Finite Group Databasebeta

← #11803859

Subgroups — #11803859

Order 1152.

1623 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic, complemented
2C2×#63979C211yesmaximal, characteristic
3C2×#63880C211yesmaximal, characteristic, complemented
4#10592912C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6#10591722C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591707C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591381C211yesmaximal, characteristic, complemented
12#10591363C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591245C211yesmaximal, characteristic, complemented
15#10591239C211yesmaximal, characteristic, complemented
16#82329—31nomaximal
17#74667—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C3×C4×#67—24no—
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39#63979C418yescomplemented
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63880—24no—
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×C4×D4—31no—
57C2×#940—31no—
58C2×#940—31no—
59C2×C4×#67D311yescharacteristic, complemented
60C2×#67⋊C4—31no—
61C2×C4×D12—31no—
62C3×#386—31no—
63#5221—31no—
64#5220—31no—
65#5213—31no—
66#5213—31no—
67#5213—31no—
68#5213—31no—
69#5213—61no—
70#5213D311yescharacteristic, complemented
71#4988—31no—
72#4977—31no—
73#4958—31no—
74#4957—31no—
75#4957—31no—
76#4956—31no—
77#4956—31no—
78#4956—31no—
79#4956—31no—
80#4956—31no—
81#4956—31no—
82#4932—31no—
83#4665—31no—
84#4665—31no—
85#4650—31no—
86#4648—31no—
87C24×C32C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—41no—
93C22×C32×C4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×#638—41no—
97C2×#638—41no—
98C2×#638C2×C414yescomplemented
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—41no—
105C2×C3×#67—41no—
106C2×C3×#67C2×C414yescomplemented
107C2×C3×#67C2×C414yescomplemented
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—41no—
120C2×#626—41no—
121C2×#626C2×C414yescomplemented
122C2×#626C2×C414yescomplemented
123C2×#625—41no—
124C2×#625—41no—
125C2×#625C2×C414yescomplemented
126C2×#624—22no—
127C2×#624—41no—
128C2×#624—41no—
129C2×D3×Dic3—22no—
130C2×D3×Dic3—41no—
131C2×D3×Dic3—41no—
132#3757—41no—
133#3752—22no—
134#3752—41no—
135C3×#217—22no—
136C3×#217—41no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—41no—
140C3×Dic3⋊C4—22no—
141C3×C4×Dic3D414yescomplemented
142Dic3⋊Dic3—22no—
143#3722—41no—
144(C2×D3)⋊Dic3—41no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3—41no—
147Dic32—22no—
148Dic32C2×C414yescomplemented
149#2328—91noSylow
150C22×C3×D4—31no—
151C22×C3×D4—31no—
152C23×C3×C4—21no—
153C23×C3×C4—31no—
154C23×C3×C4C2×D311yescharacteristic
155C23×C3×C4C2×D311yescharacteristic
156C22×#67—31no—
157C22×#67—31no—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67—31no—
161C22×#67—31no—
162C22×#67—61no—
163C22×#67C2×D311yescharacteristic
164C22×#67C2×D311yescharacteristic
165C23×Dic3—31no—
166C22×D12—31no—
167C22×D12—31no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3—31no—
171C22×C4×D3C2×D311yescharacteristic
172C3×C4×D4—64no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C42—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—61no—
186C2×#217C2×D311yescharacteristic
187C2×#217C2×D311yescharacteristic
188#940—38no—
189#940—38no—
190C4×#67—24no—
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—61no—
201C2×(C2×D3)⋊C4—61no—
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×C4⋊Dic3—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4C2×D311yescharacteristic
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3C2×D311yescharacteristic
213#67⋊C4—64no—
214C4×D12—64no—
215C3×#95—31no—
216C3×#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
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
232C3⋊#95C2×D311yescharacteristic
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×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C22×C412yes—
261C22×C3×D3C22×C412yes—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—44no—
268C2×C32×C4C2×D412yes—
269#638—44no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3C22×C412yes—
279C3×#67—28no—
280C3×#67—44no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
295C2×C3×Dic3C22×C412yes—
296C2×C3×Dic3C2×D412yes—
297C2×C3×Dic3C2×D412yes—
298C2×C3×Dic3#4112yes—
299C3×C4×D3—44no—
300#626—28no—
301#626—44no—
302#625—44no—
303#624—44no—
304D3×Dic3—44no—
305C2×#127—91no—
306C2×C4×D4—31no—
307C2×C4×D4—91no—
308#390—91no—
309#390—91no—
310#386—31no—
311#386—91no—
312#386—91no—
313#386—91no—
314#386—91no—
315#386—91no—
316#386—91no—
317#386—91no—
318#382—91no—
319#376—91no—
320C24×C3—21no—
321C24×C3—31no—
322C24×C3—31no—
323C24×C3C22×D311yescharacteristic
324C24×C3C22×D311yescharacteristic
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—61no—
328C23×D3C22×D311yescharacteristic
329C23×D3C22×D311yescharacteristic
330C2×C3×D4—34no—
331C2×C3×D4—34no—
332C2×C3×D4—62no—
333C2×C3×D4—62no—
334C2×C3×D4—121no—
335C2×C3×D4—121no—
336C22×C3×C4—22no—
337C22×C3×C4—22no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—42no—
347C22×C3×C4—41no—
348C22×C3×C4—41no—
349C22×C3×C4—41no—
350C22×C3×C4—41no—
351C22×C3×C4—42no—
352C22×C3×C4—42no—
353C22×C3×C4—62no—
354C22×C3×C4—121no—
355C22×C3×C4—121no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C2×#67—22no—
361C2×#67—22no—
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—41no—
369C2×#67—41no—
370C2×#67—64no—
371C2×#67—62no—
372C2×#67—62no—
373C2×#67—121no—
374C2×#67—121no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67—121no—
378C2×#67—121no—
379C2×#67—121no—
380C2×#67—121no—
381C2×#67—121no—
382C2×#67—121no—
383C2×#67—122no—
384C2×#67—122no—
385C2×#67C4×D314yescomplemented
386C2×#67C4×D314yescomplemented
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—62no—
397C22×Dic3—121no—
398C22×Dic3—121no—
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C2×D12—34no—
406C2×D12—34no—
407C2×D12—62no—
408C2×D12—62no—
409C2×D12—121no—
410C2×D12—121no—
411C2×C4×D3—22no—
412C2×C4×D3—41no—
413C2×C4×D3—41no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—62no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—121no—
423C3×C4⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—121no—
428C3×C22⋊C4—121no—
429C3×C42—34no—
430#217—22no—
431#217—41no—
432#217—121no—
433#217—121no—
434#217—121no—
435#217—121no—
436#217—121no—
437#217—122no—
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—41no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—122no—
444(C2×D3)⋊C4—121no—
445(C2×D3)⋊C4—121no—
446(C2×D3)⋊C4—121no—
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—
452C4⋊Dic3—62no—
453Dic3⋊C4—22no—
454Dic3⋊C4—62no—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3—62no—
458C4×Dic3—62no—
459C4×Dic3#6714yescomplemented
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32C23×C411yescharacteristic
468C22×C32C22×D411yescharacteristic
469C22×C32C2×#4111yescharacteristic
470C22×C32H(5,𝔽2)11yescharacteristic
471C22×C32H(5,𝔽2)11yescharacteristic
472C22×C32H(5,𝔽2)11yescharacteristic
473C22×C32H(5,𝔽2)11yescharacteristic
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—41no—
478C2×C3⋊D3—41no—
479C2×C3⋊D3—41no—
480C2×C3⋊D3—41no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
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×D3—41no—
495C32×C4—22no—
496C32×C4—41no—
497C3⋊Dic3—22no—
498C3⋊Dic3—41no—
499C3⋊Dic3—41no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—41no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C3×Dic3C4×D414yes—
506C22×D4—31no—
507C22×D4—31no—
508C22×D4—91no—
509C22×D4—91no—
510C22×D4—91no—
511C22×D4—91no—
512C23×C4—31no—
513C23×C4—91no—
514C23×C4—91no—
515C23×C4D3211yescharacteristic
516#127—98no—
517C4×D4—64no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C22⋊C4—31no—
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×C42—31no—
534C2×C42—91no—
535C2×C42—91no—
536#95—31no—
537#95—31no—
538#95—91no—
539#95—91no—
540#95—91no—
541#95—91no—
542#95—91no—
543#95—91no—
544C23×C3—22no—
545C23×C3—22no—
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—21no—
558C23×C3—21no—
559C23×C3—22no—
560C23×C3—32no—
561C23×C3—32no—
562C23×C3—41no—
563C23×C3—41no—
564C23×C3—41no—
565C23×C3—41no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
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×C3C2×C4×D312yes—
579C23×C3C2×C4×D312yes—
580C23×C3C23×D311yescharacteristic
581C23×C3C23×D311yescharacteristic
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
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—32no—
595C22×D3—32no—
596C22×D3—62no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
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—121no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3C2×C4×D312yes—
616C22×D3C2×C4×D312yes—
617C3×D4—68no—
618C3×D4—124no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—22no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—22no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—44no—
641C2×C3×C4—44no—
642C2×C3×C4—48no—
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×C4—124no—
657C2×C3×C4D3×D412yes—
658C2×C3×C4C2×#6712yes—
659#67—28no—
660#67—44no—
661#67—68no—
662#67—124no—
663#67—124no—
664#67—124no—
665#67—124no—
666#67—124no—
667#67—128no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
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—32no—
682C2×Dic3—32no—
683C2×Dic3—62no—
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—124no—
709C2×Dic3C2×C4×D312yes—
710C2×Dic3C2×C4×D312yes—
711C2×Dic3#23512yes—
712C2×Dic3C2×#6712yes—
713C2×Dic3C2×#6712yes—
714D12—68no—
715D12—124no—
716C4×D3—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#53511yescharacteristic
725C2×C32#53511yescharacteristic
726C2×C32#54011yescharacteristic
727C2×C32#54011yescharacteristic
728C3⋊D3—42no—
729C3×D3—42no—
730C3×D3—42no—
731C24—31no—
732C24—31no—
733C24—91no—
734C24C2×D3211yescharacteristic
735C2×D4—34no—
736C2×D4—34no—
737C2×D4—62no—
738C2×D4—62no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—94no—
742C2×D4—94no—
743C2×D4—121no—
744C2×D4—121no—
745C2×D4—182no—
746C2×D4—182no—
747C2×D4—361no—
748C2×D4—361no—
749C2×D4—361no—
750C2×D4—361no—
751C2×D4—361no—
752C2×D4—361no—
753C22×C4—22no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—62no—
763C22×C4—91no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—121no—
767C22×C4—121no—
768C22×C4—182no—
769C22×C4—182no—
770C22×C4—361no—
771C22×C4—361no—
772C22×C4—361no—
773C22×C4—361no—
774C22×C4C2×D3211yescharacteristic
775C22×C4C2×D3211yescharacteristic
776C4⋊C4—62no—
777C4⋊C4—182no—
778C22⋊C4—62no—
779C22⋊C4—62no—
780C22⋊C4—62no—
781C22⋊C4—121no—
782C22⋊C4—121no—
783C22⋊C4—182no—
784C22⋊C4—361no—
785C22⋊C4—361no—
786C22⋊C4—361no—
787C22⋊C4—361no—
788C22⋊C4—361no—
789C22⋊C4—361no—
790C42—34no—
791C42—94no—
792C42—182no—
793C22×C3—24no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3C22×C4×D311yescharacteristic
836C22×C3C22×C4×D311yescharacteristic
837C22×C3C2×#23511yescharacteristic
838C22×C3C2×D3×D411yescharacteristic
839C22×C3#100411yescharacteristic
840C22×C3#100411yescharacteristic
841C22×C3#100411yescharacteristic
842C22×C3#100411yescharacteristic
843C22×C3#100411yescharacteristic
844C22×C3D3×#4111yescharacteristic
845C22×C3#100911yescharacteristic
846C22×C3#100911yescharacteristic
847C22×C3#100911yescharacteristic
848C22×C3C22×#6711yescharacteristic
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—122no—
870C2×D3—122no—
871C2×D3—122no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—241no—
881C2×D3—241no—
882C2×D3—241no—
883C2×D3—241no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—34no—
887C3×C4—42no—
888C3×C4—42no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—62no—
892C3×C4—62no—
893C3×C4—121no—
894C3×C4—121no—
895C3×C4—121no—
896Dic3—22no—
897Dic3—22no—
898Dic3—41no—
899Dic3—41no—
900Dic3—41no—
901Dic3—62no—
902Dic3—62no—
903Dic3—122no—
904Dic3—121no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
908Dic3—241no—
909Dic3—241no—
910Dic3C4×#6714yes—
911C32#232811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—32no—
919C23—32no—
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—92no—
933C23—181no—
934C23—181no—
935C23—181no—
936C23—181no—
937C23—181no—
938C23—181no—
939C23C4×D3212yes—
940C23C22×D3211yescharacteristic
941D4—68no—
942D4—124no—
943D4—188no—
944D4—364no—
945D4—364no—
946D4—364no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—32no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—44no—
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—61no—
971C2×C4—92no—
972C2×C4—124no—
973C2×C4—181no—
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×C4—364no—
983C2×C4D3×#6712yes—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—44no—
992C2×C3—42no—
993C2×C3—42no—
994C2×C3—122no—
995C2×C3—122no—
996C2×C3#548611yescharacteristic
997C2×C3C4×D3×D411yescharacteristic
998C2×C3#554511yescharacteristic
999C2×C3#554511yescharacteristic
1000C2×C3#554511yescharacteristic
1001C2×C3#556211yescharacteristic
1002C2×C3#556211yescharacteristic
1003C2×C3#559211yescharacteristic
1004C2×C3#560711yescharacteristic
1005C2×C3#561511yescharacteristic
1006C2×C3#566311yescharacteristic
1007C2×C3C2×C4×#6711yescharacteristic
1008C2×C3#580511yescharacteristic
1009C2×C3#583011yescharacteristic
1010D3—42no—
1011D3—42no—
1012D3—122no—
1013D3—122no—
1014D3—242no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—62no—
1023C22—62no—
1024C22—62no—
1025C22—62no—
1026C22—62no—
1027C22—62no—
1028C22—121no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—121no—
1033C22—121no—
1034C22—121no—
1035C22—121no—
1036C22—182no—
1037C22—182no—
1038C22—182no—
1039C22—361no—
1040C22—361no—
1041C22—361no—
1042C22—361no—
1043C22C2×C4×D3211yescharacteristic
1044C22D3×#23511yescharacteristic
1045C22#6430711yescharacteristic
1046C22#6430811yescharacteristic
1047C22C2×D3×#6711yescharacteristic
1048C22#6433011yescharacteristic
1049C22#6433011yescharacteristic
1050C4—22no—
1051C4—34no—
1052C4—41no—
1053C4—62no—
1054C4—62no—
1055C4—121no—
1056C4—121no—
1057C4—121no—
1058C4—182no—
1059C4—361no—
1060C4—361no—
1061C3—21no—
1062C3#7466711yescharacteristic, complemented
1063C3#8232911yescharacteristic, complemented
1064C2—42no—
1065C2—122no—
1066C2—122no—
1067C2—362no—
1068C2#1059495011yescharacteristic
1069C2#1059502711yescharacteristic
1070C2C4×D3×#6711yescharacteristic
1071C2#1059505611yescharacteristic
1072C2#1059505811yescharacteristic
1073C2#1059506411yescharacteristic
1074C2#1059551311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63979C2
hypercenterC23×C4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#67C2semidirect
3. C2×#63880C2semidirect
4. #10592912C2semidirect
5. C3×#5213C2semidirect
6. #10591722C2semidirect
7. #10591721C2semidirect
8. #10591707C2semidirect
9. #10591384C2semidirect
10. #10591382C2semidirect
11. #10591381C2semidirect
12. #10591363C2semidirect
13. #10591275C2semidirect
14. #10591245C2semidirect
15. #10591239C2semidirect
39. #63979C4semidirect
59. C2×C4×#67D3semidirect
70. #5213D3semidirect
98. C2×#638C2×C4semidirect
106. C2×C3×#67C2×C4semidirect
107. C2×C3×#67C2×C4semidirect
121. C2×#626C2×C4semidirect
122. C2×#626C2×C4semidirect
125. C2×#625C2×C4semidirect
141. C3×C4×Dic3D4semidirect
148. Dic32C2×C4semidirect
385. C2×#67C4×D3semidirect
386. C2×#67C4×D3semidirect
459. C4×Dic3#67semidirect
911. C32#2328semidirect
1062. C3#74667semidirect
1063. C3#82329semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×#639792
C2×#638802
#105929122
C3×#52132
#105917222
#105917212
#105917072
#105913842
#105913822
#105913812
#105913632
#105912752
#105912452
#105912392
#823293
#746673