Finite Group Databasebeta

← #11870443

Subgroups — #11870443

Order 1152.

1051 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
1C3×#5548C211yesmaximal, characteristic, complemented
2C4×D3×D12C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591515C211yesmaximal, characteristic, complemented
6#10591429C211yesmaximal, characteristic, complemented
7#10591428C211yesmaximal, characteristic, complemented
8#10591413C211yesmaximal, characteristic, complemented
9#10590595C211yesmaximal, characteristic, complemented
10#10590464C211yesmaximal, characteristic, complemented
11#10590463C211yesmaximal, characteristic, complemented
12#10590438C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14C4×#3713C211yesmaximal, characteristic, complemented
15#10590261C211yesmaximal, characteristic, complemented
16#83298—31nomaximal
17#79590—31nomaximal
18C2×C3×#235—21no—
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21C32×C4×D4C2211yescharacteristic, complemented
22C2×#3753C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C3×#940C2211yescharacteristic, complemented
25C3×#938C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×C4×#67—21no—
28C3×#895C2211yescharacteristic
29C3×#888C2211yescharacteristic, complemented
30C3×#885—21no—
31C3×#884—21no—
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic, complemented
34C3×C42×D3C2211yescharacteristic
35D3×(C2×D3)⋊C4—21no—
36C4×#626—21no—
37#63894C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63880—21no—
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63634C2211yescharacteristic, complemented
46C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#532—31no—
62#5548D311yescharacteristic, complemented
63C4×D3×D4—31no—
64C2×C4×D12—31no—
65C3×C4×D8—31no—
66#5156—31no—
67#5150—31no—
68#5087—31no—
69#5087—31no—
70#5072—31no—
71#5072—31no—
72#5036—31no—
73#5036—31no—
74#5033—31no—
75#5033—31no—
76C4×#213—31no—
77C4×#213—31no—
78C4×#213—31no—
79C4×#213—31no—
80C4×#213—31no—
81C4×#213—61no—
82C4×#213D311yescharacteristic, complemented
83#4925—31no—
84#4890—31no—
85#4882—31no—
86#4786—31no—
87#4774—31no—
88#4773—31no—
89#4759—31no—
90C4×D24—31no—
91#4685—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C3×#235—44no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×#626—21no—
111C2×#624—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—22no—
116C4×D32—44no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42C2311yescharacteristic
120#3753—22no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141#3714—22no—
142#3713—22no—
143#3100—91noSylow
144C2×C3×#41—61no—
145C2×D3×D4—31no—
146C2×#235—21no—
147C22×D12—31no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C2×C3×D8—31no—
151C3×C4⋊Q8—31no—
152C3×#127—31no—
153C3×#124—61no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×C4×D4—21no—
158C3×C4×D4—31no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161C3×C4×D4C2×D311yescharacteristic, complemented
162C3×C4×D4C2×D311yescharacteristic, complemented
163C2×C3×C42—31no—
164#940C2×D311yescharacteristic, complemented
165#938C2×D311yescharacteristic
166D4×Dic3—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173C2×#213C2×D311yescharacteristic
174C4×#67—21no—
175C4×#67—61no—
176C2×(C2×D3)⋊C4—61no—
177C2×C4⋊Dic3—31no—
178C2×D24—31no—
179#895C2×D311yescharacteristic
180#893—31no—
181D3×C4⋊C4—31no—
182#888C2×D311yescharacteristic, complemented
183#885—21no—
184#884—21no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12—61no—
193C4×D12—61no—
194C4×D12C2×D311yescharacteristic
195C4×D12C2×D311yescharacteristic, complemented
196C42×D3C2×D311yescharacteristic
197C3×#107—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C4×C8—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—61no—
207#832C2×D311yescharacteristic, complemented
208#830—31no—
209#830—31no—
210#821—31no—
211#821—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214#818—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#809C2×D311yescharacteristic
224#807—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#807—61no—
230#807C2×D311yescharacteristic, complemented
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—31no—
235C4×C3⋊C8—61no—
236C4×C3⋊C8C2×D311yescharacteristic, complemented
237C23×C32—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—
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—42no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yescomplemented
255C4×C3⋊D3—42no—
256C3×#67—42no—
257C3×#67—42no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12#4112yescomplemented
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—41no—
272C3×C4×D3—42no—
273C3×C4×D3—42no—
274C3×C4×D3D814yescomplemented
275C3×Dic6—42no—
276#626—24no—
277#624—42no—
278D3×Dic3—42no—
279D3×Dic3—42no—
280C3⋊(C3⋊C8)—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—31no—
285C2×C4×D4—91no—
286#480—91no—
287#480—91no—
288#474—91no—
289#474—91no—
290#459—91no—
291#459—91no—
292#447—91no—
293#447—91no—
294C4×D8—31no—
295C4×D8—91no—
296C4×D8—91no—
297C4×D8—91no—
298#431—91no—
299C23×D3—61no—
300C23×D3—61no—
301C3×#41—124no—
302C2×C3×Q8—61no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C2×#67—21no—
321C2×#67—21no—
322C2×#67—21no—
323C2×#67—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326D3×D4—62no—
327D3×D4—62no—
328#235—44no—
329C2×D12—21no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—61no—
333C2×D12—62no—
334C2×D12—61no—
335C2×D12—62no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—121no—
347C2×C4×D3—124no—
348C2×C4×D3—124no—
349C2×C4×D3#6711yescharacteristic
350C2×C4×D3#6711yescharacteristic
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—21no—
353C3×D8—62no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C42—21no—
370C3×C42—31no—
371C3×C42—31no—
372C3×C42—31no—
373C3×C42C22×D311yescharacteristic
374C3×C42C22×D311yescharacteristic
375#217—21no—
376#217—61no—
377#213—22no—
378#213—62no—
379#213—62no—
380#213—62no—
381#213—62no—
382#213—64no—
383#213—62no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—121no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—61no—
401C4×Dic3#6711yescharacteristic
402C4×Dic3#6711yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D24—62no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
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×D3C2×D812yes—
429D32—48no—
430C32×C4—21no—
431C32×C4—41no—
432C32×C4C2×D812yes—
433C32×C4C2×#4111yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3C2×D812yes—
441C2×#41—61no—
442C22×D4—91no—
443C23×C4—181no—
444C2×D8—31no—
445C2×D8—91no—
446C2×D8—91no—
447C2×D8—91no—
448C4⋊Q8—31no—
449#127—31no—
450#124—61no—
451#121—31no—
452#121—31no—
453#121—61no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—61no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—181no—
461C4×D4—181no—
462C4×D4D3211yescharacteristic, complemented
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465C2×C42—31no—
466#107—31no—
467#107—91no—
468#107—91no—
469#107—91no—
470C4⋊C8—91no—
471C4⋊C8—91no—
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—91no—
481C22⋊C8—91no—
482C4×C8—31no—
483C4×C8—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—61no—
489C23×C3—61no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—64no—
493C22×D3—64no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3C2×#6711yescharacteristic
502C3×Q8—122no—
503C3×D4—22no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—32no—
509C3×D4—41no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—122no—
514C3×D4—122no—
515C3×D4—122no—
516C3×D4—122no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—34no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—82no—
534C2×C3×C4—121no—
535C2×C3×C4—122no—
536C2×C3×C4—122no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C2×#6711yescharacteristic
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—42no—
544#67—42no—
545#67—42no—
546#67—64no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—121no—
552C2×Dic3—122no—
553C2×Dic3—122no—
554C2×Dic3C2×#6711yescharacteristic
555C2×Dic3C2×#6711yescharacteristic
556C2×Dic3C2×#6711yescharacteristic
557D12—21no—
558D12—21no—
559D12—21no—
560D12—32no—
561D12—32no—
562D12—42no—
563D12—62no—
564D12—64no—
565D12—61no—
566D12—61no—
567D12—121no—
568D12#23512yescomplemented
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—41no—
572C4×D3—42no—
573C4×D3—42no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—122no—
577C4×D3—122no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—242no—
581C4×D3#21314yescomplemented
582Dic6—42no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—62no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—121no—
593C2×C32—81no—
594C2×C32#52511yescharacteristic
595C2×C32C22×D811yescharacteristic
596C2×C32#57511yescharacteristic
597C3⋊D3—42no—
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—81no—
601C24—181no—
602#41—124no—
603C2×Q8—61no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—91no—
611C2×D4—181no—
612C2×D4—182no—
613C2×D4—182no—
614C2×D4C2×D3211yescharacteristic
615C22×C4—21no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—61no—
620C22×C4—61no—
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×C8—91no—
633C2×C8—91no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4C2×D3211yescharacteristic
640C22⋊C4—21no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
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—42no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—62no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C22×#6711yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—22no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—62no—
682C2×D3—62no—
683C2×D3—122no—
684C2×D3—128no—
685C2×D3—128no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3C2×#21312yes—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—22no—
698C3×C4—32no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—61no—
703C3×C4—61no—
704C3×C4—81no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4D3×D812yes—
708C3×C4C2×#21312yes—
709C3×C4C2×#23511yescharacteristic
710C3×C4D3×#4111yescharacteristic
711C3×C4D3×#4111yescharacteristic
712C3×C4D3×#4111yescharacteristic
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—41no—
717Dic3—121no—
718Dic3—121no—
719Dic3—241no—
720Dic3C2×#21312yes—
721C32#310011yescharacteristic, complemented, Sylow
722C23—21no—
723C23—31no—
724C23—61no—
725C23—61no—
726C23—184no—
727C23—181no—
728C23—362no—
729C23—362no—
730Q8—122no—
731D4—21no—
732D4—21no—
733D4—32no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—92no—
738D4—122no—
739D4—122no—
740D4—122no—
741D4—122no—
742D4—184no—
743D4—181no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—34no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—42no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—121no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—181no—
758C2×C4—362no—
759C2×C4—362no—
760C2×C4—362no—
761C2×C4—362no—
762C2×C4D3×#6711yescharacteristic
763C2×C4D3×#6711yescharacteristic
764C2×C4C22×D3211yescharacteristic
765C8—61no—
766C8—61no—
767C8—181no—
768C8—181no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—62no—
773C2×C3—82no—
774C2×C3—81no—
775C2×C3—81no—
776C2×C3—122no—
777C2×C3—241no—
778C2×C3#554711yescharacteristic
779C2×C3C2×D3×D811yescharacteristic
780C2×C3#576811yescharacteristic
781C2×C3C22×#21311yescharacteristic
782C2×C3#582211yescharacteristic
783C2×C3#582811yescharacteristic
784D3—22no—
785D3—42no—
786D3—81no—
787D3—122no—
788D3—122no—
789D3—242no—
790C22—32no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—61no—
795C22—61no—
796C22—62no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—182no—
803C22—368no—
804C22—361no—
805C22—361no—
806C22C2×D3×#6711yescharacteristic
807C4—21no—
808C4—32no—
809C4—41no—
810C4—61no—
811C4—61no—
812C4—121no—
813C4—121no—
814C4—361no—
815C4D3×#21312yes—
816C4D3×#23511yescharacteristic
817C4#6430611yescharacteristic
818C3—21no—
819C3#7959011yescharacteristic, complemented
820C3#8329811yescharacteristic, complemented
821C2—62no—
822C2—81no—
823C2—122no—
824C2—241no—
825C2—362no—
826C2#1059506011yescharacteristic
827C2C2×D3×#21311yescharacteristic
828C2#1059545311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5548C2semidirect
2. C4×D3×D12C2semidirect
3. C4×#3753C2semidirect
4. C3×C4×#213C2semidirect
5. #10591515C2semidirect
6. #10591429C2semidirect
7. #10591428C2semidirect
8. #10591413C2semidirect
9. #10590595C2semidirect
10. #10590464C2semidirect
11. #10590463C2semidirect
12. #10590438C2semidirect
13. C4×#3714C2semidirect
14. C4×#3713C2semidirect
15. #10590261C2semidirect
21. C32×C4×D4C22semidirect
24. C3×#940C22semidirect
29. C3×#888C22semidirect
33. C3×C4×D12C22semidirect
43. #63659C22semidirect
45. #63634C22semidirect
46. C4×C3⋊(C3⋊C8)C22semidirect
47. C3×#832C22semidirect
49. C3×#807C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
62. #5548D3semidirect
82. C4×#213D3semidirect
161. C3×C4×D4C2×D3semidirect
162. C3×C4×D4C2×D3semidirect
164. #940C2×D3semidirect
182. #888C2×D3semidirect
195. C4×D12C2×D3semidirect
207. #832C2×D3semidirect
230. #807C2×D3semidirect
236. C4×C3⋊C8C2×D3semidirect
254. C4⋊(C3⋊D3)#41semidirect
268. C3×D12#41semidirect
274. C3×C4×D3D8semidirect
462. C4×D4D32semidirect
568. D12#235semidirect
581. C4×D3#213semidirect
721. C32#3100semidirect
819. C3#79590semidirect
820. C3#83298semidirect

Maximal subgroups

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

subgroupindex
C3×#55482
C4×D3×D122
C4×#37532
C3×C4×#2132
#105915152
#105914292
#105914282
#105914132
#105905952
#105904642
#105904632
#105904382
C4×#37142
C4×#37132
#105902612
#832983
#795903