Finite Group Databasebeta

← #13176594

Subgroups — #13176594

Order 1728.

1812 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723935C211yesmaximal, characteristic, complemented
2C3×#64103C211yesmaximal, characteristic, complemented
3C32×#897C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723541C211yesmaximal, characteristic, complemented
6D3×#3752C211yesmaximal, characteristic, complemented
7#11723532C211yesmaximal, characteristic, complemented
8#11723526C211yesmaximal, characteristic, complemented
9#11723514C211yesmaximal, characteristic, complemented
10#11723507C211yesmaximal, characteristic, complemented
11#11723462C211yesmaximal, characteristic, complemented
12#11723411C211yesmaximal, characteristic, complemented
13#11723407C211yesmaximal, characteristic, complemented
14#11723392C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596115—31nomaximal
17#10594650—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic, complemented
28C2×#6291C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34#88859C2211yescharacteristic, complemented
35#88857C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×C4⋊Dic3C2211yescharacteristic, complemented
43C32×C4⋊Dic3C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic, complemented
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, 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#64104—31no—
61#64104—31no—
62#64103—31no—
63#64103—34no—
64#64103—64no—
65#64103D311yescharacteristic, complemented
66#64091—31no—
67#64091—31no—
68#64090—31no—
69#64090—31no—
70C3×#897D314yescomplemented
71C3×#894—34no—
72#63923—34no—
73#63922—34no—
74D3×(C2×D3)⋊C4—34no—
75#63916—34no—
76#63909—34no—
77#63907—34no—
78#63907—34no—
79#63906—34no—
80#63881—34no—
81#63879—34no—
82#63858—34no—
83#63848—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
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
97C4⋊(C3⋊(C3⋊D3))—41no—
98C4×C3⋊(C3⋊D3)—41no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
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#6292—41no—
111#6291—22no—
112#6290—22no—
113D3×C3⋊Dic3—41no—
114#5657—91no—
115#5644—94no—
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)—31no—
126C2×C4⋊(C3⋊D3)—31no—
127C2×C4⋊(C3⋊D3)—34no—
128C2×C4⋊(C3⋊D3)—64no—
129C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
130C2×C4×C3⋊D3—31no—
131C2×C4×C3⋊D3—34no—
132C2×C4×C3⋊D3—64no—
133C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
134C2×C3×D12—34no—
135C2×C3×C4×D3—34no—
136C2×C3×C4×D3C2×D314yes—
137C2×C3×Dic6C2×D314yescomplemented
138C2×#626—34no—
139C2×#626—34no—
140C2×#626—34no—
141C2×#626—34no—
142C2×#625—34no—
143C2×D3×Dic3—34no—
144C32×C4⋊C4—24no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4C2×D314yescomplemented
148C32×C4⋊C4C2×D311yescharacteristic, complemented
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151#3752—31no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—34no—
158#3752—34no—
159#3752—34no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—64no—
164#3752—64no—
165#3752—64no—
166#3752C2×D311yescharacteristic
167#3752C2×D311yescharacteristic
168#3752C2×D311yescharacteristic, complemented
169C4⋊(C3⋊Dic3)—31no—
170#3750—31no—
171#3750—34no—
172#3750—64no—
173#3750C2×D311yescharacteristic, complemented
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—31no—
176C3×(C2×D3)⋊C4—34no—
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4—34no—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×(C2×D3)⋊C4C2×D314yes—
181C3×C4⋊Dic3C2×D314yescomplemented
182C3×C4⋊Dic3C2×D314yescomplemented
183C3×Dic3⋊C4—34no—
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—34no—
187#3722—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191Dic32—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×#123—91no—
221C3×C22⋊Q8—34no—
222#947—94no—
223#947—94no—
224#938—91no—
225#937—91no—
226#930—94no—
227#930—91no—
228C4×#67—91no—
229C2×(C2×D3)⋊C4—94no—
230#898—94no—
231#898—94no—
232#898—91no—
233#897C3⋊D311yescharacteristic, complemented
234#895—94no—
235#895—94no—
236#894—34no—
237#894—94no—
238#894—91no—
239#894—184no—
240#893—91no—
241#885—91no—
242#885—91no—
243#884—91no—
244#882—94no—
245#882—94no—
246#882—91no—
247#67⋊C4—94no—
248#67⋊C4—94no—
249D3×C22⋊C4—91no—
250#879—91no—
251C23×C32—31no—
252C22×C3⋊D3—31no—
253C22×C3⋊D3—31no—
254C22×C3⋊D3—34no—
255C22×C3⋊D3—34no—
256C22×C3⋊D3—64no—
257C22×C3⋊D3—64no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—121no—
260C22×C3⋊D3—121no—
261C22×C3⋊D3C22×D311yescharacteristic
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3×D3—34no—
264C22×C3×D3—34no—
265C22×C3×D3C22×D314yes—
266C2×D32—68no—
267C2×D32—124no—
268C2×D32—124no—
269C32×Q8—121no—
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×C4—121no—
277C2×C32×C4C22×D314yes—
278C2×C32×C4C22×D314yes—
279C2×C32×C4C22×D314yes—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283#638—62no—
284#638—62no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—34no—
288C2×C3⋊Dic3—34no—
289C2×C3⋊Dic3—64no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—121no—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C4⋊(C3⋊D3)—41no—
295C4⋊(C3⋊D3)—121no—
296C4⋊(C3⋊D3)—124no—
297C4⋊(C3⋊D3)—128no—
298C4⋊(C3⋊D3)—121no—
299C4⋊(C3⋊D3)—121no—
300C4⋊(C3⋊D3)—121no—
301C4×C3⋊D3—41no—
302C4×C3⋊D3—121no—
303C4×C3⋊D3—124no—
304C4×C3⋊D3—128no—
305C2×C3×Dic3—34no—
306C2×C3×Dic3—34no—
307C2×C3×Dic3C22×D314yes—
308C2×C3×Dic3C22×D314yes—
309C2×C3×Dic3C22×D314yes—
310C3×D12—124no—
311C3×C4×D3—44no—
312C3×C4×D3—124no—
313C3×Dic6—44no—
314#626—68no—
315#626—124no—
316#626—124no—
317#626—124no—
318#625—68no—
319D3×Dic3—124no—
320#538—271noSylow
321C2×C33C2×#4111yescharacteristic
322C2×C33H(5,𝔽2)11yescharacteristic
323C2×C33H(5,𝔽2)11yescharacteristic
324C3⋊(C3⋊D3)—41no—
325C3⋊(C3⋊D3)—41no—
326C3×C3⋊D3—41no—
327C3×C3⋊D3—41no—
328C32×D3—22no—
329C23×D3—94no—
330C23×D3—91no—
331C2×C3×Q8—34no—
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—
342C2×D12—34no—
343C2×D12—91no—
344C2×D12—94no—
345C2×D12—94no—
346C2×D12—94no—
347C2×D12—94no—
348C2×D12—91no—
349C2×D12—184no—
350C2×C4×D3—34no—
351C2×C4×D3—91no—
352C2×C4×D3—94no—
353C2×C4×D3—91no—
354C2×C4×D3—184no—
355C2×C4×D3C2×C3⋊D311yescharacteristic
356C2×Dic6C2×C3⋊D311yescharacteristic, complemented
357C3×C4⋊C4—24no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4—34no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4D3214yescomplemented
362C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4—91no—
368#217—91no—
369#217—91no—
370#217—91no—
371(C2×D3)⋊C4—34no—
372(C2×D3)⋊C4—34no—
373(C2×D3)⋊C4—34no—
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—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—94no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—184no—
390(C2×D3)⋊C4—184no—
391(C2×D3)⋊C4—184no—
392(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
393(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
394C4⋊Dic3—94no—
395C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
396C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
397Dic3⋊C4—34no—
398Dic3⋊C4—94no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—184no—
402C4×Dic3—94no—
403C4×Dic3—94no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C22×C32—24no—
407C22×C32—32no—
408C22×C32—61no—
409C22×C32—61no—
410C22×C32C23×D314yes—
411C22×C32C23×D311yescharacteristic
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—68no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—64no—
424C2×C3⋊D3—61no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—64no—
427C2×C3⋊D3—64no—
428C2×C3⋊D3—64no—
429C2×C3⋊D3—64no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—124no—
432C2×C3⋊D3—124no—
433C2×C3⋊D3—124no—
434C2×C3⋊D3—124no—
435C2×C3⋊D3—124no—
436C2×C3⋊D3—124no—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—64no—
440C2×C3×D3—64no—
441C2×C3×D3—64no—
442C2×C3×D3—64no—
443C2×C3×D3—64no—
444C2×C3×D3—64no—
445C2×C3×D3#23918yes—
446D32—1216no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—24no—
451C32×C4—24no—
452C32×C4—24no—
453C32×C4—44no—
454C32×C4—44no—
455C32×C4—44no—
456C32×C4—61no—
457C32×C4—61no—
458C32×C4—61no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—61no—
462C3⋊Dic3—61no—
463C3⋊Dic3—64no—
464C3⋊Dic3—64no—
465C3⋊Dic3—124no—
466C3⋊Dic3—124no—
467C3×Dic3—24no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—64no—
471C3×Dic3—64no—
472#126—271no—
473#126—271no—
474#124—271no—
475#124—271no—
476#123—91no—
477#123—271no—
478C22⋊Q8—31no—
479#121—271no—
480#121—271no—
481#121—271no—
482#120—271no—
483#120—271no—
484C4×D4—271no—
485C4×D4—271no—
486C2×C22⋊C4—271no—
487C33#53811yescharacteristic, complemented, Sylow
488C23×C3—34no—
489C23×C3—91no—
490C23×C3—91no—
491C22×D3—34no—
492C22×D3—34no—
493C22×D3—94no—
494C22×D3—94no—
495C22×D3—91no—
496C22×D3—91no—
497C22×D3—184no—
498C22×D3—184no—
499C22×D3—188no—
500C22×D3—182no—
501C22×D3—361no—
502C22×D3—361no—
503C22×D3—364no—
504C22×D3—364no—
505C22×D3C22×C3⋊D311yescharacteristic
506C3×Q8—124no—
507C3×D4—361no—
508C2×C3×C4—24no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—34no—
512C2×C3×C4—34no—
513C2×C3×C4—34no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—124no—
517C2×C3×C4—361no—
518C2×C3×C4C2×D3214yes—
519C2×C3×C4C2×D3214yes—
520C2×C3×C4C2×D3214yes—
521C2×C3×C4C22×C3⋊D311yescharacteristic
522C2×C3×C4C22×C3⋊D311yescharacteristic
523C2×C3×C4C22×C3⋊D311yescharacteristic
524#67—188no—
525#67—188no—
526#67—182no—
527#67—361no—
528#67—361no—
529#67—361no—
530C2×Dic3—34no—
531C2×Dic3—34no—
532C2×Dic3—94no—
533C2×Dic3—94no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—184no—
537C2×Dic3—184no—
538C2×Dic3—364no—
539C2×Dic3C22×C3⋊D311yescharacteristic
540C2×Dic3C22×C3⋊D311yescharacteristic
541C2×Dic3C22×C3⋊D311yescharacteristic
542D12—124no—
543D12—182no—
544D12—364no—
545D12—361no—
546D12—368no—
547D12—364no—
548D12—364no—
549D12—364no—
550C4×D3—41no—
551C4×D3—124no—
552C4×D3—364no—
553C4×D3—361no—
554C4×D3—361no—
555C4×D3—368no—
556Dic6—41no—
557C2×C32—24no—
558C2×C32—24no—
559C2×C32—24no—
560C2×C32—62no—
561C2×C32#100414yes—
562C2×C32#100411yescharacteristic
563C2×C32C2×#23914yes—
564C2×C32D3×#4111yescharacteristic
565C2×C32#100914yes—
566C2×C32#100911yescharacteristic
567C3⋊D3—41no—
568C3⋊D3—41no—
569C3⋊D3—128no—
570C3⋊D3—124no—
571C3⋊D3—121no—
572C3⋊D3—121no—
573C3⋊D3—124no—
574C3⋊D3—244no—
575C3×D3—28no—
576C3×D3—124no—
577C3×D3—124no—
578C24—271no—
579C2×Q8—31no—
580C2×D4—91no—
581C2×D4—271no—
582C2×D4—271no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C22×C4—31no—
588C22×C4—91no—
589C22×C4—271no—
590C22×C4—271no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—91no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4D3×C3⋊D311yescharacteristic, complemented
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C42—271no—
612C42—271no—
613C22×C3—24no—
614C22×C3—38no—
615C22×C3—64no—
616C22×C3—64no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3C22×D3214yes—
624C22×C3C23×C3⋊D311yescharacteristic
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—64no—
628C2×D3—64no—
629C2×D3—64no—
630C2×D3—64no—
631C2×D3—64no—
632C2×D3—64no—
633C2×D3—188no—
634C2×D3—184no—
635C2×D3—184no—
636C2×D3—184no—
637C2×D3—184no—
638C2×D3—184no—
639C2×D3—184no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—364no—
647C2×D3—364no—
648C2×D3—364no—
649C2×D3—364no—
650C2×D3—364no—
651C2×D3—364no—
652C2×D3—3616no—
653C2×D3#383212yes—
654C3×C4—24no—
655C3×C4—24no—
656C3×C4—24no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—44no—
661C3×C4—44no—
662C3×C4—44no—
663C3×C4—64no—
664C3×C4—64no—
665C3×C4—64no—
666C3×C4—181no—
667C3×C4—181no—
668Dic3—21no—
669Dic3—21no—
670Dic3—21no—
671Dic3—64no—
672Dic3—64no—
673Dic3—184no—
674Dic3—184no—
675Dic3—181no—
676Dic3—181no—
677Dic3—364no—
678Dic3—364no—
679C32—24no—
680C32#564414yescomplemented
681C32#565711yescharacteristic, complemented
682C23—31no—
683C23—91no—
684C23—91no—
685C23—271no—
686C23—271no—
687C23—542no—
688C23—1081no—
689C23—1081no—
690Q8—121no—
691D4—361no—
692D4—542no—
693D4—542no—
694D4—1081no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—121no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—361no—
707C2×C4—1081no—
708C2×C4—1081no—
709C2×C4C2×D3×C3⋊D311yescharacteristic
710C2×C4C2×D3×C3⋊D311yescharacteristic
711C2×C4C2×D3×C3⋊D311yescharacteristic
712C2×C3—24no—
713C2×C3—24no—
714C2×C3—24no—
715C2×C3—68no—
716C2×C3—361no—
717C2×C3—361no—
718C2×C3#6430714yes—
719C2×C3#6431414yes—
720C2×C3D3×#23914yes—
721C2×C3#6436111yescharacteristic
722C2×C3C2×#383211yescharacteristic
723C2×C3#6436611yescharacteristic
724D3—22no—
725D3—124no—
726D3—124no—
727D3—368no—
728D3—361no—
729D3—361no—
730D3—364no—
731D3—364no—
732D3—724no—
733C22—32no—
734C22—61no—
735C22—61no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—181no—
742C22—541no—
743C22—541no—
744C22—541no—
745C22—541no—
746C22—541no—
747C22—541no—
748C22—1084no—
749C22C22×D3×C3⋊D311yescharacteristic
750C4—21no—
751C4—21no—
752C4—21no—
753C4—61no—
754C4—61no—
755C4—61no—
756C4—181no—
757C4—181no—
758C4—541no—
759C4—541no—
760C3—24no—
761C3#1059465014yescomplemented
762C3#1059611511yescharacteristic, complemented
763C2—62no—
764C2—361no—
765C2—361no—
766C2—1081no—
767C2—1081no—
768C2#1172457911yescharacteristic
769C2#1172458911yescharacteristic
770C2D3×#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. #11723935C2semidirect
2. C3×#64103C2semidirect
3. C32×#897C2semidirect
4. #11723542C2semidirect
5. #11723541C2semidirect
6. D3×#3752C2semidirect
7. #11723532C2semidirect
8. #11723526C2semidirect
9. #11723514C2semidirect
10. #11723507C2semidirect
11. #11723462C2semidirect
12. #11723411C2semidirect
13. #11723407C2semidirect
14. #11723392C2semidirect
15. #11723392C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
24. C2×C32×Dic6C22semidirect
27. C2×#6292C22semidirect
31. C33×C4⋊C4C22semidirect
34. #88859C22semidirect
35. #88857C22semidirect
38. C3×#3752C22semidirect
39. C3×#3750C22semidirect
42. C32×C4⋊Dic3C22semidirect
43. C32×C4⋊Dic3C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
47. #88804C22semidirect
50. #88803C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
65. #64103D3semidirect
70. C3×#897D3semidirect
133. C2×C4×C3⋊D3C2×D3semidirect
137. C2×C3×Dic6C2×D3semidirect
147. C32×C4⋊C4C2×D3semidirect
148. C32×C4⋊C4C2×D3semidirect
168. #3752C2×D3semidirect
173. #3750C2×D3semidirect
181. C3×C4⋊Dic3C2×D3semidirect
182. C3×C4⋊Dic3C2×D3semidirect
233. #897C3⋊D3semidirect
356. C2×Dic6C2×C3⋊D3semidirect
361. C3×C4⋊C4D32semidirect
362. C3×C4⋊C4C2×C3⋊D3semidirect
395. C4⋊Dic3C2×C3⋊D3semidirect
396. C4⋊Dic3C2×C3⋊D3semidirect
487. C33#538semidirect
596. C4⋊C4D3×C3⋊D3semidirect
680. C32#5644semidirect
681. C32#5657semidirect
761. C3#10594650semidirect
762. C3#10596115semidirect

Maximal subgroups

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

subgroupindex
#117239352
C3×#641032
C32×#8972
#117235422
#117235412
D3×#37522
#117235322
#117235262
#117235142
#117235072
#117234622
#117234112
#117234072
#117233922
#105961153
#105946503