Finite Group Databasebeta

← #11803266

Subgroups — #11803266

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×#893C211yesmaximal, characteristic, complemented
2C2×#63922C211yesmaximal, characteristic
3C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4#10592689C211yesmaximal, characteristic, complemented
5C3×#4990C211yesmaximal, characteristic, complemented
6#10591399C211yesmaximal, characteristic, complemented
7#10591385C211yesmaximal, characteristic, complemented
8#10591383C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12#10591373C211yesmaximal, characteristic, complemented
13#10591305C211yesmaximal, characteristic, complemented
14C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#82395—31nomaximal
17#75826—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×#626C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
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×C4×Dic3C2211yescharacteristic, complemented
37C3×#893—24no—
38C2×#3724C2211yescharacteristic, complemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48#63922C418yescomplemented
49D3×(C2×D3)⋊C4—24no—
50#63658C2211yescharacteristic, complemented
51#63658C2211yescharacteristic, complemented
52C3×C3⋊#95C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×C3×C4×D4—31no—
57C2×#937—31no—
58C22×(C2×D3)⋊C4—31no—
59C2×#893D311yescharacteristic, complemented
60C2×#882—31no—
61C2×D3×C22⋊C4—31no—
62C3×#388—31no—
63#5220—31no—
64#5213—31no—
65#5213—31no—
66C4×#217—31no—
67#4990—31no—
68#4990—31no—
69#4990—61no—
70#4990D311yescharacteristic, complemented
71#4957—31no—
72#4957—31no—
73#4957—31no—
74#4956—31no—
75#4955—31no—
76#4955—31no—
77#4951—31no—
78#4946—31no—
79#4940—31no—
80#4940—31no—
81#4939—31no—
82C4×(C2×D3)⋊C4—31no—
83#4669—31no—
84#4668—31no—
85#4665—31no—
86#4665—31no—
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—22no—
110C2×C3×D12—22no—
111C2×C3×D12C2×C414yes—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—41no—
114C2×C3×C4×D3—41no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3D414yescomplemented
118C2×#626—41no—
119C2×#626—41no—
120C2×#626C2×C414yescomplemented
121C2×#625—41no—
122C2×#625—41no—
123C2×#625C2×C414yescomplemented
124C2×D3×Dic3—22no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3—41no—
127C32×C4⋊C4—22no—
128#3752—22no—
129#3752—41no—
130#3752C2×C414yescomplemented
131C4×C3⋊Dic3—41no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—41no—
136C3×(C2×D3)⋊C4C2×C414yescomplemented
137C3×C4×Dic3—22no—
138C3×C4×Dic3—41no—
139#3724—41no—
140Dic3⋊Dic3—41no—
141#3722—22no—
142#3722—41no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3—41no—
147(C2×D3)⋊Dic3—41no—
148(C2×D3)⋊Dic3C2×C414yescomplemented
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
164C3×C4×D4—64no—
165C2×C3×C4⋊C4—21no—
166C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
167C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C42—31no—
174C2×C3×C42—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181#937—38no—
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—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—61no—
199C2×(C2×D3)⋊C4—61no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4—64no—
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
207C2×C4⋊Dic3—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—61no—
214C2×C4×Dic3C2×D311yescharacteristic, complemented
215C2×C4×Dic3C2×D311yescharacteristic, complemented
216#893—24no—
217#882—38no—
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×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×C4C22×C412yes—
277C2×C32×C4C2×D412yes—
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⋊Dic3C22×C412yes—
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—28no—
303C3×C4×D3—44no—
304C3×C4×D3—44no—
305#626—44no—
306#625—44no—
307D3×Dic3—44no—
308C2×#120—91no—
309C2×C4×D4—31no—
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—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—62no—
348C2×C3×D4—62no—
349C22×C3×C4—21no—
350C22×C3×C4—21no—
351C22×C3×C4—21no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—34no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
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—121no—
373C2×#67—121no—
374C2×#67—121no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67—121no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—62no—
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—34no—
398C2×D12—121no—
399C2×D12—121no—
400C2×D12C4×D314yes—
401C2×C4×D3—22no—
402C2×C4×D3—41no—
403C2×C4×D3—41no—
404C2×C4×D3—41no—
405C2×C4×D3—41no—
406C2×C4×D3—62no—
407C2×C4×D3—121no—
408C2×C4×D3—121no—
409C2×C4×D3#6714yescomplemented
410C3×C4⋊C4—22no—
411C3×C4⋊C4—22no—
412C3×C4⋊C4—42no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—62no—
415C3×C22⋊C4—62no—
416C3×C22⋊C4—62no—
417C3×C22⋊C4—121no—
418C3×C42—62no—
419C3×C42—121no—
420#217—34no—
421#217—62no—
422#217—62no—
423#217—121no—
424#217—121no—
425#217—121no—
426(C2×D3)⋊C4—22no—
427(C2×D3)⋊C4—22no—
428(C2×D3)⋊C4—22no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—41no—
433(C2×D3)⋊C4—64no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—122no—
441(C2×D3)⋊C4—121no—
442(C2×D3)⋊C4—121no—
443(C2×D3)⋊C4—121no—
444(C2×D3)⋊C4—121no—
445(C2×D3)⋊C4—122no—
446(C2×D3)⋊C4—121no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4C4×D314yescomplemented
450C4⋊Dic3—121no—
451Dic3⋊C4—121no—
452Dic3⋊C4—121no—
453Dic3⋊C4—121no—
454C4×Dic3—22no—
455C4×Dic3—41no—
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—22no—
497C32×C4—41no—
498C3⋊Dic3—22no—
499C3⋊Dic3—41no—
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—64no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4D3211yescharacteristic, complemented
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—31no—
536C2×C42—31no—
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—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×D3#23512yes—
623C22×D3C2×#6712yes—
624C3×D4—68no—
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—22no—
640C2×C3×C4—22no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—41no—
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—61no—
651C2×C3×C4—61no—
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—124no—
664C2×C3×C4—124no—
665C2×C3×C4C2×C4×D312yes—
666C2×C3×C4C2×C4×D312yes—
667C2×C3×C4D3×D412yes—
668C2×C3×C4C2×#6712yes—
669#67—124no—
670#67—124no—
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—62no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—62no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—121no—
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×Dic3C2×#6712yes—
715D12—28no—
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—62no—
744C2×D4—62no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—361no—
748C2×D4—361no—
749C2×D4—361no—
750C2×D4—361no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—34no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—62no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—91no—
761C22×C4—121no—
762C22×C4—121no—
763C22×C4—121no—
764C22×C4—121no—
765C22×C4—182no—
766C22×C4—361no—
767C22×C4—361no—
768C22×C4C2×D3211yescharacteristic
769C22×C4C2×D3211yescharacteristic
770C22×C4C2×D3211yescharacteristic
771C4⋊C4—22no—
772C4⋊C4—361no—
773C4⋊C4—361no—
774C22⋊C4—34no—
775C22⋊C4—62no—
776C22⋊C4—62no—
777C22⋊C4—62no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—121no—
781C22⋊C4—182no—
782C22⋊C4—182no—
783C22⋊C4—182no—
784C22⋊C4—182no—
785C22⋊C4—361no—
786C22⋊C4—361no—
787C22⋊C4—361no—
788C22⋊C4—361no—
789C22⋊C4—361no—
790C42—62no—
791C42—121no—
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×#23511yescharacteristic
824C22×C3C2×D3×D411yescharacteristic
825C22×C3#100411yescharacteristic
826C22×C3#100411yescharacteristic
827C22×C3#100411yescharacteristic
828C22×C3D3×#4111yescharacteristic
829C22×C3#100911yescharacteristic
830C22×C3#100911yescharacteristic
831C22×C3#100911yescharacteristic
832C22×C3#100911yescharacteristic
833C22×C3#100911yescharacteristic
834C22×C3C22×#6711yescharacteristic
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×D3C4×#6714yes—
879C3×C4—22no—
880C3×C4—22no—
881C3×C4—22no—
882C3×C4—22no—
883C3×C4—42no—
884C3×C4—42no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—62no—
888C3×C4—62no—
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—122no—
901Dic3—122no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—241no—
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—68no—
945D4—364no—
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—32no—
955C2×C4—32no—
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—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—92no—
970C2×C4—124no—
971C2×C4—124no—
972C2×C4—181no—
973C2×C4—181no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—364no—
981C2×C4C4×D3212yes—
982C2×C4D3×#6712yes—
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#552111yescharacteristic
994C2×C3C4×D3×D411yescharacteristic
995C2×C3#554511yescharacteristic
996C2×C3#554511yescharacteristic
997C2×C3#554511yescharacteristic
998C2×C3#556011yescharacteristic
999C2×C3#556011yescharacteristic
1000C2×C3#560511yescharacteristic
1001C2×C3#565711yescharacteristic
1002C2×C3#567411yescharacteristic
1003C2×C3#570411yescharacteristic
1004C2×C3C2×C4×#6711yescharacteristic
1005C2×C3#580411yescharacteristic
1006C2×C3#583011yescharacteristic
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
1043C22D3×#23511yescharacteristic
1044C22#6431311yescharacteristic
1045C22#6431411yescharacteristic
1046C22#6432011yescharacteristic
1047C22#6432011yescharacteristic
1048C22C2×D3×#6711yescharacteristic
1049C4—22no—
1050C4—22no—
1051C4—41no—
1052C4—62no—
1053C4—62no—
1054C4—121no—
1055C4—121no—
1056C4—121no—
1057C4—182no—
1058C4—361no—
1059C4—361no—
1060C3—21no—
1061C3#7582611yescharacteristic, complemented
1062C3#8239511yescharacteristic, complemented
1063C2—64no—
1064C2—122no—
1065C2—122no—
1066C2—362no—
1067C2#1059460411yescharacteristic
1068C2#1059460611yescharacteristic
1069C2#1059463811yescharacteristic
1070C2#1059463911yescharacteristic
1071C2C4×D3×#6711yescharacteristic
1072C2#1059530211yescharacteristic
1073C2#1059542611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63922C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
3. C2×D3×(C2×D3)⋊C4C2semidirect
4. #10592689C2semidirect
5. C3×#4990C2semidirect
6. #10591399C2semidirect
7. #10591385C2semidirect
8. #10591383C2semidirect
9. #10591382C2semidirect
10. #10591381C2semidirect
11. #10591376C2semidirect
12. #10591373C2semidirect
13. #10591305C2semidirect
14. C4×(C2×D3)⋊Dic3C2semidirect
15. #10591202C2semidirect
21. C22×C3×C4×D3C22semidirect
25. C2×C32×C4⋊C4C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
34. C2×C3×(C2×D3)⋊C4C22semidirect
35. C2×C3×C4×Dic3C22semidirect
36. C2×C3×C4×Dic3C22semidirect
38. C2×#3724C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. #63922C4semidirect
50. #63658C22semidirect
51. #63658C22semidirect
52. C3×C3⋊#95C22semidirect
53. C3×C3⋊#95C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
59. C2×#893D3semidirect
70. #4990D3semidirect
97. C22×D32C2×C4semidirect
117. C2×C3×C4×D3D4semidirect
120. C2×#626C2×C4semidirect
123. C2×#625C2×C4semidirect
130. #3752C2×C4semidirect
136. C3×(C2×D3)⋊C4C2×C4semidirect
148. (C2×D3)⋊Dic3C2×C4semidirect
163. C22×C4×D3C2×D3semidirect
166. C2×C3×C4⋊C4C2×D3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
206. C2×(C2×D3)⋊C4C2×D3semidirect
214. C2×C4×Dic3C2×D3semidirect
215. C2×C4×Dic3C2×D3semidirect
231. C3⋊#95C2×D3semidirect
232. C3⋊#95C2×D3semidirect
409. C2×C4×D3#67semidirect
449. (C2×D3)⋊C4C4×D3semidirect
517. C2×C4⋊C4D32semidirect
907. C32#2321semidirect
1061. C3#75826semidirect
1062. C3#82395semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#639222
C2×D3×(C2×D3)⋊C42
#105926892
C3×#49902
#105913992
#105913852
#105913832
#105913822
#105913812
#105913762
#105913732
#105913052
C4×(C2×D3)⋊Dic32
#105912022
#823953
#758263