Finite Group Databasebeta

← #13177294

Subgroups — #13177294

Order 1728.

2404 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic
2C4×#6312C211yesmaximal, characteristic, complemented
3C3×C4×#638C211yesmaximal, characteristic, complemented
4C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#11723618C211yesmaximal, characteristic, complemented
6Dic3×#638C211yesmaximal, characteristic, complemented
7D3×#3757C211yesmaximal, characteristic, complemented
8#11723539C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723508C211yesmaximal, characteristic, complemented
11#11723507C211yesmaximal, characteristic, complemented
12#11723462C211yesmaximal, characteristic, complemented
13#11723461C211yesmaximal, characteristic, complemented
14#11723460C211yesmaximal, characteristic, complemented
15#11723459C211yesmaximal, characteristic, complemented
16#10595957—31nomaximal
17#10595056—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26D3×#638C418yescomplemented
27C2×#6291C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34#88864C2211yescharacteristic, complemented
35#88859C2211yescharacteristic, complemented
36#88857C2211yescharacteristic, complemented
37C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C3×#3757C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46#88807C2211yescharacteristic, complemented
47#88806C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53Dic3×C3⋊Dic3C2211yescharacteristic, complemented
54C22×#638—31no—
55C2×D3×#67—34no—
56C2×C32×C22⋊C4—31no—
57C2×#3757—31no—
58C4×#638—31no—
59C4×#638—31no—
60C4×#638—31no—
61C4×#638—34no—
62C4×#638—64no—
63C4×#638D311yescharacteristic, complemented
64#64090—31no—
65#64090—31no—
66#64090—31no—
67#64090—31no—
68C22⋊C4×C3⋊D3—31no—
69C22⋊C4×C3⋊D3—31no—
70#64086—31no—
71#64086—31no—
72C3×C4×#67—34no—
73C2×C3×(C2×D3)⋊C4D314yescomplemented
74Dic3×#67—34no—
75D3×#217—34no—
76#63952—34no—
77#63921—34no—
78D3×(C2×D3)⋊C4—34no—
79#63902—34no—
80#63881—34no—
81#63880—34no—
82#63879—34no—
83#63878—34no—
84#63877—34no—
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3—41no—
89C22×C32×D3—41no—
90C22×C32×D3C2×C414yescomplemented
91C22×C32×D3C2311yescharacteristic
92C22×C32×D3C2311yescharacteristic
93C2×D3×C3⋊D3—41no—
94C2×D3×C3⋊D3—41no—
95C2×D3×C3⋊D3C2×C414yescomplemented
96C2×C33×C4—41no—
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99#6312C2×C414yescomplemented
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C4×C3⋊(C3⋊D3)—41no—
104C3×#638C2×C414yescomplemented
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C3×C4×C3⋊D3—41no—
109C2×C32×Dic3—41no—
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112#6291C2×C414yescomplemented
113#6290C2×C414yescomplemented
114#6289—41no—
115Dic3×C3⋊D3—41no—
116D3×C3⋊Dic3—41no—
117D3×C3⋊Dic3—41no—
118D3×C3⋊Dic3C2×C414yescomplemented
119#5545—91no—
120#5486—94no—
121C24×C32—31no—
122C23×C3⋊D3—31no—
123C23×C3×D3C2×D314yes—
124C22×D32—34no—
125C22×C32×C4—24no—
126C22×C32×C4—31no—
127C22×C32×C4C2×D314yescomplemented
128C22×C32×C4C2×D311yescharacteristic, complemented
129C2×#638—31no—
130C2×#638—34no—
131C2×#638—31no—
132C2×#638—38no—
133C2×#638—31no—
134C2×#638—64no—
135C2×#638C2×D311yescharacteristic
136C22×C3⋊Dic3—31no—
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—34no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3—64no—
144C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
145C2×C3×#67—34no—
146C22×C3×Dic3C2×D314yescomplemented
147C2×C3×C4×D3—34no—
148D3×#67—332no—
149C2×#626—34no—
150C2×#625—34no—
151C2×#624—34no—
152C2×D3×Dic3—34no—
153C2×D3×Dic3—34no—
154C2×D3×Dic3—34no—
155C2×D3×Dic3—34no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160#3757—31no—
161#3757—34no—
162#3757—31no—
163#3757—31no—
164#3757—64no—
165#3757C2×D311yescharacteristic, complemented
166#3752—31no—
167#3752—31no—
168#3752—34no—
169#3752—31no—
170#3752—64no—
171#3752C2×D311yescharacteristic, complemented
172#3750—31no—
173#3750—34no—
174#3750—31no—
175#3750—31no—
176#3750—64no—
177#3750C2×D311yescharacteristic, complemented
178C4×C3⋊Dic3—31no—
179C4×C3⋊Dic3—34no—
180C4×C3⋊Dic3—31no—
181C4×C3⋊Dic3—31no—
182C4×C3⋊Dic3—64no—
183C4×C3⋊Dic3C2×D311yescharacteristic, complemented
184C3×#217—34no—
185C3×(C2×D3)⋊C4—34no—
186C3×(C2×D3)⋊C4C2×D314yes—
187C3×(C2×D3)⋊C4C2×D314yes—
188C3×(C2×D3)⋊C4C2×D314yescomplemented
189C3×(C2×D3)⋊C4C2×D314yescomplemented
190C3×Dic3⋊C4—34no—
191C3×C4×Dic3—34no—
192#3724—34no—
193Dic3⋊Dic3—34no—
194#3722—34no—
195(C2×D3)⋊Dic3—34no—
196(C2×D3)⋊Dic3—34no—
197(C2×D3)⋊Dic3—34no—
198Dic32—34no—
199Dic32—34no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33C22×C412yes—
203C22×C33C2411yescharacteristic
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)C22×C412yes—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3C22×C412yes—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—44no—
215C2×C32×D3C22×C412yes—
216C2×C32×D3C22×C412yes—
217D3×C3⋊D3—44no—
218C33×C4—21no—
219C33×C4—21no—
220C3⋊(C3⋊Dic3)—21no—
221C3⋊(C3⋊Dic3)—21no—
222C3⋊(C3⋊Dic3)C22×C412yes—
223C3×C3⋊Dic3—21no—
224C3×C3⋊Dic3—21no—
225C3×C3⋊Dic3C22×C412yes—
226C32×Dic3—21no—
227C32×Dic3—21no—
228C22×#67—94no—
229C2×D3×D4—91no—
230C3×C4×D4—91no—
231C2×C3×C22⋊C4—34no—
232C2×#217—94no—
233D4×Dic3—91no—
234C4×#67—34no—
235C4×#67—94no—
236C4×#67—94no—
237C4×#67—94no—
238C4×#67—91no—
239C4×#67—91no—
240C4×#67—184no—
241C2×(C2×D3)⋊C4—91no—
242C2×(C2×D3)⋊C4C3⋊D311yescharacteristic, complemented
243#893—91no—
244#892—91no—
245#67⋊C4—94no—
246#67⋊C4—94no—
247#67⋊C4—94no—
248#67⋊C4—94no—
249#67⋊C4—91no—
250#67⋊C4—91no—
251D3×C22⋊C4—94no—
252D3×C22⋊C4—94no—
253D3×C22⋊C4—91no—
254D3×C22⋊C4—91no—
255#877—94no—
256#877—94no—
257C4×D12—91no—
258#872—91no—
259C23×C32—24no—
260C23×C32—31no—
261C23×C32—31no—
262C23×C32—34no—
263C23×C32—121no—
264C23×C32—121no—
265C23×C32C22×D314yes—
266C23×C32C22×D311yescharacteristic
267C22×C3⋊D3—31no—
268C22×C3⋊D3—34no—
269C22×C3⋊D3—34no—
270C22×C3⋊D3—64no—
271C22×C3⋊D3—121no—
272C22×C3⋊D3—121no—
273C22×C3⋊D3C22×D311yescharacteristic
274C22×C3×D3—34no—
275C22×C3×D3—44no—
276C22×C3×D3—44no—
277C22×C3×D3C4×D3116yescomplemented
278C22×C3×D3C22×D314yes—
279C22×C3×D3C22×D314yes—
280C2×D32—316no—
281C2×D32—124no—
282C2×D32—124no—
283C2×C32×C4—24no—
284C2×C32×C4—24no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4—41no—
288C2×C32×C4—44no—
289C2×C32×C4—48no—
290C2×C32×C4—121no—
291C2×C32×C4C22×D314yes—
292C2×C32×C4C22×D314yes—
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295#638—34no—
296#638—34no—
297#638—34no—
298#638—316no—
299#638—616no—
300#638C4×D314yescomplemented
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—34no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—31no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—34no—
307C2×C3⋊Dic3—34no—
308C2×C3⋊Dic3—64no—
309C2×C3⋊Dic3—64no—
310C2×C3⋊Dic3—64no—
311C2×C3⋊Dic3—121no—
312C2×C3⋊Dic3—121no—
313C2×C3⋊Dic3C22×D311yescharacteristic
314C2×C3⋊Dic3C22×D311yescharacteristic
315C2×C3⋊Dic3C22×D311yescharacteristic
316C4×C3⋊D3—41no—
317C4×C3⋊D3—121no—
318C4×C3⋊D3—121no—
319C4×C3⋊D3—124no—
320C4×C3⋊D3—121no—
321C4×C3⋊D3—128no—
322C3×#67—316no—
323C2×C3×Dic3—34no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—44no—
327C2×C3×Dic3C22×D314yes—
328C2×C3×Dic3C22×D314yes—
329C3×C4×D3—124no—
330#626—316no—
331#625—316no—
332#624—124no—
333D3×Dic3—316no—
334D3×Dic3—124no—
335D3×Dic3—124no—
336D3×Dic3—124no—
337#518—271noSylow
338C2×C33—22no—
339C2×C33C23×C411yescharacteristic
340C2×C33H(5,𝔽2)11yescharacteristic
341C2×C33H(5,𝔽2)11yescharacteristic
342C3⋊(C3⋊D3)—22no—
343C3×C3⋊D3—22no—
344C32×D3—22no—
345C32×D3—22no—
346C24×C3—34no—
347C23×D3—94no—
348C23×D3—91no—
349C23×D3C2×C3⋊D311yescharacteristic
350C2×C3×D4—91no—
351C22×C3×C4—24no—
352C22×C3×C4—34no—
353C22×C3×C4—91no—
354C22×C3×C4D3214yescomplemented
355C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
356C2×#67—34no—
357C2×#67—94no—
358C2×#67—932no—
359C2×#67—94no—
360C2×#67—94no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—184no—
364C22×Dic3—94no—
365C22×Dic3—94no—
366C22×Dic3—94no—
367C22×Dic3—91no—
368C22×Dic3C2×C3⋊D311yescharacteristic, complemented
369D3×D4—98no—
370C2×D12—91no—
371C2×C4×D3—34no—
372C2×C4×D3—91no—
373C2×C4×D3—94no—
374C2×C4×D3—94no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—94no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—184no—
381C3×C4⋊C4—91no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—34no—
385C3×C22⋊C4—34no—
386C3×C22⋊C4—91no—
387C3×C22⋊C4—91no—
388C3×C42—91no—
389#217—34no—
390#217—94no—
391#217—94no—
392#217—94no—
393#217—91no—
394#217—91no—
395#217—184no—
396(C2×D3)⋊C4—34no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—184no—
405(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
406(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
407(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
408(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
409C4⋊Dic3—91no—
410Dic3⋊C4—34no—
411Dic3⋊C4—94no—
412Dic3⋊C4—94no—
413Dic3⋊C4—94no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—184no—
417C4×Dic3—34no—
418C4×Dic3—94no—
419C4×Dic3—94no—
420C4×Dic3—94no—
421C4×Dic3—91no—
422C4×Dic3—91no—
423C4×Dic3—91no—
424C4×Dic3—184no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—24no—
428C22×C32—28no—
429C22×C32—24no—
430C22×C32—24no—
431C22×C32—32no—
432C22×C32—32no—
433C22×C32—44no—
434C22×C32—44no—
435C22×C32—61no—
436C22×C32—61no—
437C22×C32—61no—
438C22×C32—61no—
439C22×C32—124no—
440C22×C32C2×C4×D318yes—
441C22×C32C2×C4×D312yes—
442C22×C32C23×D314yes—
443C22×C32C23×D311yescharacteristic
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3—32no—
447C2×C3⋊D3—38no—
448C2×C3⋊D3—68no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—64no—
452C2×C3⋊D3—64no—
453C2×C3⋊D3—124no—
454C2×C3⋊D3—124no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3C2×C4×D312yes—
457C2×C3×D3—24no—
458C2×C3×D3—24no—
459C2×C3×D3—24no—
460C2×C3×D3—24no—
461C2×C3×D3—38no—
462C2×C3×D3—416no—
463C2×C3×D3—64no—
464C2×C3×D3—64no—
465C2×C3×D3C2×C4×D318yes—
466C2×C3×D3C2×C4×D318yes—
467D32—1216no—
468C32×C4—28no—
469C32×C4—21no—
470C32×C4—24no—
471C32×C4—21no—
472C32×C4—24no—
473C32×C4—44no—
474C32×C4—61no—
475C32×C4—61no—
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3⋊Dic3—32no—
479C3⋊Dic3—38no—
480C3⋊Dic3—68no—
481C3⋊Dic3—61no—
482C3⋊Dic3—61no—
483C3⋊Dic3—64no—
484C3⋊Dic3—64no—
485C3⋊Dic3—124no—
486C3⋊Dic3—124no—
487C3⋊Dic3C2×C4×D312yes—
488C3×Dic3—24no—
489C3×Dic3—24no—
490C3×Dic3—38no—
491C3×Dic3—64no—
492C3×Dic3—64no—
493C22×D4—271no—
494C4×D4—91no—
495C4×D4—271no—
496C4×D4—271no—
497C4×D4—271no—
498C4×D4—271no—
499C4×D4—271no—
500C4×D4—271no—
501C4×D4—271no—
502#117—271no—
503#117—271no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—271no—
506C2×C22⋊C4—271no—
507C2×C22⋊C4—271no—
508C33#51811yescharacteristic, complemented, Sylow
509C23×C3—24no—
510C23×C3—34no—
511C23×C3—34no—
512C23×C3—316no—
513C23×C3—91no—
514C23×C3—124no—
515C23×C3—124no—
516C23×C3C2×D3214yes—
517C23×C3C22×C3⋊D311yescharacteristic
518C22×D3—34no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—916no—
522C22×D3—94no—
523C22×D3—91no—
524C22×D3—94no—
525C22×D3—184no—
526C22×D3—361no—
527C22×D3—361no—
528C22×D3—364no—
529C22×D3—364no—
530C22×D3C4×C3⋊D314yescomplemented
531C22×D3C22×C3⋊D311yescharacteristic
532C22×D3C22×C3⋊D311yescharacteristic
533C3×D4—94no—
534C2×C3×C4—24no—
535C2×C3×C4—24no—
536C2×C3×C4—34no—
537C2×C3×C4—34no—
538C2×C3×C4—44no—
539C2×C3×C4—41no—
540C2×C3×C4—48no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—124no—
545C2×C3×C4—361no—
546C2×C3×C4C2×D3214yes—
547C2×C3×C4C2×D3214yes—
548C2×C3×C4C22×C3⋊D311yescharacteristic
549C2×C3×C4C22×C3⋊D311yescharacteristic
550#67—316no—
551#67—916no—
552#67—916no—
553#67—916no—
554#67—94no—
555#67—94no—
556#67—1816no—
557C2×Dic3—34no—
558C2×Dic3—34no—
559C2×Dic3—34no—
560C2×Dic3—41no—
561C2×Dic3—916no—
562C2×Dic3—94no—
563C2×Dic3—91no—
564C2×Dic3—94no—
565C2×Dic3—94no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—184no—
569C2×Dic3—184no—
570C2×Dic3—184no—
571C2×Dic3—361no—
572C2×Dic3—364no—
573C2×Dic3—364no—
574C2×Dic3C22×C3⋊D311yescharacteristic
575C2×Dic3C22×C3⋊D311yescharacteristic
576D12—94no—
577C4×D3—94no—
578C4×D3—124no—
579C4×D3—361no—
580C4×D3—364no—
581C4×D3—364no—
582C4×D3—361no—
583C4×D3—364no—
584C4×D3—361no—
585C4×D3—361no—
586C4×D3—368no—
587C2×C32—22no—
588C2×C32—24no—
589C2×C32—24no—
590C2×C32—24no—
591C2×C32—28no—
592C2×C32—48no—
593C2×C32—62no—
594C2×C32—62no—
595C2×C32C22×C4×D314yes—
596C2×C32C22×C4×D311yescharacteristic
597C2×C32#100414yes—
598C2×C32#100414yes—
599C2×C32#100411yescharacteristic
600C2×C32#100911yescharacteristic
601C3⋊D3—22no—
602C3⋊D3—62no—
603C3⋊D3—68no—
604C3⋊D3—128no—
605C3×D3—28no—
606C3×D3—28no—
607C3×D3—68no—
608C24—31no—
609C24—271no—
610C2×D4—91no—
611C2×D4—271no—
612C2×D4—278no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—31no—
616C22×C4—91no—
617C22×C4—271no—
618C22×C4—271no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4D3×C3⋊D311yescharacteristic, complemented
624C4⋊C4—91no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—31no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C42—91no—
641C42—271no—
642C42—271no—
643C42—271no—
644C22×C3—24no—
645C22×C3—24no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—24no—
649C22×C3—28no—
650C22×C3—38no—
651C22×C3—38no—
652C22×C3—44no—
653C22×C3—44no—
654C22×C3—64no—
655C22×C3—64no—
656C22×C3—64no—
657C22×C3—64no—
658C22×C3—92no—
659C22×C3—1216no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3C4×D3218yes—
663C22×C3C2×C4×C3⋊D312yes—
664C22×C3C22×D3214yes—
665C22×C3C23×C3⋊D311yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—38no—
671C2×D3—44no—
672C2×D3—64no—
673C2×D3—64no—
674C2×D3—98no—
675C2×D3—92no—
676C2×D3—188no—
677C2×D3—184no—
678C2×D3—184no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—364no—
682C2×D3—364no—
683C2×D3—364no—
684C2×D3—3616no—
685C2×D3C2×C4×C3⋊D312yes—
686C2×D3C2×C4×C3⋊D312yes—
687C3×C4—28no—
688C3×C4—24no—
689C3×C4—24no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—44no—
693C3×C4—64no—
694C3×C4—64no—
695C3×C4—92no—
696C3×C4—181no—
697C3×C4—181no—
698Dic3—21no—
699Dic3—21no—
700Dic3—38no—
701Dic3—64no—
702Dic3—64no—
703Dic3—98no—
704Dic3—92no—
705Dic3—188no—
706Dic3—184no—
707Dic3—184no—
708Dic3—181no—
709Dic3—181no—
710Dic3—364no—
711Dic3—364no—
712C32—24no—
713C32#548614yescomplemented
714C32#554511yescharacteristic, complemented
715C23—31no—
716C23—31no—
717C23—34no—
718C23—91no—
719C23—121no—
720C23—121no—
721C23—274no—
722C23—271no—
723C23—1081no—
724C23—1081no—
725C23C2×D3×C3⋊D311yescharacteristic
726D4—94no—
727D4—274no—
728D4—274no—
729D4—274no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—41no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—121no—
737C2×C4—274no—
738C2×C4—271no—
739C2×C4—271no—
740C2×C4—271no—
741C2×C4—361no—
742C2×C4—1081no—
743C2×C4—1081no—
744C2×C4—1081no—
745C2×C4—1081no—
746C2×C4—1081no—
747C2×C4C2×D3×C3⋊D311yescharacteristic
748C2×C4C2×D3×C3⋊D311yescharacteristic
749C2×C3—22no—
750C2×C3—28no—
751C2×C3—24no—
752C2×C3—24no—
753C2×C3—24no—
754C2×C3—48no—
755C2×C3—68no—
756C2×C3—68no—
757C2×C3—182no—
758C2×C3C2×C4×D3214yes—
759C2×C3#6430714yes—
760C2×C3#6433014yes—
761C2×C3C22×C4×C3⋊D311yescharacteristic
762C2×C3#6436111yescharacteristic
763C2×C3#6436111yescharacteristic
764D3—22no—
765D3—22no—
766D3—68no—
767D3—182no—
768D3—188no—
769D3—368no—
770C22—21no—
771C22—21no—
772C22—32no—
773C22—32no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—92no—
779C22—124no—
780C22—181no—
781C22—181no—
782C22—272no—
783C22—541no—
784C22—541no—
785C22—1084no—
786C22C4×D3×C3⋊D312yes—
787C22C22×D3×C3⋊D311yescharacteristic
788C4—21no—
789C4—21no—
790C4—61no—
791C4—61no—
792C4—92no—
793C4—181no—
794C4—181no—
795C4—272no—
796C4—541no—
797C4—541no—
798C3—24no—
799C3#1059505614yescomplemented
800C3#1059595711yescharacteristic, complemented
801C2—22no—
802C2—62no—
803C2—62no—
804C2—182no—
805C2—542no—
806C2C2×C4×D3×C3⋊D311yescharacteristic
807C2#1172457911yescharacteristic
808C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC22×C33×C4C22
socle, cosocleC22×C33C24
prime radicalC2×D3×#638C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#6312C2semidirect
3. C3×C4×#638C2semidirect
4. C2×C32×(C2×D3)⋊C4C2semidirect
5. #11723618C2semidirect
6. Dic3×#638C2semidirect
7. D3×#3757C2semidirect
8. #11723539C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723508C2semidirect
11. #11723507C2semidirect
12. #11723462C2semidirect
13. #11723461C2semidirect
14. #11723460C2semidirect
15. #11723459C2semidirect
20. C22×C33×C4C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
25. C22×C32×Dic3C22semidirect
26. D3×#638C4semidirect
29. C2×#6289C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
32. C2×D3×C3⋊Dic3C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
34. #88864C22semidirect
35. #88859C22semidirect
36. #88857C22semidirect
37. C4×C3⋊(C3⋊Dic3)C22semidirect
38. C3×#3757C22semidirect
39. C3×#3752C22semidirect
40. C3×#3750C22semidirect
41. C3×C4×C3⋊Dic3C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. #88807C22semidirect
47. #88806C22semidirect
48. #88804C22semidirect
49. #88803C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
53. Dic3×C3⋊Dic3C22semidirect
63. C4×#638D3semidirect
73. C2×C3×(C2×D3)⋊C4D3semidirect
90. C22×C32×D3C2×C4semidirect
95. C2×D3×C3⋊D3C2×C4semidirect
99. #6312C2×C4semidirect
104. C3×#638C2×C4semidirect
112. #6291C2×C4semidirect
113. #6290C2×C4semidirect
118. D3×C3⋊Dic3C2×C4semidirect
127. C22×C32×C4C2×D3semidirect
128. C22×C32×C4C2×D3semidirect
144. C2×C4×C3⋊D3C2×D3semidirect
146. C22×C3×Dic3C2×D3semidirect
165. #3757C2×D3semidirect
171. #3752C2×D3semidirect
177. #3750C2×D3semidirect
183. C4×C3⋊Dic3C2×D3semidirect
188. C3×(C2×D3)⋊C4C2×D3semidirect
189. C3×(C2×D3)⋊C4C2×D3semidirect
242. C2×(C2×D3)⋊C4C3⋊D3semidirect
277. C22×C3×D3C4×D3semidirect
300. #638C4×D3semidirect
354. C22×C3×C4D32semidirect
355. C22×C3×C4C2×C3⋊D3semidirect
368. C22×Dic3C2×C3⋊D3semidirect
407. (C2×D3)⋊C4C2×C3⋊D3semidirect
408. (C2×D3)⋊C4C2×C3⋊D3semidirect
508. C33#518semidirect
530. C22×D3C4×C3⋊D3semidirect
623. C22×C4D3×C3⋊D3semidirect
713. C32#5486semidirect
714. C32#5545semidirect
799. C3#10595056semidirect
800. C3#10595957semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C4×#63122
C3×C4×#6382
C2×C32×(C2×D3)⋊C42
#117236182
Dic3×#6382
D3×#37572
#117235392
C3⋊D3×(C2×D3)⋊C42
#117235082
#117235072
#117234622
#117234612
#117234602
#117234592
#105959573
#105950563