Finite Group Databasebeta

← #11884407

Subgroups — #11884407

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×#64158C211yesmaximal, characteristic, complemented
2C3×#5834C211yesmaximal, characteristic, complemented
3C2×#63949C211yesmaximal, characteristic, complemented
4#10595018C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic, complemented
7#10591588C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591521C211yesmaximal, characteristic, complemented
10#10591472C211yesmaximal, characteristic, complemented
11#10591449C211yesmaximal, characteristic, complemented
12#10591429C211yesmaximal, characteristic, complemented
13#10591180C211yesmaximal, characteristic, complemented
14#10591168C211yesmaximal, characteristic, complemented
15#10591151C211yesmaximal, characteristic, complemented
16#83577—31nomaximal
17#80266—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic, complemented
21C2×#3799C2211yescharacteristic
22#64158—24no—
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C2×#3748C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C3×#940—21no—
31C3×#940C2211yescharacteristic, complemented
32C3×#938—21no—
33C3×#938C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C3×#930—21no—
36C3×#930C2211yescharacteristic
37C3×C4×#67—21no—
38C3×C4×#67C2211yescharacteristic
39C3×#924C2211yescharacteristic
40#63981—21no—
41#63974—21no—
42#63949—24no—
43#63910—21no—
44#63909C2211yescharacteristic
45#63897—21no—
46#63894C2211yescharacteristic
47#63864C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#550—31no—
64#5834D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#949—31no—
67C2×#949—31no—
68C2×#949—61no—
69C2×#919—31no—
70#5630—31no—
71#5550—31no—
72C3×#452—31no—
73#5239D311yescharacteristic, complemented
74#5238—31no—
75#5185—31no—
76#5176—31no—
77#5172—31no—
78#5074—31no—
79#5072—31no—
80#5049—31no—
81#5042—31no—
82#5038—31no—
83#5037—31no—
84#5036—31no—
85#5028—31no—
86#5026—31no—
87#5011—31no—
88#4817—31no—
89#4810—31no—
90#4786—31no—
91#4775—31no—
92#4732—31no—
93#4728—31no—
94C23×C3⋊D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67D411yescharacteristic
112C3×#239—22no—
113C3×#239—41no—
114C2×C3×D12—21no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—21no—
120C2×#626—21no—
121C2×#624—21no—
122C2×#624—21no—
123#3799—22no—
124#3799—41no—
125#3755—22no—
126#3755D414yescomplemented
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×#217D411yescharacteristic
135C3×#216—22no—
136C3×#214—41no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3—21no—
145C3×C4×Dic3C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148#3722—21no—
149#3722—21no—
150#3722—21no—
151#3722—21no—
152#3715—22no—
153#3714—22no—
154#3714—41no—
155D3×C3⋊C8—22no—
156#3268—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41—31no—
159C2×C3×#41C2×D311yescharacteristic
160C2×C3×#41C2×D311yescharacteristic
161C2×#239—31no—
162C2×#239C2×D311yescharacteristic, complemented
163C2×#235—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—61no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C3×#127—31no—
170C3×#127—61no—
171C3×C22⋊Q8—31no—
172C3×#121—31no—
173C3×#121—31no—
174C3×#121—61no—
175C3×#121—61no—
176C3×C4×Q8—31no—
177C3×C4×D4—31no—
178C3×C4×D4—61no—
179#950—64no—
180#949—64no—
181#949—64no—
182#949—68no—
183#947—31no—
184Q8×Dic3C2×D311yescharacteristic, complemented
185C2×#216C2×D311yescharacteristic, complemented
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—61no—
192C2×#215—61no—
193#940—21no—
194#940C2×D311yescharacteristic, complemented
195#938—21no—
196#938C2×D311yescharacteristic, complemented
197#937—61no—
198C2×#214—31no—
199C2×#214C2×D311yescharacteristic, complemented
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—61no—
207C2×#213—61no—
208#930—21no—
209#930—31no—
210#930C2×D311yescharacteristic
211C4×#67—21no—
212C4×#67C2×D311yescharacteristic
213#924C2×D311yescharacteristic
214C2×#208—31no—
215C2×#208—31no—
216C2×#208—61no—
217C22×C3⋊C8—31no—
218#919—64no—
219C2×D24—31no—
220C2×D24—31no—
221C2×D3×C8—31no—
222#895—31no—
223#895—61no—
224#894—61no—
225#894—61no—
226#893—31no—
227#884—61no—
228#882—61no—
229D3×C22⋊C4—61no—
230D3×C22⋊C4—61no—
231#875—31no—
232C4×D12—31no—
233C3×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#835C2×D311yescharacteristic, complemented
238#832—31no—
239#832C2×D311yescharacteristic, complemented
240#830—31no—
241#830C2×D311yescharacteristic
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245#815—31no—
246Dic3⋊C8—31no—
247#810—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#807—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—81no—
262C22×C3×D3—21no—
263C22×C3×D3C2×D411yescharacteristic
264C32×Q8—21no—
265C32×Q8C2×D412yes—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4—42no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—42no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—42no—
279C4⋊(C3⋊D3)C2×D412yes—
280C3×#67—41no—
281C3×#67—42no—
282C3×#67—81no—
283C3×#67—81no—
284C3×#67—81no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3C2×D411yescharacteristic
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—42no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—42no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299#626—42no—
300#626—81no—
301#624—42no—
302#624—81no—
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—31no—
310#546—91no—
311#496—91no—
312#468—91no—
313#466—91no—
314#464—91no—
315#459—91no—
316#452—31no—
317#449—91no—
318#449—91no—
319#447—91no—
320#440—91no—
321#435—91no—
322C23×D3—61no—
323C23×D3—61no—
324C23×D3—121no—
325C3×#41—24no—
326C3×#41—22no—
327C3×#41—22no—
328C3×#41—41no—
329C3×#41—41no—
330C3×#41—42no—
331C3×#41—62no—
332C3×#41—121no—
333C2×C3×Q8—21no—
334C2×C3×Q8—31no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—41no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4C22×D311yescharacteristic
349C2×C3×D4C22×D311yescharacteristic
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—31no—
354C22×C3×C4—41no—
355C22×C3×C4—61no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67#6711yescharacteristic
365#239—22no—
366#239—41no—
367#239—62no—
368#239—121no—
369#235—62no—
370#235—121no—
371C2×D12—21no—
372C2×D12—31no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—62no—
379C2×D12—62no—
380C2×D12—64no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—61no—
384C2×D12—61no—
385C2×D12—121no—
386C2×D12—121no—
387C2×D12—121no—
388C2×D12—122no—
389C2×D12C22×D311yescharacteristic
390C2×C4×D3—21no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—61no—
395C2×C4×D3C22×D311yescharacteristic
396C2×Dic6C22×D311yescharacteristic
397C3×Q16—62no—
398C3×SD16—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×C4⋊C4—61no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C42—31no—
412C3×C42—61no—
413#217—21no—
414#217—21no—
415#217#6711yescharacteristic
416#216—22no—
417#215—34no—
418#215—34no—
419#215—64no—
420#215—62no—
421#215—64no—
422#215—62no—
423#215—62no—
424#214—41no—
425#214—62no—
426#213—62no—
427#213—62no—
428#213—62no—
429#213—62no—
430#213—62no—
431#213—64no—
432#213—64no—
433#213—121no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4#6711yescharacteristic
444C4⋊Dic3—21no—
445C4⋊Dic3C22×D311yescharacteristic
446C4⋊Dic3C22×D311yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4#6711yescharacteristic
449C4×Dic3—21no—
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
463D24—62no—
464D24—121no—
465D3×C8—62no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32C22×D411yescharacteristic
473C2×C3⋊D3—22no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3⋊D3—41no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—84no—
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×C4—22no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
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×#41D3211yescharacteristic
499C22×D4—91no—
500AGL(1,ℤ/8)—184no—
501#135—184no—
502C2×Q16—31no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×D8—91no—
511C2×M16—91no—
512C22×C8—91no—
513#127—31no—
514#127—61no—
515#124—91no—
516#123—181no—
517C22⋊Q8—31no—
518#121—31no—
519#121—31no—
520#121—61no—
521#121—61no—
522#121—91no—
523#121—181no—
524#120—181no—
525C4×Q8—31no—
526C4×D4—31no—
527C4×D4—61no—
528C4×D4—91no—
529C2×C22⋊C4—181no—
530#107—91no—
531C4⋊C8—91no—
532#103—31no—
533#103—91no—
534#102—31no—
535#102—91no—
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—31no—
545C23×C3—41no—
546C23×C3—61no—
547C23×C3D3×D411yescharacteristic
548C23×C3C2×#6711yescharacteristic
549C22×D3—21no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—121no—
555C22×D3—121no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—124no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—242no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—242no—
565C22×D3C2×#6711yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—22no—
569C3×Q8—41no—
570C3×Q8—61no—
571C3×Q8—61no—
572C3×Q8D3×D412yes—
573C3×Q8D3×D412yes—
574C3×D4—22no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—41no—
580C3×D4—42no—
581C3×D4—42no—
582C3×D4—44no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—122no—
586C3×D4—121no—
587C3×D4—122no—
588C3×D4—241no—
589C3×D4—241no—
590C3×D4—241no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—31no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—41no—
605C2×C3×C4—42no—
606C2×C3×C4—42no—
607C2×C3×C4—44no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—122no—
614C2×C3×C4D3×D411yescharacteristic
615C2×C3×C4C2×#6711yescharacteristic
616C2×C3×C4C23×D311yescharacteristic
617C2×C3×C4C23×D311yescharacteristic
618#67—41no—
619#67—42no—
620#67—81no—
621#67—81no—
622#67—81no—
623#67—122no—
624#67—241no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3C2×#6711yescharacteristic
629C2×Dic3C2×#6711yescharacteristic
630C2×Dic3C2×#6711yescharacteristic
631D12—21no—
632D12—21no—
633D12—32no—
634D12—32no—
635D12—42no—
636D12—62no—
637D12—62no—
638D12—61no—
639D12—61no—
640D12—61no—
641D12—61no—
642D12—61no—
643D12—61no—
644D12—121no—
645D12—121no—
646D12—122no—
647D12—122no—
648D12—124no—
649D12—122no—
650D12—241no—
651C4×D3—21no—
652C4×D3—21no—
653C4×D3—42no—
654C4×D3—122no—
655C4×D3—122no—
656C4×D3—241no—
657C4×D3—241no—
658Dic6—21no—
659Dic6—21no—
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—81no—
672C2×C32D4211yescharacteristic
673C2×C32#57511yescharacteristic
674C2×C32#57611yescharacteristic
675C3⋊D3—42no—
676C3⋊D3—81no—
677C3×D3—41no—
678C3×D3—81no—
679C24—181no—
680#41—22no—
681#41—41no—
682#41—62no—
683#41—121no—
684#41—182no—
685#41—361no—
686C2×Q8—31no—
687C2×Q8C2×D3211yescharacteristic
688C2×D4—21no—
689C2×D4—31no—
690C2×D4—31no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—61no—
695C2×D4—61no—
696C2×D4—91no—
697C2×D4—91no—
698C2×D4—182no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4—181no—
702C2×D4—361no—
703C2×D4C2×D3211yescharacteristic
704C22×C4—21no—
705C22×C4—31no—
706C22×C4—61no—
707C22×C4—181no—
708C22×C4—181no—
709C22×C4C2×D3211yescharacteristic
710Q16—62no—
711SD16—94no—
712SD16—121no—
713SD16—182no—
714SD16—182no—
715D8—182no—
716D8—182no—
717D8—182no—
718D8—361no—
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—61no—
730C22⋊C4—31no—
731C22⋊C4—31no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C42—61no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—42no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—61no—
759C22×C3—61no—
760C22×C3—61no—
761C22×C3—81no—
762C22×C3—81no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3C2×D3×D411yescharacteristic
767C22×C3C22×#6711yescharacteristic
768C2×D3—21no—
769C2×D3—21no—
770C2×D3—21no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—122no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—122no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—241no—
789C2×D3—241no—
790C2×D3—241no—
791C2×D3—241no—
792C2×D3—244no—
793C2×D3—244no—
794C2×D3—248no—
795C3×C4—22no—
796C3×C4—22no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—22no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—42no—
803C3×C4—61no—
804C3×C4—61no—
805C3×C4—61no—
806C3×C4—121no—
807C3×C4—121no—
808C3×C4—121no—
809C3×C4C2×D3×D411yescharacteristic
810C3×C4C2×D3×D411yescharacteristic
811C3×C4#100411yescharacteristic
812C3×C4#100411yescharacteristic
813Dic3—21no—
814Dic3—21no—
815Dic3—21no—
816Dic3—41no—
817Dic3—41no—
818Dic3—41no—
819C32#326811yescharacteristic, complemented, Sylow
820C23—21no—
821C23—31no—
822C23—61no—
823C23—181no—
824C23—181no—
825C23—362no—
826C23—362no—
827C23—721no—
828C23D3×#6711yescharacteristic
829Q8—21no—
830Q8—61no—
831Q8—61no—
832Q8#381112yes—
833D4—21no—
834D4—21no—
835D4—42no—
836D4—61no—
837D4—61no—
838D4—92no—
839D4—122no—
840D4—121no—
841D4—122no—
842D4—181no—
843D4—181no—
844D4—181no—
845D4—241no—
846D4—241no—
847D4—241no—
848D4—362no—
849D4—362no—
850D4—721no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—42no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—122no—
864C2×C4—362no—
865C2×C4—721no—
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—41no—
878C2×C3—82no—
879C2×C3—81no—
880C2×C3—81no—
881C2×C3—121no—
882C2×C3—241no—
883C2×C3#559011yescharacteristic
884C2×C3#576911yescharacteristic
885C2×C3#577711yescharacteristic
886C2×C3D4×#6711yescharacteristic
887C2×C3#582211yescharacteristic
888C2×C3#583511yescharacteristic
889D3—41no—
890D3—81no—
891D3—122no—
892D3—122no—
893D3—242no—
894D3—242no—
895D3—241no—
896D3—241no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—61no—
904C22—61no—
905C22—61no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—182no—
910C22—361no—
911C22—361no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22—724no—
916C22C2×D3×#6711yescharacteristic
917C4—21no—
918C4—22no—
919C4—61no—
920C4—61no—
921C4—61no—
922C4—121no—
923C4—121no—
924C4—121no—
925C4C2×#381111yescharacteristic
926C4#6433011yescharacteristic
927C3—21no—
928C3#8026611yescharacteristic, complemented
929C3#8357711yescharacteristic, complemented
930C2—41no—
931C2—81no—
932C2—121no—
933C2—241no—
934C2—362no—
935C2—721no—
936C2#1059545611yescharacteristic
937C2#1059547011yescharacteristic
938C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64158C2semidirect
2. C3×#5834C2semidirect
3. C2×#63949C2semidirect
4. #10595018C2semidirect
5. C3×#5239C2semidirect
6. #10591607C2semidirect
7. #10591588C2semidirect
8. #10591540C2semidirect
9. #10591521C2semidirect
10. #10591472C2semidirect
11. #10591449C2semidirect
12. #10591429C2semidirect
13. #10591180C2semidirect
14. #10591168C2semidirect
15. #10591151C2semidirect
20. C2×C3×#239C22semidirect
28. C3×Q8×Dic3C22semidirect
29. C2×C3×#216C22semidirect
31. C3×#940C22semidirect
33. C3×#938C22semidirect
34. C2×C3×#214C22semidirect
48. C2×#3715C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
64. #5834D3semidirect
73. #5239D3semidirect
126. #3755D4semidirect
162. C2×#239C2×D3semidirect
184. Q8×Dic3C2×D3semidirect
185. C2×#216C2×D3semidirect
194. #940C2×D3semidirect
196. #938C2×D3semidirect
199. C2×#214C2×D3semidirect
237. #835C2×D3semidirect
239. #832C2×D3semidirect
819. C32#3268semidirect
928. C3#80266semidirect
929. C3#83577semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C3×#58342
C2×#639492
#105950182
C3×#52392
#105916072
#105915882
#105915402
#105915212
#105914722
#105914492
#105914292
#105911802
#105911682
#105911512
#835773
#802663