Finite Group Databasebeta

← #11884400

Subgroups — #11884400

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2#10595410C211yesmaximal, characteristic, complemented
3C2×#63950C211yesmaximal, characteristic, complemented
4#10595229C211yesmaximal, characteristic, complemented
5#10592871C211yesmaximal, characteristic, complemented
6C3×#5166C211yesmaximal, characteristic, complemented
7#10591597C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591483C211yesmaximal, characteristic, complemented
10#10591455C211yesmaximal, characteristic, complemented
11#10591448C211yesmaximal, characteristic, complemented
12#10590963C211yesmaximal, characteristic, complemented
13#10590850C211yesmaximal, characteristic, complemented
14#10590753C211yesmaximal, characteristic, complemented
15#10590738C211yesmaximal, characteristic, complemented
16#83955—31nomaximal
17#80628—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23#64147C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#936C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#914—24no—
31C2×C3×D24C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63977—21no—
34#63971—21no—
35#63969—21no—
36D3×#217—21no—
37#63950—24no—
38#63916—21no—
39#63916C2211yescharacteristic, complemented
40#63911—21no—
41#63911C2211yescharacteristic, complemented
42#63909—21no—
43#63909C2211yescharacteristic
44C4×#626—21no—
45C4×#626C2211yescharacteristic
46Dic3×D12C2211yescharacteristic
47#63856C2211yescharacteristic
48C2×#3717C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic
51C2×#3710C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#816C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5834—31no—
65#5806—31no—
66C2×#919—31no—
67C2×#916—31no—
68C2×#914D311yescharacteristic, complemented
69#5676—31no—
70#5577—31no—
71C3×#464—31no—
72#5239—31no—
73#5217—31no—
74#5187—31no—
75#5172—31no—
76#5172—31no—
77#5172—61no—
78#5166D311yescharacteristic, complemented
79#5164—31no—
80#5158—31no—
81#5157—31no—
82#5154—31no—
83#5150—31no—
84#5134—31no—
85#5127—31no—
86#5058—31no—
87#5026—31no—
88#4843—31no—
89#4836—31no—
90#4812—31no—
91#4810—31no—
92#4775—31no—
93#4773—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98#3832—22no—
99#3832—41no—
100C2×C4⋊(C3⋊D3)—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×#67—21no—
105C3×#239—22no—
106C3×#239—41no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#626D411yescharacteristic
121C2×D3×Dic3—21no—
122C2×D3×Dic3—21no—
123#3796—22no—
124#3796—41no—
125C32×SD16—22no—
126C2×C32×C8C2311yescharacteristic
127#3757—21no—
128#3753—41no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217—21no—
132C3×#217—21no—
133C3×#216—22no—
134C3×#215D414yescomplemented
135C3×#213—22no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—22no—
143C3×ΓL(1,𝔽25)—22no—
144#3724—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3D411yescharacteristic
152#3717—22no—
153#3715—41no—
154#3714—22no—
155#3710—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C22×C3×D4—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—31no—
162C2×#239—61no—
163C2×#239C2×D311yescharacteristic
164C2×#237—31no—
165C2×D3×D4C2×D311yescharacteristic
166C3×AGL(1,ℤ/8)—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16C2×D311yescharacteristic
171C2×C3×SD16C2×D311yescharacteristic
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×M16—31no—
175C3×#124—31no—
176C3×C4×Q8—31no—
177#953—61no—
178C2×#217—61no—
179#946—31no—
180Q8×Dic3C2×D311yescharacteristic, complemented
181C2×#216C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215—31no—
184C2×#215C2×D311yescharacteristic
185#940—31no—
186#940—61no—
187#939—61no—
188#938—31no—
189#938—31no—
190#938—31no—
191#938—61no—
192#938—61no—
193#936C2×D311yescharacteristic
194#935—61no—
195D4×Dic3—31no—
196C2×#214—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—61no—
201C2×#213C2×D311yescharacteristic
202#930—31no—
203#930—61no—
204C4×#67—31no—
205C4×#67—61no—
206#924—31no—
207#919—64no—
208#916—64no—
209#914—24no—
210C2×D24—31no—
211C2×D24C2×D311yescharacteristic
212C2×#204—31no—
213C2×ΓL(1,𝔽25)C2×D311yescharacteristic
214C2×D3×C8—31no—
215C2×D3×C8—31no—
216#895—31no—
217#895—31no—
218#895—61no—
219#895—61no—
220#884—61no—
221#883—61no—
222#882—61no—
223D3×C22⋊C4—61no—
224#874—31no—
225#874—61no—
226C4×D12—31no—
227C4×D12—31no—
228C4×D12—61no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#835—31no—
234#835—61no—
235#832—31no—
236#832—31no—
237#832C2×D311yescharacteristic
238#830—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—61no—
247#818—31no—
248#816C2×D311yescharacteristic, complemented
249#815—31no—
250Dic3⋊C8C2×D311yescharacteristic, complemented
251#809—31no—
252#807—31no—
253#803—31no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8C2×D412yes—
265C32×D4—21no—
266C32×D4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269#638—81no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3C2×D411yescharacteristic
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—42no—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277C4×C3⋊D3—42no—
278C3×#67—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—42no—
288C3×D12C2×D412yes—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—41no—
295#626—42no—
296#626—42no—
297#626—81no—
298#626—81no—
299#626—81no—
300D3×Dic3—42no—
301D3×Dic3—81no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—31no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—31no—
314#459—91no—
315#452—91no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—91no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—62no—
335C2×C3×D4—121no—
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C2×#67—21no—
341C2×#67—31no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—121no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352#239—22no—
353#239—41no—
354#239—62no—
355#239—62no—
356#239—62no—
357#239—122no—
358#239—121no—
359#239—121no—
360#239—121no—
361#239—122no—
362#237—62no—
363#237—121no—
364D3×D4—22no—
365D3×D4—41no—
366C2×D12—21no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—121no—
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—31no—
383C2×C4×D3—31no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—121no—
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6C22×D311yescharacteristic
392C3×Q16—62no—
393C3×SD16—22no—
394C3×SD16—22no—
395C3×SD16—34no—
396C3×SD16—42no—
397C3×D8—62no—
398C3×D8—62no—
399C3×M16—62no—
400C2×C3×C8—21no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410C3×C42—61no—
411#217—21no—
412#217—21no—
413#217—31no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—61no—
419#217—121no—
420#216—22no—
421#215—62no—
422#215—121no—
423#215#6714yescomplemented
424#214—121no—
425#213—22no—
426#213—62no—
427#213—121no—
428#213—121no—
429#213—122no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438C4⋊Dic3—21no—
439C4⋊Dic3—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—61no—
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—31no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447C4×Dic3—21no—
448C4×Dic3C22×D311yescharacteristic
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454D24—22no—
455D24—62no—
456#204—62no—
457ΓL(1,𝔽25)—22no—
458D3×C8—62no—
459D3×C8—62no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—22no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—84no—
480C32×C4—22no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—21no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—91no—
492C2×#41—91no—
493C22×D4—31no—
494AGL(1,ℤ/8)—64no—
495#135—184no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16D3211yescharacteristic
501C2×D8—31no—
502C2×D8—31no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—91no—
507#127—91no—
508#127—181no—
509#124—31no—
510#123—181no—
511C22⋊Q8—91no—
512#121—91no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×Q8—31no—
520C4×D4—91no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—91no—
525C4⋊C8—31no—
526#103—31no—
527#103—91no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C22⋊C8—91no—
533C22⋊C8—91no—
534#97—91no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—31no—
538C23×C3—41no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—241no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—81no—
554C22×D3—121no—
555C22×D3D3×D411yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—22no—
559C3×Q8—41no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×Q8D3×D412yes—
563C3×Q8C2×#6712yes—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—32no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—122no—
575C3×D4—122no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—31no—
582C2×C3×C4—41no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—122no—
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590#67—42no—
591#67—121no—
592#67—122no—
593#67—122no—
594#67—241no—
595#67—241no—
596#67—241no—
597#67—241no—
598#67—241no—
599#67—242no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—121no—
608C2×Dic3—122no—
609C2×Dic3—241no—
610C2×Dic3D3×D411yescharacteristic
611C2×Dic3D3×D411yescharacteristic
612C2×Dic3D3×D411yescharacteristic
613D12—21no—
614D12—21no—
615D12—21no—
616D12—42no—
617D12—62no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—121no—
623D12—122no—
624D12—122no—
625D12—124no—
626D12—121no—
627D12—122no—
628D12—122no—
629D12—241no—
630D12—241no—
631D12—241no—
632D12C2×#6712yes—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—42no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—121no—
641C4×D3—121no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—124no—
646C4×D3—241no—
647Dic6—21no—
648Dic6—21no—
649C3×C8—21no—
650C3×C8—21no—
651C3×C8—32no—
652C3×C8—41no—
653C3×C8—61no—
654C3⋊C8—21no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C3⋊C8—121no—
658C3⋊C8C2×#6712yes—
659C2×C32—81no—
660C2×C32D4211yescharacteristic
661C2×C32#57511yescharacteristic
662C2×C32#57611yescharacteristic
663C3⋊D3—41no—
664C3⋊D3—81no—
665C3×D3—41no—
666C3×D3—42no—
667C3×D3—81no—
668C24—61no—
669#41—62no—
670#41—121no—
671#41—182no—
672#41—182no—
673#41—361no—
674#41—361no—
675C2×Q8—31no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—62no—
682C2×D4—91no—
683C2×D4—91no—
684C2×D4—121no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4C2×D3211yescharacteristic
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—91no—
696C22×C4—181no—
697C22×C4—181no—
698C22×C4—181no—
699Q16—62no—
700SD16—22no—
701SD16—34no—
702SD16—182no—
703SD16—361no—
704D8—62no—
705D8—62no—
706D8—182no—
707D8—361no—
708M16—62no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—91no—
712C2×C8—182no—
713C2×C8C2×D3211yescharacteristic
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—91no—
717C4⋊C4—91no—
718C4⋊C4—181no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—91no—
722C22⋊C4—91no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C42—61no—
730C22×C3—21no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—62no—
740C22×C3—61no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—244no—
750C22×C3C2×D3×D411yescharacteristic
751C22×C3C2×D3×D411yescharacteristic
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—22no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—84no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—122no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—241no—
779C2×D3—241no—
780C3×C4—22no—
781C3×C4—22no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—42no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—61no—
788C3×C4—121no—
789C3×C4—121no—
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100411yescharacteristic
792C3×C4#100911yescharacteristic
793C3×C4C22×#6711yescharacteristic
794Dic3—21no—
795Dic3—21no—
796Dic3—21no—
797Dic3—41no—
798Dic3—41no—
799Dic3—61no—
800Dic3—61no—
801Dic3—121no—
802Dic3—121no—
803Dic3—121no—
804Dic3—241no—
805C32#326811yescharacteristic, complemented, Sylow
806C23—21no—
807C23—31no—
808C23—61no—
809C23—61no—
810C23—91no—
811C23—122no—
812C23—122no—
813C23—181no—
814C23—241no—
815Q8—21no—
816Q8—61no—
817Q8—61no—
818Q8D3×#6712yes—
819D4—21no—
820D4—21no—
821D4—32no—
822D4—61no—
823D4—61no—
824D4—61no—
825D4—122no—
826D4—122no—
827D4—181no—
828D4—181no—
829D4—362no—
830D4—361no—
831D4—362no—
832D4—362no—
833D4—721no—
834D4—721no—
835D4—721no—
836D4—721no—
837C2×C4—21no—
838C2×C4—31no—
839C2×C4—31no—
840C2×C4—31no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—91no—
846C2×C4—122no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—362no—
851C2×C4—362no—
852C2×C4—721no—
853C2×C4C22×D3211yescharacteristic
854C8—21no—
855C8—32no—
856C8—61no—
857C8—181no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—81no—
862C2×C3—81no—
863C2×C3—121no—
864C2×C3—122no—
865C2×C3—161no—
866C2×C3—241no—
867C2×C3#560911yescharacteristic
868C2×C3#576911yescharacteristic
869C2×C3#577311yescharacteristic
870C2×C3#577411yescharacteristic
871C2×C3#577711yescharacteristic
872C2×C3D4×#6711yescharacteristic
873D3—41no—
874D3—42no—
875D3—81no—
876D3—121no—
877D3—121no—
878D3—241no—
879D3—242no—
880D3—241no—
881D3—241no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—62no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—181no—
895C22—181no—
896C22—181no—
897C22—244no—
898C22—361no—
899C22—361no—
900C22—361no—
901C22D32×D411yescharacteristic
902C4—22no—
903C4—61no—
904C4—61no—
905C4—61no—
906C4—121no—
907C4—121no—
908C4—181no—
909C4—361no—
910C4#6431411yescharacteristic
911C4C2×D3×#6711yescharacteristic
912C3—21no—
913C3#8062811yescharacteristic, complemented
914C3#8395511yescharacteristic, complemented
915C2—81no—
916C2—121no—
917C2—122no—
918C2—241no—
919C2—361no—
920C2—721no—
921C2#1059474411yescharacteristic
922C2#1059475511yescharacteristic
923C2#1059529111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. #10595410C2semidirect
3. C2×#63950C2semidirect
4. #10595229C2semidirect
5. #10592871C2semidirect
6. C3×#5166C2semidirect
7. #10591597C2semidirect
8. #10591566C2semidirect
9. #10591483C2semidirect
10. #10591455C2semidirect
11. #10591448C2semidirect
12. #10590963C2semidirect
13. #10590850C2semidirect
14. #10590753C2semidirect
15. #10590738C2semidirect
18. C2×#3832C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
39. #63916C22semidirect
41. #63911C22semidirect
48. C2×#3717C22semidirect
49. C2×#3715C22semidirect
51. C2×#3710C22semidirect
52. #63662C22semidirect
53. #63648C22semidirect
54. #63647C22semidirect
56. C3×#816C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63575C22semidirect
59. #63563C22semidirect
62. #63554C22semidirect
68. C2×#914D3semidirect
78. #5166D3semidirect
134. C3×#215D4semidirect
180. Q8×Dic3C2×D3semidirect
181. C2×#216C2×D3semidirect
248. #816C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
423. #215#67semidirect
805. C32#3268semidirect
913. C3#80628semidirect
914. C3#83955semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
#105954102
C2×#639502
#105952292
#105928712
C3×#51662
#105915972
#105915662
#105914832
#105914552
#105914482
#105909632
#105908502
#105907532
#105907382
#839553
#806283