Finite Group Databasebeta

← #13177611

Subgroups — #13177611

Order 1728.

2020 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723978C211yesmaximal, characteristic, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C32×#935C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6#11723627C211yesmaximal, characteristic, complemented
7#11723623C211yesmaximal, characteristic, complemented
8#11723618C211yesmaximal, characteristic, complemented
9#11723596C211yesmaximal, characteristic, complemented
10#11723592C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723512C211yesmaximal, characteristic, complemented
13#11723485C211yesmaximal, characteristic, complemented
14#11723417C211yesmaximal, characteristic, complemented
15#11723403C211yesmaximal, characteristic, complemented
16#10596128—31nomaximal
17#10595255—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×#6293C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×#6289C2211yescharacteristic
31#88864C2211yescharacteristic
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic, complemented
36C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic, complemented
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#123—31no—
54#64147D311yescharacteristic, complemented
55#64146—31no—
56#64146—34no—
57#64146—64no—
58#64139—31no—
59C4×#638—31no—
60#64107—31no—
61#64106—31no—
62#64103—31no—
63#64102—31no—
64#64094—31no—
65#64094—31no—
66#64093—31no—
67#64091—31no—
68C22⋊C4×C3⋊D3—31no—
69#64088—31no—
70C3×#938—34no—
71C3×#935D314yescomplemented
72#63981—34no—
73#63978—34no—
74#63974—34no—
75#63959—34no—
76#63958—34no—
77#63956—34no—
78#63953—34no—
79#63952—34no—
80#63904—34no—
81#63895—34no—
82#63850—34no—
83#63848—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)—22no—
87C22×C3⋊(C3⋊D3)—41no—
88C22×C3⋊(C3⋊D3)—41no—
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C33×D4—41no—
93C2×C33×C4C2311yescharacteristic
94#6312—22no—
95#6312—41no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C3×#638—41no—
99C3×#638—41no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4×C3⋊D3—41no—
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109#6293—41no—
110#6292—22no—
111#6292—41no—
112#6289—41no—
113#6289—41no—
114#5657—94no—
115#5613—91no—
116C23×C3⋊D3—31no—
117C23×C3⋊D3—34no—
118C23×C3⋊D3—64no—
119C2×C32×D4—24no—
120C2×C32×D4C2×D314yes—
121C2×C32×D4C2×D311yescharacteristic
122C22×C32×C4—31no—
123C2×#638—31no—
124C2×#638—34no—
125C2×#638—31no—
126C2×#638—34no—
127C2×#638—64no—
128C2×#638—64no—
129C2×#638C2×D311yescharacteristic
130C2×#638C2×D311yescharacteristic, complemented
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
136C2×#634—31no—
137C2×C3×#67—34no—
138C2×C3×#67—34no—
139C22×C3×Dic3C2×D314yescomplemented
140C2×C3×C4×D3—34no—
141C2×#627—34no—
142C2×#626—34no—
143C2×#626—34no—
144C2×#624—34no—
145C2×#624—34no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151#3757—31no—
152#3757—34no—
153#3757—64no—
154#3757C2×D311yescharacteristic
155#3757C2×D311yescharacteristic, complemented
156#3752—31no—
157#3752—31no—
158#3752—31no—
159#3752—31no—
160#3752—34no—
161#3752—34no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—64no—
167#3752—64no—
168C4⋊(C3⋊Dic3)—31no—
169C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
170#3750—31no—
171#3750—31no—
172C4×C3⋊Dic3—31no—
173C4×C3⋊Dic3—31no—
174C3×#217—34no—
175C3×#217—34no—
176C3×#217C2×D314yes—
177C3×#217C2×D314yes—
178C3×#217C2×D314yescomplemented
179C3×C4⋊Dic3—34no—
180C3×Dic3⋊C4C2×D314yescomplemented
181C3×Dic3⋊C4C2×D314yescomplemented
182#3724—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—34no—
187#3722—34no—
188#3722—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191Dic32—34no—
192Dic32—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
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)—44no—
206C2×C3⋊(C3⋊D3)#4112yes—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3—21no—
210C33×C4—21no—
211C3⋊(C3⋊Dic3)—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3×C3⋊Dic3—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#123—34no—
221C3×#121—91no—
222#939—91no—
223#938—34no—
224#938—91no—
225#937—94no—
226#937—91no—
227#937—91no—
228#937—184no—
229#936—91no—
230#935C3⋊D311yescharacteristic, complemented
231#930—94no—
232#929—91no—
233C4×#67—94no—
234C4×#67—91no—
235#898—94no—
236#898—91no—
237#897—94no—
238#896—91no—
239#894—94no—
240#893—94no—
241#885—94no—
242#885—94no—
243#885—91no—
244#884—94no—
245#882—94no—
246#67⋊C4—91no—
247D3×C22⋊C4—94no—
248D3×C22⋊C4—91no—
249#879—94no—
250#879—91no—
251C23×C32—24no—
252C23×C32—24no—
253C23×C32C22×D314yes—
254C23×C32C22×D314yes—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—31no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—34no—
260C22×C3⋊D3—34no—
261C22×C3⋊D3—64no—
262C22×C3⋊D3—64no—
263C22×C3⋊D3—62no—
264C22×C3⋊D3—68no—
265C22×C3⋊D3—128no—
266C22×C3⋊D3—121no—
267C22×C3⋊D3—121no—
268C22×C3⋊D3—124no—
269C22×C3⋊D3—124no—
270C22×C3⋊D3—128no—
271C22×C3⋊D3—128no—
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3×D3—34no—
274C32×D4—41no—
275C32×D4—44no—
276C32×D4—48no—
277C2×C32×C4—24no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—31no—
282C2×C32×C4—121no—
283C2×C32×C4C22×D314yes—
284C2×C32×C4C22×D311yescharacteristic
285#638—41no—
286#638—41no—
287#638—62no—
288#638—68no—
289#638—128no—
290#638—121no—
291#638—124no—
292#638—128no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—34no—
296C2×C3⋊Dic3—34no—
297C2×C3⋊Dic3—64no—
298C2×C3⋊Dic3—64no—
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C4⋊(C3⋊D3)—62no—
303C4⋊(C3⋊D3)—121no—
304C4×C3⋊D3—41no—
305C4×C3⋊D3—121no—
306C4×C3⋊D3—121no—
307#634—121no—
308C3×#67—124no—
309C3×#67—124no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3—44no—
314C2×C3×Dic3C22×D314yes—
315C2×C3×Dic3C22×D314yes—
316C2×C3×Dic3C22×D314yes—
317C2×C3×Dic3C22×D314yes—
318C3×C4×D3—124no—
319#627—124no—
320#626—68no—
321#626—124no—
322#624—124no—
323#624—124no—
324#538—271noSylow
325C2×C33—41no—
326C2×C33—41no—
327C2×C33C2×#4111yescharacteristic
328C2×C33H(5,𝔽2)11yescharacteristic
329C2×C33H(5,𝔽2)11yescharacteristic
330C3⋊(C3⋊D3)—22no—
331C3⋊(C3⋊D3)—41no—
332C3×C3⋊D3—41no—
333C23×D3—94no—
334C23×D3—91no—
335C23×D3—184no—
336C2×C3×D4—24no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C2×C3×D4D3214yes—
340C2×C3×D4C2×C3⋊D311yescharacteristic
341C22×C3×C4—34no—
342C22×C3×C4—91no—
343C2×#67—34no—
344C2×#67—34no—
345C2×#67—94no—
346C2×#67—91no—
347C2×#67—94no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—184no—
352C2×#67—184no—
353C22×Dic3C2×C3⋊D311yescharacteristic, complemented
354C2×D12—94no—
355C2×D12—94no—
356C2×C4×D3—34no—
357C2×C4×D3—94no—
358C2×C4×D3—94no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×Dic6—94no—
362C2×Dic6—91no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4—91no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—34no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4—91no—
371#217—34no—
372#217—34no—
373#217—94no—
374#217—91no—
375#217—91no—
376#217—91no—
377#217—184no—
378#217C2×C3⋊D311yescharacteristic
379#217C2×C3⋊D311yescharacteristic
380#217C2×C3⋊D311yescharacteristic, complemented
381(C2×D3)⋊C4—94no—
382(C2×D3)⋊C4—94no—
383(C2×D3)⋊C4—94no—
384(C2×D3)⋊C4—94no—
385(C2×D3)⋊C4—94no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—94no—
388(C2×D3)⋊C4—94no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—184no—
396(C2×D3)⋊C4—184no—
397C4⋊Dic3—34no—
398C4⋊Dic3—94no—
399C4⋊Dic3—91no—
400Dic3⋊C4—94no—
401Dic3⋊C4—94no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
405Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
406C4×Dic3—94no—
407C4×Dic3—94no—
408C4×Dic3—91no—
409C4×Dic3—91no—
410C22×C32—28no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—24no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—24no—
421C22×C32—24no—
422C22×C32—24no—
423C22×C32—24no—
424C22×C32—44no—
425C22×C32—44no—
426C22×C32—44no—
427C22×C32—44no—
428C22×C32—44no—
429C22×C32C23×D314yes—
430C22×C32C23×D311yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—32no—
435C2×C3⋊D3—38no—
436C2×C3⋊D3—68no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—68no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—64no—
444C2×C3⋊D3—64no—
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—124no—
453C2×C3⋊D3—1216no—
454C2×C3⋊D3—1232no—
455C2×C3×D3—64no—
456C2×C3×D3—64no—
457C2×C3×D3—64no—
458C32×C4—21no—
459C32×C4—24no—
460C32×C4—44no—
461C32×C4—61no—
462C32×C4—61no—
463C32×C4—61no—
464C32×C4—61no—
465C3⋊Dic3—21no—
466C3⋊Dic3—21no—
467C3⋊Dic3—21no—
468C3⋊Dic3—61no—
469C3⋊Dic3—61no—
470C3⋊Dic3—64no—
471C3⋊Dic3—64no—
472C3⋊Dic3—124no—
473C3⋊Dic3—124no—
474C3×Dic3—24no—
475C3×Dic3—24no—
476C3×Dic3—24no—
477C3×Dic3—24no—
478C3×Dic3—64no—
479C3×Dic3—64no—
480C3×Dic3—64no—
481#126—271no—
482#126—271no—
483#124—271no—
484#124—271no—
485#123—31no—
486#123—271no—
487C22⋊Q8—271no—
488#121—91no—
489#121—271no—
490#121—271no—
491#120—271no—
492#120—271no—
493C4×D4—271no—
494C4×D4—271no—
495C2×C22⋊C4—271no—
496C33#53811yescharacteristic, complemented, Sylow
497C23×C3—24no—
498C23×C3—24no—
499C23×C3—91no—
500C23×C3C2×D3214yes—
501C23×C3C2×D3214yes—
502C23×C3C22×C3⋊D311yescharacteristic
503C23×C3C22×C3⋊D311yescharacteristic
504C22×D3—34no—
505C22×D3—94no—
506C22×D3—91no—
507C22×D3—94no—
508C22×D3—91no—
509C22×D3—184no—
510C22×D3—184no—
511C22×D3—182no—
512C22×D3—188no—
513C22×D3—368no—
514C22×D3—364no—
515C22×D3—364no—
516C22×D3—361no—
517C22×D3—361no—
518C22×D3—368no—
519C22×D3—368no—
520C3×D4—44no—
521C3×D4—41no—
522C3×D4—48no—
523C3×D4—361no—
524C3×D4—361no—
525C2×C3×C4—24no—
526C2×C3×C4—34no—
527C2×C3×C4—34no—
528C2×C3×C4—34no—
529C2×C3×C4—34no—
530C2×C3×C4—91no—
531C2×C3×C4—91no—
532C2×C3×C4—91no—
533C2×C3×C4—124no—
534C2×C3×C4—361no—
535C2×C3×C4C2×D3214yes—
536C2×C3×C4C22×C3⋊D311yescharacteristic
537#67—124no—
538#67—124no—
539#67—182no—
540#67—182no—
541#67—188no—
542#67—368no—
543#67—361no—
544#67—364no—
545#67—361no—
546#67—368no—
547C2×Dic3—34no—
548C2×Dic3—34no—
549C2×Dic3—34no—
550C2×Dic3—41no—
551C2×Dic3—94no—
552C2×Dic3—94no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—184no—
556C2×Dic3—184no—
557C2×Dic3C22×C3⋊D311yescharacteristic
558C2×Dic3C22×C3⋊D311yescharacteristic
559C2×Dic3C22×C3⋊D311yescharacteristic
560C2×Dic3C22×C3⋊D311yescharacteristic
561D12—188no—
562D12—364no—
563C4×D3—124no—
564C4×D3—361no—
565C4×D3—361no—
566C4×D3—364no—
567C4×D3—364no—
568Dic6—361no—
569Dic6—364no—
570C2×C32—24no—
571C2×C32—24no—
572C2×C32—24no—
573C2×C32—48no—
574C2×C32—44no—
575C2×C32—41no—
576C2×C32—41no—
577C2×C32—44no—
578C2×C32—84no—
579C2×C32#100414yes—
580C2×C32#100411yescharacteristic
581C2×C32#100411yescharacteristic
582C2×C32D3×#4114yes—
583C2×C32D3×#4111yescharacteristic
584C2×C32#100914yes—
585C3⋊D3—41no—
586C3⋊D3—62no—
587C3⋊D3—68no—
588C3⋊D3—128no—
589C3⋊D3—128no—
590C3⋊D3—124no—
591C3⋊D3—121no—
592C3×D3—124no—
593C24—271no—
594C2×Q8—271no—
595C2×D4—91no—
596C2×D4—91no—
597C2×D4—271no—
598C2×D4—271no—
599C2×D4—271no—
600C2×D4—271no—
601C2×D4D3×C3⋊D311yescharacteristic
602C22×C4—31no—
603C22×C4—91no—
604C22×C4—271no—
605C22×C4—271no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—91no—
609C4⋊C4—271no—
610C4⋊C4—271no—
611C4⋊C4—271no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—91no—
616C22⋊C4—91no—
617C22⋊C4—271no—
618C22⋊C4—271no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C42—271no—
627C42—271no—
628C22×C3—28no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—24no—
633C22×C3—24no—
634C22×C3—24no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—24no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—44no—
645C22×C3—44no—
646C22×C3—44no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3C22×D3214yes—
651C22×C3C23×C3⋊D311yescharacteristic
652C2×D3—64no—
653C2×D3—64no—
654C2×D3—64no—
655C2×D3—98no—
656C2×D3—92no—
657C2×D3—188no—
658C2×D3—184no—
659C2×D3—184no—
660C2×D3—181no—
661C2×D3—181no—
662C2×D3—188no—
663C2×D3—184no—
664C2×D3—184no—
665C2×D3—184no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—364no—
670C2×D3—364no—
671C2×D3—364no—
672C2×D3—364no—
673C2×D3—364no—
674C2×D3—3616no—
675C2×D3—3632no—
676C3×C4—24no—
677C3×C4—21no—
678C3×C4—44no—
679C3×C4—64no—
680C3×C4—64no—
681C3×C4—64no—
682C3×C4—64no—
683C3×C4—181no—
684C3×C4—181no—
685C3×C4—181no—
686Dic3—21no—
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—64no—
691Dic3—64no—
692Dic3—64no—
693Dic3—184no—
694Dic3—184no—
695Dic3—181no—
696Dic3—181no—
697Dic3—364no—
698Dic3—364no—
699C32—24no—
700C32#561311yescharacteristic, complemented
701C32#565714yescomplemented
702C23—91no—
703C23—271no—
704C23—271no—
705C23—542no—
706C23—1081no—
707C23—1081no—
708C23C2×D3×C3⋊D311yescharacteristic
709C23C2×D3×C3⋊D311yescharacteristic
710Q8—1081no—
711D4—41no—
712D4—361no—
713D4—361no—
714D4—542no—
715D4—542no—
716D4—1081no—
717D4—1081no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—121no—
726C2×C4—271no—
727C2×C4—271no—
728C2×C4—361no—
729C2×C4—1081no—
730C2×C4—1081no—
731C2×C4C2×D3×C3⋊D311yescharacteristic
732C2×C3—24no—
733C2×C3—24no—
734C2×C3—24no—
735C2×C3—48no—
736C2×C3—41no—
737C2×C3—41no—
738C2×C3—44no—
739C2×C3—44no—
740C2×C3—84no—
741C2×C3—361no—
742C2×C3#6431214yes—
743C2×C3#6431414yes—
744C2×C3#6433014yes—
745C2×C3#6436111yescharacteristic
746C2×C3#41×C3⋊D311yescharacteristic
747C2×C3#6436611yescharacteristic
748D3—124no—
749D3—182no—
750D3—188no—
751D3—368no—
752D3—368no—
753D3—361no—
754D3—364no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—181no—
762C22—181no—
763C22—181no—
764C22—272no—
765C22—541no—
766C22—541no—
767C22—541no—
768C22—541no—
769C22—541no—
770C22—1084no—
771C22C22×D3×C3⋊D311yescharacteristic
772C4—21no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—181no—
778C4—181no—
779C4—181no—
780C4—541no—
781C4—541no—
782C3—24no—
783C3#1059525514yescomplemented
784C3#1059612811yescharacteristic, complemented
785C2—41no—
786C2—41no—
787C2—361no—
788C2—542no—
789C2—1081no—
790C2#1172458611yescharacteristic
791C2#1172458911yescharacteristic
792C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11723978C2semidirect
2. C3×#64147C2semidirect
3. C32×#935C2semidirect
4. #11723639C2semidirect
5. #11723632C2semidirect
6. #11723627C2semidirect
7. #11723623C2semidirect
8. #11723618C2semidirect
9. #11723596C2semidirect
10. #11723592C2semidirect
11. #11723591C2semidirect
12. #11723512C2semidirect
13. #11723485C2semidirect
14. #11723417C2semidirect
15. #11723403C2semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
25. C22×C32×Dic3C22semidirect
26. C2×#6293C22semidirect
35. C3×#3757C22semidirect
36. C3×C4⋊(C3⋊Dic3)C22semidirect
39. C32×#217C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
54. #64147D3semidirect
71. C3×#935D3semidirect
130. C2×#638C2×D3semidirect
135. C2×C4×C3⋊D3C2×D3semidirect
139. C22×C3×Dic3C2×D3semidirect
155. #3757C2×D3semidirect
169. C4⋊(C3⋊Dic3)C2×D3semidirect
178. C3×#217C2×D3semidirect
180. C3×Dic3⋊C4C2×D3semidirect
181. C3×Dic3⋊C4C2×D3semidirect
230. #935C3⋊D3semidirect
353. C22×Dic3C2×C3⋊D3semidirect
380. #217C2×C3⋊D3semidirect
404. Dic3⋊C4C2×C3⋊D3semidirect
405. Dic3⋊C4C2×C3⋊D3semidirect
496. C33#538semidirect
700. C32#5613semidirect
701. C32#5657semidirect
783. C3#10595255semidirect
784. C3#10596128semidirect

Maximal subgroups

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

subgroupindex
#117239782
C3×#641472
C32×#9352
#117236392
#117236322
#117236272
#117236232
#117236182
#117235962
#117235922
#117235912
#117235122
#117234852
#117234172
#117234032
#105961283
#105952553