Finite Group Databasebeta

← #11803281

Subgroups — #11803281

Order 1152.

1711 conjugacy classes of subgroups.

The subgroup lattice has 1075 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#882C211yesmaximal, characteristic
2C2×D3×#217C211yesmaximal, characteristic, complemented
3C2×#63898C211yesmaximal, characteristic, complemented
4#10592650C211yesmaximal, characteristic, complemented
5C3×#4951C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591707C211yesmaximal, characteristic, complemented
8#10591706C211yesmaximal, characteristic, complemented
9#10591379C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#10591318C211yesmaximal, characteristic, complemented
14#10591307C211yesmaximal, characteristic, complemented
15#10591286C211yesmaximal, characteristic, complemented
16#82578—31nomaximal
17#75826—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
35C2×C3×C4×Dic3C2211yescharacteristic, complemented
36C3×#882C418yescomplemented
37D3×#217—24no—
38C2×Dic3⋊Dic3C2211yescharacteristic, complemented
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48C2×Dic32C2211yescharacteristic, complemented
49#63898—24no—
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×C3×#120—31no—
57C22×#217—31no—
58C2×D4×Dic3—31no—
59C2×#893—31no—
60C2×#882D311yescharacteristic
61C2×D3×C22⋊C4—31no—
62C3×#388—31no—
63#5247—31no—
64#5221—31no—
65#5221—31no—
66#5220—31no—
67#5220—31no—
68#5220—31no—
69#4990—31no—
70#4957—31no—
71#4956—31no—
72#4955—31no—
73#4951—31no—
74#4951—31no—
75#4951—31no—
76#4951—31no—
77#4951—61no—
78#4951D311yescharacteristic, complemented
79#4950—31no—
80Dic3×C22⋊C4—31no—
81#4939—31no—
82C4×(C2×D3)⋊C4—31no—
83#4669—31no—
84#4668—31no—
85#4665—31no—
86#4665—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3—22no—
89C23×C3×D3—22no—
90C23×C3×D3—41no—
91C23×C3×D3—41no—
92C23×C3×D3—41no—
93C23×C3×D3—41no—
94C23×C3×D3C2×C414yescomplemented
95C23×C3×D3C2311yescharacteristic
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C2×C3×#67C2×C414yescomplemented
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×D12—22no—
113C2×C3×D12—22no—
114C2×C3×D12—41no—
115C2×C3×D12—41no—
116C2×C3×D12C2×C414yes—
117C2×C3×D12C2×C414yescomplemented
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3—41no—
122C2×D3×Dic3—41no—
123C2×D3×Dic3—41no—
124C2×D3×Dic3—41no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3D414yescomplemented
127C32×C22⋊C4C2×C414yescomplemented
128#3757—22no—
129#3757—41no—
130C4⋊(C3⋊Dic3)—41no—
131C4×C3⋊Dic3—22no—
132C3×#217—22no—
133C3×#217—41no—
134C3×(C2×D3)⋊C4C2×C414yescomplemented
135C3×(C2×D3)⋊C4C2×C414yescomplemented
136C3×C4⋊Dic3—22no—
137C3×C4×Dic3—41no—
138Dic3⋊Dic3—41no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—41no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3—41no—
147(C2×D3)⋊Dic3—41no—
148Dic32—41no—
149#2321—91noSylow
150C25×C3—31no—
151C24×D3C2×D311yescharacteristic
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×#67C2×D311yescharacteristic
156C23×Dic3—31no—
157C23×Dic3—31no—
158C23×Dic3—31no—
159C22×D12C2×D311yescharacteristic
160C22×D12C2×D311yescharacteristic
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C3×#120—38no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—21no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4C2×D311yescharacteristic
172C2×C3×C22⋊C4C2×D311yescharacteristic
173C2×C3×C42—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—61no—
188C2×#217—61no—
189C2×#217—64no—
190C2×#217C2×D311yescharacteristic
191C2×#217C2×D311yescharacteristic
192D4×Dic3—64no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—61no—
208C2×C4⋊Dic3C2×D311yescharacteristic, complemented
209C2×Dic3⋊C4—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—61no—
215C2×C4×Dic3C2×D311yescharacteristic, complemented
216#893—64no—
217#882Dic318yescomplemented
218D3×C22⋊C4—64no—
219C3×#95—31no—
220C3×#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—61no—
230C3⋊#95—61no—
231C3⋊#95C2×D311yescharacteristic, complemented
232C3⋊#95C2×D311yescharacteristic, complemented
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—28no—
258C22×C3×D3—44no—
259C22×C3×D3—44no—
260C22×C3×D3—44no—
261C22×C3×D3—44no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3C22×C412yes—
265C22×C3×D3C22×C412yes—
266C22×C3×D3C22×C412yes—
267C22×C3×D3C2×D412yes—
268C22×C3×D3#4112yes—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C22×C412yes—
274C2×C32×C4C22×C412yes—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3C2×D412yes—
287C3×#67—44no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3C22×C412yes—
302C2×C3×Dic3C2×D412yes—
303C3×D12—28no—
304C3×D12—44no—
305D3×Dic3—44no—
306D3×Dic3—44no—
307D3×Dic3—44no—
308C2×#120—31no—
309C2×C4×D4—91no—
310C22×C22⋊C4—91no—
311#390—91no—
312#390—91no—
313#388—31no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—91no—
318#386—91no—
319#386—91no—
320#385—91no—
321#379—91no—
322C4×C22⋊C4—91no—
323C24×C3—21no—
324C24×C3—31no—
325C24×C3—31no—
326C24×C3—31no—
327C24×C3—34no—
328C24×C3—62no—
329C24×C3—62no—
330C24×C3—121no—
331C24×C3—121no—
332C24×C3—121no—
333C24×C3—121no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C23×D3—22no—
337C23×D3—22no—
338C23×D3—41no—
339C23×D3—41no—
340C23×D3—41no—
341C23×D3—41no—
342C23×D3C2×Dic314yescomplemented
343C23×D3C22×D311yescharacteristic
344C23×D3C22×D311yescharacteristic
345C23×D3C22×D311yescharacteristic
346C2×C3×D4—34no—
347C2×C3×D4—34no—
348C2×C3×D4—34no—
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—121no—
352C2×C3×D4—121no—
353C2×C3×D4—121no—
354C2×C3×D4—121no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C2×#67—41no—
367C2×#67—41no—
368C2×#67C2×Dic314yescomplemented
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—34no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—62no—
383C22×Dic3—62no—
384C22×Dic3—121no—
385C22×Dic3—121no—
386C22×Dic3—121no—
387C22×Dic3—121no—
388C22×Dic3—121no—
389C22×Dic3—121no—
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C2×D12—22no—
396C2×D12—22no—
397C2×D12—41no—
398C2×D12—41no—
399C2×D12C2×Dic314yes—
400C2×D12C2×Dic314yescomplemented
401C2×C4×D3—34no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—121no—
405C2×C4×D3—121no—
406C2×C4×D3—121no—
407C2×C4×D3—121no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C3×C4⋊C4—62no—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—62no—
415C3×C22⋊C4—121no—
416C3×C22⋊C4C4×D314yescomplemented
417C3×C22⋊C4C2×Dic314yescomplemented
418C3×C42—121no—
419#217—22no—
420#217—41no—
421#217—62no—
422#217—62no—
423#217—62no—
424#217—62no—
425#217—62no—
426#217—62no—
427#217—62no—
428#217—122no—
429#217—121no—
430#217—121no—
431#217—121no—
432#217—121no—
433#217—121no—
434#217—121no—
435#217—122no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—121no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4—121no—
444(C2×D3)⋊C4—121no—
445(C2×D3)⋊C4C2×Dic314yescomplemented
446(C2×D3)⋊C4C2×Dic314yescomplemented
447C4⋊Dic3—22no—
448C4⋊Dic3—121no—
449C4⋊Dic3—121no—
450C4⋊Dic3—121no—
451C4⋊Dic3—122no—
452Dic3⋊C4—121no—
453C4×Dic3—41no—
454C4×Dic3—62no—
455C4×Dic3—62no—
456C4×Dic3—122no—
457C4×Dic3—121no—
458C4×Dic3—121no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C23×C411yescharacteristic
467C22×C32C22×D411yescharacteristic
468C22×C32C2×#4111yescharacteristic
469C22×C32H(5,𝔽2)11yescharacteristic
470C22×C32H(5,𝔽2)11yescharacteristic
471C22×C32H(5,𝔽2)11yescharacteristic
472C22×C32H(5,𝔽2)11yescharacteristic
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—416no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3C4×D414yes—
495C32×C4—22no—
496C32×C4—22no—
497C3⋊Dic3—22no—
498C3⋊Dic3—41no—
499C3⋊Dic3—41no—
500C3⋊Dic3—41no—
501C3×Dic3—22no—
502C3×Dic3—22no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C25—31no—
507C22×D4—31no—
508C22×D4—31no—
509C22×D4—31no—
510C23×C4—91no—
511C23×C4—91no—
512C23×C4—91no—
513#120—38no—
514C4×D4—184no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4—91no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—91no—
523C2×C22⋊C4—91no—
524C2×C22⋊C4—91no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—184no—
534C2×C22⋊C4D3211yescharacteristic
535C2×C42—31no—
536C2×C42—91no—
537C2×C42—91no—
538#95—31no—
539#95—31no—
540#95—91no—
541#95—91no—
542#95—91no—
543#95—91no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—21no—
557C23×C3—22no—
558C23×C3—32no—
559C23×C3—32no—
560C23×C3—32no—
561C23×C3—32no—
562C23×C3—32no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—68no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—61no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—124no—
587C23×C3—124no—
588C23×C3—124no—
589C23×C3—124no—
590C23×C3—124no—
591C23×C3—124no—
592C23×C3C2×C4×D312yes—
593C23×C3C22×Dic312yes—
594C23×C3C23×D311yescharacteristic
595C23×C3C23×D311yescharacteristic
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—28no—
613C22×D3—44no—
614C22×D3—44no—
615C22×D3—44no—
616C22×D3—44no—
617C22×D3—44no—
618C22×D3—44no—
619C22×D3D3×D412yes—
620C22×D3#23712yes—
621C22×D3C22×Dic312yes—
622C22×D3C22×Dic312yes—
623C22×D3C22×Dic312yes—
624C3×D4—68no—
625C3×D4—124no—
626C3×D4—124no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4C2×C4×D312yes—
657C2×C3×C4C2×C4×D312yes—
658C2×C3×C4C22×Dic312yes—
659C2×C3×C4C22×Dic312yes—
660#67—44no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—62no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—62no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—121no—
701C2×Dic3—121no—
702C2×Dic3—121no—
703C2×Dic3—121no—
704C2×Dic3—121no—
705C2×Dic3—121no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—124no—
711C2×Dic3—124no—
712C2×Dic3—124no—
713C2×Dic3D3×D412yes—
714C2×Dic3C22×Dic312yes—
715D12—28no—
716D12—44no—
717C4×D3—124no—
718C4×D3—124no—
719C4×D3—124no—
720C2×C32—42no—
721C2×C32C2×C4×D411yescharacteristic
722C2×C32#51811yescharacteristic
723C2×C32#51811yescharacteristic
724C2×C32#53411yescharacteristic
725C2×C32#53511yescharacteristic
726C2×C32#53811yescharacteristic
727C2×C32#53811yescharacteristic
728C3×D3—24no—
729C3×D3—42no—
730C3×D3—42no—
731C24—31no—
732C24—31no—
733C24—31no—
734C24—34no—
735C24—62no—
736C24—62no—
737C24—121no—
738C24—121no—
739C24—121no—
740C24—121no—
741C24C2×D3211yescharacteristic
742C2×D4—34no—
743C2×D4—34no—
744C2×D4—34no—
745C2×D4—62no—
746C2×D4—62no—
747C2×D4—121no—
748C2×D4—121no—
749C2×D4—121no—
750C2×D4—121no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—94no—
757C22×C4—91no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—91no—
761C22×C4—182no—
762C22×C4—182no—
763C22×C4—361no—
764C22×C4—361no—
765C22×C4—361no—
766C22×C4—361no—
767C22×C4—361no—
768C22×C4—361no—
769C22×C4C2×D3211yescharacteristic
770C22×C4C2×D3211yescharacteristic
771C4⋊C4—62no—
772C4⋊C4—361no—
773C4⋊C4—361no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—62no—
777C22⋊C4—121no—
778C22⋊C4—182no—
779C22⋊C4—182no—
780C22⋊C4—182no—
781C22⋊C4—182no—
782C22⋊C4—182no—
783C22⋊C4—182no—
784C22⋊C4—361no—
785C22⋊C4—361no—
786C22⋊C4—361no—
787C22⋊C4—361no—
788C22⋊C4—361no—
789C22⋊C4D3×Dic314yescomplemented
790C42—121no—
791C42—182no—
792C42—361no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—34no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—81no—
831C22×C3—81no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—1216no—
835C22×C3—121no—
836C22×C3—121no—
837C22×C3—121no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3C22×C4×D311yescharacteristic
844C22×C3C2×D3×D411yescharacteristic
845C22×C3C2×D3×D411yescharacteristic
846C22×C3C2×#23711yescharacteristic
847C22×C3#100411yescharacteristic
848C22×C3#100411yescharacteristic
849C22×C3#100411yescharacteristic
850C22×C3#100411yescharacteristic
851C22×C3#100411yescharacteristic
852C22×C3D3×#4111yescharacteristic
853C22×C3#100911yescharacteristic
854C22×C3#100911yescharacteristic
855C22×C3#100911yescharacteristic
856C22×C3C23×Dic311yescharacteristic
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—416no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3D4×Dic314yes—
879C3×C4—22no—
880C3×C4—22no—
881C3×C4—22no—
882C3×C4—22no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—62no—
886C3×C4—62no—
887C3×C4—121no—
888C3×C4—121no—
889C3×C4—121no—
890Dic3—22no—
891Dic3—22no—
892Dic3—41no—
893Dic3—41no—
894Dic3—41no—
895Dic3—62no—
896Dic3—62no—
897Dic3—122no—
898Dic3—122no—
899Dic3—121no—
900Dic3—121no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—241no—
906Dic3—241no—
907C32#232111yescharacteristic, complemented, Sylow
908C23—21no—
909C23—21no—
910C23—21no—
911C23—21no—
912C23—21no—
913C23—21no—
914C23—32no—
915C23—32no—
916C23—32no—
917C23—32no—
918C23—32no—
919C23—68no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—124no—
937C23—124no—
938C23—124no—
939C23—124no—
940C23—124no—
941C23—124no—
942C23C2×D3×Dic312yes—
943C23C22×D3211yescharacteristic
944D4—68no—
945D4—124no—
946D4—124no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—32no—
952C2×C4—32no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—92no—
967C2×C4—181no—
968C2×C4—181no—
969C2×C4—181no—
970C2×C4—181no—
971C2×C4—181no—
972C2×C4—181no—
973C2×C4—181no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—364no—
979C2×C4—364no—
980C2×C4—364no—
981C2×C4C2×D3×Dic312yes—
982C2×C4C2×D3×Dic312yes—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—42no—
991C2×C3—42no—
992C2×C3—64no—
993C2×C3—82no—
994C2×C3—122no—
995C2×C3—122no—
996C2×C3#552111yescharacteristic
997C2×C3C4×D3×D411yescharacteristic
998C2×C3#554511yescharacteristic
999C2×C3#558911yescharacteristic
1000C2×C3#559211yescharacteristic
1001C2×C3#559311yescharacteristic
1002C2×C3#559311yescharacteristic
1003C2×C3#560511yescharacteristic
1004C2×C3#565711yescharacteristic
1005C2×C3#567411yescharacteristic
1006C2×C3#570411yescharacteristic
1007C2×C3C2×D4×Dic311yescharacteristic
1008C2×C3#579811yescharacteristic
1009C2×C3#579811yescharacteristic
1010D3—24no—
1011D3—42no—
1012D3—42no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—34no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—62no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—1216no—
1034C22—121no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22#6430711yescharacteristic
1043C22#6430711yescharacteristic
1044C22D32×D411yescharacteristic
1045C22D3×#23711yescharacteristic
1046C22#6431311yescharacteristic
1047C22#6431411yescharacteristic
1048C22C22×D3×Dic311yescharacteristic
1049C4—22no—
1050C4—22no—
1051C4—62no—
1052C4—62no—
1053C4—121no—
1054C4—121no—
1055C4—121no—
1056C4—182no—
1057C4—361no—
1058C4—361no—
1059C4—361no—
1060C3—21no—
1061C3#7582611yescharacteristic, complemented
1062C3#8257811yescharacteristic, complemented
1063C2—42no—
1064C2—64no—
1065C2—122no—
1066C2—122no—
1067C2#1059412611yescharacteristic
1068C2#1059421311yescharacteristic
1069C2#1059426311yescharacteristic
1070C2#1059427011yescharacteristic
1071C2#1059498211yescharacteristic
1072C2D3×D4×Dic311yescharacteristic
1073C2#1059521511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#882C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#217C2semidirect
3. C2×#63898C2semidirect
4. #10592650C2semidirect
5. C3×#4951C2semidirect
6. #10591721C2semidirect
7. #10591707C2semidirect
8. #10591706C2semidirect
9. #10591379C2semidirect
10. #10591376C2semidirect
11. #10591376C2semidirect
12. Dic3×(C2×D3)⋊C4C2semidirect
13. #10591318C2semidirect
14. #10591307C2semidirect
15. #10591286C2semidirect
24. C22×D3×Dic3C22semidirect
28. C2×C4⋊(C3⋊Dic3)C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
34. C2×C3×C4⋊Dic3C22semidirect
35. C2×C3×C4×Dic3C22semidirect
36. C3×#882C4semidirect
38. C2×Dic3⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. C2×Dic32C22semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
78. #4951D3semidirect
94. C23×C3×D3C2×C4semidirect
106. C2×C3×#67C2×C4semidirect
117. C2×C3×D12C2×C4semidirect
126. C2×D3×Dic3D4semidirect
127. C32×C22⋊C4C2×C4semidirect
134. C3×(C2×D3)⋊C4C2×C4semidirect
135. C3×(C2×D3)⋊C4C2×C4semidirect
208. C2×C4⋊Dic3C2×D3semidirect
215. C2×C4×Dic3C2×D3semidirect
217. #882Dic3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
342. C23×D3C2×Dic3semidirect
368. C2×#67C2×Dic3semidirect
400. C2×D12C2×Dic3semidirect
416. C3×C22⋊C4C4×D3semidirect
417. C3×C22⋊C4C2×Dic3semidirect
445. (C2×D3)⋊C4C2×Dic3semidirect
446. (C2×D3)⋊C4C2×Dic3semidirect
789. C22⋊C4D3×Dic3semidirect
907. C32#2321semidirect
1061. C3#75826semidirect
1062. C3#82578semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8822
C2×D3×#2172
C2×#638982
#105926502
C3×#49512
#105917212
#105917072
#105917062
#105913792
#105913762
Dic3×(C2×D3)⋊C42
#105913182
#105913072
#105912862
#825783
#758263