Finite Group Databasebeta

← #11807754

Subgroups — #11807754

Order 1152.

1295 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2#10592919C211yesmaximal, characteristic, complemented
3C3×#5220C211yesmaximal, characteristic, complemented
4#10591719C211yesmaximal, characteristic, complemented
5#10591718C211yesmaximal, characteristic, complemented
6#10591713C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic, complemented
8#10591707C211yesmaximal, characteristic, complemented
9#10591707C211yesmaximal, characteristic, complemented
10#10591702C211yesmaximal, characteristic, complemented
11#10591701C211yesmaximal, characteristic, complemented
12#10591295C211yesmaximal, characteristic, complemented
13#10591294C211yesmaximal, characteristic, complemented
14#10591270C211yesmaximal, characteristic, complemented
15#10591269C211yesmaximal, characteristic, complemented
16#82639—31nomaximal
17#74883—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C3×#938C418yescomplemented
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×#121—31no—
55C2×#938D311yescharacteristic
56C3×#386—31no—
57#5221—31no—
58#5221—31no—
59#5220—31no—
60#5220—31no—
61#5220—31no—
62#5220—31no—
63#5220—61no—
64#5220D311yescharacteristic, complemented
65#5213—31no—
66#5212—31no—
67#5211—31no—
68#5210—31no—
69#4980—31no—
70#4980—31no—
71#4958—31no—
72#4957—31no—
73#4957—31no—
74#4951—31no—
75#4951—31no—
76#4950—31no—
77#4950—31no—
78#4946—31no—
79#4945—31no—
80#4944—31no—
81#4667—31no—
82#4664—31no—
83#4654—31no—
84#4653—31no—
85C24×C32C2311yescharacteristic
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C2×C32×D4—41no—
89C2×C32×D4—41no—
90C2×C32×D4C2×C414yes—
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3—41no—
93C22×C3⋊Dic3—41no—
94C22×C3⋊Dic3—41no—
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C3×#67—41no—
100C2×C3×#67—41no—
101C2×C3×#67—41no—
102C2×C3×#67—41no—
103C2×C3×#67C2×C414yescomplemented
104C2×C3×#67C2×C414yescomplemented
105C22×C3×Dic3—41no—
106C22×C3×Dic3—41no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3—41no—
117C2×C3×C4×D3C2×C414yescomplemented
118#3757—41no—
119#3757—41no—
120#3757—41no—
121C3×#217—41no—
122C3×#217—41no—
123C3×#217—41no—
124C3×#217C2×C414yescomplemented
125C3×#217C2×C414yescomplemented
126C3×C4⋊Dic3C2×C414yescomplemented
127Dic3⋊Dic3—41no—
128Dic3⋊Dic3—41no—
129Dic3⋊Dic3—41no—
130Dic3⋊Dic3—41no—
131(C2×D3)⋊Dic3—41no—
132(C2×D3)⋊Dic3—41no—
133(C2×D3)⋊Dic3—41no—
134(C2×D3)⋊Dic3—41no—
135Dic32—41no—
136Dic32—41no—
137#2377—91noSylow
138C22×C3×D4—21no—
139C22×C3×D4—31no—
140C22×C3×D4—31no—
141C22×C3×D4C2×D311yescharacteristic
142C22×C3×D4C2×D311yescharacteristic
143C23×C3×C4—31no—
144C23×C3×C4—31no—
145C22×#67C2×D311yescharacteristic
146C22×#67C2×D311yescharacteristic
147C23×Dic3—31no—
148C23×Dic3—31no—
149C23×Dic3—61no—
150C23×Dic3C2×D311yescharacteristic
151C22×C4×D3C2×D311yescharacteristic
152C3×#121—38no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—61no—
170C2×#217—61no—
171C2×#217—61no—
172C2×#217C2×D311yescharacteristic
173C2×#217C2×D311yescharacteristic
174C2×#217C2×D311yescharacteristic
175C2×#217C2×D311yescharacteristic
176C2×#217C2×D311yescharacteristic
177#938Dic318yescomplemented
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×C4⋊Dic3C2×D311yescharacteristic
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C3×#95—31no—
196C3×#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—61no—
214C3⋊#95—61no—
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32C22×C412yes—
230C23×C32C22×C412yes—
231C23×C32C2411yescharacteristic
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C22×C412yes—
239C32×D4—44no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C22×C412yes—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—44no—
256C3×#67—44no—
257C3×#67—44no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
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—44no—
277C2×C3×Dic3C22×C412yes—
278C2×C3×Dic3C22×C412yes—
279C2×C3×Dic3C22×C412yes—
280C3×C4×D3—44no—
281C2×#121—31no—
282#390—91no—
283#390—91no—
284#388—91no—
285#388—91no—
286#387—91no—
287#387—91no—
288#386—31no—
289#386—91no—
290#386—91no—
291#386—91no—
292#385—91no—
293#385—91no—
294#381—91no—
295#380—91no—
296C24×C3—21no—
297C24×C3—21no—
298C24×C3—31no—
299C24×C3C22×D311yescharacteristic
300C24×C3C22×D311yescharacteristic
301C24×C3C22×D311yescharacteristic
302C24×C3C22×D311yescharacteristic
303C23×D3C22×D311yescharacteristic
304C2×C3×D4—24no—
305C2×C3×D4—34no—
306C2×C3×D4—34no—
307C2×C3×D4—41no—
308C2×C3×D4—41no—
309C2×C3×D4—41no—
310C2×C3×D4—41no—
311C2×C3×D4—42no—
312C2×C3×D4—42no—
313C2×C3×D4—121no—
314C2×C3×D4—121no—
315C2×C3×D4—121no—
316C2×C3×D4—121no—
317C2×C3×D4C4×D314yes—
318C2×C3×D4C2×Dic314yes—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—34no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—121no—
329C22×C3×C4—121no—
330C22×C3×C4—121no—
331C22×C3×C4—121no—
332C22×C3×C4—121no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—41no—
336C2×#67—41no—
337C2×#67—41no—
338C2×#67—41no—
339C2×#67C2×Dic314yescomplemented
340C2×#67C2×Dic314yescomplemented
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—41no—
350C22×Dic3—41no—
351C22×Dic3—41no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—121no—
357C22×Dic3—121no—
358C22×Dic3—121no—
359C22×Dic3—121no—
360C22×Dic3—121no—
361C22×Dic3—121no—
362C22×Dic3—122no—
363C22×Dic3—122no—
364C22×Dic3—122no—
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C2×C4×D3—41no—
373C2×C4×D3—41no—
374C2×C4×D3C2×Dic314yescomplemented
375C3×C4⋊C4—34no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4—34no—
378C3×C22⋊C4—121no—
379C3×C22⋊C4—121no—
380C3×C22⋊C4—121no—
381#217—41no—
382#217—41no—
383#217—41no—
384#217—121no—
385#217—121no—
386#217—121no—
387#217—121no—
388#217—121no—
389#217—121no—
390#217—121no—
391#217—121no—
392#217—121no—
393#217—121no—
394#217—122no—
395#217—122no—
396#217—122no—
397#217C2×Dic314yescomplemented
398#217C2×Dic314yescomplemented
399(C2×D3)⋊C4—121no—
400(C2×D3)⋊C4—121no—
401(C2×D3)⋊C4—121no—
402(C2×D3)⋊C4—121no—
403C4⋊Dic3—121no—
404C4⋊Dic3—121no—
405C4⋊Dic3—121no—
406C4⋊Dic3—121no—
407C4⋊Dic3C2×Dic314yescomplemented
408Dic3⋊C4—121no—
409Dic3⋊C4—121no—
410Dic3⋊C4—121no—
411Dic3⋊C4—121no—
412C4×Dic3—121no—
413C4×Dic3—121no—
414C4×Dic3—121no—
415C4×Dic3—121no—
416C22×C32—22no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C23×C411yescharacteristic
431C22×C32H(5,𝔽2)11yescharacteristic
432C22×C32H(5,𝔽2)11yescharacteristic
433C22×C32H(5,𝔽2)11yescharacteristic
434C22×C32H(5,𝔽2)11yescharacteristic
435C22×C32H(5,𝔽2)11yescharacteristic
436C22×C322−1+411yescharacteristic
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C32×C4—22no—
445C3⋊Dic3—41no—
446C3⋊Dic3—41no—
447C3⋊Dic3—41no—
448C3⋊Dic3—41no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C22×D4—31no—
457C22×D4—31no—
458C22×D4D3211yescharacteristic
459C23×C4—31no—
460C23×C4—31no—
461C23×C4—91no—
462#121—38no—
463C2×C4⋊C4—31no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—91no—
466C2×C4⋊C4—91no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—31no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4—91no—
477C2×C22⋊C4—91no—
478C2×C22⋊C4—91no—
479C2×C22⋊C4—91no—
480C2×C42—91no—
481C2×C42—91no—
482#95—31no—
483#95—31no—
484#95—91no—
485#95—91no—
486#95—91no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95—91no—
492C23×C3—22no—
493C23×C3—22no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—22no—
520C23×C3—22no—
521C23×C3—32no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3C2×C4×D312yes—
539C23×C3C2×C4×D312yes—
540C23×C3C22×Dic312yes—
541C23×C3C22×Dic312yes—
542C23×C3C23×D311yescharacteristic
543C23×C3C23×D311yescharacteristic
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3C22×Dic312yes—
551C3×D4—44no—
552C3×D4—44no—
553C3×D4—48no—
554C3×D4—124no—
555C3×D4—124no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—22no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—124no—
585C2×C3×C4—124no—
586C2×C3×C4C2×C4×D312yes—
587C2×C3×C4C22×Dic312yes—
588#67—44no—
589#67—44no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—44no—
609C2×Dic3—62no—
610C2×Dic3—62no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—121no—
636C2×Dic3—121no—
637C2×Dic3—121no—
638C2×Dic3—121no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—128no—
646C2×Dic3—124no—
647C2×Dic3—124no—
648C2×Dic3C22×Dic312yes—
649C2×Dic3C22×Dic312yes—
650C2×Dic3C22×Dic312yes—
651C4×D3—44no—
652C2×C32—42no—
653C2×C32—42no—
654C2×C32#51811yescharacteristic
655C2×C32#51811yescharacteristic
656C2×C32#52011yescharacteristic
657C2×C32#56011yescharacteristic
658C2×C32#56011yescharacteristic
659C2×C32#56211yescharacteristic
660C2×C32#56211yescharacteristic
661C3×D3—42no—
662C24—31no—
663C24C2×D3211yescharacteristic
664C24C2×D3211yescharacteristic
665C2×D4—34no—
666C2×D4—34no—
667C2×D4—41no—
668C2×D4—41no—
669C2×D4—121no—
670C2×D4—121no—
671C2×D4—121no—
672C2×D4—121no—
673C2×D4D3×Dic314yes—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—34no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—121no—
687C22×C4—121no—
688C22×C4—121no—
689C22×C4—121no—
690C22×C4—121no—
691C22×C4—361no—
692C22×C4—361no—
693C22×C4—361no—
694C22×C4C2×D3211yescharacteristic
695C4⋊C4—34no—
696C4⋊C4—361no—
697C4⋊C4—361no—
698C4⋊C4—361no—
699C4⋊C4—361no—
700C22⋊C4—34no—
701C22⋊C4—34no—
702C22⋊C4—121no—
703C22⋊C4—121no—
704C22⋊C4—121no—
705C22⋊C4—361no—
706C22⋊C4—361no—
707C22⋊C4—361no—
708C22⋊C4—361no—
709C22⋊C4—361no—
710C22⋊C4—361no—
711C22⋊C4—361no—
712C42—361no—
713C42—361no—
714C22×C3—24no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—81no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3C22×C4×D311yescharacteristic
771C22×C3#100411yescharacteristic
772C22×C3#100411yescharacteristic
773C22×C3#100411yescharacteristic
774C22×C3#100411yescharacteristic
775C22×C3#100411yescharacteristic
776C22×C3#100411yescharacteristic
777C22×C3#100411yescharacteristic
778C22×C3#100411yescharacteristic
779C22×C3#100911yescharacteristic
780C22×C3#100911yescharacteristic
781C22×C3#101011yescharacteristic
782C22×C3#101011yescharacteristic
783C22×C3C23×Dic311yescharacteristic
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C3×C4—22no—
792C3×C4—22no—
793C3×C4—42no—
794C3×C4—62no—
795C3×C4—62no—
796C3×C4—62no—
797C3×C4—121no—
798C3×C4—121no—
799C3×C4—121no—
800C3×C4—121no—
801Dic3—22no—
802Dic3—22no—
803Dic3—22no—
804Dic3—41no—
805Dic3—41no—
806Dic3—41no—
807Dic3—41no—
808Dic3—122no—
809Dic3—122no—
810Dic3—121no—
811Dic3—121no—
812Dic3—121no—
813Dic3—121no—
814Dic3—121no—
815Dic3—121no—
816Dic3—121no—
817Dic3—121no—
818Dic3—241no—
819Dic3—241no—
820C32#237711yescharacteristic, complemented, Sylow
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—32no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23C2×D3×Dic312yes—
841C23C2×D3×Dic312yes—
842C23C22×D3211yescharacteristic
843D4—44no—
844D4—124no—
845D4—124no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—124no—
870C2×C4—124no—
871C2×C4—181no—
872C2×C4—181no—
873C2×C4—181no—
874C2×C4—181no—
875C2×C4—181no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—364no—
884C2×C4C2×D3×Dic312yes—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—44no—
893C2×C3—42no—
894C2×C3—42no—
895C2×C3—42no—
896C2×C3—42no—
897C2×C3—82no—
898C2×C3—122no—
899C2×C3#548611yescharacteristic
900C2×C3#554511yescharacteristic
901C2×C3#554611yescharacteristic
902C2×C3#559511yescharacteristic
903C2×C3#562011yescharacteristic
904C2×C3#562011yescharacteristic
905C2×C3#562011yescharacteristic
906C2×C3#562111yescharacteristic
907C2×C3#562111yescharacteristic
908C2×C3#562111yescharacteristic
909C2×C3#566711yescharacteristic
910C2×C3#579811yescharacteristic
911C2×C3#579811yescharacteristic
912C2×C3#582711yescharacteristic
913D3—42no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22#6430911yescharacteristic
936C22#6431311yescharacteristic
937C22#6431411yescharacteristic
938C22#6431411yescharacteristic
939C22C22×D3×Dic311yescharacteristic
940C22#6433011yescharacteristic
941C22#6433011yescharacteristic
942C4—22no—
943C4—62no—
944C4—62no—
945C4—62no—
946C4—121no—
947C4—121no—
948C4—121no—
949C4—121no—
950C4—361no—
951C4—361no—
952C4—361no—
953C4—361no—
954C3—21no—
955C3#7488311yescharacteristic, complemented
956C3#8263911yescharacteristic, complemented
957C2—42no—
958C2—42no—
959C2—122no—
960C2#1059521511yescharacteristic
961C2#1059522211yescharacteristic
962C2#1059525711yescharacteristic
963C2#1059526011yescharacteristic
964C2#1059526311yescharacteristic
965C2#1059526411yescharacteristic
966C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10592919C2semidirect
3. C3×#5220C2semidirect
4. #10591719C2semidirect
5. #10591718C2semidirect
6. #10591713C2semidirect
7. #10591710C2semidirect
8. #10591707C2semidirect
9. #10591707C2semidirect
10. #10591702C2semidirect
11. #10591701C2semidirect
12. #10591295C2semidirect
13. #10591294C2semidirect
14. #10591270C2semidirect
15. #10591269C2semidirect
32. C3×#938C4semidirect
64. #5220D3semidirect
103. C2×C3×#67C2×C4semidirect
104. C2×C3×#67C2×C4semidirect
117. C2×C3×C4×D3C2×C4semidirect
124. C3×#217C2×C4semidirect
125. C3×#217C2×C4semidirect
126. C3×C4⋊Dic3C2×C4semidirect
177. #938Dic3semidirect
339. C2×#67C2×Dic3semidirect
340. C2×#67C2×Dic3semidirect
374. C2×C4×D3C2×Dic3semidirect
397. #217C2×Dic3semidirect
398. #217C2×Dic3semidirect
407. C4⋊Dic3C2×Dic3semidirect
820. C32#2377semidirect
955. C3#74883semidirect
956. C3#82639semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
#105929192
C3×#52202
#105917192
#105917182
#105917132
#105917102
#105917072
#105917022
#105917012
#105912952
#105912942
#105912702
#105912692
#826393
#748833