Finite Group Databasebeta

← #13176598

Subgroups — #13176598

Order 1728.

1844 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#64107C211yesmaximal, characteristic, complemented
3C32×#898C211yesmaximal, characteristic, complemented
4#11723539C211yesmaximal, characteristic
5#11723539C211yesmaximal, characteristic
6#11723539C211yesmaximal, characteristic
7#11723503C211yesmaximal, characteristic, complemented
8#11723470C211yesmaximal, characteristic, complemented
9C4×#6289C211yesmaximal, characteristic, complemented
10#11723438C211yesmaximal, characteristic, complemented
11#11723430C211yesmaximal, characteristic, complemented
12#11723428C211yesmaximal, characteristic, complemented
13#11723427C211yesmaximal, characteristic, complemented
14#11723408C211yesmaximal, characteristic, complemented
15#11723407C211yesmaximal, characteristic, complemented
16C3⋊D3×#126—31nomaximal
17#10594656—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×#6289C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic, complemented
26C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
27#88857C2211yescharacteristic, complemented
28#88857C2211yescharacteristic, complemented
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C3×#3750C2211yescharacteristic, complemented
34C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×C4⋊Dic3C2211yescharacteristic, complemented
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×C4×Dic3C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88803C2211yescharacteristic
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#126—31no—
54#64107—31no—
55#64107—31no—
56#64107D311yescharacteristic, complemented
57C4⋊C4×C3⋊D3—31no—
58C4⋊C4×C3⋊D3—31no—
59C4⋊C4×C3⋊D3—31no—
60C4⋊C4×C3⋊D3—34no—
61C4⋊C4×C3⋊D3—64no—
62C22⋊C4×C3⋊D3—31no—
63C22⋊C4×C3⋊D3—31no—
64C22⋊C4×C3⋊D3—31no—
65#64088—31no—
66#64088—31no—
67#64088—31no—
68#64085—31no—
69C42×C3⋊D3—31no—
70C3×#898—34no—
71C3×#898D314yescomplemented
72#63921—34no—
73#63921—34no—
74#63921—34no—
75#63900—34no—
76#63883—34no—
77C4×#624—34no—
78#63861—34no—
79#63861—34no—
80#63859—34no—
81#63859—34no—
82#63858—34no—
83#63858—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C2×D3×C3⋊D3—22no—
88C2×D3×C3⋊D3—22no—
89C2×D3×C3⋊D3—22no—
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C4×C3⋊(C3⋊D3)—22no—
97C4×C3⋊(C3⋊D3)—22no—
98C4×C3⋊(C3⋊D3)—22no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105#6289—22no—
106#6289—22no—
107#6289—22no—
108D3×#126—94no—
109D3×#126—91no—
110C23×C3⋊D3—31no—
111C22×D32—34no—
112C2×C4×C3⋊D3—31no—
113C2×C4×C3⋊D3—31no—
114C2×C4×C3⋊D3—31no—
115C2×C4×C3⋊D3—34no—
116C2×C4×C3⋊D3—34no—
117C2×C4×C3⋊D3—34no—
118C2×C4×C3⋊D3—31no—
119C2×C4×C3⋊D3—31no—
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—64no—
122C2×C4×C3⋊D3—64no—
123C2×C4×C3⋊D3—64no—
124C2×#624—34no—
125C2×#624—34no—
126C2×#624—34no—
127C32×C4⋊C4—24no—
128C32×C4⋊C4—31no—
129C32×C4⋊C4—31no—
130C32×C4⋊C4C2×D314yescomplemented
131C32×C4⋊C4C2×D311yescharacteristic, complemented
132C32×C22⋊C4—31no—
133C32×C22⋊C4—31no—
134C32×C22⋊C4—31no—
135C32×C42—31no—
136#3757—31no—
137#3757—31no—
138#3757—31no—
139#3752—31no—
140#3752—31no—
141#3752—31no—
142#3752C2×D311yescharacteristic
143#3752C2×D311yescharacteristic
144#3752C2×D311yescharacteristic
145C4⋊(C3⋊Dic3)—31no—
146C4⋊(C3⋊Dic3)—34no—
147C4⋊(C3⋊Dic3)—31no—
148C4⋊(C3⋊Dic3)—64no—
149C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
150#3750—31no—
151#3750—31no—
152#3750—34no—
153#3750—34no—
154#3750—31no—
155#3750—31no—
156#3750—31no—
157#3750—64no—
158#3750—64no—
159#3750C2×D311yescharacteristic, complemented
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3C2×D311yescharacteristic, complemented
163C3×(C2×D3)⋊C4—34no—
164C3×(C2×D3)⋊C4—34no—
165C3×(C2×D3)⋊C4—34no—
166C3×(C2×D3)⋊C4C2×D314yes—
167C3×(C2×D3)⋊C4C2×D314yes—
168C3×(C2×D3)⋊C4C2×D314yes—
169C3×C4⋊Dic3—34no—
170C3×C4⋊Dic3C2×D314yescomplemented
171C3×Dic3⋊C4—34no—
172C3×Dic3⋊C4C2×D314yescomplemented
173C3×C4×Dic3—34no—
174C3×C4×Dic3C2×D314yescomplemented
175#3724—34no—
176#3724—34no—
177Dic3⋊Dic3—34no—
178Dic3⋊Dic3—34no—
179(C2×D3)⋊Dic3—34no—
180(C2×D3)⋊Dic3—34no—
181(C2×D3)⋊Dic3—34no—
182(C2×D3)⋊Dic3—34no—
183(C2×D3)⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185Dic32—34no—
186Dic32—34no—
187C22×C33C2411yescharacteristic
188C2×C3⋊(C3⋊D3)#4112yes—
189C2×C3⋊(C3⋊D3)#4112yes—
190C2×C3⋊(C3⋊D3)#4112yes—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—21no—
193C2×C3×C3⋊D3—21no—
194C2×C32×D3—21no—
195C2×C32×D3—21no—
196C2×C32×D3—21no—
197D3×C3⋊D3—44no—
198C33×C4—21no—
199C33×C4—21no—
200C33×C4—21no—
201C3⋊(C3⋊Dic3)—21no—
202C3⋊(C3⋊Dic3)—21no—
203C3⋊(C3⋊Dic3)—21no—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C32×Dic3—21no—
210C3×#126—34no—
211C3×#126—91no—
212#898—34no—
213#898—94no—
214#898—94no—
215#898—91no—
216#898—91no—
217#898C3⋊D311yescharacteristic, complemented
218D3×C4⋊C4—94no—
219D3×C4⋊C4—94no—
220D3×C4⋊C4—94no—
221D3×C4⋊C4—91no—
222D3×C4⋊C4—91no—
223D3×C4⋊C4—91no—
224D3×C4⋊C4—184no—
225D3×C22⋊C4—94no—
226D3×C22⋊C4—94no—
227D3×C22⋊C4—94no—
228D3×C22⋊C4—91no—
229D3×C22⋊C4—91no—
230D3×C22⋊C4—91no—
231#879—94no—
232#879—94no—
233#879—94no—
234#879—91no—
235#879—91no—
236#879—91no—
237#876—94no—
238#876—91no—
239C42×D3—94no—
240C42×D3—91no—
241C23×C32—31no—
242C22×C3⋊D3—31no—
243C22×C3⋊D3—34no—
244C22×C3⋊D3—64no—
245C22×C3⋊D3—62no—
246C22×C3⋊D3—62no—
247C22×C3⋊D3—62no—
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3×D3—34no—
250C22×C3×D3C22×D314yes—
251C2×D32—68no—
252C2×D32—68no—
253C2×D32—68no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4C22×D314yes—
261C2×C32×C4C22×D314yes—
262C2×C32×C4C22×D314yes—
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C3⋊Dic3—31no—
267C2×C3⋊Dic3—31no—
268C2×C3⋊Dic3—31no—
269C2×C3⋊Dic3—34no—
270C2×C3⋊Dic3—34no—
271C2×C3⋊Dic3—34no—
272C2×C3⋊Dic3—64no—
273C2×C3⋊Dic3—64no—
274C2×C3⋊Dic3—64no—
275C2×C3⋊Dic3C22×D311yescharacteristic
276C2×C3⋊Dic3C22×D311yescharacteristic
277C2×C3⋊Dic3C22×D311yescharacteristic
278C4×C3⋊D3—62no—
279C4×C3⋊D3—62no—
280C4×C3⋊D3—62no—
281C4×C3⋊D3—62no—
282C4×C3⋊D3—68no—
283C4×C3⋊D3—62no—
284C4×C3⋊D3—62no—
285C4×C3⋊D3—616no—
286C4×C3⋊D3—68no—
287C4×C3⋊D3—68no—
288C4×C3⋊D3—128no—
289C4×C3⋊D3—128no—
290C2×C3×Dic3—34no—
291C2×C3×Dic3—34no—
292C2×C3×Dic3—34no—
293C2×C3×Dic3C22×D314yes—
294C2×C3×Dic3C22×D314yes—
295C2×C3×Dic3C22×D314yes—
296#624—68no—
297#624—68no—
298#624—68no—
299C2×#126—271noSylow
300C2×C33C2×#4111yescharacteristic
301C2×C33C2×#4111yescharacteristic
302C2×C33C2×#4111yescharacteristic
303C3⋊(C3⋊D3)#12614yescomplemented
304C3×C3⋊D3—41no—
305C32×D3—41no—
306C23×D3—94no—
307C23×D3—91no—
308C2×C4×D3—94no—
309C2×C4×D3—94no—
310C2×C4×D3—94no—
311C2×C4×D3—94no—
312C2×C4×D3—94no—
313C2×C4×D3—94no—
314C2×C4×D3—91no—
315C2×C4×D3—91no—
316C2×C4×D3—91no—
317C2×C4×D3—91no—
318C2×C4×D3—91no—
319C2×C4×D3—91no—
320C2×C4×D3—184no—
321C2×C4×D3—184no—
322C2×C4×D3—184no—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4D3214yescomplemented
329C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
330C3×C22⋊C4—34no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—91no—
334C3×C22⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C42—34no—
337C3×C42—91no—
338#217—94no—
339#217—94no—
340#217—94no—
341#217—91no—
342#217—91no—
343#217—91no—
344(C2×D3)⋊C4—34no—
345(C2×D3)⋊C4—34no—
346(C2×D3)⋊C4—34no—
347(C2×D3)⋊C4—94no—
348(C2×D3)⋊C4—94no—
349(C2×D3)⋊C4—94no—
350(C2×D3)⋊C4—91no—
351(C2×D3)⋊C4—91no—
352(C2×D3)⋊C4—91no—
353(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
354(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
355(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
356C4⋊Dic3—34no—
357C4⋊Dic3—94no—
358C4⋊Dic3—94no—
359C4⋊Dic3—91no—
360C4⋊Dic3—91no—
361C4⋊Dic3—184no—
362C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
363Dic3⋊C4—34no—
364Dic3⋊C4—94no—
365Dic3⋊C4—94no—
366Dic3⋊C4—94no—
367Dic3⋊C4—94no—
368Dic3⋊C4—94no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—184no—
375Dic3⋊C4—184no—
376Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
377C4×Dic3—34no—
378C4×Dic3—94no—
379C4×Dic3—94no—
380C4×Dic3—91no—
381C4×Dic3—91no—
382C4×Dic3C2×C3⋊D311yescharacteristic, complemented
383C22×C32—24no—
384C22×C32—61no—
385C22×C32—61no—
386C22×C32—61no—
387C22×C32C23×D314yes—
388C22×C32C23×D311yescharacteristic
389C2×C3⋊D3—21no—
390C2×C3⋊D3—21no—
391C2×C3⋊D3—21no—
392C2×C3⋊D3—32no—
393C2×C3⋊D3—32no—
394C2×C3⋊D3—32no—
395C2×C3⋊D3—38no—
396C2×C3⋊D3—38no—
397C2×C3⋊D3—38no—
398C2×C3⋊D3—68no—
399C2×C3⋊D3—68no—
400C2×C3⋊D3—68no—
401C2×C3⋊D3—124no—
402C2×C3×D3—24no—
403C2×C3×D3—24no—
404C2×C3×D3—24no—
405C2×C3×D3—64no—
406C2×C3×D3—64no—
407C2×C3×D3—64no—
408D32—1216no—
409C32×C4—28no—
410C32×C4—24no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—24no—
415C32×C4—24no—
416C32×C4—44no—
417C32×C4—44no—
418C32×C4—61no—
419C32×C4—61no—
420C32×C4—61no—
421C3⋊Dic3—21no—
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—68no—
425C3⋊Dic3—64no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3⋊Dic3—64no—
430C3⋊Dic3—64no—
431C3⋊Dic3—124no—
432C3⋊Dic3—124no—
433C3×Dic3—24no—
434C3×Dic3—24no—
435C3×Dic3—24no—
436C3×Dic3—64no—
437C3×Dic3—64no—
438C3×Dic3—64no—
439#126—31no—
440#126—91no—
441#126—271no—
442#126—271no—
443#126—271no—
444#126—271no—
445#126—271no—
446#126—271no—
447C2×C4⋊C4—271no—
448C2×C4⋊C4—271no—
449C2×C4⋊C4—271no—
450C2×C22⋊C4—271no—
451C2×C22⋊C4—271no—
452C2×C22⋊C4—271no—
453C2×C42—271no—
454C33C2×#12611yescharacteristic, complemented, Sylow
455C23×C3—34no—
456C23×C3—91no—
457C22×D3—34no—
458C22×D3—94no—
459C22×D3—91no—
460C22×D3—184no—
461C22×D3—182no—
462C22×D3—182no—
463C22×D3—182no—
464C22×D3—188no—
465C22×D3—188no—
466C22×D3—188no—
467C22×D3C22×C3⋊D311yescharacteristic
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—34no—
472C2×C3×C4—34no—
473C2×C3×C4—34no—
474C2×C3×C4—91no—
475C2×C3×C4—91no—
476C2×C3×C4—91no—
477C2×C3×C4C2×D3214yes—
478C2×C3×C4C2×D3214yes—
479C2×C3×C4C2×D3214yes—
480C2×C3×C4C22×C3⋊D311yescharacteristic
481C2×C3×C4C22×C3⋊D311yescharacteristic
482C2×C3×C4C22×C3⋊D311yescharacteristic
483C2×Dic3—34no—
484C2×Dic3—34no—
485C2×Dic3—34no—
486C2×Dic3—94no—
487C2×Dic3—94no—
488C2×Dic3—94no—
489C2×Dic3—91no—
490C2×Dic3—91no—
491C2×Dic3—91no—
492C2×Dic3—184no—
493C2×Dic3—184no—
494C2×Dic3—184no—
495C2×Dic3C22×C3⋊D311yescharacteristic
496C2×Dic3C22×C3⋊D311yescharacteristic
497C2×Dic3C22×C3⋊D311yescharacteristic
498C4×D3—182no—
499C4×D3—182no—
500C4×D3—182no—
501C4×D3—188no—
502C4×D3—188no—
503C4×D3—188no—
504C4×D3—188no—
505C4×D3—182no—
506C4×D3—182no—
507C4×D3—182no—
508C4×D3—188no—
509C4×D3—188no—
510C4×D3—1816no—
511C4×D3—368no—
512C4×D3—368no—
513C2×C32—24no—
514C2×C32—24no—
515C2×C32—24no—
516C2×C32—121no—
517C2×C32D3×#4114yes—
518C2×C32D3×#4114yes—
519C2×C32D3×#4114yes—
520C2×C32D3×#4111yescharacteristic
521C2×C32D3×#4111yescharacteristic
522C2×C32D3×#4111yescharacteristic
523C3⋊D3—34no—
524C3⋊D3—316no—
525C3⋊D3—41no—
526C3⋊D3—616no—
527C3×D3—44no—
528C3×D3—124no—
529C24—271no—
530C22×C4—271no—
531C22×C4—271no—
532C22×C4—271no—
533C22×C4—271no—
534C22×C4—271no—
535C22×C4—271no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4—271no—
541C4⋊C4—271no—
542C4⋊C4—271no—
543C4⋊C4—271no—
544C4⋊C4—271no—
545C4⋊C4—271no—
546C4⋊C4—271no—
547C4⋊C4D3×C3⋊D311yescharacteristic, complemented
548C22⋊C4—31no—
549C22⋊C4—31no—
550C22⋊C4—31no—
551C22⋊C4—91no—
552C22⋊C4—91no—
553C22⋊C4—91no—
554C22⋊C4—271no—
555C22⋊C4—271no—
556C22⋊C4—271no—
557C22⋊C4—271no—
558C22⋊C4—271no—
559C22⋊C4—271no—
560C42—31no—
561C42—91no—
562C42—271no—
563C42—271no—
564C22×C3—24no—
565C22×C3—64no—
566C22×C3—64no—
567C22×C3—64no—
568C22×C3—181no—
569C22×C3—181no—
570C22×C3—181no—
571C22×C3C22×D3214yes—
572C22×C3C23×C3⋊D311yescharacteristic
573C2×D3—21no—
574C2×D3—21no—
575C2×D3—21no—
576C2×D3—64no—
577C2×D3—64no—
578C2×D3—64no—
579C2×D3—98no—
580C2×D3—98no—
581C2×D3—98no—
582C2×D3—92no—
583C2×D3—92no—
584C2×D3—92no—
585C2×D3—188no—
586C2×D3—188no—
587C2×D3—188no—
588C2×D3—364no—
589C2×D3—3616no—
590C3×C4—28no—
591C3×C4—24no—
592C3×C4—24no—
593C3×C4—24no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—44no—
598C3×C4—44no—
599C3×C4—64no—
600C3×C4—64no—
601C3×C4—64no—
602C3×C4—181no—
603C3×C4—181no—
604C3×C4—181no—
605Dic3—21no—
606Dic3—21no—
607Dic3—21no—
608Dic3—64no—
609Dic3—64no—
610Dic3—64no—
611Dic3—188no—
612Dic3—184no—
613Dic3—184no—
614Dic3—184no—
615Dic3—181no—
616Dic3—181no—
617Dic3—181no—
618Dic3—364no—
619Dic3—364no—
620C32—24no—
621C32D3×#12614yescomplemented
622C32D3×#12611yescharacteristic, complemented
623C23—31no—
624C23—91no—
625C23—271no—
626C23—542no—
627C23—542no—
628C23—542no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—91no—
633C2×C4—91no—
634C2×C4—91no—
635C2×C4—271no—
636C2×C4—271no—
637C2×C4—271no—
638C2×C4—542no—
639C2×C4—542no—
640C2×C4—542no—
641C2×C4—542no—
642C2×C4—542no—
643C2×C4—542no—
644C2×C4C2×D3×C3⋊D311yescharacteristic
645C2×C4C2×D3×C3⋊D311yescharacteristic
646C2×C4C2×D3×C3⋊D311yescharacteristic
647C2×C3—24no—
648C2×C3—24no—
649C2×C3—24no—
650C2×C3—124no—
651C2×C3—361no—
652C2×C3#6430614yes—
653C2×C3#6431214yes—
654C2×C3#6431914yes—
655C2×C3#41×C3⋊D311yescharacteristic
656C2×C3#41×C3⋊D311yescharacteristic
657C2×C3#41×C3⋊D311yescharacteristic
658D3—41no—
659D3—94no—
660D3—916no—
661D3—124no—
662D3—1816no—
663C22—61no—
664C22—61no—
665C22—61no—
666C22—181no—
667C22—181no—
668C22—181no—
669C22—272no—
670C22—272no—
671C22—272no—
672C22—1084no—
673C22C22×D3×C3⋊D311yescharacteristic
674C4—21no—
675C4—21no—
676C4—21no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—181no—
681C4—181no—
682C4—181no—
683C4—541no—
684C4—541no—
685C4—541no—
686C3—24no—
687C3#1059465614yescomplemented
688C3C3⋊D3×#12611yescharacteristic, complemented
689C2—121no—
690C2—274no—
691C2—361no—
692C2#1172457811yescharacteristic
693C2#1172458611yescharacteristic
694C2#1172459611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC22×D3×C3⋊D3C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C2×#126
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C4⋊C4×C3⋊(C3⋊D3)C2semidirect
2. C3×#64107C2semidirect
3. C32×#898C2semidirect
7. #11723503C2semidirect
8. #11723470C2semidirect
9. C4×#6289C2semidirect
10. #11723438C2semidirect
11. #11723430C2semidirect
12. #11723428C2semidirect
13. #11723427C2semidirect
14. #11723408C2semidirect
15. #11723407C2semidirect
25. C33×C4⋊C4C22semidirect
26. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
27. #88857C22semidirect
28. #88857C22semidirect
32. C3×C4⋊(C3⋊Dic3)C22semidirect
33. C3×#3750C22semidirect
34. C3×C4×C3⋊Dic3C22semidirect
38. C32×C4⋊Dic3C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×C4×Dic3C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
56. #64107D3semidirect
71. C3×#898D3semidirect
130. C32×C4⋊C4C2×D3semidirect
131. C32×C4⋊C4C2×D3semidirect
149. C4⋊(C3⋊Dic3)C2×D3semidirect
159. #3750C2×D3semidirect
162. C4×C3⋊Dic3C2×D3semidirect
170. C3×C4⋊Dic3C2×D3semidirect
172. C3×Dic3⋊C4C2×D3semidirect
174. C3×C4×Dic3C2×D3semidirect
217. #898C3⋊D3semidirect
303. C3⋊(C3⋊D3)#126semidirect
328. C3×C4⋊C4D32semidirect
329. C3×C4⋊C4C2×C3⋊D3semidirect
362. C4⋊Dic3C2×C3⋊D3semidirect
376. Dic3⋊C4C2×C3⋊D3semidirect
382. C4×Dic3C2×C3⋊D3semidirect
454. C33C2×#126semidirect
547. C4⋊C4D3×C3⋊D3semidirect
621. C32D3×#126semidirect
622. C32D3×#126semidirect
687. C3#10594656semidirect
688. C3C3⋊D3×#126semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C3⋊(C3⋊D3)2
C3×#641072
C32×#8982
#117235392
#117235032
#117234702
C4×#62892
#117234382
#117234302
#117234282
#117234272
#117234082
#117234072
C3⋊D3×#1263
#105946563