Finite Group Databasebeta

← #11800925

Subgroups — #11800925

Order 1152.

1689 conjugacy classes of subgroups.

The subgroup lattice has 930 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⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6Dic3×#217C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8#10591368C211yesmaximal, characteristic, complemented
9Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10D3×C3⋊#95C211yesmaximal, characteristic, complemented
11C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
12C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
13#10591241C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#10591239C211yesmaximal, characteristic, complemented
16#82317—31nomaximal
17#73436—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×C4×C3⋊Dic3C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×#67⋊C4C418yescomplemented
36#67⋊Dic3C418yescomplemented
37Dic3×#67C418yescomplemented
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×C4×D4—31no—
57C2×D4×Dic3—31no—
58C2×D4×Dic3—31no—
59C2×C4×#67—31no—
60C2×#67⋊C4—31no—
61C2×#67⋊C4D311yescharacteristic
62C3×C4×C22⋊C4—31no—
63C4×#217—31no—
64C4×#217—31no—
65C2×C3⋊#95—31no—
66C2×C3⋊#95—31no—
67C2×C3⋊#95—31no—
68Dic3×C4⋊C4—31no—
69Dic3×C4⋊C4—31no—
70Dic3×C22⋊C4—31no—
71Dic3×C22⋊C4—31no—
72Dic3×C22⋊C4—31no—
73Dic3×C22⋊C4—31no—
74Dic3×C22⋊C4—31no—
75Dic3×C22⋊C4—61no—
76Dic3×C22⋊C4D311yescharacteristic, complemented
77C4×(C2×D3)⋊C4—31no—
78C4×(C2×D3)⋊C4—31no—
79C4×C4⋊Dic3—31no—
80#4932—31no—
81C4×Dic3⋊C4—31no—
82C4×Dic3⋊C4—31no—
83#4666—31no—
84D3×#95—31no—
85#4649—31no—
86#4648—31no—
87C24×C32C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3⋊Dic3—41no—
92C22×C3⋊Dic3—41no—
93C22×C3⋊Dic3C2×C414yescomplemented
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C3×#67C2×C414yes—
99C2×C3×#67C2×C414yes—
100C2×C3×#67C2×C414yes—
101C22×C3×Dic3—41no—
102C22×C3×Dic3—41no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3—41no—
105C22×C3×Dic3C2×C414yescomplemented
106C22×C3×Dic3C2×C414yescomplemented
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×C4×D3—41no—
115C2×C3×C4×D3—41no—
116C2×C3×C4×D3C2×C414yescomplemented
117C2×D3×Dic3—41no—
118C2×D3×Dic3—41no—
119C2×D3×Dic3—41no—
120C2×D3×Dic3—41no—
121C2×D3×Dic3C2×C414yescomplemented
122C2×D3×Dic3C2×C414yescomplemented
123C32×C22⋊C4C2×C414yescomplemented
124#3757C2×C414yescomplemented
125C4×C3⋊Dic3—41no—
126C4×C3⋊Dic3—41no—
127C3×#217C2×C414yescomplemented
128C3×(C2×D3)⋊C4C2×C414yescomplemented
129C3×Dic3⋊C4C2×C414yescomplemented
130C3×C4×Dic3—41no—
131C3×C4×Dic3—41no—
132C3×C4×Dic3C2×C414yescomplemented
133Dic3⋊Dic3C2×C414yescomplemented
134Dic3⋊Dic3C2×C414yescomplemented
135(C2×D3)⋊Dic3C2×C414yescomplemented
136(C2×D3)⋊Dic3C2×C414yescomplemented
137Dic32—41no—
138Dic32—41no—
139Dic32C2×C414yescomplemented
140Dic32C2×C414yescomplemented
141#2275—91noSylow
142C22×C3×D4—31no—
143C23×C3×C4—31no—
144C23×C3×C4—31no—
145C23×C3×C4—31no—
146C22×#67C2×D311yescharacteristic
147C23×Dic3—31no—
148C23×Dic3—31no—
149C23×Dic3—31no—
150C23×Dic3—31no—
151C23×Dic3—61no—
152C23×Dic3C2×D311yescharacteristic
153C23×Dic3C2×D311yescharacteristic
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3C2×D311yescharacteristic
157C3×C4×D4—38no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—21no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4C2×D311yescharacteristic
163C2×C3×C22⋊C4C2×D311yescharacteristic
164C2×C3×C42—31no—
165C2×C3×C42—31no—
166C2×C3×C42—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—61no—
172C2×#217C2×D311yescharacteristic
173D4×Dic3—38no—
174D4×Dic3—38no—
175C4×#67—38no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4C2×D311yescharacteristic
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4C2×D311yescharacteristic
184C2×C4×Dic3—31no—
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—31no—
196C2×C4×Dic3—61no—
197C2×C4×Dic3—61no—
198C2×C4×Dic3C2×D311yescharacteristic
199C2×C4×Dic3C2×D311yescharacteristic
200C2×C4×Dic3C2×D311yescharacteristic
201#67⋊C4—38no—
202#67⋊C4Dic318yescomplemented
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—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—61no—
222C3⋊#95—61no—
223C3⋊#95C2×D311yescharacteristic
224C3⋊#95C2×D311yescharacteristic
225C23×C32—21no—
226C23×C32—21no—
227C23×C32—21no—
228C23×C32—21no—
229C23×C32C22×C412yes—
230C23×C32C22×C412yes—
231C23×C32C22×C412yes—
232C23×C32C2411yescharacteristic
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C22×C412yes—
238C22×C3×D3C22×C412yes—
239C22×C3×D3C22×C412yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C22×C412yes—
245C2×C32×C4C22×C412yes—
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—44no—
255C2×C3⋊Dic3C22×C412yes—
256C2×C3⋊Dic3C22×C412yes—
257C2×C3⋊Dic3C22×C412yes—
258C2×C3⋊Dic3C22×C412yes—
259C3×#67C42116yescomplemented
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—44no—
273C2×C3×Dic3—44no—
274C2×C3×Dic3C22×C412yes—
275C2×C3×Dic3C22×C412yes—
276C2×C3×Dic3C22×C412yes—
277C2×C3×Dic3C22×C412yes—
278C2×C3×Dic3C22×C412yes—
279C2×C3×Dic3C22×C412yes—
280C2×C3×Dic3C22×C412yes—
281C2×C3×Dic3C22×C412yes—
282C2×C3×Dic3C22×C412yes—
283C3×C4×D3—44no—
284D3×Dic3—44no—
285D3×Dic3—44no—
286C2×C4×D4—31no—
287C2×C4×D4—91no—
288C2×C4×D4—91no—
289C4×C4⋊C4—91no—
290C4×C4⋊C4—91no—
291C4×C4⋊C4—91no—
292C4×C22⋊C4—31no—
293C4×C22⋊C4—91no—
294C4×C22⋊C4—91no—
295C4×C22⋊C4—91no—
296C4×C22⋊C4—91no—
297C4×C22⋊C4—91no—
298#376—91no—
299C2×#95—91no—
300C2×#95—91no—
301C24×C3—21no—
302C24×C3—31no—
303C24×C3C22×D311yescharacteristic
304C24×C3C22×D311yescharacteristic
305C23×D3C22×D311yescharacteristic
306C2×C3×D4—34no—
307C2×C3×D4—34no—
308C2×C3×D4—34no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
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—34no—
319C22×C3×C4—34no—
320C22×C3×C4—34no—
321C22×C3×C4—121no—
322C22×C3×C4—121no—
323C22×C3×C4—121no—
324C22×C3×C4—121no—
325C22×C3×C4—121no—
326C22×C3×C4—121no—
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C2×#67C4×D314yes—
332C2×#67C4×D314yes—
333C2×#67C2×Dic314yes—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—34no—
343C22×Dic3—34no—
344C22×Dic3—34no—
345C22×Dic3—34no—
346C22×Dic3—41no—
347C22×Dic3—41no—
348C22×Dic3—41no—
349C22×Dic3—41no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354C22×Dic3—64no—
355C22×Dic3—121no—
356C22×Dic3—121no—
357C22×Dic3—121no—
358C22×Dic3—121no—
359C22×Dic3—121no—
360C22×Dic3—121no—
361C22×Dic3—121no—
362C22×Dic3—121no—
363C22×Dic3—122no—
364C22×Dic3—122no—
365C22×Dic3C4×D314yescomplemented
366C22×Dic3C2×Dic314yescomplemented
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C2×C4×D3—34no—
375C2×C4×D3—34no—
376C2×C4×D3—41no—
377C2×C4×D3—41no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C2×C4×D3C2×Dic314yescomplemented
383C3×C4⋊C4—34no—
384C3×C22⋊C4—24no—
385C3×C22⋊C4—34no—
386C3×C22⋊C4—34no—
387C3×C22⋊C4C4×D314yescomplemented
388C3×C22⋊C4C2×Dic314yescomplemented
389C3×C42—34no—
390C3×C42—121no—
391C3×C42—121no—
392#217—34no—
393#217—34no—
394#217—34no—
395#217—34no—
396#217—64no—
397#217C4×D314yescomplemented
398(C2×D3)⋊C4—34no—
399(C2×D3)⋊C4—34no—
400(C2×D3)⋊C4C2×Dic314yescomplemented
401C4⋊Dic3—34no—
402C4⋊Dic3—34no—
403Dic3⋊C4—34no—
404Dic3⋊C4—34no—
405Dic3⋊C4C2×Dic314yescomplemented
406C4×Dic3—34no—
407C4×Dic3—34no—
408C4×Dic3—34no—
409C4×Dic3—34no—
410C4×Dic3—41no—
411C4×Dic3—41no—
412C4×Dic3—121no—
413C4×Dic3—121no—
414C4×Dic3—121no—
415C4×Dic3—121no—
416C4×Dic3—121no—
417C4×Dic3—121no—
418C4×Dic3—121no—
419C4×Dic3—121no—
420C4×Dic3—122no—
421C4×Dic3—122no—
422C4×Dic3C2×Dic314yescomplemented
423C22×C32—22no—
424C22×C32—22no—
425C22×C32—22no—
426C22×C32—22no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32C2×C4214yes—
430C22×C32C23×C411yescharacteristic
431C22×C32C23×C411yescharacteristic
432C22×C32C23×C411yescharacteristic
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—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3C2×C4214yes—
444C32×C4—22no—
445C32×C4—22no—
446C3⋊Dic3—22no—
447C3⋊Dic3—22no—
448C3⋊Dic3—22no—
449C3⋊Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3C2×C4214yes—
457C22×D4—31no—
458C23×C4—31no—
459C23×C4—31no—
460C23×C4—31no—
461C23×C4—91no—
462C23×C4—91no—
463C23×C4—91no—
464C4×D4—38no—
465C4×D4—98no—
466C4×D4—98no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—91no—
469C2×C4⋊C4—91no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—31no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C22⋊C4D3211yescharacteristic
476C2×C42—31no—
477C2×C42—31no—
478C2×C42—31no—
479C2×C42—91no—
480C2×C42—91no—
481C2×C42—91no—
482C2×C42—91no—
483C2×C42—91no—
484C2×C42—91no—
485#95—31no—
486#95—31no—
487#95—91no—
488#95—91no—
489#95—91no—
490#95—91no—
491#95—91no—
492#95—91no—
493#95—91no—
494#95—91no—
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—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—32no—
508C23×C3—32no—
509C23×C3—32no—
510C23×C3—41no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—61no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3C2×C4×D312yes—
519C23×C3C2×C4×D312yes—
520C23×C3C2×C4×D312yes—
521C23×C3C2×C4×D312yes—
522C23×C3C2×C4×D312yes—
523C23×C3C22×Dic312yes—
524C23×C3C23×D311yescharacteristic
525C23×C3C23×D311yescharacteristic
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3C2×C4×D312yes—
531C22×D3C2×C4×D312yes—
532C22×D3C22×Dic312yes—
533C3×D4—316no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—124no—
570C2×C3×C4—124no—
571C2×C3×C4—124no—
572C2×C3×C4C2×C4×D312yes—
573C2×C3×C4C2×C4×D312yes—
574C2×C3×C4C22×Dic312yes—
575C2×C3×C4C22×Dic312yes—
576#67C4×Dic3116yescomplemented
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—44no—
598C2×Dic3—44no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
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—121no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—121no—
627C2×Dic3—124no—
628C2×Dic3—124no—
629C2×Dic3—124no—
630C2×Dic3—124no—
631C2×Dic3—128no—
632C2×Dic3C2×C4×D312yes—
633C2×Dic3C2×C4×D312yes—
634C2×Dic3C2×C4×D312yes—
635C2×Dic3C2×C4×D312yes—
636C2×Dic3C2×C4×D312yes—
637C2×Dic3C2×C4×D312yes—
638C2×Dic3C22×Dic312yes—
639C2×Dic3C22×Dic312yes—
640C2×Dic3C22×Dic312yes—
641C4×D3—44no—
642C4×D3—124no—
643C4×D3—124no—
644C2×C32—24no—
645C2×C32C22×C4211yescharacteristic
646C2×C32#51811yescharacteristic
647C2×C32#51811yescharacteristic
648C2×C32#51811yescharacteristic
649C2×C32#52011yescharacteristic
650C2×C32#52011yescharacteristic
651C2×C32#52011yescharacteristic
652C3×D3—24no—
653C24—31no—
654C24C2×D3211yescharacteristic
655C2×D4—34no—
656C2×D4—34no—
657C2×D4—34no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—34no—
666C22×C4—34no—
667C22×C4—34no—
668C22×C4—94no—
669C22×C4—94no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—94no—
675C22×C4—121no—
676C22×C4—121no—
677C22×C4—121no—
678C22×C4—121no—
679C22×C4—121no—
680C22×C4—121no—
681C22×C4—361no—
682C22×C4—361no—
683C22×C4—361no—
684C22×C4—361no—
685C22×C4—361no—
686C22×C4—361no—
687C22×C4C2×D3211yescharacteristic
688C22×C4C2×D3211yescharacteristic
689C4⋊C4—34no—
690C4⋊C4—94no—
691C4⋊C4—94no—
692C22⋊C4—34no—
693C22⋊C4—34no—
694C22⋊C4—94no—
695C22⋊C4—94no—
696C22⋊C4—94no—
697C22⋊C4D3×Dic314yescomplemented
698C42—34no—
699C42—94no—
700C42—94no—
701C42—121no—
702C42—121no—
703C42—361no—
704C42—361no—
705C42—361no—
706C42—361no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—24no—
727C22×C3—34no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3C42×D314yes—
741C22×C3C2×C4×Dic314yes—
742C22×C3C22×C4×D311yescharacteristic
743C22×C3C22×C4×D311yescharacteristic
744C22×C3C22×C4×D311yescharacteristic
745C22×C3C22×C4×D311yescharacteristic
746C22×C3C22×C4×D311yescharacteristic
747C22×C3#100411yescharacteristic
748C22×C3#100411yescharacteristic
749C22×C3#100411yescharacteristic
750C22×C3#100411yescharacteristic
751C22×C3#100911yescharacteristic
752C22×C3#100911yescharacteristic
753C22×C3#101011yescharacteristic
754C22×C3#101011yescharacteristic
755C22×C3C23×Dic311yescharacteristic
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—22no—
761C2×D3—22no—
762C2×D3C2×C4×Dic314yes—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—34no—
768C3×C4—42no—
769C3×C4—42no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4—62no—
776Dic3—22no—
777Dic3—22no—
778Dic3—22no—
779Dic3—22no—
780Dic3—22no—
781Dic3—22no—
782Dic3—64no—
783Dic3—62no—
784Dic3—62no—
785Dic3—62no—
786Dic3—62no—
787Dic3—62no—
788Dic3—62no—
789Dic3—62no—
790Dic3—62no—
791Dic3—122no—
792Dic3—122no—
793Dic3—122no—
794Dic3C2×C4×Dic314yes—
795C32#227511yescharacteristic, complemented, Sylow
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—32no—
801C23—32no—
802C23—32no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23C4×D3212yes—
808C23C4×D3212yes—
809C23C2×D3×Dic312yes—
810C23C22×D3211yescharacteristic
811D4—316no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—32no—
817C2×C4—32no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—92no—
838C2×C4—92no—
839C2×C4—92no—
840C2×C4—92no—
841C2×C4—124no—
842C2×C4—124no—
843C2×C4—124no—
844C2×C4—181no—
845C2×C4—181no—
846C2×C4—181no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—364no—
853C2×C4—364no—
854C2×C4—364no—
855C2×C4C2×D3×Dic312yes—
856C2×C4C2×D3×Dic312yes—
857C2×C3—24no—
858C2×C3—24no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—44no—
867C2×C3—64no—
868C2×C3C2×C42×D311yescharacteristic
869C2×C3#548611yescharacteristic
870C2×C3#552311yescharacteristic
871C2×C3#554511yescharacteristic
872C2×C3#554511yescharacteristic
873C2×C3#554511yescharacteristic
874C2×C3#554511yescharacteristic
875C2×C3#554611yescharacteristic
876C2×C3#554611yescharacteristic
877C2×C3#554611yescharacteristic
878C2×C3#554611yescharacteristic
879C2×C3C22×C4×Dic311yescharacteristic
880C2×C3#579811yescharacteristic
881C2×C3#582711yescharacteristic
882D3—24no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—34no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—62no—
894C22—62no—
895C22—62no—
896C22C4×D3×Dic314yes—
897C22C2×C4×D3211yescharacteristic
898C22C2×C4×D3211yescharacteristic
899C22#6430911yescharacteristic
900C22#6431311yescharacteristic
901C22#6431411yescharacteristic
902C22#6431411yescharacteristic
903C22C22×D3×Dic311yescharacteristic
904C4—22no—
905C4—22no—
906C4—34no—
907C4—62no—
908C4—62no—
909C4—62no—
910C4—62no—
911C4—62no—
912C4—62no—
913C4—182no—
914C4—182no—
915C4—182no—
916C4—182no—
917C3—21no—
918C3#7343611yescharacteristic, complemented
919C3#8231711yescharacteristic, complemented
920C2—24no—
921C2—64no—
922C2#1059404911yescharacteristic
923C2#1059405111yescharacteristic
924C2#1059425411yescharacteristic
925C2#1059425611yescharacteristic
926C2C2×C4×D3×Dic311yescharacteristic
927C2#1059521511yescharacteristic
928C2#1059522211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2275
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C22⋊C4×C3⋊Dic3C2semidirect
5. C3×Dic3×C22⋊C4C2semidirect
6. Dic3×#217C2semidirect
7. C2×#63579C2semidirect
8. #10591368C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. D3×C3⋊#95C2semidirect
11. C4×Dic3⋊Dic3C2semidirect
12. C4×(C2×D3)⋊Dic3C2semidirect
13. #10591241C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
15. #10591239C2semidirect
35. C3×#67⋊C4C4semidirect
36. #67⋊Dic3C4semidirect
37. Dic3×#67C4semidirect
76. Dic3×C22⋊C4D3semidirect
93. C22×C3⋊Dic3C2×C4semidirect
105. C22×C3×Dic3C2×C4semidirect
106. C22×C3×Dic3C2×C4semidirect
116. C2×C3×C4×D3C2×C4semidirect
121. C2×D3×Dic3C2×C4semidirect
122. C2×D3×Dic3C2×C4semidirect
123. C32×C22⋊C4C2×C4semidirect
124. #3757C2×C4semidirect
127. C3×#217C2×C4semidirect
128. C3×(C2×D3)⋊C4C2×C4semidirect
129. C3×Dic3⋊C4C2×C4semidirect
132. C3×C4×Dic3C2×C4semidirect
133. Dic3⋊Dic3C2×C4semidirect
134. Dic3⋊Dic3C2×C4semidirect
135. (C2×D3)⋊Dic3C2×C4semidirect
136. (C2×D3)⋊Dic3C2×C4semidirect
139. Dic32C2×C4semidirect
140. Dic32C2×C4semidirect
202. #67⋊C4Dic3semidirect
259. C3×#67C42semidirect
365. C22×Dic3C4×D3semidirect
366. C22×Dic3C2×Dic3semidirect
382. C2×C4×D3C2×Dic3semidirect
387. C3×C22⋊C4C4×D3semidirect
388. C3×C22⋊C4C2×Dic3semidirect
397. #217C4×D3semidirect
400. (C2×D3)⋊C4C2×Dic3semidirect
405. Dic3⋊C4C2×Dic3semidirect
422. C4×Dic3C2×Dic3semidirect
576. #67C4×Dic3semidirect
697. C22⋊C4D3×Dic3semidirect
795. C32#2275semidirect
918. C3#73436semidirect
919. C3#82317semidirect

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⋊C4×C3⋊Dic32
C3×Dic3×C22⋊C42
Dic3×#2172
C2×#635792
#105913682
Dic3×(C2×D3)⋊C42
D3×C3⋊#952
C4×Dic3⋊Dic32
C4×(C2×D3)⋊Dic32
#105912412
Dic3×Dic3⋊C42
#105912392
#823173
#734363