Finite Group Databasebeta

← #13177643

Subgroups — #13177643

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×#64148C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4#11723641C211yesmaximal, characteristic, complemented
5#11723639C211yesmaximal, characteristic, complemented
6#11723632C211yesmaximal, characteristic, complemented
7#11723624C211yesmaximal, characteristic, complemented
8Dic3×#638C211yesmaximal, characteristic, complemented
9#11723612C211yesmaximal, characteristic, complemented
10C2×#88804C211yesmaximal, characteristic, complemented
11#11723592C211yesmaximal, characteristic, complemented
12#11723493C211yesmaximal, characteristic, complemented
13#11723453C211yesmaximal, characteristic, complemented
14#11723416C211yesmaximal, characteristic, complemented
15#11723411C211yesmaximal, characteristic, complemented
16#10596031—31nomaximal
17#10595221—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31#88864C2211yescharacteristic
32#88859C2211yescharacteristic
33#88859C2211yescharacteristic
34C3×#3757C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic, complemented
36C3×#3750C2211yescharacteristic, complemented
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic, complemented
39C32×C4⋊Dic3C2211yescharacteristic, complemented
40C32×C4×Dic3C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88807C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88803C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×C4×D4—31no—
54#64148D311yescharacteristic, complemented
55#64146—31no—
56#64146—34no—
57#64146—64no—
58#64139—31no—
59#64138—31no—
60C4×#638—31no—
61C2×#3752—31no—
62#64107—31no—
63#64103—31no—
64#64094—31no—
65#64093—31no—
66#64091—31no—
67#64087—31no—
68#64085—31no—
69#64084—31no—
70C3×#939—34no—
71C3×D4×Dic3D314yescomplemented
72#63981—34no—
73#63978—34no—
74Dic3×#67—34no—
75#63971—34no—
76#63966—34no—
77#63964—34no—
78C2×#3722—34no—
79#63953—34no—
80#63890—34no—
81#63868—34no—
82#63852—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—22no—
93C2×C33×C4C2311yescharacteristic
94#6312—41no—
95#6312—41no—
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C3×#638—22no—
99C3×#638—41no—
100C2×C3×C3⋊Dic3—41no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C32×Dic3—41no—
105C2×C32×Dic3—41no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110#6293—41no—
111#6292—41no—
112#6292—41no—
113Dic3×C3⋊D3—41no—
114#5617—91no—
115#5560—94no—
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—
123C22×C32×C4—31no—
124C2×#638—31no—
125C2×#638—31no—
126C2×#638—34no—
127C2×#638—34no—
128C2×#638—64no—
129C2×#638—64no—
130C2×#638C2×D311yescharacteristic
131C2×#638C2×D311yescharacteristic, complemented
132C22×C3⋊Dic3C2×D311yescharacteristic
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4×C3⋊D3—31no—
136C2×#634—31no—
137C2×C3×#67—34no—
138C2×C3×#67—34no—
139C22×C3×Dic3—34no—
140C22×C3×Dic3C2×D314yes—
141C22×C3×Dic3C2×D314yescomplemented
142C2×#627—34no—
143C2×#626—34no—
144C2×#626—34no—
145C2×D3×Dic3—34no—
146C32×C4⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C42—31no—
150#3757—31no—
151#3757—34no—
152#3757—64no—
153#3757C2×D311yescharacteristic, complemented
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—34no—
158#3752—34no—
159#3752—31no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—64no—
166#3752—64no—
167#3752C2×D311yescharacteristic, complemented
168C4⋊(C3⋊Dic3)—31no—
169#3750—31no—
170#3750—31no—
171#3750—31no—
172#3750C2×D311yescharacteristic, complemented
173C4×C3⋊Dic3—31no—
174C3×#217—34no—
175C3×#217C2×D314yes—
176C3×#217C2×D314yescomplemented
177C3×(C2×D3)⋊C4—34no—
178C3×C4⋊Dic3C2×D314yescomplemented
179C3×Dic3⋊C4—34no—
180C3×C4×Dic3C2×D314yescomplemented
181#3724—34no—
182Dic3⋊Dic3—34no—
183Dic3⋊Dic3—34no—
184Dic3⋊Dic3—34no—
185#3722—34no—
186#3722—34no—
187#3722—34no—
188#3722—34no—
189#3722—34no—
190#3722—34no—
191(C2×D3)⋊Dic3—34no—
192Dic32—34no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33#4112yes—
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)—44no—
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×#121—91no—
221C3×C4×D4—34no—
222#939—34no—
223#939—91no—
224#939—91no—
225#937—94no—
226#937—91no—
227#937—91no—
228#937—184no—
229D4×Dic3—91no—
230D4×Dic3C3⋊D311yescharacteristic, complemented
231#930—94no—
232#929—94no—
233C4×#67—94no—
234C2×(C2×D3)⋊C4—94no—
235C2×(C2×D3)⋊C4—91no—
236#924—91no—
237#898—94no—
238#898—91no—
239#898—91no—
240#894—94no—
241#886—91no—
242#886—91no—
243#885—94no—
244#885—91no—
245#885—91no—
246#884—94no—
247#882—94no—
248#878—94no—
249#876—94no—
250#875—94no—
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—22no—
275C32×D4—28no—
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×C4—121no—
284C2×C32×C4C22×D314yes—
285C2×C32×C4C22×D311yescharacteristic
286#638—22no—
287#638—41no—
288#638—121no—
289#638—121no—
290#638—124no—
291#638—124no—
292#638—128no—
293#638—128no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—31no—
296C2×C3⋊Dic3—34no—
297C2×C3⋊Dic3—34no—
298C2×C3⋊Dic3—41no—
299C2×C3⋊Dic3—64no—
300C2×C3⋊Dic3—64no—
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D311yescharacteristic
303C2×C3⋊Dic3C22×D311yescharacteristic
304C4⋊(C3⋊D3)—121no—
305C4⋊(C3⋊D3)—121no—
306C4×C3⋊D3—121no—
307#634—121no—
308C3×#67—68no—
309C3×#67—124no—
310C2×C3×Dic3—34no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3—34no—
313C2×C3×Dic3—44no—
314C2×C3×Dic3—44no—
315C2×C3×Dic3—124no—
316C2×C3×Dic3C22×D314yes—
317C2×C3×Dic3C22×D314yes—
318C2×C3×Dic3C22×D314yes—
319C2×C3×Dic3C22×D314yes—
320#627—124no—
321#626—124no—
322#626—124no—
323D3×Dic3—124no—
324#538—271noSylow
325C2×C33—22no—
326C2×C33—41no—
327C2×C33C2×#4111yescharacteristic
328C2×C33H(5,𝔽2)11yescharacteristic
329C2×C33H(5,𝔽2)11yescharacteristic
330C3⋊(C3⋊D3)—41no—
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—34no—
343C22×C3×C4—91no—
344C2×#67—34no—
345C2×#67—34no—
346C2×#67—94no—
347C2×#67—94no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—184no—
353C2×#67—184no—
354C22×Dic3—34no—
355C22×Dic3—91no—
356C22×Dic3C2×C3⋊D311yescharacteristic
357C22×Dic3C2×C3⋊D311yescharacteristic, complemented
358C2×D12—94no—
359C2×D12—94no—
360C2×C4×D3—94no—
361C2×Dic6—94no—
362C2×Dic6—91no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—91no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369C3×C42—34no—
370#217—34no—
371#217—94no—
372#217—91no—
373#217—91no—
374#217—184no—
375#217C2×C3⋊D311yescharacteristic
376#217C2×C3⋊D311yescharacteristic, complemented
377(C2×D3)⋊C4—34no—
378(C2×D3)⋊C4—94no—
379(C2×D3)⋊C4—94no—
380(C2×D3)⋊C4—94no—
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—91no—
388(C2×D3)⋊C4—91no—
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—94no—
398C4⋊Dic3—91no—
399C4⋊Dic3—91no—
400C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
401Dic3⋊C4—34no—
402Dic3⋊C4—94no—
403Dic3⋊C4—94no—
404Dic3⋊C4—94no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407C4×Dic3—94no—
408C4×Dic3—91no—
409C4×Dic3C2×C3⋊D311yescharacteristic, complemented
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—24no—
416C22×C32—28no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—24no—
421C22×C32—24no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—44no—
425C22×C32—44no—
426C22×C32—44no—
427C22×C32#23518yes—
428C22×C32#23712yes—
429C22×C32C23×D314yes—
430C22×C32C23×D311yescharacteristic
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—68no—
435C2×C3⋊D3—68no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—64no—
443C2×C3⋊D3—61no—
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—271no—
486#123—271no—
487C22⋊Q8—271no—
488#121—91no—
489#121—271no—
490#121—271no—
491#120—271no—
492#120—271no—
493C4×D4—31no—
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—94no—
507C22×D3—91no—
508C22×D3—91no—
509C22×D3—184no—
510C22×D3—184no—
511C22×D3—188no—
512C22×D3—182no—
513C22×D3—368no—
514C22×D3—364no—
515C22×D3—364no—
516C22×D3—361no—
517C22×D3—361no—
518C22×D3—368no—
519C22×D3—368no—
520C3×D4—28no—
521C3×D4—22no—
522C3×D4—48no—
523C3×D4—182no—
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—124no—
535C2×C3×C4—361no—
536C2×C3×C4C2×D3214yes—
537C2×C3×C4C22×C3⋊D311yescharacteristic
538#67—68no—
539#67—124no—
540#67—361no—
541#67—361no—
542#67—364no—
543#67—364no—
544#67—361no—
545#67—361no—
546#67—368no—
547#67—368no—
548C2×Dic3—34no—
549C2×Dic3—34no—
550C2×Dic3—34no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—94no—
554C2×Dic3—94no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—124no—
558C2×Dic3—184no—
559C2×Dic3—184no—
560C2×Dic3—361no—
561C2×Dic3C22×C3⋊D311yescharacteristic
562C2×Dic3C22×C3⋊D311yescharacteristic
563C2×Dic3C22×C3⋊D311yescharacteristic
564C2×Dic3C22×C3⋊D311yescharacteristic
565D12—364no—
566D12—364no—
567C4×D3—364no—
568Dic6—361no—
569Dic6—364no—
570C2×C32—22no—
571C2×C32—24no—
572C2×C32—24no—
573C2×C32—24no—
574C2×C32—28no—
575C2×C32—48no—
576C2×C32—41no—
577C2×C32—44no—
578C2×C32—84no—
579C2×C32C2×#23514yes—
580C2×C32C2×#23711yescharacteristic
581C2×C32#100414yes—
582C2×C32#100411yescharacteristic
583C2×C32#100914yes—
584C2×C32#100911yescharacteristic
585C3⋊D3—41no—
586C3⋊D3—128no—
587C3⋊D3—128no—
588C3⋊D3—124no—
589C3⋊D3—124no—
590C3⋊D3—121no—
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—31no—
604C22×C4—91no—
605C22×C4—271no—
606C4⋊C4—31no—
607C4⋊C4—91no—
608C4⋊C4—271no—
609C4⋊C4—271no—
610C4⋊C4—271no—
611C4⋊C4—271no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4—271no—
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—31no—
627C42—271no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—24no—
633C22×C3—24no—
634C22×C3—24no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—24no—
639C22×C3—28no—
640C22×C3—44no—
641C22×C3—44no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—44no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3#380418yes—
649C22×C3#382812yes—
650C22×C3C22×D3214yes—
651C22×C3C23×C3⋊D311yescharacteristic
652C2×D3—64no—
653C2×D3—64no—
654C2×D3—64no—
655C2×D3—188no—
656C2×D3—188no—
657C2×D3—184no—
658C2×D3—184no—
659C2×D3—184no—
660C2×D3—184no—
661C2×D3—184no—
662C2×D3—184no—
663C2×D3—181no—
664C2×D3—181no—
665C2×D3—181no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—364no—
670C2×D3—364no—
671C2×D3—364no—
672C2×D3—364no—
673C2×D3—3616no—
674C2×D3—364no—
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#556014yescomplemented
701C32#561711yescharacteristic, complemented
702C23—91no—
703C23—271no—
704C23—271no—
705C23—542no—
706C23—1081no—
707C23—1081no—
708C23C2×D3×C3⋊D311yescharacteristic
709C23C2×D3×C3⋊D311yescharacteristic
710Q8—1081no—
711D4—22no—
712D4—182no—
713D4—361no—
714D4—1081no—
715D4—1081no—
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—121no—
727C2×C4—271no—
728C2×C4—271no—
729C2×C4—361no—
730C2×C4—1081no—
731C2×C4C2×D3×C3⋊D311yescharacteristic
732C2×C3—28no—
733C2×C3—22no—
734C2×C3—24no—
735C2×C3—24no—
736C2×C3—24no—
737C2×C3—48no—
738C2×C3—44no—
739C2×C3—41no—
740C2×C3—84no—
741C2×C3—361no—
742C2×C3#6431414yes—
743C2×C3#6431414yes—
744C2×C3C2×#380414yes—
745C2×C3C2×#382811yescharacteristic
746C2×C3#6436111yescharacteristic
747C2×C3#6436611yescharacteristic
748D3—124no—
749D3—368no—
750D3—368no—
751D3—364no—
752D3—364no—
753D3—361no—
754D3—361no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—181no—
761C22—181no—
762C22—181no—
763C22—541no—
764C22—541no—
765C22—541no—
766C22—541no—
767C22—541no—
768C22—541no—
769C22—1084no—
770C22#8903112yes—
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#1059522114yescomplemented
784C3#1059603111yescharacteristic, complemented
785C2—22no—
786C2—41no—
787C2—361no—
788C2—1081no—
789C2—1081no—
790C2#1172458811yescharacteristic
791C2#1172458911yescharacteristic
792C2C2×#8903111yescharacteristic
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×#64148C2semidirect
3. C32×D4×Dic3C2semidirect
4. #11723641C2semidirect
5. #11723639C2semidirect
6. #11723632C2semidirect
7. #11723624C2semidirect
8. Dic3×#638C2semidirect
9. #11723612C2semidirect
10. C2×#88804C2semidirect
11. #11723592C2semidirect
12. #11723493C2semidirect
13. #11723453C2semidirect
14. #11723416C2semidirect
15. #11723411C2semidirect
23. C2×C3×#638C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×#6293C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
34. C3×#3757C22semidirect
35. C3×#3752C22semidirect
36. C3×#3750C22semidirect
38. C32×#217C22semidirect
39. C32×C4⋊Dic3C22semidirect
40. C32×C4×Dic3C22semidirect
41. #88807C22semidirect
42. #88807C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88803C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
54. #64148D3semidirect
71. C3×D4×Dic3D3semidirect
131. C2×#638C2×D3semidirect
141. C22×C3×Dic3C2×D3semidirect
153. #3757C2×D3semidirect
167. #3752C2×D3semidirect
172. #3750C2×D3semidirect
176. C3×#217C2×D3semidirect
178. C3×C4⋊Dic3C2×D3semidirect
180. C3×C4×Dic3C2×D3semidirect
230. D4×Dic3C3⋊D3semidirect
357. C22×Dic3C2×C3⋊D3semidirect
376. #217C2×C3⋊D3semidirect
400. C4⋊Dic3C2×C3⋊D3semidirect
409. C4×Dic3C2×C3⋊D3semidirect
496. C33#538semidirect
700. C32#5560semidirect
701. C32#5617semidirect
783. C3#10595221semidirect
784. C3#10596031semidirect

Maximal subgroups

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

subgroupindex
#117239782
C3×#641482
C32×D4×Dic32
#117236412
#117236392
#117236322
#117236242
Dic3×#6382
#117236122
C2×#888042
#117235922
#117234932
#117234532
#117234162
#117234112
#105960313
#105952213