Finite Group Databasebeta

← #13175949

Subgroups — #13175949

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#11723927C211yesmaximal, characteristic, complemented
2C3×#64093C211yesmaximal, characteristic, complemented
3C32×#885C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723637C211yesmaximal, characteristic, complemented
6#11723626C211yesmaximal, characteristic, complemented
7#11723624C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723523C211yesmaximal, characteristic, complemented
11Dic3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
12#11723453C211yesmaximal, characteristic, complemented
13#11723435C211yesmaximal, characteristic, complemented
14#11723430C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596149—31nomaximal
17#10594301—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×Dic6C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31C33×C22⋊C4C2211yescharacteristic, complemented
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
35C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic, complemented
37C3×#3750C2211yescharacteristic, complemented
38C32×#217C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×C4×Dic3C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#124—31no—
54#64156—31no—
55#64155—31no—
56#64148—31no—
57#64146—31no—
58#64095—31no—
59#64095—34no—
60#64095—64no—
61#64093—31no—
62#64093D311yescharacteristic, complemented
63#64092—31no—
64#64091—31no—
65#64090—31no—
66C22⋊C4×C3⋊D3—31no—
67#64088—31no—
68#64085—31no—
69C4×C4⋊(C3⋊D3)—31no—
70C3×#885D314yescomplemented
71C3×#884—34no—
72#63983—34no—
73#63980—34no—
74#67⋊Dic3—34no—
75#63971—34no—
76#63922—34no—
77D3×(C2×D3)⋊C4—34no—
78#63907—34no—
79Dic3×D12—34no—
80#63891—34no—
81#63868—34no—
82#63861—34no—
83#63856—34no—
84C23×C33C2311yescharacteristic
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
94#6312—41no—
95C2×C3⋊(C3⋊Dic3)—41no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C3×#638—22no—
100C3×#638—41no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4⋊(C3⋊D3)—22no—
104C3×C4×C3⋊D3—41no—
105C32×#67—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C32×Dic6—41no—
110#6292—41no—
111#6290—41no—
112Dic3×C3⋊D3—41no—
113Dic3×C3⋊D3—41no—
114#5678—94no—
115#5617—91no—
116C23×C3⋊D3—31no—
117C22×D32—34no—
118C2×C32×Q8—31no—
119C2×C32×D4—31no—
120C2×#638—31no—
121C2×#638—34no—
122C2×#638—31no—
123C2×#638—64no—
124C2×#638C2×D311yescharacteristic
125C2×#638C2×D311yescharacteristic, complemented
126C22×C3⋊Dic3—31no—
127C22×C3⋊Dic3—34no—
128C22×C3⋊Dic3—64no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3C2×D311yescharacteristic
134C2×C3×#67—34no—
135C2×C3×#67—34no—
136C2×C3×#67C2×D314yes—
137C2×C3×D12—34no—
138C2×C3×C4×D3—34no—
139C2×C3×Dic6C2×D314yescomplemented
140C2×#626—34no—
141C2×#625—34no—
142C2×D3×Dic3—34no—
143C2×D3×Dic3—34no—
144C32×C22⋊C4—24no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4C2×D314yescomplemented
149C32×C22⋊C4C2×D311yescharacteristic, complemented
150C32×C42—31no—
151#3757—31no—
152#3757—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—34no—
159#3752—34no—
160#3752—31no—
161#3752—31no—
162#3752—64no—
163#3752—64no—
164#3752C2×D311yescharacteristic, complemented
165C4⋊(C3⋊Dic3)—31no—
166C4⋊(C3⋊Dic3)—31no—
167C4⋊(C3⋊Dic3)—34no—
168C4⋊(C3⋊Dic3)—34no—
169C4⋊(C3⋊Dic3)—64no—
170C4⋊(C3⋊Dic3)—64no—
171#3750—31no—
172#3750—31no—
173#3750—31no—
174#3750C2×D311yescharacteristic, complemented
175C4×C3⋊Dic3—31no—
176C3×#217C2×D314yescomplemented
177C3×(C2×D3)⋊C4—34no—
178C3×(C2×D3)⋊C4C2×D314yes—
179C3×(C2×D3)⋊C4C2×D314yes—
180C3×Dic3⋊C4—34no—
181C3×C4×Dic3C2×D314yescomplemented
182#3724—34no—
183#3724—34no—
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—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×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33C2411yescharacteristic
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—
212C3⋊(C3⋊Dic3)—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×#124—34no—
221C3×#121—91no—
222#947—94no—
223#946—94no—
224#939—94no—
225#939—91no—
226#939—91no—
227#937—94no—
228#937—91no—
229#937—91no—
230D4×Dic3—91no—
231D4×Dic3—91no—
232C2×(C2×D3)⋊C4—91no—
233#924—91no—
234#898—91no—
235#898—91no—
236#886—94no—
237#886—91no—
238#886—91no—
239#886—184no—
240#885—91no—
241#885C3⋊D311yescharacteristic, complemented
242#884—34no—
243#884—94no—
244#883—94no—
245#882—94no—
246#67⋊C4—94no—
247D3×C22⋊C4—94no—
248#879—94no—
249#876—94no—
250C4×D12—94no—
251C23×C32—24no—
252C23×C32—31no—
253C23×C32C22×D314yes—
254C23×C32C22×D311yescharacteristic
255C22×C3⋊D3—31no—
256C22×C3⋊D3—34no—
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—
270C32×D4—121no—
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×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280#638—22no—
281#638—41no—
282#638—121no—
283#638—121no—
284#638—124no—
285#638—128no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—31no—
288C2×C3⋊Dic3—31no—
289C2×C3⋊Dic3—34no—
290C2×C3⋊Dic3—34no—
291C2×C3⋊Dic3—34no—
292C2×C3⋊Dic3—64no—
293C2×C3⋊Dic3—64no—
294C2×C3⋊Dic3—64no—
295C2×C3⋊Dic3—121no—
296C2×C3⋊Dic3—124no—
297C2×C3⋊Dic3—128no—
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C4⋊(C3⋊D3)—22no—
301C4⋊(C3⋊D3)—121no—
302C4×C3⋊D3—41no—
303C4×C3⋊D3—121no—
304C4×C3⋊D3—121no—
305C3×#67—44no—
306C3×#67—68no—
307C3×#67—124no—
308C2×C3×Dic3—34no—
309C2×C3×Dic3—34no—
310C2×C3×Dic3C22×D314yes—
311C2×C3×Dic3C22×D314yes—
312C2×C3×Dic3C22×D314yes—
313C3×D12—68no—
314C3×C4×D3—124no—
315C3×Dic6—44no—
316#626—124no—
317#625—124no—
318D3×Dic3—124no—
319D3×Dic3—124no—
320#538—271noSylow
321C2×C33—41no—
322C2×C33C2×#4111yescharacteristic
323C2×C33H(5,𝔽2)11yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C3⋊(C3⋊D3)—41no—
326C3×C3⋊D3—22no—
327C3×C3⋊D3—41no—
328C32×D3—41no—
329C23×D3—94no—
330C23×D3—91no—
331C2×C3×Q8—34no—
332C2×C3×D4—34no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C22×C3×C4—91no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—94no—
340C2×#67—94no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—184no—
345C2×#67C2×C3⋊D311yescharacteristic
346C22×Dic3—94no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3—184no—
351C2×D12—34no—
352C2×D12—94no—
353C2×C4×D3—34no—
354C2×C4×D3—94no—
355C2×C4×D3—94no—
356C2×Dic6C2×C3⋊D311yescharacteristic, complemented
357C3×C4⋊C4—91no—
358C3×C22⋊C4—24no—
359C3×C22⋊C4—34no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4D3214yescomplemented
364C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
365C3×C42—34no—
366#217—94no—
367#217—94no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217C2×C3⋊D311yescharacteristic, complemented
372(C2×D3)⋊C4—34no—
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—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—94no—
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—184no—
387(C2×D3)⋊C4—184no—
388(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
389(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
390C4⋊Dic3—94no—
391C4⋊Dic3—94no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—184no—
396C4⋊Dic3—184no—
397Dic3⋊C4—34no—
398Dic3⋊C4—94no—
399Dic3⋊C4—94no—
400Dic3⋊C4—94no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403C4×Dic3—94no—
404C4×Dic3—91no—
405C4×Dic3C2×C3⋊D311yescharacteristic, complemented
406C22×C32—28no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—24no—
410C22×C32—21no—
411C22×C32—24no—
412C22×C32—24no—
413C22×C32—24no—
414C22×C32—44no—
415C22×C32—44no—
416C22×C32—61no—
417C22×C32—61no—
418C22×C32—61no—
419C22×C32C23×D314yes—
420C22×C32C23×D311yescharacteristic
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—61no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—64no—
430C2×C3⋊D3—64no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—124no—
433C2×C3⋊D3—124no—
434C2×C3⋊D3—124no—
435C2×C3⋊D3—124no—
436C2×C3⋊D3#23712yes—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—38no—
441C2×C3×D3—64no—
442C2×C3×D3—64no—
443C2×C3×D3—64no—
444C2×C3×D3—64no—
445C2×C3×D3—64no—
446D32—1216no—
447C32×C4—21no—
448C32×C4—21no—
449C32×C4—24no—
450C32×C4—24no—
451C32×C4—44no—
452C32×C4—44no—
453C32×C4—61no—
454C32×C4—61no—
455C32×C4—61no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—61no—
459C3⋊Dic3—61no—
460C3⋊Dic3—61no—
461C3⋊Dic3—64no—
462C3⋊Dic3—64no—
463C3⋊Dic3—64no—
464C3⋊Dic3—124no—
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—31no—
475#124—271no—
476#123—271no—
477#123—271no—
478C22⋊Q8—271no—
479#121—91no—
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—24no—
489C23×C3—34no—
490C23×C3—91no—
491C23×C3—91no—
492C23×C3C2×D3214yes—
493C23×C3C22×C3⋊D311yescharacteristic
494C22×D3—34no—
495C22×D3—34no—
496C22×D3—94no—
497C22×D3—91no—
498C22×D3—184no—
499C22×D3—182no—
500C22×D3—188no—
501C22×D3—361no—
502C22×D3—361no—
503C22×D3—364no—
504C22×D3—364no—
505C22×D3C22×C3⋊D311yescharacteristic
506C3×Q8—124no—
507C3×D4—124no—
508C3×D4—182no—
509C3×D4—182no—
510C3×D4—361no—
511C2×C3×C4—24no—
512C2×C3×C4—24no—
513C2×C3×C4—34no—
514C2×C3×C4—34no—
515C2×C3×C4—34no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—361no—
519C2×C3×C4C2×D3214yes—
520C2×C3×C4C2×D3214yes—
521C2×C3×C4C22×C3⋊D311yescharacteristic
522C2×C3×C4C22×C3⋊D311yescharacteristic
523#67—41no—
524#67—68no—
525#67—124no—
526#67—361no—
527#67—361no—
528#67—364no—
529#67—364no—
530#67—361no—
531#67—368no—
532C2×Dic3—34no—
533C2×Dic3—34no—
534C2×Dic3—94no—
535C2×Dic3—94no—
536C2×Dic3—94no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—184no—
541C2×Dic3—184no—
542C2×Dic3—184no—
543C2×Dic3—361no—
544C2×Dic3—361no—
545C2×Dic3—364no—
546C2×Dic3—361no—
547C2×Dic3—368no—
548C2×Dic3C22×C3⋊D311yescharacteristic
549C2×Dic3C22×C3⋊D311yescharacteristic
550C2×Dic3C22×C3⋊D311yescharacteristic
551D12—68no—
552D12—364no—
553C4×D3—124no—
554C4×D3—364no—
555C4×D3—364no—
556Dic6—41no—
557C2×C32—24no—
558C2×C32—24no—
559C2×C32—24no—
560C2×C32—48no—
561C2×C32—44no—
562C2×C32—41no—
563C2×C32—121no—
564C2×C32C2×#23711yescharacteristic
565C2×C32#100414yes—
566C2×C32#100411yescharacteristic
567C2×C32D3×#4114yes—
568C2×C32#100914yes—
569C2×C32#100911yescharacteristic
570C3⋊D3—22no—
571C3⋊D3—41no—
572C3⋊D3—121no—
573C3⋊D3—124no—
574C3⋊D3—244no—
575C3×D3—44no—
576C3×D3—68no—
577C3×D3—124no—
578C24—271no—
579C2×Q8—31no—
580C2×D4—31no—
581C2×D4—91no—
582C2×D4—91no—
583C2×D4—91no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C22×C4—91no—
588C22×C4—271no—
589C22×C4—271no—
590C22×C4—271no—
591C4⋊C4—91no—
592C4⋊C4—271no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—91no—
601C22⋊C4—271no—
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⋊C4D3×C3⋊D311yescharacteristic, complemented
611C42—31no—
612C42—271no—
613C22×C3—28no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—24no—
621C22×C3—44no—
622C22×C3—44no—
623C22×C3—64no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—92no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3C22×D3214yes—
633C22×C3C23×C3⋊D311yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—38no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—184no—
644C2×D3—184no—
645C2×D3—184no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—364no—
650C2×D3—364no—
651C2×D3—364no—
652C2×D3—364no—
653C2×D3—3616no—
654C3×C4—24no—
655C3×C4—24no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—44no—
659C3×C4—44no—
660C3×C4—64no—
661C3×C4—64no—
662C3×C4—64no—
663C3×C4—181no—
664C3×C4—181no—
665Dic3—21no—
666Dic3—21no—
667Dic3—21no—
668Dic3—64no—
669Dic3—64no—
670Dic3—184no—
671Dic3—184no—
672Dic3—184no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—364no—
677Dic3—364no—
678Dic3—364no—
679C32—24no—
680C32#561711yescharacteristic, complemented
681C32#567814yescomplemented
682C23—31no—
683C23—91no—
684C23—91no—
685C23—271no—
686C23—542no—
687C23—1081no—
688C23—1081no—
689C23C2×D3×C3⋊D311yescharacteristic
690Q8—121no—
691D4—121no—
692D4—182no—
693D4—182no—
694D4—361no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—361no—
707C2×C4—1081no—
708C2×C4—1081no—
709C2×C4—1081no—
710C2×C4C2×D3×C3⋊D311yescharacteristic
711C2×C4C2×D3×C3⋊D311yescharacteristic
712C2×C3—24no—
713C2×C3—24no—
714C2×C3—24no—
715C2×C3—48no—
716C2×C3—41no—
717C2×C3—44no—
718C2×C3—124no—
719C2×C3—182no—
720C2×C3—361no—
721C2×C3#6430814yes—
722C2×C3D3×#23714yes—
723C2×C3#6431314yes—
724C2×C3#6436111yescharacteristic
725C2×C3#41×C3⋊D311yescharacteristic
726C2×C3#6436611yescharacteristic
727D3—41no—
728D3—68no—
729D3—124no—
730D3—361no—
731D3—364no—
732D3—724no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—92no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—181no—
745C22—541no—
746C22—541no—
747C22—541no—
748C22—1084no—
749C22C22×D3×C3⋊D311yescharacteristic
750C4—21no—
751C4—21no—
752C4—61no—
753C4—61no—
754C4—61no—
755C4—181no—
756C4—181no—
757C4—541no—
758C4—541no—
759C4—541no—
760C3—24no—
761C3#1059430114yescomplemented
762C3#1059614911yescharacteristic, complemented
763C2—41no—
764C2—121no—
765C2—182no—
766C2—361no—
767C2—1081no—
768C2#1172458111yescharacteristic
769C2C3⋊D3×#23711yescharacteristic
770C2#1172458711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723927C2semidirect
2. C3×#64093C2semidirect
3. C32×#885C2semidirect
4. #11723643C2semidirect
5. #11723637C2semidirect
6. #11723626C2semidirect
7. #11723624C2semidirect
8. #11723541C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723523C2semidirect
11. Dic3×C4⋊(C3⋊D3)C2semidirect
12. #11723453C2semidirect
13. #11723435C2semidirect
14. #11723430C2semidirect
15. #11723392C2semidirect
20. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C3×#638C22semidirect
26. C2×C32×Dic6C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
31. C33×C22⋊C4C22semidirect
34. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
35. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
36. C3×#3752C22semidirect
37. C3×#3750C22semidirect
38. C32×#217C22semidirect
41. C32×C4×Dic3C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. #88806C22semidirect
49. #88803C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
62. #64093D3semidirect
70. C3×#885D3semidirect
125. C2×#638C2×D3semidirect
139. C2×C3×Dic6C2×D3semidirect
148. C32×C22⋊C4C2×D3semidirect
149. C32×C22⋊C4C2×D3semidirect
164. #3752C2×D3semidirect
174. #3750C2×D3semidirect
176. C3×#217C2×D3semidirect
181. C3×C4×Dic3C2×D3semidirect
241. #885C3⋊D3semidirect
356. C2×Dic6C2×C3⋊D3semidirect
363. C3×C22⋊C4D32semidirect
364. C3×C22⋊C4C2×C3⋊D3semidirect
371. #217C2×C3⋊D3semidirect
405. C4×Dic3C2×C3⋊D3semidirect
487. C33#538semidirect
610. C22⋊C4D3×C3⋊D3semidirect
680. C32#5617semidirect
681. C32#5678semidirect
761. C3#10594301semidirect
762. C3#10596149semidirect

Maximal subgroups

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

subgroupindex
#117239272
C3×#640932
C32×#8852
#117236432
#117236372
#117236262
#117236242
#117235412
C3⋊D3×(C2×D3)⋊C42
#117235232
Dic3×C4⋊(C3⋊D3)2
#117234532
#117234352
#117234302
#117233922
#105961493
#105943013