Finite Group Databasebeta

← #11871271

Subgroups — #11871271

Order 1152.

1075 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595139C211yesmaximal, characteristic, complemented
2D4×#624C211yesmaximal, characteristic, complemented
3#10592855C211yesmaximal, characteristic, complemented
4C3×#5152C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6#10591456C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8#10591429C211yesmaximal, characteristic, complemented
9#10591419C211yesmaximal, characteristic, complemented
10#10591408C211yesmaximal, characteristic, complemented
11#10591404C211yesmaximal, characteristic, complemented
12#10590759C211yesmaximal, characteristic, complemented
13#10590746C211yesmaximal, characteristic, complemented
14#10590665C211yesmaximal, characteristic, complemented
15#10590649C211yesmaximal, characteristic, complemented
16#80314—31nomaximal
17#79869—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C22×#624—21no—
20C2×#3804—21no—
21C2×C32×D8C2211yescharacteristic
22#64147C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24C3×#940C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29#63974—21no—
30Dic3×#67—21no—
31#63959—21no—
32#63958—21no—
33#63952—21no—
34#63952—21no—
35#63918C2211yescharacteristic, complemented
36#63916C2211yescharacteristic
37#63900C2211yescharacteristic
38#63894C2211yescharacteristic
39#63894C2211yescharacteristic
40Dic3×D12C2211yescharacteristic, complemented
41C4×#624C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45#63647C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5716—31no—
62#5548—31no—
63C4×D3×D4—31no—
64C4×D3×D4—31no—
65C3×#459—31no—
66C3×#442—31no—
67#5156—31no—
68#5156—31no—
69#5156—31no—
70#5156—61no—
71#5152—31no—
72#5152D311yescharacteristic, complemented
73#5150D311yescharacteristic, complemented
74#5072—31no—
75#5014—31no—
76#5014—31no—
77#5008—31no—
78#4870—31no—
79#4863—31no—
80#4842—31no—
81#4835—31no—
82#4786—31no—
83#4785—31no—
84#4785—31no—
85#4777—31no—
86#4777—31no—
87#4777—31no—
88#4773—31no—
89#4761—31no—
90#4711—31no—
91#4705—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97D4×C3⋊D3—22no—
98D4×C3⋊D3—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C22×C3×Dic3—21no—
106C2×C3×D12C2311yescharacteristic
107C2×#627—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×#624—21no—
111C2×#624—21no—
112C2×#624—44no—
113C2×#624D411yescharacteristic
114C2×#624D411yescharacteristic
115#3804—44no—
116C2×D3×Dic3—21no—
117C32×D8—22no—
118C2×C32×C8C2311yescharacteristic
119#3757—21no—
120#3753—22no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#217—21no—
125C3×#217—21no—
126C3×#213—22no—
127C3×C4⋊Dic3C2311yescharacteristic
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
144C2×#237—61no—
145C2×D3×D4—31no—
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×#235—61no—
149C22×C4×D3—61no—
150C22×C4×D3—61no—
151C2×C3×D8—21no—
152C2×C3×D8—31no—
153C2×C3×D8C2×D311yescharacteristic
154C2×C3×D8C2×D311yescharacteristic
155C3×#127—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159#940C2×D311yescharacteristic, complemented
160#938—31no—
161#938—31no—
162#938—31no—
163#938—61no—
164#938—61no—
165#936—61no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168D4×Dic3C2×D311yescharacteristic
169D4×Dic3C2×D311yescharacteristic
170D4×Dic3C2×D311yescharacteristic, complemented
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—61no—
175C2×#213C2×D311yescharacteristic
176C4×#67—61no—
177C4×#67—61no—
178C4×#67—61no—
179C2×D24—31no—
180#895—31no—
181#893—31no—
182#893—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185#888—31no—
186#885—61no—
187#884—61no—
188#67⋊C4—61no—
189#67⋊C4—61no—
190D3×C22⋊C4—61no—
191D3×C22⋊C4—61no—
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—31no—
195C42×D3—31no—
196C42×D3—31no—
197#869—31no—
198C3×#106—31no—
199C3×C4⋊C8—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#97—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#832C2×D311yescharacteristic
210#832C2×D311yescharacteristic, complemented
211#832C2×D311yescharacteristic, complemented
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821C2×D311yescharacteristic, complemented
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222#817—31no—
223#817—31no—
224#817C2×D311yescharacteristic, complemented
225#815—31no—
226#815C2×D311yescharacteristic, complemented
227Dic3⋊C8—31no—
228Dic3⋊C8C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235C4⋊(C3⋊C8)—31no—
236#803—31no—
237C23×C32—21no—
238C23×C32—21no—
239C22×C3⋊D3—24no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4#4112yescomplemented
249C2×C32×C4C2411yescharacteristic
250#638—24no—
251#638—42no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)#4112yescomplemented
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C3×#67—42no—
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×Dic3—42no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272#627—42no—
273#626—42no—
274#624—22no—
275#624—22no—
276#624—42no—
277#624—42no—
278#624—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—31no—
291#459—91no—
292#447—91no—
293#447—91no—
294#442—31no—
295#442—91no—
296#442—91no—
297#442—91no—
298#432—91no—
299C23×D3—61no—
300C23×D3—61no—
301C23×D3—121no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C2×#67—21no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—121no—
322C2×#67—121no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—61no—
327#237—124no—
328D3×D4—62no—
329D3×D4—62no—
330D3×D4—62no—
331D3×D4—62no—
332D3×D4—122no—
333D3×D4—122no—
334#235—124no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—61no—
338C2×D12—61no—
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—31no—
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—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—124no—
355C2×C4×D3—124no—
356C2×Dic6—61no—
357C2×Dic6—61no—
358C3×D8—22no—
359C3×D8—22no—
360C3×D8—42no—
361C3×D8—62no—
362C2×C3×C8—21no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8C22×D311yescharacteristic
366C2×C3×C8C22×D311yescharacteristic
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—31no—
374C3×C42—31no—
375#217—21no—
376#217—21no—
377#217—21no—
378#217—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—121no—
383#213—22no—
384#213—62no—
385#213—62no—
386#213—62no—
387#213—122no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3C22×D311yescharacteristic
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415D24—62no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—22no—
426C2×C3⋊D3—48no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3AGL(1,ℤ/8)12yes—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3AGL(1,ℤ/8)12yes—
444C2×#41—181no—
445C22×D4—91no—
446C23×C4—181no—
447C2×D8—31no—
448C2×D8—91no—
449C2×D8—91no—
450C2×D8D3211yescharacteristic
451C4⋊Q8—91no—
452#127—31no—
453#124—181no—
454#121—91no—
455#121—91no—
456#121—181no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—181no—
464C4×D4—181no—
465C4×D4—181no—
466C2×C4⋊C4—91no—
467C2×C22⋊C4—181no—
468C2×C42—91no—
469#106—31no—
470#106—91no—
471#106—91no—
472#106—91no—
473C4⋊C8—31no—
474C4⋊C8—91no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483C22⋊C8—91no—
484C22⋊C8—91no—
485#97—31no—
486#97—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—31no—
496C22×D3—31no—
497C22×D3—61no—
498C22×D3—64no—
499C22×D3—64no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—121no—
503C22×D3—124no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—242no—
509C22×D3—242no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—22no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—122no—
523C3×D4—122no—
524C3×D4#23512yescomplemented
525C3×D4#23712yescomplemented
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536C2×C3×C4—122no—
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—42no—
540#67—42no—
541#67—64no—
542#67—64no—
543#67—124no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—242no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—42no—
554C2×Dic3—42no—
555C2×Dic3—42no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—122no—
561C2×Dic3D3×D411yescharacteristic
562C2×Dic3D3×D411yescharacteristic
563C2×Dic3D3×D411yescharacteristic
564C2×Dic3D3×D411yescharacteristic
565D12—21no—
566D12—21no—
567D12—32no—
568D12—32no—
569D12—62no—
570D12—61no—
571D12—61no—
572D12—121no—
573D12—122no—
574C4×D3—62no—
575C4×D3—62no—
576C4×D3—62no—
577C4×D3—61no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—62no—
582C4×D3—121no—
583C4×D3—121no—
584C4×D3—122no—
585C4×D3—122no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—122no—
589C4×D3—122no—
590C4×D3—122no—
591Dic6—122no—
592Dic6—122no—
593C3×C8—21no—
594C3×C8—21no—
595C3×C8—41no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—121no—
603C2×C32—42no—
604C2×C32—81no—
605C2×C32#52511yescharacteristic
606C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
607C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
608C3⋊D3—22no—
609C3⋊D3—42no—
610C3×D3—81no—
611C24—181no—
612#41—364no—
613C2×Q8—181no—
614C2×D4—31no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—91no—
618C2×D4—181no—
619C2×D4—181no—
620C2×D4—182no—
621C2×D4—182no—
622C2×D4—181no—
623C2×D4C2×D3211yescharacteristic
624C2×D4C2×D3211yescharacteristic
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—181no—
632C22×C4—181no—
633C22×C4—181no—
634C22×C4—181no—
635C22×C4—364no—
636D8—22no—
637D8—62no—
638D8—182no—
639D8—182no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8C2×D3211yescharacteristic
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—91no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C42—31no—
659C42—31no—
660C42—91no—
661C42—91no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—21no—
665C22×C3—42no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3C2×D3×D411yescharacteristic
685C22×C3C2×D3×D411yescharacteristic
686C2×D3—32no—
687C2×D3—32no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—62no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—62no—
697C2×D3—62no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—122no—
701C2×D3—128no—
702C2×D3—128no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—248no—
708C2×D3—241no—
709C2×D3—241no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—32no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4C2×#23511yescharacteristic
720C3×C4C2×#23711yescharacteristic
721C3×C4D3×#4111yescharacteristic
722C3×C4D3×#4111yescharacteristic
723Dic3—21no—
724Dic3—21no—
725Dic3—21no—
726Dic3—41no—
727Dic3—41no—
728Dic3—41no—
729Dic3—61no—
730Dic3—61no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—241no—
735Dic3#91112yes—
736C32#310911yescharacteristic, complemented, Sylow
737C23—21no—
738C23—21no—
739C23—61no—
740C23—91no—
741C23—184no—
742C23—181no—
743C23—362no—
744C23—362no—
745Q8—362no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—61no—
750D4—61no—
751D4—92no—
752D4—122no—
753D4—122no—
754D4—184no—
755D4—181no—
756D4—362no—
757D4—362no—
758D4#380412yescomplemented
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—31no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—91no—
767C2×C4—122no—
768C2×C4—122no—
769C2×C4—122no—
770C2×C4—182no—
771C2×C4—182no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—362no—
776C2×C4—362no—
777C2×C4—362no—
778C2×C4—362no—
779C2×C4C22×D3211yescharacteristic
780C8—21no—
781C8—61no—
782C8—61no—
783C8—181no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—42no—
788C2×C3—42no—
789C2×C3—82no—
790C2×C3—81no—
791C2×C3—81no—
792C2×C3—161no—
793C2×C3—241no—
794C2×C3#554711yescharacteristic
795C2×C3#560611yescharacteristic
796C2×C3C2×#91111yescharacteristic
797C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
798C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
799C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
800D3—62no—
801D3—62no—
802D3—81no—
803D3—122no—
804D3—122no—
805D3—122no—
806D3—242no—
807C22—22no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—92no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—181no—
818C22—181no—
819C22—182no—
820C22—368no—
821C22—361no—
822C22—361no—
823C22D32×D411yescharacteristic
824C4—32no—
825C4—61no—
826C4—61no—
827C4—61no—
828C4—121no—
829C4—121no—
830C4—121no—
831C4—181no—
832C4—361no—
833C4#6431211yescharacteristic
834C4C2×#380411yescharacteristic
835C3—21no—
836C3#7986911yescharacteristic, complemented
837C3#8031411yescharacteristic, complemented
838C2—42no—
839C2—81no—
840C2—182no—
841C2—241no—
842C2—362no—
843C2D3×#91111yescharacteristic
844C2#1059472611yescharacteristic
845C2#1059513811yescharacteristic
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. #10595139C2semidirect
2. D4×#624C2semidirect
3. #10592855C2semidirect
4. C3×#5152C2semidirect
5. C3×#5150C2semidirect
6. #10591456C2semidirect
7. #10591430C2semidirect
8. #10591429C2semidirect
9. #10591419C2semidirect
10. #10591408C2semidirect
11. #10591404C2semidirect
12. #10590759C2semidirect
13. #10590746C2semidirect
14. #10590665C2semidirect
15. #10590649C2semidirect
24. C3×#940C22semidirect
27. C3×D4×Dic3C22semidirect
35. #63918C22semidirect
40. Dic3×D12C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#821C22semidirect
50. C3×#817C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
60. #63554C22semidirect
72. #5152D3semidirect
73. #5150D3semidirect
159. #940C2×D3semidirect
170. D4×Dic3C2×D3semidirect
210. #832C2×D3semidirect
211. #832C2×D3semidirect
216. #821C2×D3semidirect
224. #817C2×D3semidirect
226. #815C2×D3semidirect
228. Dic3⋊C8C2×D3semidirect
248. C32×D4#41semidirect
255. C4⋊(C3⋊D3)#41semidirect
524. C3×D4#235semidirect
525. C3×D4#237semidirect
736. C32#3109semidirect
758. D4#3804semidirect
836. C3#79869semidirect
837. C3#80314semidirect

Maximal subgroups

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

subgroupindex
#105951392
D4×#6242
#105928552
C3×#51522
C3×#51502
#105914562
#105914302
#105914292
#105914192
#105914082
#105914042
#105907592
#105907462
#105906652
#105906492
#803143
#798693