Finite Group Databasebeta

← #11871290

Subgroups — #11871290

Order 1152.

1042 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×D12C211yesmaximal, characteristic, complemented
2#10593968C211yesmaximal, characteristic, complemented
3#10592410C211yesmaximal, characteristic, complemented
4C3×#4711C211yesmaximal, characteristic, complemented
5C3×#4705C211yesmaximal, characteristic, complemented
6#10590947C211yesmaximal, characteristic, complemented
7#10590944C211yesmaximal, characteristic, complemented
8#10590765C211yesmaximal, characteristic, complemented
9#10590759C211yesmaximal, characteristic, complemented
10#10590757C211yesmaximal, characteristic, complemented
11#10590753C211yesmaximal, characteristic, complemented
12#10590677C211yesmaximal, characteristic, complemented
13#10590676C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590346C211yesmaximal, characteristic, complemented
16#79869—31nomaximal
17#79343—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20C2×#3798—21no—
21C2×#3745C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×D24C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic, complemented
27C3×C42×D3C2211yescharacteristic
28D3×(C2×D3)⋊C4—21no—
29#63918C2211yescharacteristic, complemented
30#63911C2211yescharacteristic, complemented
31#63909C2211yescharacteristic
32#63908C2211yescharacteristic
33#63906—21no—
34C4×#626—21no—
35C4×#626—21no—
36#63894C2211yescharacteristic
37Dic3×D12C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic
39#63880—21no—
40#63852—21no—
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#97C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic, complemented
46#63644C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×#803C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#5548—31no—
62C4×D3×D4—31no—
63#5477—31no—
64C2×C4×D12—31no—
65C3×#442—31no—
66C3×#432—31no—
67#5156—31no—
68#5150—31no—
69#5014—31no—
70#5014—31no—
71#4870—31no—
72#4863—31no—
73#4843—31no—
74#4843—31no—
75#4842—31no—
76#4842—31no—
77#4786—31no—
78#4777—31no—
79#4773—31no—
80#4761—31no—
81#4735—31no—
82#4735—31no—
83#4732—31no—
84#4732—31no—
85#4711—31no—
86#4711—31no—
87#4711—31no—
88#4711—31no—
89#4711—61no—
90#4711D311yescharacteristic, complemented
91#4705D311yescharacteristic, complemented
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3D411yescharacteristic
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625—21no—
110C2×#624—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113D3×D12—22no—
114D3×D12—22no—
115C4×D32—44no—
116#3798—44no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C42C2311yescharacteristic
120#3752—21no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3745—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4×Dic3D411yescharacteristic
130C3×C4×Dic3D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—22no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3714—22no—
142#3714—22no—
143#3109—91noSylow
144C2×D3×D4—31no—
145C2×#235—61no—
146C2×#235—61no—
147C22×D12—31no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C2×C3×D8—31no—
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153C2×C3×C42—31no—
154#940—31no—
155#938—31no—
156D4×Dic3—31no—
157C2×#213—31no—
158C2×#213—31no—
159#930—31no—
160#930—31no—
161#930—61no—
162C4×#67—61no—
163C4×#67—61no—
164C2×(C2×D3)⋊C4—61no—
165C2×C4⋊Dic3—31no—
166C2×D24—31no—
167C2×D24—31no—
168C2×D24—31no—
169C2×D24—31no—
170C2×D24—61no—
171C2×D24C2×D311yescharacteristic
172#895—31no—
173#893—31no—
174D3×C4⋊C4—31no—
175#888—31no—
176#885—61no—
177#884—61no—
178#67⋊C4—61no—
179D3×C22⋊C4—61no—
180#875—61no—
181#874—31no—
182C4×D12—31no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12—61no—
190C4×D12—61no—
191C4×D12—61no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194C4×D12C2×D311yescharacteristic, complemented
195C42×D3C2×D311yescharacteristic
196#869—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203C3×C22⋊C8—31no—
204C3×#97—21no—
205C3×#97—31no—
206C3×#97C2×D311yescharacteristic, complemented
207C3×#97C2×D311yescharacteristic, complemented
208#832—31no—
209#832—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821—61no—
220#821C2×D311yescharacteristic
221#821C2×D311yescharacteristic, complemented
222(C2×D3)⋊C8C2×D311yescharacteristic
223(C2×D3)⋊C8C2×D311yescharacteristic
224#817—31no—
225#817—31no—
226#817—31no—
227#817—31no—
228#817—61no—
229#817C2×D311yescharacteristic, complemented
230Dic3⋊C8C2×D311yescharacteristic, complemented
231Dic3⋊C8C2×D311yescharacteristic, complemented
232#809—31no—
233#809—31no—
234#808—31no—
235#808—31no—
236#803C2×D311yescharacteristic, complemented
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—24no—
243C2×D32—42no—
244C2×D32—42no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yescomplemented
254C4×C3⋊D3—42no—
255C4×C3⋊D3—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yescomplemented
265C3×C4×D3—22no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—22no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271#627—42no—
272#626—24no—
273#626—42no—
274#626—42no—
275#626—42no—
276#625—42no—
277#624—42no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280C32×C8—21no—
281C32×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—91no—
293#447—91no—
294#442—31no—
295#442—91no—
296#442—91no—
297#442—91no—
298#432—31no—
299C23×D3—61no—
300C23×D3—61no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316D3×D4—62no—
317D3×D4—62no—
318#235—124no—
319#235—124no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—62no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12C22×D311yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—121no—
345C2×C4×D3—121no—
346C2×C4×D3—124no—
347C2×C4×D3—124no—
348C2×C4×D3D1211yescharacteristic
349C2×C4×D3D1211yescharacteristic
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6—61no—
352C2×Dic6—61no—
353C3×D8—62no—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C2×C3×C8C22×D311yescharacteristic
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—21no—
367C3×C42—31no—
368C3×C42—31no—
369C3×C42—31no—
370C3×C42C22×D311yescharacteristic
371C3×C42C22×D311yescharacteristic
372#217—61no—
373#217—61no—
374#213—62no—
375#213—62no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—121no—
389(C2×D3)⋊C4—121no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402C4×Dic3D1211yescharacteristic
403C4×Dic3D1211yescharacteristic
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407D24—22no—
408D24—62no—
409D24—62no—
410D24—64no—
411D24—62no—
412D24—62no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3AGL(1,ℤ/8)12yes—
429D32—48no—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4C2×#4111yescharacteristic
433C32×C4C2×#4111yescharacteristic
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3AGL(1,ℤ/8)12yes—
441C2×#41—181no—
442C22×D4—91no—
443C23×C4—181no—
444C2×D8—31no—
445C2×D8—91no—
446C2×D8—91no—
447C2×D8—91no—
448C4⋊Q8—91no—
449#127—91no—
450#124—181no—
451#121—91no—
452#121—91no—
453#121—181no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462C4×D4—181no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465C2×C42—31no—
466#106—31no—
467#106—91no—
468#106—91no—
469#106—91no—
470C4⋊C8—31no—
471C4⋊C8—31no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8—31no—
482#97—31no—
483#97D3211yescharacteristic, complemented
484C23×C3—31no—
485C23×C3—61no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—64no—
490C22×D3—64no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—121no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3C2×D1211yescharacteristic
502C3×D4—32no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—61no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—122no—
519C2×C3×C4—122no—
520C2×C3×C4C2×D1211yescharacteristic
521C2×C3×C4C2×D1211yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—64no—
527#67—122no—
528#67—122no—
529#67—122no—
530#67—122no—
531#67—122no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3C2×D1211yescharacteristic
543C2×Dic3C2×D1211yescharacteristic
544C2×Dic3C2×D1211yescharacteristic
545D12—21no—
546D12—21no—
547D12—21no—
548D12—32no—
549D12—32no—
550D12—62no—
551D12—62no—
552D12—64no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—121no—
560D12—121no—
561D12—122no—
562D12—122no—
563D12—122no—
564D12#23512yescomplemented
565C4×D3—22no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—22no—
569C4×D3—42no—
570C4×D3—42no—
571C4×D3—122no—
572C4×D3—122no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—242no—
580C4×D3—242no—
581Dic6—122no—
582Dic6—122no—
583C3×C8—22no—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—41no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C2×C32#52511yescharacteristic
594C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
595C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
596C3⋊D3—42no—
597C3⋊D3—81no—
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—81no—
601C24—181no—
602#41—364no—
603C2×Q8—181no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—91no—
607C2×D4—91no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—182no—
612C2×D4—182no—
613C2×D4—181no—
614C2×D4—181no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4—364no—
626D8—62no—
627D8—182no—
628D8—182no—
629D8—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8C2×D3211yescharacteristic
633C2×C8C2×D3211yescharacteristic
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—91no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—31no—
650C42—31no—
651C42C2×D3211yescharacteristic
652C22×C3—21no—
653C22×C3—32no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—62no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3C22×D1211yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—122no—
675C2×D3—128no—
676C2×D3—128no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—122no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—241no—
689C2×D3—241no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3#90812yes—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—32no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—61no—
703C3×C4—61no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4C2×#23511yescharacteristic
707C3×C4D3×#4111yescharacteristic
708C3×C4D3×#4111yescharacteristic
709C3×C4D3×#4111yescharacteristic
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—241no—
719Dic3—241no—
720Dic3#90812yes—
721C32#310911yescharacteristic, complemented, Sylow
722C23—31no—
723C23—61no—
724C23—61no—
725C23—184no—
726C23—181no—
727C23—181no—
728C23—362no—
729C23—362no—
730Q8—362no—
731D4—32no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—92no—
736D4—184no—
737D4—181no—
738D4—181no—
739D4—181no—
740D4—362no—
741D4—362no—
742D4—362no—
743D4—362no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—62no—
748C2×C4—62no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—362no—
758C2×C4—362no—
759C2×C4—362no—
760C2×C4—362no—
761C2×C4—362no—
762C2×C4D3×D1211yescharacteristic
763C2×C4D3×D1211yescharacteristic
764C2×C4C22×D3211yescharacteristic
765C8—21no—
766C8—21no—
767C8—61no—
768C8—61no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—62no—
773C2×C3—122no—
774C2×C3—241no—
775C2×C3#552411yescharacteristic
776C2×C3#554711yescharacteristic
777C2×C3C2×#90811yescharacteristic
778C2×C3C2×#90811yescharacteristic
779C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
780C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
781D3—22no—
782D3—42no—
783D3—81no—
784D3—122no—
785D3—122no—
786D3—242no—
787D3—242no—
788D3—241no—
789D3—241no—
790C22—32no—
791C22—61no—
792C22—61no—
793C22—62no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—182no—
800C22—368no—
801C22—361no—
802C22—361no—
803C22—361no—
804C22—361no—
805C22—361no—
806C22C2×D3×D1211yescharacteristic
807C4—21no—
808C4—21no—
809C4—32no—
810C4—61no—
811C4—61no—
812C4—121no—
813C4—121no—
814C4—361no—
815C4—361no—
816C4D3×#23511yescharacteristic
817C4#6430611yescharacteristic
818C3—21no—
819C3#7934311yescharacteristic, complemented
820C3#7986911yescharacteristic, complemented
821C2—62no—
822C2—122no—
823C2—241no—
824C2—362no—
825C2—721no—
826C2#1059399711yescharacteristic
827C2D3×#90811yescharacteristic
828C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
hypercenter#97D32
hypocenterC32#3109
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C4×D3×D12C2semidirect
2. #10593968C2semidirect
3. #10592410C2semidirect
4. C3×#4711C2semidirect
5. C3×#4705C2semidirect
6. #10590947C2semidirect
7. #10590944C2semidirect
8. #10590765C2semidirect
9. #10590759C2semidirect
10. #10590757C2semidirect
11. #10590753C2semidirect
12. #10590677C2semidirect
13. #10590676C2semidirect
14. #10590346C2semidirect
15. #10590346C2semidirect
23. C4×C4⋊(C3⋊D3)C22semidirect
26. C3×C4×D12C22semidirect
29. #63918C22semidirect
30. #63911C22semidirect
43. C32×#97C22semidirect
45. #63648C22semidirect
46. #63644C22semidirect
48. C3×#821C22semidirect
51. C3×#817C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×#803C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
58. #63564C22semidirect
60. #63563C22semidirect
90. #4711D3semidirect
91. #4705D3semidirect
194. C4×D12C2×D3semidirect
206. C3×#97C2×D3semidirect
207. C3×#97C2×D3semidirect
221. #821C2×D3semidirect
229. #817C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
231. Dic3⋊C8C2×D3semidirect
236. #803C2×D3semidirect
253. C4⋊(C3⋊D3)#41semidirect
264. C3×D12#41semidirect
483. #97D32semidirect
564. D12#235semidirect
721. C32#3109semidirect
819. C3#79343semidirect
820. C3#79869semidirect

Maximal subgroups

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

subgroupindex
C4×D3×D122
#105939682
#105924102
C3×#47112
C3×#47052
#105909472
#105909442
#105907652
#105907592
#105907572
#105907532
#105906772
#105906762
#105903462
#798693
#793433