Finite Group Databasebeta

← #11805677

Subgroups — #11805677

Order 1152.

1449 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
2C2×Dic3×#67C211yesmaximal, characteristic
3C2×#63878C211yesmaximal, characteristic, complemented
4C4×#3757C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic
6#10591716C211yesmaximal, characteristic, complemented
7#10591710C211yesmaximal, characteristic
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591366C211yesmaximal, characteristic, complemented
10#10591334C211yesmaximal, characteristic, complemented
11#10591285C211yesmaximal, characteristic, complemented
12#10591283C211yesmaximal, characteristic, complemented
13#10591254C211yesmaximal, characteristic, complemented
14#10591245C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#82161—31nomaximal
17#74673—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4—24no—
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35Dic3×#67C418yescomplemented
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63878—24no—
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C22×C3×C4⋊C4—31no—
57C2×D4×Dic3—31no—
58C2×C4×#67—31no—
59C22×Dic3⋊C4D311yescharacteristic, complemented
60C2×#892—31no—
61C2×#877—31no—
62C3×#386—31no—
63#5220—31no—
64#5213—31no—
65#5213D311yescharacteristic
66#5212—31no—
67C4×#217—31no—
68C4×#217—31no—
69C4×#217—31no—
70C4×#217—61no—
71#4990—31no—
72#4990—31no—
73#4987—31no—
74#4978—31no—
75#4978—31no—
76#4977—31no—
77Dic3×C4⋊C4—31no—
78#4945—31no—
79#4944—31no—
80#4942—31no—
81#4942—31no—
82Dic3×C22⋊C4—31no—
83#4654—31no—
84#4653—31no—
85#4650—31no—
86#4649—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4—41no—
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67C2×C414yes—
101C22×C3×Dic3—22no—
102C22×C3×Dic3—22no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—41no—
106C22×C3×Dic3C2×C414yes—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3C2×C414yescomplemented
117#3757—22no—
118#3757C2×C414yes—
119C4×C3⋊Dic3—22no—
120C4×C3⋊Dic3—41no—
121C3×#217—22no—
122C3×(C2×D3)⋊C4—22no—
123C3×(C2×D3)⋊C4—41no—
124C3×Dic3⋊C4—22no—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4—22no—
127C3×Dic3⋊C4D414yescomplemented
128Dic3⋊Dic3—22no—
129Dic3⋊Dic3—22no—
130Dic3⋊Dic3C2×C414yescomplemented
131(C2×D3)⋊Dic3—22no—
132(C2×D3)⋊Dic3—41no—
133(C2×D3)⋊Dic3C2×C414yescomplemented
134Dic32—22no—
135Dic32—41no—
136Dic32C2×C414yescomplemented
137#2352—91noSylow
138C22×C3×D4—31no—
139C23×C3×C4—21no—
140C23×C3×C4—31no—
141C23×C3×C4—31no—
142C23×C3×C4C2×D311yescharacteristic
143C23×C3×C4C2×D311yescharacteristic
144C22×#67C2×D311yescharacteristic
145C23×Dic3—31no—
146C23×Dic3C2×D311yescharacteristic
147C23×Dic3C2×D311yescharacteristic
148C22×C4×D3—31no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—64no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×#217—31no—
158C2×#217—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—61no—
165C2×#217—61no—
166C2×#217C2×D311yescharacteristic
167D4×Dic3—38no—
168C4×#67—38no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4C2×D311yescharacteristic
173C2×(C2×D3)⋊C4C2×D311yescharacteristic
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×Dic3⋊C4—24no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4C2×D311yescharacteristic
182C2×Dic3⋊C4C2×D311yescharacteristic
183C2×Dic3⋊C4C2×D311yescharacteristic
184C2×Dic3⋊C4C2×D311yescharacteristic
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—61no—
196C2×C4×Dic3—61no—
197#892—64no—
198#877—64no—
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—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—61no—
218C3⋊#95—61no—
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—21no—
224C23×C32—21no—
225C23×C32C22×C412yes—
226C23×C32#4112yes—
227C23×C32#4112yes—
228C23×C32C2411yescharacteristic
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3C22×C412yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—44no—
242C2×C32×C4C2×D412yes—
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⋊Dic3C22×C412yes—
254C2×C3⋊Dic3C22×C412yes—
255C3×#67—28no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—28no—
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—44no—
273C2×C3×Dic3C22×C412yes—
274C2×C3×Dic3C22×C412yes—
275C2×C3×Dic3C22×C412yes—
276C2×C3×Dic3C2×D412yes—
277C2×C3×Dic3C2×D412yes—
278C2×C3×Dic3#4112yes—
279D3×Dic3—28no—
280C2×C4×D4—91no—
281C2×#117—91no—
282C22×C4⋊C4—31no—
283#388—91no—
284#388—91no—
285#387—91no—
286#387—91no—
287#386—31no—
288#386—91no—
289#382—91no—
290#380—91no—
291#380—91no—
292C4×C4⋊C4—91no—
293C4×C22⋊C4—91no—
294C4×C22⋊C4—91no—
295C24×C3—21no—
296C24×C3—31no—
297C24×C3C22×D311yescharacteristic
298C24×C3C22×D311yescharacteristic
299C23×D3C22×D311yescharacteristic
300C2×C3×D4—34no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C22×C3×C4—24no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—22no—
307C22×C3×C4—22no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—34no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—42no—
319C22×C3×C4—41no—
320C22×C3×C4—41no—
321C22×C3×C4—42no—
322C22×C3×C4—62no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4—62no—
326C22×C3×C4—121no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C2×#67—22no—
332C2×#67—22no—
333C2×#67C4×D314yes—
334C22×Dic3—22no—
335C22×Dic3—22no—
336C22×Dic3—22no—
337C22×Dic3—22no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—34no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—41no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—62no—
353C22×Dic3—62no—
354C22×Dic3C4×D314yes—
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C2×C4×D3—34no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C3×C4⋊C4—34no—
366C3×C4⋊C4—62no—
367C3×C4⋊C4—62no—
368C3×C4⋊C4—62no—
369C3×C22⋊C4—62no—
370C3×C22⋊C4—62no—
371C3×C22⋊C4—121no—
372#217—22no—
373#217—34no—
374#217—34no—
375#217—34no—
376#217—64no—
377#217—64no—
378#217—62no—
379#217—62no—
380#217—62no—
381#217—121no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—41no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—121no—
387C4⋊Dic3—34no—
388C4⋊Dic3—62no—
389C4⋊Dic3—62no—
390Dic3⋊C4—22no—
391Dic3⋊C4—22no—
392Dic3⋊C4—22no—
393Dic3⋊C4—34no—
394Dic3⋊C4—62no—
395Dic3⋊C4—62no—
396Dic3⋊C4#6714yescomplemented
397C4×Dic3—34no—
398C4×Dic3—34no—
399C4×Dic3—62no—
400C4×Dic3—62no—
401C4×Dic3—62no—
402C4×Dic3—62no—
403C4×Dic3—122no—
404C4×Dic3—121no—
405C4×Dic3—121no—
406C4×Dic3—121no—
407C4×Dic3—121no—
408C4×Dic3—122no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—22no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32#11714yescomplemented
416C22×C32C23×C411yescharacteristic
417C22×C32C22×D411yescharacteristic
418C22×C32C2×#4111yescharacteristic
419C22×C32C2×#4111yescharacteristic
420C22×C32C2×#4111yescharacteristic
421C22×C32H(5,𝔽2)11yescharacteristic
422C22×C322−1+411yescharacteristic
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C32×C4—22no—
431C32×C4—41no—
432C3⋊Dic3—22no—
433C3⋊Dic3—22no—
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3C4×D414yes—
443C22×D4—31no—
444C23×C4—31no—
445C23×C4—31no—
446C23×C4—91no—
447C23×C4D3211yescharacteristic
448C4×D4—98no—
449#117—184no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—64no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—91no—
458C2×C22⋊C4—31no—
459C2×C22⋊C4—31no—
460C2×C22⋊C4—31no—
461C2×C22⋊C4—91no—
462C2×C22⋊C4—91no—
463C2×C22⋊C4—91no—
464C2×C22⋊C4—91no—
465C2×C22⋊C4—91no—
466C2×C42—91no—
467C2×C42—91no—
468C2×C42—91no—
469C2×C42—91no—
470C2×C42—91no—
471#95—31no—
472#95—31no—
473#95—91no—
474#95—91no—
475#95—91no—
476#95—91no—
477#95—91no—
478#95—91no—
479#95—91no—
480#95—91no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—22no—
493C23×C3—32no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3C2×C4×D312yes—
505C23×C3C2×C4×D312yes—
506C23×C3#23712yes—
507C23×C3#23712yes—
508C23×C3#23712yes—
509C23×C3#23912yes—
510C23×C3C23×D311yescharacteristic
511C23×C3C23×D311yescharacteristic
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3C2×C4×D312yes—
519C3×D4—68no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—22no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—44no—
543C2×C3×C4—44no—
544C2×C3×C4—48no—
545C2×C3×C4—68no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—124no—
562C2×C3×C4D3×D412yes—
563C2×C3×C4C2×#6712yes—
564#67—28no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—28no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—32no—
582C2×Dic3—32no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—44no—
586C2×Dic3—62no—
587C2×Dic3—62no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—68no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—121no—
612C2×Dic3—121no—
613C2×Dic3—121no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—121no—
618C2×Dic3—121no—
619C2×Dic3C2×C4×D312yes—
620C2×Dic3C2×C4×D312yes—
621C2×Dic3C2×C4×D312yes—
622C2×Dic3#23512yes—
623C2×Dic3C2×#6712yes—
624C2×Dic3C2×#6712yes—
625C4×D3—68no—
626C2×C32—24no—
627C2×C32C2×#11711yescharacteristic
628C2×C32C2×C4×D411yescharacteristic
629C2×C32#52011yescharacteristic
630C2×C32#54611yescharacteristic
631C2×C32#54811yescharacteristic
632C2×C32#55211yescharacteristic
633C2×C32#55311yescharacteristic
634C3×D3—42no—
635C24—31no—
636C24C2×D3211yescharacteristic
637C2×D4—34no—
638C2×D4—62no—
639C2×D4—62no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—34no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—41no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—94no—
656C22×C4—91no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—91no—
660C22×C4—121no—
661C22×C4—182no—
662C22×C4—182no—
663C22×C4C2×D3211yescharacteristic
664C22×C4C2×D3211yescharacteristic
665C4⋊C4—34no—
666C4⋊C4—62no—
667C4⋊C4—62no—
668C4⋊C4—62no—
669C4⋊C4—94no—
670C4⋊C4—182no—
671C4⋊C4—182no—
672C22⋊C4—62no—
673C22⋊C4—62no—
674C22⋊C4—94no—
675C22⋊C4—94no—
676C22⋊C4—121no—
677C22⋊C4—182no—
678C22⋊C4—182no—
679C22⋊C4—361no—
680C42—94no—
681C42—182no—
682C42—182no—
683C42—361no—
684C42—361no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—24no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—62no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—121no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3#87714yescomplemented
719C22×C3#89214yescomplemented
720C22×C3C22×C4×D311yescharacteristic
721C22×C3C22×C4×D311yescharacteristic
722C22×C3C2×#23511yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C2×#23711yescharacteristic
725C22×C3C2×#23711yescharacteristic
726C22×C3C2×#23711yescharacteristic
727C22×C3#100411yescharacteristic
728C22×C3#100411yescharacteristic
729C22×C3C2×#23911yescharacteristic
730C22×C3#100711yescharacteristic
731C22×C3D3×#4111yescharacteristic
732C22×C3#101011yescharacteristic
733C22×C3C22×#6711yescharacteristic
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C3×C4—24no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—34no—
745C3×C4—42no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—62no—
749C3×C4—62no—
750C3×C4—62no—
751C3×C4—121no—
752C3×C4—121no—
753C3×C4—121no—
754Dic3—22no—
755Dic3—22no—
756Dic3—22no—
757Dic3—41no—
758Dic3—41no—
759Dic3—41no—
760Dic3—62no—
761Dic3—62no—
762Dic3—62no—
763Dic3—62no—
764Dic3—122no—
765Dic3—122no—
766Dic3—122no—
767Dic3—122no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—121no—
772Dic3C4×#6714yes—
773C32#235211yescharacteristic, complemented, Sylow
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—32no—
779C23—61no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—61no—
785C23#379612yes—
786C23C4×D3212yes—
787C23#380512yes—
788C23C22×D3211yescharacteristic
789D4—68no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—44no—
802C2×C4—68no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—92no—
819C2×C4—92no—
820C2×C4—124no—
821C2×C4—188no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—181no—
828C2×C4—181no—
829C2×C4—181no—
830C2×C4—181no—
831C2×C4—181no—
832C2×C4D3×#6712yes—
833C2×C3—24no—
834C2×C3—24no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—44no—
843C2×C3—122no—
844C2×C3C2×#87711yescharacteristic
845C2×C3C2×#89211yescharacteristic
846C2×C3#550411yescharacteristic
847C2×C3#551311yescharacteristic
848C2×C3#551411yescharacteristic
849C2×C3C4×D3×D411yescharacteristic
850C2×C3#554611yescharacteristic
851C2×C3#559111yescharacteristic
852C2×C3#559811yescharacteristic
853C2×C3#560111yescharacteristic
854C2×C3#565011yescharacteristic
855C2×C3C2×C4×#6711yescharacteristic
856C2×C3#580611yescharacteristic
857C2×C3#581711yescharacteristic
858D3—42no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—62no—
866C22—62no—
867C22—62no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22#6387814yescomplemented
873C22C2×#379611yescharacteristic
874C22#6429711yescharacteristic
875C22C2×C4×D3211yescharacteristic
876C22D3×#23511yescharacteristic
877C22C2×#380511yescharacteristic
878C22C2×D3×#6711yescharacteristic
879C22#6433011yescharacteristic
880C4—22no—
881C4—34no—
882C4—41no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—121no—
887C4—121no—
888C4—121no—
889C4—182no—
890C4—182no—
891C4—361no—
892C4—361no—
893C3—21no—
894C3#7467311yescharacteristic, complemented
895C3#8216111yescharacteristic, complemented
896C2—24no—
897C2—122no—
898C2C2×#6387811yescharacteristic
899C2#1059487411yescharacteristic
900C2#1059490011yescharacteristic
901C2#1059495211yescharacteristic
902C2#1059495311yescharacteristic
903C2C4×D3×#6711yescharacteristic
904C2#1059549411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic3⋊C4C2semidirect
3. C2×#63878C2semidirect
4. C4×#3757C2semidirect
6. #10591716C2semidirect
8. Dic3×#217C2semidirect
9. #10591366C2semidirect
10. #10591334C2semidirect
11. #10591285C2semidirect
12. #10591283C2semidirect
13. #10591254C2semidirect
14. #10591245C2semidirect
15. #10591241C2semidirect
35. Dic3×#67C4semidirect
59. C22×Dic3⋊C4D3semidirect
116. C2×D3×Dic3C2×C4semidirect
127. C3×Dic3⋊C4D4semidirect
130. Dic3⋊Dic3C2×C4semidirect
133. (C2×D3)⋊Dic3C2×C4semidirect
136. Dic32C2×C4semidirect
396. Dic3⋊C4#67semidirect
415. C22×C32#117semidirect
718. C22×C3#877semidirect
719. C22×C3#892semidirect
773. C32#2352semidirect
872. C22#63878semidirect
894. C3#74673semidirect
895. C3#82161semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C2×Dic3×#672
C2×#638782
C4×#37572
C3×#52132
#105917162
#105917102
Dic3×#2172
#105913662
#105913342
#105912852
#105912832
#105912542
#105912452
#105912412
#821613
#746733