Finite Group Databasebeta

← #11871272

Subgroups — #11871272

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
1#10595133C211yesmaximal, characteristic, complemented
2D3×D4×Dic3C211yesmaximal, characteristic, complemented
3#10592851C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591436C211yesmaximal, characteristic, complemented
8#10591436C211yesmaximal, characteristic, complemented
9#10591428C211yesmaximal, characteristic, complemented
10#10591415C211yesmaximal, characteristic, complemented
11#10591408C211yesmaximal, characteristic, complemented
12#10590757C211yesmaximal, characteristic, complemented
13#10590741C211yesmaximal, characteristic, complemented
14#10590676C211yesmaximal, characteristic, complemented
15#10590661C211yesmaximal, characteristic, complemented
16#80314—31nomaximal
17#79990—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3805—21no—
20C22×D3×Dic3—21no—
21C2×C32×D8C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23D4×C3⋊Dic3C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic, complemented
25C3×#938C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29#67⋊Dic3—21no—
30#67⋊Dic3—21no—
31Dic3×#67—21no—
32#63970—21no—
33D3×#217—21no—
34#63959—21no—
35#63918C2211yescharacteristic, complemented
36#63908C2211yescharacteristic
37#63898C2211yescharacteristic
38#63898C2211yescharacteristic, complemented
39Dic3×D12C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41C4×D3×Dic3C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic, complemented
45#63644C2211yescharacteristic, complemented
46#63642C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61C2×D4×Dic3—31no—
62#5716—31no—
63#5596—31no—
64C4×D3×D4—31no—
65C3×#459—31no—
66C3×#447—31no—
67#5217—31no—
68#5156—31no—
69#5156D311yescharacteristic, complemented
70#5152—31no—
71#5152—31no—
72#5152—31no—
73#5152—31no—
74#5152—61no—
75#5150—31no—
76#5150D311yescharacteristic, complemented
77#5072—31no—
78#5034—31no—
79#5008—31no—
80#4842—31no—
81#4835—31no—
82#4785—31no—
83#4785—31no—
84#4785—31no—
85#4785—31no—
86#4777—31no—
87#4777—31no—
88#4761—31no—
89#4761—31no—
90#4735—31no—
91#4719—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C22×C3⋊Dic3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×D4—22no—
103C3×D3×D4—22no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#627—21no—
108C2×#625—21no—
109#3805—44no—
110C2×D3×Dic3—21no—
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#3757—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#217—21no—
127C3×#213—22no—
128C3×#213—22no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
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×#237—61no—
148C2×D3×D4C2×D311yescharacteristic
149C22×C4×D3—61no—
150C2×C3×D8—21no—
151C2×C3×D8—31no—
152C2×C3×D8—31no—
153C2×C3×D8C2×D311yescharacteristic
154C2×C3×D8C2×D311yescharacteristic
155C3×#127—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158C2×#217—61no—
159#940C2×D311yescharacteristic, complemented
160#939—61no—
161#938—31no—
162#938—61no—
163#938C2×D311yescharacteristic
164#936—61no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—31no—
172D4×Dic3—61no—
173D4×Dic3—61no—
174D4×Dic3—61no—
175D4×Dic3—61no—
176D4×Dic3—61no—
177D4×Dic3C2×D311yescharacteristic
178C2×#213—31no—
179C2×#213—31no—
180C2×#213C2×D311yescharacteristic
181C2×#213C2×D311yescharacteristic
182#930—31no—
183C4×#67—61no—
184C2×C4⋊Dic3—31no—
185C2×C4×Dic3—31no—
186#893—31no—
187#893—31no—
188D3×C4⋊C4—31no—
189#888—31no—
190#885—61no—
191#67⋊C4—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194C4×D12—31no—
195C42×D3—31no—
196#869—31no—
197C3×C4⋊C8—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—61no—
210#832—61no—
211#832C2×D311yescharacteristic
212#832C2×D311yescharacteristic, complemented
213#830—31no—
214#821—31no—
215#821—31no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic, complemented
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#817—31no—
221#817—31no—
222#817—31no—
223#817—31no—
224#817—61no—
225#815—31no—
226#815—31no—
227#815—31no—
228#815—31no—
229#815—61no—
230Dic3⋊C8—31no—
231Dic3⋊C8C2×D311yescharacteristic, complemented
232#808—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236C4⋊(C3⋊C8)—31no—
237C23×C32—21no—
238C23×C32—21no—
239C22×C3×D3—24no—
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—21no—
247C32×D4—21no—
248C32×D4#4112yescomplemented
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—42no—
253C2×C3⋊Dic3—42no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C3×#67—24no—
257C3×#67—42no—
258C3×#67—42no—
259C3×#67—42no—
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×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12#4112yescomplemented
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272#627—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—31no—
291#459—91no—
292#447—31no—
293#447—91no—
294#442—91no—
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—31no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—21no—
321C2×#67—61no—
322C2×#67—61no—
323C22×Dic3—21no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—121no—
335C22×Dic3—121no—
336C22×Dic3—124no—
337#237—124no—
338#237—124no—
339D3×D4—22no—
340D3×D4—22no—
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—31no—
344C2×C4×D3—31no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—124no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6—61no—
352C2×Dic6—61no—
353C3×D8—24no—
354C3×D8—22no—
355C3×D8—22no—
356C3×D8—62no—
357C3×D8—62no—
358C2×C3×C8—21no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368#217—21no—
369#217—21no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—121no—
379#217—121no—
380#213—22no—
381#213—22no—
382#213—62no—
383#213—62no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
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
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—48no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3AGL(1,ℤ/8)12yes—
430C32×C4C2×#4111yescharacteristic
431C32×C4C2×#4111yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—21no—
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—31no—
443C23×C4—181no—
444C2×D8—31no—
445C2×D8—31no—
446C2×D8—91no—
447C2×D8D3211yescharacteristic
448C4⋊Q8—91no—
449#127—31no—
450#124—181no—
451#121—31no—
452#121—91no—
453#121—181no—
454C4×D4—31no—
455C4×D4—91no—
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—91no—
466#106—91no—
467#106—91no—
468#106—91no—
469#106—91no—
470C4⋊C8—31no—
471C4⋊C8—91no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8—91no—
482#97—91no—
483#97—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—64no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—122no—
495C23×C3—122no—
496C22×D3—24no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3D3×D411yescharacteristic
502C3×D4—22no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—22no—
510C3×D4—32no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—64no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—122no—
518C3×D4—122no—
519C3×D4—122no—
520C3×D4#23712yescomplemented
521C3×D4#23712yescomplemented
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—24no—
534#67—42no—
535#67—42no—
536#67—42no—
537#67—122no—
538#67—122no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—42no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—62no—
549C2×Dic3—62no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—121no—
555C2×Dic3—121no—
556C2×Dic3—122no—
557C2×Dic3—122no—
558C2×Dic3—122no—
559C2×Dic3—122no—
560C2×Dic3—122no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—122no—
564C2×Dic3—242no—
565C2×Dic3—242no—
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568C2×Dic3D3×D411yescharacteristic
569D12—21no—
570D12—21no—
571D12—21no—
572D12#23712yescomplemented
573C4×D3—21no—
574C4×D3—21no—
575C4×D3—62no—
576C4×D3—62no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—122no—
581Dic6—122no—
582Dic6—122no—
583C3×C8—22no—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—121no—
593C2×C32—42no—
594C2×C32—81no—
595C2×C32#52511yescharacteristic
596C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
597C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—81no—
601C24—61no—
602#41—364no—
603C2×Q8—181no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—62no—
610C2×D4—62no—
611C2×D4—61no—
612C2×D4—181no—
613C2×D4C2×D3211yescharacteristic
614C2×D4C2×D3211yescharacteristic
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4—364no—
626D8—22no—
627D8—62no—
628D8—62no—
629D8—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
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—91no—
650C42—91no—
651C42—91no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—62no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—128no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—22no—
686C2×D3—48no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3#91112yes—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—32no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4C2×#23711yescharacteristic
701C3×C4C2×#23711yescharacteristic
702C3×C4C2×#23711yescharacteristic
703C3×C4D3×#4111yescharacteristic
704Dic3—21no—
705Dic3—21no—
706Dic3—41no—
707Dic3—41no—
708Dic3—61no—
709Dic3—61no—
710Dic3—61no—
711Dic3—61no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—241no—
719Dic3—241no—
720Dic3#91112yes—
721C32#310911yescharacteristic, complemented, Sylow
722C23—21no—
723C23—21no—
724C23—31no—
725C23—64no—
726C23—61no—
727C23—61no—
728C23—122no—
729C23—122no—
730Q8—362no—
731D4—21no—
732D4—21no—
733D4—21no—
734D4—32no—
735D4—64no—
736D4—61no—
737D4—61no—
738D4—61no—
739D4—122no—
740D4—122no—
741D4—122no—
742D4—362no—
743D4#380512yescomplemented
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—91no—
752C2×C4—91no—
753C2×C4—122no—
754C2×C4—182no—
755C2×C4—182no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—362no—
759C2×C4—362no—
760C2×C4—362no—
761C2×C4—362no—
762C2×C4—362no—
763C2×C4—362no—
764C2×C4C22×D3211yescharacteristic
765C8—21no—
766C8—61no—
767C8—61no—
768C8—181no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—42no—
773C2×C3—42no—
774C2×C3—62no—
775C2×C3—82no—
776C2×C3—82no—
777C2×C3—81no—
778C2×C3—81no—
779C2×C3—122no—
780C2×C3—241no—
781C2×C3#558611yescharacteristic
782C2×C3#560611yescharacteristic
783C2×C3C2×#91111yescharacteristic
784C2×C3C2×#91111yescharacteristic
785C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
786C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
787D3—22no—
788D3—42no—
789D3—81no—
790C22—22no—
791C22—32no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—61no—
798C22—61no—
799C22—62no—
800C22—128no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22D32×D411yescharacteristic
807C4—32no—
808C4—61no—
809C4—61no—
810C4—121no—
811C4—121no—
812C4—181no—
813C4—181no—
814C4—361no—
815C4—361no—
816C4D3×#23711yescharacteristic
817C4C2×#380511yescharacteristic
818C3—21no—
819C3#7999011yescharacteristic, complemented
820C3#8031411yescharacteristic, complemented
821C2—42no—
822C2—62no—
823C2—81no—
824C2—122no—
825C2—241no—
826C2D3×#91111yescharacteristic
827C2D3×#91111yescharacteristic
828C2#1059513011yescharacteristic
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. #10595133C2semidirect
2. D3×D4×Dic3C2semidirect
3. #10592851C2semidirect
4. C3×#5156C2semidirect
5. C3×#5150C2semidirect
6. #10591447C2semidirect
7. #10591436C2semidirect
8. #10591436C2semidirect
9. #10591428C2semidirect
10. #10591415C2semidirect
11. #10591408C2semidirect
12. #10590757C2semidirect
13. #10590741C2semidirect
14. #10590676C2semidirect
15. #10590661C2semidirect
23. D4×C3⋊Dic3C22semidirect
24. C3×#940C22semidirect
35. #63918C22semidirect
38. #63898C22semidirect
44. #63659C22semidirect
45. #63644C22semidirect
46. #63642C22semidirect
48. C3×#832C22semidirect
50. C3×#821C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63563C22semidirect
60. #63555C22semidirect
69. #5156D3semidirect
76. #5150D3semidirect
159. #940C2×D3semidirect
212. #832C2×D3semidirect
217. #821C2×D3semidirect
231. Dic3⋊C8C2×D3semidirect
248. C32×D4#41semidirect
269. C3×D12#41semidirect
520. C3×D4#237semidirect
521. C3×D4#237semidirect
572. D12#237semidirect
721. C32#3109semidirect
743. D4#3805semidirect
819. C3#79990semidirect
820. C3#80314semidirect

Maximal subgroups

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

subgroupindex
#105951332
D3×D4×Dic32
#105928512
C3×#51562
C3×#51502
#105914472
#105914362
#105914282
#105914152
#105914082
#105907572
#105907412
#105906762
#105906612
#803143
#799903