Finite Group Databasebeta

← #13175924

Subgroups — #13175924

Order 1728.

2596 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
3#11723923C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C32×#884C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723638C211yesmaximal, characteristic, complemented
8#11723616C211yesmaximal, characteristic, complemented
9#11723542C211yesmaximal, characteristic, complemented
10D3×#3752C211yesmaximal, characteristic, complemented
11#11723516C211yesmaximal, characteristic, complemented
12#11723498C211yesmaximal, characteristic, complemented
13#11723475C211yesmaximal, characteristic, complemented
14#11723422C211yesmaximal, characteristic, complemented
15#11723417C211yesmaximal, characteristic, complemented
16#10596076—31nomaximal
17#10594264—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
23C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×D12C2211yescharacteristic, complemented
29C2×C32×C4×D3C2211yescharacteristic, complemented
30#89039—24no—
31C2×#6292C2211yescharacteristic
32C2×#6291C2211yescharacteristic
33C2×#6291C2211yescharacteristic, complemented
34C2×#6291C2211yescharacteristic, complemented
35C2×#6291C2211yescharacteristic, complemented
36C2×#6289C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38C3⋊D3×D12—24no—
39C33×C22⋊C4C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C3×#3750C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C2×D4×C3⋊D3—31no—
57C2×#3811—34no—
58C2×D3×D12—34no—
59C32×#121—31no—
60#64148—31no—
61#64148—31no—
62#64146—31no—
63#64146—31no—
64#64139—31no—
65C2×#3752—31no—
66#64103—31no—
67#64103—31no—
68#64092—31no—
69#64092D311yescharacteristic, complemented
70#64091—31no—
71#64091—31no—
72#64091—34no—
73#64091—64no—
74C3×#884D314yescomplemented
75C3×#883—34no—
76#63983—34no—
77#63981—34no—
78#63971—34no—
79#63923—34no—
80D3×(C2×D3)⋊C4—34no—
81#63909—34no—
82#63897—34no—
83#63886—34no—
84#63854—34no—
85#63850—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—41no—
89C22×C3⋊(C3⋊D3)—41no—
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C3×C3⋊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—41no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊(C3⋊D3))—22no—
107C4⋊(C3⋊(C3⋊D3))—41no—
108C3×#638—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4×C3⋊D3—22no—
113C32×#67—22no—
114C32×#67—41no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—22no—
118C32×C4×D3—41no—
119#6292—22no—
120#6291—22no—
121#6291—22no—
122#6291—22no—
123#6291—41no—
124#6289—22no—
125D3×C3⋊Dic3—41no—
126#5653—91no—
127#5605—94no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3—31no—
130C23×C3⋊D3—34no—
131C23×C3⋊D3—31no—
132C23×C3⋊D3—64no—
133C22×D32—34no—
134C22×D32—34no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×C32×D4—31no—
138C22×C32×C4—31no—
139C2×#638—31no—
140C2×#638—34no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—64no—
146C2×#638C2×D311yescharacteristic
147C22×C3⋊Dic3—31no—
148D4×C3⋊D3—64no—
149D4×C3⋊D3—64no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)—34no—
153C2×C4⋊(C3⋊D3)—31no—
154C2×C4⋊(C3⋊D3)—34no—
155C2×C4⋊(C3⋊D3)—64no—
156C2×C4⋊(C3⋊D3)—64no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
159C2×C3×#67—34no—
160C2×C3×#67C2×D314yescomplemented
161C2×C3×#67C2×D314yescomplemented
162C2×C3×D12C2×D314yescomplemented
163C2×C3×C4×D3—34no—
164C2×C3×C4×D3C2×D314yescomplemented
165#3811—616no—
166C2×#626—34no—
167C2×#626—34no—
168C2×#626—34no—
169C2×#626—34no—
170C2×#626—34no—
171C2×#624—34no—
172C2×D3×Dic3—34no—
173D3×D12—616no—
174C32×C4⋊C4—31no—
175C32×C22⋊C4—24no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4C2×D314yescomplemented
178C32×C22⋊C4C2×D311yescharacteristic, complemented
179#3757—31no—
180#3757C2×D311yescharacteristic, complemented
181#3752—31no—
182#3752—31no—
183#3752—31no—
184#3752—34no—
185#3752—34no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—31no—
190#3752—64no—
191#3752—64no—
192#3752C2×D311yescharacteristic, complemented
193C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
194#3750—31no—
195#3750C2×D311yescharacteristic, complemented
196C3×#217—34no—
197C3×(C2×D3)⋊C4—34no—
198C3×(C2×D3)⋊C4C2×D314yescomplemented
199C3×C4⋊Dic3—34no—
200C3×Dic3⋊C4—34no—
201C3×Dic3⋊C4C2×D314yescomplemented
202#3724—34no—
203#3722—34no—
204#3722—34no—
205#3722—34no—
206#3722—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)—21no—
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⋊D3C2×D412yes—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C2×C32×D3—21no—
229C2×C32×D3—21no—
230C2×C32×D3—21no—
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—
240C32×Dic3—21no—
241C32×Dic3—21no—
242C2×D3×D4—94no—
243C2×D3×D4—94no—
244C2×D3×D4—91no—
245C22×D12—91no—
246C3×#123—91no—
247C3×#121—34no—
248#939—94no—
249#939—94no—
250#937—94no—
251#937—94no—
252#937—91no—
253#930—94no—
254#929—91no—
255C2×(C2×D3)⋊C4—94no—
256#895—91no—
257#895—91no—
258#894—94no—
259#894—94no—
260#894—91no—
261#894—91no—
262#884—91no—
263#884C3⋊D311yescharacteristic, complemented
264#883—34no—
265#883—94no—
266#882—94no—
267#882—91no—
268#882—94no—
269#882—91no—
270#882—91no—
271#882—184no—
272D3×C22⋊C4—91no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32—31no—
276C23×C32C22×D314yes—
277C23×C32C22×D311yescharacteristic
278C22×C3⋊D3—31no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—31no—
281C22×C3⋊D3—31no—
282C22×C3⋊D3—34no—
283C22×C3⋊D3—34no—
284C22×C3⋊D3—34no—
285C22×C3⋊D3—64no—
286C22×C3⋊D3—64no—
287C22×C3⋊D3—64no—
288C22×C3⋊D3—62no—
289C22×C3⋊D3—62no—
290C22×C3⋊D3—68no—
291C22×C3⋊D3—128no—
292C22×C3⋊D3—121no—
293C22×C3⋊D3—121no—
294C22×C3⋊D3—121no—
295C22×C3⋊D3—121no—
296C22×C3⋊D3—121no—
297C22×C3⋊D3—121no—
298C22×C3⋊D3—124no—
299C22×C3⋊D3—124no—
300C22×C3⋊D3—128no—
301C22×C3⋊D3—128no—
302C22×C3⋊D3C22×D311yescharacteristic
303C22×C3×D3—34no—
304C22×C3×D3C22×D314yes—
305C22×C3×D3C22×D314yes—
306C2×D32—316no—
307C2×D32—68no—
308C2×D32—124no—
309C2×D32—124no—
310C2×D32—124no—
311C2×D32—124no—
312C32×D4—62no—
313C32×D4—62no—
314C32×D4—121no—
315C2×C32×C4—24no—
316C2×C32×C4—24no—
317C2×C32×C4—31no—
318C2×C32×C4—31no—
319C2×C32×C4—121no—
320C2×C32×C4C22×D314yes—
321C2×C32×C4C22×D314yes—
322C2×C32×C4C22×D311yescharacteristic
323C2×C32×C4C22×D311yescharacteristic
324#638—22no—
325#638—62no—
326#638—62no—
327#638—62no—
328#638—121no—
329#638—121no—
330#638—124no—
331#638—128no—
332C2×C3⋊Dic3—31no—
333C2×C3⋊Dic3—34no—
334C2×C3⋊Dic3—64no—
335C2×C3⋊Dic3—121no—
336C2×C3⋊Dic3C22×D311yescharacteristic
337C2×C3⋊Dic3C22×D311yescharacteristic
338C2×C3⋊Dic3C22×D311yescharacteristic
339C4⋊(C3⋊D3)—62no—
340C4⋊(C3⋊D3)—62no—
341C4⋊(C3⋊D3)—68no—
342C4⋊(C3⋊D3)—128no—
343C4⋊(C3⋊D3)—121no—
344C4⋊(C3⋊D3)—124no—
345C4⋊(C3⋊D3)—128no—
346C4×C3⋊D3—22no—
347C4×C3⋊D3—62no—
348C3×#67—28no—
349C3×#67—44no—
350C3×#67—68no—
351C2×C3×Dic3—34no—
352C2×C3×Dic3—34no—
353C2×C3×Dic3—34no—
354C2×C3×Dic3C22×D314yes—
355C2×C3×Dic3C22×D314yes—
356C3×D12—28no—
357C3×C4×D3—44no—
358C3×C4×D3—68no—
359#626—68no—
360#626—68no—
361#626—68no—
362#626—68no—
363#626—124no—
364#624—68no—
365D3×Dic3—124no—
366#534—271noSylow
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—22no—
375C32×D3—22no—
376C32×D3—41no—
377C23×D3—94no—
378C23×D3—94no—
379C23×D3—91no—
380C23×D3—94no—
381C23×D3—91no—
382C23×D3—91no—
383C23×D3—184no—
384C2×C3×D4—34no—
385C2×C3×D4—34no—
386C2×C3×D4—34no—
387C2×C3×D4—91no—
388C22×C3×C4—34no—
389C22×C3×C4—91no—
390C2×#67—34no—
391C2×#67—94no—
392C2×#67—94no—
393C2×#67—94no—
394C2×#67—94no—
395C2×#67—94no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—184no—
399C2×#67C2×C3⋊D311yescharacteristic, complemented
400C2×#67C2×C3⋊D311yescharacteristic, complemented
401C22×Dic3—94no—
402D3×D4—1816no—
403D3×D4—184no—
404D3×D4—1816no—
405C2×D12—94no—
406C2×D12—91no—
407C2×D12—91no—
408C2×D12—91no—
409C2×D12—94no—
410C2×D12—91no—
411C2×D12—91no—
412C2×D12—94no—
413C2×D12—91no—
414C2×D12—184no—
415C2×D12—184no—
416C2×D12—184no—
417C2×D12C2×C3⋊D311yescharacteristic, complemented
418C2×C4×D3—34no—
419C2×C4×D3—94no—
420C2×C4×D3—91no—
421C2×C4×D3—91no—
422C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
423C3×C4⋊C4—34no—
424C3×C4⋊C4—91no—
425C3×C4⋊C4—91no—
426C3×C22⋊C4—24no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4D3214yescomplemented
431C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
432#217—34no—
433#217—94no—
434#217—91no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—94no—
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—91no—
449(C2×D3)⋊C4—91no—
450(C2×D3)⋊C4—184no—
451(C2×D3)⋊C4—184no—
452(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
453C4⋊Dic3—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—94no—
456Dic3⋊C4—91no—
457Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
458C22×C32—28no—
459C22×C32—21no—
460C22×C32—24no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—24no—
466C22×C32—32no—
467C22×C32—44no—
468C22×C32—44no—
469C22×C32—61no—
470C22×C32—61no—
471C22×C32—61no—
472C22×C32—61no—
473C22×C32—61no—
474C22×C32C23×D314yes—
475C22×C32C23×D311yescharacteristic
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—32no—
479C2×C3⋊D3—38no—
480C2×C3⋊D3—68no—
481C2×C3⋊D3—61no—
482C2×C3⋊D3—61no—
483C2×C3⋊D3—68no—
484C2×C3⋊D3—61no—
485C2×C3⋊D3—61no—
486C2×C3⋊D3—64no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—61no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—64no—
492C2×C3⋊D3—64no—
493C2×C3⋊D3—64no—
494C2×C3⋊D3—64no—
495C2×C3⋊D3—64no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—124no—
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⋊D3—124no—
507C2×C3⋊D3—124no—
508C2×C3⋊D3—1216no—
509C2×C3⋊D3—1232no—
510C2×C3⋊D3D3×D412yes—
511C2×C3×D3—24no—
512C2×C3×D3—24no—
513C2×C3×D3—24no—
514C2×C3×D3—24no—
515C2×C3×D3—24no—
516C2×C3×D3—38no—
517C2×C3×D3—64no—
518C2×C3×D3—64no—
519C2×C3×D3D3×D418yes—
520D32—1216no—
521D32—1216no—
522C32×C4—21no—
523C32×C4—21no—
524C32×C4—24no—
525C32×C4—24no—
526C32×C4—44no—
527C32×C4—44no—
528C32×C4—61no—
529C32×C4—61no—
530C3⋊Dic3—21no—
531C3⋊Dic3—21no—
532C3⋊Dic3—21no—
533C3⋊Dic3—61no—
534C3⋊Dic3—64no—
535C3⋊Dic3—124no—
536C3×Dic3—24no—
537C3×Dic3—24no—
538C3×Dic3—64no—
539C3×Dic3—64no—
540C3×Dic3—64no—
541C22×D4—271no—
542C22×D4—271no—
543#123—91no—
544#123—271no—
545#123—271no—
546#123—271no—
547#121—31no—
548#121—271no—
549#121—271no—
550#121—271no—
551#120—271no—
552#120—271no—
553#120—271no—
554#120—271no—
555C2×C22⋊C4—271no—
556C33#53411yescharacteristic, complemented, Sylow
557C23×C3—24no—
558C23×C3—34no—
559C23×C3—34no—
560C23×C3—91no—
561C23×C3C2×D3214yes—
562C23×C3C22×C3⋊D311yescharacteristic
563C22×D3—34no—
564C22×D3—916no—
565C22×D3—94no—
566C22×D3—91no—
567C22×D3—94no—
568C22×D3—94no—
569C22×D3—94no—
570C22×D3—91no—
571C22×D3—91no—
572C22×D3—184no—
573C22×D3—184no—
574C22×D3—184no—
575C22×D3—182no—
576C22×D3—188no—
577C22×D3—182no—
578C22×D3—188no—
579C22×D3—368no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3—364no—
585C22×D3—364no—
586C22×D3—364no—
587C22×D3—364no—
588C22×D3—364no—
589C22×D3—364no—
590C22×D3—361no—
591C22×D3—361no—
592C22×D3—368no—
593C22×D3—368no—
594C22×D3C22×C3⋊D311yescharacteristic
595C22×D3C22×C3⋊D311yescharacteristic
596C3×D4—68no—
597C3×D4—68no—
598C3×D4—124no—
599C3×D4—182no—
600C2×C3×C4—24no—
601C2×C3×C4—24no—
602C2×C3×C4—34no—
603C2×C3×C4—34no—
604C2×C3×C4—91no—
605C2×C3×C4—91no—
606C2×C3×C4—91no—
607C2×C3×C4—124no—
608C2×C3×C4—182no—
609C2×C3×C4C2×D3214yes—
610C2×C3×C4C2×D3214yes—
611C2×C3×C4C22×C3⋊D311yescharacteristic
612C2×C3×C4C22×C3⋊D311yescharacteristic
613#67—22no—
614#67—41no—
615#67—68no—
616#67—182no—
617#67—188no—
618#67—188no—
619#67—188no—
620#67—364no—
621#67—364no—
622#67—361no—
623#67—368no—
624C2×Dic3—34no—
625C2×Dic3—34no—
626C2×Dic3—34no—
627C2×Dic3—94no—
628C2×Dic3—91no—
629C2×Dic3—184no—
630C2×Dic3—364no—
631C2×Dic3C22×C3⋊D311yescharacteristic
632C2×Dic3C22×C3⋊D311yescharacteristic
633D12—22no—
634D12—182no—
635D12—188no—
636D12—188no—
637D12—182no—
638D12—182no—
639D12—182no—
640D12—368no—
641D12—364no—
642D12—361no—
643D12—368no—
644D12—361no—
645C4×D3—41no—
646C4×D3—68no—
647C4×D3—182no—
648C4×D3—188no—
649C4×D3—361no—
650C2×C32—24no—
651C2×C32—24no—
652C2×C32—24no—
653C2×C32—48no—
654C2×C32—41no—
655C2×C32—44no—
656C2×C32—62no—
657C2×C32—121no—
658C2×C32C2×D3×D414yes—
659C2×C32C2×D3×D411yescharacteristic
660C2×C32#100414yes—
661C2×C32#100914yes—
662C2×C32#100911yescharacteristic
663C2×C32#100911yescharacteristic
664C3⋊D3—22no—
665C3⋊D3—62no—
666C3⋊D3—68no—
667C3⋊D3—128no—
668C3⋊D3—128no—
669C3⋊D3—121no—
670C3⋊D3—121no—
671C3⋊D3—124no—
672C3⋊D3—124no—
673C3⋊D3—244no—
674C3×D3—28no—
675C3×D3—44no—
676C3×D3—68no—
677C24—271no—
678C24—271no—
679C24—271no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—91no—
684C2×D4—271no—
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×D4—544no—
694C22×C4—31no—
695C22×C4—91no—
696C22×C4—271no—
697C22×C4—271no—
698C4⋊C4—31no—
699C4⋊C4—91no—
700C4⋊C4—91no—
701C4⋊C4—271no—
702C22⋊C4—31no—
703C22⋊C4—91no—
704C22⋊C4—91no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4—271no—
709C22⋊C4—271no—
710C22⋊C4—271no—
711C22⋊C4—271no—
712C22⋊C4—271no—
713C22⋊C4D3×C3⋊D311yescharacteristic, complemented
714C22×C3—28no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—24no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—24no—
722C22×C3—38no—
723C22×C3—44no—
724C22×C3—44no—
725C22×C3—64no—
726C22×C3—64no—
727C22×C3—64no—
728C22×C3—64no—
729C22×C3—64no—
730C22×C3—92no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3C22×D3214yes—
734C22×C3C23×C3⋊D311yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—38no—
741C2×D3—64no—
742C2×D3—64no—
743C2×D3—98no—
744C2×D3—92no—
745C2×D3—188no—
746C2×D3—184no—
747C2×D3—184no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—188no—
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—364no—
771C2×D3—364no—
772C2×D3—3616no—
773C2×D3—3616no—
774C2×D3—3616no—
775C2×D3—364no—
776C2×D3—3632no—
777C2×D3D4×C3⋊D312yes—
778C3×C4—24no—
779C3×C4—24no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—44no—
783C3×C4—44no—
784C3×C4—64no—
785C3×C4—64no—
786C3×C4—181no—
787C3×C4—181no—
788C3×C4—181no—
789Dic3—21no—
790Dic3—21no—
791Dic3—64no—
792Dic3—64no—
793Dic3—64no—
794Dic3—184no—
795Dic3—181no—
796Dic3—364no—
797C32—24no—
798C32#560514yescomplemented
799C32#565311yescharacteristic, complemented
800C23—31no—
801C23—31no—
802C23—91no—
803C23—274no—
804C23—271no—
805C23—271no—
806C23—271no—
807C23—542no—
808C23—542no—
809C23—1081no—
810C23—1081no—
811C23—1081no—
812C23—1081no—
813C23—1081no—
814C23—1081no—
815C23C2×D3×C3⋊D311yescharacteristic
816D4—62no—
817D4—62no—
818D4—121no—
819D4—182no—
820D4—542no—
821D4—542no—
822D4—542no—
823D4—542no—
824D4—542no—
825D4—1081no—
826D4—1081no—
827D4—1081no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—91no—
831C2×C4—91no—
832C2×C4—91no—
833C2×C4—121no—
834C2×C4—182no—
835C2×C4—271no—
836C2×C4—542no—
837C2×C4—1081no—
838C2×C4C2×D3×C3⋊D311yescharacteristic
839C2×C4C2×D3×C3⋊D311yescharacteristic
840C2×C3—24no—
841C2×C3—24no—
842C2×C3—24no—
843C2×C3—48no—
844C2×C3—44no—
845C2×C3—41no—
846C2×C3—68no—
847C2×C3—124no—
848C2×C3—182no—
849C2×C3#6430814yes—
850C2×C3D32×D414yes—
851C2×C3#6431414yes—
852C2×C3C2×D4×C3⋊D311yescharacteristic
853C2×C3#6436111yescharacteristic
854C2×C3#6436611yescharacteristic
855D3—22no—
856D3—41no—
857D3—68no—
858D3—188no—
859D3—182no—
860D3—368no—
861D3—368no—
862D3—364no—
863D3—364no—
864D3—361no—
865D3—361no—
866D3—724no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—32no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—61no—
875C22—61no—
876C22—92no—
877C22—181no—
878C22—181no—
879C22—272no—
880C22—541no—
881C22—541no—
882C22—541no—
883C22—541no—
884C22—541no—
885C22—541no—
886C22—541no—
887C22—541no—
888C22—1084no—
889C22—1084no—
890C22—1084no—
891C22C22×D3×C3⋊D311yescharacteristic
892C4—21no—
893C4—21no—
894C4—61no—
895C4—61no—
896C4—181no—
897C4—181no—
898C4—181no—
899C4—541no—
900C3—24no—
901C3#1059426414yescomplemented
902C3#1059607611yescharacteristic, complemented
903C2—41no—
904C2—62no—
905C2—121no—
906C2—182no—
907C2—542no—
908C2—1081no—
909C2—1081no—
910C2#1172458111yescharacteristic
911C2D3×D4×C3⋊D311yescharacteristic
912C2#1172458811yescharacteristic
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×#89039C2semidirect
2. C2×C3⋊D3×D12C2semidirect
3. #11723923C2semidirect
4. C3×#64092C2semidirect
5. C32×#884C2semidirect
6. #11723643C2semidirect
7. #11723638C2semidirect
8. #11723616C2semidirect
9. #11723542C2semidirect
10. D3×#3752C2semidirect
11. #11723516C2semidirect
12. #11723498C2semidirect
13. #11723475C2semidirect
14. #11723422C2semidirect
15. #11723417C2semidirect
18. C23×C3⋊(C3⋊D3)C22semidirect
20. C22×D3×C3⋊D3C22semidirect
21. C2×#6312C22semidirect
23. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
26. C2×C32×#67C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×D12C22semidirect
29. C2×C32×C4×D3C22semidirect
33. C2×#6291C22semidirect
34. C2×#6291C22semidirect
35. C2×#6291C22semidirect
36. C2×#6289C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
39. C33×C22⋊C4C22semidirect
40. #88859C22semidirect
41. #88859C22semidirect
42. C3×#3757C22semidirect
43. C3×#3752C22semidirect
44. C3×C4⋊(C3⋊Dic3)C22semidirect
45. C3×#3750C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. #88806C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
69. #64092D3semidirect
74. C3×#884D3semidirect
101. C2×D3×C3⋊D3D4semidirect
158. C2×C4×C3⋊D3C2×D3semidirect
160. C2×C3×#67C2×D3semidirect
161. C2×C3×#67C2×D3semidirect
162. C2×C3×D12C2×D3semidirect
164. C2×C3×C4×D3C2×D3semidirect
177. C32×C22⋊C4C2×D3semidirect
178. C32×C22⋊C4C2×D3semidirect
180. #3757C2×D3semidirect
192. #3752C2×D3semidirect
193. C4⋊(C3⋊Dic3)C2×D3semidirect
195. #3750C2×D3semidirect
198. C3×(C2×D3)⋊C4C2×D3semidirect
201. C3×Dic3⋊C4C2×D3semidirect
263. #884C3⋊D3semidirect
399. C2×#67C2×C3⋊D3semidirect
400. C2×#67C2×C3⋊D3semidirect
417. C2×D12C2×C3⋊D3semidirect
422. C2×C4×D3C2×C3⋊D3semidirect
430. C3×C22⋊C4D32semidirect
431. C3×C22⋊C4C2×C3⋊D3semidirect
452. (C2×D3)⋊C4C2×C3⋊D3semidirect
457. Dic3⋊C4C2×C3⋊D3semidirect
556. C33#534semidirect
713. C22⋊C4D3×C3⋊D3semidirect
798. C32#5605semidirect
799. C32#5653semidirect
901. C3#10594264semidirect
902. C3#10596076semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×C3⋊D3×D122
#117239232
C3×#640922
C32×#8842
#117236432
#117236382
#117236162
#117235422
D3×#37522
#117235162
#117234982
#117234752
#117234222
#117234172
#105960763
#105942643