Finite Group Databasebeta

← #11878656

Subgroups — #11878656

Order 1152.

1145 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#940C211yesmaximal, characteristic, complemented
2#10595131C211yesmaximal, characteristic, complemented
3#10592850C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591484C211yesmaximal, characteristic, complemented
8#10591481C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10#10591429C211yesmaximal, characteristic, complemented
11#10591402C211yesmaximal, characteristic, complemented
12#10590947C211yesmaximal, characteristic, complemented
13#10590885C211yesmaximal, characteristic, complemented
14#10590765C211yesmaximal, characteristic, complemented
15#10590656C211yesmaximal, characteristic, complemented
16#80336—31nomaximal
17#79994—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×#3804—21no—
22C2×D3×D12C2211yescharacteristic
23C2×C32×D8C2211yescharacteristic, complemented
24#64149C2211yescharacteristic
25#64149C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic, complemented
27C2×#3753C2211yescharacteristic, complemented
28C2×#3745C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic
30C3×#938C2211yescharacteristic
31C3×D4×Dic3C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic, complemented
34#63979—21no—
35#63979—21no—
36#63971—21no—
37#63953—21no—
38#63952—21no—
39#63919C2211yescharacteristic, complemented
40#63914C2211yescharacteristic
41#63911C2211yescharacteristic
42#63909C2211yescharacteristic
43#63894C2211yescharacteristic, complemented
44C4×D3×Dic3C2211yescharacteristic
45C2×#3714C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61C2×#940—31no—
62D3×#127—31no—
63#5596—31no—
64#5548—31no—
65C3×#459—31no—
66C3×#447—31no—
67#5217—31no—
68#5156—31no—
69#5156D311yescharacteristic, complemented
70#5151—31no—
71#5151—31no—
72#5151—31no—
73#5151—31no—
74#5151—61no—
75#5150—31no—
76#5150D311yescharacteristic, complemented
77#5072—31no—
78#5036—31no—
79#5015—31no—
80#4843—31no—
81#4833—31no—
82#4786—31no—
83#4786—31no—
84#4773—31no—
85#4773—31no—
86#4760—31no—
87#4760—31no—
88#4760—31no—
89#4760—31no—
90#4732—31no—
91#4718—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C2×#638—21no—
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C3×D3×D4—41no—
108C3×D3×D4—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112D3×#67—44no—
113D3×#67—44no—
114C2×#627—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×#625—21no—
121C2×#624—21no—
122#3804—44no—
123C2×D3×Dic3D411yescharacteristic
124C2×D3×Dic3D411yescharacteristic
125D3×D12—41no—
126D3×D12—41no—
127C32×D8—41no—
128C2×C32×C8C2311yescharacteristic
129#3753—41no—
130#3753—41no—
131C4×C3⋊Dic3C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3745—41no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#213—41no—
137C3×#213—41no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144#3722—21no—
145#3722—21no—
146Dic32D411yescharacteristic
147Dic32D411yescharacteristic
148#3714—41no—
149#3714—41no—
150#3205—91noSylow
151C22×C3×D4—31no—
152C22×#67—61no—
153C22×#67—61no—
154C2×#237—61no—
155C2×D3×D4—31no—
156C2×D3×D4—61no—
157C2×D3×D4—61no—
158C2×D3×D4C2×D311yescharacteristic
159C2×#235—61no—
160C22×D12—31no—
161C2×C3×D8—21no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C2×C3×D8C2×D311yescharacteristic, complemented
165C2×C3×D8C2×D311yescharacteristic, complemented
166C3×#127—31no—
167C3×#121—31no—
168C3×C4×D4—31no—
169#940—31no—
170#940—31no—
171#940—31no—
172#940—31no—
173#940—31no—
174#940—31no—
175#940—31no—
176#940—61no—
177#940—61no—
178#940—61no—
179#940—61no—
180#940—61no—
181#940—61no—
182#940C2×D311yescharacteristic
183#939—61no—
184#938C2×D311yescharacteristic
185D4×Dic3C2×D311yescharacteristic, complemented
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213—31no—
191C2×#213—31no—
192C2×#213—61no—
193C2×#213—61no—
194C2×#213C2×D311yescharacteristic, complemented
195C2×#213C2×D311yescharacteristic, complemented
196#930—31no—
197C4×#67—61no—
198C2×C4×Dic3—31no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—61no—
204#895—31no—
205#893—31no—
206#888—31no—
207#888—31no—
208#885—61no—
209#885—61no—
210#884—61no—
211#67⋊C4—61no—
212#874—31no—
213C4×D12—31no—
214C42×D3—31no—
215C3×C4⋊C8—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×C22⋊C8—31no—
221#832—31no—
222#832—31no—
223#832C2×D311yescharacteristic, complemented
224#832C2×D311yescharacteristic, complemented
225#830—31no—
226#821—31no—
227#821—31no—
228#821C2×D311yescharacteristic, complemented
229#821C2×D311yescharacteristic, complemented
230(C2×D3)⋊C8—31no—
231(C2×D3)⋊C8C2×D311yescharacteristic
232Dic3⋊C8—31no—
233Dic3⋊C8C2×D311yescharacteristic, complemented
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3—31no—
237C8×Dic3—31no—
238C8×Dic3—61no—
239#809—31no—
240#809—31no—
241#809—31no—
242#809—31no—
243C4⋊(C3⋊C8)—31no—
244C23×C32—21no—
245C23×C32—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—42no—
251C22×C3×D3—42no—
252C22×C3×D3—42no—
253C22×C3×D3C2×D411yescharacteristic
254C2×D32—42no—
255C2×D32—42no—
256C2×D32—42no—
257C32×D4—21no—
258C32×D4—21no—
259C32×D4—21no—
260C32×D4—21no—
261C2×C32×C4C2411yescharacteristic
262#638—42no—
263#638—42no—
264#638—42no—
265#638—42no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288#627—42no—
289#626—42no—
290#626—42no—
291#626—42no—
292#626—42no—
293#625—42no—
294#625—42no—
295#624—42no—
296D3×Dic3—22no—
297D3×Dic3D814yescomplemented
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302#532—91no—
303C2×#127—91no—
304#493—91no—
305#493—91no—
306#486—91no—
307#486—91no—
308#459—31no—
309#459—91no—
310#459—91no—
311#459—91no—
312#447—31no—
313#447—91no—
314#447—91no—
315#447—91no—
316#431—91no—
317C24×C3—61no—
318C23×D3—21no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—121no—
330C2×C3×D4—121no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—121no—
358C2×#67—121no—
359C2×#67—121no—
360C2×#67—121no—
361C2×#67—124no—
362C2×#67—124no—
363C22×Dic3—21no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366#237—124no—
367D3×D4—41no—
368D3×D4—41no—
369D3×D4—121no—
370D3×D4—121no—
371D3×D4—124no—
372D3×D4—124no—
373#235—124no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—61no—
384C2×D12—121no—
385C2×D12—121no—
386C2×D12C22×D311yescharacteristic
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—31no—
389C2×C4×D3—31no—
390C2×C4×D3—61no—
391C2×C4×D3—61no—
392C2×C4×D3C22×D311yescharacteristic
393C2×Dic6—61no—
394C2×Dic6—61no—
395C3×D8—41no—
396C3×D8—41no—
397C3×D8—42no—
398C3×D8—121no—
399C3×D8—121no—
400C2×C3×C8—21no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—31no—
406C3×C4⋊C4—31no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410#217—21no—
411#217—21no—
412#213—41no—
413#213—41no—
414#213—121no—
415#213—121no—
416#213—121no—
417#213—121no—
418#213—121no—
419#213—121no—
420#213—122no—
421#213—122no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426C4⋊Dic3C22×D311yescharacteristic
427C4⋊Dic3C22×D311yescharacteristic
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3—31no—
436C4×Dic3—61no—
437C4×Dic3C22×D311yescharacteristic
438C2×C3⋊C8—31no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—61no—
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443D24—121no—
444D24—121no—
445D24—122no—
446D24—121no—
447D24—121no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—84no—
470C2×C3×D3C2×D812yes—
471D32—84no—
472C32×C4H(5,𝔽2)11yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3C2×D812yes—
475C3⋊Dic3AGL(1,ℤ/8)12yes—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C3×Dic3C2×D812yes—
481C2×#41—181no—
482C22×D4—31no—
483C22×D4—91no—
484C22×D4—181no—
485C22×D4—181no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—91no—
493C2×D8D3211yescharacteristic, complemented
494C4⋊Q8—91no—
495#127—31no—
496#127—91no—
497#127—91no—
498#127—91no—
499#127—91no—
500#127—181no—
501#127—181no—
502#124—181no—
503#121—31no—
504#121—91no—
505#121—181no—
506C4×D4—31no—
507C4×D4—91no—
508C4×D4—181no—
509C2×C42—91no—
510C4⋊C8—31no—
511C4⋊C8—91no—
512#102—31no—
513#102—31no—
514#102—31no—
515#102—31no—
516#102—91no—
517#102—91no—
518#102—91no—
519#102—91no—
520C22⋊C8—31no—
521C22⋊C8—91no—
522C4×C8—91no—
523C4×C8—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C23×C3—122no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—121no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3D3×D411yescharacteristic
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—41no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—122no—
574C2×C3×C4—21no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—122no—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—42no—
586#67—42no—
587#67—42no—
588#67—42no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—242no—
606#67—242no—
607#67—242no—
608#67—242no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—34no—
616C2×Dic3—42no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—62no—
620C2×Dic3D3×D411yescharacteristic
621C2×Dic3D3×D411yescharacteristic
622C2×Dic3D3×D411yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—121no—
636D12—121no—
637D12—121no—
638D12—121no—
639D12—122no—
640D12—122no—
641D12—122no—
642D12—122no—
643C4×D3—21no—
644C4×D3—21no—
645C4×D3—34no—
646C4×D3—62no—
647C4×D3—122no—
648C4×D3—122no—
649Dic6—122no—
650Dic6—122no—
651C3×C8—22no—
652C3×C8—21no—
653C3×C8—21no—
654C3×C8—61no—
655C3×C8—61no—
656C3⋊C8—21no—
657C3⋊C8—21no—
658C3⋊C8—62no—
659C3⋊C8—61no—
660C3⋊C8—61no—
661C2×C32—81no—
662C2×C32—81no—
663C2×C32#53511yescharacteristic
664C2×C32C22×D811yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C3⋊D3—81no—
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—81no—
670C3×D3—81no—
671C24—61no—
672C24—181no—
673#41—364no—
674C2×Q8—181no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—121no—
684C2×D4—121no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—361no—
696C2×D4—361no—
697C2×D4—364no—
698C2×D4—364no—
699C2×D4C2×D3211yescharacteristic
700C2×D4C2×D3211yescharacteristic
701C22×C4—31no—
702C22×C4—61no—
703C22×C4—91no—
704C22×C4—91no—
705C22×C4—181no—
706D8—41no—
707D8—121no—
708D8—121no—
709D8—361no—
710D8—361no—
711D8—361no—
712D8—361no—
713D8—361no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—91no—
717C2×C8C2×D3211yescharacteristic
718C4⋊C4—31no—
719C4⋊C4—31no—
720C4⋊C4—181no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C42—31no—
726C42—91no—
727C42—91no—
728C42—91no—
729C22×C3—21no—
730C22×C3—32no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—84no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3—241no—
784C2×D3—241no—
785C2×D3—241no—
786C2×D3—241no—
787C2×D3—244no—
788C2×D3—244no—
789C2×D3D3×D812yes—
790C3×C4—21no—
791C3×C4—21no—
792C3×C4—32no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4#100411yescharacteristic
798C3×C4#100411yescharacteristic
799C3×C4#100411yescharacteristic
800C3×C4#100911yescharacteristic
801Dic3—21no—
802Dic3—21no—
803Dic3—32no—
804Dic3—32no—
805Dic3—32no—
806Dic3—32no—
807Dic3—41no—
808Dic3—41no—
809Dic3—62no—
810Dic3—62no—
811Dic3D3×D812yes—
812C32#320511yescharacteristic, complemented, Sylow
813C23—21no—
814C23—21no—
815C23—31no—
816C23—61no—
817C23—61no—
818C23—122no—
819C23—122no—
820C23—122no—
821C23—181no—
822C23—181no—
823C23—362no—
824C23—362no—
825C23—362no—
826Q8—362no—
827D4—21no—
828D4—21no—
829D4—21no—
830D4—21no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—122no—
839D4—181no—
840D4—181no—
841D4—181no—
842D4—181no—
843D4—362no—
844D4—362no—
845D4—362no—
846D4—362no—
847D4—362no—
848D4—362no—
849D4—362no—
850D4—362no—
851D4—362no—
852D4—362no—
853C2×C4—31no—
854C2×C4—31no—
855C2×C4—31no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—94no—
861C2×C4—91no—
862C2×C4—91no—
863C2×C4—122no—
864C2×C4—182no—
865C2×C4—362no—
866C2×C4C22×D3211yescharacteristic
867C8—21no—
868C8—61no—
869C8—61no—
870C8—181no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—62no—
875C2×C3—81no—
876C2×C3—81no—
877C2×C3—81no—
878C2×C3—81no—
879C2×C3—161no—
880C2×C3—161no—
881C2×C3—241no—
882C2×C3—241no—
883C2×C3#559211yescharacteristic
884C2×C3#560711yescharacteristic
885C2×C3C2×D3×D811yescharacteristic
886C2×C3C2×D3×D811yescharacteristic
887C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
888C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
889D3—22no—
890D3—81no—
891D3—81no—
892D3—241no—
893D3—241no—
894D3—241no—
895D3—241no—
896D3—481no—
897D3—481no—
898C22—32no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—61no—
906C22—61no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22—121no—
913C22—244no—
914C22—361no—
915C22—361no—
916C22—361no—
917C22—361no—
918C22—361no—
919C22—361no—
920C22—724no—
921C22D32×D411yescharacteristic
922C4—32no—
923C4—61no—
924C4—61no—
925C4—92no—
926C4—92no—
927C4—121no—
928C4—121no—
929C4#6431411yescharacteristic
930C4#6433011yescharacteristic
931C3—21no—
932C3#7999411yescharacteristic, complemented
933C3#8033611yescharacteristic, complemented
934C2—62no—
935C2—81no—
936C2—81no—
937C2—241no—
938C2—241no—
939C2—721no—
940C2—721no—
941C2D32×D811yescharacteristic
942C2#1059472611yescharacteristic
943C2#1059528511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3205
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. D3×#940C2semidirect
2. #10595131C2semidirect
3. #10592850C2semidirect
4. C3×#5156C2semidirect
5. C3×#5150C2semidirect
6. #10591515C2semidirect
7. #10591484C2semidirect
8. #10591481C2semidirect
9. #10591448C2semidirect
10. #10591429C2semidirect
11. #10591402C2semidirect
12. #10590947C2semidirect
13. #10590885C2semidirect
14. #10590765C2semidirect
15. #10590656C2semidirect
23. C2×C32×D8C22semidirect
25. #64149C22semidirect
26. C2×#3753C22semidirect
27. C2×#3753C22semidirect
28. C2×#3745C22semidirect
31. C3×D4×Dic3C22semidirect
32. C2×C3×#213C22semidirect
33. C2×C3×#213C22semidirect
39. #63919C22semidirect
43. #63894C22semidirect
45. C2×#3714C22semidirect
46. C2×#3714C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
60. #63553C22semidirect
69. #5156D3semidirect
76. #5150D3semidirect
164. C2×C3×D8C2×D3semidirect
165. C2×C3×D8C2×D3semidirect
185. D4×Dic3C2×D3semidirect
194. C2×#213C2×D3semidirect
195. C2×#213C2×D3semidirect
223. #832C2×D3semidirect
224. #832C2×D3semidirect
228. #821C2×D3semidirect
229. #821C2×D3semidirect
233. Dic3⋊C8C2×D3semidirect
297. D3×Dic3D8semidirect
493. C2×D8D32semidirect
812. C32#3205semidirect
932. C3#79994semidirect
933. C3#80336semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
#105951312
#105928502
C3×#51562
C3×#51502
#105915152
#105914842
#105914812
#105914482
#105914292
#105914022
#105909472
#105908852
#105907652
#105906562
#803363
#799943