Finite Group Databasebeta

← #11871278

Subgroups — #11871278

Order 1152.

1030 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×D4×Dic3C211yesmaximal, characteristic, complemented
2#10594367C211yesmaximal, characteristic, complemented
3#10592460C211yesmaximal, characteristic, complemented
4C3×#4785C211yesmaximal, characteristic, complemented
5C3×#4773C211yesmaximal, characteristic, complemented
6#10591486C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic, complemented
8#10591430C211yesmaximal, characteristic, complemented
9#10590771C211yesmaximal, characteristic, complemented
10#10590749C211yesmaximal, characteristic, complemented
11#10590676C211yesmaximal, characteristic, complemented
12#10590660C211yesmaximal, characteristic, complemented
13#10590472C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590441C211yesmaximal, characteristic, complemented
16#79990—31nomaximal
17#79869—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×D3×Dic3—21no—
20C2×#3795—21no—
21D4×C3⋊Dic3C2211yescharacteristic
22#64097C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×#893C2211yescharacteristic, complemented
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31D3×#217—21no—
32#63914C2211yescharacteristic, complemented
33#63913—21no—
34#63908C2211yescharacteristic
35#63898C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37Dic3×D12C2211yescharacteristic, complemented
38D3×C4⋊Dic3C2211yescharacteristic
39#63885—21no—
40#63879—21no—
41C4×D3×Dic3C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63659C2211yescharacteristic
45#63644C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#815C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
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#5156—31no—
69#5152—31no—
70#5152—31no—
71#5150—31no—
72#5150—31no—
73#5150—31no—
74#5034—31no—
75#5014—31no—
76#5014—31no—
77#4870—31no—
78#4863—31no—
79#4786—31no—
80#4785—31no—
81#4785D311yescharacteristic, complemented
82#4777—31no—
83#4773D311yescharacteristic, complemented
84#4761—31no—
85#4761—31no—
86#4761—31no—
87#4761—61no—
88#4735—31no—
89#4719—31no—
90#4711—31no—
91#4705—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#625—21no—
107C2×#625—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—44no—
114C2×D3×Dic3D411yescharacteristic
115C2×D3×Dic3D411yescharacteristic
116#3795—44no—
117C2×C32×C8C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3757—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#213—22no—
127C3×#213—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D24—22no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32D411yescharacteristic
141Dic32D411yescharacteristic
142#3713—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—31no—
151C2×C3×D8—31no—
152C2×C3×D8—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C2×#217—61no—
157#940—31no—
158#940—31no—
159#939—61no—
160#938—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#213—31no—
171C2×#213—31no—
172C2×#213C2×D311yescharacteristic
173C2×#213C2×D311yescharacteristic
174#930—31no—
175C4×#67—61no—
176C4×#67—61no—
177C2×C4⋊Dic3—31no—
178C2×C4×Dic3—31no—
179C2×D24C2×D311yescharacteristic
180#895C2×D311yescharacteristic
181#893—31no—
182#893C2×D311yescharacteristic, complemented
183D3×C4⋊C4—31no—
184#888—31no—
185#888—31no—
186#888—61no—
187#885—61no—
188#885—61no—
189#884—61no—
190#67⋊C4—61no—
191#67⋊C4—61no—
192D3×C22⋊C4—61no—
193C4×D12—31no—
194C4×D12—31no—
195C42×D3—31no—
196C3×#106—31no—
197C3×#102—21no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102C2×D311yescharacteristic
201C3×#102C2×D311yescharacteristic
202C3×C22⋊C8—31no—
203C3×#97—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—61no—
211#830—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821C2×D311yescharacteristic, complemented
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#817—31no—
219#817—31no—
220#817—31no—
221#817—61no—
222#815—31no—
223#815C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—61no—
229#809—31no—
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808C2×D311yescharacteristic, complemented
236#803—31no—
237C23×C32—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yescomplemented
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—42no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254#634—42no—
255C3×#67—24no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—42no—
267C3×D12#4112yescomplemented
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271#625—42no—
272#625—42no—
273#625—42no—
274D3×Dic3—22no—
275D3×Dic3—22no—
276D3×Dic3—42no—
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—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—62no—
308C2×C3×D4—62no—
309C2×C3×D4C22×D311yescharacteristic
310C2×C3×D4C22×D311yescharacteristic
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C22×Dic3—21no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—121no—
331C22×Dic3—124no—
332#237—124no—
333D3×D4—22no—
334D3×D4—22no—
335#235—124no—
336C2×D12—21no—
337C2×D12C22×D311yescharacteristic
338C2×D12C22×D311yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—124no—
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—61no—
350C2×Dic6—61no—
351C2×Dic6—121no—
352C3×D8—62no—
353C3×D8—62no—
354C3×D8—62no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368#217—21no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—121no—
376#213—22no—
377#213—22no—
378#213—62no—
379#213—62no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—22no—
412C22×C32—22no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—48no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
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—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3⋊Dic3AGL(1,ℤ/8)12yes—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C2×#41—181no—
441C22×D4—31no—
442C23×C4—181no—
443C2×D8—31no—
444C2×D8—31no—
445C2×D8—31no—
446C2×D8—91no—
447C4⋊Q8—91no—
448#127—91no—
449#124—181no—
450#121—31no—
451#121—91no—
452#121—181no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—181no—
460C4×D4—181no—
461C4×D4—181no—
462C2×C4⋊C4—91no—
463C2×C22⋊C4—181no—
464C2×C42—91no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469C4⋊C8—91no—
470C4⋊C8—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102D3211yescharacteristic
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—31no—
482#97—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—41no—
487C23×C3—64no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—122no—
492C23×C3—122no—
493C22×D3—24no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—42no—
498C22×D3—42no—
499C22×D3D3×D411yescharacteristic
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—22no—
503C3×D4—32no—
504C3×D4—41no—
505C3×D4—64no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—122no—
512C3×D4#23512yescomplemented
513C3×D4#23712yescomplemented
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—24no—
529#67—122no—
530#67—122no—
531#67—122no—
532#67—122no—
533#67—122no—
534#67—122no—
535C2×Dic3—21no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—42no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—122no—
552C2×Dic3—122no—
553C2×Dic3—122no—
554C2×Dic3—122no—
555C2×Dic3—122no—
556C2×Dic3—122no—
557C2×Dic3—242no—
558C2×Dic3D3×D411yescharacteristic
559C2×Dic3D3×D411yescharacteristic
560C2×Dic3D3×D411yescharacteristic
561D12—21no—
562D12—21no—
563D12—21no—
564D12—21no—
565D12—21no—
566D12—42no—
567D12#23712yescomplemented
568C4×D3—21no—
569C4×D3—21no—
570C4×D3—42no—
571C4×D3—62no—
572C4×D3—62no—
573C4×D3—122no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577Dic6—122no—
578Dic6—122no—
579Dic6—242no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—41no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—121no—
590C2×C32—42no—
591C2×C32#52511yescharacteristic
592C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
593C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
594C3×D3—22no—
595C3×D3—42no—
596C3×D3—81no—
597C3×D3—81no—
598C24—61no—
599#41—364no—
600C2×Q8—181no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—62no—
607C2×D4—62no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4C2×D3211yescharacteristic
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—364no—
623D8—62no—
624D8—62no—
625D8—62no—
626D8—182no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—91no—
630C2×C8C2×D3211yescharacteristic
631C4⋊C4—31no—
632C4⋊C4—91no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C42—31no—
646C42—91no—
647C42—91no—
648C42—91no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—42no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—62no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—128no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C2×D3×D411yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—22no—
677C2×D3—48no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3#91112yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—81no—
695C3×C4—121no—
696C3×C4C2×#23511yescharacteristic
697C3×C4C2×#23711yescharacteristic
698C3×C4C2×#23711yescharacteristic
699C3×C4D3×#4111yescharacteristic
700Dic3—21no—
701Dic3—21no—
702Dic3—21no—
703Dic3—32no—
704Dic3—32no—
705Dic3—41no—
706Dic3—62no—
707Dic3—61no—
708Dic3—61no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—121no—
714Dic3—241no—
715Dic3—241no—
716C32#310911yescharacteristic, complemented, Sylow
717C23—21no—
718C23—31no—
719C23—64no—
720C23—61no—
721C23—61no—
722C23—61no—
723C23—122no—
724C23—122no—
725Q8—362no—
726D4—21no—
727D4—32no—
728D4—64no—
729D4—61no—
730D4—61no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—122no—
735D4—362no—
736D4—362no—
737D4—362no—
738D4#379512yescomplemented
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—91no—
747C2×C4—91no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—182no—
751C2×C4—182no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—362no—
755C2×C4—362no—
756C2×C4—362no—
757C2×C4—362no—
758C2×C4—362no—
759C2×C4C22×D3211yescharacteristic
760C8—21no—
761C8—61no—
762C8—61no—
763C8—181no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—42no—
768C2×C3—42no—
769C2×C3—62no—
770C2×C3—82no—
771C2×C3—122no—
772C2×C3—241no—
773C2×C3—241no—
774C2×C3#554711yescharacteristic
775C2×C3#558611yescharacteristic
776C2×C3C2×#91111yescharacteristic
777C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
778C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
779C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
780D3—22no—
781D3—42no—
782D3—81no—
783D3—81no—
784C22—22no—
785C22—32no—
786C22—41no—
787C22—41no—
788C22—61no—
789C22—61no—
790C22—62no—
791C22—128no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22D32×D411yescharacteristic
801C4—41no—
802C4—61no—
803C4—61no—
804C4—61no—
805C4—92no—
806C4—121no—
807C4—181no—
808C4—361no—
809C4—361no—
810C4C2×#379511yescharacteristic
811C4D3×#23711yescharacteristic
812C3—21no—
813C3#7986911yescharacteristic, complemented
814C3#7999011yescharacteristic, complemented
815C2—42no—
816C2—62no—
817C2—122no—
818C2—241no—
819C2—241no—
820C2#1059405411yescharacteristic
821C2D3×#91111yescharacteristic
822C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3109
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D3×D4×Dic3C2semidirect
2. #10594367C2semidirect
3. #10592460C2semidirect
4. C3×#4785C2semidirect
5. C3×#4773C2semidirect
6. #10591486C2semidirect
7. #10591447C2semidirect
8. #10591430C2semidirect
9. #10590771C2semidirect
10. #10590749C2semidirect
11. #10590676C2semidirect
12. #10590660C2semidirect
13. #10590472C2semidirect
14. #10590455C2semidirect
15. #10590441C2semidirect
22. #64097C22semidirect
28. C3×#893C22semidirect
32. #63914C22semidirect
37. Dic3×D12C22semidirect
45. #63644C22semidirect
46. #63641C22semidirect
47. #63635C22semidirect
48. C3×#821C22semidirect
50. C3×#815C22semidirect
52. C3×#808C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
60. #63554C22semidirect
81. #4785D3semidirect
83. #4773D3semidirect
182. #893C2×D3semidirect
215. #821C2×D3semidirect
223. #815C2×D3semidirect
235. #808C2×D3semidirect
246. C32×D4#41semidirect
267. C3×D12#41semidirect
512. C3×D4#235semidirect
513. C3×D4#237semidirect
567. D12#237semidirect
716. C32#3109semidirect
738. D4#3795semidirect
813. C3#79869semidirect
814. C3#79990semidirect

Maximal subgroups

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

subgroupindex
D3×D4×Dic32
#105943672
#105924602
C3×#47852
C3×#47732
#105914862
#105914472
#105914302
#105907712
#105907492
#105906762
#105906602
#105904722
#105904552
#105904412
#799903
#798693