Finite Group Databasebeta

← #11884497

Subgroups — #11884497

Order 1152.

1090 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595236C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×#63808C211yesmaximal, characteristic, complemented
4#10594633C211yesmaximal, characteristic, complemented
5#10592485C211yesmaximal, characteristic, complemented
6C3×#4783C211yesmaximal, characteristic, complemented
7C3×#4775C211yesmaximal, characteristic, complemented
8#10591521C211yesmaximal, characteristic, complemented
9#10591475C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590797C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590615C211yesmaximal, characteristic, complemented
14#10590585C211yesmaximal, characteristic, complemented
15#10590484C211yesmaximal, characteristic, complemented
16#80728—31nomaximal
17#80266—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22#64149C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24C2×#3745C2211yescharacteristic
25#64102C2211yescharacteristic
26C3×#938C2211yescharacteristic, complemented
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×Dic12C2211yescharacteristic, complemented
30C2×C3×D3×C8C2211yescharacteristic, complemented
31C3×#897C2211yescharacteristic
32C3×#895C2211yescharacteristic
33#63979—21no—
34#63978—21no—
35#63958—21no—
36#63952—21no—
37#63925—24no—
38#63922—21no—
39#63921—21no—
40#63916—21no—
41#63909C2211yescharacteristic
42C4×#625C2211yescharacteristic
43#63863C2211yescharacteristic
44#63854—21no—
45#63843C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51#63808—24no—
52C32×#102C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#810C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63#5834—31no—
64C2×#949—31no—
65C2×#919—31no—
66C2×#911—31no—
67C2×#904—31no—
68#5630—31no—
69#5612—31no—
70#5599—31no—
71C3×#466—31no—
72C3×#452—31no—
73#5185—31no—
74#5176—31no—
75#5172—31no—
76#5154—31no—
77#5111—31no—
78#5049—31no—
79#5037—31no—
80#5037—31no—
81#4889—31no—
82#4886—31no—
83#4817—31no—
84#4810—31no—
85#4786—31no—
86#4786—31no—
87#4786—61no—
88#4783D311yescharacteristic, complemented
89#4775D311yescharacteristic, complemented
90#4773—31no—
91#4767—31no—
92#4732—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C3×#237—22no—
105C3×#237—41no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625D411yescharacteristic
117C2×#624—21no—
118C2×#624—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3799—22no—
122#3799—22no—
123#3799—41no—
124#3799—41no—
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127#3753—22no—
128#3752—21no—
129C4×C3⋊Dic3C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131#3745—22no—
132C3×#217—21no—
133C3×#214—41no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—22no—
142C3×D3×C8—22no—
143#3724D411yescharacteristic
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3D411yescharacteristic
149(C2×D3)⋊Dic3D411yescharacteristic
150Dic32—21no—
151#3717—22no—
152#3717D414yescomplemented
153#3715—22no—
154#3714—41no—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#237C2×D311yescharacteristic
161C2×D3×D4—31no—
162C2×#235—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×Q16—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C22×C3×C8—31no—
169C3×C22⋊Q8—31no—
170C3×#121—31no—
171C3×#121—31no—
172#949—64no—
173#947—31no—
174Q8×Dic3—31no—
175C2×#215—31no—
176C2×#215—31no—
177C2×#215—31no—
178#940—31no—
179#940—31no—
180#940—61no—
181#940—61no—
182#940—61no—
183#939—61no—
184#938—61no—
185#938—61no—
186#938C2×D311yescharacteristic, complemented
187#937—61no—
188#936—31no—
189C2×#214—31no—
190C2×#214C2×D311yescharacteristic, complemented
191C2×#213—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—61no—
195C2×#213C2×D311yescharacteristic
196#930—31no—
197#930—61no—
198C4×#67—31no—
199C4×#67—31no—
200C4×#67—61no—
201C2×#208—31no—
202#919—64no—
203#911—64no—
204C2×Dic12C2×D311yescharacteristic, complemented
205#904—64no—
206C2×D24—31no—
207C2×D24—31no—
208C2×D24—31no—
209C2×D24—61no—
210C2×#204—31no—
211C2×#204—31no—
212C2×ΓL(1,𝔽25)—31no—
213C2×D3×C8C2×D311yescharacteristic, complemented
214#897C2×D311yescharacteristic
215#895—31no—
216#895—61no—
217#895C2×D311yescharacteristic
218#894—61no—
219#893—31no—
220#893—31no—
221#893—61no—
222#887—31no—
223#884—61no—
224#883—61no—
225#882—61no—
226#67⋊C4—61no—
227D3×C22⋊C4—61no—
228D3×C22⋊C4—61no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—21no—
232C3×#102—31no—
233C3×#102C2×D311yescharacteristic, complemented
234C3×#102C2×D311yescharacteristic, complemented
235C3×C22⋊C8—31no—
236#835—31no—
237#830—31no—
238#821—31no—
239#821C2×D311yescharacteristic
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8C2×D311yescharacteristic
242#815—31no—
243#815—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247#810—31no—
248#810C2×D311yescharacteristic, complemented
249#809—31no—
250#809—31no—
251#809—31no—
252#809—61no—
253#807C2×D311yescharacteristic, complemented
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×D4—21no—
264C32×D4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268#638—81no—
269C2×C3⋊Dic3C2×D411yescharacteristic
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—81no—
276C3×#67—42no—
277C3×#67—81no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—81no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6C2×D412yes—
295#626—42no—
296#626—42no—
297#626—42no—
298#626—81no—
299#625—41no—
300#624—42no—
301#624—42no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—31no—
313#464—91no—
314#459—91no—
315#452—31no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—31no—
340C2×#67—31no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—121no—
350C2×#67—121no—
351C22×Dic3—21no—
352#239—62no—
353#239—62no—
354#239—121no—
355#239—121no—
356#237—22no—
357#237—41no—
358D3×D4—62no—
359D3×D4—121no—
360#235—62no—
361#235—62no—
362#235—121no—
363#235—121no—
364C2×D12—21no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—62no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12C22×D311yescharacteristic
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—121no—
385C2×C4×D3C22×D311yescharacteristic
386C2×C4×D3C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C2×Dic6C22×D311yescharacteristic
389C3×Q16—62no—
390C3×SD16—121no—
391C3×D8—62no—
392C2×C3×C8—21no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8—62no—
396C2×C3×C8C22×D311yescharacteristic
397C2×C3×C8C22×D311yescharacteristic
398C3×C4⋊C4—21no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—61no—
401C3×C4⋊C4C22×D311yescharacteristic
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406#217—21no—
407#217—31no—
408#217—31no—
409#217—61no—
410#217—61no—
411#215—34no—
412#215—62no—
413#215—62no—
414#214—41no—
415#214—62no—
416#213—22no—
417#213—62no—
418#213—62no—
419#213—122no—
420#213—121no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—121no—
432C4⋊Dic3—21no—
433C4⋊Dic3—61no—
434C4⋊Dic3C22×D311yescharacteristic
435Dic3⋊C4—31no—
436Dic3⋊C4—31no—
437Dic3⋊C4—61no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—61no—
441C4×Dic3—61no—
442C4×Dic3—61no—
443#208—62no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—22no—
450D24—62no—
451D24—62no—
452D24—122no—
453D24—121no—
454#204—34no—
455#204—62no—
456ΓL(1,𝔽25)—62no—
457D3×C8—22no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32—41no—
461C22×C32C22×D411yescharacteristic
462C2×C3⋊D3—22no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477D32—84no—
478C32×C4—41no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—91no—
490C2×#41—91no—
491C22×D4—91no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—31no—
505#127—91no—
506#127—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—31no—
510#121—31no—
511#121—31no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121—181no—
516#120—181no—
517C4×Q8—91no—
518C4×D4—91no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—31no—
523C4⋊C8—91no—
524#103—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102D3211yescharacteristic, complemented
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—61no—
539C22×D3—21no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—121no—
545C22×D3—121no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—241no—
551C22×D3—241no—
552C22×D3D3×D411yescharacteristic
553C22×D3D3×D411yescharacteristic
554C3×Q8—32no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—122no—
567C3×D4—241no—
568C3×D4—241no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—122no—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—42no—
586#67—81no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—121no—
591#67—121no—
592#67—122no—
593#67—122no—
594#67—242no—
595#67—241no—
596#67—241no—
597#67—241no—
598#67—242no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—42no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611D12—21no—
612D12—21no—
613D12—32no—
614D12—32no—
615D12—62no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—81no—
623D12—121no—
624D12—121no—
625D12—121no—
626D12—122no—
627D12—122no—
628D12—122no—
629D12—241no—
630C4×D3—21no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—241no—
639C4×D3—241no—
640C4×D3—242no—
641Dic6—21no—
642Dic6—21no—
643Dic6—21no—
644Dic6D3×D412yes—
645C3×C8—21no—
646C3×C8—21no—
647C3×C8—32no—
648C3×C8—41no—
649C3×C8—61no—
650C3⋊C8—21no—
651C3⋊C8—61no—
652C3⋊C8—61no—
653C3⋊C8—121no—
654C3⋊C8D3×D412yes—
655C2×C32—81no—
656C2×C32D4211yescharacteristic
657C2×C32#57511yescharacteristic
658C2×C32#57611yescharacteristic
659C3⋊D3—42no—
660C3⋊D3—81no—
661C3×D3—41no—
662C3×D3—41no—
663C3×D3—81no—
664C24—181no—
665#41—62no—
666#41—121no—
667#41—182no—
668#41—182no—
669#41—361no—
670#41—361no—
671C2×Q8—31no—
672C2×Q8—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—91no—
678C2×D4—91no—
679C2×D4—91no—
680C2×D4—181no—
681C2×D4—182no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—361no—
688C2×D4C2×D3211yescharacteristic
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—61no—
692C22×C4—181no—
693C22×C4—181no—
694C22×C4—181no—
695Q16—62no—
696SD16—94no—
697SD16—121no—
698SD16—182no—
699SD16—182no—
700D8—62no—
701D8—182no—
702D8—182no—
703D8—361no—
704M16—182no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—62no—
708C2×C8—91no—
709C2×C8C2×D3211yescharacteristic
710C4⋊C4—31no—
711C4⋊C4—61no—
712C4⋊C4—91no—
713C4⋊C4—181no—
714C4⋊C4C2×D3211yescharacteristic
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—61no—
718C22⋊C4—91no—
719C22⋊C4—91no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C42—91no—
725C42—181no—
726C22×C3—21no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3C2×D3×D411yescharacteristic
746C22×C3C2×D3×D411yescharacteristic
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—122no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—241no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—244no—
775C2×D3—244no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—61no—
781C3×C4—62no—
782C3×C4—61no—
783C3×C4—81no—
784C3×C4—121no—
785C3×C4—121no—
786C3×C4C2×D3×D411yescharacteristic
787C3×C4C2×D3×D411yescharacteristic
788C3×C4#100411yescharacteristic
789C3×C4#100911yescharacteristic
790Dic3—22no—
791Dic3—21no—
792Dic3—21no—
793Dic3—41no—
794Dic3—41no—
795Dic3—62no—
796Dic3—61no—
797Dic3—61no—
798Dic3—61no—
799Dic3—61no—
800Dic3—121no—
801C32#326811yescharacteristic, complemented, Sylow
802C23—21no—
803C23—31no—
804C23—31no—
805C23—61no—
806C23—181no—
807C23—181no—
808C23—362no—
809C23—362no—
810C23—721no—
811Q8—32no—
812Q8—61no—
813Q8—61no—
814Q8—61no—
815D4—21no—
816D4—21no—
817D4—61no—
818D4—61no—
819D4—92no—
820D4—122no—
821D4—181no—
822D4—181no—
823D4—181no—
824D4—241no—
825D4—241no—
826D4—362no—
827D4—362no—
828D4—362no—
829D4—362no—
830D4—361no—
831D4—721no—
832D4—721no—
833C2×C4—21no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—91no—
844C2×C4—91no—
845C2×C4—122no—
846C2×C4—362no—
847C2×C4—362no—
848C2×C4—721no—
849C2×C4C22×D3211yescharacteristic
850C8—21no—
851C8—32no—
852C8—61no—
853C8—181no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—81no—
858C2×C3—81no—
859C2×C3—121no—
860C2×C3—121no—
861C2×C3—161no—
862C2×C3—241no—
863C2×C3#559011yescharacteristic
864C2×C3#560911yescharacteristic
865C2×C3#575711yescharacteristic
866C2×C3#576811yescharacteristic
867C2×C3#576911yescharacteristic
868C2×C3#577711yescharacteristic
869D3—41no—
870D3—41no—
871D3—81no—
872D3—122no—
873D3—122no—
874D3—242no—
875D3—241no—
876D3—241no—
877D3—481no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—182no—
891C22—361no—
892C22—361no—
893C22—361no—
894C22—361no—
895C22—361no—
896C22—724no—
897C22D32×D411yescharacteristic
898C4—41no—
899C4—61no—
900C4—61no—
901C4—62no—
902C4—121no—
903C4—121no—
904C4—181no—
905C4—181no—
906C4#6430711yescharacteristic
907C4D32×D411yescharacteristic
908C3—21no—
909C3#8026611yescharacteristic, complemented
910C3#8072811yescharacteristic, complemented
911C2—81no—
912C2—121no—
913C2—121no—
914C2—241no—
915C2—362no—
916C2—721no—
917C2#1059427511yescharacteristic
918C2#1059473411yescharacteristic
919C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595236C2semidirect
2. C2×#63925C2semidirect
3. C2×#63808C2semidirect
4. #10594633C2semidirect
5. #10592485C2semidirect
6. C3×#4783C2semidirect
7. C3×#4775C2semidirect
8. #10591521C2semidirect
9. #10591475C2semidirect
10. #10590947C2semidirect
11. #10590797C2semidirect
12. #10590723C2semidirect
13. #10590615C2semidirect
14. #10590585C2semidirect
15. #10590484C2semidirect
21. C2×#3799C22semidirect
22. #64149C22semidirect
26. C3×#938C22semidirect
27. C2×C3×#214C22semidirect
29. C2×C3×Dic12C22semidirect
30. C2×C3×D3×C8C22semidirect
45. #63843C22semidirect
47. C2×#3717C22semidirect
52. C32×#102C22semidirect
53. #63641C22semidirect
54. #63636C22semidirect
57. C3×#810C22semidirect
58. C3×#807C22semidirect
59. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63555C22semidirect
88. #4783D3semidirect
89. #4775D3semidirect
152. #3717D4semidirect
186. #938C2×D3semidirect
190. C2×#214C2×D3semidirect
204. C2×Dic12C2×D3semidirect
213. C2×D3×C8C2×D3semidirect
233. C3×#102C2×D3semidirect
234. C3×#102C2×D3semidirect
248. #810C2×D3semidirect
253. #807C2×D3semidirect
529. #102D32semidirect
801. C32#3268semidirect
909. C3#80266semidirect
910. C3#80728semidirect

Maximal subgroups

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

subgroupindex
#105952362
C2×#639252
C2×#638082
#105946332
#105924852
C3×#47832
C3×#47752
#105915212
#105914752
#105909472
#105907972
#105907232
#105906152
#105905852
#105904842
#807283
#802663