Finite Group Databasebeta

← #11860601

Subgroups — #11860601

Order 1152.

995 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic
2#10595394C211yesmaximal, characteristic
3#10595347C211yesmaximal, characteristic, complemented
4Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#5184C211yesmaximal, characteristic, complemented
6#10591582C211yesmaximal, characteristic, complemented
7Dic3×#216C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9Dic3×#215C211yesmaximal, characteristic, complemented
10#10591556C211yesmaximal, characteristic
11D3×#835C211yesmaximal, characteristic, complemented
12#10590909C211yesmaximal, characteristic, complemented
13#10590775C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590681C211yesmaximal, characteristic, complemented
16#83965—31nomaximal
17#79830—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#918C418yescomplemented
28C2×C3×#204C2211yescharacteristic
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30#63898—21no—
31#63898C2211yescharacteristic
32Dic3×D12—21no—
33Dic3×D12C2211yescharacteristic
34D3×C4⋊Dic3—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63855—21no—
37#63855—21no—
38#63855C2211yescharacteristic
39#63843—21no—
40#63843C2211yescharacteristic
41Dic3×Dic6—21no—
42Dic3×Dic6C2211yescharacteristic
43#63841—21no—
44#63841C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63645C2211yescharacteristic
49C8×C3⋊Dic3C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#815C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63555C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×C3×#137—31no—
63#5827—31no—
64#5812—31no—
65C2×#918D311yescharacteristic
66#5574—31no—
67#5572—31no—
68C3×#441—31no—
69#5233—31no—
70C2×#835—31no—
71#5184—31no—
72#5184D311yescharacteristic, complemented
73Dic3×Q16—31no—
74Dic3×Q16—31no—
75Dic3×Q16—31no—
76Dic3×Q16—61no—
77#5164—31no—
78#5164—31no—
79Dic3×SD16—31no—
80Dic3×SD16—31no—
81#5122—31no—
82#5121—31no—
83C4×#216—31no—
84C4×#215—31no—
85#4861—31no—
86#4852—31no—
87#4817—31no—
88#4804—31no—
89D3×#103—31no—
90#4789—31no—
91#4710—31no—
92#4708—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C3×#239—22no—
96C3×#239C2×C414yes—
97C3×D3×Q8—22no—
98C3×D3×Q8C2×C414yescomplemented
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C32×Q16C2×C414yescomplemented
110C2×C32×C8C2311yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#216C2×C414yescomplemented
120C3×#215C2×C414yescomplemented
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×#204C2×C414yescomplemented
131C3×ΓL(1,𝔽25)C2×C414yescomplemented
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136Dic3⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143Dic32—21no—
144Dic32—21no—
145D3×C3⋊C8—22no—
146#2947—91noSylow
147C2×C3×#41—31no—
148C22×C3×Q8—31no—
149C2×#239C2×D311yescharacteristic
150C2×D3×Q8C2×D311yescharacteristic
151C3×#137—38no—
152C2×C3×Q16—21no—
153C2×C3×Q16—31no—
154C2×C3×Q16C2×D311yescharacteristic
155C2×C3×Q16C2×D311yescharacteristic
156C2×C3×SD16—31no—
157C2×C3×SD16—31no—
158C2×C3×M16—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—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×Dic3—61no—
171Q8×Dic3C2×D311yescharacteristic
172Q8×Dic3C2×D311yescharacteristic
173C2×#216C2×D311yescharacteristic
174C2×#215C2×D311yescharacteristic
175D4×Dic3—31no—
176D4×Dic3—31no—
177D4×Dic3—61no—
178D4×Dic3—61no—
179#926—31no—
180#926—31no—
181#926—61no—
182#926—61no—
183#926—61no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—61no—
186C22×C3⋊C8—31no—
187#918Dic318yescomplemented
188C2×#204C2×D311yescharacteristic
189C2×ΓL(1,𝔽25)C2×D311yescharacteristic
190C2×D3×C8—31no—
191#893—31no—
192#893—61no—
193#892—31no—
194#892—61no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4—61no—
197#887—31no—
198#887—61no—
199C4×D12—31no—
200C4×D12—61no—
201#872—31no—
202#872—61no—
203#872—61no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#97—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—31no—
216#835—61no—
217#835—61no—
218#835C2×D311yescharacteristic
219#835C2×D311yescharacteristic
220#832—31no—
221#832—31no—
222#821—31no—
223#818—31no—
224#818—31no—
225#818—31no—
226#818—61no—
227#817—31no—
228#817C2×D311yescharacteristic
229#816—31no—
230#815—31no—
231#815—31no—
232#815C2×D311yescharacteristic
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3—61no—
237#810—31no—
238#809—31no—
239#808—31no—
240#807—31no—
241C4×C3⋊C8—31no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C32×Q8C22×C412yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—24no—
262C3×D12—21no—
263C3×D12C22×C412yes—
264C3×C4×D3—24no—
265C3×C4×D3—24no—
266C3×C4×D3C22×C412yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6—24no—
270C3×Dic6C22×C412yes—
271D3×Dic3—81no—
272D3×Dic3—81no—
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—31no—
282#441—91no—
283#440—91no—
284#440—91no—
285C4×Q16—91no—
286C4×Q16—91no—
287C4×SD16—91no—
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—21no—
297C2×C3×Q8—34no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313#239—22no—
314#239C2×Dic314yes—
315D3×Q8—22no—
316D3×Q8C2×Dic314yescomplemented
317C2×D12—21no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—21no—
326C2×Dic6C22×D311yescharacteristic
327C3×Q16—24no—
328C3×Q16—34no—
329C3×Q16C4×D314yescomplemented
330C3×Q16C2×Dic314yescomplemented
331C3×SD16—34no—
332C3×SD16—34no—
333C3×M16—34no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C42—31no—
344C3×C42—61no—
345C3×C42—61no—
346#217—31no—
347#217—31no—
348#217—61no—
349#217—61no—
350#217—61no—
351#216C2×Dic314yescomplemented
352#215C2×Dic314yescomplemented
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358C4⋊Dic3—21no—
359C4⋊Dic3—21no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
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—61no—
375C4⋊Dic3—121no—
376C4⋊Dic3—121no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—31no—
387C4×Dic3—31no—
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—121no—
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
408#204C2×Dic314yescomplemented
409ΓL(1,𝔽25)C2×Dic314yescomplemented
410D3×C8—62no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3C4×D412yes—
418C32×C4—22no—
419C32×C4—22no—
420C32×C4C23×C411yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
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×Q16D3211yescharacteristic
437C2×SD16—31no—
438C2×SD16—31no—
439C2×M16—31no—
440C22×C8—91no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×Q8—91no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—181no—
448C4×Q8—181no—
449C4×D4—91no—
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—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—91no—
471#102—91no—
472#97—31no—
473#97—91no—
474C4×C8—91no—
475C4×C8—91no—
476C23×C3—31no—
477C23×C3—61no—
478C22×D3—21no—
479C22×D3D3×D411yescharacteristic
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—22no—
486C3×Q8—32no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—64no—
490C3×Q8—61no—
491C3×Q8C2×C4×D312yes—
492C3×Q8C2×C4×D312yes—
493C3×Q8C22×Dic312yes—
494C3×Q8C22×Dic312yes—
495C3×D4—32no—
496C3×D4—64no—
497C3×D4—61no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—32no—
505C2×C3×C4—32no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—64no—
511C2×C3×C4—64no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—241no—
533C2×Dic3—241no—
534C2×Dic3—241no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—24no—
539D12—21no—
540D12C22×Dic312yes—
541C4×D3—24no—
542C4×D3—24no—
543C4×D3—241no—
544C4×D3—241no—
545C4×D3—241no—
546C4×D3#23712yes—
547C4×D3C22×Dic312yes—
548Dic6—21no—
549Dic6—24no—
550Dic6C22×Dic312yes—
551C3×C8—22no—
552C3×C8—32no—
553C3×C8—61no—
554C3×C8C2×C4×D312yes—
555C3×C8C22×Dic312yes—
556C3⋊C8—21no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C3⋊C8C22×Dic312yes—
561C2×C32C2×C4×D411yescharacteristic
562C2×C32#57711yescharacteristic
563C2×C32#57811yescharacteristic
564C3×D3—22no—
565C3×D3—42no—
566#41—34no—
567#41—62no—
568C2×Q8—34no—
569C2×Q8—31no—
570C2×Q8—61no—
571C2×Q8—62no—
572C2×Q8C2×D3211yescharacteristic
573C2×Q8C2×D3211yescharacteristic
574C2×D4—31no—
575C2×D4—61no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582Q16—34no—
583Q16D3×Dic314yescomplemented
584SD16—34no—
585SD16—34no—
586M16—34no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—91no—
590C2×C8—182no—
591C2×C8C2×D3211yescharacteristic
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—61no—
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—
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—31no—
611C42—61no—
612C42—61no—
613C42—91no—
614C42—181no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42—181no—
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—62no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3C2×D3×D411yescharacteristic
627C22×C3C2×D3×D411yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—22no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3D4×Dic312yes—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—32no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—62no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4C22×C4×D311yescharacteristic
649C3×C4C2×#23711yescharacteristic
650C3×C4D3×#4111yescharacteristic
651C3×C4C23×Dic311yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—22no—
655Dic3—41no—
656Dic3—41no—
657Dic3—62no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668Dic3—241no—
669Dic3D4×Dic312yes—
670C32#294711yescharacteristic, complemented, Sylow
671C23—31no—
672C23—61no—
673Q8—21no—
674Q8—21no—
675Q8—32no—
676Q8—64no—
677Q8—61no—
678Q8C2×D3×Dic312yes—
679Q8C2×D3×Dic312yes—
680D4—32no—
681D4—64no—
682D4—61no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—31no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—64no—
691C2×C4—64no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—181no—
698C2×C4—181no—
699C2×C4—721no—
700C2×C4—721no—
701C2×C4—721no—
702C2×C4C22×D3211yescharacteristic
703C8—32no—
704C8—61no—
705C8—181no—
706C8C2×D3×Dic312yes—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—62no—
711C2×C3—122no—
712C2×C3C4×D3×D411yescharacteristic
713C2×C3#577811yescharacteristic
714C2×C3#577811yescharacteristic
715C2×C3#577911yescharacteristic
716C2×C3#577911yescharacteristic
717C2×C3C2×D4×Dic311yescharacteristic
718D3—22no—
719D3—42no—
720C22—32no—
721C22—61no—
722C22—61no—
723C22—62no—
724C22—121no—
725C22—121no—
726C22D32×D411yescharacteristic
727C4—22no—
728C4—22no—
729C4—32no—
730C4—62no—
731C4—61no—
732C4—61no—
733C4—121no—
734C4—121no—
735C4—181no—
736C4—181no—
737C4—361no—
738C4—361no—
739C4D3×#23711yescharacteristic
740C4C22×D3×Dic311yescharacteristic
741C3—21no—
742C3#7983011yescharacteristic, complemented
743C3#8396511yescharacteristic, complemented
744C2—62no—
745C2—122no—
746C2#1059476711yescharacteristic
747C2#1059476911yescharacteristic
748C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
cosocleC2×C32×C4C24
hypercenterC2×Q16D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #10595347C2semidirect
4. Q16×C3⋊Dic3C2semidirect
5. C3×#5184C2semidirect
6. #10591582C2semidirect
7. Dic3×#216C2semidirect
8. #10591572C2semidirect
9. Dic3×#215C2semidirect
11. D3×#835C2semidirect
12. #10590909C2semidirect
13. #10590775C2semidirect
14. #10590766C2semidirect
15. #10590681C2semidirect
27. C3×#918C4semidirect
72. #5184D3semidirect
98. C3×D3×Q8C2×C4semidirect
109. C32×Q16C2×C4semidirect
119. C3×#216C2×C4semidirect
120. C3×#215C2×C4semidirect
130. C3×#204C2×C4semidirect
131. C3×ΓL(1,𝔽25)C2×C4semidirect
187. #918Dic3semidirect
316. D3×Q8C2×Dic3semidirect
329. C3×Q16C4×D3semidirect
330. C3×Q16C2×Dic3semidirect
351. #216C2×Dic3semidirect
352. #215C2×Dic3semidirect
408. #204C2×Dic3semidirect
409. ΓL(1,𝔽25)C2×Dic3semidirect
583. Q16D3×Dic3semidirect
670. C32#2947semidirect
742. C3#79830semidirect
743. C3#83965semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
#105953942
#105953472
Q16×C3⋊Dic32
C3×#51842
#105915822
Dic3×#2162
#105915722
Dic3×#2152
#105915562
D3×#8352
#105909092
#105907752
#105907662
#105906812
#839653
#798303