Finite Group Databasebeta

← #11871273

Subgroups — #11871273

Order 1152.

1046 conjugacy classes of subgroups.

The subgroup lattice has 837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595131C211yesmaximal, characteristic, complemented
2D3×D4×Dic3C211yesmaximal, characteristic, complemented
3#10592849C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5152C211yesmaximal, characteristic, complemented
6#10591495C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9#10591430C211yesmaximal, characteristic, complemented
10#10591415C211yesmaximal, characteristic, complemented
11#10591404C211yesmaximal, characteristic, complemented
12#10590776C211yesmaximal, characteristic, complemented
13#10590746C211yesmaximal, characteristic, complemented
14#10590677C211yesmaximal, characteristic, complemented
15#10590660C211yesmaximal, characteristic, complemented
16#79990—31nomaximal
17#79869—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3804—21no—
20C22×D3×Dic3—21no—
21C2×C32×D8C2211yescharacteristic
22#64149C2211yescharacteristic, complemented
23D4×C3⋊Dic3C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31#63971—21no—
32D3×#217—21no—
33#63953—21no—
34#63952—21no—
35#63919C2211yescharacteristic, complemented
36#63909C2211yescharacteristic
37#63898C2211yescharacteristic
38#63894C2211yescharacteristic, complemented
39Dic3×D12C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41C4×D3×Dic3C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63659C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61C2×D4×Dic3—31no—
62#5596—31no—
63#5548—31no—
64C4×D3×D4—31no—
65C3×#447—31no—
66C3×#442—31no—
67#5217—31no—
68#5156D311yescharacteristic, complemented
69#5152—31no—
70#5152D311yescharacteristic, complemented
71#5150—31no—
72#5150—31no—
73#5150—31no—
74#5150—61no—
75#5034—31no—
76#5014—31no—
77#5014—31no—
78#4870—31no—
79#4863—31no—
80#4786—31no—
81#4785—31no—
82#4785—31no—
83#4777—31no—
84#4773—31no—
85#4761—31no—
86#4761—31no—
87#4761—31no—
88#4735—31no—
89#4719—31no—
90#4711—31no—
91#4705—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#627—21no—
108C2×#626—21no—
109C2×#624—21no—
110#3804—44no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—44no—
115C2×D3×Dic3D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117C32×D8—22no—
118C2×C32×C8C2311yescharacteristic
119#3757—21no—
120#3753—22no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4×C3⋊Dic3C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#217—21no—
125C3×#217—21no—
126C3×#217—21no—
127C3×#213—22no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32D411yescharacteristic
141Dic32D411yescharacteristic
142#3714—22no—
143#3109—91noSylow
144C22×C3×D4—31no—
145C23×Dic3—61no—
146C2×#237—61no—
147C2×D3×D4C2×D311yescharacteristic
148C2×#235—61no—
149C22×C4×D3—61no—
150C2×C3×D8—21no—
151C2×C3×D8—31no—
152C2×C3×D8C2×D311yescharacteristic
153C2×C3×D8C2×D311yescharacteristic
154C3×#121—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C2×#217—61no—
158#940—31no—
159#940—31no—
160#940—61no—
161#939—61no—
162#938C2×D311yescharacteristic
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170D4×Dic3C2×D311yescharacteristic
171D4×Dic3C2×D311yescharacteristic, complemented
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—61no—
176C2×#213C2×D311yescharacteristic
177#930—31no—
178C4×#67—61no—
179C4×#67—61no—
180C2×C4⋊Dic3—31no—
181C2×C4×Dic3—31no—
182C2×D24—31no—
183#895—31no—
184#893—31no—
185#893—31no—
186D3×C4⋊C4—31no—
187#888—31no—
188#888—31no—
189#885—61no—
190#885—61no—
191#884—61no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195C4×D12—31no—
196C4×D12—31no—
197C42×D3—31no—
198C3×#106—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204C3×#97—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#832C2×D311yescharacteristic
210#832C2×D311yescharacteristic
211#832C2×D311yescharacteristic, complemented
212#830—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#817—31no—
221#817—31no—
222#817C2×D311yescharacteristic, complemented
223#815—31no—
224#815C2×D311yescharacteristic, complemented
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—61no—
230#809—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236#803—31no—
237C23×C32—21no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—24no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4#4112yescomplemented
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251#638—42no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—42no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C3×#67—24no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12#4112yescomplemented
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272#627—42no—
273#626—42no—
274#624—42no—
275D3×Dic3—22no—
276D3×Dic3—22no—
277D3×Dic3—42no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280C32×C8—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—91no—
286#481—91no—
287#481—91no—
288#476—91no—
289#476—91no—
290#459—91no—
291#459—91no—
292#447—31no—
293#447—91no—
294#442—31no—
295#442—91no—
296#442—91no—
297#442—91no—
298#432—91no—
299C24×C3—61no—
300C23×D3—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C2×C3×D4—62no—
306C2×C3×D4—62no—
307C2×C3×D4—61no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—121no—
323C2×#67—121no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—121no—
334C22×Dic3—124no—
335#237—124no—
336D3×D4—22no—
337D3×D4—22no—
338#235—124no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12C22×D311yescharacteristic
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—124no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—61no—
354C2×Dic6—61no—
355C3×D8—22no—
356C3×D8—22no—
357C3×D8—42no—
358C3×D8—62no—
359C2×C3×C8—21no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8C22×D311yescharacteristic
363C2×C3×C8C22×D311yescharacteristic
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—31no—
371#217—21no—
372#217—21no—
373#217—21no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—121no—
379#213—22no—
380#213—62no—
381#213—62no—
382#213—62no—
383#213—122no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—61no—
407C4×Dic3C22×D311yescharacteristic
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D24—62no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—48no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3AGL(1,ℤ/8)12yes—
431C32×C4C2×#4111yescharacteristic
432C32×C4C2×#4111yescharacteristic
433C3⋊Dic3—21no—
434C3⋊Dic3—41no—
435C3⋊Dic3AGL(1,ℤ/8)12yes—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—181no—
443C22×D4—31no—
444C23×C4—181no—
445C2×D8—31no—
446C2×D8—91no—
447C2×D8—91no—
448C2×D8D3211yescharacteristic
449C4⋊Q8—91no—
450#127—91no—
451#124—181no—
452#121—31no—
453#121—91no—
454#121—181no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463C4×D4—181no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466C2×C42—91no—
467#106—31no—
468#106—91no—
469#106—91no—
470#106—91no—
471C4⋊C8—91no—
472C4⋊C8—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—31no—
482C22⋊C8—91no—
483#97—31no—
484#97—91no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—64no—
493C23×C3—61no—
494C23×C3—122no—
495C23×C3—122no—
496C22×D3—24no—
497C22×D3—21no—
498C22×D3—42no—
499C22×D3—42no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—121no—
503C22×D3D3×D411yescharacteristic
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—22no—
511C3×D4—32no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—64no—
516C3×D4—61no—
517C3×D4—122no—
518C3×D4#23512yescomplemented
519C3×D4#23712yescomplemented
520C2×C3×C4—21no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—24no—
534#67—42no—
535#67—122no—
536#67—122no—
537#67—122no—
538#67—122no—
539#67—122no—
540#67—242no—
541#67—242no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—42no—
550C2×Dic3—42no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—121no—
558C2×Dic3—122no—
559C2×Dic3—122no—
560C2×Dic3—122no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—242no—
564C2×Dic3D3×D411yescharacteristic
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567D12—21no—
568D12—61no—
569D12—61no—
570D12—61no—
571D12—61no—
572D12—121no—
573D12—121no—
574D12—122no—
575D12#23712yescomplemented
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—62no—
579C4×D3—62no—
580C4×D3—122no—
581C4×D3—122no—
582C4×D3—122no—
583C4×D3—122no—
584C4×D3—122no—
585Dic6—122no—
586Dic6—122no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—41no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—121no—
597C2×C32—42no—
598C2×C32—81no—
599C2×C32#52511yescharacteristic
600C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C3⋊D3—81no—
603C3×D3—22no—
604C3×D3—42no—
605C24—61no—
606#41—364no—
607C2×Q8—181no—
608C2×D4—31no—
609C2×D4—61no—
610C2×D4—62no—
611C2×D4—62no—
612C2×D4—61no—
613C2×D4—91no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4C2×D3211yescharacteristic
618C2×D4C2×D3211yescharacteristic
619C22×C4—31no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—91no—
623C22×C4—91no—
624C22×C4—181no—
625C22×C4—181no—
626C22×C4—181no—
627C22×C4—181no—
628C22×C4—181no—
629C22×C4—364no—
630D8—22no—
631D8—62no—
632D8—182no—
633D8—182no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—91no—
637C2×C8C2×D3211yescharacteristic
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—91no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C42—31no—
653C42—91no—
654C42—91no—
655C42—91no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—21no—
659C22×C3—32no—
660C22×C3—42no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—61no—
672C22×C3—61no—
673C22×C3—62no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—128no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3C2×D3×D411yescharacteristic
683C22×C3C2×D3×D411yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—22no—
687C2×D3—48no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3—241no—
699C2×D3#91112yes—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—61no—
703C3×C4—61no—
704C3×C4—61no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4C2×#23511yescharacteristic
709C3×C4C2×#23711yescharacteristic
710C3×C4C2×#23711yescharacteristic
711C3×C4D3×#4111yescharacteristic
712Dic3—21no—
713Dic3—21no—
714Dic3—21no—
715Dic3—32no—
716Dic3—32no—
717Dic3—41no—
718Dic3—41no—
719Dic3—41no—
720Dic3—62no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—241no—
727C32#310911yescharacteristic, complemented, Sylow
728C23—21no—
729C23—21no—
730C23—31no—
731C23—64no—
732C23—61no—
733C23—122no—
734C23—122no—
735C23—181no—
736Q8—362no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—32no—
741D4—64no—
742D4—61no—
743D4—122no—
744D4—181no—
745D4—181no—
746D4—362no—
747D4—362no—
748D4—362no—
749D4#380412yescomplemented
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—91no—
759C2×C4—91no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—182no—
763C2×C4—182no—
764C2×C4—181no—
765C2×C4—362no—
766C2×C4—362no—
767C2×C4—362no—
768C2×C4—362no—
769C2×C4—362no—
770C2×C4C22×D3211yescharacteristic
771C8—21no—
772C8—61no—
773C8—61no—
774C8—181no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—42no—
779C2×C3—42no—
780C2×C3—62no—
781C2×C3—82no—
782C2×C3—81no—
783C2×C3—81no—
784C2×C3—122no—
785C2×C3—161no—
786C2×C3#554711yescharacteristic
787C2×C3#558611yescharacteristic
788C2×C3C2×#91111yescharacteristic
789C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
790C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
791C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
792D3—22no—
793D3—42no—
794D3—241no—
795D3—241no—
796D3—481no—
797C22—22no—
798C22—32no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—61no—
805C22—61no—
806C22—62no—
807C22—128no—
808C22—121no—
809C22—121no—
810C22—361no—
811C22—361no—
812C22—361no—
813C22D32×D411yescharacteristic
814C4—61no—
815C4—61no—
816C4—61no—
817C4—92no—
818C4—121no—
819C4—121no—
820C4—121no—
821C4—181no—
822C4—361no—
823C4D3×#23711yescharacteristic
824C4C2×#380411yescharacteristic
825C3—21no—
826C3#7986911yescharacteristic, complemented
827C3#7999011yescharacteristic, complemented
828C2—42no—
829C2—62no—
830C2—81no—
831C2—122no—
832C2—721no—
833C2D3×#91111yescharacteristic
834C2#1059472611yescharacteristic
835C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3109
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595131C2semidirect
2. D3×D4×Dic3C2semidirect
3. #10592849C2semidirect
4. C3×#5156C2semidirect
5. C3×#5152C2semidirect
6. #10591495C2semidirect
7. #10591448C2semidirect
8. #10591433C2semidirect
9. #10591430C2semidirect
10. #10591415C2semidirect
11. #10591404C2semidirect
12. #10590776C2semidirect
13. #10590746C2semidirect
14. #10590677C2semidirect
15. #10590660C2semidirect
22. #64149C22semidirect
27. C3×D4×Dic3C22semidirect
35. #63919C22semidirect
38. #63894C22semidirect
43. #63659C22semidirect
44. #63648C22semidirect
45. #63641C22semidirect
48. C3×#832C22semidirect
51. C3×#817C22semidirect
52. C3×#815C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63564C22semidirect
60. #63554C22semidirect
68. #5156D3semidirect
70. #5152D3semidirect
171. D4×Dic3C2×D3semidirect
211. #832C2×D3semidirect
222. #817C2×D3semidirect
224. #815C2×D3semidirect
248. C32×D4#41semidirect
269. C3×D12#41semidirect
518. C3×D4#235semidirect
519. C3×D4#237semidirect
575. D12#237semidirect
727. C32#3109semidirect
749. D4#3804semidirect
826. C3#79869semidirect
827. C3#79990semidirect

Maximal subgroups

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

subgroupindex
#105951312
D3×D4×Dic32
#105928492
C3×#51562
C3×#51522
#105914952
#105914482
#105914332
#105914302
#105914152
#105914042
#105907762
#105907462
#105906772
#105906602
#799903
#798693