Finite Group Databasebeta

← #11805432

Subgroups — #11805432

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#67⋊C4C211yesmaximal, characteristic
2C2×#67⋊Dic3C211yesmaximal, characteristic
3C2×Dic3×#67C211yesmaximal, characteristic
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#10592645C211yesmaximal, characteristic, complemented
7C3×#4942C211yesmaximal, characteristic, complemented
8#10591693C211yesmaximal, characteristic, complemented
9#10591373C211yesmaximal, characteristic, complemented
10#10591366C211yesmaximal, characteristic, complemented
11#10591327C211yesmaximal, characteristic, complemented
12#10591278C211yesmaximal, characteristic, complemented
13#10591244C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#10591234C211yesmaximal, characteristic, complemented
16D4×Dic3⋊C4—31nomaximal
17#74010—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×#67⋊C4—24no—
36#67⋊Dic3—24no—
37Dic3×#67C418yescomplemented
38C2×#3724C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×Dic3⋊Dic3—24no—
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51D3×Dic3⋊C4—24no—
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C2×C3×C4×D4—31no—
59C2×D4×Dic3—31no—
60C2×D4×Dic3—31no—
61C2×C4×#67—31no—
62C22×C4⋊Dic3—31no—
63C22×Dic3⋊C4—31no—
64C22×Dic3⋊C4—31no—
65C2×D3×C4⋊C4—31no—
66C2×#67⋊C4—31no—
67C2×#67⋊C4D311yescharacteristic
68C3×#380—31no—
69#5210—31no—
70#5210—31no—
71#4987—31no—
72#4975—31no—
73#4975—31no—
74Dic3×C4⋊C4—31no—
75#4972—31no—
76#4946—31no—
77#4946—31no—
78#4946—31no—
79#4946—31no—
80#4946—61no—
81#4942—31no—
82#4942D311yescharacteristic, complemented
83C4×Dic3⋊C4—31no—
84#4928—31no—
85#4668—31no—
86#4668—31no—
87#4647—31no—
88#4647—31no—
89C24×C32C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—22no—
94C22×C3⋊Dic3—22no—
95C22×C3⋊Dic3—41no—
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C2×C3×#67C2×C414yes—
101C2×C3×#67D414yes—
102C2×C3×#67Q814yes—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3—22no—
107C22×C3×Dic3—41no—
108C22×C3×Dic3C2×C414yescomplemented
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—41no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124C2×D3×Dic3C2×C414yescomplemented
125C32×C22⋊C4—22no—
126#3757C2×C414yescomplemented
127#3750—22no—
128#3750—41no—
129C3×#217—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×C4×Dic3—22no—
135#3724—22no—
136#3724—41no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3C2×C414yescomplemented
142Dic3⋊Dic3D414yescomplemented
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3C2×C414yescomplemented
145Dic32—22no—
146Dic32C2×C414yescomplemented
147D4×C4⋊C4—91noSylow
148C22×C3×D4—31no—
149C23×C3×C4—31no—
150C23×C3×C4—31no—
151C23×C3×C4—31no—
152C22×#67C2×D311yescharacteristic
153C23×Dic3—31no—
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3—31no—
157C23×Dic3—61no—
158C23×Dic3C2×D311yescharacteristic
159C23×Dic3C2×D311yescharacteristic
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3C2×D311yescharacteristic
163C3×C4×D4—64no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—21no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4C2×D311yescharacteristic
171C2×C3×C22⋊C4C2×D311yescharacteristic
172C2×C3×C42—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—61no—
178C2×#217C2×D311yescharacteristic
179D4×Dic3—38no—
180D4×Dic3—64no—
181C4×#67—38no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊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—64no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—61no—
207C2×Dic3⋊C4—61no—
208C2×Dic3⋊C4—64no—
209C2×Dic3⋊C4—64no—
210C2×Dic3⋊C4C2×D311yescharacteristic
211C2×Dic3⋊C4C2×D311yescharacteristic
212C2×Dic3⋊C4C2×D311yescharacteristic
213C2×C4×Dic3—31no—
214C2×C4×Dic3—31no—
215C2×C4×Dic3—31no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3C2×D311yescharacteristic
218D3×C4⋊C4—64no—
219#67⋊C4—24no—
220#67⋊C4—64no—
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—31no—
230C3⋊#95—31no—
231C3⋊#95—61no—
232C3⋊#95—61no—
233C3⋊#95C2×D311yescharacteristic
234C3⋊#95C2×D311yescharacteristic
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—21no—
239C23×C32C22×C412yes—
240C23×C32C2×D412yes—
241C23×C32C2×Q812yes—
242C23×C32C2411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C22×C412yes—
248C22×C3×D3C2×D412yes—
249C22×C3×D3C2×Q812yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
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—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—44no—
266C2×C3⋊Dic3C22×C412yes—
267C2×C3⋊Dic3C22×C412yes—
268C2×C3⋊Dic3C2×D412yes—
269C3×#67C4⋊C4116yescomplemented
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—28no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—44no—
285C2×C3×Dic3C22×C412yes—
286C2×C3×Dic3C22×C412yes—
287C2×C3×Dic3C22×C412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×Q812yes—
292C2×C3×Dic3#4112yes—
293C3×C4×D3—44no—
294D3×Dic3—28no—
295D3×Dic3—44no—
296C2×C4×D4—31no—
297C2×C4×D4—91no—
298C2×C4×D4—91no—
299C22×C4⋊C4—91no—
300C22×C4⋊C4—91no—
301#389—91no—
302#389—91no—
303#385—91no—
304#385—91no—
305#385—91no—
306#385—91no—
307#384—91no—
308#380—31no—
309#380—91no—
310C4×C4⋊C4—91no—
311C24×C3—21no—
312C24×C3—31no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C2×C3×D4—34no—
317C2×C3×D4—34no—
318C2×C3×D4—34no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
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—31no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—121no—
336C22×C3×C4—121no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67Dic614yes—
342C2×#67C4×D314yes—
343C2×#67#6714yes—
344C22×Dic3—22no—
345C22×Dic3—22no—
346C22×Dic3—22no—
347C22×Dic3—22no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—34no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—41no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3—62no—
368C22×Dic3—62no—
369C22×Dic3—62no—
370C22×Dic3—122no—
371C22×Dic3—122no—
372C22×Dic3—121no—
373C22×Dic3—121no—
374C22×Dic3—121no—
375C22×Dic3—122no—
376C22×Dic3C4×D314yescomplemented
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C2×C4×D3—22no—
385C2×C4×D3—22no—
386C2×C4×D3—34no—
387C2×C4×D3—41no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—121no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4—62no—
395C3×C4⋊C4—62no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—22no—
398C3×C22⋊C4—42no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C42—62no—
402#217—22no—
403#217—34no—
404#217—34no—
405#217—34no—
406#217—64no—
407#217—62no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—62no—
411C4⋊Dic3—34no—
412C4⋊Dic3—34no—
413C4⋊Dic3—62no—
414C4⋊Dic3—62no—
415C4⋊Dic3—62no—
416C4⋊Dic3—62no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—34no—
421Dic3⋊C4—34no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—122no—
431Dic3⋊C4—121no—
432Dic3⋊C4—121no—
433Dic3⋊C4—121no—
434Dic3⋊C4—121no—
435Dic3⋊C4—122no—
436C4×Dic3—22no—
437C4×Dic3—34no—
438C4×Dic3—34no—
439C4×Dic3—62no—
440C4×Dic3—62no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32C2×C4⋊C414yescomplemented
448C22×C32C23×C411yescharacteristic
449C22×C32C22×D411yescharacteristic
450C22×C32C22×D411yescharacteristic
451C22×C32C22×Q811yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C22×C32H(5,𝔽2)11yescharacteristic
454C22×C322−1+411yescharacteristic
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3C2×C4⋊C414yescomplemented
462C32×C4—41no—
463C32×C4—41no—
464C3⋊Dic3—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—41no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3C2×C4⋊C414yescomplemented
474C3×Dic3C4×D414yescomplemented
475C22×D4—31no—
476C23×C4—31no—
477C23×C4—31no—
478C23×C4—31no—
479C23×C4—91no—
480C23×C4—91no—
481C23×C4—91no—
482C4×D4—64no—
483C4×D4—98no—
484C4×D4—184no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—184no—
499C2×C4⋊C4—184no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4D3211yescharacteristic
506C2×C42—31no—
507C2×C42—91no—
508C2×C42—91no—
509#95—31no—
510#95—31no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95—91no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—32no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3C2×Dic612yes—
539C23×C3C2×C4×D312yes—
540C23×C3C2×C4×D312yes—
541C23×C3D3×D412yes—
542C23×C3D3×Q812yes—
543C23×C3C2×#6712yes—
544C23×C3C23×D311yescharacteristic
545C23×C3C23×D311yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3C2×Dic612yes—
551C22×D3C2×C4×D312yes—
552C22×D3C2×#6712yes—
553C3×D4—316no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—68no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—124no—
595C2×C3×C4—124no—
596#67Dic3⋊C4116yescomplemented
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—28no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—44no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
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—68no—
634C2×Dic3—62no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—124no—
650C2×Dic3—124no—
651C2×Dic3—124no—
652C2×Dic3—128no—
653C2×Dic3C2×Dic612yes—
654C2×Dic3C2×C4×D312yes—
655C2×Dic3C2×C4×D312yes—
656C2×Dic3C2×C4×D312yes—
657C2×Dic3D3×D412yes—
658C2×Dic3D3×D412yes—
659C2×Dic3#23712yes—
660C2×Dic3C2×#6712yes—
661C4×D3—44no—
662C4×D3—68no—
663C4×D3—124no—
664C2×C32—24no—
665C2×C32C22×C4⋊C411yescharacteristic
666C2×C32C2×C4×D411yescharacteristic
667C2×C32#52011yescharacteristic
668C2×C32D4211yescharacteristic
669C2×C32#54711yescharacteristic
670C2×C32D4×Q811yescharacteristic
671C2×C32#55411yescharacteristic
672C3×D3—24no—
673C24—31no—
674C24C2×D3211yescharacteristic
675C2×D4—34no—
676C2×D4—34no—
677C2×D4—34no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—34no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—94no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—121no—
698C22×C4—121no—
699C22×C4—182no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4—361no—
706C22×C4—361no—
707C22×C4C2×D3211yescharacteristic
708C22×C4C2×D3211yescharacteristic
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—94no—
713C4⋊C4—94no—
714C4⋊C4—182no—
715C4⋊C4—182no—
716C4⋊C4—182no—
717C4⋊C4—182no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—361no—
721C4⋊C4—361no—
722C22⋊C4—22no—
723C22⋊C4—62no—
724C22⋊C4—62no—
725C22⋊C4—94no—
726C22⋊C4—94no—
727C22⋊C4—182no—
728C42—62no—
729C42—94no—
730C42—182no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—24no—
751C22×C3—34no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3D3×C4⋊C414yescomplemented
765C22×C3C2×Dic3⋊C414yescomplemented
766C22×C3C22×Dic611yescharacteristic
767C22×C3C22×C4×D311yescharacteristic
768C22×C3C22×C4×D311yescharacteristic
769C22×C3C2×D3×D411yescharacteristic
770C22×C3C2×D3×D411yescharacteristic
771C22×C3C2×D3×D411yescharacteristic
772C22×C3C2×#23711yescharacteristic
773C22×C3#100411yescharacteristic
774C22×C3C2×D3×Q811yescharacteristic
775C22×C3D3×#4111yescharacteristic
776C22×C3#100911yescharacteristic
777C22×C3#101011yescharacteristic
778C22×C3#101011yescharacteristic
779C22×C3C22×#6711yescharacteristic
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3C2×Dic3⋊C414yescomplemented
787C3×C4—34no—
788C3×C4—34no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—62no—
794C3×C4—62no—
795C3×C4—81no—
796C3×C4—81no—
797C3×C4—121no—
798C3×C4—121no—
799C3×C4—121no—
800Dic3—22no—
801Dic3—22no—
802Dic3—41no—
803Dic3—41no—
804Dic3—41no—
805Dic3—62no—
806Dic3—62no—
807Dic3—62no—
808Dic3—62no—
809Dic3—62no—
810Dic3—62no—
811Dic3—122no—
812Dic3—122no—
813Dic3—122no—
814Dic3—122no—
815Dic3—121no—
816Dic3—121no—
817Dic3#67⋊C414yescomplemented
818Dic3C2×Dic3⋊C414yescomplemented
819C32D4×C4⋊C411yescharacteristic, complemented, Sylow
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—32no—
825C23—32no—
826C23—32no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23D3×Dic612yes—
832C23C4×D3212yes—
833C23D3×#6712yes—
834C23C22×D3211yescharacteristic
835D4—316no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—32no—
843C2×C4—32no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—32no—
847C2×C4—32no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—68no—
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—92no—
865C2×C4—92no—
866C2×C4—92no—
867C2×C4—124no—
868C2×C4—124no—
869C2×C4—188no—
870C2×C4—181no—
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—364no—
880C2×C4—364no—
881C2×C3—24no—
882C2×C3—24no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—44no—
891C2×C3—64no—
892C2×C3C2×#67⋊C411yescharacteristic
893C2×C3C2×D3×C4⋊C411yescharacteristic
894C2×C3#552311yescharacteristic
895C2×C3D4×Dic611yescharacteristic
896C2×C3#553911yescharacteristic
897C2×C3C4×D3×D411yescharacteristic
898C2×C3#554611yescharacteristic
899C2×C3#560911yescharacteristic
900C2×C3#561111yescharacteristic
901C2×C3#563211yescharacteristic
902C2×C3#563511yescharacteristic
903C2×C3C22×Dic3⋊C411yescharacteristic
904C2×C3D4×#6711yescharacteristic
905C2×C3#582411yescharacteristic
906D3—24no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—34no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22D3×Dic3⋊C414yescomplemented
921C22C2×D3×Dic611yescharacteristic
922C22C2×C4×D3211yescharacteristic
923C22#6430911yescharacteristic
924C22D32×D411yescharacteristic
925C22D3×#23711yescharacteristic
926C22#6431411yescharacteristic
927C22C2×D3×#6711yescharacteristic
928C4—34no—
929C4—34no—
930C4—41no—
931C4—41no—
932C4—62no—
933C4—62no—
934C4—121no—
935C4—121no—
936C4—121no—
937C4—182no—
938C4—182no—
939C4—182no—
940C4—361no—
941C3—21no—
942C3#7401011yescharacteristic, complemented
943C3D4×Dic3⋊C411yescharacteristic, complemented
944C2—24no—
945C2—64no—
946C2#1059404911yescharacteristic
947C2#1059407111yescharacteristic
948C2#1059413311yescharacteristic
949C2D3×#67⋊C411yescharacteristic
950C2C2×D3×Dic3⋊C411yescharacteristic
951C2#1059515111yescharacteristic
952C2#1059529111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22×Dic3⋊Dic3C2semidirect
5. C2×D3×Dic3⋊C4C2semidirect
6. #10592645C2semidirect
7. C3×#4942C2semidirect
8. #10591693C2semidirect
9. #10591373C2semidirect
10. #10591366C2semidirect
11. #10591327C2semidirect
12. #10591278C2semidirect
13. #10591244C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
15. #10591234C2semidirect
37. Dic3×#67C4semidirect
82. #4942D3semidirect
108. C22×C3×Dic3C2×C4semidirect
124. C2×D3×Dic3C2×C4semidirect
126. #3757C2×C4semidirect
141. Dic3⋊Dic3C2×C4semidirect
142. Dic3⋊Dic3D4semidirect
144. (C2×D3)⋊Dic3C2×C4semidirect
146. Dic32C2×C4semidirect
269. C3×#67C4⋊C4semidirect
376. C22×Dic3C4×D3semidirect
447. C22×C32C2×C4⋊C4semidirect
461. C2×C3×D3C2×C4⋊C4semidirect
473. C3×Dic3C2×C4⋊C4semidirect
474. C3×Dic3C4×D4semidirect
596. #67Dic3⋊C4semidirect
764. C22×C3D3×C4⋊C4semidirect
765. C22×C3C2×Dic3⋊C4semidirect
786. C2×D3C2×Dic3⋊C4semidirect
817. Dic3#67⋊C4semidirect
818. Dic3C2×Dic3⋊C4semidirect
819. C32D4×C4⋊C4semidirect
920. C22D3×Dic3⋊C4semidirect
942. C3#74010semidirect
943. C3D4×Dic3⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#67⋊C42
C2×#67⋊Dic32
C2×Dic3×#672
C22×Dic3⋊Dic32
C2×D3×Dic3⋊C42
#105926452
C3×#49422
#105916932
#105913732
#105913662
#105913272
#105912782
#105912442
Dic3×Dic3⋊C42
#105912342
D4×Dic3⋊C43
#740103