Finite Group Databasebeta

← #13175926

Subgroups — #13175926

Order 1728.

2388 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#89026C211yesmaximal, characteristic, complemented
3#11723924C211yesmaximal, characteristic, complemented
4C3×#64093C211yesmaximal, characteristic, complemented
5C32×#882C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723631C211yesmaximal, characteristic, complemented
8#11723629C211yesmaximal, characteristic, complemented
9#11723540C211yesmaximal, characteristic, complemented
10C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11723522C211yesmaximal, characteristic, complemented
12#11723519C211yesmaximal, characteristic, complemented
13#11723480C211yesmaximal, characteristic, complemented
14#11723473C211yesmaximal, characteristic, complemented
15#11723420C211yesmaximal, characteristic, complemented
16#10596060—31nomaximal
17#10594263—34nomaximal
18C23×C32×D3C2211yescharacteristic, complemented
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×D12C2211yescharacteristic
29C2×C32×D12C2211yescharacteristic, complemented
30D3×#638—24no—
31C2×#6291C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×#6290C2211yescharacteristic, complemented
34C2×#6290C2211yescharacteristic, complemented
35C2×#6290C2211yescharacteristic, complemented
36C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#89026—24no—
39C33×C22⋊C4C2211yescharacteristic, complemented
40#88864C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
43#88857C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3750C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×D4×C3⋊D3—31no—
57C2×D3×#67—34no—
58C2×#3802—34no—
59C32×#120—31no—
60#64162—31no—
61#64147—31no—
62#64147—31no—
63#64146—31no—
64#64146—31no—
65#64144—31no—
66#64095—31no—
67#64093—31no—
68#64093D311yescharacteristic, complemented
69#64092—31no—
70#64092—31no—
71#64092—34no—
72#64092—64no—
73C22⋊C4×C3⋊D3—31no—
74C3×#884—34no—
75C3×#882D314yescomplemented
76#63983—34no—
77#63976—34no—
78#63970—34no—
79#63922—34no—
80D3×(C2×D3)⋊C4—34no—
81#63908—34no—
82#63891—34no—
83#63885—34no—
84#63884—34no—
85#63853—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3—22no—
91C22×C32×D3—41no—
92C22×C32×D3—41no—
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×D3×C3⋊D3—41no—
99C2×D3×C3⋊D3—41no—
100C2×D3×C3⋊D3—41no—
101C2×D3×C3⋊D3D414yescomplemented
102C2×C33×C4C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104#6312—22no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊(C3⋊D3)—22no—
109C3×#638—22no—
110C3×#638—41no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C3×C4⋊(C3⋊D3)—22no—
114C3×C4×C3⋊D3—41no—
115C32×#67—41no—
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—22no—
118C32×D12—41no—
119#6291—22no—
120#6290—22no—
121#6290—22no—
122#6290—22no—
123#6290—41no—
124Dic3×C3⋊D3—41no—
125D3×C3⋊Dic3—22no—
126#5605—91no—
127#5589—94no—
128C24×C32—31no—
129C23×C3⋊D3—31no—
130C23×C3⋊D3—31no—
131C23×C3×D3C2×D314yescomplemented
132C22×D32—34no—
133C22×D32—34no—
134C2×C32×D4—31no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—64no—
145C2×#638—64no—
146C2×#638C2×D311yescharacteristic, complemented
147C2×#638C2×D311yescharacteristic, complemented
148C22×C3⋊Dic3—31no—
149D4×C3⋊D3—64no—
150C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—34no—
153C2×C4×C3⋊D3—31no—
154C2×C4×C3⋊D3—64no—
155C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
156C2×C3×#67—34no—
157C2×C3×#67—34no—
158C2×C3×#67C2×D314yescomplemented
159C2×C3×D12—34no—
160C2×C3×D12C2×D314yes—
161C2×C3×D12C2×D314yescomplemented
162C2×C3×C4×D3—34no—
163D3×#67—616no—
164C2×#626—34no—
165C2×#625—34no—
166C2×#625—34no—
167C2×#625—34no—
168C2×#625—34no—
169C2×D3×Dic3—34no—
170C2×D3×Dic3—34no—
171#3802—616no—
172C32×C22⋊C4—24no—
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4C2×D314yescomplemented
176C32×C22⋊C4C2×D311yescharacteristic, complemented
177#3757—31no—
178#3757—34no—
179#3757—31no—
180#3757—31no—
181#3757—31no—
182#3757—31no—
183#3757—64no—
184#3752—31no—
185#3752—31no—
186#3752—34no—
187#3752—31no—
188#3752—64no—
189#3752C2×D311yescharacteristic, complemented
190C4⋊(C3⋊Dic3)—31no—
191C4⋊(C3⋊Dic3)—34no—
192C4⋊(C3⋊Dic3)—31no—
193C4⋊(C3⋊Dic3)—64no—
194#3750—31no—
195#3750—34no—
196#3750—64no—
197#3750C2×D311yescharacteristic, complemented
198C3×(C2×D3)⋊C4—34no—
199C3×(C2×D3)⋊C4C2×D314yescomplemented
200C3×(C2×D3)⋊C4C2×D314yescomplemented
201C3×Dic3⋊C4—34no—
202Dic3⋊Dic3—34no—
203#3722—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208(C2×D3)⋊Dic3—34no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C2411yescharacteristic
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)C2×D412yes—
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⋊D3C2×D412yes—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C2×C32×D3—21no—
229C2×C32×D3—21no—
230C2×C32×D3—44no—
231C2×C32×D3C2×D412yes—
232D3×C3⋊D3—44no—
233D3×C3⋊D3—44no—
234C33×C4—21no—
235C33×C4—21no—
236C3⋊(C3⋊Dic3)—21no—
237C3⋊(C3⋊Dic3)—21no—
238C3⋊(C3⋊Dic3)—21no—
239C3×C3⋊Dic3—21no—
240C3×C3⋊Dic3—21no—
241C32×Dic3—21no—
242C22×#67—94no—
243C2×D3×D4—94no—
244C2×D3×D4—91no—
245C2×D3×D4—91no—
246C3×#121—91no—
247C3×#120—34no—
248#953—94no—
249#939—91no—
250#939—91no—
251#938—94no—
252#938—94no—
253#937—94no—
254#937—94no—
255#937—91no—
256#937—91no—
257#935—94no—
258#930—91no—
259C2×(C2×D3)⋊C4—91no—
260#894—91no—
261#894—91no—
262#886—94no—
263#884—34no—
264#884—94no—
265#883—94no—
266#883—94no—
267#883—91no—
268#883—91no—
269#883—184no—
270#882—91no—
271#882C3⋊D311yescharacteristic, complemented
272D3×C22⋊C4—94no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32—31no—
276C23×C32—31no—
277C23×C32—62no—
278C23×C32—121no—
279C23×C32—121no—
280C23×C32C22×D314yes—
281C23×C32C22×D311yescharacteristic
282C22×C3⋊D3—31no—
283C22×C3⋊D3—34no—
284C22×C3⋊D3—34no—
285C22×C3⋊D3—64no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—121no—
288C22×C3⋊D3—121no—
289C22×C3⋊D3—121no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—28no—
294C22×C3×D3—34no—
295C22×C3×D3—34no—
296C22×C3×D3—44no—
297C22×C3×D3—44no—
298C22×C3×D3C22×D314yes—
299C22×C3×D3C22×D314yes—
300C22×C3×D3C22×D314yes—
301C2×D32—316no—
302C2×D32—68no—
303C2×D32—124no—
304C2×D32—124no—
305C2×D32—124no—
306C2×D32—124no—
307C32×D4—62no—
308C32×D4—121no—
309C32×D4—121no—
310C2×C32×C4—24no—
311C2×C32×C4—24no—
312C2×C32×C4—31no—
313C2×C32×C4C22×D314yes—
314C2×C32×C4C22×D314yes—
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C22×D311yescharacteristic
317#638—22no—
318#638—41no—
319#638—62no—
320#638—62no—
321#638—62no—
322#638—62no—
323#638—62no—
324#638—68no—
325#638—128no—
326#638—121no—
327C2×C3⋊Dic3—31no—
328C2×C3⋊Dic3—31no—
329C2×C3⋊Dic3—31no—
330C2×C3⋊Dic3—34no—
331C2×C3⋊Dic3—34no—
332C2×C3⋊Dic3—34no—
333C2×C3⋊Dic3—64no—
334C2×C3⋊Dic3—64no—
335C2×C3⋊Dic3—64no—
336C2×C3⋊Dic3—62no—
337C2×C3⋊Dic3C22×D311yescharacteristic
338C2×C3⋊Dic3C22×D311yescharacteristic
339C4⋊(C3⋊D3)—22no—
340C4×C3⋊D3—41no—
341C4×C3⋊D3—62no—
342C4×C3⋊D3—68no—
343C4×C3⋊D3—128no—
344C4×C3⋊D3—121no—
345C3×#67—44no—
346C3×#67—68no—
347C3×#67—124no—
348C2×C3×Dic3—34no—
349C2×C3×Dic3—34no—
350C2×C3×Dic3C22×D314yes—
351C3×D12—28no—
352C3×D12—44no—
353C3×D12—68no—
354C3×C4×D3—124no—
355#626—68no—
356#625—68no—
357#625—68no—
358#625—68no—
359#625—124no—
360D3×Dic3—68no—
361D3×Dic3—124no—
362#534—271noSylow
363C2×C33—41no—
364C2×C33C22×D411yescharacteristic
365C2×C33H(5,𝔽2)11yescharacteristic
366C2×C33H(5,𝔽2)11yescharacteristic
367C3⋊(C3⋊D3)—22no—
368C3×C3⋊D3—22no—
369C3×C3⋊D3—41no—
370C32×D3—22no—
371C32×D3—41no—
372C32×D3—41no—
373C24×C3—34no—
374C23×D3—94no—
375C23×D3—94no—
376C23×D3—91no—
377C23×D3—91no—
378C23×D3C2×C3⋊D311yescharacteristic, complemented
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C22×C3×C4—91no—
386C2×#67—34no—
387C2×#67—34no—
388C2×#67—94no—
389C2×#67—94no—
390C2×#67—94no—
391C2×#67—94no—
392C2×#67—94no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—94no—
398C2×#67—91no—
399C2×#67—184no—
400C2×#67—1816no—
401C2×#67C2×C3⋊D311yescharacteristic, complemented
402C22×Dic3—94no—
403C22×Dic3—91no—
404D3×D4—184no—
405D3×D4—1816no—
406D3×D4—184no—
407C2×D12—34no—
408C2×D12—91no—
409C2×D12C2×C3⋊D311yescharacteristic
410C2×D12C2×C3⋊D311yescharacteristic, complemented
411C2×C4×D3—34no—
412C2×C4×D3—91no—
413C2×C4×D3—94no—
414C2×C4×D3—91no—
415C2×C4×D3—94no—
416C2×C4×D3—184no—
417C3×C4⋊C4—91no—
418C3×C22⋊C4—24no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—91no—
422C3×C22⋊C4D3214yescomplemented
423C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
424#217—94no—
425#217—94no—
426#217—94no—
427#217—94no—
428#217—94no—
429#217—91no—
430#217—91no—
431#217—184no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—94no—
434(C2×D3)⋊C4—94no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—94no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—184no—
443(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
444(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
445C4⋊Dic3—94no—
446C4⋊Dic3—94no—
447C4⋊Dic3—91no—
448C4⋊Dic3—184no—
449Dic3⋊C4—34no—
450Dic3⋊C4—94no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—184no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—24no—
458C22×C32—24no—
459C22×C32—24no—
460C22×C32—24no—
461C22×C32—32no—
462C22×C32—44no—
463C22×C32—44no—
464C22×C32—44no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—61no—
468C22×C32—61no—
469C22×C32—61no—
470C22×C32—61no—
471C22×C32—61no—
472C22×C32—61no—
473C22×C32—124no—
474C22×C32C23×D314yes—
475C22×C32C23×D311yescharacteristic
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—21no—
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3—32no—
482C2×C3⋊D3—38no—
483C2×C3⋊D3—68no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—64no—
488C2×C3⋊D3—124no—
489C2×C3⋊D3—124no—
490C2×C3⋊D3—124no—
491C2×C3⋊D3—124no—
492C2×C3⋊D3D3×D412yes—
493C2×C3×D3—24no—
494C2×C3×D3—24no—
495C2×C3×D3—24no—
496C2×C3×D3—24no—
497C2×C3×D3—24no—
498C2×C3×D3—24no—
499C2×C3×D3—24no—
500C2×C3×D3—24no—
501C2×C3×D3—38no—
502C2×C3×D3—416no—
503C2×C3×D3—64no—
504C2×C3×D3—64no—
505C2×C3×D3—64no—
506C2×C3×D3—64no—
507C2×C3×D3—64no—
508C2×C3×D3D3×D418yes—
509D32—1216no—
510D32—1216no—
511C32×C4—21no—
512C32×C4—21no—
513C32×C4—24no—
514C32×C4—24no—
515C32×C4—44no—
516C32×C4—44no—
517C32×C4—61no—
518C3⋊Dic3—21no—
519C3⋊Dic3—21no—
520C3⋊Dic3—61no—
521C3⋊Dic3—61no—
522C3⋊Dic3—61no—
523C3⋊Dic3—64no—
524C3⋊Dic3—64no—
525C3⋊Dic3—64no—
526C3⋊Dic3—124no—
527C3⋊Dic3—124no—
528C3⋊Dic3—124no—
529C3×Dic3—24no—
530C3×Dic3—64no—
531C3×Dic3—64no—
532C22×D4—271no—
533C22×D4—271no—
534#123—271no—
535#123—271no—
536#123—271no—
537#123—271no—
538#121—91no—
539#121—271no—
540#121—271no—
541#121—271no—
542#120—31no—
543#120—271no—
544#120—271no—
545#120—271no—
546C2×C22⋊C4—271no—
547C33#53411yescharacteristic, complemented, Sylow
548C23×C3—24no—
549C23×C3—34no—
550C23×C3—34no—
551C23×C3—34no—
552C23×C3—68no—
553C23×C3—91no—
554C23×C3—91no—
555C23×C3—124no—
556C23×C3—124no—
557C23×C3C2×D3214yes—
558C23×C3C22×C3⋊D311yescharacteristic
559C22×D3—22no—
560C22×D3—34no—
561C22×D3—34no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—916no—
565C22×D3—94no—
566C22×D3—91no—
567C22×D3—94no—
568C22×D3—184no—
569C22×D3—182no—
570C22×D3—188no—
571C22×D3—361no—
572C22×D3—361no—
573C22×D3—361no—
574C22×D3—361no—
575C22×D3—364no—
576C22×D3—364no—
577C22×D3—364no—
578C22×D3—364no—
579C22×D3C22×C3⋊D311yescharacteristic
580C22×D3C22×C3⋊D311yescharacteristic
581C22×D3C22×C3⋊D311yescharacteristic
582C3×D4—68no—
583C3×D4—124no—
584C3×D4—124no—
585C3×D4—182no—
586C3×D4—182no—
587C3×D4—361no—
588C2×C3×C4—24no—
589C2×C3×C4—24no—
590C2×C3×C4—34no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—361no—
594C2×C3×C4C2×D3214yes—
595C2×C3×C4C2×D3214yes—
596C2×C3×C4C22×C3⋊D311yescharacteristic
597C2×C3×C4C22×C3⋊D311yescharacteristic
598#67—41no—
599#67—68no—
600#67—124no—
601#67—188no—
602#67—182no—
603#67—182no—
604#67—188no—
605#67—188no—
606#67—188no—
607#67—182no—
608#67—188no—
609#67—182no—
610#67—368no—
611#67—361no—
612#67—364no—
613C2×Dic3—34no—
614C2×Dic3—34no—
615C2×Dic3—94no—
616C2×Dic3—94no—
617C2×Dic3—94no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—91no—
621C2×Dic3—184no—
622C2×Dic3—184no—
623C2×Dic3—184no—
624C2×Dic3—188no—
625C2×Dic3—361no—
626C2×Dic3C22×C3⋊D311yescharacteristic
627D12—22no—
628D12—41no—
629D12—68no—
630D12—182no—
631C4×D3—124no—
632C4×D3—182no—
633C4×D3—188no—
634C4×D3—182no—
635C4×D3—368no—
636C4×D3—364no—
637C2×C32—24no—
638C2×C32—24no—
639C2×C32—24no—
640C2×C32—41no—
641C2×C32—44no—
642C2×C32—62no—
643C2×C32—84no—
644C2×C32—121no—
645C2×C32—121no—
646C2×C32C2×D3×D414yes—
647C2×C32C2×D3×D411yescharacteristic
648C2×C32#100414yes—
649C2×C32#100414yes—
650C2×C32#100411yescharacteristic
651C2×C32#100911yescharacteristic
652C3⋊D3—22no—
653C3⋊D3—41no—
654C3⋊D3—62no—
655C3⋊D3—68no—
656C3⋊D3—128no—
657C3×D3—28no—
658C3×D3—44no—
659C3×D3—44no—
660C3×D3—68no—
661C3×D3—124no—
662C24—31no—
663C24—271no—
664C24—271no—
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—91no—
669C2×D4—91no—
670C2×D4—91no—
671C2×D4—271no—
672C2×D4—271no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—544no—
678C2×D4—544no—
679C22×C4—91no—
680C22×C4—271no—
681C22×C4—271no—
682C22×C4—271no—
683C4⋊C4—91no—
684C4⋊C4—271no—
685C4⋊C4—271no—
686C4⋊C4—271no—
687C22⋊C4—31no—
688C22⋊C4—31no—
689C22⋊C4—91no—
690C22⋊C4—271no—
691C22⋊C4—271no—
692C22⋊C4—271no—
693C22⋊C4—271no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4D3×C3⋊D311yescharacteristic, complemented
699C22×C3—24no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—24no—
706C22×C3—38no—
707C22×C3—44no—
708C22×C3—44no—
709C22×C3—44no—
710C22×C3—64no—
711C22×C3—64no—
712C22×C3—64no—
713C22×C3—64no—
714C22×C3—64no—
715C22×C3—64no—
716C22×C3—64no—
717C22×C3—64no—
718C22×C3—92no—
719C22×C3—1216no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3C22×D3214yes—
726C22×C3C23×C3⋊D311yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—38no—
736C2×D3—44no—
737C2×D3—64no—
738C2×D3—64no—
739C2×D3—64no—
740C2×D3—64no—
741C2×D3—64no—
742C2×D3—98no—
743C2×D3—92no—
744C2×D3—188no—
745C2×D3—184no—
746C2×D3—184no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—364no—
750C2×D3—364no—
751C2×D3—364no—
752C2×D3—364no—
753C2×D3—3616no—
754C2×D3—3616no—
755C2×D3D4×C3⋊D312yes—
756C3×C4—24no—
757C3×C4—24no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—44no—
761C3×C4—44no—
762C3×C4—64no—
763C3×C4—181no—
764C3×C4—181no—
765Dic3—21no—
766Dic3—64no—
767Dic3—64no—
768Dic3—184no—
769Dic3—184no—
770Dic3—184no—
771Dic3—181no—
772Dic3—181no—
773Dic3—181no—
774Dic3—364no—
775Dic3—364no—
776Dic3—364no—
777C32—24no—
778C32#558914yescomplemented
779C32#560511yescharacteristic, complemented
780C23—31no—
781C23—31no—
782C23—31no—
783C23—62no—
784C23—91no—
785C23—91no—
786C23—121no—
787C23—121no—
788C23—274no—
789C23—271no—
790C23—542no—
791C23—1081no—
792C23—1081no—
793C23—1081no—
794C23—1081no—
795C23C2×D3×C3⋊D311yescharacteristic
796D4—62no—
797D4—121no—
798D4—121no—
799D4—182no—
800D4—182no—
801D4—361no—
802D4—542no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808C2×C4—31no—
809C2×C4—91no—
810C2×C4—91no—
811C2×C4—271no—
812C2×C4—271no—
813C2×C4—271no—
814C2×C4—361no—
815C2×C4—542no—
816C2×C4—542no—
817C2×C4—1081no—
818C2×C4C2×D3×C3⋊D311yescharacteristic
819C2×C4C2×D3×C3⋊D311yescharacteristic
820C2×C3—24no—
821C2×C3—24no—
822C2×C3—24no—
823C2×C3—44no—
824C2×C3—41no—
825C2×C3—68no—
826C2×C3—84no—
827C2×C3—124no—
828C2×C3—124no—
829C2×C3—182no—
830C2×C3—361no—
831C2×C3#6430714yes—
832C2×C3D32×D414yes—
833C2×C3#6431314yes—
834C2×C3C2×D4×C3⋊D311yescharacteristic
835C2×C3#6436111yescharacteristic
836C2×C3#6436111yescharacteristic
837D3—22no—
838D3—41no—
839D3—41no—
840D3—68no—
841D3—124no—
842D3—188no—
843D3—182no—
844D3—368no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—32no—
849C22—61no—
850C22—61no—
851C22—61no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—92no—
858C22—124no—
859C22—181no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—272no—
865C22—541no—
866C22—541no—
867C22—1084no—
868C22—1084no—
869C22C22×D3×C3⋊D311yescharacteristic
870C4—21no—
871C4—21no—
872C4—61no—
873C4—181no—
874C4—181no—
875C4—541no—
876C4—541no—
877C4—541no—
878C3—24no—
879C3#1059426314yescomplemented
880C3#1059606011yescharacteristic, complemented
881C2—41no—
882C2—62no—
883C2—121no—
884C2—121no—
885C2—182no—
886C2—361no—
887C2—542no—
888C2#1172457911yescharacteristic
889C2D3×D4×C3⋊D311yescharacteristic
890C2#1172458711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#638C2semidirect
2. C2×#89026C2semidirect
3. #11723924C2semidirect
4. C3×#64093C2semidirect
5. C32×#882C2semidirect
6. #11723643C2semidirect
7. #11723631C2semidirect
8. #11723629C2semidirect
9. #11723540C2semidirect
10. C3⋊D3×(C2×D3)⋊C4C2semidirect
11. #11723522C2semidirect
12. #11723519C2semidirect
13. #11723480C2semidirect
14. #11723473C2semidirect
15. #11723420C2semidirect
18. C23×C32×D3C22semidirect
20. C22×D3×C3⋊D3C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C32×#67C22semidirect
29. C2×C32×D12C22semidirect
33. C2×#6290C22semidirect
34. C2×#6290C22semidirect
35. C2×#6290C22semidirect
36. C2×Dic3×C3⋊D3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
39. C33×C22⋊C4C22semidirect
40. #88864C22semidirect
41. #88859C22semidirect
42. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
43. #88857C22semidirect
44. C3×#3752C22semidirect
45. C3×#3750C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
68. #64093D3semidirect
75. C3×#882D3semidirect
101. C2×D3×C3⋊D3D4semidirect
131. C23×C3×D3C2×D3semidirect
146. C2×#638C2×D3semidirect
147. C2×#638C2×D3semidirect
150. C2×C4⋊(C3⋊D3)C2×D3semidirect
155. C2×C4×C3⋊D3C2×D3semidirect
158. C2×C3×#67C2×D3semidirect
161. C2×C3×D12C2×D3semidirect
175. C32×C22⋊C4C2×D3semidirect
176. C32×C22⋊C4C2×D3semidirect
189. #3752C2×D3semidirect
197. #3750C2×D3semidirect
199. C3×(C2×D3)⋊C4C2×D3semidirect
200. C3×(C2×D3)⋊C4C2×D3semidirect
271. #882C3⋊D3semidirect
378. C23×D3C2×C3⋊D3semidirect
401. C2×#67C2×C3⋊D3semidirect
410. C2×D12C2×C3⋊D3semidirect
422. C3×C22⋊C4D32semidirect
423. C3×C22⋊C4C2×C3⋊D3semidirect
443. (C2×D3)⋊C4C2×C3⋊D3semidirect
444. (C2×D3)⋊C4C2×C3⋊D3semidirect
547. C33#534semidirect
698. C22⋊C4D3×C3⋊D3semidirect
778. C32#5589semidirect
779. C32#5605semidirect
879. C3#10594263semidirect
880. C3#10596060semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#890262
#117239242
C3×#640932
C32×#8822
#117236432
#117236312
#117236292
#117235402
C3⋊D3×(C2×D3)⋊C42
#117235222
#117235192
#117234802
#117234732
#117234202
#105960603
#105942633