Finite Group Databasebeta

← #13175909

Subgroups — #13175909

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×C3⋊D3×#67C211yesmaximal, characteristic
2#11723922C211yesmaximal, characteristic, complemented
3C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#67⋊C4C211yesmaximal, characteristic, complemented
5#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6#11723618C211yesmaximal, characteristic, complemented
7C2×#88803C211yesmaximal, characteristic, complemented
8#11723539C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10#11723512C211yesmaximal, characteristic, complemented
11C4×#6292C211yesmaximal, characteristic, complemented
12#11723507C211yesmaximal, characteristic, complemented
13C4×#6290C211yesmaximal, characteristic, complemented
14#11723466C211yesmaximal, characteristic, complemented
15#11723464C211yesmaximal, characteristic, complemented
16#10596016—31nomaximal
17#10594254—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28C3⋊D3×#67C418yescomplemented
29C2×#6292C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6289C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2211yescharacteristic
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34C33×C22⋊C4C2211yescharacteristic, complemented
35#88859C2211yescharacteristic, complemented
36#88857C2211yescharacteristic, complemented
37C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C3×#3757C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53Dic3×C3⋊Dic3C2211yescharacteristic, complemented
54C2×D4×C3⋊D3—31no—
55C2×D3×#67—34no—
56C32×C4×D4—31no—
57D4×C3⋊Dic3—31no—
58C4×#638—31no—
59C4×#638—31no—
60C2×#3752—31no—
61C2×#3752—31no—
62#64102—31no—
63#64101—31no—
64#64090—31no—
65#64090—31no—
66#64090—34no—
67#64090—64no—
68C22⋊C4×C3⋊D3—31no—
69C22⋊C4×C3⋊D3D311yescharacteristic, complemented
70C4×C4⋊(C3⋊D3)—31no—
71#64081—31no—
72C3×#67⋊C4D314yescomplemented
73C3×D3×C22⋊C4—34no—
74#67⋊Dic3—34no—
75C2×(C2×D3)⋊Dic3—34no—
76#63952—34no—
77#63921—34no—
78D3×(C2×D3)⋊C4—34no—
79#63904—34no—
80C4×#626—34no—
81C4×#625—34no—
82#63879—34no—
83#63878—34no—
84#63877—34no—
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3—41no—
88C22×C3×C3⋊D3—41no—
89C22×C3×C3⋊D3C2×C414yescomplemented
90C22×C3×C3⋊D3C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C32×D3C2311yescharacteristic
93C2×D3×C3⋊D3—41no—
94C2×D3×C3⋊D3—41no—
95C2×D3×C3⋊D3C2×C414yescomplemented
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98#6312C2×C414yescomplemented
99C2×C3⋊(C3⋊Dic3)—41no—
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C4×C3⋊(C3⋊D3)—41no—
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C3×C4×C3⋊D3—41no—
107C3×C4×C3⋊D3—41no—
108C32×#67C2×C414yescomplemented
109C2×C32×Dic3—41no—
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C32×C4×D3—41no—
114#6292C2×C414yescomplemented
115#6290C2×C414yescomplemented
116#6289—41no—
117Dic3×C3⋊D3C2×C414yescomplemented
118D3×C3⋊Dic3—41no—
119#5545—94no—
120#5486—91no—
121C23×C3⋊D3—31no—
122C23×C3⋊D3C2×D311yescharacteristic
123C23×C3×D3—34no—
124C22×D32—34no—
125C2×C32×D4—31no—
126C22×C32×C4—31no—
127C22×C32×C4—31no—
128C2×#638—31no—
129C2×#638—34no—
130C2×#638—31no—
131C2×#638—64no—
132C22×C3⋊Dic3—31no—
133C22×C3⋊Dic3—34no—
134C22×C3⋊Dic3—31no—
135C22×C3⋊Dic3—64no—
136D4×C3⋊D3—38no—
137C2×C4⋊(C3⋊D3)—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—34no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—64no—
143C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
144C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
145C2×C3×#67C2×D314yes—
146C22×C3×Dic3C2×D314yescomplemented
147C2×C3×C4×D3—34no—
148C2×C3×C4×D3—34no—
149C2×C3×C4×D3C2×D314yescomplemented
150D3×#67—332no—
151C2×#626—34no—
152C2×#625—34no—
153C2×#624—34no—
154C2×D3×Dic3—34no—
155C2×D3×Dic3—34no—
156C32×C4⋊C4—31no—
157C32×C22⋊C4—24no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4C2×D314yescomplemented
160C32×C22⋊C4C2×D311yescharacteristic, complemented
161C32×C42—31no—
162#3757—31no—
163#3757C2×D311yescharacteristic, complemented
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—34no—
170#3752—31no—
171#3752—64no—
172#3752C2×D311yescharacteristic
173#3752C2×D311yescharacteristic
174C4⋊(C3⋊Dic3)—31no—
175#3750—31no—
176#3750—34no—
177#3750—31no—
178#3750—64no—
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3—34no—
181C4×C3⋊Dic3—31no—
182C4×C3⋊Dic3—31no—
183C4×C3⋊Dic3—64no—
184C3×#217—34no—
185C3×(C2×D3)⋊C4—34no—
186C3×(C2×D3)⋊C4—34no—
187C3×(C2×D3)⋊C4C2×D314yescomplemented
188C3×Dic3⋊C4C2×D314yescomplemented
189C3×C4×Dic3C2×D314yescomplemented
190#3724—34no—
191Dic3⋊Dic3—34no—
192#3722—34no—
193(C2×D3)⋊Dic3—34no—
194(C2×D3)⋊Dic3—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⋊D3—21no—
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—44no—
212C2×C3×C3⋊D3C22×C412yes—
213C2×C3×C3⋊D3C22×C412yes—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
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—
225C32×Dic3—21no—
226C32×Dic3—21no—
227C32×Dic3C22×C412yes—
228C22×#67—91no—
229C2×D3×D4—94no—
230C3×C4×D4—34no—
231C2×C3×C22⋊C4—91no—
232C2×#217—91no—
233D4×Dic3—94no—
234C4×#67—94no—
235C4×#67—94no—
236C4×#67—91no—
237C4×#67—91no—
238C4×#67—91no—
239C4×#67—91no—
240C2×(C2×D3)⋊C4—94no—
241C2×(C2×D3)⋊C4—94no—
242#893—94no—
243#892—94no—
244#67⋊C4—94no—
245#67⋊C4—91no—
246#67⋊C4—91no—
247#67⋊C4—94no—
248#67⋊C4—91no—
249#67⋊C4—184no—
250#67⋊C4C3⋊D311yescharacteristic, complemented
251D3×C22⋊C4—34no—
252D3×C22⋊C4—94no—
253D3×C22⋊C4—91no—
254D3×C22⋊C4—91no—
255#877—91no—
256#877—91no—
257C4×D12—94no—
258#872—94no—
259C23×C32—24no—
260C23×C32—31no—
261C23×C32C22×D314yes—
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3⋊D3—34no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—41no—
267C22×C3⋊D3—41no—
268C22×C3⋊D3—64no—
269C22×C3⋊D3—121no—
270C22×C3⋊D3—121no—
271C22×C3⋊D3C4×D314yescomplemented
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3⋊D3C22×D311yescharacteristic
274C22×C3×D3—34no—
275C22×C3×D3—34no—
276C22×C3×D3—316no—
277C22×C3×D3—124no—
278C22×C3×D3—124no—
279C22×C3×D3C22×D314yes—
280C2×D32—316no—
281C2×D32—124no—
282C2×D32—124no—
283C32×D4—34no—
284C2×C32×C4—24no—
285C2×C32×C4—24no—
286C2×C32×C4—31no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—121no—
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—316no—
298#638—616no—
299C2×C3⋊Dic3—31no—
300C2×C3⋊Dic3—31no—
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—34no—
303C2×C3⋊Dic3—34no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—64no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—121no—
309C2×C3⋊Dic3—121no—
310C2×C3⋊Dic3—124no—
311C2×C3⋊Dic3—128no—
312C2×C3⋊Dic3C22×D311yescharacteristic
313C2×C3⋊Dic3C22×D311yescharacteristic
314C4⋊(C3⋊D3)—34no—
315C4×C3⋊D3—34no—
316C4×C3⋊D3—41no—
317C4×C3⋊D3—41no—
318C4×C3⋊D3—121no—
319C4×C3⋊D3—121no—
320C4×C3⋊D3—124no—
321C4×C3⋊D3—128no—
322C3×#67C4×D3116yescomplemented
323C2×C3×Dic3—34no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—44no—
326C2×C3×Dic3C22×D314yes—
327C2×C3×Dic3C22×D314yes—
328C2×C3×Dic3C22×D314yes—
329C3×C4×D3—44no—
330C3×C4×D3—124no—
331C3×C4×D3—124no—
332#626—316no—
333#625—316no—
334#624—124no—
335D3×Dic3—316no—
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—
344C3×C3⋊D3—22no—
345C32×D3—22no—
346C24×C3—91no—
347C23×D3—34no—
348C23×D3—94no—
349C23×D3—91no—
350C2×C3×D4—34no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—91no—
354C22×C3×C4—91no—
355C2×#67—94no—
356C2×#67—94no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—98no—
360C2×#67—91no—
361C2×#67—184no—
362C2×#67C2×C3⋊D311yescharacteristic
363C22×Dic3—94no—
364C22×Dic3—91no—
365C22×Dic3—94no—
366C22×Dic3—91no—
367C22×Dic3—184no—
368C22×Dic3C2×C3⋊D311yescharacteristic, complemented
369D3×D4—932no—
370C2×D12—94no—
371C2×C4×D3—34no—
372C2×C4×D3—34no—
373C2×C4×D3—94no—
374C2×C4×D3—94no—
375C2×C4×D3—91no—
376C2×C4×D3—94no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—184no—
380C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
381C3×C4⋊C4—34no—
382C3×C22⋊C4—24no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387C3×C22⋊C4D3214yescomplemented
388C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
389C3×C42—34no—
390#217—34no—
391#217—94no—
392#217—91no—
393#217—91no—
394#217—91no—
395#217—91no—
396(C2×D3)⋊C4—34no—
397(C2×D3)⋊C4—34no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—94no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—94no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—184no—
408(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
409C4⋊Dic3—94no—
410Dic3⋊C4—94no—
411Dic3⋊C4—94no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—184no—
416Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
417C4×Dic3—94no—
418C4×Dic3—94no—
419C4×Dic3—94no—
420C4×Dic3—91no—
421C4×Dic3—91no—
422C4×Dic3—91no—
423C4×Dic3—184no—
424C4×Dic3C2×C3⋊D311yescharacteristic, complemented
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—24no—
428C22×C32—28no—
429C22×C32—24no—
430C22×C32—24no—
431C22×C32—32no—
432C22×C32—44no—
433C22×C32—44no—
434C22×C32—61no—
435C22×C32—61no—
436C22×C32C2×C4×D318yes—
437C22×C32C2×C4×D312yes—
438C22×C32C23×D314yes—
439C22×C32C23×D311yescharacteristic
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C2×C3⋊D3—21no—
444C2×C3⋊D3—32no—
445C2×C3⋊D3—38no—
446C2×C3⋊D3—44no—
447C2×C3⋊D3—68no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—64no—
451C2×C3⋊D3—64no—
452C2×C3⋊D3—124no—
453C2×C3⋊D3—124no—
454C2×C3⋊D3—124no—
455C2×C3⋊D3C2×C4×D312yes—
456C2×C3⋊D3C2×C4×D312yes—
457C2×C3×D3—24no—
458C2×C3×D3—24no—
459C2×C3×D3—38no—
460C2×C3×D3—38no—
461C2×C3×D3—64no—
462C2×C3×D3—64no—
463C2×C3×D3—64no—
464C2×C3×D3—64no—
465C2×C3×D3—1216no—
466C2×C3×D3C2×C4×D318yes—
467D32—1216no—
468C32×C4—21no—
469C32×C4—21no—
470C32×C4—24no—
471C32×C4—24no—
472C32×C4—32no—
473C32×C4—44no—
474C32×C4—44no—
475C32×C4—61no—
476C32×C4—61no—
477C3⋊Dic3—21no—
478C3⋊Dic3—21no—
479C3⋊Dic3—32no—
480C3⋊Dic3—38no—
481C3⋊Dic3—68no—
482C3⋊Dic3—68no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3⋊Dic3—64no—
486C3⋊Dic3—64no—
487C3⋊Dic3—124no—
488C3×Dic3—24no—
489C3×Dic3—24no—
490C3×Dic3—64no—
491C3×Dic3—64no—
492C3×Dic3C2×C4×D318yes—
493C22×D4—271no—
494C4×D4—31no—
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—91no—
505C2×C22⋊C4—271no—
506C2×C22⋊C4—271no—
507C2×C22⋊C4—271no—
508C33#51811yescharacteristic, complemented, Sylow
509C23×C3—24no—
510C23×C3—34no—
511C23×C3—91no—
512C23×C3—91no—
513C23×C3—94no—
514C23×C3—361no—
515C23×C3—361no—
516C23×C3C2×D3214yes—
517C23×C3C22×C3⋊D311yescharacteristic
518C22×D3—34no—
519C22×D3—34no—
520C22×D3—316no—
521C22×D3—916no—
522C22×D3—94no—
523C22×D3—91no—
524C22×D3—94no—
525C22×D3—124no—
526C22×D3—124no—
527C22×D3—184no—
528C22×D3—361no—
529C22×D3—361no—
530C22×D3—364no—
531C22×D3—364no—
532C22×D3C22×C3⋊D311yescharacteristic
533C3×D4—316no—
534C2×C3×C4—24no—
535C2×C3×C4—24no—
536C2×C3×C4—34no—
537C2×C3×C4—34no—
538C2×C3×C4—34no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—124no—
542C2×C3×C4—124no—
543C2×C3×C4—361no—
544C2×C3×C4—361no—
545C2×C3×C4C2×D3214yes—
546C2×C3×C4C2×D3214yes—
547C2×C3×C4C22×C3⋊D311yescharacteristic
548C2×C3×C4C22×C3⋊D311yescharacteristic
549#67—916no—
550#67—916no—
551#67—94no—
552#67—94no—
553#67—94no—
554#67—1816no—
555#67C4×C3⋊D314yescomplemented
556C2×Dic3—34no—
557C2×Dic3—34no—
558C2×Dic3—41no—
559C2×Dic3—94no—
560C2×Dic3—91no—
561C2×Dic3—94no—
562C2×Dic3—94no—
563C2×Dic3—94no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—184no—
567C2×Dic3—184no—
568C2×Dic3—184no—
569C2×Dic3—364no—
570C2×Dic3—364no—
571C2×Dic3—361no—
572C2×Dic3—368no—
573C2×Dic3C22×C3⋊D311yescharacteristic
574C2×Dic3C22×C3⋊D311yescharacteristic
575C2×Dic3C22×C3⋊D311yescharacteristic
576D12—916no—
577C4×D3—41no—
578C4×D3—916no—
579C4×D3—124no—
580C4×D3—124no—
581C4×D3—361no—
582C4×D3—364no—
583C4×D3—364no—
584C4×D3—361no—
585C4×D3—368no—
586C4×D3—361no—
587C2×C32—22no—
588C2×C32—24no—
589C2×C32—24no—
590C2×C32—24no—
591C2×C32—28no—
592C2×C32—48no—
593C2×C32—62no—
594C2×C32C22×C4×D314yes—
595C2×C32C22×C4×D311yescharacteristic
596C2×C32#100414yes—
597C2×C32#100411yescharacteristic
598C2×C32#100411yescharacteristic
599C2×C32#100914yes—
600C3⋊D3—22no—
601C3⋊D3—22no—
602C3⋊D3—62no—
603C3⋊D3—68no—
604C3⋊D3—128no—
605C3×D3—28no—
606C3×D3—68no—
607C3×D3—68no—
608C24—91no—
609C24—271no—
610C2×D4—31no—
611C2×D4—271no—
612C2×D4—278no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C4⋊C4—31no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C22⋊C4—31no—
629C22⋊C4—91no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4D3×C3⋊D311yescharacteristic, complemented
640C42—31no—
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—44no—
652C22×C3—44no—
653C22×C3—64no—
654C22×C3—64no—
655C22×C3—92no—
656C22×C3—92no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3—181no—
661C22×C3—364no—
662C22×C3C4×D3218yes—
663C22×C3C2×C4×C3⋊D312yes—
664C22×C3C22×D3214yes—
665C22×C3C23×C3⋊D311yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—38no—
669C2×D3—38no—
670C2×D3—64no—
671C2×D3—64no—
672C2×D3—64no—
673C2×D3—64no—
674C2×D3—98no—
675C2×D3—92no—
676C2×D3—1216no—
677C2×D3—188no—
678C2×D3—184no—
679C2×D3—184no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—364no—
683C2×D3—364no—
684C2×D3—364no—
685C2×D3—3616no—
686C2×D3C2×C4×C3⋊D312yes—
687C3×C4—24no—
688C3×C4—24no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—38no—
692C3×C4—44no—
693C3×C4—44no—
694C3×C4—64no—
695C3×C4—64no—
696C3×C4—181no—
697C3×C4—181no—
698Dic3—21no—
699Dic3—21no—
700Dic3—64no—
701Dic3—64no—
702Dic3—98no—
703Dic3—92no—
704Dic3—188no—
705Dic3—188no—
706Dic3—184no—
707Dic3—184no—
708Dic3—181no—
709Dic3—181no—
710Dic3—364no—
711Dic3C2×C4×C3⋊D312yes—
712C32—24no—
713C32#548611yescharacteristic, complemented
714C32#554514yescomplemented
715C23—31no—
716C23—91no—
717C23—91no—
718C23—94no—
719C23—274no—
720C23—271no—
721C23—361no—
722C23—361no—
723C23—1081no—
724C23—1081no—
725C23C2×D3×C3⋊D311yescharacteristic
726D4—34no—
727D4—274no—
728D4—274no—
729D4—274no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—274no—
738C2×C4—271no—
739C2×C4—271no—
740C2×C4—271no—
741C2×C4—361no—
742C2×C4—361no—
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—182no—
757C2×C3—182no—
758C2×C3C2×C4×D3214yes—
759C2×C3#6431314yes—
760C2×C3#6431414yes—
761C2×C3C22×C4×C3⋊D311yescharacteristic
762C2×C3#6436111yescharacteristic
763C2×C3#6436611yescharacteristic
764D3—22no—
765D3—68no—
766D3—68no—
767D3—182no—
768D3—188no—
769D3—368no—
770C22—21no—
771C22—21no—
772C22—32no—
773C22—61no—
774C22—61no—
775C22—92no—
776C22—92no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—272no—
782C22—364no—
783C22—541no—
784C22—541no—
785C22—1084no—
786C22C4×D3×C3⋊D312yes—
787C22C22×D3×C3⋊D311yescharacteristic
788C4—21no—
789C4—21no—
790C4—32no—
791C4—61no—
792C4—61no—
793C4—181no—
794C4—181no—
795C4—272no—
796C4—541no—
797C4—541no—
798C3—24no—
799C3#1059425414yescomplemented
800C3#1059601611yescharacteristic, complemented
801C2—22no—
802C2—62no—
803C2—182no—
804C2—182no—
805C2—542no—
806C2C2×C4×D3×C3⋊D311yescharacteristic
807C2#1172458711yescharacteristic
808C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC33×C22⋊C4C22
socle, cosocleC22×C33C24
prime radicalC2×C3⋊D3×#67C2
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. #11723922C2semidirect
3. C3×C22⋊C4×C3⋊D3C2semidirect
4. C32×#67⋊C4C2semidirect
5. #67⋊(C3⋊Dic3)C2semidirect
6. #11723618C2semidirect
7. C2×#88803C2semidirect
8. #11723539C2semidirect
9. D3×#3752C2semidirect
10. #11723512C2semidirect
11. C4×#6292C2semidirect
12. #11723507C2semidirect
13. C4×#6290C2semidirect
14. #11723466C2semidirect
15. #11723464C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×C32×C4×D3C22semidirect
28. C3⋊D3×#67C4semidirect
31. C2×#6289C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
34. C33×C22⋊C4C22semidirect
35. #88859C22semidirect
36. #88857C22semidirect
37. C4×C3⋊(C3⋊Dic3)C22semidirect
38. C3×#3757C22semidirect
41. C32×(C2×D3)⋊C4C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
44. #88806C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. #88804C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
53. Dic3×C3⋊Dic3C22semidirect
69. C22⋊C4×C3⋊D3D3semidirect
72. C3×#67⋊C4D3semidirect
89. C22×C3×C3⋊D3C2×C4semidirect
95. C2×D3×C3⋊D3C2×C4semidirect
98. #6312C2×C4semidirect
108. C32×#67C2×C4semidirect
114. #6292C2×C4semidirect
115. #6290C2×C4semidirect
117. Dic3×C3⋊D3C2×C4semidirect
143. C2×C4×C3⋊D3C2×D3semidirect
144. C2×C4×C3⋊D3C2×D3semidirect
146. C22×C3×Dic3C2×D3semidirect
149. C2×C3×C4×D3C2×D3semidirect
159. C32×C22⋊C4C2×D3semidirect
160. C32×C22⋊C4C2×D3semidirect
163. #3757C2×D3semidirect
187. C3×(C2×D3)⋊C4C2×D3semidirect
188. C3×Dic3⋊C4C2×D3semidirect
189. C3×C4×Dic3C2×D3semidirect
250. #67⋊C4C3⋊D3semidirect
271. C22×C3⋊D3C4×D3semidirect
322. C3×#67C4×D3semidirect
368. C22×Dic3C2×C3⋊D3semidirect
380. C2×C4×D3C2×C3⋊D3semidirect
387. C3×C22⋊C4D32semidirect
388. C3×C22⋊C4C2×C3⋊D3semidirect
408. (C2×D3)⋊C4C2×C3⋊D3semidirect
416. Dic3⋊C4C2×C3⋊D3semidirect
424. C4×Dic3C2×C3⋊D3semidirect
508. C33#518semidirect
555. #67C4×C3⋊D3semidirect
639. C22⋊C4D3×C3⋊D3semidirect
713. C32#5486semidirect
714. C32#5545semidirect
799. C3#10594254semidirect
800. C3#10596016semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
#117239222
C3×C22⋊C4×C3⋊D32
C32×#67⋊C42
#67⋊(C3⋊Dic3)2
#117236182
C2×#888032
#117235392
D3×#37522
#117235122
C4×#62922
#117235072
C4×#62902
#117234662
#117234642
#105960163
#105942543