Finite Group Databasebeta

← #11860595

Subgroups — #11860595

Order 1152.

1000 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic
2#10595347C211yesmaximal, characteristic, complemented
3#10595222C211yesmaximal, characteristic
4#10592863C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591581C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591445C211yesmaximal, characteristic, complemented
10#10591440C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic
12#10590908C211yesmaximal, characteristic, complemented
13#10590819C211yesmaximal, characteristic, complemented
14Dic3×Dic12C211yesmaximal, characteristic, complemented
15#10590681C211yesmaximal, characteristic, complemented
16#83965—31nomaximal
17#79648—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×#915C418yescomplemented
28C2×C3×Dic12C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30#67⋊Dic3—21no—
31Dic3×#67—21no—
32C2×Dic3⋊Dic3—21no—
33#63955—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63855—21no—
36#63855C2211yescharacteristic
37#63843—21no—
38#63843C2211yescharacteristic
39#63843C2211yescharacteristic
40Dic3×Dic6—21no—
41Dic3×Dic6C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43#63841—21no—
44#63841C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63659C2211yescharacteristic
48#63645C2211yescharacteristic
49#63642C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63554C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×C3×#137—31no—
63#5827—31no—
64#5812—31no—
65C2×#915D311yescharacteristic
66#5572—31no—
67#5546—31no—
68C3×C4×SD16—31no—
69#5233—31no—
70C2×#835—31no—
71#5184—31no—
72#5184—31no—
73Dic3×Q16—31no—
74Dic3×Q16—31no—
75#5164—31no—
76#5164—31no—
77#5164—31no—
78#5164—61no—
79Dic3×SD16—31no—
80Dic3×SD16D311yescharacteristic, complemented
81#5122—31no—
82#5121—31no—
83#5030—31no—
84#5018—31no—
85#4861—31no—
86#4853—31no—
87D3×#103—31no—
88#4790—31no—
89#4772—31no—
90#4758—31no—
91C4×Dic12—31no—
92#4689—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8C2×C414yescomplemented
101C3×#237—22no—
102C3×#237C2×C414yes—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×D3×Dic3—21no—
109C32×SD16C2×C414yescomplemented
110C2×C32×C8C2311yescharacteristic
111#3757—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#216C2×C414yescomplemented
120C3×#214C2×C414yescomplemented
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×Dic12C2×C414yescomplemented
129C3×ΓL(1,𝔽25)C2×C414yescomplemented
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136Dic3⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144Dic32—21no—
145D3×C3⋊C8—22no—
146#2947—91noSylow
147C2×C3×#41—31no—
148C22×C3×Q8—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×#237C2×D311yescharacteristic
151C3×#137—38no—
152C2×C3×Q16—31no—
153C2×C3×Q16—31no—
154C2×C3×SD16—21no—
155C2×C3×SD16—31no—
156C2×C3×SD16C2×D311yescharacteristic
157C2×C3×SD16C2×D311yescharacteristic
158C2×C3×M16—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—31no—
166Q8×Dic3—31no—
167Q8×Dic3—61no—
168Q8×Dic3—61no—
169Q8×Dic3—61no—
170Q8×Dic3C2×D311yescharacteristic
171C2×#216C2×D311yescharacteristic
172D4×Dic3—31no—
173D4×Dic3—31no—
174D4×Dic3—61no—
175D4×Dic3—61no—
176D4×Dic3—61no—
177D4×Dic3C2×D311yescharacteristic
178C2×#214C2×D311yescharacteristic
179C4×#67—61no—
180#926—31no—
181#926—31no—
182#926—61no—
183#926—61no—
184#926—61no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3—61no—
187C2×Dic3⋊C4—61no—
188C22×C3⋊C8—31no—
189#915Dic318yescomplemented
190C2×Dic12C2×D311yescharacteristic
191C2×ΓL(1,𝔽25)C2×D311yescharacteristic
192C2×D3×C8—31no—
193#892—31no—
194#892—61no—
195D3×C4⋊C4—31no—
196#887—31no—
197#887—31no—
198#887—61no—
199#67⋊C4—61no—
200#877—61no—
201#872—31no—
202#872—61no—
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—31no—
216#835—61no—
217#835C2×D311yescharacteristic
218#832—31no—
219#832—31no—
220#832—61no—
221#832C2×D311yescharacteristic
222#818—31no—
223#818—31no—
224#818—31no—
225#818—61no—
226#817—31no—
227#817C2×D311yescharacteristic
228#816—31no—
229#816—31no—
230#815—31no—
231#815—31no—
232#815—31no—
233#815—61no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3C2×D311yescharacteristic
237#810—31no—
238#810—31no—
239#808—31no—
240#807—31no—
241#803—31no—
242C23×C32—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8C22×C412yes—
246C32×D4—21no—
247C32×D4C22×C412yes—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—81no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C3×#67—24no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—24no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—24no—
266C3×C4×D3C22×C412yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—24no—
271C3×Dic6C22×C412yes—
272C3×Dic6C22×C412yes—
273D3×Dic3—81no—
274C32×C8C22×C412yes—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8C22×C412yes—
278C2×#137—31no—
279#520—91no—
280#519—91no—
281#441—91no—
282#441—91no—
283#440—91no—
284#440—91no—
285C4×Q16—91no—
286C4×Q16—91no—
287C4×SD16—31no—
288C4×SD16—91no—
289#428—91no—
290#416—91no—
291C2×#103—91no—
292#405—91no—
293C3×#41—34no—
294C3×#41—62no—
295C2×C3×Q8—21no—
296C2×C3×Q8—34no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—21no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—121no—
318D3×Q8—22no—
319D3×Q8C2×Dic314yescomplemented
320#237—22no—
321#237C2×Dic314yes—
322C2×C4×D3—21no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—21no—
326C2×Dic6C22×D311yescharacteristic
327C2×Dic6C22×D311yescharacteristic
328C3×Q16—34no—
329C3×Q16—34no—
330C3×SD16—24no—
331C3×SD16—34no—
332C3×SD16C4×D314yescomplemented
333C3×SD16C2×Dic314yescomplemented
334C3×M16—34no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—31no—
345C3×C42—61no—
346#217—21no—
347#217—31no—
348#217—31no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—121no—
353#216C2×Dic314yescomplemented
354#214C2×Dic314yescomplemented
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—61no—
358C4⋊Dic3—21no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—121no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384C4×Dic3—21no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—62no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12C2×Dic314yescomplemented
409ΓL(1,𝔽25)C2×Dic314yescomplemented
410D3×C8—62no—
411C22×C32—22no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C4×D412yes—
418C32×C4—22no—
419C32×C4C23×C411yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3—21no—
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C4×D412yes—
432C2×#41—31no—
433C22×Q8—31no—
434#137—38no—
435C2×Q16—31no—
436C2×Q16—31no—
437C2×SD16—31no—
438C2×SD16D3211yescharacteristic
439C2×M16—31no—
440C22×C8—91no—
441C4×Q8—31no—
442C4×Q8—91no—
443C4×Q8—91no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—181no—
448C4×Q8—181no—
449C4×D4—31no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—91no—
454#117—91no—
455#117—181no—
456#117—181no—
457#117—181no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—91no—
461#107—91no—
462#106—31no—
463#106—91no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—91no—
472#97—91no—
473#97—91no—
474C4×C8—31no—
475C4×C8—91no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—41no—
480C22×D3D3×D411yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—22no—
484C3×Q8—32no—
485C3×Q8—32no—
486C3×Q8—41no—
487C3×Q8—64no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×Q8C2×C4×D312yes—
491C3×Q8C22×Dic312yes—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—22no—
495C3×D4—41no—
496C3×D4—64no—
497C3×D4C2×C4×D312yes—
498C3×D4C22×Dic312yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—64no—
509C2×C3×C4—64no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—24no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—24no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—81no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3—242no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543C4×D3—24no—
544C4×D3—241no—
545C4×D3#23712yes—
546C4×D3C22×Dic312yes—
547Dic6—21no—
548Dic6—21no—
549Dic6—24no—
550Dic6C22×Dic312yes—
551Dic6C22×Dic312yes—
552C3×C8—22no—
553C3×C8—32no—
554C3×C8—61no—
555C3×C8C2×C4×D312yes—
556C3×C8C22×Dic312yes—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C3⋊C8C22×Dic312yes—
562C2×C32—42no—
563C2×C32C2×C4×D411yescharacteristic
564C2×C32#57711yescharacteristic
565C2×C32#57811yescharacteristic
566C3×D3—22no—
567#41—34no—
568#41—62no—
569C2×Q8—34no—
570C2×Q8—31no—
571C2×Q8—31no—
572C2×Q8—61no—
573C2×Q8—62no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—61no—
576C2×D4C2×D3211yescharacteristic
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—181no—
582C22×C4—181no—
583Q16—34no—
584Q16—34no—
585SD16—34no—
586SD16D3×Dic314yescomplemented
587M16—34no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8—182no—
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—61no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C42—31no—
612C42—61no—
613C42—91no—
614C42—181no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42—181no—
619C42—181no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—32no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C2×D3×D411yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3D4×Dic312yes—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—42no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—62no—
647C3×C4—62no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C22×C4×D311yescharacteristic
651C3×C4C2×#23711yescharacteristic
652C3×C4D3×#4111yescharacteristic
653C3×C4C23×Dic311yescharacteristic
654Dic3—21no—
655Dic3—21no—
656Dic3—22no—
657Dic3—22no—
658Dic3—41no—
659Dic3—41no—
660Dic3—61no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—241no—
671Dic3—241no—
672Dic3D4×Dic312yes—
673C32#294711yescharacteristic, complemented, Sylow
674C23—21no—
675C23—31no—
676Q8—21no—
677Q8—32no—
678Q8—32no—
679Q8—64no—
680Q8—61no—
681Q8—61no—
682Q8C2×D3×Dic312yes—
683D4—21no—
684D4—64no—
685D4C2×D3×Dic312yes—
686C2×C4—21no—
687C2×C4—31no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—64no—
693C2×C4—64no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—241no—
703C2×C4—721no—
704C2×C4—721no—
705C2×C4C22×D3211yescharacteristic
706C8—32no—
707C8—61no—
708C8—181no—
709C8C2×D3×Dic312yes—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—42no—
714C2×C3—42no—
715C2×C3—62no—
716C2×C3—82no—
717C2×C3C4×D3×D411yescharacteristic
718C2×C3#576211yescharacteristic
719C2×C3#577111yescharacteristic
720C2×C3#577811yescharacteristic
721C2×C3#577911yescharacteristic
722C2×C3C2×D4×Dic311yescharacteristic
723D3—22no—
724C22—22no—
725C22—32no—
726C22—41no—
727C22—41no—
728C22—61no—
729C22—61no—
730C22D32×D411yescharacteristic
731C4—22no—
732C4—32no—
733C4—62no—
734C4—62no—
735C4—61no—
736C4—61no—
737C4—121no—
738C4—121no—
739C4—181no—
740C4—181no—
741C4—361no—
742C4—361no—
743C4D3×#23711yescharacteristic
744C4C22×D3×Dic311yescharacteristic
745C3—21no—
746C3#7964811yescharacteristic, complemented
747C3#8396511yescharacteristic, complemented
748C2—42no—
749C2—62no—
750C2#1059475111yescharacteristic
751C2#1059475611yescharacteristic
752C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×#237C22
cosocleC2×C32×C4C24
hypercenterC2×SD16D32
hypocenterC32#2947
LCSG ▷ 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
2. #10595347C2semidirect
4. #10592863C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591581C2semidirect
7. #10591576C2semidirect
8. D3×#835C2semidirect
9. #10591445C2semidirect
10. #10591440C2semidirect
12. #10590908C2semidirect
13. #10590819C2semidirect
14. Dic3×Dic12C2semidirect
15. #10590681C2semidirect
27. C3×#915C4semidirect
80. Dic3×SD16D3semidirect
100. C3×D3×Q8C2×C4semidirect
109. C32×SD16C2×C4semidirect
119. C3×#216C2×C4semidirect
120. C3×#214C2×C4semidirect
128. C3×Dic12C2×C4semidirect
129. C3×ΓL(1,𝔽25)C2×C4semidirect
189. #915Dic3semidirect
319. D3×Q8C2×Dic3semidirect
332. C3×SD16C4×D3semidirect
333. C3×SD16C2×Dic3semidirect
353. #216C2×Dic3semidirect
354. #214C2×Dic3semidirect
408. Dic12C2×Dic3semidirect
409. ΓL(1,𝔽25)C2×Dic3semidirect
586. SD16D3×Dic3semidirect
673. C32#2947semidirect
746. C3#79648semidirect
747. C3#83965semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
#105953472
#105952222
#105928632
C3×Dic3×SD162
#105915812
#105915762
D3×#8352
#105914452
#105914402
#105914202
#105909082
#105908192
Dic3×Dic122
#105906812
#839653
#796483