Finite Group Databasebeta

← #11860388

Subgroups — #11860388

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic
2D3×Q8×Dic3C211yesmaximal, characteristic, complemented
3Dic3×#237C211yesmaximal, characteristic
4SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#5164C211yesmaximal, characteristic, complemented
6#10591581C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8#10591557C211yesmaximal, characteristic, complemented
9#10591445C211yesmaximal, characteristic, complemented
10#10591440C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic
12#10590818C211yesmaximal, characteristic, complemented
13#10590812C211yesmaximal, characteristic, complemented
14#10590683C211yesmaximal, characteristic, complemented
15#10590667C211yesmaximal, characteristic, complemented
16Dic3×#137—31nomaximal
17#79774—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—
32#63955—21no—
33C2×Dic32—21no—
34D3×C4⋊Dic3—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36C4×D3×Dic3—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63843—21no—
39#63843C2211yescharacteristic
40#63843C2211yescharacteristic
41Dic3×Dic6—21no—
42Dic3×Dic6C2211yescharacteristic
43Dic3×Dic6C2211yescharacteristic
44#63841C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63662C2211yescharacteristic
47#63659C2211yescharacteristic
48#63644C2211yescharacteristic
49C8×C3⋊Dic3C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#815C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63554C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×C3×#137—31no—
63Dic3×#41—31no—
64C2×Q8×Dic3—31no—
65C2×#915D311yescharacteristic
66C4×D3×Q8—31no—
67C4×#237—31no—
68C3×#440—31no—
69#5232—31no—
70#5225—31no—
71#5184—31no—
72#5184—31no—
73Dic3×Q16—31no—
74Dic3×Q16—31no—
75#5164—31no—
76#5164D311yescharacteristic, complemented
77Dic3×SD16—31no—
78Dic3×SD16—31no—
79Dic3×SD16—31no—
80Dic3×SD16—61no—
81#5121—31no—
82Dic3×M16—31no—
83#5030—31no—
84#5018—31no—
85#4881—31no—
86#4873—31no—
87#4802—31no—
88#4790—31no—
89#4771—31no—
90#4758—31no—
91#4716—31no—
92#4707—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—
109C2×D3×Dic3D411yescharacteristic
110C2×D3×Dic3D411yescharacteristic
111C32×SD16C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#216C2×C414yescomplemented
122C3×#214C2×C414yescomplemented
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×Dic12C2×C414yescomplemented
131C3×ΓL(1,𝔽25)C2×C414yescomplemented
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32D411yescharacteristic
144Dic32D411yescharacteristic
145#3711—22no—
146C4×#137—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—61no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—61no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—61no—
186C2×C4×Dic3—61no—
187C2×C4×Dic3—61no—
188C2×#208—31no—
189#915Dic318yescomplemented
190C2×Dic12C2×D311yescharacteristic
191C2×ΓL(1,𝔽25)—31no—
192C2×ΓL(1,𝔽25)C2×D311yescharacteristic
193#892—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4—61no—
196#887—31no—
197#887—31no—
198#887—61no—
199#67⋊C4—61no—
200#877—61no—
201C42×D3—31no—
202C42×D3—61no—
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—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#835C2×D311yescharacteristic
218#832—31no—
219#832—31no—
220#832—61no—
221#832C2×D311yescharacteristic
222#818—31no—
223#818C2×D311yescharacteristic
224#817—31no—
225#817—31no—
226#817—31no—
227#817—61no—
228#816—31no—
229#816—31no—
230#815—31no—
231#815C2×D311yescharacteristic
232C8×Dic3—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3—61no—
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—42no—
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—42no—
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—22no—
274D3×Dic3—41no—
275D3×Dic3—42no—
276C32×C8C22×C412yes—
277C3⋊(C3⋊C8)—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8C22×C412yes—
280C2×#137—31no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—91no—
284#441—91no—
285#440—31no—
286#440—91no—
287C4×Q16—91no—
288C4×Q16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—91no—
294C4×M16—91no—
295C3×#41—34no—
296C3×#41—62no—
297C2×C3×Q8—21no—
298C2×C3×Q8—34no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×D4—21no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322D3×Q8—22no—
323D3×Q8C2×Dic314yescomplemented
324#237—22no—
325#237C2×Dic314yes—
326C2×C4×D3—21no—
327C2×C4×D3—31no—
328C2×C4×D3—31no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—21no—
332C2×Dic6C22×D311yescharacteristic
333C2×Dic6C22×D311yescharacteristic
334C3×Q16—34no—
335C3×Q16—34no—
336C3×SD16—24no—
337C3×SD16—34no—
338C3×SD16C4×D314yescomplemented
339C3×SD16C2×Dic314yescomplemented
340C3×M16—34no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352#217—21no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—121no—
357#216C2×Dic314yescomplemented
358#214C2×Dic314yescomplemented
359(C2×D3)⋊C4—61no—
360C4⋊Dic3—21no—
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—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382C4×Dic3—21no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
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—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C4×Dic3C22×D311yescharacteristic
404#208—62no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410Dic12C2×Dic314yescomplemented
411ΓL(1,𝔽25)—62no—
412ΓL(1,𝔽25)C2×Dic314yescomplemented
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3C4×D412yes—
420C32×C4—22no—
421C32×C4C23×C411yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—21no—
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3⋊Dic3#13712yescomplemented
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3C4×D412yes—
434C2×#41—31no—
435C22×Q8—31no—
436#137—38no—
437C2×Q16—31no—
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16D3211yescharacteristic
441C2×M16—31no—
442C2×M16—91no—
443C4×Q8—31no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×D4—31no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—181no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—181no—
459C2×C42—91no—
460C2×C42—181no—
461C2×C42—181no—
462#107—31no—
463#107—91no—
464#106—91no—
465#106—91no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—91no—
474#97—31no—
475#97—91no—
476C4×C8—91no—
477C4×C8—91no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—41no—
482C22×D3D3×D411yescharacteristic
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—22no—
486C3×Q8—32no—
487C3×Q8—32no—
488C3×Q8—41no—
489C3×Q8—64no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8C2×C4×D312yes—
493C3×Q8C22×Dic312yes—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—22no—
497C3×D4—41no—
498C3×D4—64no—
499C3×D4C2×C4×D312yes—
500C3×D4C22×Dic312yes—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
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×C4—61no—
516C2×C3×C4—122no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—24no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—24no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—42no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—62no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3—122no—
543C2×Dic3—242no—
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C4×D3—24no—
548C4×D3—62no—
549C4×D3—121no—
550C4×D3—122no—
551C4×D3#23712yes—
552C4×D3C22×Dic312yes—
553Dic6—21no—
554Dic6—21no—
555Dic6—24no—
556Dic6C22×Dic312yes—
557Dic6C22×Dic312yes—
558C3×C8—22no—
559C3×C8—32no—
560C3×C8—61no—
561C3×C8C2×C4×D312yes—
562C3×C8C22×Dic312yes—
563C3⋊C8—21no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—121no—
567C3⋊C8C22×Dic312yes—
568C2×C32—42no—
569C2×C32C2×C4×D411yescharacteristic
570C2×C32C2×#13711yescharacteristic
571C2×C32#57511yescharacteristic
572C3×D3—22no—
573#41—34no—
574#41—62no—
575C2×Q8—34no—
576C2×Q8—31no—
577C2×Q8—31no—
578C2×Q8—61no—
579C2×Q8—62no—
580C2×Q8C2×D3211yescharacteristic
581C2×D4—61no—
582C2×D4C2×D3211yescharacteristic
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—181no—
590C22×C4—181no—
591Q16—34no—
592Q16—34no—
593SD16—34no—
594SD16D3×Dic314yescomplemented
595M16—34no—
596M16—182no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8C2×D3211yescharacteristic
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C22⋊C4—61no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—61no—
617C42—91no—
618C42—91no—
619C42—91no—
620C42—181no—
621C42—181no—
622C42—181no—
623C42—181no—
624C42—181no—
625C42—181no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—21no—
629C22×C3—32no—
630C22×C3—42no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3D4×Dic312yes—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—32no—
649C3×C4—42no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4C22×C4×D311yescharacteristic
657C3×C4C2×#23711yescharacteristic
658C3×C4D3×#4111yescharacteristic
659C3×C4C23×Dic311yescharacteristic
660Dic3—21no—
661Dic3—21no—
662Dic3—22no—
663Dic3—22no—
664Dic3—32no—
665Dic3—32no—
666Dic3—41no—
667Dic3—41no—
668Dic3—62no—
669Dic3—61no—
670Dic3—61no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—241no—
677Dic3—241no—
678Dic3D4×Dic312yes—
679C32C4×#13711yescharacteristic, complemented, Sylow
680C23—21no—
681C23—31no—
682Q8—21no—
683Q8—32no—
684Q8—32no—
685Q8—64no—
686Q8—61no—
687Q8—61no—
688Q8C2×D3×Dic312yes—
689D4—21no—
690D4—64no—
691D4C2×D3×Dic312yes—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—64no—
699C2×C4—64no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—122no—
707C2×C4—182no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—361no—
711C2×C4—362no—
712C2×C4—362no—
713C2×C4C22×D3211yescharacteristic
714C8—32no—
715C8—61no—
716C8—181no—
717C8C2×D3×Dic312yes—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—42no—
722C2×C3—42no—
723C2×C3—62no—
724C2×C3—82no—
725C2×C3C4×D3×D411yescharacteristic
726C2×C3#577311yescharacteristic
727C2×C3D3×#13711yescharacteristic
728C2×C3D3×#13711yescharacteristic
729C2×C3#577711yescharacteristic
730C2×C3C2×D4×Dic311yescharacteristic
731D3—22no—
732C22—22no—
733C22—32no—
734C22—41no—
735C22—41no—
736C22—61no—
737C22—61no—
738C22D32×D411yescharacteristic
739C4—22no—
740C4—32no—
741C4—62no—
742C4—62no—
743C4—61no—
744C4—61no—
745C4—92no—
746C4—121no—
747C4—121no—
748C4—181no—
749C4—361no—
750C4—361no—
751C4D3×#23711yescharacteristic
752C4C22×D3×Dic311yescharacteristic
753C3—21no—
754C3#7977411yescharacteristic, complemented
755C3Dic3×#13711yescharacteristic, complemented
756C2—42no—
757C2—62no—
758C2#1059474211yescharacteristic
759C2#1059474411yescharacteristic
760C2D3×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
hypocenterC32C4×#137
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. D3×Q8×Dic3C2semidirect
4. SD16×C3⋊Dic3C2semidirect
5. C3×#5164C2semidirect
6. #10591581C2semidirect
7. #10591576C2semidirect
8. #10591557C2semidirect
9. #10591445C2semidirect
10. #10591440C2semidirect
12. #10590818C2semidirect
13. #10590812C2semidirect
14. #10590683C2semidirect
15. #10590667C2semidirect
27. C3×#915C4semidirect
76. #5164D3semidirect
100. C3×D3×Q8C2×C4semidirect
111. C32×SD16C2×C4semidirect
121. C3×#216C2×C4semidirect
122. C3×#214C2×C4semidirect
130. C3×Dic12C2×C4semidirect
131. C3×ΓL(1,𝔽25)C2×C4semidirect
189. #915Dic3semidirect
323. D3×Q8C2×Dic3semidirect
338. C3×SD16C4×D3semidirect
339. C3×SD16C2×Dic3semidirect
357. #216C2×Dic3semidirect
358. #214C2×Dic3semidirect
410. Dic12C2×Dic3semidirect
412. ΓL(1,𝔽25)C2×Dic3semidirect
426. C3⋊Dic3#137semidirect
594. SD16D3×Dic3semidirect
679. C32C4×#137semidirect
754. C3#79774semidirect
755. C3Dic3×#137semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
D3×Q8×Dic32
Dic3×#2372
SD16×C3⋊Dic32
C3×#51642
#105915812
#105915762
#105915572
#105914452
#105914402
#105914142
#105908182
#105908122
#105906832
#105906672
Dic3×#1373
#797743