Finite Group Databasebeta

← #13177351

Subgroups — #13177351

Order 1728.

1888 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723971C211yesmaximal, characteristic, complemented
2C3×#64138C211yesmaximal, characteristic, complemented
3C32×#930C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723633C211yesmaximal, characteristic, complemented
6#11723616C211yesmaximal, characteristic, complemented
7#11723599C211yesmaximal, characteristic, complemented
8#11723542C211yesmaximal, characteristic, complemented
9#11723540C211yesmaximal, characteristic, complemented
10#11723525C211yesmaximal, characteristic, complemented
11#11723504C211yesmaximal, characteristic, complemented
12#11723480C211yesmaximal, characteristic, complemented
13#11723475C211yesmaximal, characteristic, complemented
14#11723430C211yesmaximal, characteristic, complemented
15#11723411C211yesmaximal, characteristic, complemented
16#10596091—31nomaximal
17#10595090—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×D12C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic
30C2×#6291C2211yescharacteristic, complemented
31C2×#6290C2211yescharacteristic
32C2×#6289C2211yescharacteristic, complemented
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34#88859C2211yescharacteristic
35#88859C2211yescharacteristic, complemented
36C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
37C3×#3757C2211yescharacteristic, complemented
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3750C2211yescharacteristic, complemented
41C3×#3750C2211yescharacteristic, complemented
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C32×C4⋊Dic3C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
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#64139—34no—
62#64139—64no—
63#64138D311yescharacteristic, complemented
64#64107—31no—
65#64103—31no—
66#64095—31no—
67#64093—31no—
68#64091—31no—
69#64088—31no—
70C3×#930D314yescomplemented
71C3×#929—34no—
72#63983—34no—
73#63979—34no—
74#63971—34no—
75#63958—34no—
76#63923—34no—
77#63922—34no—
78#63910—34no—
79#63891—34no—
80#63886—34no—
81#63861—34no—
82#63854—34no—
83#63848—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
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×C4—41no—
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96#6312—41no—
97#6312—41no—
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C4⋊(C3⋊(C3⋊D3))—41no—
101C3×#638—41no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C32×#67—41no—
106C32×#67—41no—
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C32×D12—41no—
110#6292—41no—
111#6291—41no—
112#6291—41no—
113#6291—41no—
114#6290—41no—
115#6289—41no—
116D3×C3⋊Dic3—41no—
117#5666—91no—
118#5620—94no—
119C23×C3⋊D3—31no—
120C22×D32—34no—
121C2×C32×D4—31no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C22×C32×C4—24no—
125C22×C32×C4C2×D314yescomplemented
126C22×C32×C4C2×D311yescharacteristic, complemented
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—34no—
130C2×#638—34no—
131C2×#638—31no—
132C2×#638—31no—
133C2×#638—31no—
134C2×#638—31no—
135C2×#638—64no—
136C2×#638—64no—
137C2×#638C2×D311yescharacteristic
138C22×C3⋊Dic3—31no—
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4⋊(C3⋊D3)—34no—
142C2×C4⋊(C3⋊D3)—64no—
143C2×C4×C3⋊D3—31no—
144C2×C3×#67—34no—
145C2×C3×#67C2×D314yes—
146C2×C3×#67C2×D314yescomplemented
147C2×C3×D12C2×D314yes—
148C2×#626—34no—
149C2×#626—34no—
150C2×#626—34no—
151C2×#626—34no—
152C2×#625—34no—
153C2×#624—34no—
154C2×D3×Dic3—34no—
155C32×C4⋊C4—31no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158#3757—31no—
159#3757—31no—
160#3757C2×D311yescharacteristic, complemented
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—34no—
165#3752—34no—
166#3752—31no—
167#3752—31no—
168#3752—64no—
169#3752—64no—
170#3752C2×D311yescharacteristic
171#3752C2×D311yescharacteristic
172C4⋊(C3⋊Dic3)—31no—
173C4⋊(C3⋊Dic3)—34no—
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—64no—
176#3750—31no—
177#3750C2×D311yescharacteristic, complemented
178#3750C2×D311yescharacteristic, complemented
179C4×C3⋊Dic3—31no—
180C3×#217—34no—
181C3×(C2×D3)⋊C4—34no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4C2×D314yes—
184C3×(C2×D3)⋊C4C2×D314yescomplemented
185C3×C4⋊Dic3C2×D314yescomplemented
186C3×Dic3⋊C4—34no—
187C3×Dic3⋊C4—34no—
188#3724—34no—
189Dic3⋊Dic3—34no—
190#3722—34no—
191#3722—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×#123—91no—
226C3×#121—34no—
227#940—94no—
228#940—91no—
229#939—94no—
230#939—94no—
231#938—94no—
232#937—94no—
233#937—94no—
234#937—91no—
235#930—94no—
236#930—91no—
237#930—184no—
238#930C3⋊D311yescharacteristic, complemented
239#929—34no—
240#898—94no—
241#898—91no—
242#898—91no—
243#895—91no—
244#895—91no—
245#894—94no—
246#886—94no—
247#884—94no—
248#884—91no—
249#884—91no—
250#883—91no—
251#883—91no—
252#882—94no—
253#882—91no—
254#882—91no—
255#879—94no—
256C23×C32—24no—
257C23×C32—31no—
258C23×C32—31no—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C22×C3⋊D3—31no—
262C22×C3⋊D3—31no—
263C22×C3⋊D3—34no—
264C22×C3⋊D3—34no—
265C22×C3⋊D3—64no—
266C22×C3⋊D3—64no—
267C22×C3⋊D3—121no—
268C22×C3⋊D3—121no—
269C22×C3⋊D3—121no—
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3×D3—34no—
272C22×C3×D3C22×D314yes—
273C22×C3×D3C22×D314yes—
274C2×D32—124no—
275C2×D32—124no—
276C2×D32—124no—
277C32×D4—121no—
278C32×D4—121no—
279C32×D4—121no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—31no—
283C2×C32×C4—31no—
284C2×C32×C4—41no—
285C2×C32×C4—44no—
286C2×C32×C4—48no—
287C2×C32×C4C22×D314yes—
288C2×C32×C4C22×D314yes—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—41no—
292#638—121no—
293#638—121no—
294#638—121no—
295#638—121no—
296#638—121no—
297#638—121no—
298#638—124no—
299#638—124no—
300#638—128no—
301#638—128no—
302C2×C3⋊Dic3—31no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—121no—
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C2×C3⋊Dic3C22×D311yescharacteristic
312C4⋊(C3⋊D3)—121no—
313C4⋊(C3⋊D3)—124no—
314C4⋊(C3⋊D3)—128no—
315C4⋊(C3⋊D3)—121no—
316C4×C3⋊D3—121no—
317C3×#67—44no—
318C3×#67—44no—
319C3×#67—124no—
320C2×C3×Dic3—34no—
321C2×C3×Dic3—34no—
322C2×C3×Dic3—34no—
323C2×C3×Dic3C22×D314yes—
324C2×C3×Dic3C22×D314yes—
325C3×D12—44no—
326#626—124no—
327#626—124no—
328#626—124no—
329#626—124no—
330#625—124no—
331#624—124no—
332D3×Dic3—124no—
333#560—271noSylow
334C2×C33—41no—
335C2×C33H(5,𝔽2)11yescharacteristic
336C2×C33H(5,𝔽2)11yescharacteristic
337C2×C33H(5,𝔽2)11yescharacteristic
338C3⋊(C3⋊D3)—41no—
339C3⋊(C3⋊D3)—41no—
340C3×C3⋊D3—41no—
341C32×D3—41no—
342C32×D3—41no—
343C23×D3—94no—
344C23×D3—91no—
345C2×C3×D4—34no—
346C2×C3×D4—34no—
347C2×C3×D4—34no—
348C2×C3×D4—91no—
349C22×C3×C4—24no—
350C22×C3×C4D3214yescomplemented
351C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
352C2×#67—34no—
353C2×#67—94no—
354C2×#67—94no—
355C2×#67—94no—
356C2×#67—94no—
357C2×#67—94no—
358C2×#67—94no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—184no—
364C2×#67—184no—
365C2×#67C2×C3⋊D311yescharacteristic
366C2×#67C2×C3⋊D311yescharacteristic, complemented
367C22×Dic3—94no—
368C2×D12—94no—
369C2×D12—91no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—94no—
373C2×D12—91no—
374C2×D12—184no—
375C2×D12C2×C3⋊D311yescharacteristic
376C2×C4×D3—94no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C3×C4⋊C4—34no—
380C3×C4⋊C4—91no—
381C3×C4⋊C4—91no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387#217—34no—
388#217—94no—
389#217—94no—
390#217—91no—
391(C2×D3)⋊C4—34no—
392(C2×D3)⋊C4—34no—
393(C2×D3)⋊C4—94no—
394(C2×D3)⋊C4—94no—
395(C2×D3)⋊C4—94no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—94no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—184no—
405(C2×D3)⋊C4—184no—
406(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
407(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
408C4⋊Dic3—94no—
409C4⋊Dic3—94no—
410C4⋊Dic3—91no—
411C4⋊Dic3—184no—
412C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
413Dic3⋊C4—34no—
414Dic3⋊C4—34no—
415Dic3⋊C4—94no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418C4×Dic3—94no—
419C4×Dic3—91no—
420C22×C32—28no—
421C22×C32—21no—
422C22×C32—24no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—24no—
426C22×C32—24no—
427C22×C32—24no—
428C22×C32—44no—
429C22×C32—44no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32—61no—
435C22×C32—61no—
436C22×C32C23×D314yes—
437C22×C32C23×D311yescharacteristic
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—64no—
448C2×C3⋊D3—64no—
449C2×C3⋊D3—64no—
450C2×C3⋊D3—64no—
451C2×C3⋊D3—64no—
452C2×C3⋊D3—64no—
453C2×C3⋊D3—124no—
454C2×C3⋊D3—124no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3—124no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3—124no—
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—24no—
465C2×C3×D3—24no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3—64no—
469D32—1216no—
470C32×C4—28no—
471C32×C4—24no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—24no—
475C32×C4—44no—
476C32×C4—61no—
477C32×C4—61no—
478C3⋊Dic3—21no—
479C3⋊Dic3—21no—
480C3⋊Dic3—21no—
481C3⋊Dic3—61no—
482C3⋊Dic3—61no—
483C3⋊Dic3—64no—
484C3⋊Dic3—64no—
485C3⋊Dic3—124no—
486C3⋊Dic3—124no—
487C3×Dic3—24no—
488C3×Dic3—24no—
489C3×Dic3—64no—
490C3×Dic3—64no—
491C3×Dic3—64no—
492#127—271no—
493#126—271no—
494#126—271no—
495#123—91no—
496#123—271no—
497#123—271no—
498#121—31no—
499#121—271no—
500#121—271no—
501#121—271no—
502#121—271no—
503#121—271no—
504#120—271no—
505#120—271no—
506#120—271no—
507C33#56011yescharacteristic, complemented, Sylow
508C23×C3—24no—
509C23×C3—34no—
510C23×C3—34no—
511C23×C3—91no—
512C23×C3C2×D3214yes—
513C23×C3C22×C3⋊D311yescharacteristic
514C22×D3—34no—
515C22×D3—94no—
516C22×D3—94no—
517C22×D3—91no—
518C22×D3—91no—
519C22×D3—184no—
520C22×D3—184no—
521C22×D3—361no—
522C22×D3—361no—
523C22×D3—361no—
524C22×D3—364no—
525C22×D3—364no—
526C22×D3—364no—
527C22×D3C22×C3⋊D311yescharacteristic
528C22×D3C22×C3⋊D311yescharacteristic
529C3×D4—124no—
530C3×D4—124no—
531C3×D4—124no—
532C3×D4—361no—
533C2×C3×C4—24no—
534C2×C3×C4—24no—
535C2×C3×C4—34no—
536C2×C3×C4—34no—
537C2×C3×C4—44no—
538C2×C3×C4—41no—
539C2×C3×C4—48no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4C2×D3214yes—
544C2×C3×C4C2×D3214yes—
545C2×C3×C4C22×C3⋊D311yescharacteristic
546C2×C3×C4C22×C3⋊D311yescharacteristic
547#67—41no—
548#67—41no—
549#67—124no—
550#67—361no—
551#67—364no—
552#67—364no—
553#67—364no—
554#67—361no—
555#67—364no—
556#67—364no—
557#67—364no—
558#67—361no—
559#67—361no—
560#67—368no—
561#67—368no—
562C2×Dic3—34no—
563C2×Dic3—34no—
564C2×Dic3—34no—
565C2×Dic3—94no—
566C2×Dic3—94no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—184no—
570C2×Dic3—184no—
571C2×Dic3—364no—
572C2×Dic3C22×C3⋊D311yescharacteristic
573C2×Dic3C22×C3⋊D311yescharacteristic
574D12—41no—
575D12—364no—
576D12—361no—
577D12—368no—
578D12—364no—
579D12—361no—
580D12—361no—
581D12—361no—
582C4×D3—361no—
583C4×D3—364no—
584C4×D3—361no—
585C2×C32—24no—
586C2×C32—24no—
587C2×C32—24no—
588C2×C32—48no—
589C2×C32—41no—
590C2×C32—44no—
591C2×C32—121no—
592C2×C32—121no—
593C2×C32#100414yes—
594C2×C32#100414yes—
595C2×C32#100411yescharacteristic
596C2×C32#100914yes—
597C2×C32#100911yescharacteristic
598C2×C32#100911yescharacteristic
599C3⋊D3—41no—
600C3⋊D3—121no—
601C3⋊D3—121no—
602C3⋊D3—124no—
603C3⋊D3—124no—
604C3⋊D3—244no—
605C3⋊D3—244no—
606C3×D3—44no—
607C3×D3—44no—
608C3×D3—124no—
609C24—271no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C2×D4—271no—
621C2×D4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4D3×C3⋊D311yescharacteristic, complemented
625C4⋊C4—31no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C4⋊C4—271no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C42—271no—
644C22×C3—28no—
645C22×C3—24no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—24no—
652C22×C3—44no—
653C22×C3—44no—
654C22×C3—64no—
655C22×C3—64no—
656C22×C3—64no—
657C22×C3—64no—
658C22×C3—64no—
659C22×C3—64no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3—181no—
663C22×C3C22×D3214yes—
664C22×C3C23×C3⋊D311yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—64no—
672C2×D3—64no—
673C2×D3—64no—
674C2×D3—184no—
675C2×D3—184no—
676C2×D3—184no—
677C2×D3—184no—
678C2×D3—184no—
679C2×D3—184no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—364no—
687C2×D3—364no—
688C2×D3—364no—
689C2×D3—364no—
690C2×D3—364no—
691C2×D3—364no—
692C2×D3—364no—
693C2×D3—3616no—
694C3×C4—28no—
695C3×C4—24no—
696C3×C4—24no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—44no—
700C3×C4—64no—
701C3×C4—64no—
702C3×C4—181no—
703C3×C4—181no—
704C3×C4—181no—
705Dic3—21no—
706Dic3—21no—
707Dic3—64no—
708Dic3—64no—
709Dic3—64no—
710Dic3—184no—
711Dic3—184no—
712Dic3—181no—
713Dic3—181no—
714Dic3—364no—
715Dic3—364no—
716C32—24no—
717C32#562014yescomplemented
718C32#566611yescharacteristic, complemented
719C23—31no—
720C23—31no—
721C23—91no—
722C23—271no—
723C23—271no—
724C23—1081no—
725C23—1081no—
726C23—1081no—
727C23C2×D3×C3⋊D311yescharacteristic
728D4—121no—
729D4—121no—
730D4—121no—
731D4—361no—
732D4—1081no—
733D4—1081no—
734D4—1081no—
735D4—1081no—
736D4—1081no—
737D4—1081no—
738D4—1081no—
739D4—1081no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—41no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—91no—
746C2×C4—271no—
747C2×C4—271no—
748C2×C4—1081no—
749C2×C4—1081no—
750C2×C4C2×D3×C3⋊D311yescharacteristic
751C2×C4C2×D3×C3⋊D311yescharacteristic
752C2×C3—24no—
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—48no—
756C2×C3—44no—
757C2×C3—41no—
758C2×C3—124no—
759C2×C3—124no—
760C2×C3—361no—
761C2×C3#6430714yes—
762C2×C3#6430814yes—
763C2×C3#6433014yes—
764C2×C3#6436111yescharacteristic
765C2×C3#6436111yescharacteristic
766C2×C3#6436611yescharacteristic
767D3—41no—
768D3—41no—
769D3—124no—
770D3—364no—
771D3—364no—
772D3—361no—
773D3—361no—
774D3—724no—
775D3—724no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—181no—
786C22—181no—
787C22—181no—
788C22—541no—
789C22—541no—
790C22—541no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22—1084no—
795C22C22×D3×C3⋊D311yescharacteristic
796C4—21no—
797C4—21no—
798C4—61no—
799C4—61no—
800C4—181no—
801C4—181no—
802C4—181no—
803C4—541no—
804C4—541no—
805C3—24no—
806C3#1059509014yescomplemented
807C3#1059609111yescharacteristic, complemented
808C2—41no—
809C2—121no—
810C2—121no—
811C2—361no—
812C2—1081no—
813C2—1081no—
814C2#1172457911yescharacteristic
815C2#1172458111yescharacteristic
816C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×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. #11723971C2semidirect
2. C3×#64138C2semidirect
3. C32×#930C2semidirect
4. #11723643C2semidirect
5. #11723633C2semidirect
6. #11723616C2semidirect
7. #11723599C2semidirect
8. #11723542C2semidirect
9. #11723540C2semidirect
10. #11723525C2semidirect
11. #11723504C2semidirect
12. #11723480C2semidirect
13. #11723475C2semidirect
14. #11723430C2semidirect
15. #11723411C2semidirect
19. C22×C33×C4C22semidirect
21. C2×#6312C22semidirect
25. C2×C32×#67C22semidirect
30. C2×#6291C22semidirect
32. C2×#6289C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
35. #88859C22semidirect
36. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
37. C3×#3757C22semidirect
40. C3×#3750C22semidirect
41. C3×#3750C22semidirect
43. C32×(C2×D3)⋊C4C22semidirect
44. C32×C4⋊Dic3C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
63. #64138D3semidirect
70. C3×#930D3semidirect
125. C22×C32×C4C2×D3semidirect
126. C22×C32×C4C2×D3semidirect
146. C2×C3×#67C2×D3semidirect
160. #3757C2×D3semidirect
177. #3750C2×D3semidirect
178. #3750C2×D3semidirect
184. C3×(C2×D3)⋊C4C2×D3semidirect
185. C3×C4⋊Dic3C2×D3semidirect
238. #930C3⋊D3semidirect
350. C22×C3×C4D32semidirect
351. C22×C3×C4C2×C3⋊D3semidirect
366. C2×#67C2×C3⋊D3semidirect
407. (C2×D3)⋊C4C2×C3⋊D3semidirect
412. C4⋊Dic3C2×C3⋊D3semidirect
507. C33#560semidirect
624. C22×C4D3×C3⋊D3semidirect
717. C32#5620semidirect
718. C32#5666semidirect
806. C3#10595090semidirect
807. C3#10596091semidirect

Maximal subgroups

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

subgroupindex
#117239712
C3×#641382
C32×#9302
#117236432
#117236332
#117236162
#117235992
#117235422
#117235402
#117235252
#117235042
#117234802
#117234752
#117234302
#117234112
#105960913
#105950903