Finite Group Databasebeta

← #13177412

Subgroups — #13177412

Order 1728.

2128 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723980C211yesmaximal, characteristic, complemented
4C3×#64144C211yesmaximal, characteristic, complemented
5#11723640C211yesmaximal, characteristic, complemented
6#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7#11723618C211yesmaximal, characteristic, complemented
8#11723616C211yesmaximal, characteristic, complemented
9#11723614C211yesmaximal, characteristic, complemented
10#11723612C211yesmaximal, characteristic, complemented
11C2×#88806C211yesmaximal, characteristic, complemented
12#11723477C211yesmaximal, characteristic, complemented
13D3×#3750C211yesmaximal, characteristic, complemented
14#11723414C211yesmaximal, characteristic, complemented
15#11723393C211yesmaximal, characteristic, complemented
16#10596295—31nomaximal
17#10595149—34nomaximal
18C2×C33×D4C2211yescharacteristic
19C2×#6312C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C32×#237—24no—
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×Dic6C2211yescharacteristic
30C2×#6293C2211yescharacteristic
31C2×#6291C2211yescharacteristic
32C2×#6289C2211yescharacteristic
33#89028—24no—
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic
36#88864C2211yescharacteristic
37#88859C2211yescharacteristic
38#88857C2211yescharacteristic
39C3×#3757C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×#3757C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C3×#3750C2211yescharacteristic
44#88807C2211yescharacteristic
45#88807C2211yescharacteristic
46#88806C2211yescharacteristic
47#88806C2211yescharacteristic
48#88806C2211yescharacteristic
49#88806C2211yescharacteristic
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic
51#88804C2211yescharacteristic
52#88804C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×C32×#41—31no—
56C2×#3830—31no—
57C2×C3×#237D314yescomplemented
58C2×#3804—34no—
59#64155—31no—
60#64153—31no—
61#64148—31no—
62#64148—31no—
63#64148—34no—
64#64148—64no—
65#64144—31no—
66#64144D311yescharacteristic, complemented
67D4×C3⋊Dic3—31no—
68#64138—31no—
69#64138—31no—
70C4×#638—31no—
71#64133—31no—
72C2×#3750—31no—
73C2×#3750—31no—
74C3×#935—34no—
75#67⋊Dic3—34no—
76#63971—34no—
77#63969—34no—
78C2×#3724—34no—
79#63966—34no—
80#63964—34no—
81#63952—34no—
82#63888—34no—
83D3×Dic3⋊C4—34no—
84#63850—34no—
85#63839—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C33×D4—22no—
91C2×C33×C4C2311yescharacteristic
92#6312—22no—
93#6312—22no—
94C2×C3⋊(C3⋊Dic3)—22no—
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3×C3⋊Dic3—22no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C32×#67—22no—
104C32×#67D414yescomplemented
105C2×C32×Dic3—22no—
106C2×C32×Dic3—22no—
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C32×C4×D3—22no—
111C32×Dic6—22no—
112#6293—22no—
113#6291—22no—
114#6289—22no—
115D3×C3⋊Dic3—22no—
116D3×C3⋊Dic3—22no—
117#5824—94no—
118#5655—91no—
119C32×#41—64no—
120C2×C32×Q8—31no—
121C2×C32×D4—24no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C2×C32×D4C2×D314yes—
125C2×C32×D4C2×D311yescharacteristic
126C22×C32×C4—31no—
127C22×C32×C4—31no—
128C22×C32×C4—31no—
129C2×#638—31no—
130C2×#638—31no—
131C2×#638—34no—
132C2×#638—34no—
133C2×#638—31no—
134C2×#638—64no—
135C2×#638—64no—
136C22×C3⋊Dic3—31no—
137C22×C3⋊Dic3—34no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3—64no—
141C22×C3⋊Dic3C2×D311yescharacteristic
142#3830—64no—
143C2×C4×C3⋊D3—31no—
144C2×#634—31no—
145C2×C3×#67C2×D314yes—
146C2×C3×#67C2×D314yes—
147C22×C3×Dic3—34no—
148C22×C3×Dic3C2×D314yes—
149C22×C3×Dic3C2×D314yes—
150C3×#237—216no—
151C2×C3×C4×D3C2×D314yes—
152C2×C3×Dic6C2×D314yes—
153C2×#627—34no—
154C2×#626—34no—
155C2×#624—34no—
156#3804—616no—
157C2×D3×Dic3—34no—
158C2×D3×Dic3—34no—
159#3757—31no—
160#3757—34no—
161#3757—31no—
162#3757—64no—
163#3757C2×D311yescharacteristic
164#3757C2×D311yescharacteristic
165#3757C2×D311yescharacteristic
166#3752—31no—
167#3752—34no—
168#3752—31no—
169#3752—31no—
170#3752—64no—
171C4⋊(C3⋊Dic3)—31no—
172#3750—31no—
173#3750—34no—
174#3750—31no—
175#3750—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750—31no—
180#3750—64no—
181#3750C2×D311yescharacteristic
182#3750C2×D311yescharacteristic
183C4×C3⋊Dic3—31no—
184C3×#217—34no—
185C3×#217—34no—
186C3×#217—34no—
187C3×Dic3⋊C4—34no—
188C3×Dic3⋊C4—34no—
189#3724—34no—
190#3724—34no—
191#3724—34no—
192#3724—34no—
193Dic3⋊Dic3—34no—
194Dic3⋊Dic3—34no—
195Dic3⋊Dic3—34no—
196#3722—34no—
197#3722—34no—
198(C2×D3)⋊Dic3—34no—
199Dic32—34no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33—21no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33C2×D412yes—
206C22×C33C2411yescharacteristic
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3C2×D412yes—
213C33×C4—21no—
214C3⋊(C3⋊Dic3)—21no—
215C3⋊(C3⋊Dic3)—21no—
216C3⋊(C3⋊Dic3)#4112yescomplemented
217C3×C3⋊Dic3—21no—
218C3×C3⋊Dic3—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3—21no—
221C32×Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3C2×D412yes—
224C2×C3×#41—34no—
225C2×#237—94no—
226C2×#237C3⋊D311yescharacteristic, complemented
227C2×#235—91no—
228C3×#123—91no—
229#946—94no—
230#944—94no—
231#939—94no—
232#939—94no—
233#939—91no—
234#939—184no—
235#935—34no—
236#935—94no—
237D4×Dic3—94no—
238#929—94no—
239#929—94no—
240C4×#67—94no—
241#924—94no—
242C2×Dic3⋊C4—94no—
243C2×Dic3⋊C4—94no—
244C2×Dic3⋊C4—91no—
245#896—91no—
246#894—91no—
247D3×C4⋊C4—91no—
248#888—91no—
249#886—91no—
250#884—91no—
251#883—91no—
252#67⋊C4—91no—
253#67⋊C4—91no—
254#878—91no—
255C23×C32—24no—
256C23×C32—24no—
257C23×C32—31no—
258C23×C32C22×D314yes—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3⋊D3—34no—
264C22×C3⋊D3—64no—
265C22×C3×D3C22×D314yes—
266C32×Q8—62no—
267C32×D4—22no—
268C32×D4—28no—
269C32×D4—34no—
270C32×D4—48no—
271C32×D4—62no—
272C2×C32×C4—24no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—31no—
276C2×C32×C4—62no—
277C2×C32×C4—62no—
278C2×C32×C4—62no—
279C2×C32×C4C22×D314yes—
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—62no—
283#638—62no—
284#638—68no—
285#638—68no—
286#638—128no—
287#638—128no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—34no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—34no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3—64no—
298C2×C3⋊Dic3—62no—
299C2×C3⋊Dic3—62no—
300C2×C3⋊Dic3—62no—
301C2×C3⋊Dic3—68no—
302C2×C3⋊Dic3—128no—
303C2×C3⋊Dic3C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D311yescharacteristic
306C2×C3⋊Dic3C22×D311yescharacteristic
307C4×C3⋊D3—62no—
308#634—62no—
309C3×#67—28no—
310C3×#67#67116yescomplemented
311C2×C3×Dic3—28no—
312C2×C3×Dic3—28no—
313C2×C3×Dic3—34no—
314C2×C3×Dic3—34no—
315C2×C3×Dic3—34no—
316C2×C3×Dic3—34no—
317C2×C3×Dic3—68no—
318C2×C3×Dic3C22×D314yes—
319C2×C3×Dic3C22×D314yes—
320C2×C3×Dic3C22×D314yes—
321C3×C4×D3—28no—
322C3×Dic6—28no—
323#627—68no—
324#626—68no—
325#624—68no—
326D3×Dic3—68no—
327D3×Dic3—68no—
328#547—271noSylow
329C2×C33—22no—
330C2×C33—41no—
331C2×C33C22×D411yescharacteristic
332C2×C33C2×#4111yescharacteristic
333C2×C332−1+411yescharacteristic
334C3⋊(C3⋊D3)—41no—
335C32×D3—22no—
336C3×#41—616no—
337C2×C3×Q8—34no—
338C2×C3×D4—24no—
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C2×C3×D4D3214yes—
342C2×C3×D4C2×C3⋊D311yescharacteristic
343C22×C3×C4—34no—
344C22×C3×C4—34no—
345C22×C3×C4—34no—
346C22×C3×C4—91no—
347C2×#67—94no—
348C2×#67—94no—
349C2×#67—94no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—184no—
353C2×#67—184no—
354C2×#67C2×C3⋊D311yescharacteristic
355C2×#67C2×C3⋊D311yescharacteristic
356C22×Dic3—34no—
357C22×Dic3—94no—
358C22×Dic3—94no—
359C22×Dic3—94no—
360C22×Dic3—91no—
361C22×Dic3—184no—
362C22×Dic3C2×C3⋊D311yescharacteristic
363C22×Dic3C2×C3⋊D311yescharacteristic
364#237—24no—
365#237—1816no—
366#235—184no—
367C2×D12—91no—
368C2×C4×D3—94no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C2×C4×D3—91no—
372C2×C4×D3C2×C3⋊D311yescharacteristic
373C2×Dic6—94no—
374C2×Dic6—91no—
375C2×Dic6C2×C3⋊D311yescharacteristic
376C3×C4⋊C4—91no—
377C3×C4⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381#217—34no—
382#217—34no—
383#217—34no—
384#217—94no—
385#217—94no—
386#217—91no—
387#217—184no—
388(C2×D3)⋊C4—94no—
389(C2×D3)⋊C4—94no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—94no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—184no—
396C4⋊Dic3—94no—
397C4⋊Dic3—91no—
398C4⋊Dic3—91no—
399Dic3⋊C4—34no—
400Dic3⋊C4—34no—
401Dic3⋊C4—94no—
402Dic3⋊C4—94no—
403Dic3⋊C4—94no—
404Dic3⋊C4—94no—
405Dic3⋊C4—94no—
406Dic3⋊C4—94no—
407Dic3⋊C4—94no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—184no—
415C4×Dic3—94no—
416C4×Dic3—91no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—24no—
423C22×C32—28no—
424C22×C32—24no—
425C22×C32—24no—
426C22×C32—24no—
427C22×C32—24no—
428C22×C32—24no—
429C22×C32—32no—
430C22×C32—44no—
431C22×C32—44no—
432C22×C32—44no—
433C22×C32—44no—
434C22×C32—44no—
435C22×C32—61no—
436C22×C32—61no—
437C22×C32D3×D412yes—
438C22×C32C2×#6718yes—
439C22×C32C23×D314yes—
440C22×C32C23×D311yescharacteristic
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—61no—
444C2×C3⋊D3—64no—
445C2×C3⋊D3—64no—
446C2×C3⋊D3—64no—
447C2×C3⋊D3—124no—
448C2×C3⋊D3—124no—
449C2×C3⋊D3—124no—
450C2×C3×D3—24no—
451C2×C3×D3—24no—
452C2×C3×D3C2×#6718yes—
453C32×C4—21no—
454C32×C4—24no—
455C32×C4—32no—
456C32×C4—44no—
457C32×C4—61no—
458C32×C4—61no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3—21no—
463C3⋊Dic3—32no—
464C3⋊Dic3—38no—
465C3⋊Dic3—68no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3⋊Dic3—64no—
469C3⋊Dic3—64no—
470C3⋊Dic3—124no—
471C3⋊Dic3—124no—
472C3×Dic3—24no—
473C3×Dic3—24no—
474C3×Dic3—64no—
475C3×Dic3—64no—
476C3×Dic3—64no—
477C3×Dic3—64no—
478C3×Dic3C2×#6718yes—
479C2×#41—31no—
480C2×#41—271no—
481C4⋊Q8—271no—
482#123—91no—
483#123—271no—
484#123—271no—
485#123—271no—
486C22⋊Q8—271no—
487C22⋊Q8—271no—
488#121—271no—
489#121—271no—
490C4×D4—271no—
491C4×D4—271no—
492C2×C4⋊C4—271no—
493C2×C4⋊C4—271no—
494C33#54711yescharacteristic, complemented, Sylow
495C23×C3—24no—
496C23×C3—24no—
497C23×C3—34no—
498C23×C3C2×D3214yes—
499C23×C3C2×D3214yes—
500C23×C3C22×C3⋊D311yescharacteristic
501C23×C3C22×C3⋊D311yescharacteristic
502C22×D3—94no—
503C22×D3—91no—
504C22×D3—184no—
505C22×D3C22×C3⋊D311yescharacteristic
506C3×Q8—68no—
507C3×D4—28no—
508C3×D4—22no—
509C3×D4—316no—
510C3×D4—48no—
511C3×D4—68no—
512C2×C3×C4—24no—
513C2×C3×C4—34no—
514C2×C3×C4—34no—
515C2×C3×C4—34no—
516C2×C3×C4—68no—
517C2×C3×C4—68no—
518C2×C3×C4—68no—
519C2×C3×C4—91no—
520C2×C3×C4—91no—
521C2×C3×C4—91no—
522C2×C3×C4—91no—
523C2×C3×C4—182no—
524C2×C3×C4C2×D3214yes—
525C2×C3×C4C22×C3⋊D311yescharacteristic
526#67—22no—
527#67—188no—
528#67—182no—
529#67—188no—
530#67—188no—
531#67—182no—
532#67—368no—
533#67—368no—
534#67#63814yescomplemented
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—34no—
538C2×Dic3—34no—
539C2×Dic3—34no—
540C2×Dic3—34no—
541C2×Dic3—68no—
542C2×Dic3—94no—
543C2×Dic3—91no—
544C2×Dic3—94no—
545C2×Dic3—94no—
546C2×Dic3—91no—
547C2×Dic3—91no—
548C2×Dic3—184no—
549C2×Dic3—184no—
550C2×Dic3—184no—
551C2×Dic3—188no—
552C2×Dic3—188no—
553C2×Dic3—182no—
554C2×Dic3—188no—
555C2×Dic3—368no—
556C2×Dic3C22×C3⋊D311yescharacteristic
557C2×Dic3C22×C3⋊D311yescharacteristic
558C2×Dic3C22×C3⋊D311yescharacteristic
559D12—182no—
560C4×D3—22no—
561C4×D3—188no—
562C4×D3—182no—
563C4×D3—182no—
564C4×D3—182no—
565Dic6—22no—
566Dic6—188no—
567Dic6—182no—
568C2×C32—22no—
569C2×C32—24no—
570C2×C32—24no—
571C2×C32—24no—
572C2×C32—28no—
573C2×C32—48no—
574C2×C32—41no—
575C2×C32—44no—
576C2×C32—62no—
577C2×C32—84no—
578C2×C32C2×D3×D411yescharacteristic
579C2×C32D3×#4114yes—
580C2×C32D3×#4111yescharacteristic
581C2×C32#101014yes—
582C2×C32#101011yescharacteristic
583C2×C32C22×#6714yes—
584C3⋊D3—121no—
585C3⋊D3—124no—
586C3⋊D3—244no—
587C3×D3—28no—
588#41—64no—
589#41—544no—
590C2×Q8—31no—
591C2×Q8—271no—
592C2×D4—31no—
593C2×D4—31no—
594C2×D4—271no—
595C2×D4—271no—
596C2×D4—271no—
597C2×D4D3×C3⋊D311yescharacteristic
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—91no—
602C22×C4—271no—
603C22×C4—271no—
604C22×C4—271no—
605C22×C4—271no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—271no—
609C4⋊C4—271no—
610C4⋊C4—271no—
611C4⋊C4—271no—
612C4⋊C4—271no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C42—271no—
625C22×C3—24no—
626C22×C3—24no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—24no—
636C22×C3—28no—
637C22×C3—38no—
638C22×C3—44no—
639C22×C3—44no—
640C22×C3—44no—
641C22×C3—44no—
642C22×C3—44no—
643C22×C3—64no—
644C22×C3—64no—
645C22×C3D3×#6718yes—
646C22×C3C2×#63812yes—
647C22×C3C22×D3214yes—
648C22×C3C23×C3⋊D311yescharacteristic
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—184no—
652C2×D3—184no—
653C2×D3—184no—
654C2×D3—181no—
655C2×D3—181no—
656C2×D3—181no—
657C2×D3—364no—
658C2×D3—364no—
659C2×D3—364no—
660C2×D3C2×#63812yes—
661C3×C4—24no—
662C3×C4—21no—
663C3×C4—38no—
664C3×C4—44no—
665C3×C4—64no—
666C3×C4—64no—
667C3×C4—181no—
668C3×C4—181no—
669C3×C4—181no—
670C3×C4—181no—
671Dic3—21no—
672Dic3—21no—
673Dic3—64no—
674Dic3—64no—
675Dic3—64no—
676Dic3—64no—
677Dic3—98no—
678Dic3—92no—
679Dic3—188no—
680Dic3—184no—
681Dic3—184no—
682Dic3—181no—
683Dic3—181no—
684Dic3—364no—
685Dic3—364no—
686Dic3C2×#63812yes—
687C32—24no—
688C32#565511yescharacteristic, complemented
689C32#582414yescomplemented
690C23—31no—
691C23—271no—
692C23C2×D3×C3⋊D311yescharacteristic
693C23C2×D3×C3⋊D311yescharacteristic
694Q8—62no—
695Q8—542no—
696D4—22no—
697D4—34no—
698D4—62no—
699D4—542no—
700D4—542no—
701D4—542no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—62no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—182no—
713C2×C4—271no—
714C2×C4—271no—
715C2×C4—271no—
716C2×C4—542no—
717C2×C4—542no—
718C2×C4—542no—
719C2×C4—542no—
720C2×C4C2×D3×C3⋊D311yescharacteristic
721C2×C3—28no—
722C2×C3—22no—
723C2×C3—24no—
724C2×C3—24no—
725C2×C3—24no—
726C2×C3—48no—
727C2×C3—44no—
728C2×C3—41no—
729C2×C3—68no—
730C2×C3—84no—
731C2×C3#6430914yes—
732C2×C3#6431214yes—
733C2×C3C2×D3×#6714yes—
734C2×C3#41×C3⋊D311yescharacteristic
735C2×C3#6436711yescharacteristic
736C2×C3C22×#63811yescharacteristic
737D3—22no—
738D3—364no—
739D3—361no—
740D3—724no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—32no—
747C22—61no—
748C22—61no—
749C22—541no—
750C22—541no—
751C22—541no—
752C22D3×#63812yes—
753C22C22×D3×C3⋊D311yescharacteristic
754C4—21no—
755C4—32no—
756C4—61no—
757C4—61no—
758C4—181no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—272no—
763C4—541no—
764C4—541no—
765C3—24no—
766C3#1059514914yescomplemented
767C3#1059629511yescharacteristic, complemented
768C2—22no—
769C2—41no—
770C2—62no—
771C2—1081no—
772C2#1172458211yescharacteristic
773C2#1172458611yescharacteristic
774C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×#89028C2semidirect
3. #11723980C2semidirect
4. C3×#64144C2semidirect
5. #11723640C2semidirect
6. #67⋊(C3⋊Dic3)C2semidirect
7. #11723618C2semidirect
8. #11723616C2semidirect
9. #11723614C2semidirect
10. #11723612C2semidirect
11. C2×#88806C2semidirect
12. #11723477C2semidirect
13. D3×#3750C2semidirect
14. #11723414C2semidirect
15. #11723393C2semidirect
57. C2×C3×#237D3semidirect
66. #64144D3semidirect
104. C32×#67D4semidirect
216. C3⋊(C3⋊Dic3)#41semidirect
226. C2×#237C3⋊D3semidirect
310. C3×#67#67semidirect
494. C33#547semidirect
534. #67#638semidirect
688. C32#5655semidirect
689. C32#5824semidirect
766. C3#10595149semidirect
767. C3#10596295semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×#890282
#117239802
C3×#641442
#117236402
#67⋊(C3⋊Dic3)2
#117236182
#117236162
#117236142
#117236122
C2×#888062
#117234772
D3×#37502
#117234142
#117233932
#105962953
#105951493