Finite Group Databasebeta

← #11860750

Subgroups — #11860750

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic
2C2×D3×#214C211yesmaximal, characteristic
3#10593885C211yesmaximal, characteristic, complemented
4#10592717C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6Dic3×#214C211yesmaximal, characteristic, complemented
7#10591421C211yesmaximal, characteristic
8#10591405C211yesmaximal, characteristic, complemented
9#10590600C211yesmaximal, characteristic, complemented
10#10590572C211yesmaximal, characteristic, complemented
11#10590479C211yesmaximal, characteristic, complemented
12#10590478C211yesmaximal, characteristic, complemented
13C4×#3716C211yesmaximal, characteristic, complemented
14#10590358C211yesmaximal, characteristic, complemented
15#10590318C211yesmaximal, characteristic, complemented
16#82543—31nomaximal
17#79649—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C4×#634C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×C4×#67—21no—
26C2×C3×(C2×D3)⋊C4—21no—
27C3×#893C2211yescharacteristic
28C3×#892C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×D3×C22⋊C4—21no—
31C3×C4×D12C2211yescharacteristic
32C3×#872C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic, complemented
34D3×#214C418yescomplemented
35#63878—21no—
36#63877—21no—
37#63844C2211yescharacteristic, complemented
38Dic3×Dic6C2211yescharacteristic, complemented
39#63841C2211yescharacteristic
40#63838—21no—
41#63837—21no—
42C2×#3716C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63659C2211yescharacteristic
47#63637C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49#63630C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#810C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C3×#518—31no—
63C22×#214—31no—
64C2×D3×SD16—31no—
65#5572—31no—
66#5545D311yescharacteristic
67#5516—31no—
68C3×C4×SD16—31no—
69#5215—31no—
70Dic3×SD16—31no—
71#5026—31no—
72#5018—31no—
73#5018—31no—
74#5018—31no—
75#5018—31no—
76#5018—31no—
77#5018—61no—
78C4×#214—31no—
79C4×#214—31no—
80C4×#214—31no—
81C4×#214D311yescharacteristic, complemented
82#5004—31no—
83#4998—31no—
84#4997—31no—
85#4860—31no—
86#4852—31no—
87#4817—31no—
88#4802—31no—
89#4770—31no—
90#4757—31no—
91C4×#204—31no—
92#4689—31no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4C2×C414yes—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6C2×C414yescomplemented
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3754C2×C414yescomplemented
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#214C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136#3724—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142#3716C2×C414yescomplemented
143#3715C2×C414yescomplemented
144#3711—22no—
145D3×C3⋊C8C2×C414yescomplemented
146#2949—91noSylow
147C22×C3×D4—31no—
148C2×D3×Q8—31no—
149C2×D3×D4C2×D311yescharacteristic
150C22×Dic6—31no—
151C2×C3×SD16—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—21no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—61no—
158C3×C4×D4—61no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C3×#117—31no—
162C3×#117—31no—
163C2×C3×C22⋊C4—61no—
164C2×C3×C22⋊C4—61no—
165Q8×Dic3—31no—
166C2×#215—31no—
167D4×Dic3C2×D311yescharacteristic
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—38no—
172C2×#214—31no—
173C2×#214—61no—
174C2×#214C2×D311yescharacteristic
175C4×#67—21no—
176C2×(C2×D3)⋊C4—21no—
177#926—31no—
178C2×#208—31no—
179C22×C3⋊C8—31no—
180D3×SD16—38no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8—31no—
184#893C2×D311yescharacteristic
185#892—31no—
186#892—61no—
187#892C2×D311yescharacteristic
188#887—31no—
189#887—61no—
190#887—61no—
191#887—61no—
192#67⋊C4—21no—
193D3×C22⋊C4—21no—
194#877—61no—
195#877—61no—
196C4×D12C2×D311yescharacteristic
197#872—61no—
198#872C2×D311yescharacteristic
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—61no—
204C4×Dic6—61no—
205C4×Dic6C2×D311yescharacteristic, complemented
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#821—31no—
218#817—31no—
219#816—31no—
220#815—31no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#808—31no—
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236#803—31no—
237#803—31no—
238#803—31no—
239#803—61no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8C2×D311yescharacteristic, complemented
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3—24no—
245C22×C3×D3—81no—
246C22×C3×D3—81no—
247C22×C3×D3C2×D411yescharacteristic
248C32×D4—21no—
249C32×D4C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4—81no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257#634—21no—
258#634C22×C412yes—
259C3×#67—24no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12C22×C412yes—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×C4×D3C22×C412yes—
272C3×C4×D3#4112yes—
273C3×Dic6—21no—
274C3×Dic6C22×C412yes—
275#627—24no—
276D3×Dic3—24no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C22×SD16—91no—
282#519—91no—
283#518—31no—
284#440—91no—
285#440—91no—
286#440—91no—
287#440—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292#427—91no—
293#419—91no—
294#418—91no—
295#405—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4—34no—
301C2×C3×D4—31no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—41no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C22×Dic3—21no—
315C22×Dic3—61no—
316D3×Q8—34no—
317D3×Q8—62no—
318D3×D4—22no—
319D3×D4C4×D314yes—
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—34no—
328C2×Dic6—61no—
329C2×Dic6—62no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—34no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—21no—
354C3×C42—31no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359#217—21no—
360#217—61no—
361#215—34no—
362#214—34no—
363#214—34no—
364#214—34no—
365#214—34no—
366#214—64no—
367#214C4×D314yescomplemented
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4#6711yescharacteristic
373(C2×D3)⋊C4#6711yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387Dic3⋊C4#6711yescharacteristic
388Dic3⋊C4#6711yescharacteristic
389C4×Dic3—21no—
390C4×Dic3—21no—
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×Dic3C22×D311yescharacteristic
401#208—62no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—34no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—34no—
412ΓL(1,𝔽25)—62no—
413D3×C8—34no—
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×D3—84no—
424C2×C3×D3C4×D412yes—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C23×C411yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—22no—
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C4×D412yes—
438C22×Q8—91no—
439C22×D4—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×SD16—98no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×M16—91no—
446C22×C8—91no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×Q8—181no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—61no—
457C4×D4—61no—
458C4×D4D3211yescharacteristic
459#117—31no—
460#117—31no—
461#117—91no—
462#117—181no—
463#117—181no—
464C2×C22⋊C4—61no—
465C2×C22⋊C4—61no—
466#107—91no—
467#107—91no—
468#106—31no—
469#106—91no—
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#97—91no—
479#97—91no—
480C4×C8—31no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—64no—
487C23×C3—61no—
488C23×C3—241no—
489C23×C3—241no—
490C22×D3—21no—
491C22×D3—24no—
492C22×D3—81no—
493C22×D3—81no—
494C22×D3C2×#6711yescharacteristic
495C3×Q8—32no—
496C3×Q8—61no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—32no—
501C3×D4—41no—
502C3×D4—64no—
503C3×D4—61no—
504C3×D4C2×C4×D312yes—
505C3×D4C2×C4×D312yes—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—81no—
521C2×C3×C4—81no—
522C2×C3×C4—82no—
523C2×C3×C4—241no—
524C2×C3×C4—241no—
525C2×C3×C4—241no—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×#6711yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—24no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—64no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—81no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546C2×Dic3C2×#6711yescharacteristic
547D12—21no—
548D12C2×C4×D312yes—
549C4×D3—64no—
550C4×D3—81no—
551C4×D3—81no—
552C4×D3C2×C4×D312yes—
553C4×D3#23512yes—
554Dic6—21no—
555Dic6—32no—
556Dic6—32no—
557Dic6—62no—
558Dic6—64no—
559Dic6—61no—
560Dic6—61no—
561Dic6—64no—
562Dic6—121no—
563Dic6C2×C4×D312yes—
564C3×C8—32no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—32no—
568C3⋊C8—32no—
569C3⋊C8—62no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8C2×C4×D312yes—
574C2×C32—42no—
575C2×C32C2×C4×D411yescharacteristic
576C2×C32#57711yescharacteristic
577C2×C32#57711yescharacteristic
578C3×D3—22no—
579C3×D3—42no—
580C24—61no—
581C2×Q8—31no—
582C2×Q8—94no—
583C2×Q8—91no—
584C2×Q8—181no—
585C2×Q8—182no—
586C2×D4—34no—
587C2×D4—31no—
588C2×D4—62no—
589C2×D4—61no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—21no—
592C22×C4—31no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—181no—
597SD16—34no—
598SD16—94no—
599SD16—94no—
600SD16—94no—
601M16—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—94no—
605C2×C8—91no—
606C2×C8—91no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—21no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—61no—
628C42—181no—
629C42—181no—
630C42—181no—
631C42—181no—
632C42C2×D3211yescharacteristic
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—32no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—244no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×#6711yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C2×D3C4×#6712yes—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—32no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—62no—
673C3×C4—81no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4C22×C4×D311yescharacteristic
677C3×C4C22×C4×D311yescharacteristic
678C3×C4C2×#23511yescharacteristic
679C3×C4D3×#4111yescharacteristic
680Dic3—22no—
681Dic3—21no—
682Dic3—21no—
683Dic3—41no—
684Dic3—41no—
685Dic3—62no—
686Dic3—62no—
687Dic3—122no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3C4×#6712yes—
692C32#294911yescharacteristic, complemented, Sylow
693C23—21no—
694C23—31no—
695C23—64no—
696C23—61no—
697C23—241no—
698C23—241no—
699Q8—32no—
700Q8—61no—
701Q8—92no—
702Q8—184no—
703Q8—181no—
704D4—21no—
705D4—32no—
706D4—64no—
707D4—61no—
708D4C4×D3212yes—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—81no—
719C2×C4—184no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—241no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4D3×#6711yescharacteristic
726C2×C4D3×#6711yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—32no—
729C8—61no—
730C8—92no—
731C8—181no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—42no—
736C2×C3—42no—
737C2×C3—62no—
738C2×C3—82no—
739C2×C3—122no—
740C2×C3C4×D3×D411yescharacteristic
741C2×C3#576211yescharacteristic
742C2×C3#577011yescharacteristic
743C2×C3C2×C4×#6711yescharacteristic
744C2×C3#583611yescharacteristic
745C2×C3#583611yescharacteristic
746D3—22no—
747D3—42no—
748C22—22no—
749C22—32no—
750C22—41no—
751C22—41no—
752C22—61no—
753C22—61no—
754C22—62no—
755C22—121no—
756C22—121no—
757C22—244no—
758C22C2×D3×#6711yescharacteristic
759C4—21no—
760C4—21no—
761C4—32no—
762C4—41no—
763C4—61no—
764C4—61no—
765C4—62no—
766C4—121no—
767C4—121no—
768C4—182no—
769C4—361no—
770C4C2×C4×D3211yescharacteristic
771C4D3×#23511yescharacteristic
772C3—21no—
773C3#7964911yescharacteristic, complemented
774C3#8254311yescharacteristic, complemented
775C2—42no—
776C2—62no—
777C2—122no—
778C2C4×D3×#6711yescharacteristic
779C2#1059510511yescharacteristic
780C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593885C2semidirect
4. #10592717C2semidirect
5. C3×C4×#214C2semidirect
6. Dic3×#214C2semidirect
8. #10591405C2semidirect
9. #10590600C2semidirect
10. #10590572C2semidirect
11. #10590479C2semidirect
12. #10590478C2semidirect
13. C4×#3716C2semidirect
14. #10590358C2semidirect
15. #10590318C2semidirect
22. C4×#634C22semidirect
33. C3×C4×Dic6C22semidirect
34. D3×#214C4semidirect
37. #63844C22semidirect
38. Dic3×Dic6C22semidirect
47. #63637C22semidirect
48. #63634C22semidirect
49. #63630C22semidirect
51. C3×#810C22semidirect
52. C3×#808C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63576C22semidirect
55. #63573C22semidirect
56. #63567C22semidirect
57. #63565C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
81. C4×#214D3semidirect
109. D3×Dic6C2×C4semidirect
113. #3754C2×C4semidirect
120. C3×#214C2×C4semidirect
142. #3716C2×C4semidirect
143. #3715C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
205. C4×Dic6C2×D3semidirect
227. #810C2×D3semidirect
230. #808C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
367. #214C4×D3semidirect
692. C32#2949semidirect
773. C3#79649semidirect
774. C3#82543semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
C2×D3×#2142
#105938852
#105927172
C3×C4×#2142
Dic3×#2142
#105914212
#105914052
#105906002
#105905722
#105904792
#105904782
C4×#37162
#105903582
#105903182
#825433
#796493