Finite Group Databasebeta

← #11803312

Subgroups — #11803312

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×#63922C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×#63879C211yesmaximal, characteristic, complemented
4#10592368C211yesmaximal, characteristic, complemented
5C3×#4668C211yesmaximal, characteristic, complemented
6C3×#4665C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591384C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591368C211yesmaximal, characteristic, complemented
12#10591323C211yesmaximal, characteristic, complemented
13#10591285C211yesmaximal, characteristic, complemented
14#10591281C211yesmaximal, characteristic, complemented
15#10591266C211yesmaximal, characteristic, complemented
16#74876—31nomaximal
17#74592—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×#626C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic, complemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
45C2×Dic32C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63922C418yescomplemented
48D3×(C2×D3)⋊C4—24no—
49#63879—24no—
50C32×#95C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×#937—31no—
57C2×C4×#67—31no—
58C22×(C2×D3)⋊C4—31no—
59C2×#882—31no—
60C2×#67⋊C4—31no—
61C2×D3×C22⋊C4—31no—
62C3×#386—31no—
63C3×#385—31no—
64#5221—31no—
65#5213—31no—
66#5213—31no—
67#4990—31no—
68#4990—31no—
69#4988—31no—
70#4988—31no—
71#4957—31no—
72#4956—31no—
73#4955—31no—
74#4955—31no—
75#4944—31no—
76#4944—31no—
77Dic3×C22⋊C4—31no—
78#4670—31no—
79#4669—31no—
80#4669—31no—
81#4669—31no—
82#4669—61no—
83#4668D311yescharacteristic, complemented
84#4666—31no—
85#4665—31no—
86#4665D311yescharacteristic, complemented
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×D32—22no—
92C22×D32—22no—
93C22×D32—41no—
94C22×D32—41no—
95C22×D32—41no—
96C22×D32—41no—
97C22×D32C2×C414yescomplemented
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C2×C3×D12—41no—
110C2×C3×D12—41no—
111C2×C3×D12C2×C414yescomplemented
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—41no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3—41no—
118C2×#626—41no—
119C2×#626—41no—
120C2×#626C2×C414yescomplemented
121C2×#625—22no—
122C2×#625—22no—
123C2×#625C2×C414yes—
124C2×D3×Dic3—41no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3D414yescomplemented
127#3752—22no—
128#3752—41no—
129#3752C2×C414yescomplemented
130#3750—22no—
131C4×C3⋊Dic3—41no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—41no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4C2×C414yescomplemented
137C3×C4⋊Dic3—41no—
138C3×Dic3⋊C4—41no—
139#3722—22no—
140#3722—41no—
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)⋊Dic3C2×C414yescomplemented
147Dic32—22no—
148Dic32—41no—
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C22×C3×D4—31no—
153C23×C3×C4—31no—
154C23×C3×C4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C23×Dic3—31no—
159C22×D12—31no—
160C22×D12C2×D311yescharacteristic
161C22×C4×D3—31no—
162C22×C4×D3C2×D311yescharacteristic
163C22×C4×D3C2×D311yescharacteristic, complemented
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177#937—38no—
178C4×#67—64no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—61no—
196C2×(C2×D3)⋊C4—61no—
197C2×(C2×D3)⋊C4—61no—
198C2×(C2×D3)⋊C4—64no—
199C2×(C2×D3)⋊C4C2×D311yescharacteristic
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
204C2×C4⋊Dic3C2×D311yescharacteristic, complemented
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—61no—
208C2×Dic3⋊C4C2×D311yescharacteristic, complemented
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—61no—
216#882—38no—
217#67⋊C4—64no—
218D3×C22⋊C4—64no—
219C3×#95—21no—
220C3×#95—31no—
221C3×#95—31no—
222C3×#95C2×D311yescharacteristic, complemented
223C3×#95C2×D311yescharacteristic, complemented
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—61no—
231C3⋊#95C2×D311yescharacteristic, complemented
232C3⋊#95C2×D311yescharacteristic, complemented
233C23×C32C2411yescharacteristic
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C22×C412yes—
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×D3C22×C412yes—
258C22×C3×D3C22×C412yes—
259C22×C3×D3C22×C412yes—
260C22×C3×D3C2×D412yes—
261C22×C3×D3#4112yes—
262C2×D32—28no—
263C2×D32—44no—
264C2×D32—44no—
265C2×D32—44no—
266C2×D32—44no—
267C2×D32—44no—
268C2×D32—44no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C22×C412yes—
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⋊Dic3C22×C412yes—
286C2×C3⋊Dic3C2×D412yes—
287C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
301C2×C3×Dic3C2×D412yes—
302C3×D12—44no—
303C3×C4×D3—44no—
304C3×C4×D3—44no—
305#626—44no—
306#625—28no—
307D3×Dic3—44no—
308C2×#120—91no—
309C2×C4×D4—91no—
310C22×C22⋊C4—91no—
311#390—91no—
312#390—91no—
313#388—91no—
314#388—91no—
315#388—91no—
316#388—91no—
317#386—31no—
318#386—91no—
319#386—91no—
320#385—31no—
321#379—91no—
322C4×C22⋊C4—91no—
323C24×C3—31no—
324C24×C3—31no—
325C24×C3—31no—
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—34no—
329C23×D3—34no—
330C23×D3—61no—
331C23×D3—62no—
332C23×D3—62no—
333C23×D3—62no—
334C23×D3—62no—
335C23×D3—121no—
336C23×D3—121no—
337C23×D3—121no—
338C23×D3—121no—
339C23×D3—121no—
340C23×D3—121no—
341C23×D3—121no—
342C23×D3—121no—
343C23×D3C22×D311yescharacteristic
344C23×D3C22×D311yescharacteristic
345C23×D3C22×D311yescharacteristic
346C2×C3×D4—34no—
347C2×C3×D4—121no—
348C2×C3×D4—121no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—62no—
358C22×C3×C4—62no—
359C22×C3×C4—121no—
360C22×C3×C4—121no—
361C22×C3×C4—121no—
362C22×C3×C4—121no—
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—62no—
373C2×#67—62no—
374C2×#67—62no—
375C2×#67—62no—
376C2×#67—121no—
377C2×#67—121no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—34no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—61no—
388C22×Dic3—121no—
389C22×Dic3—121no—
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C2×D12—34no—
396C2×D12—41no—
397C2×D12—41no—
398C2×D12—121no—
399C2×D12—121no—
400C2×D12C4×D314yescomplemented
401C2×C4×D3—22no—
402C2×C4×D3—22no—
403C2×C4×D3—34no—
404C2×C4×D3—41no—
405C2×C4×D3—41no—
406C2×C4×D3—41no—
407C2×C4×D3—41no—
408C2×C4×D3—121no—
409C2×C4×D3—121no—
410C3×C4⋊C4—121no—
411C3×C4⋊C4—121no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—62no—
414C3×C22⋊C4—62no—
415C3×C22⋊C4—121no—
416C3×C22⋊C4—121no—
417#217—34no—
418#217—62no—
419#217—62no—
420#217—62no—
421#217—121no—
422#217—121no—
423(C2×D3)⋊C4—22no—
424(C2×D3)⋊C4—22no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—41no—
429(C2×D3)⋊C4—41no—
430(C2×D3)⋊C4—64no—
431(C2×D3)⋊C4—62no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—122no—
439(C2×D3)⋊C4—121no—
440(C2×D3)⋊C4—121no—
441(C2×D3)⋊C4—121no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4—122no—
444(C2×D3)⋊C4—121no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4C4×D314yescomplemented
447C4⋊Dic3—41no—
448Dic3⋊C4—41no—
449Dic3⋊C4—62no—
450Dic3⋊C4—62no—
451Dic3⋊C4—122no—
452C4×Dic3—62no—
453C4×Dic3—62no—
454C4×Dic3—121no—
455C4×Dic3—121no—
456C4×Dic3—121no—
457C4×Dic3—121no—
458C4×Dic3—122no—
459C22×C32C23×C411yescharacteristic
460C22×C32C22×D411yescharacteristic
461C22×C32C2×#4111yescharacteristic
462C22×C32H(5,𝔽2)11yescharacteristic
463C22×C32H(5,𝔽2)11yescharacteristic
464C22×C32H(5,𝔽2)11yescharacteristic
465C22×C32H(5,𝔽2)11yescharacteristic
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3—22no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
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—41no—
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×D3C4×D414yes—
494D32—416no—
495C32×C4—22no—
496C32×C4—41no—
497C32×C4—41no—
498C3⋊Dic3—22no—
499C3⋊Dic3—22no—
500C3⋊Dic3—41no—
501C3×Dic3—22no—
502C3×Dic3—22no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3—41no—
506C25—91no—
507C22×D4—31no—
508C22×D4—91no—
509C22×D4—91no—
510C23×C4—31no—
511C23×C4—31no—
512C23×C4—91no—
513#120—98no—
514C4×D4—184no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—91no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—31no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
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—91no—
534C2×C22⋊C4—184no—
535C2×C42—91no—
536C2×C42—91no—
537C2×C42—91no—
538#95—31no—
539#95—31no—
540#95—91no—
541#95—91no—
542#95—91no—
543#95D3211yescharacteristic, complemented
544C23×C3—21no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—32no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3C23×D311yescharacteristic
567C23×C3C23×D311yescharacteristic
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—62no—
587C22×D3—68no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—68no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3—121no—
607C22×D3—124no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—124no—
611C22×D3—124no—
612C22×D3—124no—
613C22×D3—124no—
614C22×D3—124no—
615C22×D3—124no—
616C22×D3—124no—
617C22×D3—124no—
618C22×D3—124no—
619C22×D3C2×C4×D312yes—
620C22×D3C2×C4×D312yes—
621C22×D3C2×C4×D312yes—
622C22×D3D3×D412yes—
623C22×D3#23912yes—
624C3×D4—124no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
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—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—22no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—41no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—124no—
666C2×C3×C4—124no—
667C2×C3×C4C2×C4×D312yes—
668C2×C3×C4C2×C4×D312yes—
669#67—68no—
670#67—68no—
671#67—124no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—32no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—62no—
690C2×Dic3—62no—
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—62no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—61no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—121no—
711C2×Dic3—121no—
712C2×Dic3—124no—
713C2×Dic3C2×C4×D312yes—
714C2×Dic3D3×D412yes—
715D12—44no—
716D12—124no—
717C4×D3—44no—
718C4×D3—44no—
719C4×D3—124no—
720C2×C32C2×C4×D411yescharacteristic
721C2×C32#51811yescharacteristic
722C2×C32#51811yescharacteristic
723C2×C32#53411yescharacteristic
724C2×C32#53511yescharacteristic
725C2×C32#53811yescharacteristic
726C2×C32#53811yescharacteristic
727C3⋊D3—42no—
728C3×D3—24no—
729C3×D3—42no—
730C3×D3—42no—
731C24—31no—
732C24—31no—
733C24—31no—
734C24—94no—
735C24—91no—
736C24—182no—
737C24—182no—
738C24—361no—
739C24—361no—
740C24—361no—
741C24—361no—
742C2×D4—34no—
743C2×D4—94no—
744C2×D4—94no—
745C2×D4—121no—
746C2×D4—121no—
747C2×D4—182no—
748C2×D4—182no—
749C2×D4—361no—
750C2×D4—361no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—62no—
757C22×C4—62no—
758C22×C4—94no—
759C22×C4—91no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—121no—
763C22×C4—121no—
764C22×C4—121no—
765C22×C4—121no—
766C22×C4—361no—
767C22×C4—361no—
768C22×C4C2×D3211yescharacteristic
769C22×C4C2×D3211yescharacteristic
770C22×C4C2×D3211yescharacteristic
771C4⋊C4—121no—
772C4⋊C4—121no—
773C4⋊C4—182no—
774C22⋊C4—34no—
775C22⋊C4—62no—
776C22⋊C4—62no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—121no—
780C22⋊C4—121no—
781C22⋊C4—182no—
782C22⋊C4—182no—
783C22⋊C4—182no—
784C22⋊C4—182no—
785C22⋊C4—182no—
786C22⋊C4—361no—
787C22⋊C4—361no—
788C22⋊C4—361no—
789C22⋊C4—361no—
790C42—182no—
791C42—361no—
792C42—361no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—34no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3C22×C4×D311yescharacteristic
822C22×C3C22×C4×D311yescharacteristic
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
825C22×C3#100411yescharacteristic
826C22×C3#100411yescharacteristic
827C22×C3#100411yescharacteristic
828C22×C3#100411yescharacteristic
829C22×C3#100411yescharacteristic
830C22×C3C2×#23911yescharacteristic
831C22×C3D3×#4111yescharacteristic
832C22×C3#100911yescharacteristic
833C22×C3#100911yescharacteristic
834C22×C3#100911yescharacteristic
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—122no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—1216no—
865C2×D3—1216no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—241no—
875C2×D3—241no—
876C2×D3—241no—
877C2×D3—241no—
878C2×D3#89314yes—
879C3×C4—22no—
880C3×C4—22no—
881C3×C4—42no—
882C3×C4—41no—
883C3×C4—41no—
884C3×C4—41no—
885C3×C4—41no—
886C3×C4—62no—
887C3×C4—62no—
888C3×C4—81no—
889C3×C4—81no—
890C3×C4—121no—
891C3×C4—121no—
892C3×C4—121no—
893Dic3—22no—
894Dic3—22no—
895Dic3—41no—
896Dic3—41no—
897Dic3—41no—
898Dic3—62no—
899Dic3—62no—
900Dic3—62no—
901Dic3—62no—
902Dic3—122no—
903Dic3—122no—
904Dic3—122no—
905Dic3—121no—
906Dic3—121no—
907C32#232111yescharacteristic, complemented, Sylow
908C23—32no—
909C23—32no—
910C23—32no—
911C23—32no—
912C23—32no—
913C23—61no—
914C23—61no—
915C23—61no—
916C23—61no—
917C23—61no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—61no—
922C23—61no—
923C23—61no—
924C23—61no—
925C23—61no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—92no—
930C23—188no—
931C23—181no—
932C23—181no—
933C23—181no—
934C23—181no—
935C23—181no—
936C23—181no—
937C23—364no—
938C23—364no—
939C23—364no—
940C23—364no—
941C23—364no—
942C23—364no—
943C23C22×D3211yescharacteristic
944D4—124no—
945D4—188no—
946D4—364no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—32no—
956C2×C4—32no—
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—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—92no—
971C2×C4—92no—
972C2×C4—124no—
973C2×C4—124no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—364no—
982C2×C4C4×D3212yes—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—64no—
991C2×C3—122no—
992C2×C3—122no—
993C2×C3#548611yescharacteristic
994C2×C3C2×#89311yescharacteristic
995C2×C3C4×D3×D411yescharacteristic
996C2×C3#554511yescharacteristic
997C2×C3#554511yescharacteristic
998C2×C3#554511yescharacteristic
999C2×C3#558911yescharacteristic
1000C2×C3#559211yescharacteristic
1001C2×C3#560711yescharacteristic
1002C2×C3#561311yescharacteristic
1003C2×C3#564411yescharacteristic
1004C2×C3#564411yescharacteristic
1005C2×C3#565311yescharacteristic
1006C2×C3#565711yescharacteristic
1007D3—24no—
1008D3—42no—
1009D3—42no—
1010D3—122no—
1011D3—122no—
1012D3—242no—
1013C22—34no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—121no—
1027C22—121no—
1028C22—121no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—182no—
1035C22—182no—
1036C22—182no—
1037C22—3616no—
1038C22—361no—
1039C22—361no—
1040C22—361no—
1041C22—361no—
1042C22C2×C4×D3211yescharacteristic
1043C22#6430711yescharacteristic
1044C22#6430711yescharacteristic
1045C22D32×D411yescharacteristic
1046C22#6431311yescharacteristic
1047C22#6431411yescharacteristic
1048C22D3×#23911yescharacteristic
1049C4—22no—
1050C4—41no—
1051C4—41no—
1052C4—62no—
1053C4—62no—
1054C4—121no—
1055C4—121no—
1056C4—121no—
1057C4—182no—
1058C4—182no—
1059C4—361no—
1060C3—21no—
1061C3#7459211yescharacteristic, complemented
1062C3#7487611yescharacteristic, complemented
1063C2—64no—
1064C2—122no—
1065C2—122no—
1066C2—362no—
1067C2#1059399611yescharacteristic
1068C2#1059425411yescharacteristic
1069C2#1059426211yescharacteristic
1070C2#1059426911yescharacteristic
1071C2D3×#89311yescharacteristic
1072C2#1059465011yescharacteristic
1073C2#1059465111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63922C2
hypercenter#95D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×D3×(C2×D3)⋊C4C2semidirect
3. C2×#63879C2semidirect
4. #10592368C2semidirect
5. C3×#4668C2semidirect
6. C3×#4665C2semidirect
7. #10591399C2semidirect
8. #10591384C2semidirect
9. #10591382C2semidirect
10. #10591381C2semidirect
11. #10591368C2semidirect
12. #10591323C2semidirect
13. #10591285C2semidirect
14. #10591281C2semidirect
15. #10591266C2semidirect
21. C22×C3×C4×D3C22semidirect
28. C2×#3750C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
43. C2×(C2×D3)⋊Dic3C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×Dic32C22semidirect
46. C2×Dic32C22semidirect
47. #63922C4semidirect
50. C32×#95C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
83. #4668D3semidirect
86. #4665D3semidirect
97. C22×D32C2×C4semidirect
111. C2×C3×D12C2×C4semidirect
120. C2×#626C2×C4semidirect
126. C2×D3×Dic3D4semidirect
129. #3752C2×C4semidirect
136. C3×(C2×D3)⋊C4C2×C4semidirect
146. (C2×D3)⋊Dic3C2×C4semidirect
163. C22×C4×D3C2×D3semidirect
203. C2×(C2×D3)⋊C4C2×D3semidirect
204. C2×C4⋊Dic3C2×D3semidirect
208. C2×Dic3⋊C4C2×D3semidirect
222. C3×#95C2×D3semidirect
223. C3×#95C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
400. C2×D12C4×D3semidirect
446. (C2×D3)⋊C4C4×D3semidirect
543. #95D32semidirect
907. C32#2321semidirect
1061. C3#74592semidirect
1062. C3#74876semidirect

Maximal subgroups

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

subgroupindex
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#638792
#105923682
C3×#46682
C3×#46652
#105913992
#105913842
#105913822
#105913812
#105913682
#105913232
#105912852
#105912812
#105912662
#748763
#745923