Finite Group Databasebeta

← #11857065

Subgroups — #11857065

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592632C211yesmaximal, characteristic, complemented
2C3×#4940C211yesmaximal, characteristic
3C3×C42×Dic3C211yesmaximal, characteristic, complemented
4#10591333C211yesmaximal, characteristic, complemented
5#10591332C211yesmaximal, characteristic, complemented
6#10591331C211yesmaximal, characteristic, complemented
7#10591305C211yesmaximal, characteristic
8#10591305C211yesmaximal, characteristic
9#10591280C211yesmaximal, characteristic
10#10591280C211yesmaximal, characteristic
11#10591279C211yesmaximal, characteristic
12#10591279C211yesmaximal, characteristic
13#10591201C211yesmaximal, characteristic, complemented
14#10591197C211yesmaximal, characteristic, complemented
15#10591193C211yesmaximal, characteristic, complemented
16#75823—31nomaximal
17#73317—31nomaximal
18C2×C32×C42C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39#63658C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×#388—31no—
54C3×C43—31no—
55#4980—31no—
56#4978—31no—
57#4951—31no—
58#4951—31no—
59#4945—31no—
60#4945—31no—
61#4944—31no—
62#4944—31no—
63#4940—31no—
64#4940—31no—
65#4940—31no—
66#4940—31no—
67#4940—31no—
68#4940—31no—
69#4940D311yescharacteristic
70#4933—31no—
71#4933—31no—
72#4933—31no—
73#4933—31no—
74#4933—31no—
75#4933—31no—
76#4933—31no—
77#4933—31no—
78#4933—61no—
79C42×Dic3D311yescharacteristic, complemented
80#4655—31no—
81#4654—31no—
82#4653—31no—
83#4652—31no—
84C23×C3×D3C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C32×C42—22no—
100#3750—22no—
101#3750—22no—
102C3×(C2×D3)⋊C4—22no—
103C3×(C2×D3)⋊C4—22no—
104C3×(C2×D3)⋊C4—22no—
105C3×Dic3⋊C4—22no—
106C3×C4×Dic3—22no—
107C3×C4×Dic3—22no—
108C3×C4×Dic3—22no—
109C3×C4×Dic3—22no—
110C3×C4×Dic3—22no—
111C3×C4×Dic3—22no—
112#3724—22no—
113#3724—22no—
114Dic3⋊Dic3—22no—
115Dic3⋊Dic3—22no—
116(C2×D3)⋊Dic3—22no—
117(C2×D3)⋊Dic3—22no—
118(C2×D3)⋊Dic3—22no—
119(C2×D3)⋊Dic3—22no—
120#2866—91noSylow
121C2×C3×C4⋊C4—31no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C42—21no—
126C2×C3×C42—31no—
127C2×C3×C42—31no—
128C2×C3×C42—31no—
129C2×C3×C42—31no—
130C2×C3×C42—31no—
131C2×C3×C42—31no—
132C2×C3×C42C2×D311yescharacteristic
133C2×C3×C42C2×D311yescharacteristic
134C2×#217—31no—
135C2×#217—31no—
136C2×#217—31no—
137C2×#217—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4C2×D311yescharacteristic
143C2×(C2×D3)⋊C4C2×D311yescharacteristic
144C2×(C2×D3)⋊C4C2×D311yescharacteristic
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—61no—
158C2×Dic3⋊C4—61no—
159C2×Dic3⋊C4C2×D311yescharacteristic
160C2×C4×Dic3C2×D311yescharacteristic
161C2×C4×Dic3C2×D311yescharacteristic
162C2×C4×Dic3C2×D311yescharacteristic
163C2×C4×Dic3C2×D311yescharacteristic
164C2×C4×Dic3C2×D311yescharacteristic
165C2×C4×Dic3C2×D311yescharacteristic
166C3×#95—31no—
167C3×#95—31no—
168C3⋊#95—31no—
169C3⋊#95—31no—
170C3⋊#95—31no—
171C3⋊#95—31no—
172C3⋊#95—31no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
182C3⋊#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—61no—
193C3⋊#95—61no—
194C3⋊#95—61no—
195C3⋊#95—61no—
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32C2411yescharacteristic
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—21no—
202C22×C3×D3—21no—
203C22×C3×D3—21no—
204C22×C3×D3—21no—
205C22×C3×D3—21no—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4#4112yes—
213C2×C32×C4#4112yes—
214C2×C32×C4#4112yes—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3#4112yes—
245C2×C3×Dic3#4112yes—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248#388—31no—
249#388—91no—
250#388—91no—
251#388—91no—
252#388—91no—
253#388—91no—
254#388—91no—
255#387—91no—
256#387—91no—
257#387—91no—
258#387—91no—
259#387—91no—
260#387—91no—
261#387—91no—
262C43—31no—
263C24×C3—31no—
264C23×D3C22×D311yescharacteristic
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×Dic3—31no—
282C22×Dic3—31no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C3×C4⋊C4—62no—
301C3×C22⋊C4—62no—
302C3×C22⋊C4—62no—
303C3×C22⋊C4—62no—
304C3×C42—22no—
305C3×C42—22no—
306C3×C42—42no—
307C3×C42—62no—
308C3×C42—62no—
309C3×C42—62no—
310C3×C42—62no—
311C3×C42—62no—
312C3×C42—62no—
313#217—62no—
314#217—62no—
315#217—62no—
316#217—62no—
317(C2×D3)⋊C4—22no—
318(C2×D3)⋊C4—22no—
319(C2×D3)⋊C4—22no—
320(C2×D3)⋊C4—62no—
321(C2×D3)⋊C4—62no—
322(C2×D3)⋊C4—62no—
323(C2×D3)⋊C4—62no—
324C4⋊Dic3—62no—
325C4⋊Dic3—62no—
326Dic3⋊C4—22no—
327Dic3⋊C4—62no—
328Dic3⋊C4—62no—
329Dic3⋊C4—62no—
330Dic3⋊C4—62no—
331Dic3⋊C4—64no—
332Dic3⋊C4—62no—
333Dic3⋊C4—62no—
334Dic3⋊C4—62no—
335Dic3⋊C4—62no—
336Dic3⋊C4—62no—
337Dic3⋊C4—62no—
338Dic3⋊C4—122no—
339C4×Dic3—22no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C22×C32C2×#4111yescharacteristic
346C22×C32C2×#4111yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4111yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C2×C3×D3—41no—
353C2×C3×D3—41no—
354C2×C3×D3—41no—
355C2×C3×D3—41no—
356C2×C3×D3—41no—
357C2×C3×D3—41no—
358C2×C3×D3—41no—
359C32×C4—22no—
360C32×C4—22no—
361C32×C4—22no—
362C3⋊Dic3—41no—
363C3⋊Dic3—41no—
364C3⋊Dic3—41no—
365C3⋊Dic3—41no—
366C3×Dic3—22no—
367C3×Dic3—22no—
368C3×Dic3—22no—
369C3×Dic3—22no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C2×C4⋊C4—31no—
374C2×C4⋊C4—91no—
375C2×C4⋊C4—91no—
376C2×C4⋊C4—91no—
377C2×C4⋊C4—91no—
378C2×C4⋊C4—91no—
379C2×C4⋊C4—91no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—91no—
384C2×C22⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—91no—
387C2×C42—31no—
388C2×C42—31no—
389C2×C42—31no—
390C2×C42—31no—
391C2×C42—31no—
392C2×C42—31no—
393C2×C42D3211yescharacteristic
394#95—31no—
395#95—31no—
396#95—91no—
397#95—91no—
398#95—91no—
399#95—91no—
400#95—91no—
401#95—91no—
402#95—91no—
403#95—91no—
404#95—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408C23×C3—21no—
409C23×C3—61no—
410C23×C3—61no—
411C23×C3—61no—
412C23×C3—61no—
413C23×C3—61no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3C23×D311yescharacteristic
417C23×C3C23×D311yescharacteristic
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—32no—
441C2×C3×C4—32no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4#23512yes—
468C2×C3×C4#23512yes—
469C2×C3×C4#23512yes—
470C2×C3×C4#23512yes—
471C2×C3×C4#23712yes—
472C2×C3×C4#23712yes—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—62no—
491C2×Dic3—62no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—121no—
517C2×Dic3—121no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3#23512yes—
527C2×Dic3#23512yes—
528C2×Dic3#23512yes—
529C2×Dic3#23512yes—
530C2×C32#52911yescharacteristic
531C2×C32#52911yescharacteristic
532C2×C32#52911yescharacteristic
533C2×C32#52911yescharacteristic
534C2×C32#52911yescharacteristic
535C2×C32#52911yescharacteristic
536C2×C32#52911yescharacteristic
537C3×D3—81no—
538C24—31no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—91no—
547C22×C4—91no—
548C22×C4—91no—
549C22×C4—91no—
550C22×C4C2×D3211yescharacteristic
551C22×C4C2×D3211yescharacteristic
552C22×C4C2×D3211yescharacteristic
553C4⋊C4—62no—
554C4⋊C4—182no—
555C4⋊C4—182no—
556C4⋊C4—182no—
557C4⋊C4—182no—
558C4⋊C4—182no—
559C4⋊C4—182no—
560C22⋊C4—62no—
561C22⋊C4—62no—
562C22⋊C4—62no—
563C22⋊C4—182no—
564C22⋊C4—182no—
565C22⋊C4—182no—
566C22⋊C4—182no—
567C42—22no—
568C42—62no—
569C42—62no—
570C42—62no—
571C42—62no—
572C42—62no—
573C42—62no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3—121no—
585C22×C3—121no—
586C22×C3—121no—
587C22×C3—121no—
588C22×C3C2×#23511yescharacteristic
589C22×C3C2×#23511yescharacteristic
590C22×C3C2×#23511yescharacteristic
591C22×C3C2×#23511yescharacteristic
592C22×C3C2×#23511yescharacteristic
593C22×C3C2×#23511yescharacteristic
594C22×C3C2×#23511yescharacteristic
595C22×C3C2×#23511yescharacteristic
596C22×C3C2×#23711yescharacteristic
597C22×C3C2×#23711yescharacteristic
598C22×C3D3×#4111yescharacteristic
599C22×C3D3×#4111yescharacteristic
600C22×C3D3×#4111yescharacteristic
601C22×C3D3×#4111yescharacteristic
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—62no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—62no—
622C3×C4—121no—
623C3×C4—121no—
624C3×C4—121no—
625Dic3—22no—
626Dic3—22no—
627Dic3—22no—
628Dic3—22no—
629Dic3—41no—
630Dic3—41no—
631Dic3—41no—
632Dic3—122no—
633Dic3—122no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637Dic3—121no—
638Dic3—121no—
639Dic3—121no—
640Dic3—121no—
641Dic3—121no—
642Dic3—241no—
643Dic3—241no—
644C32#286611yescharacteristic, complemented, Sylow
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23C22×D3211yescharacteristic
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—181no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4—181no—
686C2×C4—181no—
687C2×C4—181no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4#379512yes—
693C2×C4#379812yes—
694C2×C4#380412yes—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—241no—
703C2×C3#547911yescharacteristic
704C2×C3#547911yescharacteristic
705C2×C3#547911yescharacteristic
706C2×C3#547911yescharacteristic
707C2×C3#547911yescharacteristic
708C2×C3#547911yescharacteristic
709C2×C3#547911yescharacteristic
710C2×C3#552811yescharacteristic
711C2×C3#553811yescharacteristic
712C2×C3#555711yescharacteristic
713C2×C3#560011yescharacteristic
714C2×C3#564911yescharacteristic
715C2×C3#568011yescharacteristic
716C2×C3#570611yescharacteristic
717D3—81no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22—121no—
725C22C2×#379511yescharacteristic
726C22C2×#379811yescharacteristic
727C22D3×#23511yescharacteristic
728C22D3×#23511yescharacteristic
729C22D3×#23511yescharacteristic
730C22D3×#23511yescharacteristic
731C22C2×#380411yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—62no—
736C4—62no—
737C4—62no—
738C4—62no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—361no—
743C4—361no—
744C4—361no—
745C4—361no—
746C3—21no—
747C3#7331711yescharacteristic, complemented
748C3#7582311yescharacteristic, complemented
749C2—241no—
750C2#1059392111yescharacteristic
751C2#1059397311yescharacteristic
752C2#1059397411yescharacteristic
753C2#1059397511yescharacteristic
754C2#1059483911yescharacteristic
755C2#1059494811yescharacteristic
756C2#1059494911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2866
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10592632C2semidirect
3. C3×C42×Dic3C2semidirect
4. #10591333C2semidirect
5. #10591332C2semidirect
6. #10591331C2semidirect
13. #10591201C2semidirect
14. #10591197C2semidirect
15. #10591193C2semidirect
79. C42×Dic3D3semidirect
644. C32#2866semidirect
747. C3#73317semidirect
748. C3#75823semidirect

Maximal subgroups

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

subgroupindex
#105926322
C3×#49402
C3×C42×Dic32
#105913332
#105913322
#105913312
#105913052
#105912802
#105912792
#105912012
#105911972
#105911932
#758233
#733173