Finite Group Databasebeta

← #11802449

Subgroups — #11802449

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63861C211yesmaximal, characteristic
2C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#4990C211yesmaximal, characteristic
4C3×#4978C211yesmaximal, characteristic, complemented
5#10591368C211yesmaximal, characteristic
6#10591368C211yesmaximal, characteristic
7#10591368C211yesmaximal, characteristic
8#10591333C211yesmaximal, characteristic, complemented
9#10591284C211yesmaximal, characteristic
10#10591279C211yesmaximal, characteristic
11#10591271C211yesmaximal, characteristic, complemented
12#10591257C211yesmaximal, characteristic, complemented
13#10591248C211yesmaximal, characteristic, complemented
14#10591241C211yesmaximal, characteristic, complemented
15C4×Dic32C211yesmaximal, characteristic, complemented
16#75455—31nomaximal
17#74942—31nomaximal
18C22×D3×Dic3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63861C418yescomplemented
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#898—31no—
55C2×#879—31no—
56C3×#388—31no—
57C3×#387—31no—
58#4990D311yescharacteristic
59#4978D311yescharacteristic, complemented
60Dic3×C4⋊C4—31no—
61Dic3×C4⋊C4—31no—
62Dic3×C4⋊C4—31no—
63Dic3×C4⋊C4—61no—
64#4945—31no—
65#4944—31no—
66Dic3×C22⋊C4—31no—
67Dic3×C22⋊C4—31no—
68Dic3×C22⋊C4—31no—
69#4940—31no—
70#4933—31no—
71C42×Dic3—31no—
72C42×Dic3—31no—
73#4670—31no—
74#4666—31no—
75#4666—31no—
76#4666—31no—
77#4655—31no—
78#4654—31no—
79#4653—31no—
80#4651—31no—
81#4651—31no—
82#4649—31no—
83#4649—31no—
84#4649—31no—
85C23×C3×D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
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
99C22×C3×Dic3C2311yescharacteristic
100C2×D3×Dic3—22no—
101C2×D3×Dic3—22no—
102C2×D3×Dic3—22no—
103C32×C4⋊C4—22no—
104C4⋊(C3⋊Dic3)C2×C414yescomplemented
105C4×C3⋊Dic3—22no—
106C4×C3⋊Dic3—22no—
107C4×C3⋊Dic3—22no—
108C3×(C2×D3)⋊C4—22no—
109C3×(C2×D3)⋊C4—22no—
110C3×(C2×D3)⋊C4C2×C414yes—
111C3×Dic3⋊C4C2×C414yescomplemented
112C3×C4×Dic3—22no—
113C3×C4×Dic3—22no—
114#3724—22no—
115#3724C2×C414yescomplemented
116Dic3⋊Dic3—22no—
117(C2×D3)⋊Dic3—22no—
118(C2×D3)⋊Dic3C2×C414yes—
119(C2×D3)⋊Dic3C2×C414yes—
120Dic32—22no—
121Dic32—22no—
122Dic32—22no—
123Dic32—22no—
124Dic32C2×C414yescomplemented
125C4×#126—91noSylow
126C23×Dic3—31no—
127C22×C4×D3—31no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C22⋊C4—31no—
133C2×C3×C22⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×#217—31no—
138C2×#217—31no—
139C2×#217—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4C2×D311yescharacteristic
144C2×(C2×D3)⋊C4C2×D311yescharacteristic
145C2×(C2×D3)⋊C4C2×D311yescharacteristic
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—61no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4C2×D311yescharacteristic
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3—61no—
174C2×C4×Dic3—61no—
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#898—38no—
178#879—38no—
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—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—61no—
198C3⋊#95—61no—
199C3⋊#95C2×D311yescharacteristic
200C3⋊#95C2×D311yescharacteristic
201C3⋊#95C2×D311yescharacteristic
202C3⋊#95C2×D311yescharacteristic
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3C22×C412yes—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4C22×C412yes—
221C2×C32×C4#4112yes—
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⋊Dic3C22×C412yes—
230C2×C3⋊Dic3C22×C412yes—
231C2×C3⋊Dic3#4112yes—
232C2×C3⋊Dic3#4112yes—
233C2×C3⋊Dic3#4112yes—
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—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C22×C412yes—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3#4112yes—
254C2×C3×Dic3#4112yes—
255D3×Dic3—44no—
256C2×#126—91no—
257#388—31no—
258#388—91no—
259#388—91no—
260#387—31no—
261#387—91no—
262#387—91no—
263#383—91no—
264C4×C4⋊C4—91no—
265C4×C4⋊C4—91no—
266C4×C4⋊C4—91no—
267C4×C22⋊C4—91no—
268C4×C22⋊C4—91no—
269C4×C22⋊C4—91no—
270C43—91no—
271C24×C3—31no—
272C23×D3C22×D311yescharacteristic
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—62no—
302C22×Dic3—62no—
303C22×Dic3—62no—
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—34no—
318C3×C22⋊C4—34no—
319C3×C22⋊C4—62no—
320C3×C22⋊C4—62no—
321C3×C42—62no—
322C3×C42—62no—
323#217—34no—
324#217—34no—
325#217—62no—
326(C2×D3)⋊C4—22no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—34no—
329(C2×D3)⋊C4—34no—
330(C2×D3)⋊C4—62no—
331(C2×D3)⋊C4C4×D314yes—
332C4⋊Dic3—34no—
333C4⋊Dic3—34no—
334C4⋊Dic3—64no—
335C4⋊Dic3—62no—
336Dic3⋊C4—34no—
337Dic3⋊C4—34no—
338Dic3⋊C4—62no—
339Dic3⋊C4—62no—
340Dic3⋊C4—62no—
341Dic3⋊C4C4×D314yescomplemented
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—34no—
345C4×Dic3—34no—
346C4×Dic3—62no—
347C4×Dic3—62no—
348C4×Dic3—62no—
349C4×Dic3—62no—
350C4×Dic3—62no—
351C4×Dic3—62no—
352C4×Dic3—62no—
353C4×Dic3—62no—
354C4×Dic3—62no—
355C4×Dic3—62no—
356C4×Dic3—62no—
357C4×Dic3—62no—
358C4×Dic3—62no—
359C4×Dic3—64no—
360C4×Dic3—62no—
361C4×Dic3—122no—
362C4×Dic3—122no—
363C22×C32C23×C411yescharacteristic
364C22×C32C2×#4111yescharacteristic
365C22×C32C2×#4111yescharacteristic
366C22×C32C2×#4111yescharacteristic
367C22×C32C2×#4111yescharacteristic
368C22×C32C2×#4111yescharacteristic
369C22×C32C2×#4111yescharacteristic
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—41no—
374C2×C3×D3—41no—
375C2×C3×D3—41no—
376C2×C3×D3—41no—
377C32×C4—22no—
378C32×C4—22no—
379C32×C4—41no—
380C3⋊Dic3—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—41no—
383C3⋊Dic3#12614yescomplemented
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C23×C4—91no—
392#126—98no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—91no—
395C2×C4⋊C4—91no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4D3211yescharacteristic
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4—91no—
404C2×C22⋊C4—91no—
405C2×C42—31no—
406C2×C42—31no—
407C2×C42—91no—
408C2×C42—91no—
409C2×C42—91no—
410C2×C42—91no—
411C2×C42—91no—
412C2×C42—91no—
413C2×C42—91no—
414C2×C42—91no—
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—31no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427C23×C3—21no—
428C23×C3—32no—
429C23×C3—61no—
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—61no—
434C23×C3—61no—
435C23×C3C23×D311yescharacteristic
436C23×C3C23×D311yescharacteristic
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3C2×C4×D312yes—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4C2×C4×D312yes—
489C2×C3×C4C2×C4×D312yes—
490C2×C3×C4#23712yes—
491C2×C3×C4#23712yes—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—32no—
509C2×Dic3—32no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—62no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—62no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—124no—
545C2×Dic3C2×C4×D312yes—
546C2×Dic3C2×C4×D312yes—
547C2×Dic3C2×C4×D312yes—
548C2×Dic3#23712yes—
549C2×Dic3#23912yes—
550C4×D3—124no—
551C2×C32C4×#4111yescharacteristic
552C2×C32C4×#4111yescharacteristic
553C2×C32C4×#4111yescharacteristic
554C2×C32C2×#12611yescharacteristic
555C2×C32#52911yescharacteristic
556C2×C32#52911yescharacteristic
557C2×C32#52911yescharacteristic
558C3×D3—42no—
559C24—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4—182no—
572C22×C4—182no—
573C22×C4—182no—
574C22×C4C2×D3211yescharacteristic
575C22×C4C2×D3211yescharacteristic
576C22×C4C2×D3211yescharacteristic
577C4⋊C4—22no—
578C4⋊C4—34no—
579C4⋊C4—94no—
580C4⋊C4—94no—
581C4⋊C4—182no—
582C4⋊C4—182no—
583C22⋊C4—34no—
584C22⋊C4—62no—
585C22⋊C4—62no—
586C22⋊C4—94no—
587C22⋊C4—94no—
588C22⋊C4—182no—
589C42—62no—
590C42—62no—
591C42—94no—
592C42—182no—
593C42—182no—
594C42—182no—
595C42—182no—
596C42—182no—
597C42—182no—
598C42—182no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—62no—
607C22×C3—62no—
608C22×C3—62no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3C22×C4×D311yescharacteristic
614C22×C3C22×C4×D311yescharacteristic
615C22×C3C2×#23711yescharacteristic
616C22×C3C2×#23711yescharacteristic
617C22×C3C2×#23711yescharacteristic
618C22×C3C2×#23911yescharacteristic
619C22×C3D3×#4111yescharacteristic
620C22×C3D3×#4111yescharacteristic
621C22×C3D3×#4111yescharacteristic
622C22×C3D3×#4111yescharacteristic
623C22×C3D3×#4111yescharacteristic
624C22×C3D3×#4111yescharacteristic
625C22×C3D3×#4111yescharacteristic
626C22×C3D3×#4111yescharacteristic
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—22no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C3×C4—24no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—62no—
644C3×C4—62no—
645C3×C4—62no—
646C3×C4—62no—
647C3×C4—62no—
648C3×C4—121no—
649C3×C4—121no—
650Dic3—22no—
651Dic3—22no—
652Dic3—22no—
653Dic3—22no—
654Dic3—22no—
655Dic3—34no—
656Dic3—34no—
657Dic3—41no—
658Dic3—41no—
659Dic3—64no—
660Dic3—62no—
661Dic3—62no—
662Dic3—62no—
663Dic3—62no—
664Dic3—122no—
665Dic3—122no—
666Dic3—122no—
667Dic3—121no—
668Dic3—121no—
669C32C4×#12611yescharacteristic, complemented, Sylow
670C23—32no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23C22×D3211yescharacteristic
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—92no—
707C2×C4—92no—
708C2×C4—92no—
709C2×C4—92no—
710C2×C4—92no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—364no—
719C2×C4C4×D3212yes—
720C2×C4#380512yes—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—122no—
729C2×C3#552211yescharacteristic
730C2×C3#552211yescharacteristic
731C2×C3C4×#23711yescharacteristic
732C2×C3C4×#23711yescharacteristic
733C2×C3C4×#23711yescharacteristic
734C2×C3C4×#23911yescharacteristic
735C2×C3#560011yescharacteristic
736C2×C3#562411yescharacteristic
737C2×C3#564911yescharacteristic
738C2×C3#564911yescharacteristic
739C2×C3#568011yescharacteristic
740C2×C3#569111yescharacteristic
741C2×C3D3×#12611yescharacteristic
742C2×C3D3×#12611yescharacteristic
743D3—42no—
744C22—62no—
745C22—62no—
746C22—62no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22C2×C4×D3211yescharacteristic
752C22#6430611yescharacteristic
753C22D3×#23711yescharacteristic
754C22#6431211yescharacteristic
755C22D3×#23911yescharacteristic
756C22#6431911yescharacteristic
757C22C2×#380511yescharacteristic
758C4—22no—
759C4—22no—
760C4—41no—
761C4—62no—
762C4—62no—
763C4—62no—
764C4—62no—
765C4—62no—
766C4—94no—
767C4—121no—
768C4—121no—
769C4—182no—
770C4—182no—
771C4—361no—
772C3—21no—
773C3#7494211yescharacteristic, complemented
774C3#7545511yescharacteristic, complemented
775C2—122no—
776C2#1059435811yescharacteristic
777C2#1059436211yescharacteristic
778C2#1059444111yescharacteristic
779C2#1059465611yescharacteristic
780C2C4×#380511yescharacteristic
781C2#1059520211yescharacteristic
782C2#1059537711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C3⋊Dic3C2semidirect
4. C3×#4978C2semidirect
8. #10591333C2semidirect
11. #10591271C2semidirect
12. #10591257C2semidirect
13. #10591248C2semidirect
14. #10591241C2semidirect
15. C4×Dic32C2semidirect
41. #63861C4semidirect
59. #4978D3semidirect
104. C4⋊(C3⋊Dic3)C2×C4semidirect
111. C3×Dic3⋊C4C2×C4semidirect
115. #3724C2×C4semidirect
124. Dic32C2×C4semidirect
341. Dic3⋊C4C4×D3semidirect
383. C3⋊Dic3#126semidirect
669. C32C4×#126semidirect
773. C3#74942semidirect
774. C3#75455semidirect

Maximal subgroups

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

subgroupindex
C2×#638612
C4⋊C4×C3⋊Dic32
C3×#49902
C3×#49782
#105913682
#105913332
#105912842
#105912792
#105912712
#105912572
#105912482
#105912412
C4×Dic322
#754553
#749423