Finite Group Databasebeta

← #11803271

Subgroups — #11803271

Order 1152.

1745 conjugacy classes of subgroups.

The subgroup lattice has 1091 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
2C2×#63983C211yesmaximal, characteristic
3C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4#10592656C211yesmaximal, characteristic, complemented
5C3×#4957C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591711C211yesmaximal, characteristic, complemented
8#10591710C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591372C211yesmaximal, characteristic, complemented
11#10591289C211yesmaximal, characteristic, complemented
12#10591289C211yesmaximal, characteristic, complemented
13#10591283C211yesmaximal, characteristic, complemented
14#10591280C211yesmaximal, characteristic, complemented
15C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16#82395—31nomaximal
17#76429—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic, complemented
23C22×C3×C4×D3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic, complemented
26C2×#3757C2211yescharacteristic, complemented
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3750C2211yescharacteristic, complemented
30C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
31C2×C3×#217C2211yescharacteristic, complemented
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×C4×Dic3C2211yescharacteristic, complemented
38C2×C3×C4×Dic3C2211yescharacteristic, complemented
39C3×#67⋊C4—24no—
40#63983C418yescomplemented
41C2×#3722C2211yescharacteristic
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49D3×(C2×D3)⋊C4—24no—
50#63579C2211yescharacteristic, complemented
51#63579C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56C2×C3×C4×D4—31no—
57C2×#937—31no—
58C2×#937—31no—
59C22×(C2×D3)⋊C4—31no—
60C2×#67⋊C4D311yescharacteristic, complemented
61C2×D3×C22⋊C4—31no—
62C3×#390—31no—
63#5220—31no—
64#5220—31no—
65#5213—31no—
66#5213—31no—
67C4×#217—31no—
68#4990—31no—
69#4990—31no—
70#4990—31no—
71#4989—31no—
72#4958—31no—
73#4957—31no—
74#4957—31no—
75#4957—61no—
76#4957D311yescharacteristic, complemented
77#4956—31no—
78#4955—31no—
79#4955—31no—
80#4946—31no—
81#4945—31no—
82#4945—31no—
83#4940—31no—
84#4940—31no—
85#4940—31no—
86C4×(C2×D3)⋊C4—31no—
87C24×C32C2311yescharacteristic
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
100C2×#638—41no—
101C2×#638—41no—
102C2×#638C2×C414yescomplemented
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C2×C3×#67—22no—
107C2×C3×#67—22no—
108C2×C3×#67—41no—
109C2×C3×#67—41no—
110C2×C3×#67C2×C414yes—
111C2×C3×#67C2×C414yescomplemented
112C22×C3×Dic3—22no—
113C22×C3×Dic3—41no—
114C22×C3×Dic3—41no—
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×C4×D3—41no—
122C2×C3×C4×D3—41no—
123C2×C3×C4×D3D414yescomplemented
124C2×D3×Dic3—22no—
125C2×D3×Dic3—41no—
126C2×D3×Dic3—41no—
127C32×C22⋊C4—22no—
128#3757—41no—
129#3752—22no—
130#3752—41no—
131#3750—41no—
132C4×C3⋊Dic3—41no—
133C3×#217—41no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—41no—
137C3×Dic3⋊C4—22no—
138C3×Dic3⋊C4—41no—
139C3×C4×Dic3—22no—
140C3×C4×Dic3—41no—
141#3722—22no—
142#3722—41no—
143#3722C2×C414yescomplemented
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—41no—
147(C2×D3)⋊Dic3C2×C414yescomplemented
148(C2×D3)⋊Dic3C2×C414yescomplemented
149#2321—91noSylow
150C24×D3—31no—
151C24×D3—31no—
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C23×C3×C4—31no—
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—61no—
159C22×#67C2×D311yescharacteristic
160C22×#67C2×D311yescharacteristic
161C23×Dic3—31no—
162C23×Dic3C2×D311yescharacteristic, complemented
163C22×C4×D3—31no—
164C22×C4×D3C2×D311yescharacteristic
165C3×C4×D4—64no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C22⋊C4—21no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
174C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
175C2×C3×C42—31no—
176C2×C3×C42—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—61no—
185C2×#217C2×D311yescharacteristic, complemented
186#937—38no—
187#937—38no—
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—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—64no—
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—61no—
212C2×Dic3⋊C4C2×D311yescharacteristic, complemented
213C2×Dic3⋊C4C2×D311yescharacteristic, complemented
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—61no—
217C2×C4×Dic3C2×D311yescharacteristic, complemented
218C2×C4×Dic3C2×D311yescharacteristic, complemented
219#67⋊C4—24no—
220D3×C22⋊C4—64no—
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—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
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⋊D3C22×C412yes—
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—21no—
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×C4C2×D412yes—
275#638—44no—
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⋊Dic3C22×C412yes—
285C3×#67—28no—
286C3×#67—44no—
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×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—44no—
303C2×C3×Dic3C22×C412yes—
304C2×C3×Dic3C22×C412yes—
305C2×C3×Dic3C2×D412yes—
306C3×C4×D3—44no—
307D3×Dic3—44no—
308C2×#120—91no—
309C2×C4×D4—31no—
310C22×C22⋊C4—91no—
311#390—31no—
312#390—91no—
313#388—91no—
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×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C23×D3—31no—
329C23×D3—31no—
330C23×D3—34no—
331C23×D3—34no—
332C23×D3—61no—
333C23×D3—62no—
334C23×D3—62no—
335C23×D3—62no—
336C23×D3—62no—
337C23×D3—121no—
338C23×D3—121no—
339C23×D3—121no—
340C23×D3—121no—
341C23×D3—121no—
342C23×D3—121no—
343C23×D3—121no—
344C23×D3—121no—
345C23×D3C22×D311yescharacteristic
346C23×D3C22×D311yescharacteristic
347C2×C3×D4—34no—
348C2×C3×D4—34no—
349C2×C3×D4—62no—
350C2×C3×D4—62no—
351C2×C3×D4—121no—
352C2×C3×D4—121no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—34no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—62no—
363C22×C3×C4—121no—
364C22×C3×C4—121no—
365C22×C3×C4—121no—
366C22×C3×C4—121no—
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C2×#67—22no—
372C2×#67—22no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—41no—
376C2×#67—41no—
377C2×#67—64no—
378C2×#67—121no—
379C2×#67—121no—
380C2×#67—121no—
381C2×#67—121no—
382C2×#67—122no—
383C2×#67—122no—
384C2×#67C4×D314yes—
385C2×#67C4×D314yescomplemented
386C22×Dic3—22no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—41no—
394C22×Dic3—41no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398C22×Dic3—62no—
399C22×Dic3—121no—
400C22×Dic3—121no—
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C2×C4×D3—41no—
408C2×C4×D3—41no—
409C2×C4×D3—62no—
410C2×C4×D3—121no—
411C2×C4×D3—121no—
412C2×C4×D3#6714yescomplemented
413C3×C4⋊C4—62no—
414C3×C4⋊C4—121no—
415C3×C22⋊C4—22no—
416C3×C22⋊C4—22no—
417C3×C22⋊C4—42no—
418C3×C22⋊C4—62no—
419C3×C22⋊C4—62no—
420C3×C22⋊C4—121no—
421C3×C22⋊C4—121no—
422C3×C42—62no—
423C3×C42—121no—
424#217—34no—
425#217—34no—
426#217—41no—
427#217—62no—
428#217—62no—
429#217—121no—
430#217—121no—
431#217—121no—
432#217—122no—
433(C2×D3)⋊C4—22no—
434(C2×D3)⋊C4—22no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—41no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—122no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—122no—
452(C2×D3)⋊C4—121no—
453Dic3⋊C4—22no—
454Dic3⋊C4—41no—
455Dic3⋊C4—121no—
456Dic3⋊C4—121no—
457Dic3⋊C4—122no—
458C4×Dic3—22no—
459C4×Dic3—41no—
460C4×Dic3—121no—
461C4×Dic3—121no—
462C4×Dic3—122no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32C23×C411yescharacteristic
471C22×C32C22×D411yescharacteristic
472C22×C32C2×#4111yescharacteristic
473C22×C32H(5,𝔽2)11yescharacteristic
474C22×C32H(5,𝔽2)11yescharacteristic
475C22×C32H(5,𝔽2)11yescharacteristic
476C22×C32H(5,𝔽2)11yescharacteristic
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3C4×D414yes—
498D32—416no—
499C32×C4—22no—
500C32×C4—41no—
501C3⋊Dic3—22no—
502C3⋊Dic3—41no—
503C3⋊Dic3—41no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—41no—
508C3×Dic3—41no—
509C3×Dic3—41no—
510C25—91no—
511C22×D4—31no—
512C22×D4—31no—
513C22×D4—91no—
514C23×C4—31no—
515C23×C4—31no—
516C23×C4—91no—
517#120—98no—
518C4×D4—64no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—91no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
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—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—184no—
538C2×C22⋊C4D3211yescharacteristic, complemented
539C2×C42—31no—
540C2×C42—31no—
541C2×C42—91no—
542#95—91no—
543#95—91no—
544#95—91no—
545#95—91no—
546#95—91no—
547#95—91no—
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—21no—
558C23×C3—21no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—22no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—41no—
567C23×C3—41no—
568C23×C3—41no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—41no—
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×C3C2×C4×D312yes—
583C23×C3C2×C4×D312yes—
584C23×C3C23×D311yescharacteristic
585C23×C3C23×D311yescharacteristic
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—32no—
597C22×D3—32no—
598C22×D3—62no—
599C22×D3—68no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—61no—
604C22×D3—61no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—68no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—121no—
616C22×D3—121no—
617C22×D3—121no—
618C22×D3—121no—
619C22×D3—124no—
620C22×D3—124no—
621C22×D3—124no—
622C22×D3—124no—
623C22×D3—124no—
624C22×D3—124no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3—124no—
628C22×D3—124no—
629C22×D3—124no—
630C22×D3—124no—
631C22×D3C2×C4×D312yes—
632C22×D3C2×C4×D312yes—
633C22×D3#23512yes—
634C22×D3C2×#6712yes—
635C3×D4—68no—
636C3×D4—124no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—22no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
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—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—124no—
672C2×C3×C4—124no—
673C2×C3×C4D3×D412yes—
674C2×C3×C4C2×#6712yes—
675#67—28no—
676#67—44no—
677#67—124no—
678#67—124no—
679#67—128no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—21no—
686C2×Dic3—21no—
687C2×Dic3—21no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—44no—
698C2×Dic3—62no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—62no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—61no—
710C2×Dic3—61no—
711C2×Dic3—61no—
712C2×Dic3—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—121no—
719C2×Dic3—121no—
720C2×Dic3—121no—
721C2×Dic3—121no—
722C2×Dic3—121no—
723C2×Dic3—124no—
724C2×Dic3C2×C4×D312yes—
725C2×Dic3C2×C4×D312yes—
726C2×Dic3C2×#6712yes—
727C4×D3—44no—
728C4×D3—124no—
729C2×C32—42no—
730C2×C32C2×C4×D411yescharacteristic
731C2×C32#51811yescharacteristic
732C2×C32#51811yescharacteristic
733C2×C32#53411yescharacteristic
734C2×C32#53511yescharacteristic
735C2×C32#53811yescharacteristic
736C2×C32#53811yescharacteristic
737C3⋊D3—42no—
738C3×D3—24no—
739C3×D3—42no—
740C24—31no—
741C24—31no—
742C24—94no—
743C24—91no—
744C24—182no—
745C24—182no—
746C24—361no—
747C24—361no—
748C24—361no—
749C24—361no—
750C24C2×D3211yescharacteristic
751C2×D4—34no—
752C2×D4—34no—
753C2×D4—62no—
754C2×D4—62no—
755C2×D4—94no—
756C2×D4—121no—
757C2×D4—121no—
758C2×D4—361no—
759C2×D4—361no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—34no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—62no—
768C22×C4—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—121no—
772C22×C4—121no—
773C22×C4—121no—
774C22×C4—121no—
775C22×C4—182no—
776C22×C4—361no—
777C22×C4—361no—
778C22×C4C2×D3211yescharacteristic
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—62no—
781C4⋊C4—121no—
782C4⋊C4—361no—
783C22⋊C4—22no—
784C22⋊C4—62no—
785C22⋊C4—62no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—121no—
790C22⋊C4—121no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22⋊C4—361no—
796C22⋊C4—361no—
797C22⋊C4—361no—
798C22⋊C4—361no—
799C42—62no—
800C42—121no—
801C42—361no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—34no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—81no—
837C22×C3—81no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3C22×C4×D311yescharacteristic
845C22×C3C22×C4×D311yescharacteristic
846C22×C3C2×#23511yescharacteristic
847C22×C3C2×D3×D411yescharacteristic
848C22×C3#100411yescharacteristic
849C22×C3#100411yescharacteristic
850C22×C3#100411yescharacteristic
851C22×C3#100411yescharacteristic
852C22×C3#100411yescharacteristic
853C22×C3D3×#4111yescharacteristic
854C22×C3#100911yescharacteristic
855C22×C3#100911yescharacteristic
856C22×C3#100911yescharacteristic
857C22×C3C22×#6711yescharacteristic
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—41no—
868C2×D3—41no—
869C2×D3—41no—
870C2×D3—41no—
871C2×D3—62no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—122no—
878C2×D3—122no—
879C2×D3—122no—
880C2×D3—1216no—
881C2×D3—1216no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—121no—
887C2×D3—121no—
888C2×D3—121no—
889C2×D3—121no—
890C2×D3—241no—
891C2×D3—241no—
892C2×D3—241no—
893C2×D3—241no—
894C2×D3C4×#6714yes—
895C3×C4—22no—
896C3×C4—22no—
897C3×C4—42no—
898C3×C4—41no—
899C3×C4—41no—
900C3×C4—62no—
901C3×C4—62no—
902C3×C4—62no—
903C3×C4—81no—
904C3×C4—121no—
905C3×C4—121no—
906C3×C4—121no—
907Dic3—22no—
908Dic3—22no—
909Dic3—22no—
910Dic3—41no—
911Dic3—41no—
912Dic3—41no—
913Dic3—64no—
914Dic3—62no—
915Dic3—62no—
916Dic3—122no—
917Dic3—121no—
918Dic3—121no—
919Dic3—121no—
920Dic3—121no—
921Dic3—241no—
922C32#232111yescharacteristic, complemented, Sylow
923C23—21no—
924C23—21no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—32no—
930C23—32no—
931C23—32no—
932C23—32no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23—61no—
939C23—61no—
940C23—61no—
941C23—61no—
942C23—61no—
943C23—92no—
944C23—188no—
945C23—181no—
946C23—181no—
947C23—181no—
948C23—181no—
949C23—181no—
950C23—181no—
951C23—364no—
952C23—364no—
953C23—364no—
954C23—364no—
955C23—364no—
956C23—364no—
957C23C4×D3212yes—
958C23C22×D3211yescharacteristic
959D4—68no—
960D4—124no—
961D4—364no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—32no—
968C2×C4—32no—
969C2×C4—32no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—61no—
977C2×C4—61no—
978C2×C4—61no—
979C2×C4—61no—
980C2×C4—61no—
981C2×C4—61no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—92no—
986C2×C4—124no—
987C2×C4—124no—
988C2×C4—181no—
989C2×C4—181no—
990C2×C4—181no—
991C2×C4—181no—
992C2×C4—181no—
993C2×C4—181no—
994C2×C4—181no—
995C2×C4—181no—
996C2×C4—364no—
997C2×C4D3×#6712yes—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—42no—
1006C2×C3—42no—
1007C2×C3—64no—
1008C2×C3—82no—
1009C2×C3—122no—
1010C2×C3#548611yescharacteristic
1011C2×C3C4×D3×D411yescharacteristic
1012C2×C3#554511yescharacteristic
1013C2×C3#554511yescharacteristic
1014C2×C3#554511yescharacteristic
1015C2×C3#556011yescharacteristic
1016C2×C3#556011yescharacteristic
1017C2×C3#560511yescharacteristic
1018C2×C3#561311yescharacteristic
1019C2×C3#567811yescharacteristic
1020C2×C3#571511yescharacteristic
1021C2×C3C2×C4×#6711yescharacteristic
1022C2×C3#580411yescharacteristic
1023C2×C3#583011yescharacteristic
1024D3—24no—
1025D3—42no—
1026D3—122no—
1027D3—122no—
1028D3—242no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—34no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—41no—
1037C22—62no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—62no—
1045C22—62no—
1046C22—121no—
1047C22—121no—
1048C22—121no—
1049C22—121no—
1050C22—182no—
1051C22—182no—
1052C22—182no—
1053C22—3616no—
1054C22—361no—
1055C22—361no—
1056C22—361no—
1057C22—361no—
1058C22C2×C4×D3211yescharacteristic
1059C22D3×#23511yescharacteristic
1060C22#6431311yescharacteristic
1061C22#6431411yescharacteristic
1062C22#6431411yescharacteristic
1063C22#6431411yescharacteristic
1064C22C2×D3×#6711yescharacteristic
1065C4—22no—
1066C4—41no—
1067C4—62no—
1068C4—62no—
1069C4—62no—
1070C4—121no—
1071C4—121no—
1072C4—121no—
1073C4—182no—
1074C4—361no—
1075C4—361no—
1076C3—21no—
1077C3#7642911yescharacteristic, complemented
1078C3#8239511yescharacteristic, complemented
1079C2—42no—
1080C2—64no—
1081C2—122no—
1082C2—362no—
1083C2#1059425411yescharacteristic
1084C2#1059425611yescharacteristic
1085C2#1059429711yescharacteristic
1086C2#1059429811yescharacteristic
1087C2C4×D3×#6711yescharacteristic
1088C2#1059530211yescharacteristic
1089C2#1059530311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63983C2
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
1. C2×C3×#67⋊C4C2semidirect
3. C2×D3×(C2×D3)⋊C4C2semidirect
4. #10592656C2semidirect
5. C3×#4957C2semidirect
6. #10591721C2semidirect
7. #10591711C2semidirect
8. #10591710C2semidirect
9. #10591399C2semidirect
10. #10591372C2semidirect
11. #10591289C2semidirect
12. #10591289C2semidirect
13. #10591283C2semidirect
14. #10591280C2semidirect
15. C4×(C2×D3)⋊Dic3C2semidirect
22. C23×C3×Dic3C22semidirect
25. C2×C32×C22⋊C4C22semidirect
26. C2×#3757C22semidirect
29. C2×#3750C22semidirect
30. C2×C4×C3⋊Dic3C22semidirect
31. C2×C3×#217C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×C4×Dic3C22semidirect
38. C2×C3×C4×Dic3C22semidirect
40. #63983C4semidirect
50. #63579C22semidirect
51. #63579C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
60. C2×#67⋊C4D3semidirect
76. #4957D3semidirect
97. C22×D32C2×C4semidirect
102. C2×#638C2×C4semidirect
111. C2×C3×#67C2×C4semidirect
123. C2×C3×C4×D3D4semidirect
143. #3722C2×C4semidirect
147. (C2×D3)⋊Dic3C2×C4semidirect
148. (C2×D3)⋊Dic3C2×C4semidirect
162. C23×Dic3C2×D3semidirect
173. C2×C3×C22⋊C4C2×D3semidirect
174. C2×C3×C22⋊C4C2×D3semidirect
185. C2×#217C2×D3semidirect
212. C2×Dic3⋊C4C2×D3semidirect
213. C2×Dic3⋊C4C2×D3semidirect
217. C2×C4×Dic3C2×D3semidirect
218. C2×C4×Dic3C2×D3semidirect
385. C2×#67C4×D3semidirect
412. C2×C4×D3#67semidirect
538. C2×C22⋊C4D32semidirect
922. C32#2321semidirect
1077. C3#76429semidirect
1078. C3#82395semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#639832
C2×D3×(C2×D3)⋊C42
#105926562
C3×#49572
#105917212
#105917112
#105917102
#105913992
#105913722
#105912892
#105912832
#105912802
C4×(C2×D3)⋊Dic32
#823953
#764293