Finite Group Databasebeta

← #13175968

Subgroups — #13175968

Order 1728.

1824 conjugacy classes of subgroups.

The subgroup lattice has 808 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×#884C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723637C211yesmaximal, characteristic, complemented
6#11723637C211yesmaximal, characteristic, complemented
7#11723633C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9#11723540C211yesmaximal, characteristic, complemented
10#11723522C211yesmaximal, characteristic, complemented
11#11723515C211yesmaximal, characteristic, complemented
12#11723430C211yesmaximal, characteristic, complemented
13#11723417C211yesmaximal, characteristic, complemented
14#11723414C211yesmaximal, characteristic, complemented
15#11723408C211yesmaximal, characteristic, complemented
16#10596091—31nomaximal
17#10594310—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, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic, complemented
27C2×C32×D12C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×#6290C2211yescharacteristic, complemented
34C33×C22⋊C4C2211yescharacteristic, complemented
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic
37C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
38C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3750C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88803C2211yescharacteristic
47#88803C2211yescharacteristic
48#88803C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#121—31no—
54#64149—31no—
55#64148—31no—
56#64148—31no—
57#64147—31no—
58#64146—31no—
59#64146—31no—
60#64139—31no—
61#64138—31no—
62#64107—31no—
63#64103—31no—
64#64095—31no—
65#64095—34no—
66#64095—64no—
67#64093D311yescharacteristic, complemented
68#64091—31no—
69#64088—31no—
70C3×#884—34no—
71C3×#884D314yescomplemented
72#63983—34no—
73#63980—34no—
74#63980—34no—
75#63979—34no—
76#63922—34no—
77#63922—34no—
78#63908—34no—
79#63908—34no—
80#63861—34no—
81#63861—34no—
82#63850—34no—
83#63850—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×D3×C3⋊D3—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95#6312—41no—
96C2×C3⋊(C3⋊Dic3)—41no—
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C3×#638—41no—
101C3×#638—41no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C3×C4⋊(C3⋊D3)—41no—
105C3×C4×C3⋊D3—41no—
106C32×#67—41no—
107C32×#67—41no—
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C32×D12—41no—
111C32×C4×D3—41no—
112#6292—41no—
113#6291—41no—
114#6290—41no—
115#6290—41no—
116#6290—41no—
117#5620—94no—
118#5620—91no—
119C23×C3⋊D3—31no—
120C22×D32—34no—
121C2×C32×D4—31no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C22×C32×C4—31no—
125C2×#638—31no—
126C2×#638—34no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—31no—
131C2×#638—64no—
132C2×#638C2×D311yescharacteristic
133C2×#638C2×D311yescharacteristic, complemented
134C22×C3⋊Dic3—31no—
135C22×C3⋊Dic3—34no—
136C22×C3⋊Dic3—64no—
137C2×C4⋊(C3⋊D3)—31no—
138C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
139C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
140C2×C3×#67—34no—
141C2×C3×#67—34no—
142C2×C3×#67C2×D314yes—
143C2×C3×#67C2×D314yescomplemented
144C2×C3×D12—34no—
145C2×C3×D12C2×D314yes—
146C2×C3×C4×D3—34no—
147C2×C3×C4×D3C2×D314yescomplemented
148C2×#626—34no—
149C2×#626—34no—
150C2×#625—34no—
151C2×#625—34no—
152C2×#625—34no—
153C32×C4⋊C4—31no—
154C32×C22⋊C4—24no—
155C32×C22⋊C4—31no—
156C32×C22⋊C4C2×D314yescomplemented
157C32×C22⋊C4C2×D311yescharacteristic, complemented
158#3757—31no—
159#3757—31no—
160#3757—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—34no—
167#3752—34no—
168#3752—31no—
169#3752—64no—
170#3752—64no—
171#3752C2×D311yescharacteristic
172C4⋊(C3⋊Dic3)—31no—
173C4⋊(C3⋊Dic3)—31no—
174C4⋊(C3⋊Dic3)—34no—
175C4⋊(C3⋊Dic3)—34no—
176C4⋊(C3⋊Dic3)—64no—
177C4⋊(C3⋊Dic3)—64no—
178#3750—31no—
179#3750—31no—
180#3750C2×D311yescharacteristic, complemented
181C4×C3⋊Dic3—31no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4C2×D314yes—
184C3×Dic3⋊C4—34no—
185C3×Dic3⋊C4C2×D314yescomplemented
186#3724—34no—
187#3724—34no—
188#3722—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191(C2×D3)⋊Dic3—34no—
192(C2×D3)⋊Dic3—34no—
193(C2×D3)⋊Dic3—34no—
194(C2×D3)⋊Dic3—34no—
195Dic32—34no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33C2411yescharacteristic
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—21no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215D3×C3⋊D3—44no—
216C33×C4—21no—
217C33×C4—21no—
218C3⋊(C3⋊Dic3)—21no—
219C3⋊(C3⋊Dic3)—21no—
220C3⋊(C3⋊Dic3)—21no—
221C3×C3⋊Dic3—21no—
222C3×C3⋊Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C3×#121—34no—
226C3×#121—91no—
227#940—94no—
228#940—91no—
229#939—94no—
230#939—94no—
231#939—91no—
232#939—91no—
233#938—94no—
234#938—91no—
235#937—94no—
236#937—94no—
237#937—91no—
238#937—91no—
239#930—94no—
240#930—91no—
241#929—94no—
242#929—91no—
243#898—94no—
244#898—91no—
245#894—94no—
246#894—91no—
247#886—94no—
248#886—91no—
249#886—184no—
250#884—34no—
251#884C3⋊D311yescharacteristic, complemented
252#882—94no—
253#882—91no—
254#879—94no—
255#879—91no—
256C23×C32—24no—
257C23×C32—31no—
258C23×C32—31no—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C22×C3⋊D3—31no—
262C22×C3⋊D3—34no—
263C22×C3⋊D3—64no—
264C22×C3⋊D3—121no—
265C22×C3⋊D3—121no—
266C22×C3⋊D3—121no—
267C22×C3⋊D3C22×D311yescharacteristic
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3×D3—34no—
270C22×C3×D3—34no—
271C22×C3×D3C22×D314yes—
272C22×C3×D3C22×D314yes—
273C2×D32—124no—
274C2×D32—124no—
275C2×D32—124no—
276C32×D4—121no—
277C32×D4—121no—
278C32×D4—121no—
279C2×C32×C4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4—121no—
284C2×C32×C4C22×D314yes—
285C2×C32×C4C22×D314yes—
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288#638—41no—
289#638—41no—
290#638—121no—
291#638—121no—
292#638—121no—
293#638—121no—
294#638—121no—
295#638—124no—
296#638—128no—
297C2×C3⋊Dic3—31no—
298C2×C3⋊Dic3—31no—
299C2×C3⋊Dic3—31no—
300C2×C3⋊Dic3—34no—
301C2×C3⋊Dic3—34no—
302C2×C3⋊Dic3—34no—
303C2×C3⋊Dic3—64no—
304C2×C3⋊Dic3—64no—
305C2×C3⋊Dic3—64no—
306C2×C3⋊Dic3—121no—
307C2×C3⋊Dic3—124no—
308C2×C3⋊Dic3—128no—
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C4⋊(C3⋊D3)—41no—
312C4⋊(C3⋊D3)—121no—
313C4×C3⋊D3—41no—
314C3×#67—44no—
315C3×#67—44no—
316C3×#67—124no—
317C3×#67—124no—
318C2×C3×Dic3—34no—
319C2×C3×Dic3—34no—
320C2×C3×Dic3C22×D314yes—
321C2×C3×Dic3C22×D314yes—
322C3×D12—44no—
323C3×D12—124no—
324C3×C4×D3—44no—
325C3×C4×D3—124no—
326#626—124no—
327#626—124no—
328#625—124no—
329#625—124no—
330#625—124no—
331#560—271noSylow
332C2×C33—41no—
333C2×C33H(5,𝔽2)11yescharacteristic
334C2×C33H(5,𝔽2)11yescharacteristic
335C2×C33H(5,𝔽2)11yescharacteristic
336C3⋊(C3⋊D3)—41no—
337C3×C3⋊D3—41no—
338C3×C3⋊D3—41no—
339C32×D3—41no—
340C32×D3—41no—
341C23×D3—94no—
342C23×D3—91no—
343C2×C3×D4—34no—
344C2×C3×D4—34no—
345C2×C3×D4—34no—
346C2×C3×D4—91no—
347C2×C3×D4—91no—
348C2×C3×D4—91no—
349C22×C3×C4—34no—
350C22×C3×C4—91no—
351C2×#67—34no—
352C2×#67—34no—
353C2×#67—94no—
354C2×#67—94no—
355C2×#67—94no—
356C2×#67—94no—
357C2×#67—94no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—184no—
364C2×#67C2×C3⋊D311yescharacteristic
365C2×#67C2×C3⋊D311yescharacteristic, complemented
366C22×Dic3—94no—
367C22×Dic3—91no—
368C22×Dic3—184no—
369C2×D12—34no—
370C2×D12—94no—
371C2×D12—91no—
372C2×D12C2×C3⋊D311yescharacteristic
373C2×C4×D3—34no—
374C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
375C3×C4⋊C4—34no—
376C3×C4⋊C4—91no—
377C3×C22⋊C4—24no—
378C3×C22⋊C4—34no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4D3214yescomplemented
381C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
382#217—94no—
383#217—94no—
384#217—94no—
385#217—91no—
386#217—91no—
387#217—91no—
388(C2×D3)⋊C4—34no—
389(C2×D3)⋊C4—94no—
390(C2×D3)⋊C4—94no—
391(C2×D3)⋊C4—94no—
392(C2×D3)⋊C4—94no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—94no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—184no—
402(C2×D3)⋊C4—184no—
403(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
404C4⋊Dic3—94no—
405C4⋊Dic3—94no—
406C4⋊Dic3—91no—
407C4⋊Dic3—91no—
408C4⋊Dic3—184no—
409C4⋊Dic3—184no—
410Dic3⋊C4—34no—
411Dic3⋊C4—94no—
412Dic3⋊C4—94no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
416C4×Dic3—94no—
417C4×Dic3—91no—
418C22×C32—28no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—24no—
422C22×C32—21no—
423C22×C32—24no—
424C22×C32—24no—
425C22×C32—24no—
426C22×C32—44no—
427C22×C32—44no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32C23×D314yes—
435C22×C32C23×D311yescharacteristic
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—64no—
446C2×C3⋊D3—64no—
447C2×C3⋊D3—64no—
448C2×C3⋊D3—124no—
449C2×C3⋊D3—124no—
450C2×C3⋊D3—124no—
451C2×C3⋊D3—124no—
452C2×C3×D3—24no—
453C2×C3×D3—24no—
454C2×C3×D3—24no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—24no—
458C2×C3×D3—64no—
459C2×C3×D3—64no—
460C2×C3×D3—64no—
461C2×C3×D3—64no—
462C2×C3×D3—64no—
463C2×C3×D3—64no—
464D32—1216no—
465C32×C4—21no—
466C32×C4—21no—
467C32×C4—24no—
468C32×C4—24no—
469C32×C4—44no—
470C32×C4—44no—
471C32×C4—61no—
472C32×C4—61no—
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3⋊Dic3—61no—
476C3⋊Dic3—61no—
477C3⋊Dic3—61no—
478C3⋊Dic3—64no—
479C3⋊Dic3—64no—
480C3⋊Dic3—64no—
481C3⋊Dic3—124no—
482C3⋊Dic3—124no—
483C3⋊Dic3—124no—
484C3×Dic3—24no—
485C3×Dic3—24no—
486C3×Dic3—64no—
487C3×Dic3—64no—
488#127—271no—
489#126—271no—
490#126—271no—
491#123—271no—
492#123—271no—
493#123—271no—
494#121—31no—
495#121—91no—
496#121—271no—
497#121—271no—
498#121—271no—
499#121—271no—
500#120—271no—
501#120—271no—
502#120—271no—
503C33#56011yescharacteristic, complemented, Sylow
504C23×C3—24no—
505C23×C3—34no—
506C23×C3—34no—
507C23×C3—91no—
508C23×C3—91no—
509C23×C3C2×D3214yes—
510C23×C3C22×C3⋊D311yescharacteristic
511C22×D3—34no—
512C22×D3—34no—
513C22×D3—94no—
514C22×D3—91no—
515C22×D3—184no—
516C22×D3—361no—
517C22×D3—361no—
518C22×D3—361no—
519C22×D3—364no—
520C22×D3—364no—
521C22×D3—364no—
522C22×D3C22×C3⋊D311yescharacteristic
523C22×D3C22×C3⋊D311yescharacteristic
524C3×D4—124no—
525C3×D4—124no—
526C3×D4—124no—
527C3×D4—361no—
528C3×D4—361no—
529C3×D4—361no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—34no—
533C2×C3×C4—34no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—124no—
537C2×C3×C4—361no—
538C2×C3×C4C2×D3214yes—
539C2×C3×C4C2×D3214yes—
540C2×C3×C4C22×C3⋊D311yescharacteristic
541C2×C3×C4C22×C3⋊D311yescharacteristic
542#67—41no—
543#67—41no—
544#67—124no—
545#67—124no—
546#67—361no—
547#67—364no—
548#67—361no—
549#67—361no—
550#67—361no—
551#67—364no—
552#67—364no—
553#67—364no—
554#67—364no—
555#67—361no—
556#67—368no—
557C2×Dic3—34no—
558C2×Dic3—34no—
559C2×Dic3—94no—
560C2×Dic3—94no—
561C2×Dic3—94no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—184no—
566C2×Dic3—184no—
567C2×Dic3—184no—
568C2×Dic3—364no—
569C2×Dic3—361no—
570C2×Dic3—368no—
571C2×Dic3C22×C3⋊D311yescharacteristic
572C2×Dic3C22×C3⋊D311yescharacteristic
573D12—41no—
574D12—124no—
575D12—364no—
576D12—361no—
577C4×D3—41no—
578C4×D3—124no—
579C2×C32—24no—
580C2×C32—24no—
581C2×C32—24no—
582C2×C32—48no—
583C2×C32—44no—
584C2×C32—41no—
585C2×C32—121no—
586C2×C32—121no—
587C2×C32#100414yes—
588C2×C32#100414yes—
589C2×C32#100411yescharacteristic
590C2×C32#100411yescharacteristic
591C2×C32#100914yes—
592C2×C32#100911yescharacteristic
593C3⋊D3—41no—
594C3⋊D3—41no—
595C3⋊D3—121no—
596C3⋊D3—124no—
597C3⋊D3—244no—
598C3×D3—44no—
599C3×D3—44no—
600C3×D3—124no—
601C3×D3—124no—
602C24—271no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—91no—
607C2×D4—91no—
608C2×D4—91no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—31no—
616C22×C4—91no—
617C22×C4—271no—
618C4⋊C4—31no—
619C4⋊C4—91no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C4⋊C4—271no—
624C22⋊C4—31no—
625C22⋊C4—91no—
626C22⋊C4—271no—
627C22⋊C4—271no—
628C22⋊C4—271no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4D3×C3⋊D311yescharacteristic, complemented
636C42—271no—
637C22×C3—28no—
638C22×C3—24no—
639C22×C3—24no—
640C22×C3—24no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—24no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3—64no—
648C22×C3—64no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—64no—
652C22×C3—64no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3C22×D3214yes—
660C22×C3C23×C3⋊D311yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—64no—
668C2×D3—64no—
669C2×D3—64no—
670C2×D3—64no—
671C2×D3—64no—
672C2×D3—64no—
673C2×D3—184no—
674C2×D3—184no—
675C2×D3—184no—
676C2×D3—181no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—364no—
680C2×D3—364no—
681C2×D3—364no—
682C2×D3—364no—
683C2×D3—3616no—
684C3×C4—24no—
685C3×C4—24no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—44no—
689C3×C4—44no—
690C3×C4—64no—
691C3×C4—64no—
692C3×C4—181no—
693C3×C4—181no—
694Dic3—21no—
695Dic3—21no—
696Dic3—64no—
697Dic3—64no—
698Dic3—184no—
699Dic3—184no—
700Dic3—184no—
701Dic3—181no—
702Dic3—181no—
703Dic3—181no—
704Dic3—364no—
705Dic3—364no—
706Dic3—364no—
707C32—24no—
708C32#562014yescomplemented
709C32#562011yescharacteristic, complemented
710C23—31no—
711C23—31no—
712C23—91no—
713C23—91no—
714C23—271no—
715C23—1081no—
716C23—1081no—
717C23—1081no—
718C23C2×D3×C3⋊D311yescharacteristic
719D4—121no—
720D4—121no—
721D4—121no—
722D4—361no—
723D4—361no—
724D4—361no—
725D4—1081no—
726D4—1081no—
727D4—1081no—
728D4—1081no—
729D4—1081no—
730D4—1081no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—121no—
736C2×C4—271no—
737C2×C4—271no—
738C2×C4—271no—
739C2×C4—361no—
740C2×C4—1081no—
741C2×C4C2×D3×C3⋊D311yescharacteristic
742C2×C4C2×D3×C3⋊D311yescharacteristic
743C2×C3—24no—
744C2×C3—24no—
745C2×C3—24no—
746C2×C3—48no—
747C2×C3—44no—
748C2×C3—41no—
749C2×C3—124no—
750C2×C3—124no—
751C2×C3—361no—
752C2×C3—361no—
753C2×C3#6430814yes—
754C2×C3#6431314yes—
755C2×C3#6431314yes—
756C2×C3#6436111yescharacteristic
757C2×C3#6436111yescharacteristic
758C2×C3#6436611yescharacteristic
759D3—41no—
760D3—41no—
761D3—124no—
762D3—124no—
763D3—364no—
764D3—361no—
765D3—724no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—541no—
782C22—541no—
783C22—541no—
784C22—1084no—
785C22C22×D3×C3⋊D311yescharacteristic
786C4—21no—
787C4—21no—
788C4—61no—
789C4—61no—
790C4—181no—
791C4—181no—
792C4—541no—
793C4—541no—
794C4—541no—
795C3—24no—
796C3#1059431014yescomplemented
797C3#1059609111yescharacteristic, complemented
798C2—41no—
799C2—121no—
800C2—121no—
801C2—361no—
802C2—361no—
803C2—1081no—
804C2#1172458111yescharacteristic
805C2#1172458711yescharacteristic
806C2#1172458711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33#560
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×#884C2semidirect
4. #11723643C2semidirect
5. #11723637C2semidirect
6. #11723637C2semidirect
7. #11723633C2semidirect
8. #11723541C2semidirect
9. #11723540C2semidirect
10. #11723522C2semidirect
11. #11723515C2semidirect
12. #11723430C2semidirect
13. #11723417C2semidirect
14. #11723414C2semidirect
15. #11723408C2semidirect
20. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C3×#638C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
26. C2×C32×#67C22semidirect
28. C2×C32×C4×D3C22semidirect
33. C2×#6290C22semidirect
34. C33×C22⋊C4C22semidirect
37. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
38. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
40. C3×#3750C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. #88806C22semidirect
44. #88806C22semidirect
48. #88803C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
67. #64093D3semidirect
71. C3×#884D3semidirect
133. C2×#638C2×D3semidirect
139. C2×C4×C3⋊D3C2×D3semidirect
143. C2×C3×#67C2×D3semidirect
147. C2×C3×C4×D3C2×D3semidirect
156. C32×C22⋊C4C2×D3semidirect
157. C32×C22⋊C4C2×D3semidirect
180. #3750C2×D3semidirect
185. C3×Dic3⋊C4C2×D3semidirect
251. #884C3⋊D3semidirect
365. C2×#67C2×C3⋊D3semidirect
374. C2×C4×D3C2×C3⋊D3semidirect
380. C3×C22⋊C4D32semidirect
381. C3×C22⋊C4C2×C3⋊D3semidirect
415. Dic3⋊C4C2×C3⋊D3semidirect
503. C33#560semidirect
635. C22⋊C4D3×C3⋊D3semidirect
708. C32#5620semidirect
709. C32#5620semidirect
796. C3#10594310semidirect
797. C3#10596091semidirect

Maximal subgroups

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

subgroupindex
#117239272
C3×#640932
C32×#8842
#117236432
#117236372
#117236332
#117235412
#117235402
#117235222
#117235152
#117234302
#117234172
#117234142
#117234082
#105960913
#105943103