Finite Group Databasebeta

← #11884194

Subgroups — #11884194

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63800C211yesmaximal, characteristic, complemented
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10594003C211yesmaximal, characteristic
4#10593904C211yesmaximal, characteristic, complemented
5#10592544C211yesmaximal, characteristic, complemented
6C3×#4841C211yesmaximal, characteristic, complemented
7C3×#4836C211yesmaximal, characteristic, complemented
8#10590960C211yesmaximal, characteristic, complemented
9#10590952C211yesmaximal, characteristic, complemented
10#10590951C211yesmaximal, characteristic, complemented
11#10590942C211yesmaximal, characteristic, complemented
12#10590850C211yesmaximal, characteristic, complemented
13#10590848C211yesmaximal, characteristic, complemented
14#10590374C211yesmaximal, characteristic, complemented
15#10590360C211yesmaximal, characteristic, complemented
16#80444—31nomaximal
17#79495—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22C2×#3746C2211yescharacteristic, complemented
23C2×#3744C2211yescharacteristic
24#64084C2211yescharacteristic
25C4×#634C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
29C2×C3×D3×C8C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×#869C2211yescharacteristic, complemented
33#63922—21no—
34D3×(C2×D3)⋊C4—21no—
35#63919—21no—
36#63909C2211yescharacteristic
37#63906—21no—
38#63899—21no—
39#63899—21no—
40#63898—21no—
41#63890—21no—
42#63857C2211yescharacteristic
43#63856C2211yescharacteristic
44#63856C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50#63800—24no—
51D3×#204—24no—
52C32×C4⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63643C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#803C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63C2×#915—31no—
64C2×D3×SD16—31no—
65C2×#909—31no—
66C22×#204—31no—
67#5727—31no—
68#5554—31no—
69#5550—31no—
70D4×Dic6—31no—
71C3×#461—31no—
72C3×#435—31no—
73#5173—31no—
74#5169—31no—
75#5134—31no—
76#5116—31no—
77#5086—31no—
78#5018—31no—
79#4845—31no—
80#4845—31no—
81#4845—61no—
82#4841D311yescharacteristic, complemented
83#4836D311yescharacteristic, complemented
84#4813—31no—
85#4812—31no—
86#4809—31no—
87#4806—31no—
88#4739—31no—
89#4738—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4710—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×D12D411yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113D3×D12—22no—
114D3×D12—41no—
115#3795—22no—
116#3795—41no—
117D3×Dic6—22no—
118D3×Dic6—22no—
119D3×Dic6—41no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C42C2311yescharacteristic
124#3752—21no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128C4×C3⋊Dic3—21no—
129#3746—22no—
130#3744—22no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3D411yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141C3×#204—22no—
142C3×ΓL(1,𝔽25)—22no—
143C3×D3×C8—22no—
144#3724—21no—
145#3724—21no—
146Dic3⋊Dic3—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3719—22no—
152#3719—41no—
153#3717—22no—
154#3717—41no—
155#3716D414yescomplemented
156#3266—91noSylow
157C2×D3×Q8—31no—
158C2×D3×Q8—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C22×D12—31no—
163C22×Dic6—31no—
164C22×Dic6—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×C4⋊Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172#946—31no—
173#946—31no—
174C2×#216—31no—
175C2×#216—31no—
176C2×#215—31no—
177C2×#215—31no—
178#937—61no—
179D4×Dic3—61no—
180C2×#214—31no—
181#930—31no—
182#930—61no—
183C2×(C2×D3)⋊C4—61no—
184#924—31no—
185#924—31no—
186#924—31no—
187#915—64no—
188D3×SD16—64no—
189#909—64no—
190C2×Dic12—31no—
191C2×Dic12—31no—
192C2×Dic12—31no—
193C2×Dic12—31no—
194C2×Dic12—61no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—61no—
201C2×#204—64no—
202C2×#204C2×D311yescharacteristic
203C2×#204C2×D311yescharacteristic
204C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
205C2×D3×C8C2×D311yescharacteristic
206#897—31no—
207#896—61no—
208#896—61no—
209#895—31no—
210#894—61no—
211#893—61no—
212#888—61no—
213#888—61no—
214#886—61no—
215#884—61no—
216#882—61no—
217D3×C22⋊C4—61no—
218#878—61no—
219#878—61no—
220#875—31no—
221#875—31no—
222#875—61no—
223C4×D12C2×D311yescharacteristic
224C4×D12C2×D311yescharacteristic
225#869C2×D311yescharacteristic, complemented
226C4×Dic6—31no—
227C4×Dic6—31no—
228C4×Dic6—61no—
229C3×C4⋊C8—21no—
230C3×C4⋊C8C2×D311yescharacteristic, complemented
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×#103—31no—
233C3×#103—31no—
234C3×C22⋊C8—31no—
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242(C2×D3)⋊C8C2×D311yescharacteristic
243(C2×D3)⋊C8C2×D311yescharacteristic, complemented
244#818—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—61no—
249#816C2×D311yescharacteristic, complemented
250#816C2×D311yescharacteristic, complemented
251#810—31no—
252#807—31no—
253#803C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269#634—21no—
270#634—21no—
271#634—21no—
272#634C2×D412yes—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—22no—
279C3×D12—21no—
280C3×D12C2×D412yes—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—81no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290#627—42no—
291#627—42no—
292#626—42no—
293#626—81no—
294#625—42no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—31no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—31no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—31no—
320C2×C3×Q8—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333D3×Q8—62no—
334D3×Q8—62no—
335D3×Q8—121no—
336D3×Q8—121no—
337#237—62no—
338#237—121no—
339D3×D4—62no—
340D3×D4—121no—
341#235—62no—
342#235—121no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—61no—
346C2×D12—62no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—121no—
350C2×D12D1211yescharacteristic
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3—61no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6—31no—
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—61no—
363C2×Dic6—61no—
364C2×Dic6—62no—
365C2×Dic6—62no—
366C2×Dic6—61no—
367C2×Dic6—61no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—121no—
371C2×Dic6—121no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×SD16—62no—
375C3×SD16—62no—
376C3×M16—62no—
377C2×C3×C8—21no—
378C2×C3×C8—21no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C2×C3×C8—62no—
382C2×C3×C8C22×D311yescharacteristic
383C2×C3×C8C22×D311yescharacteristic
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C22⋊C4—31no—
391C3×C22⋊C4—31no—
392C3×C22⋊C4—61no—
393C3×C42—21no—
394C3×C42C22×D311yescharacteristic
395C3×C42C22×D311yescharacteristic
396#217—61no—
397#217—61no—
398#217—61no—
399#216—62no—
400#216—121no—
401#215—62no—
402#215—121no—
403#214—34no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4—121no—
416(C2×D3)⋊C4D1211yescharacteristic
417(C2×D3)⋊C4D1211yescharacteristic
418C4⋊Dic3—21no—
419C4⋊Dic3—21no—
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3D1211yescharacteristic
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—121no—
434C4×Dic3—61no—
435C4×Dic3—61no—
436C4×Dic3—121no—
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439Dic12—62no—
440Dic12—62no—
441Dic12—62no—
442Dic12—122no—
443Dic12—121no—
444#204—22no—
445#204—22no—
446#204—34no—
447#204—62no—
448#204—62no—
449#204—62no—
450#204—122no—
451#204—121no—
452ΓL(1,𝔽25)—22no—
453D3×C8—22no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#13712yescomplemented
467D32—84no—
468C32×C4—21no—
469C32×C4—21no—
470C32×C4C22×D411yescharacteristic
471C32×C4H(5,𝔽2)11yescharacteristic
472C3⋊Dic3—22no—
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—91no—
481C22×Q8—91no—
482C22×Q8—91no—
483C22×D4—91no—
484#137—184no—
485C2×Q16—91no—
486C2×Q16—91no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—31no—
496C22×C8—31no—
497C4⋊Q8—31no—
498C4⋊Q8—181no—
499#124—91no—
500#123—181no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503C22⋊Q8—91no—
504C22⋊Q8—181no—
505C22⋊Q8—181no—
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8—91no—
510C4×D4—31no—
511C4×D4—31no—
512C4×D4—181no—
513C2×C22⋊C4—181no—
514#107—91no—
515C4⋊C8D3211yescharacteristic, complemented
516#103—31no—
517#103—31no—
518#103—91no—
519#103—91no—
520#102—91no—
521#102—91no—
522C22⋊C8—31no—
523C22⋊C8—31no—
524#97—31no—
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—61no—
528C22×D3—21no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—121no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—241no—
537C22×D3—241no—
538C22×D3C2×D1211yescharacteristic
539C22×D3C2×D1211yescharacteristic
540C3×Q8—61no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×Q8—61no—
544C3×D4—32no—
545C3×D4—62no—
546C3×D4—61no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—241no—
560C2×C3×C4C2×D1211yescharacteristic
561C2×C3×C4C2×D1211yescharacteristic
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—122no—
567#67—122no—
568#67—122no—
569#67—241no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—121no—
580C2×Dic3—121no—
581C2×Dic3—121no—
582C2×Dic3—122no—
583C2×Dic3—122no—
584C2×Dic3—122no—
585C2×Dic3C2×D1211yescharacteristic
586C2×Dic3C2×D1211yescharacteristic
587D12—22no—
588D12—21no—
589D12—61no—
590D12—61no—
591D12—61no—
592D12—61no—
593D12—121no—
594D12—121no—
595D12—122no—
596D12—241no—
597D12D3×D412yes—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—21no—
601C4×D3—21no—
602C4×D3—81no—
603C4×D3—122no—
604C4×D3—122no—
605C4×D3—122no—
606Dic6—21no—
607Dic6—21no—
608Dic6—21no—
609Dic6—21no—
610Dic6—32no—
611Dic6—32no—
612Dic6—62no—
613Dic6—61no—
614Dic6—61no—
615Dic6—61no—
616Dic6—61no—
617Dic6—61no—
618Dic6—61no—
619Dic6—121no—
620Dic6—121no—
621Dic6—121no—
622Dic6—122no—
623Dic6—122no—
624Dic6—122no—
625Dic6—122no—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—21no—
630C3×C8—32no—
631C3×C8—41no—
632C3×C8—41no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8D3×D412yes—
636C2×C32D4211yescharacteristic
637C2×C32C2×#13711yescharacteristic
638C2×C32#57711yescharacteristic
639C3⋊D3—81no—
640C3×D3—22no—
641C3×D3—42no—
642C3×D3—41no—
643C24—181no—
644#41—182no—
645#41—361no—
646C2×Q8—31no—
647C2×Q8—31no—
648C2×Q8—91no—
649C2×Q8—91no—
650C2×Q8—181no—
651C2×Q8—181no—
652C2×Q8—182no—
653C2×Q8—182no—
654C2×Q8—361no—
655C2×Q8—361no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—91no—
659C2×D4—181no—
660C2×D4—182no—
661C2×D4—181no—
662C2×D4—181no—
663C2×D4—361no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—181no—
668C22×C4—181no—
669C22×C4—181no—
670Q16—182no—
671Q16—182no—
672Q16—361no—
673SD16—62no—
674SD16—62no—
675SD16—94no—
676SD16—182no—
677SD16—182no—
678SD16—361no—
679M16—62no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—62no—
683C2×C8C2×D3211yescharacteristic
684C2×C8C2×D3211yescharacteristic
685C4⋊C4—31no—
686C4⋊C4—31no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—91no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4—181no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—61no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—181no—
704C42C2×D3211yescharacteristic
705C22×C3—21no—
706C22×C3—32no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—62no—
712C22×C3—61no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3C22×D1211yescharacteristic
716C22×C3C2×D3×D411yescharacteristic
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—22no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—241no—
732C2×D3—241no—
733C2×D3—241no—
734C2×D3—244no—
735C2×D3—244no—
736C2×D3#90912yescomplemented
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—121no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4C2×D3×D411yescharacteristic
751C3×C4C2×D3×D411yescharacteristic
752C3×C4#100911yescharacteristic
753C3×C4#100911yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—41no—
757Dic3—41no—
758Dic3—41no—
759Dic3—62no—
760Dic3—62no—
761Dic3—122no—
762Dic3—121no—
763Dic3—121no—
764Dic3—121no—
765Dic3—121no—
766Dic3—241no—
767Dic3—241no—
768C32#326611yescharacteristic, complemented, Sylow
769C23—31no—
770C23—31no—
771C23—61no—
772C23—181no—
773C23—362no—
774C23—362no—
775C23—721no—
776Q8—61no—
777Q8—61no—
778Q8—61no—
779Q8—61no—
780Q8—92no—
781Q8—181no—
782Q8—181no—
783Q8—181no—
784Q8—362no—
785Q8—362no—
786D4—32no—
787D4—62no—
788D4—61no—
789D4—181no—
790D4—181no—
791D4—362no—
792D4—362no—
793D4—721no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—241no—
807C2×C4—362no—
808C2×C4—362no—
809C2×C4—362no—
810C2×C4D3×D1211yescharacteristic
811C2×C4D3×D1211yescharacteristic
812C2×C4C22×D3211yescharacteristic
813C8—21no—
814C8—21no—
815C8—32no—
816C8—61no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—62no—
821C2×C3—121no—
822C2×C3—122no—
823C2×C3D4×D1211yescharacteristic
824C2×C3#560911yescharacteristic
825C2×C3C2×#90911yescharacteristic
826C2×C3#575111yescharacteristic
827C2×C3#576211yescharacteristic
828C2×C3D3×#13711yescharacteristic
829D3—22no—
830D3—42no—
831D3—41no—
832D3—241no—
833D3—241no—
834D3—481no—
835C22—32no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—62no—
840C22—61no—
841C22—61no—
842C22—121no—
843C22—121no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—724no—
848C22C2×D3×D1211yescharacteristic
849C4—21no—
850C4—21no—
851C4—61no—
852C4—61no—
853C4—121no—
854C4—121no—
855C4—121no—
856C4—182no—
857C4—361no—
858C4—361no—
859C4D32×D411yescharacteristic
860C4#6432011yescharacteristic
861C3—21no—
862C3#7949511yescharacteristic, complemented
863C3#8044411yescharacteristic, complemented
864C2—62no—
865C2—121no—
866C2—122no—
867C2—721no—
868C2#1059462111yescharacteristic
869C2#1059467711yescharacteristic
870C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594003C2
hypercenterC4⋊C8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63800C2semidirect
2. C2×D3×#204C2semidirect
4. #10593904C2semidirect
5. #10592544C2semidirect
6. C3×#4841C2semidirect
7. C3×#4836C2semidirect
8. #10590960C2semidirect
9. #10590952C2semidirect
10. #10590951C2semidirect
11. #10590942C2semidirect
12. #10590850C2semidirect
13. #10590848C2semidirect
14. #10590374C2semidirect
15. #10590360C2semidirect
21. C2×D3×Dic6C22semidirect
22. C2×#3746C22semidirect
25. C4×#634C22semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
32. C3×#869C22semidirect
44. #63856C22semidirect
45. C2×#3719C22semidirect
46. C2×#3719C22semidirect
52. C32×C4⋊C8C22semidirect
54. #63643C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#816C22semidirect
58. C3×#816C22semidirect
59. C3×#803C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
82. #4841D3semidirect
83. #4836D3semidirect
155. #3716D4semidirect
204. C2×ΓL(1,𝔽25)C2×D3semidirect
225. #869C2×D3semidirect
230. C3×C4⋊C8C2×D3semidirect
231. C3×C4⋊C8C2×D3semidirect
243. (C2×D3)⋊C8C2×D3semidirect
249. #816C2×D3semidirect
250. #816C2×D3semidirect
253. #803C2×D3semidirect
466. C2×C3×D3#137semidirect
515. C4⋊C8D32semidirect
736. C2×D3#909semidirect
768. C32#3266semidirect
862. C3#79495semidirect
863. C3#80444semidirect

Maximal subgroups

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

subgroupindex
C2×#638002
C2×D3×#2042
#105940032
#105939042
#105925442
C3×#48412
C3×#48362
#105909602
#105909522
#105909512
#105909422
#105908502
#105908482
#105903742
#105903602
#804443
#794953