—81no—
883C2×C3—81no—
884C2×C3—121no—
885C2×C3—241no—
886C2×C3#559011yescharacteristic
887C2×C3#575711yescharacteristic
888C2×C3#577311yescharacteristic
889C2×C3D4×#6711yescharacteristic
890C2×C3#582211yescharacteristic
891C2×C3#583511yescharacteristic
892D3—41no—
893D3—81no—
894D3—242no—
895D3—241no—
896D3—241no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—61no—
907C22—61no—
908C22—61no—
909C22—84no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—361no—
914C22—361no—
915C22—361no—
916C22C2×D3×#6711yescharacteristic
917C4—21no—
918C4—61no—
919C4—61no—
920C4—61no—
921C4—121no—
922C4—121no—
923C4—121no—
924C4—182no—
925C4C2×#381111yescharacteristic
926C4#6433011yescharacteristic
927C3—21no—
928C3#8001311yescharacteristic, complemented
929C3#8350711yescharacteristic, complemented
930C2—41no—
931C2—42no—
932C2—81no—
933C2—121no—
934C2—241no—
935C2—721no—
936C2#1059509511yescharacteristic
937C2#1059509611yescharacteristic
938C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64141C2semidirect
2. C3×#5806C2semidirect
3. C2×#63933C2semidirect
4. #10594919C2semidirect
5. C3×#5217C2semidirect
6. #10591519C2semidirect
7. #10591483C2semidirect
8. #10591481C2semidirect
9. #10591452C2semidirect
10. #10591449C2semidirect
11. #10591441C2semidirect
12. #10591405C2semidirect
13. #10591184C2semidirect
14. #10591180C2semidirect
15. #10591151C2semidirect
21. C2×#3795C22semidirect
44. #63911C22semidirect
45. #63909C22semidirect
47. #63844C22semidirect
48. C2×#3719C22semidirect
49. C2×#3717C22semidirect
50. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63564C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
65. #5806D3semidirect
74. #5217D3semidirect
126. #3754D4semidirect
819. C32#3268semidirect
928. C3#80013semidirect
929. C3#83507semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C3×#58062
C2×#639332
#105949192
C3×#52172
#105915192
#105914832
#105914812
#105914522
#105914492
#105914412
#105914052
#105911842
#105911802
#105911512
#835073
#800133