Finite Group Databasebeta

← #11884437

Subgroups — #11884437

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 934 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×#63932C211yesmaximal, characteristic, complemented
4#10594919C211yesmaximal, characteristic, complemented
5C3×#5238C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591589C211yesmaximal, characteristic, complemented
9#10591577C211yesmaximal, characteristic, complemented
10#10591481C211yesmaximal, characteristic, complemented
11#10591448C211yesmaximal, characteristic, complemented
12#10591405C211yesmaximal, characteristic, complemented
13#10591182C211yesmaximal, characteristic, complemented
14#10591166C211yesmaximal, characteristic, complemented
15#10591158C211yesmaximal, characteristic, complemented
16#83507—31nomaximal
17#80128—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22#64159—24no—
23C2×#3756C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic
29C3×#946C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic, complemented
31C3×#939—21no—
32C3×#937—21no—
33C3×D4×Dic3C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic
35C3×#930C2211yescharacteristic
36C3×#930C2211yescharacteristic, complemented
37C3×#929—21no—
38C3×C4×#67C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4—21no—
40#63979—21no—
41#63971—21no—
42#63932—24no—
43#63912—21no—
44#63911C2211yescharacteristic, complemented
45#63909C2211yescharacteristic
46#63881—21no—
47#63844C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#830C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64#5829D311yescharacteristic, complemented
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—61no—
68C2×#932—31no—
69C2×#911—31no—
70#5599—31no—
71#5553—31no—
72C3×#449—31no—
73#5238D311yescharacteristic, complemented
74#5217—31no—
75#5176—31no—
76#5173—31no—
77#5150—31no—
78#5058—31no—
79#5054—31no—
80#5049—31no—
81#5047—31no—
82#5038—31no—
83#5038—31no—
84#5037—31no—
85#5018—31no—
86#5015—31no—
87#5011—31no—
88#4812—31no—
89#4798—31no—
90#4773—31no—
91#4757—31no—
92#4734—31no—
93#4730—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×#638—21no—
103#3828—22no—
104#3828—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67D411yescharacteristic
112C22×C3×Dic3—21no—
113C3×D3×D4—22no—
114C3×D3×D4—41no—
115C2×C3×D12C2311yescharacteristic
116C2×C3×D12C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#625—21no—
122C2×D3×Dic3—21no—
123#3795—22no—
124#3795—41no—
125#3756—22no—
126#3755—22no—
127#3754D414yescomplemented
128#3753—22no—
129C2×C3⋊(C3⋊C8)—22no—
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C3×#217—21no—
133C3×#217D411yescharacteristic
134C3×#215—41no—
135C3×#213—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
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#3716—22no—
153#3714—41no—
154#3713—22no—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C2×D311yescharacteristic
160C22×C3×D4—31no—
161C2×#237—31no—
162C2×D3×D4C2×D311yescharacteristic
163C2×#235—31no—
164C2×#235—31no—
165C2×#235—31no—
166C2×#235—61no—
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
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#940—31no—
192#940—61no—
193#940—61no—
194#939—21no—
195#939—61no—
196#937—21no—
197D4×Dic3C2×D311yescharacteristic
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—61no—
202#932—64no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—61no—
209C2×#213C2×D311yescharacteristic
210#930—31no—
211#930C2×D311yescharacteristic
212#930C2×D311yescharacteristic, complemented
213#929—21no—
214C4×#67C2×D311yescharacteristic
215C2×(C2×D3)⋊C4—21no—
216C2×#208—31no—
217C22×C3⋊C8—31no—
218C22×C3⋊C8—31no—
219C22×C3⋊C8—61no—
220#911—64no—
221C2×D24—31no—
222C2×#204—31no—
223C2×ΓL(1,𝔽25)—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×#103—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835C2×D311yescharacteristic, complemented
237#832—31no—
238#832—31no—
239#832C2×D311yescharacteristic
240#830—31no—
241#830C2×D311yescharacteristic, complemented
242#821—31no—
243(C2×D3)⋊C8—31no—
244#816—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—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C32×Q8—21no—
265C32×Q8—21no—
266C32×D4—21no—
267C32×D4—42no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—42no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275#638—42no—
276C2×C3⋊Dic3—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C4×C3⋊D3—42no—
280#634—21no—
281#634C2×D412yes—
282C3×#67—41no—
283C3×#67—42no—
284C3×#67—81no—
285C3×#67—81no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—81no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×D12—21no—
293C3×D12—21no—
294C3×D12—21no—
295C3×D12—21no—
296C3×C4×D3—21no—
297C3×C4×D3—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—31no—
318#449—91no—
319#447—91no—
320#440—91no—
321#435—91no—
322C24×C3—61no—
323C23×D3—21no—
324C3×#41—24no—
325C3×#41—22no—
326C3×#41—22no—
327C3×#41—41no—
328C3×#41—41no—
329C3×#41—42no—
330C2×C3×Q8—21no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—41no—
340C2×C3×D4—61no—
341C2×C3×D4—62no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—121no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—41no—
352C22×C3×C4—61no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—121no—
366C2×#67#6711yescharacteristic
367C22×Dic3—21no—
368C22×Dic3—61no—
369#237—62no—
370#237—121no—
371D3×D4—22no—
372D3×D4—41no—
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×D12C22×D311yescharacteristic
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3—121no—
393C2×C4×D3C22×D311yescharacteristic
394C2×Dic6—31no—
395C2×Dic6—31no—
396C2×Dic6—61no—
397C3×SD16—121no—
398C3×D8—62no—
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#6711yescharacteristic
416#216—62no—
417#216—62no—
418#216—64no—
419#215—41no—
420#215—62no—
421#215—62no—
422#215—64no—
423#214—34no—
424#214—34no—
425#214—64no—
426#214—62no—
427#213—22no—
428#213—62no—
429#213—62no—
430#213—64no—
431#213—62no—
432#213—62no—
433#213—121no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
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—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—61no—
458C2×C3⋊C8—62no—
459C2×C3⋊C8—62no—
460C2×C3⋊C8—64no—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463D24—121no—
464#204—62no—
465ΓL(1,𝔽25)—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—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—84no—
486C32×C4—21no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3⋊Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C3×Dic3—41no—
495C3×Dic3—41no—
496C2×#41—91no—
497C2×#41—91no—
498C2×#41D3211yescharacteristic
499C22×D4—31no—
500AGL(1,ℤ/8)—184no—
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×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—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×C3—61no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—241no—
551C23×C3D3×D411yescharacteristic
552C23×C3C2×#6711yescharacteristic
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—81no—
560C22×D3—121no—
561C22×D3C2×#6711yescharacteristic
562C3×Q8—22no—
563C3×Q8—21no—
564C3×Q8—21no—
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—41no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—22no—
571C3×D4—41no—
572C3×D4—42no—
573C3×D4—42no—
574C3×D4—44no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—121no—
580C3×D4—122no—
581C3×D4—241no—
582C3×D4—241no—
583C3×D4D3×D412yes—
584C3×D4D3×D412yes—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—41no—
599C2×C3×C4—42no—
600C2×C3×C4—42no—
601C2×C3×C4—44no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
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—61no—
626C2×Dic3—61no—
627C2×Dic3—81no—
628C2×Dic3—121no—
629C2×Dic3—122no—
630C2×Dic3C2×#6711yescharacteristic
631C2×Dic3C2×#6711yescharacteristic
632C2×Dic3C2×#6711yescharacteristic
633D12—21no—
634D12—21no—
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—32no—
653Dic6—32no—
654Dic6—62no—
655Dic6—61no—
656Dic6—61no—
657Dic6—121no—
658C3×C8—61no—
659C3×C8—61no—
660C3⋊C8—21no—
661C3⋊C8—21no—
662C3⋊C8—32no—
663C3⋊C8—32no—
664C3⋊C8—62no—
665C3⋊C8—62no—
666C3⋊C8—61no—
667C3⋊C8—61no—
668C2×C32—41no—
669C2×C32—42no—
670C2×C32D4211yescharacteristic
671C2×C32#57511yescharacteristic
672C2×C32#57611yescharacteristic
673C3⋊D3—81no—
674C3×D3—41no—
675C3×D3—81no—
676C3×D3—81no—
677C24—61no—
678#41—22no—
679#41—41no—
680#41—182no—
681#41—182no—
682#41—361no—
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—181no—
698C2×D4—181no—
699C2×D4—181no—
700C2×D4—181no—
701C2×D4C2×D3211yescharacteristic
702C22×C4—21no—
703C22×C4—31no—
704C22×C4—61no—
705C22×C4—181no—
706C22×C4—181no—
707C22×C4C2×D3211yescharacteristic
708Q16—182no—
709SD16—94no—
710SD16—121no—
711SD16—182no—
712SD16—182no—
713D8—62no—
714D8—182no—
715D8—182no—
716D8—361no—
717M16—182no—
718C2×C8—31no—
719C2×C8—31no—
720C2×C8—91no—
721C2×C8—91no—
722C2×C8—182no—
723C4⋊C4—31no—
724C4⋊C4—31no—
725C4⋊C4—31no—
726C4⋊C4—61no—
727C4⋊C4—181no—
728C22⋊C4—31no—
729C22⋊C4—31no—
730C22⋊C4—61no—
731C22⋊C4—61no—
732C22⋊C4—61no—
733C22⋊C4—61no—
734C22⋊C4—61no—
735C22⋊C4—61no—
736C22⋊C4—181no—
737C42—31no—
738C42—181no—
739C22×C3—22no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—22no—
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—61no—
757C22×C3—61no—
758C22×C3—61no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—121no—
762C22×C3—121no—
763C22×C3—121no—
764C22×C3—121no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—244no—
768C22×C3C2×D3×D411yescharacteristic
769C22×C3C22×#6711yescharacteristic
770C2×D3—21no—
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—84no—
780C2×D3—122no—
781C2×D3—121no—
782C2×D3—121no—
783C2×D3—121no—
784C2×D3—121no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—241no—
788C2×D3—241no—
789C3×C4—22no—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—21no—
794C3×C4—42no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—61no—
798C3×C4—61no—
799C3×C4—61no—
800C3×C4—121no—
801C3×C4—121no—
802C3×C4C2×D3×D411yescharacteristic
803C3×C4C2×D3×D411yescharacteristic
804C3×C4#100411yescharacteristic
805C3×C4#100411yescharacteristic
806Dic3—21no—
807Dic3—21no—
808Dic3—21no—
809Dic3—41no—
810Dic3—41no—
811Dic3—62no—
812Dic3—62no—
813Dic3—122no—
814C32#326811yescharacteristic, complemented, Sylow
815C23—21no—
816C23—31no—
817C23—61no—
818C23—61no—
819C23—122no—
820C23—122no—
821C23—181no—
822C23—241no—
823C23D3×#6711yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—92no—
827Q8—181no—
828D4—21no—
829D4—42no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—121no—
835D4—122no—
836D4—181no—
837D4—181no—
838D4—241no—
839D4—241no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—721no—
844D4—721no—
845D4#381112yes—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—42no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—181no—
858C2×C4—241no—
859C2×C4—362no—
860C2×C4—362no—
861C2×C4D3×#6711yescharacteristic
862C2×C4C22×D3211yescharacteristic
863C8—61no—
864C8—61no—
865C8—92no—
866C8—181no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—42no—
871C2×C3—41no—
872C2×C3—42no—
873C2×C3—42no—
874C2×C3—41no—
875C2×C3—82no—
876C2×C3—121no—
877C2×C3—241no—
878C2×C3—241no—
879C2×C3#559011yescharacteristic
880C2×C3#576811yescharacteristic
881C2×C3#577411yescharacteristic
882C2×C3D4×#6711yescharacteristic
883C2×C3#582211yescharacteristic
884C2×C3#583511yescharacteristic
885D3—41no—
886D3—81no—
887D3—81no—
888D3—242no—
889D3—241no—
890D3—241no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—22no—
895C22—41no—
896C22—41no—
897C22—61no—
898C22—61no—
899C22—61no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—244no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22C2×D3×#6711yescharacteristic
911C4—21no—
912C4—41no—
913C4—61no—
914C4—61no—
915C4—61no—
916C4—121no—
917C4—121no—
918C4—182no—
919C4C2×#381111yescharacteristic
920C4#6433011yescharacteristic
921C3—21no—
922C3#8012811yescharacteristic, complemented
923C3#8350711yescharacteristic, complemented
924C2—41no—
925C2—42no—
926C2—121no—
927C2—241no—
928C2—241no—
929C2—721no—
930C2#1059545311yescharacteristic
931C2#1059545411yescharacteristic
932C2#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×#64159C2semidirect
2. C3×#5829C2semidirect
3. C2×#63932C2semidirect
4. #10594919C2semidirect
5. C3×#5238C2semidirect
6. #10591655C2semidirect
7. #10591619C2semidirect
8. #10591589C2semidirect
9. #10591577C2semidirect
10. #10591481C2semidirect
11. #10591448C2semidirect
12. #10591405C2semidirect
13. #10591182C2semidirect
14. #10591166C2semidirect
15. #10591158C2semidirect
19. C2×#3828C22semidirect
23. C2×#3756C22semidirect
24. C2×#3755C22semidirect
27. C22×C3⋊(C3⋊C8)C22semidirect
30. C2×C3×#215C22semidirect
36. C3×#930C22semidirect
44. #63911C22semidirect
47. #63844C22semidirect
52. C3×#835C22semidirect
54. C3×#830C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63564C22semidirect
60. #63562C22semidirect
62. #63554C22semidirect
64. #5829D3semidirect
73. #5238D3semidirect
127. #3754D4semidirect
190. C2×#215C2×D3semidirect
212. #930C2×D3semidirect
236. #835C2×D3semidirect
241. #830C2×D3semidirect
814. C32#3268semidirect
922. C3#80128semidirect
923. C3#83507semidirect

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×#639322
#105949192
C3×#52382
#105916552
#105916192
#105915892
#105915772
#105914812
#105914482
#105914052
#105911822
#105911662
#105911582
#835073
#801283