Finite Group Databasebeta

← #13176592

Subgroups — #13176592

Order 1728.

1740 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723939C211yesmaximal, characteristic, complemented
2C3×#64104C211yesmaximal, characteristic, complemented
3C32×#896C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic, complemented
5#11723541C211yesmaximal, characteristic, complemented
6D3×#3752C211yesmaximal, characteristic, complemented
7#11723515C211yesmaximal, characteristic, complemented
8#11723508C211yesmaximal, characteristic, complemented
9#11723507C211yesmaximal, characteristic, complemented
10#11723488C211yesmaximal, characteristic, complemented
11#11723482C211yesmaximal, characteristic, complemented
12#11723436C211yesmaximal, characteristic, complemented
13#11723417C211yesmaximal, characteristic, complemented
14#11723408C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596115—31nomaximal
17#10594651—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34#88859C2211yescharacteristic
35C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
36#88857C2211yescharacteristic, complemented
37C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×C22⋊Q8—31no—
54#64156—31no—
55#64156—31no—
56#64139—31no—
57C2×#3752—31no—
58#64107—31no—
59#64107—31no—
60#64107—34no—
61#64107—64no—
62#64104—31no—
63#64104D311yescharacteristic, complemented
64#64103—31no—
65#64103—31no—
66#64091—31no—
67#64091—31no—
68#64090—31no—
69#64090—31no—
70C3×#896D314yescomplemented
71C3×#895—34no—
72#63922—34no—
73#63922—34no—
74D3×(C2×D3)⋊C4—34no—
75#63908—34no—
76#63907—34no—
77#63902—34no—
78#63886—34no—
79#63884—34no—
80#63879—34no—
81#63863—34no—
82#63861—34no—
83#63850—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
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
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C3×C4⋊(C3⋊D3)—41no—
100C3×C4⋊(C3⋊D3)—41no—
101C3×C4⋊(C3⋊D3)—41no—
102C3×C4×C3⋊D3—41no—
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×C4×D3—41no—
107C32×Dic6—41no—
108#6292—41no—
109#6292—41no—
110#6290—22no—
111#6290—22no—
112Dic3×C3⋊D3—41no—
113D3×C3⋊Dic3—41no—
114#5644—94no—
115#5613—91no—
116C23×C3⋊D3—31no—
117C22×D32—34no—
118C2×C32×Q8—31no—
119C22×C32×C4—31no—
120C2×#638—31no—
121C2×#638—31no—
122C22×C3⋊Dic3—31no—
123C2×C4⋊(C3⋊D3)—31no—
124C2×C4⋊(C3⋊D3)—31no—
125C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
126C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
127C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
128C2×C4×C3⋊D3—31no—
129C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
130C2×C3×D12—34no—
131C2×C3×D12—34no—
132C2×C3×D12—34no—
133C2×C3×C4×D3—34no—
134C2×C3×C4×D3C2×D314yes—
135C2×C3×Dic6C2×D314yescomplemented
136C2×#626—34no—
137C2×#626—34no—
138C2×#625—34no—
139C2×#625—34no—
140C2×D3×Dic3—34no—
141C2×D3×Dic3—34no—
142C32×C4⋊C4—24no—
143C32×C4⋊C4—31no—
144C32×C4⋊C4—31no—
145C32×C4⋊C4C2×D314yescomplemented
146C32×C4⋊C4C2×D311yescharacteristic, complemented
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149#3752—31no—
150#3752—31no—
151#3752—31no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—34no—
159#3752—34no—
160#3752—34no—
161#3752—31no—
162#3752—64no—
163#3752—64no—
164#3752—64no—
165#3752C2×D311yescharacteristic
166#3752C2×D311yescharacteristic, complemented
167C4⋊(C3⋊Dic3)—31no—
168C4⋊(C3⋊Dic3)—34no—
169C4⋊(C3⋊Dic3)—64no—
170#3750—31no—
171#3750—34no—
172#3750—31no—
173#3750—64no—
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—34no—
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—64no—
178C3×(C2×D3)⋊C4—34no—
179C3×(C2×D3)⋊C4—34no—
180C3×(C2×D3)⋊C4C2×D314yes—
181C3×(C2×D3)⋊C4C2×D314yes—
182C3×Dic3⋊C4C2×D314yescomplemented
183C3×Dic3⋊C4C2×D314yescomplemented
184#3724—34no—
185#3722—34no—
186(C2×D3)⋊Dic3—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—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—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3#4112yes—
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×C22⋊Q8—34no—
221C3×#121—91no—
222#947—94no—
223#947—94no—
224#939—91no—
225#938—91no—
226#937—91no—
227#937—91no—
228#936—91no—
229#935—91no—
230#930—94no—
231#929—91no—
232C4×#67—91no—
233C2×(C2×D3)⋊C4—94no—
234#898—94no—
235#898—94no—
236#898—91no—
237#898—184no—
238#896C3⋊D311yescharacteristic, complemented
239#895—34no—
240#895—94no—
241#894—94no—
242#894—94no—
243#885—91no—
244#882—94no—
245#882—94no—
246#67⋊C4—94no—
247#67⋊C4—94no—
248#67⋊C4—91no—
249D3×C22⋊C4—91no—
250#879—91no—
251C23×C32—31no—
252C22×C3⋊D3—31no—
253C22×C3⋊D3—34no—
254C22×C3⋊D3—64no—
255C22×C3⋊D3—62no—
256C22×C3⋊D3—121no—
257C22×C3⋊D3—121no—
258C22×C3⋊D3C22×D311yescharacteristic
259C22×C3⋊D3C22×D311yescharacteristic
260C22×C3⋊D3C22×D311yescharacteristic
261C22×C3×D3—34no—
262C22×C3×D3—34no—
263C22×C3×D3—34no—
264C22×C3×D3C22×D314yes—
265C2×D32—68no—
266C2×D32—124no—
267C2×D32—124no—
268C32×Q8—121no—
269C2×C32×C4—24no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—121no—
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—62no—
283#638—62no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—64no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3—121no—
294C2×C3⋊Dic3C22×D311yescharacteristic
295C4⋊(C3⋊D3)—41no—
296C4⋊(C3⋊D3)—41no—
297C4⋊(C3⋊D3)—41no—
298C4⋊(C3⋊D3)—121no—
299C4⋊(C3⋊D3)—121no—
300C4×C3⋊D3—41no—
301C4×C3⋊D3—121no—
302C2×C3×Dic3—34no—
303C2×C3×Dic3C22×D314yes—
304C2×C3×Dic3C22×D314yes—
305C2×C3×Dic3C22×D314yes—
306C3×D12—124no—
307C3×D12—124no—
308C3×D12—124no—
309C3×C4×D3—44no—
310C3×C4×D3—124no—
311C3×Dic6—44no—
312#626—124no—
313#626—124no—
314#625—68no—
315#625—68no—
316D3×Dic3—124no—
317D3×Dic3—124no—
318#538—271noSylow
319C2×C33C2×#4111yescharacteristic
320C2×C33H(5,𝔽2)11yescharacteristic
321C2×C33H(5,𝔽2)11yescharacteristic
322C3⋊(C3⋊D3)—41no—
323C3×C3⋊D3—41no—
324C3×C3⋊D3—41no—
325C3×C3⋊D3—41no—
326C32×D3—22no—
327C23×D3—94no—
328C23×D3—91no—
329C2×C3×Q8—34no—
330C2×C3×D4—91no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C22×C3×C4—34no—
334C22×C3×C4—91no—
335C2×#67—94no—
336C2×#67—94no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C22×Dic3—94no—
342C22×Dic3—91no—
343C2×D12—34no—
344C2×D12—34no—
345C2×D12—34no—
346C2×D12—94no—
347C2×D12—94no—
348C2×C4×D3—34no—
349C2×C4×D3—94no—
350C2×C4×D3—91no—
351C2×C4×D3C2×C3⋊D311yescharacteristic
352C2×Dic6C2×C3⋊D311yescharacteristic, complemented
353C3×C4⋊C4—24no—
354C3×C4⋊C4—34no—
355C3×C4⋊C4—34no—
356C3×C4⋊C4D3214yescomplemented
357C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
358C3×C22⋊C4—34no—
359C3×C22⋊C4—34no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362#217—91no—
363#217—91no—
364#217—91no—
365#217—91no—
366#217—91no—
367#217—91no—
368(C2×D3)⋊C4—34no—
369(C2×D3)⋊C4—34no—
370(C2×D3)⋊C4—94no—
371(C2×D3)⋊C4—94no—
372(C2×D3)⋊C4—94no—
373(C2×D3)⋊C4—94no—
374(C2×D3)⋊C4—94no—
375(C2×D3)⋊C4—94no—
376(C2×D3)⋊C4—94no—
377(C2×D3)⋊C4—94no—
378(C2×D3)⋊C4—94no—
379(C2×D3)⋊C4—94no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—184no—
385(C2×D3)⋊C4—184no—
386(C2×D3)⋊C4—184no—
387(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
388(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
389C4⋊Dic3—94no—
390C4⋊Dic3—91no—
391C4⋊Dic3—184no—
392Dic3⋊C4—94no—
393Dic3⋊C4—94no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—184no—
397Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
398Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
399C4×Dic3—94no—
400C4×Dic3—94no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C4×Dic3—184no—
404C22×C32—24no—
405C22×C32—32no—
406C22×C32—61no—
407C22×C32—61no—
408C22×C32C23×D314yes—
409C22×C32C23×D311yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—64no—
423C2×C3⋊D3—64no—
424C2×C3⋊D3—64no—
425C2×C3⋊D3—124no—
426C2×C3⋊D3—124no—
427C2×C3⋊D3—124no—
428C2×C3⋊D3—124no—
429C2×C3×D3—24no—
430C2×C3×D3—24no—
431C2×C3×D3—64no—
432C2×C3×D3—64no—
433C2×C3×D3—64no—
434C2×C3×D3—64no—
435C2×C3×D3—64no—
436C2×C3×D3—64no—
437C2×C3×D3—64no—
438C2×C3×D3—64no—
439C2×C3×D3—64no—
440C2×C3×D3#23918yes—
441D32—1216no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—24no—
446C32×C4—24no—
447C32×C4—24no—
448C32×C4—44no—
449C32×C4—44no—
450C32×C4—44no—
451C32×C4—61no—
452C32×C4—61no—
453C32×C4—61no—
454C3⋊Dic3—21no—
455C3⋊Dic3—61no—
456C3⋊Dic3—61no—
457C3⋊Dic3—61no—
458C3⋊Dic3—64no—
459C3⋊Dic3—64no—
460C3⋊Dic3—64no—
461C3⋊Dic3—124no—
462C3⋊Dic3—124no—
463C3⋊Dic3—124no—
464C3×Dic3—24no—
465C3×Dic3—24no—
466C3×Dic3—24no—
467C3×Dic3—64no—
468#126—271no—
469#126—271no—
470#124—271no—
471#124—271no—
472#123—271no—
473#123—271no—
474C22⋊Q8—31no—
475#121—91no—
476#121—271no—
477#121—271no—
478#120—271no—
479#120—271no—
480C4×D4—271no—
481C4×D4—271no—
482C2×C22⋊C4—271no—
483C33#53811yescharacteristic, complemented, Sylow
484C23×C3—34no—
485C23×C3—91no—
486C23×C3—91no—
487C23×C3—91no—
488C22×D3—34no—
489C22×D3—34no—
490C22×D3—34no—
491C22×D3—94no—
492C22×D3—91no—
493C22×D3—184no—
494C22×D3—188no—
495C22×D3—182no—
496C22×D3—361no—
497C22×D3—361no—
498C22×D3—364no—
499C22×D3—364no—
500C22×D3C22×C3⋊D311yescharacteristic
501C3×Q8—124no—
502C3×D4—361no—
503C3×D4—361no—
504C3×D4—361no—
505C2×C3×C4—24no—
506C2×C3×C4—24no—
507C2×C3×C4—24no—
508C2×C3×C4—34no—
509C2×C3×C4—34no—
510C2×C3×C4—34no—
511C2×C3×C4—91no—
512C2×C3×C4—124no—
513C2×C3×C4—361no—
514C2×C3×C4C2×D3214yes—
515C2×C3×C4C2×D3214yes—
516C2×C3×C4C2×D3214yes—
517C2×C3×C4C22×C3⋊D311yescharacteristic
518C2×C3×C4C22×C3⋊D311yescharacteristic
519C2×C3×C4C22×C3⋊D311yescharacteristic
520#67—188no—
521#67—188no—
522#67—182no—
523#67—182no—
524#67—361no—
525#67—361no—
526C2×Dic3—34no—
527C2×Dic3—94no—
528C2×Dic3—94no—
529C2×Dic3—94no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—184no—
534C2×Dic3—184no—
535C2×Dic3—184no—
536C2×Dic3—361no—
537C2×Dic3—364no—
538C2×Dic3C22×C3⋊D311yescharacteristic
539C2×Dic3C22×C3⋊D311yescharacteristic
540C2×Dic3C22×C3⋊D311yescharacteristic
541D12—124no—
542D12—124no—
543D12—124no—
544D12—364no—
545D12—364no—
546C4×D3—41no—
547C4×D3—124no—
548C4×D3—364no—
549C4×D3—361no—
550Dic6—41no—
551C2×C32—24no—
552C2×C32—24no—
553C2×C32—24no—
554C2×C32—62no—
555C2×C32#100414yes—
556C2×C32#100411yescharacteristic
557C2×C32#100411yescharacteristic
558C2×C32C2×#23914yes—
559C2×C32D3×#4111yescharacteristic
560C2×C32#100914yes—
561C3⋊D3—41no—
562C3⋊D3—41no—
563C3⋊D3—41no—
564C3⋊D3—121no—
565C3⋊D3—124no—
566C3⋊D3—244no—
567C3×D3—28no—
568C3×D3—124no—
569C3×D3—124no—
570C3×D3—124no—
571C24—271no—
572C2×Q8—31no—
573C2×D4—91no—
574C2×D4—91no—
575C2×D4—91no—
576C2×D4—271no—
577C2×D4—271no—
578C2×D4—271no—
579C2×D4—271no—
580C22×C4—31no—
581C22×C4—91no—
582C22×C4—271no—
583C22×C4—271no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—271no—
587C4⋊C4—271no—
588C4⋊C4—271no—
589C4⋊C4D3×C3⋊D311yescharacteristic, complemented
590C22⋊C4—31no—
591C22⋊C4—31no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—271no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C42—271no—
605C42—271no—
606C22×C3—24no—
607C22×C3—38no—
608C22×C3—64no—
609C22×C3—64no—
610C22×C3—181no—
611C22×C3—181no—
612C22×C3—181no—
613C22×C3—181no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3C22×D3214yes—
620C22×C3C23×C3⋊D311yescharacteristic
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—64no—
624C2×D3—64no—
625C2×D3—64no—
626C2×D3—64no—
627C2×D3—64no—
628C2×D3—64no—
629C2×D3—64no—
630C2×D3—64no—
631C2×D3—64no—
632C2×D3—184no—
633C2×D3—184no—
634C2×D3—184no—
635C2×D3—181no—
636C2×D3—181no—
637C2×D3—181no—
638C2×D3—364no—
639C2×D3—364no—
640C2×D3—364no—
641C2×D3—364no—
642C2×D3—3616no—
643C2×D3#383212yes—
644C3×C4—24no—
645C3×C4—24no—
646C3×C4—24no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—44no—
651C3×C4—44no—
652C3×C4—44no—
653C3×C4—64no—
654C3×C4—64no—
655C3×C4—64no—
656C3×C4—181no—
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—64no—
661Dic3—184no—
662Dic3—184no—
663Dic3—184no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—364no—
668Dic3—364no—
669Dic3—364no—
670C32—24no—
671C32#561311yescharacteristic, complemented
672C32#564414yescomplemented
673C23—31no—
674C23—91no—
675C23—91no—
676C23—91no—
677C23—271no—
678C23—542no—
679C23—1081no—
680C23—1081no—
681Q8—121no—
682D4—361no—
683D4—361no—
684D4—361no—
685D4—542no—
686D4—542no—
687D4—1081no—
688D4—1081no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—91no—
693C2×C4—121no—
694C2×C4—271no—
695C2×C4—271no—
696C2×C4—271no—
697C2×C4—361no—
698C2×C4—1081no—
699C2×C4—1081no—
700C2×C4C2×D3×C3⋊D311yescharacteristic
701C2×C4C2×D3×C3⋊D311yescharacteristic
702C2×C4C2×D3×C3⋊D311yescharacteristic
703C2×C3—24no—
704C2×C3—24no—
705C2×C3—24no—
706C2×C3—68no—
707C2×C3—361no—
708C2×C3—361no—
709C2×C3—361no—
710C2×C3#6430714yes—
711C2×C3#6431314yes—
712C2×C3D3×#23914yes—
713C2×C3#6436111yescharacteristic
714C2×C3C2×#383211yescharacteristic
715C2×C3#6436611yescharacteristic
716D3—22no—
717D3—124no—
718D3—124no—
719D3—124no—
720D3—361no—
721D3—364no—
722D3—724no—
723C22—32no—
724C22—61no—
725C22—61no—
726C22—181no—
727C22—181no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—541no—
736C22—541no—
737C22—541no—
738C22—1084no—
739C22C22×D3×C3⋊D311yescharacteristic
740C4—21no—
741C4—21no—
742C4—21no—
743C4—61no—
744C4—61no—
745C4—61no—
746C4—181no—
747C4—541no—
748C4—541no—
749C4—541no—
750C3—24no—
751C3#1059465114yescomplemented
752C3#1059611511yescharacteristic, complemented
753C2—62no—
754C2—361no—
755C2—361no—
756C2—361no—
757C2—1081no—
758C2#1172458011yescharacteristic
759C2#1172458711yescharacteristic
760C2D3×#383211yescharacteristic
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. #11723939C2semidirect
2. C3×#64104C2semidirect
3. C32×#896C2semidirect
4. #11723541C2semidirect
5. #11723541C2semidirect
6. D3×#3752C2semidirect
7. #11723515C2semidirect
8. #11723508C2semidirect
9. #11723507C2semidirect
10. #11723488C2semidirect
11. #11723482C2semidirect
12. #11723436C2semidirect
13. #11723417C2semidirect
14. #11723408C2semidirect
15. #11723392C2semidirect
21. C2×C3×C4⋊(C3⋊D3)C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
24. C2×C32×Dic6C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
31. C33×C4⋊C4C22semidirect
35. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
36. #88857C22semidirect
37. C4×C3⋊(C3⋊Dic3)C22semidirect
39. C3×#3752C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×Dic3⋊C4C22semidirect
44. #88806C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
63. #64104D3semidirect
70. C3×#896D3semidirect
127. C2×C4⋊(C3⋊D3)C2×D3semidirect
129. C2×C4×C3⋊D3C2×D3semidirect
135. C2×C3×Dic6C2×D3semidirect
145. C32×C4⋊C4C2×D3semidirect
146. C32×C4⋊C4C2×D3semidirect
166. #3752C2×D3semidirect
182. C3×Dic3⋊C4C2×D3semidirect
183. C3×Dic3⋊C4C2×D3semidirect
238. #896C3⋊D3semidirect
352. C2×Dic6C2×C3⋊D3semidirect
356. C3×C4⋊C4D32semidirect
357. C3×C4⋊C4C2×C3⋊D3semidirect
397. Dic3⋊C4C2×C3⋊D3semidirect
398. Dic3⋊C4C2×C3⋊D3semidirect
483. C33#538semidirect
589. C4⋊C4D3×C3⋊D3semidirect
671. C32#5613semidirect
672. C32#5644semidirect
751. C3#10594651semidirect
752. C3#10596115semidirect

Maximal subgroups

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

subgroupindex
#117239392
C3×#641042
C32×#8962
#117235412
D3×#37522
#117235152
#117235082
#117235072
#117234882
#117234822
#117234362
#117234172
#117234082
#117233922
#105961153
#105946513