Finite Group Databasebeta

← #13177382

Subgroups — #13177382

Order 1728.

2524 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×#89031C211yesmaximal, characteristic, complemented
3#11723978C211yesmaximal, characteristic, complemented
4C3×#64149C211yesmaximal, characteristic, complemented
5C32×#939C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723639C211yesmaximal, characteristic, complemented
8#11723633C211yesmaximal, characteristic, complemented
9#11723632C211yesmaximal, characteristic, complemented
10#11723631C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723541C211yesmaximal, characteristic, complemented
13#11723482C211yesmaximal, characteristic, complemented
14#11723469C211yesmaximal, characteristic, complemented
15#11723419C211yesmaximal, characteristic, complemented
16#10596078—31nomaximal
17#10595299—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic, complemented
27C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic
29C2×C32×#67C2211yescharacteristic, complemented
30C22×C32×Dic3C2211yescharacteristic, complemented
31#89039—24no—
32C2×#6293C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic
34C2×#6292C2211yescharacteristic
35C2×#6292C2211yescharacteristic, complemented
36C2×#6291C2211yescharacteristic
37C2×#6290C2211yescharacteristic, complemented
38C2×#6289C2211yescharacteristic
39#89031—24no—
40C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
41#88864C2211yescharacteristic, complemented
42#88859C2211yescharacteristic
43#88859C2211yescharacteristic, complemented
44C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×#3828—31no—
57C2×#3811—34no—
58C2×#3804—34no—
59C32×#121—31no—
60#64149—31no—
61#64149D311yescharacteristic, complemented
62#64147—31no—
63#64146—31no—
64#64146—31no—
65#64146—34no—
66#64146—64no—
67#64139—31no—
68#64104—31no—
69#64101—31no—
70#64094—31no—
71#64094—31no—
72#64091—31no—
73#64091—31no—
74C3×#940—34no—
75C3×#939D314yescomplemented
76#63983—34no—
77#63981—34no—
78#63979—34no—
79#63978—34no—
80#63970—34no—
81#63959—34no—
82#63922—34no—
83#63886—34no—
84#63852—34no—
85#63836—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—41no—
90C22×C3⋊(C3⋊D3)—41no—
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
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—41no—
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C3×#638—22no—
106C3×#638—22no—
107C3×#638—41no—
108C3×#638—41no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C3×C4⋊(C3⋊D3)—41no—
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—22no—
123#6290—41no—
124#6289D414yescomplemented
125Dic3×C3⋊D3—22no—
126#5715—91no—
127#5607—94no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3—34no—
130C23×C3⋊D3—31no—
131C23×C3⋊D3—64no—
132C22×D32—34no—
133C2×C32×D4—24no—
134C2×C32×D4—31no—
135C2×C32×D4—31no—
136C2×C32×D4C2×D314yescomplemented
137C2×C32×D4C2×D311yescharacteristic, complemented
138C22×C32×C4—31no—
139C2×#638—31no—
140C2×#638—34no—
141C2×#638—31no—
142C2×#638—34no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—64no—
146C2×#638—64no—
147C2×#638C2×D311yescharacteristic
148C2×#638C2×D311yescharacteristic, complemented
149C2×#638C2×D311yescharacteristic, complemented
150C2×#638C2×D311yescharacteristic, complemented
151D4×C3⋊D3—64no—
152#3828—64no—
153C2×C4⋊(C3⋊D3)—31no—
154C2×C4⋊(C3⋊D3)—31no—
155C2×C4⋊(C3⋊D3)—31no—
156C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×#634—31no—
160C2×C3×#67—34no—
161C2×C3×#67—34no—
162C2×C3×#67—34no—
163C2×C3×#67—34no—
164C2×C3×#67C2×D314yes—
165C2×C3×#67C2×D314yescomplemented
166C22×C3×Dic3C2×D314yescomplemented
167C2×C3×D12—34no—
168#3811—616no—
169C2×#627—34no—
170C2×#626—34no—
171C2×#626—34no—
172C2×#626—34no—
173C2×#626—34no—
174C2×#625—34no—
175C2×#624—34no—
176#3804—616no—
177C2×D3×Dic3—34no—
178C32×C4⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181#3757—31no—
182#3757—34no—
183#3757—31no—
184#3757—64no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—34no—
190#3752—34no—
191#3752—31no—
192#3752—31no—
193#3752—64no—
194#3752—64no—
195C4⋊(C3⋊Dic3)—31no—
196C4×C3⋊Dic3—31no—
197C4×C3⋊Dic3C2×D311yescharacteristic, complemented
198C3×#217C2×D314yescomplemented
199C3×(C2×D3)⋊C4C2×D314yescomplemented
200C3×Dic3⋊C4C2×D314yescomplemented
201C3×C4×Dic3—34no—
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)—44no—
222C2×C3⋊(C3⋊D3)C2×D412yes—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3—21no—
225C2×C3×C3⋊D3—21no—
226C2×C3×C3⋊D3—21no—
227C2×C3×C3⋊D3—21no—
228C2×C3×C3⋊D3—21no—
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)—21no—
236C3×C3⋊Dic3—21no—
237C3×C3⋊Dic3C2×D412yes—
238C32×Dic3—21no—
239C32×Dic3—21no—
240C32×Dic3C2×D412yes—
241C2×#237—91no—
242C2×D3×D4—94no—
243C2×D3×D4—91no—
244C2×#235—94no—
245C3×#127—91no—
246C3×#121—34no—
247#940—34no—
248#940—94no—
249#940—91no—
250#939—91no—
251#939—91no—
252#939—91no—
253#939C3⋊D311yescharacteristic, complemented
254#938—94no—
255#937—94no—
256#937—94no—
257#937—91no—
258#937—91no—
259#937—91no—
260#937—91no—
261#937—184no—
262#936—91no—
263#930—94no—
264#895—94no—
265#892—94no—
266#885—94no—
267#885—94no—
268#882—94no—
269#882—94no—
270#875—91no—
271#872—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—31no—
280C22×C3⋊D3—31no—
281C22×C3⋊D3—34no—
282C22×C3⋊D3—34no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—64no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—68no—
288C22×C3⋊D3—128no—
289C22×C3⋊D3—121no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3—121no—
293C22×C3⋊D3—124no—
294C22×C3⋊D3—124no—
295C22×C3⋊D3—128no—
296C22×C3⋊D3—128no—
297C22×C3⋊D3C22×D311yescharacteristic
298C22×C3⋊D3C22×D311yescharacteristic
299C22×C3×D3—34no—
300C22×C3×D3—34no—
301C22×C3×D3C22×D314yes—
302C2×D32—68no—
303C2×D32—124no—
304C2×D32—124no—
305C32×D4—41no—
306C32×D4—44no—
307C32×D4—48no—
308C32×D4—62no—
309C32×D4—121no—
310C2×C32×C4—24no—
311C2×C32×C4—31no—
312C2×C32×C4—31no—
313C2×C32×C4—31no—
314C2×C32×C4—62no—
315C2×C32×C4C22×D314yes—
316C2×C32×C4C22×D311yescharacteristic
317#638—22no—
318#638—22no—
319#638—41no—
320#638—41no—
321#638—62no—
322#638—62no—
323#638—68no—
324#638—128no—
325#638—121no—
326#638—121no—
327#638—124no—
328#638—128no—
329C2×C3⋊Dic3—31no—
330C2×C3⋊Dic3—31no—
331C2×C3⋊Dic3—34no—
332C2×C3⋊Dic3—34no—
333C2×C3⋊Dic3—64no—
334C2×C3⋊Dic3—64no—
335C2×C3⋊Dic3C22×D311yescharacteristic
336C2×C3⋊Dic3C22×D311yescharacteristic
337C4⋊(C3⋊D3)—41no—
338C4⋊(C3⋊D3)—62no—
339C4⋊(C3⋊D3)—62no—
340C4⋊(C3⋊D3)—121no—
341C4×C3⋊D3—34no—
342C4×C3⋊D3—62no—
343#634—62no—
344C3×#67—28no—
345C3×#67—44no—
346C3×#67—68no—
347C3×#67—68no—
348C3×#67—124no—
349C3×#67—124no—
350C2×C3×Dic3—28no—
351C2×C3×Dic3—34no—
352C2×C3×Dic3—34no—
353C2×C3×Dic3C22×D314yes—
354C2×C3×Dic3C22×D314yes—
355C2×C3×Dic3C22×D314yes—
356C3×D12—124no—
357#627—68no—
358#626—68no—
359#626—68no—
360#626—68no—
361#626—124no—
362#625—124no—
363#624—316no—
364D3×Dic3—68no—
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)—22no—
372C3⋊(C3⋊D3)—41no—
373C3×C3⋊D3—41no—
374C3×C3⋊D3—41no—
375C32×D3—41no—
376C23×D3—94no—
377C23×D3—94no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—184no—
381C2×C3×D4—24no—
382C2×C3×D4—34no—
383C2×C3×D4—34no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C2×C3×D4—91no—
389C2×C3×D4D3214yescomplemented
390C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
391C22×C3×C4—34no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—94no—
397C2×#67—94no—
398C2×#67—91no—
399C2×#67—94no—
400C2×#67—94no—
401C2×#67—91no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—91no—
405C2×#67—91no—
406C2×#67—184no—
407C2×#67—184no—
408C2×#67C2×C3⋊D311yescharacteristic
409C2×#67C2×C3⋊D311yescharacteristic, complemented
410C22×Dic3—91no—
411C22×Dic3C2×C3⋊D311yescharacteristic, complemented
412#237—184no—
413D3×D4—184no—
414D3×D4—1816no—
415#235—1816no—
416C2×D12—34no—
417C2×D12—94no—
418C2×D12—94no—
419C2×D12—91no—
420C2×D12—94no—
421C2×C4×D3—94no—
422C2×C4×D3—91no—
423C2×C4×D3—94no—
424C2×Dic6—94no—
425C2×Dic6—91no—
426C3×C4⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—34no—
429C3×C42—91no—
430#217—94no—
431#217—94no—
432#217—91no—
433#217—91no—
434#217—91no—
435#217—184no—
436#217C2×C3⋊D311yescharacteristic, complemented
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—94no—
440(C2×D3)⋊C4—94no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—94no—
443(C2×D3)⋊C4—94no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—184no—
449(C2×D3)⋊C4—184no—
450(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
451C4⋊Dic3—94no—
452Dic3⋊C4—91no—
453Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
454C4×Dic3—34no—
455C4×Dic3—94no—
456C4×Dic3—91no—
457C22×C32—28no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—24no—
464C22×C32—21no—
465C22×C32—24no—
466C22×C32—24no—
467C22×C32—24no—
468C22×C32—24no—
469C22×C32—24no—
470C22×C32—24no—
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—21no—
487C2×C3⋊D3—32no—
488C2×C3⋊D3—38no—
489C2×C3⋊D3—68no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—68no—
493C2×C3⋊D3—61no—
494C2×C3⋊D3—61no—
495C2×C3⋊D3—61no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—64no—
500C2×C3⋊D3—64no—
501C2×C3⋊D3—124no—
502C2×C3⋊D3—124no—
503C2×C3⋊D3—124no—
504C2×C3⋊D3—124no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—124no—
507C2×C3⋊D3—1216no—
508C2×C3⋊D3—1232no—
509C2×C3×D3—24no—
510C2×C3×D3—24no—
511C2×C3×D3—24no—
512C2×C3×D3—64no—
513C2×C3×D3—64no—
514C2×C3×D3—64no—
515C2×C3×D3—64no—
516C2×C3×D3—64no—
517C2×C3×D3—64no—
518D32—1216no—
519C32×C4—21no—
520C32×C4—24no—
521C32×C4—32no—
522C32×C4—44no—
523C32×C4—61no—
524C32×C4—61no—
525C3⋊Dic3—21no—
526C3⋊Dic3—61no—
527C3⋊Dic3—61no—
528C3⋊Dic3—64no—
529C3⋊Dic3—64no—
530C3⋊Dic3—124no—
531C3⋊Dic3—124no—
532C3⋊Dic3D3×D412yes—
533C3×Dic3—24no—
534C3×Dic3—24no—
535C3×Dic3—38no—
536C3×Dic3—64no—
537C3×Dic3D3×D418yes—
538C2×#41—271no—
539C22×D4—271no—
540#127—91no—
541#127—271no—
542#124—271no—
543#124—271no—
544#121—31no—
545#121—271no—
546#121—271no—
547#121—271no—
548#120—271no—
549#120—271no—
550#120—271no—
551#120—271no—
552#117—271no—
553C33#53511yescharacteristic, complemented, Sylow
554C23×C3—24no—
555C23×C3—24no—
556C23×C3—34no—
557C23×C3—91no—
558C23×C3—91no—
559C23×C3C2×D3214yes—
560C23×C3C2×D3214yes—
561C23×C3C22×C3⋊D311yescharacteristic
562C23×C3C22×C3⋊D311yescharacteristic
563C22×D3—34no—
564C22×D3—34no—
565C22×D3—94no—
566C22×D3—91no—
567C22×D3—94no—
568C22×D3—91no—
569C22×D3—184no—
570C22×D3—184no—
571C22×D3—182no—
572C22×D3—188no—
573C22×D3—182no—
574C22×D3—188no—
575C22×D3—368no—
576C22×D3—361no—
577C22×D3—361no—
578C22×D3—364no—
579C22×D3—364no—
580C22×D3—364no—
581C22×D3—364no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3—368no—
585C22×D3—368no—
586C22×D3C22×C3⋊D311yescharacteristic
587C3×D4—44no—
588C3×D4—41no—
589C3×D4—48no—
590C3×D4—68no—
591C3×D4—124no—
592C3×D4—182no—
593C3×D4—182no—
594C3×D4—361no—
595C3×D4—361no—
596C3×D4—361no—
597C2×C3×C4—24no—
598C2×C3×C4—34no—
599C2×C3×C4—34no—
600C2×C3×C4—34no—
601C2×C3×C4—68no—
602C2×C3×C4—91no—
603C2×C3×C4—91no—
604C2×C3×C4C2×D3214yes—
605C2×C3×C4C22×C3⋊D311yescharacteristic
606#67—22no—
607#67—41no—
608#67—68no—
609#67—68no—
610#67—124no—
611#67—124no—
612#67—182no—
613#67—188no—
614#67—182no—
615#67—188no—
616#67—182no—
617#67—368no—
618#67—361no—
619#67—361no—
620#67—364no—
621#67—364no—
622#67—361no—
623#67—368no—
624C2×Dic3—22no—
625C2×Dic3—34no—
626C2×Dic3—34no—
627C2×Dic3—94no—
628C2×Dic3—94no—
629C2×Dic3—91no—
630C2×Dic3—91no—
631C2×Dic3—184no—
632C2×Dic3—184no—
633C2×Dic3—182no—
634C2×Dic3C22×C3⋊D311yescharacteristic
635C2×Dic3C22×C3⋊D311yescharacteristic
636C2×Dic3C22×C3⋊D311yescharacteristic
637D12—124no—
638D12—188no—
639D12—188no—
640D12—182no—
641D12—364no—
642C4×D3—916no—
643C4×D3—94no—
644C4×D3—188no—
645Dic6—182no—
646Dic6—188no—
647C2×C32—24no—
648C2×C32—24no—
649C2×C32—24no—
650C2×C32—48no—
651C2×C32—41no—
652C2×C32—41no—
653C2×C32—44no—
654C2×C32—44no—
655C2×C32—84no—
656C2×C32—121no—
657C2×C32C2×D3×D414yes—
658C2×C32C2×D3×D411yescharacteristic
659C2×C32#100414yes—
660C2×C32#100411yescharacteristic
661C2×C32#100411yescharacteristic
662C2×C32#100914yes—
663C3⋊D3—41no—
664C3⋊D3—41no—
665C3⋊D3—62no—
666C3⋊D3—68no—
667C3⋊D3—128no—
668C3⋊D3—128no—
669C3⋊D3—121no—
670C3⋊D3—124no—
671C3×D3—44no—
672C3×D3—124no—
673C3×D3—124no—
674C24—271no—
675C24—271no—
676#41—544no—
677C2×Q8—271no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—91no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—91no—
684C2×D4—91no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—271no—
689C2×D4—271no—
690C2×D4—271no—
691C2×D4—271no—
692C2×D4—544no—
693C2×D4D3×C3⋊D311yescharacteristic, complemented
694C22×C4—31no—
695C22×C4—271no—
696C22×C4—271no—
697C4⋊C4—31no—
698C4⋊C4—271no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4—271no—
709C42—91no—
710C42—271no—
711C22×C3—28no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—24no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—24no—
725C22×C3—44no—
726C22×C3—44no—
727C22×C3—44no—
728C22×C3—44no—
729C22×C3—44no—
730C22×C3—64no—
731C22×C3—64no—
732C22×C3—64no—
733C22×C3—181no—
734C22×C3—181no—
735C22×C3—181no—
736C22×C3—181no—
737C22×C3—181no—
738C22×C3—181no—
739C22×C3C22×D3214yes—
740C22×C3C23×C3⋊D311yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—64no—
745C2×D3—64no—
746C2×D3—64no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—98no—
751C2×D3—92no—
752C2×D3—188no—
753C2×D3—184no—
754C2×D3—184no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—188no—
758C2×D3—184no—
759C2×D3—184no—
760C2×D3—184no—
761C2×D3—181no—
762C2×D3—181no—
763C2×D3—181no—
764C2×D3—364no—
765C2×D3—364no—
766C2×D3—364no—
767C2×D3—364no—
768C2×D3—364no—
769C2×D3—3616no—
770C2×D3—3616no—
771C2×D3—364no—
772C2×D3—3632no—
773C3×C4—24no—
774C3×C4—21no—
775C3×C4—38no—
776C3×C4—44no—
777C3×C4—64no—
778C3×C4—64no—
779C3×C4—92no—
780C3×C4—181no—
781Dic3—21no—
782Dic3—21no—
783Dic3—38no—
784Dic3—64no—
785Dic3—184no—
786Dic3—184no—
787Dic3—181no—
788Dic3—181no—
789Dic3—364no—
790Dic3—364no—
791Dic3D4×C3⋊D312yes—
792C32—24no—
793C32#560714yescomplemented
794C32#571511yescharacteristic, complemented
795C23—31no—
796C23—91no—
797C23—91no—
798C23—271no—
799C23—271no—
800C23—542no—
801C23—542no—
802C23—1081no—
803C23—1081no—
804C23—1081no—
805C23—1081no—
806C23C2×D3×C3⋊D311yescharacteristic
807C23C2×D3×C3⋊D311yescharacteristic
808Q8—542no—
809D4—41no—
810D4—62no—
811D4—121no—
812D4—182no—
813D4—182no—
814D4—361no—
815D4—361no—
816D4—361no—
817D4—542no—
818D4—542no—
819D4—542no—
820D4—542no—
821D4—1081no—
822D4—1081no—
823D4—1081no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—62no—
828C2×C4—91no—
829C2×C4—91no—
830C2×C4—274no—
831C2×C4—271no—
832C2×C4—271no—
833C2×C4—542no—
834C2×C4C2×D3×C3⋊D311yescharacteristic
835C2×C3—24no—
836C2×C3—24no—
837C2×C3—24no—
838C2×C3—48no—
839C2×C3—44no—
840C2×C3—44no—
841C2×C3—41no—
842C2×C3—41no—
843C2×C3—84no—
844C2×C3—124no—
845C2×C3—361no—
846C2×C3—361no—
847C2×C3D32×D414yes—
848C2×C3#6431414yes—
849C2×C3#6433014yes—
850C2×C3C2×D4×C3⋊D311yescharacteristic
851C2×C3#6436111yescharacteristic
852C2×C3#6436611yescharacteristic
853D3—41no—
854D3—124no—
855D3—124no—
856D3—188no—
857D3—182no—
858D3—368no—
859D3—368no—
860D3—364no—
861D3—361no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22—181no—
875C22—181no—
876C22—181no—
877C22—272no—
878C22—541no—
879C22—541no—
880C22—541no—
881C22—541no—
882C22—541no—
883C22—1084no—
884C22—1084no—
885C22C22×D3×C3⋊D311yescharacteristic
886C4—21no—
887C4—32no—
888C4—61no—
889C4—61no—
890C4—92no—
891C4—181no—
892C4—541no—
893C4—541no—
894C3—24no—
895C3#1059529914yescomplemented
896C3#1059607811yescharacteristic, complemented
897C2—41no—
898C2—41no—
899C2—121no—
900C2—361no—
901C2—361no—
902C2—542no—
903C2—1081no—
904C2D3×D4×C3⋊D311yescharacteristic
905C2#1172458911yescharacteristic
906C2#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×#89039C2semidirect
2. C2×#89031C2semidirect
3. #11723978C2semidirect
4. C3×#64149C2semidirect
5. C32×#939C2semidirect
6. #11723643C2semidirect
7. #11723639C2semidirect
8. #11723633C2semidirect
9. #11723632C2semidirect
10. #11723631C2semidirect
11. #11723591C2semidirect
12. #11723541C2semidirect
13. #11723482C2semidirect
14. #11723469C2semidirect
15. #11723419C2semidirect
20. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×#638C22semidirect
27. C2×C3×C4⋊(C3⋊D3)C22semidirect
29. C2×C32×#67C22semidirect
30. C22×C32×Dic3C22semidirect
32. C2×#6293C22semidirect
35. C2×#6292C22semidirect
37. C2×#6290C22semidirect
40. C2×Dic3×C3⋊D3C22semidirect
41. #88864C22semidirect
43. #88859C22semidirect
44. C3×C4×C3⋊Dic3C22semidirect
45. C32×#217C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
50. #88804C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
61. #64149D3semidirect
75. C3×#939D3semidirect
124. #6289D4semidirect
136. C2×C32×D4C2×D3semidirect
137. C2×C32×D4C2×D3semidirect
148. C2×#638C2×D3semidirect
149. C2×#638C2×D3semidirect
150. C2×#638C2×D3semidirect
156. C2×C4⋊(C3⋊D3)C2×D3semidirect
165. C2×C3×#67C2×D3semidirect
166. C22×C3×Dic3C2×D3semidirect
197. C4×C3⋊Dic3C2×D3semidirect
198. C3×#217C2×D3semidirect
199. C3×(C2×D3)⋊C4C2×D3semidirect
200. C3×Dic3⋊C4C2×D3semidirect
253. #939C3⋊D3semidirect
389. C2×C3×D4D32semidirect
390. C2×C3×D4C2×C3⋊D3semidirect
409. C2×#67C2×C3⋊D3semidirect
411. C22×Dic3C2×C3⋊D3semidirect
436. #217C2×C3⋊D3semidirect
450. (C2×D3)⋊C4C2×C3⋊D3semidirect
453. Dic3⋊C4C2×C3⋊D3semidirect
553. C33#535semidirect
693. C2×D4D3×C3⋊D3semidirect
793. C32#5607semidirect
794. C32#5715semidirect
895. C3#10595299semidirect
896. C3#10596078semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×#890312
#117239782
C3×#641492
C32×#9392
#117236432
#117236392
#117236332
#117236322
#117236312
#117235912
#117235412
#117234822
#117234692
#117234192
#105960783
#105952993