Finite Group Databasebeta

← #11860217

Subgroups — #11860217

Order 1152.

1050 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×C4×#237C211yesmaximal, characteristic, complemented
2C2×#63935C211yesmaximal, characteristic
3C4×#3799C211yesmaximal, characteristic, complemented
4#10592713C211yesmaximal, characteristic, complemented
5C3×#5018C211yesmaximal, characteristic, complemented
6#10591440C211yesmaximal, characteristic, complemented
7#10591420C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590571C211yesmaximal, characteristic, complemented
11#10590477C211yesmaximal, characteristic, complemented
12#10590457C211yesmaximal, characteristic, complemented
13#10590381C211yesmaximal, characteristic, complemented
14#10590362C211yesmaximal, characteristic, complemented
15D3×#803C211yesmaximal, characteristic, complemented
16#82506—31nomaximal
17#79772—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×C4×#67—21no—
26C2×C3×C4×Dic3—21no—
27C3×#892C2211yescharacteristic
28C3×#887C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×#877—21no—
31C3×C42×D3C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63935C418yescomplemented
35#63904—21no—
36C4×#626—21no—
37#63894C2211yescharacteristic
38C4×#624—21no—
39Dic3×Dic6C2211yescharacteristic
40#63841C2211yescharacteristic
41#63836—21no—
42C2×#3718C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63659C2211yescharacteristic
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic
49#63630C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#807C2211yescharacteristic
53C3×#803C2211yescharacteristic
54#63575C2211yescharacteristic
55#63574C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63564C2211yescharacteristic
60#63554C2211yescharacteristic
61#63554C2211yescharacteristic
62C3×C4×#41—31no—
63C2×#950—31no—
64C2×#916—31no—
65C4×#239—31no—
66C4×#237D311yescharacteristic, complemented
67C4×#235—31no—
68C3×#440—31no—
69#5233—31no—
70#5164—31no—
71#5030—31no—
72#5030—31no—
73#5030—31no—
74#5026—31no—
75#5026—31no—
76#5018—31no—
77#5018D311yescharacteristic, complemented
78#5014—31no—
79#5014—31no—
80#5014—31no—
81#5014—61no—
82#5002—31no—
83#4998—31no—
84C2×#803—31no—
85#4889—31no—
86#4880—31no—
87#4804—31no—
88#4789—31no—
89#4785—31no—
90#4772—31no—
91#4710—31no—
92D3×#97—31no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C3×#237—22no—
101C3×#237C2×C414yescomplemented
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3799—22no—
111#3799C2×C414yescomplemented
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3753C2×C414yescomplemented
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#214C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3D411yescharacteristic
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3718C2×C414yescomplemented
143#3717C2×C414yescomplemented
144D3×C3⋊C8—22no—
145D3×C3⋊C8C2×C414yescomplemented
146#2943—91noSylow
147C2×C3×#41—31no—
148C2×#239—31no—
149C2×#237C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×SD16—31no—
152C3×C4×Q8—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—21no—
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—61no—
163C2×C3×C42—31no—
164C2×C3×C42—61no—
165#950—38no—
166Q8×Dic3—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#215—31no—
170D4×Dic3C2×D311yescharacteristic
171C2×#214C2×D311yescharacteristic
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—61no—
175C4×#67—21no—
176C4×#67—61no—
177C4×#67—61no—
178#926—31no—
179C2×C4×Dic3—21no—
180C22×C3⋊C8—31no—
181C22×C3⋊C8—31no—
182#916—38no—
183C2×#204—31no—
184C2×D3×C8—31no—
185C2×D3×C8—31no—
186#893—31no—
187#893—61no—
188#892—31no—
189#892—61no—
190#892C2×D311yescharacteristic
191#887C2×D311yescharacteristic
192#67⋊C4—21no—
193#877—21no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—61no—
198C4×D12—61no—
199#872—61no—
200C42×D3—61no—
201C42×D3—61no—
202C42×D3C2×D311yescharacteristic
203C4×Dic6—31no—
204C4×Dic6C2×D311yescharacteristic
205C4×Dic6C2×D311yescharacteristic
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#97—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#821—31no—
218#818—31no—
219#816—31no—
220#815—31no—
221#815—31no—
222#810—31no—
223#810—31no—
224#810C2×D311yescharacteristic
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#807—31no—
235#807C2×D311yescharacteristic
236#803—31no—
237#803—31no—
238#803—31no—
239#803—31no—
240#803—61no—
241#803C2×D311yescharacteristic
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4—42no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)C22×C412yes—
255C4×C3⋊D3—42no—
256C3×#67—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—24no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—42no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×C4×D3—41no—
267C3×C4×D3—41no—
268C3×C4×D3C22×C412yes—
269C3×C4×D3#4112yes—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273C3×Dic6C22×C412yes—
274#626—24no—
275#624—24no—
276#624—42no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282C4×#41—31no—
283C4×#41—91no—
284#442—91no—
285#442—91no—
286#441—91no—
287#441—91no—
288#440—31no—
289#440—91no—
290#440—91no—
291#440—91no—
292#427—91no—
293#416—91no—
294#416—91no—
295C2×#97—91no—
296C3×#41—34no—
297C3×#41—62no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—41no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—61no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316#239—34no—
317#239—62no—
318#237—22no—
319#237C4×D314yescomplemented
320#235—34no—
321#235—62no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—121no—
333C2×C4×D3#6711yescharacteristic
334C2×C4×D3#6711yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C2×Dic6C22×D311yescharacteristic
338C3×SD16—34no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—41no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—21no—
355C3×C42—31no—
356C3×C42—31no—
357C3×C42—31no—
358C3×C42—61no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42—61no—
362C3×C42C22×D311yescharacteristic
363C3×C42C22×D311yescharacteristic
364#217—21no—
365#217—61no—
366#216—34no—
367#216—34no—
368#215—34no—
369#214C4×D314yescomplemented
370#213—34no—
371#213—34no—
372#213—64no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—121no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—61no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3#6711yescharacteristic
399C4×Dic3#6711yescharacteristic
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—34no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—62no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—34no—
412D3×C8—34no—
413D3×C8—62no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3C4×D412yes—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4C23×C411yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3⋊Dic3—41no—
430C3×Dic3—22no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—31no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×D8—91no—
444C22×C8—91no—
445C22×C8—91no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—31no—
449C4×Q8—91no—
450C4×D4—31no—
451C4×D4—61no—
452C4×D4—61no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—181no—
456C4×D4—181no—
457C4×D4D3211yescharacteristic
458#117—31no—
459#117—61no—
460#117—91no—
461#117—181no—
462C2×C42—31no—
463C2×C42—61no—
464C2×C42—181no—
465#107—31no—
466#107—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—31no—
478#97—91no—
479#97—91no—
480#97—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—41no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3C2×#6711yescharacteristic
489C3×Q8—32no—
490C3×Q8—32no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—22no—
496C3×D4—41no—
497C3×D4—64no—
498C3×D4C2×C4×D312yes—
499C3×D4C2×C4×D312yes—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×C3×C4—64no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—82no—
519C2×C3×C4—121no—
520C2×C3×C4—121no—
521C2×C3×C4—122no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—24no—
529#67—64no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—24no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—42no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3C2×#6711yescharacteristic
540C2×Dic3C2×#6711yescharacteristic
541C2×Dic3C2×#6711yescharacteristic
542D12—32no—
543D12—32no—
544D12—62no—
545D12—64no—
546D12—61no—
547D12—61no—
548D12—121no—
549C4×D3—41no—
550C4×D3—41no—
551C4×D3—64no—
552C4×D3—64no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—242no—
558C4×D3C2×C4×D312yes—
559C4×D3#23512yes—
560Dic6—21no—
561Dic6—21no—
562Dic6C2×C4×D312yes—
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#57511yescharacteristic
577C2×C32#57511yescharacteristic
578C3⋊D3—42no—
579C3×D3—22no—
580#41—34no—
581#41—62no—
582#41—94no—
583#41—182no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×D4—61no—
587C2×D4—91no—
588C2×D4—181no—
589C2×D4C2×D3211yescharacteristic
590C22×C4—21no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599Q16—94no—
600SD16—34no—
601SD16—94no—
602D8—94no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—94no—
606C2×C8—91no—
607C2×C8—91no—
608C2×C8—182no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—21no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C42—31no—
624C42—31no—
625C42—31no—
626C42—61no—
627C42—61no—
628C42—61no—
629C42—61no—
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—81no—
645C22×C3—81no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C22×#6711yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—241no—
658C2×D3—241no—
659C2×D3C4×#6712yes—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—32no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—62no—
674C3×C4—62no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C22×C4×D311yescharacteristic
679C3×C4C22×C4×D311yescharacteristic
680C3×C4C2×#23511yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—22no—
683Dic3—22no—
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3C4×#6712yes—
692C32#294311yescharacteristic, complemented, Sylow
693C23—21no—
694C23—31no—
695C23—181no—
696Q8—32no—
697Q8—32no—
698Q8—61no—
699Q8—61no—
700D4—21no—
701D4—64no—
702D4—92no—
703D4—184no—
704D4—181no—
705D4C4×D3212yes—
706C2×C4—21no—
707C2×C4—31no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—42no—
713C2×C4—64no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—121no—
719C2×C4—121no—
720C2×C4—122no—
721C2×C4—184no—
722C2×C4—181no—
723C2×C4—362no—
724C2×C4—362no—
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×C3C4×D3×D411yescharacteristic
740C2×C3#577311yescharacteristic
741C2×C3#577711yescharacteristic
742C2×C3C2×C4×#6711yescharacteristic
743C2×C3#582211yescharacteristic
744C2×C3#582211yescharacteristic
745D3—22no—
746D3—122no—
747D3—122no—
748D3—242no—
749C22—22no—
750C22—32no—
751C22—41no—
752C22—41no—
753C22—61no—
754C22—61no—
755C22—182no—
756C22—361no—
757C22—361no—
758C22C2×D3×#6711yescharacteristic
759C4—21no—
760C4—21no—
761C4—32no—
762C4—41no—
763C4—61no—
764C4—61no—
765C4—62no—
766C4—62no—
767C4—121no—
768C4—121no—
769C4—361no—
770C4C2×C4×D3211yescharacteristic
771C4D3×#23511yescharacteristic
772C3—21no—
773C3#7977211yescharacteristic, complemented
774C3#8250611yescharacteristic, complemented
775C2—42no—
776C2—62no—
777C2—362no—
778C2C4×D3×#6711yescharacteristic
779C2#1059509511yescharacteristic
780C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63935C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2943
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
1. C3×C4×#237C2semidirect
3. C4×#3799C2semidirect
4. #10592713C2semidirect
5. C3×#5018C2semidirect
6. #10591440C2semidirect
7. #10591420C2semidirect
8. #10591404C2semidirect
9. #10590610C2semidirect
10. #10590571C2semidirect
11. #10590477C2semidirect
12. #10590457C2semidirect
13. #10590381C2semidirect
14. #10590362C2semidirect
15. D3×#803C2semidirect
34. #63935C4semidirect
66. C4×#237D3semidirect
77. #5018D3semidirect
101. C3×#237C2×C4semidirect
111. #3799C2×C4semidirect
115. #3753C2×C4semidirect
121. C3×#214C2×C4semidirect
142. #3718C2×C4semidirect
143. #3717C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
319. #237C4×D3semidirect
369. #214C4×D3semidirect
692. C32#2943semidirect
773. C3#79772semidirect
774. C3#82506semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2372
C2×#639352
C4×#37992
#105927132
C3×#50182
#105914402
#105914202
#105914042
#105906102
#105905712
#105904772
#105904572
#105903812
#105903622
D3×#8032
#825063
#797723