Finite Group Databasebeta

← #11860940

Subgroups — #11860940

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic
2#10595394C211yesmaximal, characteristic, complemented
3#10595222C211yesmaximal, characteristic, complemented
4SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591582C211yesmaximal, characteristic, complemented
7#10591576C211yesmaximal, characteristic, complemented
8#10591550C211yesmaximal, characteristic, complemented
9#10591436C211yesmaximal, characteristic, complemented
10#10591430C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic, complemented
12#10590775C211yesmaximal, characteristic, complemented
13Dic3×#204C211yesmaximal, characteristic, complemented
14#10590692C211yesmaximal, characteristic, complemented
15D3×#817C211yesmaximal, characteristic, complemented
16#83899—31nomaximal
17#79650—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#916C418yescomplemented
28C2×C3×#204C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30#67⋊Dic3—21no—
31Dic3×#67—21no—
32C2×Dic3⋊Dic3—21no—
33#63955—21no—
34#63898—21no—
35#63898C2211yescharacteristic
36Dic3×D12—21no—
37Dic3×D12C2211yescharacteristic
38D3×C4⋊Dic3—21no—
39D3×C4⋊Dic3C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41#63855—21no—
42#63855C2211yescharacteristic
43#63843C2211yescharacteristic
44Dic3×Dic6C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46#63662C2211yescharacteristic
47#63659C2211yescharacteristic
48#63644C2211yescharacteristic
49C8×C3⋊Dic3C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63555C2211yescharacteristic
61#63554C2211yescharacteristic
62C2×C3×#135—31no—
63#5827—31no—
64#5827—31no—
65C2×#916D311yescharacteristic
66#5574—31no—
67#5546—31no—
68C3×C4×SD16—31no—
69#5232—31no—
70#5232—31no—
71#5184—31no—
72#5184—31no—
73Dic3×SD16—31no—
74Dic3×SD16—31no—
75Dic3×SD16—31no—
76Dic3×SD16—31no—
77Dic3×SD16—61no—
78Dic3×SD16D311yescharacteristic, complemented
79#5152—31no—
80#5152—31no—
81C2×#817—31no—
82#5101—31no—
83#5030—31no—
84#5014—31no—
85D3×#106—31no—
86#4852—31no—
87#4803—31no—
88#4789—31no—
89#4785—31no—
90#4771—31no—
91C4×#204—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×#239—22no—
100C3×#239C2×C414yescomplemented
101C3×#237—22no—
102C3×#237C2×C414yescomplemented
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C32×SD16C2×C414yescomplemented
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#216C2×C414yescomplemented
123C3×#213C2×C414yescomplemented
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204C2×C414yescomplemented
132C3×D3×C8C2×C414yescomplemented
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138Dic3⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142(C2×D3)⋊Dic3D411yescharacteristic
143Dic32—21no—
144Dic32—21no—
145#3711—22no—
146#2952—91noSylow
147C2×C3×#41—31no—
148C2×C3×#41—31no—
149C2×#239C2×D311yescharacteristic
150C2×#237C2×D311yescharacteristic
151C3×#135—38no—
152C2×C3×Q16—31no—
153C2×C3×SD16—21no—
154C2×C3×SD16—31no—
155C2×C3×SD16C2×D311yescharacteristic
156C2×C3×SD16C2×D311yescharacteristic
157C2×C3×D8—31no—
158C22×C3×C8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—61no—
166Q8×Dic3C2×D311yescharacteristic
167C2×#216C2×D311yescharacteristic
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—31no—
172D4×Dic3—61no—
173D4×Dic3—61no—
174D4×Dic3—61no—
175D4×Dic3—61no—
176D4×Dic3—61no—
177D4×Dic3C2×D311yescharacteristic
178C2×#213C2×D311yescharacteristic
179C4×#67—61no—
180#926—31no—
181#926—61no—
182#926—61no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—61no—
186C2×C4⋊Dic3—61no—
187C2×Dic3⋊C4—61no—
188C2×#208—31no—
189#916Dic318yescomplemented
190C2×#204C2×D311yescharacteristic
191C2×ΓL(1,𝔽25)—31no—
192C2×D3×C8C2×D311yescharacteristic
193#893—31no—
194#893—61no—
195D3×C4⋊C4—31no—
196D3×C4⋊C4—31no—
197D3×C4⋊C4—61no—
198#887—31no—
199#67⋊C4—61no—
200#877—61no—
201C4×D12—31no—
202C4×D12—61no—
203#872—31no—
204#872—61no—
205C4×Dic6—31no—
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—61no—
215#835C2×D311yescharacteristic
216#832—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—61no—
221#832C2×D311yescharacteristic
222#821—31no—
223#817—31no—
224#817—31no—
225#817—31no—
226#817—31no—
227#817—61no—
228#817C2×D311yescharacteristic
229#816—31no—
230#815—31no—
231#815—31no—
232#815—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—61no—
236C8×Dic3C2×D311yescharacteristic
237#810—31no—
238#809—31no—
239#808—31no—
240#808—31no—
241#803—31no—
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C32×D4—21no—
248C32×D4C22×C412yes—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—81no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C3×#67—24no—
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×D12—24no—
266C3×D12—21no—
267C3×D12C22×C412yes—
268C3×C4×D3—24no—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273D3×Dic3—81no—
274D3×Dic3—81no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8C22×C412yes—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—31no—
282#520—91no—
283#520—91no—
284#442—91no—
285#442—91no—
286#441—91no—
287#441—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292C2×#106—91no—
293#417—91no—
294#417—91no—
295#405—91no—
296C3×#41—34no—
297C3×#41—34no—
298C3×#41—62no—
299C3×#41—62no—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—121no—
324#239—22no—
325#239C2×Dic314yescomplemented
326#237—22no—
327#237C2×Dic314yescomplemented
328C2×D12—21no—
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×Q16—34no—
338C3×SD16—24no—
339C3×SD16—34no—
340C3×SD16C4×D314yescomplemented
341C3×SD16C2×Dic314yescomplemented
342C3×D8—34no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—34no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—61no—
355#217—21no—
356#217—31no—
357#217—31no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—121no—
363#216C2×Dic314yescomplemented
364#213C2×Dic314yescomplemented
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369C4⋊Dic3—21no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—121no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—21no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404C4×Dic3C22×D311yescharacteristic
405#208—62no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204C2×Dic314yescomplemented
412ΓL(1,𝔽25)—62no—
413D3×C8C2×Dic314yescomplemented
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—22no—
425C32×C4C23×C411yescharacteristic
426C32×C4C2×#4111yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—31no—
438C2×#41—31no—
439#135—38no—
440C2×Q16—31no—
441C2×SD16—31no—
442C2×SD16D3211yescharacteristic
443C2×D8—31no—
444C2×M16—91no—
445C22×C8—31no—
446C4×Q8—31no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×D4—31no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456C4×D4—181no—
457C4×D4—181no—
458#117—91no—
459#117—181no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—181no—
464C2×C4⋊C4—181no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#97—91no—
478#97—91no—
479C4×C8—31no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C23×C3—61no—
486C22×D3—21no—
487C22×D3D3×D411yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—22no—
491C3×Q8—32no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8C2×C4×D312yes—
495C3×Q8C22×Dic312yes—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—22no—
499C3×D4—32no—
500C3×D4—41no—
501C3×D4—64no—
502C3×D4—64no—
503C3×D4—61no—
504C3×D4C2×C4×D312yes—
505C3×D4C22×Dic312yes—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—64no—
516C2×C3×C4—64no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—241no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—24no—
524C2×Dic3—21no—
525C2×Dic3—24no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—81no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—241no—
542C2×Dic3—241no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3—241no—
547C2×Dic3—242no—
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550C2×Dic3D3×D411yescharacteristic
551D12—24no—
552D12—21no—
553D12C22×Dic312yes—
554C4×D3—24no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3#23712yes—
560C4×D3C22×Dic312yes—
561Dic6—21no—
562Dic6C22×Dic312yes—
563C3×C8—22no—
564C3×C8—32no—
565C3×C8—61no—
566C3×C8C2×C4×D312yes—
567C3×C8C22×Dic312yes—
568C3⋊C8—21no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8C22×Dic312yes—
573C2×C32—42no—
574C2×C32C2×C4×D411yescharacteristic
575C2×C32#57711yescharacteristic
576C2×C32#57711yescharacteristic
577C3×D3—22no—
578C3×D3—42no—
579#41—34no—
580#41—34no—
581#41—62no—
582#41—62no—
583C2×Q8—31no—
584C2×Q8C2×D3211yescharacteristic
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4C2×D3211yescharacteristic
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—34no—
599SD16—34no—
600SD16D3×Dic314yescomplemented
601D8—34no—
602M16—182no—
603C2×C8—31no—
604C2×C8—34no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C22⋊C4—61no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—61no—
628C42—91no—
629C42—181no—
630C42—181no—
631C42—181no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—62no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C2×D3×D411yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3D4×Dic312yes—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—32no—
661C3×C4—42no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—62no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C22×C4×D311yescharacteristic
668C3×C4C2×#23711yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4C23×Dic311yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—22no—
674Dic3—41no—
675Dic3—41no—
676Dic3—62no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—241no—
687Dic3—241no—
688Dic3D4×Dic312yes—
689C32#295211yescharacteristic, complemented, Sylow
690C23—21no—
691C23—31no—
692C23—61no—
693Q8—21no—
694Q8—32no—
695Q8—61no—
696Q8C2×D3×Dic312yes—
697D4—21no—
698D4—32no—
699D4—64no—
700D4—64no—
701D4—61no—
702D4C2×D3×Dic312yes—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—64no—
710C2×C4—64no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—241no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4—721no—
723C2×C4—721no—
724C2×C4C22×D3211yescharacteristic
725C8—32no—
726C8—61no—
727C8—181no—
728C8C2×D3×Dic312yes—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—42no—
734C2×C3—62no—
735C2×C3—82no—
736C2×C3—122no—
737C2×C3C4×D3×D411yescharacteristic
738C2×C3#576211yescharacteristic
739C2×C3#577011yescharacteristic
740C2×C3#577011yescharacteristic
741C2×C3#577011yescharacteristic
742C2×C3C2×D4×Dic311yescharacteristic
743D3—22no—
744D3—42no—
745C22—22no—
746C22—32no—
747C22—41no—
748C22—41no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22D32×D411yescharacteristic
755C4—22no—
756C4—32no—
757C4—62no—
758C4—61no—
759C4—61no—
760C4—121no—
761C4—121no—
762C4—181no—
763C4—181no—
764C4—361no—
765C4—361no—
766C4D3×#23711yescharacteristic
767C4C22×D3×Dic311yescharacteristic
768C3—21no—
769C3#7965011yescharacteristic, complemented
770C3#8389911yescharacteristic, complemented
771C2—42no—
772C2—62no—
773C2—122no—
774C2#1059475311yescharacteristic
775C2#1059475711yescharacteristic
776C2D3×D4×Dic311yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×#916C2
cosocleC2×C32×C4C24
hypercenterC2×SD16D32
hypocenterC32#2952
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. #10595394C2semidirect
3. #10595222C2semidirect
4. SD16×C3⋊Dic3C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591582C2semidirect
7. #10591576C2semidirect
8. #10591550C2semidirect
9. #10591436C2semidirect
10. #10591430C2semidirect
11. #10591414C2semidirect
12. #10590775C2semidirect
13. Dic3×#204C2semidirect
14. #10590692C2semidirect
15. D3×#817C2semidirect
27. C3×#916C4semidirect
78. Dic3×SD16D3semidirect
100. C3×#239C2×C4semidirect
102. C3×#237C2×C4semidirect
112. C32×SD16C2×C4semidirect
122. C3×#216C2×C4semidirect
123. C3×#213C2×C4semidirect
131. C3×#204C2×C4semidirect
132. C3×D3×C8C2×C4semidirect
189. #916Dic3semidirect
325. #239C2×Dic3semidirect
327. #237C2×Dic3semidirect
340. C3×SD16C4×D3semidirect
341. C3×SD16C2×Dic3semidirect
363. #216C2×Dic3semidirect
364. #213C2×Dic3semidirect
411. #204C2×Dic3semidirect
413. D3×C8C2×Dic3semidirect
600. SD16D3×Dic3semidirect
689. C32#2952semidirect
769. C3#79650semidirect
770. C3#83899semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
#105953942
#105952222
SD16×C3⋊Dic32
C3×Dic3×SD162
#105915822
#105915762
#105915502
#105914362
#105914302
#105914142
#105907752
Dic3×#2042
#105906922
D3×#8172
#838993
#796503