Finite Group Databasebeta

← #13176575

Subgroups — #13176575

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723936C211yesmaximal, characteristic, complemented
2C3×#64105C211yesmaximal, characteristic, complemented
3C32×#898C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723542C211yesmaximal, characteristic, complemented
6C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#11723526C211yesmaximal, characteristic, complemented
8#11723525C211yesmaximal, characteristic, complemented
9#11723521C211yesmaximal, characteristic, complemented
10#11723498C211yesmaximal, characteristic, complemented
11#11723472C211yesmaximal, characteristic, complemented
12#11723471C211yesmaximal, characteristic, complemented
13#11723441C211yesmaximal, characteristic, complemented
14#11723420C211yesmaximal, characteristic, complemented
15#11723411C211yesmaximal, characteristic, complemented
16#10596175—31nomaximal
17#10594652—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C3×#634C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×Dic3×C3⋊D3C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic, complemented
34C3×#3752C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3750C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×C4⋊Dic3C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×C4×Dic3C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#126—31no—
54#64107—31no—
55#64105D311yescharacteristic, complemented
56#64104—31no—
57#64104—31no—
58#64104—34no—
59#64104—64no—
60#64103—31no—
61#64102—31no—
62#64094—31no—
63#64093—31no—
64#64092—31no—
65#64091—31no—
66#64091—31no—
67C22⋊C4×C3⋊D3—31no—
68#64084—31no—
69C4×C4⋊(C3⋊D3)—31no—
70C3×#898D314yescomplemented
71C3×#896—34no—
72#63923—34no—
73#63923—34no—
74D3×(C2×D3)⋊C4—34no—
75#63910—34no—
76#63909—34no—
77#63907—34no—
78#63897—34no—
79#63881—34no—
80#63880—34no—
81#63864—34no—
82#63853—34no—
83#63848—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C2×D3×C3⋊D3—22no—
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C4⋊(C3⋊(C3⋊D3))—41no—
97C4⋊(C3⋊(C3⋊D3))—41no—
98C4⋊(C3⋊(C3⋊D3))—41no—
99C4×C3⋊(C3⋊D3)—41no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4×C3⋊D3—41no—
104C3×#634—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108#6292—22no—
109#6292—22no—
110#6291—41no—
111#6291—41no—
112#6289—41no—
113Dic3×C3⋊D3—41no—
114#5704—94no—
115#5644—91no—
116C23×C3⋊D3—31no—
117C22×D32—34no—
118C2×#638—31no—
119C2×#638—31no—
120C2×C4⋊(C3⋊D3)—31no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4⋊(C3⋊D3)—31no—
123C2×C4⋊(C3⋊D3)—31no—
124C2×C4⋊(C3⋊D3)—31no—
125C2×C4⋊(C3⋊D3)—34no—
126C2×C4⋊(C3⋊D3)—34no—
127C2×C4⋊(C3⋊D3)—34no—
128C2×C4⋊(C3⋊D3)—64no—
129C2×C4⋊(C3⋊D3)—64no—
130C2×C4⋊(C3⋊D3)—64no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—34no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—64no—
136C2×C4×C3⋊D3C2×D311yescharacteristic
137C2×#634C2×D311yescharacteristic, complemented
138C2×C3×C4×D3—34no—
139C2×C3×Dic6—34no—
140C2×#626—34no—
141C2×#626—34no—
142C2×#626—34no—
143C2×#626—34no—
144C2×#624—34no—
145C2×D3×Dic3—34no—
146C32×C4⋊C4—24no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4C2×D314yescomplemented
150C32×C4⋊C4C2×D311yescharacteristic, complemented
151C32×C22⋊C4—31no—
152C32×C22⋊C4—31no—
153C32×C22⋊C4—31no—
154C32×C42—31no—
155#3757—31no—
156#3752—31no—
157#3752—31no—
158#3752—34no—
159#3752—34no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—64no—
167#3752—64no—
168#3752C2×D311yescharacteristic
169#3752C2×D311yescharacteristic
170C4⋊(C3⋊Dic3)—31no—
171#3750C2×D311yescharacteristic, complemented
172#3750C2×D311yescharacteristic, complemented
173C4×C3⋊Dic3—31no—
174C3×(C2×D3)⋊C4—34no—
175C3×(C2×D3)⋊C4—34no—
176C3×(C2×D3)⋊C4C2×D314yes—
177C3×(C2×D3)⋊C4C2×D314yes—
178C3×(C2×D3)⋊C4C2×D314yes—
179C3×C4⋊Dic3C2×D314yescomplemented
180C3×Dic3⋊C4—34no—
181C3×Dic3⋊C4—34no—
182C3×Dic3⋊C4C2×D314yescomplemented
183C3×C4×Dic3C2×D314yescomplemented
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—34no—
187#3722—34no—
188#3722—34no—
189#3722—34no—
190#3722—34no—
191(C2×D3)⋊Dic3—34no—
192Dic32—34no—
193C22×C33C2411yescharacteristic
194C2×C3⋊(C3⋊D3)—21no—
195C2×C3⋊(C3⋊D3)—21no—
196C2×C3⋊(C3⋊D3)—21no—
197C2×C3⋊(C3⋊D3)—21no—
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)—21no—
202C2×C3⋊(C3⋊D3)—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3#4112yes—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209D3×C3⋊D3—44no—
210C33×C4—21no—
211C33×C4—21no—
212C33×C4—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#126—34no—
221C3×C22⋊Q8—91no—
222#947—91no—
223#947—91no—
224#930—91no—
225C2×(C2×D3)⋊C4—91no—
226#898—94no—
227#898—91no—
228#898C3⋊D311yescharacteristic, complemented
229#896—34no—
230#895—94no—
231#895—94no—
232#895—91no—
233#895—91no—
234#895—184no—
235#894—94no—
236#894—91no—
237#894—91no—
238#893—94no—
239#885—94no—
240#884—94no—
241#883—94no—
242#882—94no—
243#882—94no—
244#882—91no—
245#882—91no—
246#67⋊C4—91no—
247#67⋊C4—91no—
248D3×C22⋊C4—94no—
249#875—94no—
250C4×D12—94no—
251C23×C32—31no—
252C22×C3⋊D3—31no—
253C22×C3⋊D3—31no—
254C22×C3⋊D3—31no—
255C22×C3⋊D3—34no—
256C22×C3⋊D3—34no—
257C22×C3⋊D3—34no—
258C22×C3⋊D3—64no—
259C22×C3⋊D3—64no—
260C22×C3⋊D3—64no—
261C22×C3⋊D3—62no—
262C22×C3⋊D3—121no—
263C22×C3⋊D3—121no—
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3×D3—34no—
266C22×C3×D3C22×D314yes—
267C2×D32—68no—
268C2×D32—124no—
269C2×D32—124no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—24no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—31no—
276C2×C32×C4C22×D314yes—
277C2×C32×C4C22×D314yes—
278C2×C32×C4C22×D314yes—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282#638—121no—
283#638—121no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—34no—
286C2×C3⋊Dic3—64no—
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C4⋊(C3⋊D3)—62no—
291C4⋊(C3⋊D3)—62no—
292C4⋊(C3⋊D3)—121no—
293C4⋊(C3⋊D3)—121no—
294C4⋊(C3⋊D3)—121no—
295C4⋊(C3⋊D3)—124no—
296C4⋊(C3⋊D3)—124no—
297C4⋊(C3⋊D3)—124no—
298C4⋊(C3⋊D3)—128no—
299C4⋊(C3⋊D3)—128no—
300C4⋊(C3⋊D3)—128no—
301C4×C3⋊D3—41no—
302C4×C3⋊D3—121no—
303C4×C3⋊D3—121no—
304C4×C3⋊D3—124no—
305C4×C3⋊D3—121no—
306C4×C3⋊D3—128no—
307#634—41no—
308C2×C3×Dic3—34no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3C22×D314yes—
312C2×C3×Dic3C22×D314yes—
313C2×C3×Dic3C22×D314yes—
314C3×C4×D3—124no—
315C3×Dic6—124no—
316#626—68no—
317#626—68no—
318#626—124no—
319#626—124no—
320#624—124no—
321D3×Dic3—124no—
322#538—271noSylow
323C2×C33C2×#4111yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C3⋊(C3⋊D3)—41no—
327C3⋊(C3⋊D3)—41no—
328C3⋊(C3⋊D3)—41no—
329C3×C3⋊D3—22no—
330C32×D3—41no—
331C23×D3—94no—
332C23×D3—91no—
333C2×C3×Q8—91no—
334C22×C3×C4—91no—
335C2×#67—94no—
336C2×#67—94no—
337C2×#67—91no—
338C2×#67—91no—
339C22×Dic3—91no—
340C2×D12—94no—
341C2×D12—94no—
342C2×D12—91no—
343C2×D12—91no—
344C2×D12—94no—
345C2×D12—94no—
346C2×D12—94no—
347C2×D12—91no—
348C2×D12—91no—
349C2×D12—91no—
350C2×D12—184no—
351C2×D12—184no—
352C2×D12—184no—
353C2×C4×D3—34no—
354C2×C4×D3—94no—
355C2×C4×D3—94no—
356C2×C4×D3—94no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—184no—
360C2×Dic6—34no—
361C3×C4⋊C4—24no—
362C3×C4⋊C4—34no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4D3214yescomplemented
367C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
368C3×C22⋊C4—34no—
369C3×C22⋊C4—34no—
370C3×C22⋊C4—34no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C42—34no—
374#217—94no—
375(C2×D3)⋊C4—34no—
376(C2×D3)⋊C4—34no—
377(C2×D3)⋊C4—94no—
378(C2×D3)⋊C4—94no—
379(C2×D3)⋊C4—94no—
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—94no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—184no—
395(C2×D3)⋊C4—184no—
396(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
397(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
398(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
399C4⋊Dic3—94no—
400C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
401Dic3⋊C4—34no—
402Dic3⋊C4—34no—
403Dic3⋊C4—91no—
404Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
405C4×Dic3—94no—
406C4×Dic3—91no—
407C4×Dic3C2×C3⋊D311yescharacteristic, complemented
408C22×C32—24no—
409C22×C32—61no—
410C22×C32—61no—
411C22×C32—61no—
412C22×C32C23×D314yes—
413C22×C32C23×D311yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—68no—
417C2×C3⋊D3—61no—
418C2×C3⋊D3—61no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
424C2×C3⋊D3—61no—
425C2×C3⋊D3—64no—
426C2×C3⋊D3—61no—
427C2×C3⋊D3—64no—
428C2×C3⋊D3—64no—
429C2×C3⋊D3—64no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—64no—
434C2×C3⋊D3—64no—
435C2×C3⋊D3—124no—
436C2×C3⋊D3—124no—
437C2×C3⋊D3—124no—
438C2×C3⋊D3—124no—
439C2×C3⋊D3—124no—
440C2×C3⋊D3—124no—
441C2×C3⋊D3—124no—
442C2×C3⋊D3—124no—
443C2×C3⋊D3—124no—
444C2×C3⋊D3#23912yes—
445C2×C3×D3—24no—
446C2×C3×D3—24no—
447C2×C3×D3—24no—
448C2×C3×D3—38no—
449C2×C3×D3—64no—
450C2×C3×D3—64no—
451D32—1216no—
452C32×C4—28no—
453C32×C4—21no—
454C32×C4—21no—
455C32×C4—24no—
456C32×C4—21no—
457C32×C4—24no—
458C32×C4—24no—
459C32×C4—44no—
460C32×C4—44no—
461C32×C4—61no—
462C32×C4—61no—
463C32×C4—61no—
464C3⋊Dic3—21no—
465C3⋊Dic3—21no—
466C3⋊Dic3—21no—
467C3⋊Dic3—61no—
468C3⋊Dic3—64no—
469C3⋊Dic3—124no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—24no—
473C3×Dic3—64no—
474C3×Dic3—64no—
475C3×Dic3—64no—
476#126—31no—
477#126—271no—
478#124—271no—
479#124—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—91no—
483#121—271no—
484#121—271no—
485#121—271no—
486#120—271no—
487#120—271no—
488C4×D4—271no—
489C4×D4—271no—
490C2×C22⋊C4—271no—
491C33#53811yescharacteristic, complemented, Sylow
492C23×C3—34no—
493C23×C3—91no—
494C22×D3—34no—
495C22×D3—94no—
496C22×D3—94no—
497C22×D3—94no—
498C22×D3—91no—
499C22×D3—91no—
500C22×D3—91no—
501C22×D3—184no—
502C22×D3—184no—
503C22×D3—184no—
504C22×D3—182no—
505C22×D3—188no—
506C22×D3—361no—
507C22×D3—361no—
508C22×D3—364no—
509C22×D3—364no—
510C22×D3C22×C3⋊D311yescharacteristic
511C3×Q8—361no—
512C2×C3×C4—24no—
513C2×C3×C4—24no—
514C2×C3×C4—24no—
515C2×C3×C4—34no—
516C2×C3×C4—34no—
517C2×C3×C4—34no—
518C2×C3×C4—91no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—361no—
522C2×C3×C4C2×D3214yes—
523C2×C3×C4C2×D3214yes—
524C2×C3×C4C2×D3214yes—
525C2×C3×C4C22×C3⋊D311yescharacteristic
526C2×C3×C4C22×C3⋊D311yescharacteristic
527C2×C3×C4C22×C3⋊D311yescharacteristic
528#67—182no—
529#67—182no—
530#67—364no—
531#67—364no—
532C2×Dic3—34no—
533C2×Dic3—34no—
534C2×Dic3—34no—
535C2×Dic3—94no—
536C2×Dic3—91no—
537C2×Dic3—184no—
538C2×Dic3—361no—
539C2×Dic3C22×C3⋊D311yescharacteristic
540C2×Dic3C22×C3⋊D311yescharacteristic
541C2×Dic3C22×C3⋊D311yescharacteristic
542D12—188no—
543D12—188no—
544D12—364no—
545D12—364no—
546D12—364no—
547D12—361no—
548D12—361no—
549D12—361no—
550D12—368no—
551D12—368no—
552D12—368no—
553D12—361no—
554D12—361no—
555C4×D3—124no—
556C4×D3—361no—
557C4×D3—364no—
558C4×D3—364no—
559C4×D3—361no—
560C4×D3—364no—
561C4×D3—368no—
562Dic6—124no—
563C2×C32—24no—
564C2×C32—24no—
565C2×C32—24no—
566C2×C32—121no—
567C2×C32#100411yescharacteristic
568C2×C32C2×#23911yescharacteristic
569C2×C32D3×#4114yes—
570C2×C32#100914yes—
571C2×C32#100914yes—
572C2×C32#100911yescharacteristic
573C3⋊D3—22no—
574C3⋊D3—128no—
575C3⋊D3—121no—
576C3⋊D3—121no—
577C3⋊D3—121no—
578C3⋊D3—124no—
579C3⋊D3—124no—
580C3⋊D3—124no—
581C3⋊D3—244no—
582C3⋊D3—244no—
583C3×D3—44no—
584C3×D3—68no—
585C24—271no—
586C2×Q8—91no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C2×D4—271no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—271no—
603C4⋊C4D3×C3⋊D311yescharacteristic, complemented
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C22⋊C4—271no—
618C42—31no—
619C42—271no—
620C22×C3—24no—
621C22×C3—64no—
622C22×C3—64no—
623C22×C3—64no—
624C22×C3—92no—
625C22×C3—181no—
626C22×C3—181no—
627C22×C3C22×D3214yes—
628C22×C3C23×C3⋊D311yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—38no—
633C2×D3—64no—
634C2×D3—64no—
635C2×D3—188no—
636C2×D3—184no—
637C2×D3—184no—
638C2×D3—184no—
639C2×D3—184no—
640C2×D3—184no—
641C2×D3—184no—
642C2×D3—184no—
643C2×D3—184no—
644C2×D3—184no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—181no—
652C2×D3—181no—
653C2×D3—181no—
654C2×D3—364no—
655C2×D3—364no—
656C2×D3—364no—
657C2×D3—364no—
658C2×D3—364no—
659C2×D3—364no—
660C2×D3—364no—
661C2×D3—364no—
662C2×D3—364no—
663C2×D3—3616no—
664C3×C4—28no—
665C3×C4—24no—
666C3×C4—24no—
667C3×C4—24no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—44no—
672C3×C4—44no—
673C3×C4—64no—
674C3×C4—64no—
675C3×C4—64no—
676C3×C4—181no—
677C3×C4—181no—
678C3×C4—181no—
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—64no—
683Dic3—64no—
684Dic3—64no—
685Dic3—184no—
686Dic3—181no—
687Dic3—364no—
688C32—24no—
689C32#564411yescharacteristic, complemented
690C32#570414yescomplemented
691C23—31no—
692C23—91no—
693C23—271no—
694C23—271no—
695C23—271no—
696C23—542no—
697C23—1081no—
698C23—1081no—
699Q8—361no—
700D4—542no—
701D4—542no—
702D4—1081no—
703D4—1081no—
704D4—1081no—
705D4—1081no—
706D4—1081no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—271no—
714C2×C4—361no—
715C2×C4—1081no—
716C2×C4—1081no—
717C2×C4—1081no—
718C2×C4C2×D3×C3⋊D311yescharacteristic
719C2×C4C2×D3×C3⋊D311yescharacteristic
720C2×C4C2×D3×C3⋊D311yescharacteristic
721C2×C3—24no—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—124no—
725C2×C3—182no—
726C2×C3#6430814yes—
727C2×C3#6431414yes—
728C2×C3D3×#23914yes—
729C2×C3#41×C3⋊D311yescharacteristic
730C2×C3#6436611yescharacteristic
731C2×C3#6436611yescharacteristic
732D3—41no—
733D3—68no—
734D3—368no—
735D3—361no—
736D3—361no—
737D3—361no—
738D3—364no—
739D3—364no—
740D3—364no—
741D3—724no—
742D3—724no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—92no—
747C22—181no—
748C22—181no—
749C22—541no—
750C22—541no—
751C22—541no—
752C22—541no—
753C22—541no—
754C22—541no—
755C22—541no—
756C22—541no—
757C22—541no—
758C22—1084no—
759C22C22×D3×C3⋊D311yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—61no—
764C4—61no—
765C4—61no—
766C4—181no—
767C4—181no—
768C4—181no—
769C4—541no—
770C3—24no—
771C3#1059465214yescomplemented
772C3#1059617511yescharacteristic, complemented
773C2—121no—
774C2—182no—
775C2—1081no—
776C2—1081no—
777C2—1081no—
778C2#1172458111yescharacteristic
779C2#1172458911yescharacteristic
780C2C3⋊D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723936C2semidirect
2. C3×#64105C2semidirect
3. C32×#898C2semidirect
4. #11723542C2semidirect
5. #11723542C2semidirect
6. C3⋊D3×(C2×D3)⋊C4C2semidirect
7. #11723526C2semidirect
8. #11723525C2semidirect
9. #11723521C2semidirect
10. #11723498C2semidirect
11. #11723472C2semidirect
12. #11723471C2semidirect
13. #11723441C2semidirect
14. #11723420C2semidirect
15. #11723411C2semidirect
21. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C3×#634C22semidirect
29. C2×#6289C22semidirect
31. C33×C4⋊C4C22semidirect
33. #88859C22semidirect
36. C3×#3750C22semidirect
37. C3×#3750C22semidirect
41. C32×C4⋊Dic3C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×C4×Dic3C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88804C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
55. #64105D3semidirect
70. C3×#898D3semidirect
137. C2×#634C2×D3semidirect
149. C32×C4⋊C4C2×D3semidirect
150. C32×C4⋊C4C2×D3semidirect
171. #3750C2×D3semidirect
172. #3750C2×D3semidirect
179. C3×C4⋊Dic3C2×D3semidirect
182. C3×Dic3⋊C4C2×D3semidirect
183. C3×C4×Dic3C2×D3semidirect
228. #898C3⋊D3semidirect
366. C3×C4⋊C4D32semidirect
367. C3×C4⋊C4C2×C3⋊D3semidirect
400. C4⋊Dic3C2×C3⋊D3semidirect
404. Dic3⋊C4C2×C3⋊D3semidirect
407. C4×Dic3C2×C3⋊D3semidirect
491. C33#538semidirect
603. C4⋊C4D3×C3⋊D3semidirect
689. C32#5644semidirect
690. C32#5704semidirect
771. C3#10594652semidirect
772. C3#10596175semidirect

Maximal subgroups

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

subgroupindex
#117239362
C3×#641052
C32×#8982
#117235422
C3⋊D3×(C2×D3)⋊C42
#117235262
#117235252
#117235212
#117234982
#117234722
#117234712
#117234412
#117234202
#117234112
#105961753
#105946523