Finite Group Databasebeta

← #11803865

Subgroups — #11803865

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×#940C211yesmaximal, characteristic
2C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
3C2×Dic3×#67C211yesmaximal, characteristic, complemented
4#10592919C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6#10591721C211yesmaximal, characteristic, complemented
7#10591721C211yesmaximal, characteristic, complemented
8#10591713C211yesmaximal, characteristic, complemented
9#10591710C211yesmaximal, characteristic, complemented
10#10591707C211yesmaximal, characteristic, complemented
11#10591707C211yesmaximal, characteristic, complemented
12#10591376C211yesmaximal, characteristic, complemented
13#10591376C211yesmaximal, characteristic, complemented
14#10591239C211yesmaximal, characteristic, complemented
15#10591206C211yesmaximal, characteristic, complemented
16#83172—31nomaximal
17#74667—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C3×#940C418yescomplemented
35C2×C3×C4×Dic3C2211yescharacteristic
36#67⋊Dic3—24no—
37Dic3×#67—24no—
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×#127—31no—
57C2×#940D311yescharacteristic
58C2×D4×Dic3—31no—
59C2×D4×Dic3—31no—
60C2×C4×#67—31no—
61C2×#67⋊C4—31no—
62C3×#386—31no—
63#5221—31no—
64#5221—31no—
65#5220—31no—
66#5220—31no—
67#5220—31no—
68#5220—31no—
69#5220—31no—
70#5220—31no—
71#5220—31no—
72#5220—31no—
73#5220—61no—
74#5220D311yescharacteristic, complemented
75#5213—31no—
76#4958—31no—
77#4957—31no—
78#4957—31no—
79#4956—31no—
80#4956—31no—
81#4936—31no—
82#4932—31no—
83#4665—31no—
84#4665—31no—
85#4650—31no—
86#4648—31no—
87C24×C32C2311yescharacteristic
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C2×C32×D4—41no—
92C2×C32×D4—41no—
93C2×C32×D4C2×C414yescomplemented
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—22no—
96C22×C3⋊Dic3—41no—
97C22×C3⋊Dic3—41no—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C2×C3×#67—41no—
107C2×C3×#67—41no—
108C2×C3×#67—41no—
109C2×C3×#67—41no—
110C2×C3×#67C2×C414yescomplemented
111C2×C3×#67C2×C414yescomplemented
112C2×C3×#67C2×C414yescomplemented
113C2×C3×#67C2×C414yescomplemented
114C22×C3×Dic3—22no—
115C22×C3×Dic3—41no—
116C22×C3×Dic3—41no—
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×D12—41no—
124C2×C3×D12—41no—
125C2×C3×D12C2×C414yescomplemented
126C2×D3×Dic3—22no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3—41no—
129C2×D3×Dic3—41no—
130C2×D3×Dic3—41no—
131C2×D3×Dic3—41no—
132#3757—22no—
133#3757—41no—
134#3757—41no—
135C3×#217—22no—
136C3×#217—41no—
137C3×#217—41no—
138C3×C4×Dic3C2×C414yescomplemented
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—41no—
144(C2×D3)⋊Dic3—41no—
145(C2×D3)⋊Dic3—41no—
146(C2×D3)⋊Dic3—41no—
147Dic32—22no—
148Dic32D414yescomplemented
149#2328—91noSylow
150C22×C3×D4—21no—
151C22×C3×D4—31no—
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×C3×D4—31no—
156C22×C3×D4C2×D311yescharacteristic
157C22×C3×D4C2×D311yescharacteristic
158C23×C3×C4—31no—
159C22×#67C2×D311yescharacteristic
160C22×#67C2×D311yescharacteristic
161C22×#67C2×D311yescharacteristic
162C22×#67C2×D311yescharacteristic
163C23×Dic3—31no—
164C23×Dic3—31no—
165C23×Dic3—31no—
166C23×Dic3—31no—
167C23×Dic3—61no—
168C23×Dic3C2×D311yescharacteristic
169C22×D12C2×D311yescharacteristic
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C3×#127—38no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—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—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—61no—
190C2×#217—61no—
191C2×#217—61no—
192C2×#217C2×D311yescharacteristic
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic
195#940Dic318yescomplemented
196D4×Dic3—64no—
197D4×Dic3—64no—
198C4×#67—64no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3C2×D311yescharacteristic
214#67⋊C4—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×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—21no—
245C23×C32C22×C412yes—
246C23×C32C22×C412yes—
247C23×C32C2411yescharacteristic
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—
262C32×D4—44no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C22×C412yes—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
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—44no—
278C2×C3⋊Dic3C2×D412yes—
279C3×#67—28no—
280C3×#67—28no—
281C3×#67—44no—
282C3×#67—44no—
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×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—44no—
297C2×C3×Dic3C22×C412yes—
298C2×C3×Dic3C22×C412yes—
299C2×C3×Dic3C2×D412yes—
300C2×C3×Dic3C2×D412yes—
301C2×C3×Dic3#4112yes—
302C3×D12—44no—
303D3×Dic3—44no—
304D3×Dic3—44no—
305C2×#127—31no—
306C2×C4×D4—91no—
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—21no—
322C24×C3—31no—
323C24×C3—31no—
324C24×C3C22×D311yescharacteristic
325C24×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C23×D3C22×D311yescharacteristic
330C2×C3×D4—24no—
331C2×C3×D4—34no—
332C2×C3×D4—34no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—41no—
337C2×C3×D4—41no—
338C2×C3×D4—41no—
339C2×C3×D4—41no—
340C2×C3×D4—42no—
341C2×C3×D4—42no—
342C2×C3×D4—62no—
343C2×C3×D4—62no—
344C2×C3×D4—62no—
345C2×C3×D4—62no—
346C2×C3×D4—121no—
347C2×C3×D4—121no—
348C2×C3×D4—121no—
349C2×C3×D4—121no—
350C2×C3×D4—121no—
351C2×C3×D4—121no—
352C2×C3×D4C4×D314yescomplemented
353C2×C3×D4C2×Dic314yescomplemented
354C22×C3×C4—21no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—62no—
362C22×C3×C4—121no—
363C22×C3×C4—121no—
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C2×#67—22no—
367C2×#67—22no—
368C2×#67—22no—
369C2×#67—22no—
370C2×#67—41no—
371C2×#67—41no—
372C2×#67—41no—
373C2×#67—41no—
374C2×#67C2×Dic314yescomplemented
375C2×#67C2×Dic314yescomplemented
376C2×#67C2×Dic314yescomplemented
377C2×#67C2×Dic314yescomplemented
378C22×Dic3—22no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—41no—
388C22×Dic3—41no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—62no—
394C22×Dic3—62no—
395C22×Dic3—62no—
396C22×Dic3—62no—
397C22×Dic3—122no—
398C22×Dic3—121no—
399C22×Dic3—121no—
400C22×Dic3—121no—
401C22×Dic3—121no—
402C22×Dic3—121no—
403C22×Dic3—121no—
404C22×Dic3—121no—
405C22×Dic3—121no—
406C22×Dic3—122no—
407C22×Dic3—122no—
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C2×D12—41no—
415C2×D12—41no—
416C2×D12C2×Dic314yescomplemented
417C2×C4×D3—62no—
418C2×C4×D3—62no—
419C2×C4×D3—121no—
420C2×C4×D3—121no—
421C2×C4×D3—121no—
422C2×C4×D3—121no—
423C3×C22⋊C4—62no—
424C3×C22⋊C4—121no—
425C3×C22⋊C4—121no—
426C3×C42—34no—
427#217—22no—
428#217—41no—
429#217—41no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—62no—
434#217—122no—
435#217—121no—
436#217—121no—
437#217—121no—
438#217—121no—
439#217—121no—
440#217—121no—
441#217—121no—
442#217—121no—
443#217—122no—
444#217—122no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—121no—
448(C2×D3)⋊C4—121no—
449(C2×D3)⋊C4—121no—
450(C2×D3)⋊C4—121no—
451C4⋊Dic3—62no—
452C4⋊Dic3—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—62no—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3—62no—
458C4×Dic3—62no—
459C4×Dic3C2×Dic314yescomplemented
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—41no—
470C22×C32—41no—
471C22×C32—41no—
472C22×C32—41no—
473C22×C32—41no—
474C22×C32C23×C411yescharacteristic
475C22×C32C22×D411yescharacteristic
476C22×C32C2×#4111yescharacteristic
477C22×C32H(5,𝔽2)11yescharacteristic
478C22×C32H(5,𝔽2)11yescharacteristic
479C22×C32H(5,𝔽2)11yescharacteristic
480C22×C32H(5,𝔽2)11yescharacteristic
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—
496C3⋊Dic3—22no—
497C3⋊Dic3—41no—
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—31no—
509C22×D4—31no—
510C22×D4—31no—
511C22×D4D3211yescharacteristic
512C23×C4—31no—
513C23×C4—91no—
514C23×C4—91no—
515C23×C4—91no—
516#127—38no—
517C4×D4—184no—
518C4×D4—184no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C22⋊C4—31no—
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
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×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—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—22no—
572C23×C3—22no—
573C23×C3—32no—
574C23×C3—32no—
575C23×C3—41no—
576C23×C3—41no—
577C23×C3—41no—
578C23×C3—41no—
579C23×C3—41no—
580C23×C3—41no—
581C23×C3—41no—
582C23×C3—41no—
583C23×C3—41no—
584C23×C3—41no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3C2×C4×D312yes—
598C23×C3C2×C4×D312yes—
599C23×C3C22×Dic312yes—
600C23×C3C22×Dic312yes—
601C23×C3C23×D311yescharacteristic
602C23×C3C23×D311yescharacteristic
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3C22×Dic312yes—
616C22×D3C22×Dic312yes—
617C3×D4—44no—
618C3×D4—44no—
619C3×D4—48no—
620C3×D4—68no—
621C3×D4—68no—
622C3×D4—124no—
623C3×D4—124no—
624C3×D4—124no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—22no—
630C2×C3×C4—32no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
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—124no—
651C2×C3×C4C2×C4×D312yes—
652C2×C3×C4C22×Dic312yes—
653#67—28no—
654#67—28no—
655#67—44no—
656#67—44no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—44no—
673C2×Dic3—62no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—62no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—121no—
698C2×Dic3—121no—
699C2×Dic3—121no—
700C2×Dic3—121no—
701C2×Dic3—121no—
702C2×Dic3—121no—
703C2×Dic3—121no—
704C2×Dic3—121no—
705C2×Dic3—121no—
706C2×Dic3—121no—
707C2×Dic3—124no—
708C2×Dic3—124no—
709C2×Dic3—124no—
710C2×Dic3—124no—
711C2×Dic3—128no—
712C2×Dic3D3×D412yes—
713C2×Dic3D3×D412yes—
714C2×Dic3#23712yes—
715C2×Dic3C22×Dic312yes—
716C2×Dic3C22×Dic312yes—
717D12—44no—
718C4×D3—124no—
719C4×D3—124no—
720C2×C32—42no—
721C2×C32—42no—
722C2×C32C2×C4×D411yescharacteristic
723C2×C32#51811yescharacteristic
724C2×C32#51811yescharacteristic
725C2×C32#53511yescharacteristic
726C2×C32#53511yescharacteristic
727C2×C32#54011yescharacteristic
728C2×C32#54011yescharacteristic
729C3×D3—42no—
730C3×D3—42no—
731C24—31no—
732C24—31no—
733C24C2×D3211yescharacteristic
734C24C2×D3211yescharacteristic
735C2×D4—34no—
736C2×D4—34no—
737C2×D4—34no—
738C2×D4—34no—
739C2×D4—34no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—62no—
743C2×D4—62no—
744C2×D4—62no—
745C2×D4—62no—
746C2×D4—121no—
747C2×D4—121no—
748C2×D4—121no—
749C2×D4—121no—
750C2×D4—121no—
751C2×D4—121no—
752C2×D4D3×Dic314yescomplemented
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—62no—
760C22×C4—91no—
761C22×C4—91no—
762C22×C4—91no—
763C22×C4—91no—
764C22×C4—121no—
765C22×C4—121no—
766C22×C4—182no—
767C22×C4—182no—
768C22×C4—182no—
769C22×C4—361no—
770C22×C4—361no—
771C22×C4—361no—
772C22×C4—361no—
773C22×C4—361no—
774C22×C4—361no—
775C22×C4C2×D3211yescharacteristic
776C4⋊C4—182no—
777C4⋊C4—182no—
778C22⋊C4—62no—
779C22⋊C4—121no—
780C22⋊C4—121no—
781C22⋊C4—182no—
782C22⋊C4—182no—
783C22⋊C4—182no—
784C22⋊C4—361no—
785C22⋊C4—361no—
786C22⋊C4—361no—
787C22⋊C4—361no—
788C22⋊C4—361no—
789C22⋊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—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—62no—
839C22×C3—62no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—81no—
845C22×C3—81no—
846C22×C3—81no—
847C22×C3—81no—
848C22×C3—121no—
849C22×C3—121no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3C22×C4×D311yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C22×C3C2×D3×D411yescharacteristic
859C22×C3C2×#23711yescharacteristic
860C22×C3#100411yescharacteristic
861C22×C3#100411yescharacteristic
862C22×C3#100411yescharacteristic
863C22×C3#100411yescharacteristic
864C22×C3#100411yescharacteristic
865C22×C3#100411yescharacteristic
866C22×C3#100411yescharacteristic
867C22×C3D3×#4111yescharacteristic
868C22×C3#100911yescharacteristic
869C22×C3C23×Dic311yescharacteristic
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—41no—
883C2×D3—41no—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—34no—
887C3×C4—42no—
888C3×C4—62no—
889C3×C4—62no—
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—121no—
907Dic3—121no—
908Dic3—241no—
909Dic3—241no—
910Dic3D4×Dic314yes—
911C32#232811yescharacteristic, complemented, Sylow
912C23—21no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—21no—
921C23—21no—
922C23—21no—
923C23—21no—
924C23—32no—
925C23—32no—
926C23—61no—
927C23—61no—
928C23—61no—
929C23—61no—
930C23—61no—
931C23—61no—
932C23—61no—
933C23—61no—
934C23—61no—
935C23—61no—
936C23—61no—
937C23—61no—
938C23C2×D3×Dic312yes—
939C23C2×D3×Dic312yes—
940C23C22×D3211yescharacteristic
941D4—44no—
942D4—68no—
943D4—68no—
944D4—124no—
945D4—124no—
946D4—124no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—32no—
950C2×C4—32no—
951C2×C4—32no—
952C2×C4—32no—
953C2×C4—32no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—92no—
968C2×C4—124no—
969C2×C4—181no—
970C2×C4—181no—
971C2×C4—181no—
972C2×C4—181no—
973C2×C4—181no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4—181no—
979C2×C4—181no—
980C2×C4—364no—
981C2×C4—364no—
982C2×C4—364no—
983C2×C4C2×D3×Dic312yes—
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—42no—
995C2×C3—42no—
996C2×C3—82no—
997C2×C3—122no—
998C2×C3—122no—
999C2×C3#548611yescharacteristic
1000C2×C3C4×D3×D411yescharacteristic
1001C2×C3#554511yescharacteristic
1002C2×C3#559211yescharacteristic
1003C2×C3#560711yescharacteristic
1004C2×C3#561511yescharacteristic
1005C2×C3#566311yescharacteristic
1006C2×C3#571511yescharacteristic
1007C2×C3#571511yescharacteristic
1008C2×C3#571911yescharacteristic
1009C2×C3#571911yescharacteristic
1010C2×C3C2×D4×Dic311yescharacteristic
1011C2×C3#579811yescharacteristic
1012C2×C3#579811yescharacteristic
1013D3—42no—
1014D3—42no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—41no—
1028C22—41no—
1029C22—62no—
1030C22—62no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—62no—
1035C22—121no—
1036C22—121no—
1037C22—121no—
1038C22—121no—
1039C22—121no—
1040C22—121no—
1041C22—121no—
1042C22—121no—
1043C22D32×D411yescharacteristic
1044C22D3×#23711yescharacteristic
1045C22#6431311yescharacteristic
1046C22#6431411yescharacteristic
1047C22C22×D3×Dic311yescharacteristic
1048C22#6433011yescharacteristic
1049C22#6433011yescharacteristic
1050C4—22no—
1051C4—34no—
1052C4—62no—
1053C4—62no—
1054C4—121no—
1055C4—121no—
1056C4—121no—
1057C4—182no—
1058C4—361no—
1059C4—361no—
1060C4—361no—
1061C3—21no—
1062C3#7466711yescharacteristic, complemented
1063C3#8317211yescharacteristic, complemented
1064C2—42no—
1065C2—42no—
1066C2—122no—
1067C2—122no—
1068C2D3×D4×Dic311yescharacteristic
1069C2#1059518811yescharacteristic
1070C2#1059519211yescharacteristic
1071C2#1059521511yescharacteristic
1072C2#1059528611yescharacteristic
1073C2#1059529911yescharacteristic
1074C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#67⋊Dic3C2semidirect
3. C2×Dic3×#67C2semidirect
4. #10592919C2semidirect
5. C3×#5220C2semidirect
6. #10591721C2semidirect
7. #10591721C2semidirect
8. #10591713C2semidirect
9. #10591710C2semidirect
10. #10591707C2semidirect
11. #10591707C2semidirect
12. #10591376C2semidirect
13. #10591376C2semidirect
14. #10591239C2semidirect
15. #10591206C2semidirect
34. C3×#940C4semidirect
74. #5220D3semidirect
93. C2×C32×D4C2×C4semidirect
110. C2×C3×#67C2×C4semidirect
111. C2×C3×#67C2×C4semidirect
112. C2×C3×#67C2×C4semidirect
113. C2×C3×#67C2×C4semidirect
125. C2×C3×D12C2×C4semidirect
138. C3×C4×Dic3C2×C4semidirect
148. Dic32D4semidirect
195. #940Dic3semidirect
352. C2×C3×D4C4×D3semidirect
353. C2×C3×D4C2×Dic3semidirect
374. C2×#67C2×Dic3semidirect
375. C2×#67C2×Dic3semidirect
376. C2×#67C2×Dic3semidirect
377. C2×#67C2×Dic3semidirect
416. C2×D12C2×Dic3semidirect
459. C4×Dic3C2×Dic3semidirect
752. C2×D4D3×Dic3semidirect
911. C32#2328semidirect
1062. C3#74667semidirect
1063. C3#83172semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×#67⋊Dic32
C2×Dic3×#672
#105929192
C3×#52202
#105917212
#105917132
#105917102
#105917072
#105913762
#105912392
#105912062
#831723
#746673