Finite Group Databasebeta

← #11885823

Subgroups — #11885823

Order 1152.

1185 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64159C211yesmaximal, characteristic, complemented
2C3×#5829C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10595078C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591606C211yesmaximal, characteristic, complemented
8#10591596C211yesmaximal, characteristic, complemented
9#10591568C211yesmaximal, characteristic, complemented
10#10591468C211yesmaximal, characteristic, complemented
11#10591459C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10591182C211yesmaximal, characteristic, complemented
14#10591166C211yesmaximal, characteristic, complemented
15#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
16#83505—31nomaximal
17#80101—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×#3828C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22#64159—24no—
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic, complemented
29C3×#946C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic, complemented
31C3×#939—21no—
32C3×#937—21no—
33C3×D4×Dic3C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic
35C3×#930C2211yescharacteristic, complemented
36C3×#930C2211yescharacteristic, complemented
37C3×#929—21no—
38C3×C4×#67C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4—21no—
40#63983—21no—
41#63958—21no—
42D3×#213—24no—
43#63921—21no—
44#63894C2211yescharacteristic, complemented
45#63860C2211yescharacteristic, complemented
46#63857C2211yescharacteristic
47#63853—21no—
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C3×#546—31no—
64#5829D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—61no—
68C22×#213—31no—
69C2×D3×D8—31no—
70#5612—31no—
71#5550—31no—
72C3×#449—31no—
73#5238D311yescharacteristic, complemented
74#5218—31no—
75#5169—31no—
76#5168—31no—
77#5153—31no—
78#5059—31no—
79#5057—31no—
80#5051—31no—
81#5046—31no—
82#5038—31no—
83#5038—31no—
84#5037—31no—
85#5016—31no—
86C4×#213—31no—
87D4×C3⋊C8—31no—
88#4819—31no—
89#4813—31no—
90#4776—31no—
91#4756—31no—
92#4734—31no—
93#67⋊C8—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C32×#41—22no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×#638—21no—
104#3828—22no—
105#3828—41no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3—21no—
108C2×#634C2311yescharacteristic
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67D411yescharacteristic
113C22×C3×Dic3—21no—
114C3×D3×D4—22no—
115C3×D3×D4—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×#626—21no—
120C2×#624—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3756—22no—
124#3755—22no—
125#3754—22no—
126#3753D414yescomplemented
127C2×C3⋊(C3⋊C8)—22no—
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#217—21no—
131C3×#217D411yescharacteristic
132C3×#215—41no—
133C3×#213—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3716—41no—
153#3714—22no—
154#3713—22no—
155D3×C3⋊C8—22no—
156#3280—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic, complemented
159C2×C3×#41C2×D311yescharacteristic, complemented
160C22×C3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×#235—61no—
166C22×D12—31no—
167C2×C3×SD16—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#950—64no—
180#950—64no—
181#950—68no—
182#947C2×D311yescharacteristic, complemented
183#946C2×D311yescharacteristic
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—61no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—61no—
190C2×#215C2×D311yescharacteristic, complemented
191#939—21no—
192#938—61no—
193#937—21no—
194#937—61no—
195#937—61no—
196#936—31no—
197D4×Dic3C2×D311yescharacteristic, complemented
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—61no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—61no—
208C2×#213—64no—
209C2×#213C2×D311yescharacteristic
210#930C2×D311yescharacteristic, complemented
211#930C2×D311yescharacteristic, complemented
212#929—21no—
213C4×#67C2×D311yescharacteristic
214C2×(C2×D3)⋊C4—21no—
215#924—31no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—31no—
218C22×C3⋊C8—31no—
219C22×C3⋊C8—61no—
220D3×D8—64no—
221C2×D24—31no—
222C2×#204—31no—
223C2×D3×C8—31no—
224#897—31no—
225#894—61no—
226#893—31no—
227#884—61no—
228#883—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#835C2×D311yescharacteristic, complemented
237#832—31no—
238#832—31no—
239#832C2×D311yescharacteristic, complemented
240#830—31no—
241#830C2×D311yescharacteristic, complemented
242#821—31no—
243(C2×D3)⋊C8—31no—
244#816—31no—
245Dic3⋊C8—31no—
246C8×Dic3—31no—
247#810—31no—
248#809—31no—
249#809—31no—
250#809—31no—
251#807—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254C4×C3⋊C8—31no—
255C23×C32—21no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C32×D4—21no—
270C32×D4—42no—
271C32×D4C2×D412yes—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—42no—
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278#638—42no—
279C2×C3⋊Dic3—21no—
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)C2×D412yes—
282C4×C3⋊D3—42no—
283#634—21no—
284#634—21no—
285C3×#67—22no—
286C3×#67—42no—
287C3×#67—81no—
288C3×#67—81no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—81no—
292C2×C3×Dic3C2×D411yescharacteristic
293C2×C3×Dic3C2×D411yescharacteristic
294C2×C3×Dic3C2×D411yescharacteristic
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12—21no—
299C3×C4×D3—21no—
300C3×C4×D3—21no—
301#626—42no—
302#624—81no—
303C3⋊(C3⋊C8)—21no—
304C3⋊(C3⋊C8)C2×D412yes—
305C3×C3⋊C8—21no—
306C3×C3⋊C8—21no—
307C2×#135—91no—
308C22×D8—91no—
309#546—31no—
310#546—91no—
311#495—91no—
312#467—91no—
313#466—91no—
314#463—91no—
315#463—91no—
316#450—91no—
317#450—91no—
318#449—31no—
319#449—91no—
320C4×D8—91no—
321C8×D4—91no—
322C24×C3—61no—
323C23×D3—21no—
324C23×D3—61no—
325C23×D3—61no—
326C3×#41—24no—
327C3×#41—22no—
328C3×#41—22no—
329C3×#41—41no—
330C3×#41—41no—
331C3×#41—42no—
332C2×C3×Q8—21no—
333C2×C3×Q8C22×D311yescharacteristic
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—41no—
342C2×C3×D4—61no—
343C2×C3×D4—62no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—121no—
347C2×C3×D4C22×D311yescharacteristic
348C2×C3×D4C22×D311yescharacteristic
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—31no—
353C22×C3×C4—41no—
354C22×C3×C4—61no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C2×#67—21no—
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—121no—
364C2×#67#6711yescharacteristic
365C22×Dic3—21no—
366D3×D4—22no—
367D3×D4—41no—
368D3×D4—62no—
369D3×D4—121no—
370#235—62no—
371#235—62no—
372#235—64no—
373#235—121no—
374#235—121no—
375#235—122no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—61no—
381C2×D12—121no—
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—121no—
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6—31no—
391C2×Dic6—31no—
392C2×Dic6—61no—
393C3×SD16—121no—
394C3×D8—62no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C3×C4⋊C4—31no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—61no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410#217—21no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217#6711yescharacteristic
415#216—62no—
416#216—62no—
417#216—64no—
418#215—41no—
419#215—62no—
420#215—62no—
421#215—64no—
422#214—64no—
423#214—62no—
424#214—62no—
425#214—121no—
426#213—22no—
427#213—34no—
428#213—34no—
429#213—64no—
430#213—62no—
431#213—62no—
432#213—62no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
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—61no—
445C4⋊Dic3C22×D311yescharacteristic
446C4⋊Dic3C22×D311yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4—61no—
449Dic3⋊C4#6711yescharacteristic
450C4×Dic3C22×D311yescharacteristic
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—62no—
458C2×C3⋊C8—62no—
459C2×C3⋊C8—62no—
460C2×C3⋊C8—64no—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463D24—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×C32C22×D411yescharacteristic
473C2×C3⋊D3—22no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—84no—
485C2×C3×D3#13512yescomplemented
486D32—84no—
487C32×C4—21no—
488C32×C4—41no—
489C32×C4C22×D411yescharacteristic
490C32×C4H(5,𝔽2)11yescharacteristic
491C3⋊Dic3—41no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—21no—
495C3×Dic3—41no—
496C3×Dic3—41no—
497C2×#41—91no—
498C2×#41D3211yescharacteristic, complemented
499C22×D4—31no—
500C22×D4—91no—
501#135—184no—
502C2×Q16—91no—
503C2×SD16—31no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×D8—91no—
511C2×D8—184no—
512C22×C8—91no—
513C22×C8—91no—
514#124—31no—
515#124—91no—
516#123—61no—
517#123—181no—
518C22⋊Q8—31no—
519C22⋊Q8—91no—
520#121—31no—
521#121—31no—
522#121—61no—
523#121—181no—
524#120—61no—
525#120—181no—
526C4×D4—31no—
527C4×D4—31no—
528C4×D4—91no—
529C2×C22⋊C4—61no—
530C2×C22⋊C4—181no—
531#107—91no—
532C4⋊C8—91no—
533#103—31no—
534#103—91no—
535#102—31no—
536#102—91no—
537#102—91no—
538#102—91no—
539C22⋊C8—31no—
540C22⋊C8—91no—
541C4×C8—91no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—31no—
546C23×C3—41no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—122no—
550C23×C3—122no—
551C23×C3—241no—
552C23×C3D3×D411yescharacteristic
553C23×C3C2×#6711yescharacteristic
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—81no—
561C22×D3—121no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3—241no—
567C22×D3—241no—
568C22×D3C2×#6711yescharacteristic
569C3×Q8—22no—
570C3×Q8—21no—
571C3×Q8—21no—
572C3×Q8—21no—
573C3×Q8—21no—
574C3×Q8—41no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—22no—
578C3×D4—41no—
579C3×D4—42no—
580C3×D4—42no—
581C3×D4—44no—
582C3×D4—62no—
583C3×D4—61no—
584C3×D4—61no—
585C3×D4—61no—
586C3×D4—61no—
587C3×D4—122no—
588C3×D4—241no—
589C3×D4—241no—
590C3×D4D3×D412yes—
591C3×D4D3×D412yes—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
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—21no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—31no—
605C2×C3×C4—41no—
606C2×C3×C4—42no—
607C2×C3×C4—42no—
608C2×C3×C4—44no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—241no—
614C2×C3×C4D3×D411yescharacteristic
615C2×C3×C4C2×#6711yescharacteristic
616C2×C3×C4C23×D311yescharacteristic
617C2×C3×C4C23×D311yescharacteristic
618#67—22no—
619#67—42no—
620#67—81no—
621#67—81no—
622#67—122no—
623#67—122no—
624#67—122no—
625#67—124no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—81no—
631C2×Dic3—121no—
632C2×Dic3C2×#6711yescharacteristic
633C2×Dic3C2×#6711yescharacteristic
634C2×Dic3C2×#6711yescharacteristic
635D12—21no—
636D12—21no—
637D12—21no—
638D12—21no—
639D12—32no—
640D12—32no—
641D12—62no—
642D12—61no—
643D12—61no—
644D12—121no—
645D12—122no—
646C4×D3—21no—
647C4×D3—21no—
648C4×D3—122no—
649C4×D3—122no—
650C4×D3—124no—
651C4×D3—241no—
652C4×D3—241no—
653Dic6—62no—
654Dic6—61no—
655Dic6—61no—
656Dic6—61no—
657Dic6—61no—
658Dic6—121no—
659C3×C8—61no—
660C3×C8—61no—
661C3⋊C8—21no—
662C3⋊C8—21no—
663C3⋊C8—32no—
664C3⋊C8—32no—
665C3⋊C8—62no—
666C3⋊C8—62no—
667C3⋊C8—61no—
668C3⋊C8—61no—
669C2×C32—41no—
670C2×C32—42no—
671C2×C32D4211yescharacteristic
672C2×C32C2×#13511yescharacteristic
673C2×C32#57611yescharacteristic
674C3⋊D3—42no—
675C3×D3—22no—
676C3×D3—81no—
677C3×D3—81no—
678C24—61no—
679C24—181no—
680#41—22no—
681#41—41no—
682#41—182no—
683#41—361no—
684C2×Q8—91no—
685C2×Q8C2×D3211yescharacteristic
686C2×D4—21no—
687C2×D4—31no—
688C2×D4—31no—
689C2×D4—31no—
690C2×D4—61no—
691C2×D4—62no—
692C2×D4—61no—
693C2×D4—61no—
694C2×D4—91no—
695C2×D4—121no—
696C2×D4—181no—
697C2×D4—182no—
698C2×D4—181no—
699C2×D4—361no—
700C2×D4C2×D3211yescharacteristic
701C22×C4—21no—
702C22×C4—31no—
703C22×C4—61no—
704C22×C4—181no—
705C22×C4—181no—
706C22×C4C2×D3211yescharacteristic
707Q16—182no—
708SD16—121no—
709SD16—182no—
710SD16—182no—
711SD16—361no—
712D8—62no—
713D8—94no—
714D8—182no—
715D8—182no—
716C2×C8—31no—
717C2×C8—31no—
718C2×C8—91no—
719C2×C8—91no—
720C2×C8—182no—
721C2×C8—182no—
722C4⋊C4—31no—
723C4⋊C4—31no—
724C4⋊C4—31no—
725C4⋊C4—61no—
726C4⋊C4—181no—
727C22⋊C4—31no—
728C22⋊C4—31no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—181no—
736C22⋊C4—181no—
737C22⋊C4—181no—
738C22⋊C4—181no—
739C42—31no—
740C22×C3—22no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—22no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—32no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—42no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—61no—
759C22×C3—61no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—244no—
769C22×C3C2×D3×D411yescharacteristic
770C22×C3C22×#6711yescharacteristic
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—84no—
782C2×D3—122no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C2×D3—244no—
790C2×D3—244no—
791C2×D3#95012yescomplemented
792C3×C4—22no—
793C3×C4—21no—
794C3×C4—21no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—42no—
798C3×C4—41no—
799C3×C4—41no—
800C3×C4—61no—
801C3×C4—61no—
802C3×C4—61no—
803C3×C4—121no—
804C3×C4—121no—
805C3×C4C2×D3×D411yescharacteristic
806C3×C4C2×D3×D411yescharacteristic
807C3×C4#100411yescharacteristic
808C3×C4#100411yescharacteristic
809Dic3—21no—
810Dic3—21no—
811Dic3—21no—
812Dic3—41no—
813Dic3—41no—
814Dic3—122no—
815Dic3—121no—
816Dic3—121no—
817C32#328011yescharacteristic, complemented, Sylow
818C23—21no—
819C23—31no—
820C23—61no—
821C23—61no—
822C23—122no—
823C23—122no—
824C23—181no—
825C23—241no—
826C23—362no—
827C23—362no—
828C23—721no—
829C23D3×#6711yescharacteristic
830Q8—21no—
831Q8—21no—
832Q8—181no—
833Q8—181no—
834D4—21no—
835D4—42no—
836D4—62no—
837D4—61no—
838D4—61no—
839D4—61no—
840D4—61no—
841D4—92no—
842D4—122no—
843D4—181no—
844D4—241no—
845D4—241no—
846D4—362no—
847D4—362no—
848D4#381112yes—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—31no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—42no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—181no—
861C2×C4—241no—
862C2×C4—362no—
863C2×C4—721no—
864C2×C4D3×#6711yescharacteristic
865C2×C4C22×D3211yescharacteristic
866C8—61no—
867C8—61no—
868C8—92no—
869C8—181no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—42no—
874C2×C3—42no—
875C2×C3—41no—
876C2×C3—41no—
877C2×C3—42no—
878C2×C3—62no—
879C2×C3—82no—
880C2×C3—241no—
881C2×C3—241no—
882C2×C3#559011yescharacteristic
883C2×C3D3×#13511yescharacteristic
884C2×C3#577411yescharacteristic
885C2×C3D4×#6711yescharacteristic
886C2×C3C2×#95011yescharacteristic
887C2×C3#583511yescharacteristic
888D3—22no—
889D3—81no—
890D3—81no—
891D3—122no—
892D3—122no—
893D3—242no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—22no—
898C22—32no—
899C22—41no—
900C22—41no—
901C22—61no—
902C22—61no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—121no—
909C22—182no—
910C22—244no—
911C22—361no—
912C22—361no—
913C22—724no—
914C22C2×D3×#6711yescharacteristic
915C4—21no—
916C4—41no—
917C4—61no—
918C4—61no—
919C4—61no—
920C4—121no—
921C4—121no—
922C4—361no—
923C4C2×#381111yescharacteristic
924C4#6433011yescharacteristic
925C3—21no—
926C3#8010111yescharacteristic, complemented
927C3#8350511yescharacteristic, complemented
928C2—41no—
929C2—42no—
930C2—62no—
931C2—241no—
932C2—241no—
933C2—362no—
934C2D3×#95011yescharacteristic
935C2#1059545411yescharacteristic
936C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3280
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×#64159C2semidirect
2. C3×#5829C2semidirect
3. C2×D3×#213C2semidirect
4. #10595078C2semidirect
5. C3×#5238C2semidirect
6. #10591651C2semidirect
7. #10591606C2semidirect
8. #10591596C2semidirect
9. #10591568C2semidirect
10. #10591468C2semidirect
11. #10591459C2semidirect
12. #10591400C2semidirect
13. #10591182C2semidirect
14. #10591166C2semidirect
15. #67⋊(C3⋊C8)C2semidirect
18. C2×C32×#41C22semidirect
19. C2×#3828C22semidirect
23. C2×#3756C22semidirect
24. C2×#3755C22semidirect
25. C2×#3754C22semidirect
27. C22×C3⋊(C3⋊C8)C22semidirect
28. C3×#947C22semidirect
30. C2×C3×#215C22semidirect
33. C3×D4×Dic3C22semidirect
35. C3×#930C22semidirect
36. C3×#930C22semidirect
44. #63894C22semidirect
45. #63860C22semidirect
48. C2×#3716C22semidirect
52. C3×#835C22semidirect
53. C3×#832C22semidirect
54. C3×#830C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63564C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
62. Dic3×C3⋊C8C22semidirect
64. #5829D3semidirect
73. #5238D3semidirect
126. #3753D4semidirect
158. C2×C3×#41C2×D3semidirect
159. C2×C3×#41C2×D3semidirect
182. #947C2×D3semidirect
190. C2×#215C2×D3semidirect
197. D4×Dic3C2×D3semidirect
210. #930C2×D3semidirect
211. #930C2×D3semidirect
236. #835C2×D3semidirect
239. #832C2×D3semidirect
241. #830C2×D3semidirect
485. C2×C3×D3#135semidirect
498. C2×#41D32semidirect
791. C2×D3#950semidirect
817. C32#3280semidirect
926. C3#80101semidirect
927. C3#83505semidirect

Maximal subgroups

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

subgroupindex
C2×#641592
C3×#58292
C2×D3×#2132
#105950782
C3×#52382
#105916512
#105916062
#105915962
#105915682
#105914682
#105914592
#105914002
#105911822
#105911662
#67⋊(C3⋊C8)2
#835053
#801013