Finite Group Databasebeta

← #13177359

Subgroups — #13177359

Order 1728.

2436 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723981C211yesmaximal, characteristic, complemented
4C3×#64146C211yesmaximal, characteristic, complemented
5C32×#939C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723636C211yesmaximal, characteristic, complemented
8#11723633C211yesmaximal, characteristic, complemented
9#11723632C211yesmaximal, characteristic, complemented
10#11723599C211yesmaximal, characteristic, complemented
11#11723592C211yesmaximal, characteristic, complemented
12#11723542C211yesmaximal, characteristic, complemented
13#11723530C211yesmaximal, characteristic, complemented
14#11723486C211yesmaximal, characteristic, complemented
15#11723466C211yesmaximal, characteristic, complemented
16#10596078—31nomaximal
17#10595285—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic, complemented
24C2×#6312C2211yescharacteristic, complemented
25C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic
27C2×C3×#638C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic
29C2×C32×#67C2211yescharacteristic, complemented
30C22×C32×Dic3C2211yescharacteristic, complemented
31C3⋊D3×#67—24no—
32C2×#6293C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic
34C2×#6292C2211yescharacteristic
35C2×#6292C2211yescharacteristic, complemented
36C2×#6291C2211yescharacteristic, complemented
37C2×#6290C2211yescharacteristic
38C2×#6289C2211yescharacteristic, complemented
39#89031—24no—
40C2×Dic3×C3⋊D3C2211yescharacteristic
41C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic
44C3×#3752C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×#3828—31no—
57C2×D3×#67—34no—
58C2×#3804—34no—
59C32×#121—31no—
60#64149—31no—
61#64149—31no—
62#64149—34no—
63#64149—64no—
64#64147—31no—
65#64146—31no—
66#64146D311yescharacteristic, complemented
67#64139—31no—
68#64104—31no—
69#64101—31no—
70#64094—31no—
71#64094—31no—
72#64091—31no—
73#64091—31no—
74C3×#939D314yescomplemented
75C3×#937—34no—
76#63983—34no—
77#63979—34no—
78#63978—34no—
79#63977—34no—
80#63958—34no—
81#63953—34no—
82#63923—34no—
83#63915—34no—
84#63910—34no—
85#63878—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3×C3⋊D3—22no—
91C22×C3×C3⋊D3—41no—
92C22×C3×C3⋊D3—41no—
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C3×C3⋊D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×D3×C3⋊D3—41no—
99C33×D4—41no—
100C2×C33×C4C2311yescharacteristic
101#6312—22no—
102#6312—22no—
103#6312—41no—
104#6312—41no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊(C3⋊D3))—41no—
108C3×#638—22no—
109C3×#638—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C32×#67—22no—
113C32×#67—41no—
114C2×C32×Dic3—22no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6293—22no—
119#6292—22no—
120#6292—22no—
121#6292—41no—
122#6291—41no—
123#6290—22no—
124#6289—22no—
125Dic3×C3⋊D3D414yescomplemented
126#5607—94no—
127#5592—91no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3C2×D311yescharacteristic
130C23×C3×D3—34no—
131C22×D32—34no—
132C2×C32×D4—24no—
133C2×C32×D4—31no—
134C2×C32×D4—31no—
135C2×C32×D4C2×D314yescomplemented
136C2×C32×D4C2×D311yescharacteristic, complemented
137C22×C32×C4—31no—
138C2×#638—31no—
139C2×#638—31no—
140C2×#638—34no—
141C2×#638—34no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—34no—
146C2×#638—34no—
147C2×#638—31no—
148C2×#638—64no—
149C2×#638—64no—
150C2×#638—64no—
151C2×#638—64no—
152C2×#638C2×D311yescharacteristic
153C2×#638C2×D311yescharacteristic, complemented
154D4×C3⋊D3—64no—
155#3828—64no—
156C2×C4⋊(C3⋊D3)—31no—
157C2×C4⋊(C3⋊D3)—31no—
158C2×C4⋊(C3⋊D3)—31no—
159C2×C4⋊(C3⋊D3)—31no—
160C2×C4⋊(C3⋊D3)—34no—
161C2×C4⋊(C3⋊D3)—64no—
162C2×C4×C3⋊D3—31no—
163C2×C4×C3⋊D3—31no—
164C2×#634—31no—
165C2×C3×#67—34no—
166C2×C3×#67—34no—
167C2×C3×#67C2×D314yes—
168C2×C3×#67C2×D314yescomplemented
169C22×C3×Dic3C2×D314yescomplemented
170D3×#67—616no—
171C2×#627—34no—
172C2×#626—34no—
173C2×#626—34no—
174C2×#626—34no—
175C2×#626—34no—
176C2×#625—34no—
177C2×#624—34no—
178#3804—616no—
179C2×D3×Dic3—34no—
180C32×C4⋊C4—31no—
181C32×C22⋊C4—31no—
182C32×C22⋊C4—31no—
183#3757—31no—
184#3757C2×D311yescharacteristic, complemented
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752C2×D311yescharacteristic
190#3752C2×D311yescharacteristic, complemented
191C4⋊(C3⋊Dic3)—31no—
192C4×C3⋊Dic3—31no—
193C4×C3⋊Dic3—34no—
194C4×C3⋊Dic3—31no—
195C4×C3⋊Dic3—64no—
196C3×#217—34no—
197C3×#217C2×D314yescomplemented
198C3×(C2×D3)⋊C4—34no—
199C3×(C2×D3)⋊C4—34no—
200C3×(C2×D3)⋊C4C2×D314yescomplemented
201C3×Dic3⋊C4C2×D314yescomplemented
202Dic3⋊Dic3—34no—
203#3722—34no—
204#3722—34no—
205(C2×D3)⋊Dic3—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208Dic32—34no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33—21no—
213C22×C33—21no—
214C22×C33—21no—
215C22×C33C2411yescharacteristic
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)—21no—
219C2×C3⋊(C3⋊D3)—21no—
220C2×C3⋊(C3⋊D3)—21no—
221C2×C3⋊(C3⋊D3)—21no—
222C2×C3×C3⋊D3—21no—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3—21no—
225C2×C3×C3⋊D3—21no—
226C2×C3×C3⋊D3—21no—
227C2×C3×C3⋊D3—44no—
228C2×C3×C3⋊D3C2×D412yes—
229C2×C32×D3—21no—
230C2×C32×D3—21no—
231C2×C32×D3—21no—
232D3×C3⋊D3—44no—
233C33×C4—21no—
234C3⋊(C3⋊Dic3)—21no—
235C3⋊(C3⋊Dic3)C2×D412yes—
236C3×C3⋊Dic3—21no—
237C3×C3⋊Dic3—21no—
238C32×Dic3—21no—
239C32×Dic3—21no—
240C32×Dic3C2×D412yes—
241C22×#67—91no—
242C2×#237—91no—
243C2×D3×D4—94no—
244C2×#235—94no—
245C3×#121—34no—
246C3×#120—91no—
247#953—91no—
248#940—94no—
249#940—94no—
250#940—91no—
251#940—91no—
252#940—184no—
253#939—91no—
254#939C3⋊D311yescharacteristic, complemented
255#938—94no—
256#937—34no—
257#937—94no—
258#937—91no—
259#930—94no—
260#895—94no—
261#892—94no—
262#885—94no—
263#885—94no—
264#885—91no—
265#885—91no—
266#884—91no—
267#884—91no—
268#882—94no—
269#882—94no—
270#882—91no—
271#877—91no—
272C23×C32—24no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32C22×D314yes—
276C23×C32C22×D314yes—
277C23×C32C22×D311yescharacteristic
278C23×C32C22×D311yescharacteristic
279C22×C3⋊D3—22no—
280C22×C3⋊D3—31no—
281C22×C3⋊D3—31no—
282C22×C3⋊D3—34no—
283C22×C3⋊D3—34no—
284C22×C3⋊D3—41no—
285C22×C3⋊D3—41no—
286C22×C3⋊D3—64no—
287C22×C3⋊D3—64no—
288C22×C3⋊D3—62no—
289C22×C3⋊D3—121no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—34no—
294C22×C3×D3—34no—
295C22×C3×D3—68no—
296C22×C3×D3—124no—
297C22×C3×D3—124no—
298C22×C3×D3C22×D314yes—
299C2×D32—68no—
300C2×D32—124no—
301C2×D32—124no—
302C32×D4—41no—
303C32×D4—44no—
304C32×D4—48no—
305C32×D4—62no—
306C32×D4—121no—
307C2×C32×C4—24no—
308C2×C32×C4—31no—
309C2×C32×C4—31no—
310C2×C32×C4—31no—
311C2×C32×C4—62no—
312C2×C32×C4C22×D314yes—
313C2×C32×C4C22×D311yescharacteristic
314#638—22no—
315#638—41no—
316#638—62no—
317#638—62no—
318#638—62no—
319#638—68no—
320#638—68no—
321#638—128no—
322#638—128no—
323#638—121no—
324#638—121no—
325#638—121no—
326#638—124no—
327#638—124no—
328#638—128no—
329#638—128no—
330C2×C3⋊Dic3—31no—
331C2×C3⋊Dic3—31no—
332C2×C3⋊Dic3—34no—
333C2×C3⋊Dic3—34no—
334C2×C3⋊Dic3—64no—
335C2×C3⋊Dic3—64no—
336C2×C3⋊Dic3C22×D311yescharacteristic
337C2×C3⋊Dic3C22×D311yescharacteristic
338C4⋊(C3⋊D3)—62no—
339C4⋊(C3⋊D3)—62no—
340C4⋊(C3⋊D3)—121no—
341C4⋊(C3⋊D3)—124no—
342C4⋊(C3⋊D3)—128no—
343C4⋊(C3⋊D3)—121no—
344C4×C3⋊D3—34no—
345C4×C3⋊D3—62no—
346#634—62no—
347C3×#67—28no—
348C3×#67—44no—
349C3×#67—68no—
350C3×#67—124no—
351C2×C3×Dic3—28no—
352C2×C3×Dic3—34no—
353C2×C3×Dic3—34no—
354C2×C3×Dic3C22×D314yes—
355C2×C3×Dic3C22×D314yes—
356C2×C3×Dic3C22×D314yes—
357#627—68no—
358#626—68no—
359#626—68no—
360#626—124no—
361#626—124no—
362#625—68no—
363#624—68no—
364D3×Dic3—316no—
365#535—271noSylow
366C2×C33—41no—
367C2×C33—41no—
368C2×C33C22×D411yescharacteristic
369C2×C33H(5,𝔽2)11yescharacteristic
370C2×C33H(5,𝔽2)11yescharacteristic
371C3⋊(C3⋊D3)—41no—
372C3⋊(C3⋊D3)—41no—
373C3×C3⋊D3—22no—
374C3×C3⋊D3—41no—
375C32×D3—41no—
376C24×C3—91no—
377C23×D3—34no—
378C23×D3—94no—
379C23×D3—91no—
380C2×C3×D4—24no—
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4D3214yescomplemented
386C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
387C22×C3×C4—34no—
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—94no—
391C2×#67—94no—
392C2×#67—94no—
393C2×#67—94no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—94no—
398C2×#67—94no—
399C2×#67—91no—
400C2×#67—91no—
401C2×#67—91no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—184no—
405C2×#67—184no—
406C2×#67—184no—
407C2×#67—184no—
408C2×#67—184no—
409C2×#67C2×C3⋊D311yescharacteristic
410C2×#67C2×C3⋊D311yescharacteristic, complemented
411C22×Dic3—91no—
412C22×Dic3C2×C3⋊D311yescharacteristic, complemented
413#237—184no—
414D3×D4—1816no—
415#235—1816no—
416C2×D12—94no—
417C2×D12—94no—
418C2×D12—94no—
419C2×D12—91no—
420C2×D12—94no—
421C2×D12—91no—
422C2×D12—184no—
423C2×C4×D3—94no—
424C2×C4×D3—94no—
425C2×C4×D3—91no—
426C2×Dic6—94no—
427C2×Dic6—91no—
428C3×C4⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—91no—
432C3×C22⋊C4—91no—
433C3×C22⋊C4—91no—
434#217—34no—
435#217—94no—
436#217—91no—
437#217—91no—
438#217C2×C3⋊D311yescharacteristic, complemented
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—94no—
442(C2×D3)⋊C4—94no—
443(C2×D3)⋊C4—94no—
444(C2×D3)⋊C4—94no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
449C4⋊Dic3—94no—
450Dic3⋊C4—91no—
451Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
452C4×Dic3—94no—
453C4×Dic3—94no—
454C4×Dic3—91no—
455C4×Dic3—91no—
456C4×Dic3—184no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—24no—
466C22×C32—24no—
467C22×C32—24no—
468C22×C32—24no—
469C22×C32—24no—
470C22×C32—44no—
471C22×C32—44no—
472C22×C32—44no—
473C22×C32—44no—
474C22×C32—44no—
475C22×C32—44no—
476C22×C32—61no—
477C22×C32—61no—
478C22×C32—61no—
479C22×C32C23×D314yes—
480C22×C32C23×D311yescharacteristic
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—44no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—61no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—61no—
493C2×C3⋊D3—64no—
494C2×C3⋊D3—64no—
495C2×C3⋊D3—64no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—124no—
500C2×C3⋊D3—124no—
501C2×C3⋊D3—124no—
502C2×C3⋊D3—124no—
503C2×C3⋊D3—124no—
504C2×C3⋊D3—124no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3D3×D412yes—
507C2×C3×D3—24no—
508C2×C3×D3—24no—
509C2×C3×D3—24no—
510C2×C3×D3—38no—
511C2×C3×D3—64no—
512C2×C3×D3—64no—
513C2×C3×D3—64no—
514C2×C3×D3—64no—
515C2×C3×D3—64no—
516C2×C3×D3—1216no—
517D32—1216no—
518C32×C4—28no—
519C32×C4—24no—
520C32×C4—21no—
521C32×C4—32no—
522C32×C4—61no—
523C32×C4—61no—
524C3⋊Dic3—21no—
525C3⋊Dic3—21no—
526C3⋊Dic3—32no—
527C3⋊Dic3—38no—
528C3⋊Dic3—68no—
529C3⋊Dic3—68no—
530C3⋊Dic3—61no—
531C3⋊Dic3—64no—
532C3×Dic3—24no—
533C3×Dic3—24no—
534C3×Dic3—64no—
535C3×Dic3—64no—
536C3×Dic3D3×D418yes—
537C2×#41—271no—
538C22×D4—271no—
539#127—271no—
540#127—271no—
541#124—271no—
542#124—271no—
543#121—31no—
544#121—271no—
545#121—271no—
546#121—271no—
547#120—91no—
548#120—271no—
549#120—271no—
550#120—271no—
551#117—271no—
552C33#53511yescharacteristic, complemented, Sylow
553C23×C3—24no—
554C23×C3—24no—
555C23×C3—34no—
556C23×C3—91no—
557C23×C3—91no—
558C23×C3—182no—
559C23×C3—361no—
560C23×C3—361no—
561C23×C3C2×D3214yes—
562C23×C3C2×D3214yes—
563C23×C3C22×C3⋊D311yescharacteristic
564C23×C3C22×C3⋊D311yescharacteristic
565C22×D3—34no—
566C22×D3—34no—
567C22×D3—68no—
568C22×D3—94no—
569C22×D3—94no—
570C22×D3—91no—
571C22×D3—91no—
572C22×D3—124no—
573C22×D3—124no—
574C22×D3—184no—
575C22×D3—184no—
576C22×D3—182no—
577C22×D3—188no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—364no—
581C22×D3—364no—
582C22×D3C22×C3⋊D311yescharacteristic
583C3×D4—44no—
584C3×D4—41no—
585C3×D4—48no—
586C3×D4—68no—
587C3×D4—124no—
588C3×D4—182no—
589C3×D4—361no—
590C2×C3×C4—24no—
591C2×C3×C4—34no—
592C2×C3×C4—34no—
593C2×C3×C4—34no—
594C2×C3×C4—68no—
595C2×C3×C4—91no—
596C2×C3×C4—91no—
597C2×C3×C4C2×D3214yes—
598C2×C3×C4C22×C3⋊D311yescharacteristic
599#67—22no—
600#67—41no—
601#67—68no—
602#67—124no—
603#67—182no—
604#67—182no—
605#67—188no—
606#67—182no—
607#67—182no—
608#67—188no—
609#67—188no—
610#67—182no—
611#67—368no—
612#67—368no—
613#67—361no—
614#67—364no—
615#67—364no—
616#67—364no—
617#67—361no—
618#67—361no—
619#67—368no—
620#67—368no—
621C2×Dic3—22no—
622C2×Dic3—34no—
623C2×Dic3—34no—
624C2×Dic3—94no—
625C2×Dic3—91no—
626C2×Dic3—94no—
627C2×Dic3—94no—
628C2×Dic3—91no—
629C2×Dic3—184no—
630C2×Dic3—184no—
631C2×Dic3C22×C3⋊D311yescharacteristic
632C2×Dic3C22×C3⋊D311yescharacteristic
633C2×Dic3C22×C3⋊D311yescharacteristic
634D12—188no—
635D12—188no—
636D12—364no—
637D12—361no—
638D12—368no—
639D12—364no—
640D12—361no—
641C4×D3—916no—
642C4×D3—188no—
643C4×D3—182no—
644Dic6—182no—
645Dic6—188no—
646C2×C32—24no—
647C2×C32—24no—
648C2×C32—24no—
649C2×C32—41no—
650C2×C32—41no—
651C2×C32—44no—
652C2×C32—44no—
653C2×C32—84no—
654C2×C32—84no—
655C2×C32—121no—
656C2×C32C2×D3×D414yes—
657C2×C32C2×D3×D411yescharacteristic
658C2×C32#100414yes—
659C2×C32#100411yescharacteristic
660C2×C32#100411yescharacteristic
661C2×C32#100914yes—
662C3⋊D3—22no—
663C3⋊D3—41no—
664C3⋊D3—121no—
665C3⋊D3—121no—
666C3⋊D3—124no—
667C3⋊D3—124no—
668C3⋊D3—244no—
669C3⋊D3—244no—
670C3×D3—44no—
671C3×D3—68no—
672C3×D3—124no—
673C24—91no—
674C24—271no—
675#41—544no—
676C2×Q8—271no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—91no—
680C2×D4—91no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—271no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—271no—
689C2×D4—271no—
690C2×D4—271no—
691C2×D4—544no—
692C2×D4D3×C3⋊D311yescharacteristic, complemented
693C22×C4—31no—
694C22×C4—271no—
695C22×C4—271no—
696C4⋊C4—31no—
697C4⋊C4—271no—
698C22⋊C4—31no—
699C22⋊C4—31no—
700C22⋊C4—91no—
701C22⋊C4—91no—
702C22⋊C4—91no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C42—271no—
709C42—271no—
710C22×C3—24no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—24no—
723C22×C3—44no—
724C22×C3—44no—
725C22×C3—44no—
726C22×C3—44no—
727C22×C3—44no—
728C22×C3—44no—
729C22×C3—64no—
730C22×C3—64no—
731C22×C3—64no—
732C22×C3—92no—
733C22×C3—181no—
734C22×C3—181no—
735C22×C3—181no—
736C22×C3—181no—
737C22×C3—181no—
738C22×C3—364no—
739C22×C3C22×D3214yes—
740C22×C3C23×C3⋊D311yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—38no—
745C2×D3—64no—
746C2×D3—64no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—1216no—
751C2×D3—184no—
752C2×D3—184no—
753C2×D3—184no—
754C2×D3—184no—
755C2×D3—184no—
756C2×D3—184no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—181no—
760C2×D3—181no—
761C2×D3—181no—
762C2×D3—181no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3—364no—
766C2×D3—364no—
767C2×D3—364no—
768C2×D3—364no—
769C2×D3—364no—
770C2×D3—3616no—
771C3×C4—28no—
772C3×C4—24no—
773C3×C4—21no—
774C3×C4—38no—
775C3×C4—64no—
776C3×C4—64no—
777C3×C4—181no—
778C3×C4—181no—
779Dic3—21no—
780Dic3—21no—
781Dic3—64no—
782Dic3—64no—
783Dic3—98no—
784Dic3—92no—
785Dic3—188no—
786Dic3—188no—
787Dic3—184no—
788Dic3—181no—
789Dic3D4×C3⋊D312yes—
790C32—24no—
791C32#559211yescharacteristic, complemented
792C32#560714yescomplemented
793C23—31no—
794C23—91no—
795C23—91no—
796C23—182no—
797C23—271no—
798C23—271no—
799C23—361no—
800C23—361no—
801C23—542no—
802C23—1081no—
803C23—1081no—
804C23C2×D3×C3⋊D311yescharacteristic
805C23C2×D3×C3⋊D311yescharacteristic
806Q8—542no—
807D4—41no—
808D4—62no—
809D4—121no—
810D4—182no—
811D4—361no—
812D4—542no—
813D4—542no—
814D4—542no—
815D4—542no—
816D4—542no—
817D4—1081no—
818D4—1081no—
819D4—1081no—
820D4—1081no—
821D4—1081no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—31no—
825C2×C4—62no—
826C2×C4—91no—
827C2×C4—91no—
828C2×C4—274no—
829C2×C4—271no—
830C2×C4—271no—
831C2×C4—542no—
832C2×C4C2×D3×C3⋊D311yescharacteristic
833C2×C3—24no—
834C2×C3—24no—
835C2×C3—24no—
836C2×C3—44no—
837C2×C3—44no—
838C2×C3—41no—
839C2×C3—41no—
840C2×C3—84no—
841C2×C3—84no—
842C2×C3—124no—
843C2×C3—182no—
844C2×C3—361no—
845C2×C3D32×D414yes—
846C2×C3#6431414yes—
847C2×C3#6433014yes—
848C2×C3C2×D4×C3⋊D311yescharacteristic
849C2×C3#6436111yescharacteristic
850C2×C3#6436611yescharacteristic
851D3—41no—
852D3—68no—
853D3—124no—
854D3—364no—
855D3—364no—
856D3—361no—
857D3—361no—
858D3—724no—
859D3—724no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—61no—
867C22—61no—
868C22—61no—
869C22—92no—
870C22—181no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22—181no—
875C22—364no—
876C22—541no—
877C22—541no—
878C22—541no—
879C22—541no—
880C22—541no—
881C22—541no—
882C22—1084no—
883C22C22×D3×C3⋊D311yescharacteristic
884C4—21no—
885C4—32no—
886C4—61no—
887C4—61no—
888C4—181no—
889C4—181no—
890C4—272no—
891C4—541no—
892C3—24no—
893C3#1059528514yescomplemented
894C3#1059607811yescharacteristic, complemented
895C2—41no—
896C2—41no—
897C2—121no—
898C2—182no—
899C2—361no—
900C2—1081no—
901C2—1081no—
902C2D3×D4×C3⋊D311yescharacteristic
903C2#1172458911yescharacteristic
904C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#535
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×#67C2semidirect
2. C2×#89031C2semidirect
3. #11723981C2semidirect
4. C3×#64146C2semidirect
5. C32×#939C2semidirect
6. #11723643C2semidirect
7. #11723636C2semidirect
8. #11723633C2semidirect
9. #11723632C2semidirect
10. #11723599C2semidirect
11. #11723592C2semidirect
12. #11723542C2semidirect
13. #11723530C2semidirect
14. #11723486C2semidirect
15. #11723466C2semidirect
20. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
23. C2×#6312C22semidirect
24. C2×#6312C22semidirect
25. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
27. C2×C3×#638C22semidirect
29. C2×C32×#67C22semidirect
30. C22×C32×Dic3C22semidirect
32. C2×#6293C22semidirect
35. C2×#6292C22semidirect
36. C2×#6291C22semidirect
38. C2×#6289C22semidirect
41. C4×C3⋊(C3⋊Dic3)C22semidirect
42. C3×#3757C22semidirect
44. C3×#3752C22semidirect
45. C32×#217C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
66. #64146D3semidirect
74. C3×#939D3semidirect
125. Dic3×C3⋊D3D4semidirect
135. C2×C32×D4C2×D3semidirect
136. C2×C32×D4C2×D3semidirect
153. C2×#638C2×D3semidirect
168. C2×C3×#67C2×D3semidirect
169. C22×C3×Dic3C2×D3semidirect
184. #3757C2×D3semidirect
190. #3752C2×D3semidirect
197. C3×#217C2×D3semidirect
200. C3×(C2×D3)⋊C4C2×D3semidirect
201. C3×Dic3⋊C4C2×D3semidirect
254. #939C3⋊D3semidirect
385. C2×C3×D4D32semidirect
386. C2×C3×D4C2×C3⋊D3semidirect
410. C2×#67C2×C3⋊D3semidirect
412. C22×Dic3C2×C3⋊D3semidirect
438. #217C2×C3⋊D3semidirect
448. (C2×D3)⋊C4C2×C3⋊D3semidirect
451. Dic3⋊C4C2×C3⋊D3semidirect
552. C33#535semidirect
692. C2×D4D3×C3⋊D3semidirect
791. C32#5592semidirect
792. C32#5607semidirect
893. C3#10595285semidirect
894. C3#10596078semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×#672
C2×#890312
#117239812
C3×#641462
C32×#9392
#117236432
#117236362
#117236332
#117236322
#117235992
#117235922
#117235422
#117235302
#117234862
#117234662
#105960783
#105952853