Finite Group Databasebeta

← #13150364

Subgroups — #13150364

Order 1728.

968 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#235C211yesmaximal, characteristic, complemented
2C2×#88663C211yesmaximal, characteristic, complemented
3C2×#88534C211yesmaximal, characteristic, complemented
4C3×#63491C211yesmaximal, characteristic, complemented
5#11721290C211yesmaximal, characteristic, complemented
6#67⋊Dic9C211yesmaximal, characteristic, complemented
7#11721266C211yesmaximal, characteristic, complemented
8#11721032C211yesmaximal, characteristic, complemented
9#11721016C211yesmaximal, characteristic, complemented
10#11721015C211yesmaximal, characteristic, complemented
11D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
12#11720984C211yesmaximal, characteristic, complemented
13#11720976C211yesmaximal, characteristic, complemented
14#11720955C211yesmaximal, characteristic, complemented
15#11720903C211yesmaximal, characteristic, complemented
16#10594888—31nomaximal
17#10589926—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C9×#235—24no—
25C2×C9×D12C2211yescharacteristic
26C2×C4×D3×C9C2211yescharacteristic
27C2×C4×D3×C9C2211yescharacteristic
28C2×C9×Dic6C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31#88663—24no—
32C2×D3×Dic9C2211yescharacteristic
33C2×D3×Dic9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic
35C2×#6189C2211yescharacteristic
36#88534C2211yescharacteristic
37#88534C2211yescharacteristic
38#88534C2211yescharacteristic
39#88534C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×C3×#235D311yescharacteristic
56C2×#3805—31no—
57C2×#3750—31no—
58C3×#929—31no—
59#63980—31no—
60#67⋊Dic3—31no—
61#63962—31no—
62#63905—31no—
63#63887—31no—
64#63885—31no—
65#63884—31no—
66#63879—31no—
67D3×Dic3⋊C4—31no—
68#63851—31no—
69#63839—31no—
70C2×C9×#41—31no—
71C2×#3699—31no—
72#63508—31no—
73#63506—31no—
74#63501—31no—
75#63501—31no—
76#63497—31no—
77#63497—31no—
78D4×Dic9—31no—
79#63491—31no—
80#63491D311yescharacteristic, complemented
81C4×#611—31no—
82#63486—31no—
83C2×Dic9⋊C4—31no—
84C2×Dic9⋊C4—31no—
85C2×Dic9⋊C4—61no—
86C23×C3×C9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9—22no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9—22no—
94C2×C3⋊Dic9—22no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C9×#67—22no—
100C9×#67D414yescomplemented
101C3×#611—22no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C9×D12—22no—
108C4×D3×C9—22no—
109C4×D3×C9—22no—
110C9×Dic6—22no—
111#6194—22no—
112#6194—22no—
113D3×Dic9—22no—
114D3×Dic9—22no—
115Dic3×D9—22no—
116#6189—22no—
117#5824—91no—
118#5655—91no—
119C22×C32×C4C2×D311yescharacteristic
120C22×C3⋊Dic3—31no—
121C22×C3⋊Dic3—31no—
122C2×C3×#67—31no—
123C2×C3×#67C2×D311yescharacteristic
124C2×C3×#67C2×D311yescharacteristic
125C3×#235—24no—
126C2×C3×D12C2×D311yescharacteristic
127C2×C3×C4×D3C2×D311yescharacteristic
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×Dic6C2×D311yescharacteristic
130C2×#627—31no—
131C2×#625—31no—
132C2×#625—31no—
133#3805—64no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137#3750—31no—
138#3750—31no—
139#3750—31no—
140#3750—31no—
141C3×#217—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146#3724—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C9×#41—64no—
157C2×Q8×C9—31no—
158C2×D4×C9—31no—
159C2×D4×C9—31no—
160C2×D4×C9—31no—
161C22×C4×C9—21no—
162C22×C4×C9—31no—
163C22×C4×C9—31no—
164C22×C4×C9C2×D311yescharacteristic
165C2×#611—31no—
166C2×#611—31no—
167C2×#611C2×D311yescharacteristic
168C22×Dic9—31no—
169C22×Dic9—31no—
170C22×Dic9—31no—
171C22×Dic9—31no—
172C22×Dic9—61no—
173C22×Dic9—61no—
174#3699—64no—
175C2×C4×D9—31no—
176C2×Dic18—31no—
177#3676—31no—
178#3676—31no—
179#3676—31no—
180#3676—31no—
181#3676C2×D311yescharacteristic
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4C2×D311yescharacteristic
184(C2×D9)⋊C4C2×D311yescharacteristic
185C4⋊Dic9—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—61no—
194Dic9⋊C4—61no—
195Dic9⋊C4—61no—
196Dic9⋊C4—61no—
197Dic9⋊C4C2×D311yescharacteristic
198Dic9⋊C4C2×D311yescharacteristic
199C4×Dic9—31no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9C2×D412yes—
203C22×C3×C9C2411yescharacteristic
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×D3×C9—21no—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9C2×D412yes—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9—21no—
218C3⋊Dic9#4112yescomplemented
219C9×Dic3—21no—
220C9×Dic3C2×D412yes—
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9—21no—
224C2×C3×#41—31no—
225C2×#237—91no—
226C2×#237—91no—
227C2×#235D911yescharacteristic, complemented
228C3×#123—91no—
229#946—91no—
230#944—91no—
231#939—91no—
232#939—91no—
233#939—91no—
234#935—91no—
235#935—91no—
236D4×Dic3—91no—
237#929—31no—
238#929—91no—
239C4×#67—91no—
240#924—91no—
241C2×Dic3⋊C4—91no—
242C2×Dic3⋊C4—91no—
243C2×Dic3⋊C4—91no—
244C2×Dic3⋊C4—181no—
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×C32C22×D311yescharacteristic
256C22×C3×D3—31no—
257C22×C3×D3C22×D311yescharacteristic
258C22×C3×D3C22×D311yescharacteristic
259C2×C32×C4—22no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C2×C3⋊Dic3—62no—
267C2×C3⋊Dic3—62no—
268C3×#67—22no—
269C3×#67—62no—
270C3×#67#6714yes—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C3×D12—22no—
277C3×C4×D3—22no—
278C3×C4×D3—22no—
279C3×Dic6—22no—
280#627—62no—
281#625—62no—
282#625—62no—
283D3×Dic3—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—21no—
287C23×C9—31no—
288C23×C9—31no—
289C23×C9C22×D311yescharacteristic
290C22×D9C22×D311yescharacteristic
291Q8×C9—62no—
292D4×C9—34no—
293D4×C9—62no—
294D4×C9—62no—
295C2×C4×C9—22no—
296C2×C4×C9—21no—
297C2×C4×C9—21no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—42no—
301C2×C4×C9—62no—
302C2×C4×C9—62no—
303C2×C4×C9C22×D311yescharacteristic
304C2×C4×C9C22×D311yescharacteristic
305#611—22no—
306#611—62no—
307#611—62no—
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—31no—
311C2×Dic9—31no—
312C2×Dic9—61no—
313C2×Dic9—61no—
314C2×Dic9—61no—
315C2×Dic9—61no—
316C2×Dic9—62no—
317C2×Dic9—62no—
318C2×Dic9—62no—
319C2×Dic9—64no—
320C2×Dic9—62no—
321C2×Dic9—122no—
322C2×Dic9C22×D311yescharacteristic
323C2×Dic9C22×D311yescharacteristic
324C2×Dic9C22×D311yescharacteristic
325C4×D9—62no—
326Dic18—62no—
327#547—271noSylow
328C2×C3×C9—22no—
329C2×C3×C9C22×D411yescharacteristic
330C2×C3×C9C2×#4111yescharacteristic
331C2×C3×C92−1+411yescharacteristic
332D3×C9—22no—
333D3×C9—41no—
334C3×D9—41no—
335C3×#41—64no—
336C2×C3×Q8—31no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—91no—
341C22×C3×C4—21no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4C2×D911yescharacteristic
345C22×C3×C4D3211yescharacteristic
346C2×#67—31no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67C2×D911yescharacteristic
352C2×#67C2×D911yescharacteristic
353C22×Dic3—91no—
354C22×Dic3—91no—
355C22×Dic3—91no—
356C22×Dic3—91no—
357C22×Dic3—91no—
358C22×Dic3—91no—
359C22×Dic3—91no—
360C22×Dic3—181no—
361C22×Dic3—181no—
362#237—184no—
363#237—184no—
364#235—24no—
365C2×D12C2×D911yescharacteristic
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×C4×D3C2×D911yescharacteristic
370C2×C4×D3C2×D911yescharacteristic
371C2×Dic6—91no—
372C2×Dic6—91no—
373C2×Dic6C2×D911yescharacteristic
374C3×C4⋊C4—91no—
375C3×C4⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379#217—31no—
380#217—91no—
381#217—91no—
382#217—91no—
383#217—91no—
384#217—91no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4—31no—
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—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395Dic3⋊C4—31no—
396Dic3⋊C4—31no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—181no—
411Dic3⋊C4—181no—
412Dic3⋊C4—181no—
413Dic3⋊C4—181no—
414C4×Dic3—91no—
415C4×Dic3—91no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C2×#6712yes—
419C22×C32C23×D311yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C2×C3×D3C2×#6712yes—
429C32×C4—21no—
430C32×C4—21no—
431C3⋊Dic3—32no—
432C3⋊Dic3—61no—
433C3⋊Dic3—61no—
434C3⋊Dic3—61no—
435C3×Dic3—21no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C3×Dic3C2×#6712yes—
440C22×C9—22no—
441C22×C9—22no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—22no—
446C22×C9—32no—
447C22×C9—61no—
448C22×C9—61no—
449C22×C9—61no—
450C22×C9—61no—
451C22×C9—61no—
452C22×C9D3×D412yes—
453C22×C9C23×D311yescharacteristic
454C2×D9—21no—
455C2×D9—21no—
456C2×D9—21no—
457C4×C9—21no—
458C4×C9—21no—
459C4×C9—32no—
460C4×C9—41no—
461C4×C9—41no—
462C4×C9—61no—
463Dic9—21no—
464Dic9—21no—
465Dic9—21no—
466Dic9—32no—
467Dic9—62no—
468Dic9—62no—
469Dic9—61no—
470Dic9—61no—
471Dic9—61no—
472Dic9—121no—
473Dic9—121no—
474C2×#41—31no—
475C2×#41—271no—
476C4⋊Q8—271no—
477#123—91no—
478#123—271no—
479#123—271no—
480#123—271no—
481C22⋊Q8—271no—
482C22⋊Q8—271no—
483#121—271no—
484#121—271no—
485C4×D4—271no—
486C4×D4—271no—
487C2×C4⋊C4—271no—
488C2×C4⋊C4—271no—
489C3×C9#54711yescharacteristic, complemented, Sylow
490C23×C3—21no—
491C23×C3—31no—
492C23×C3—31no—
493C23×C3—91no—
494C23×C3C22×D911yescharacteristic
495C23×C3C2×D3211yescharacteristic
496C22×D3—31no—
497C22×D3C22×D911yescharacteristic
498C22×D3C22×D911yescharacteristic
499C3×Q8—62no—
500C3×D4—34no—
501C3×D4—62no—
502C3×D4—62no—
503C3×D4—182no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—42no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C22×D911yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520#67—22no—
521#67—62no—
522#67—182no—
523#67—182no—
524#67—182no—
525#67—182no—
526#67#61114yescomplemented
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—181no—
539C2×Dic3—181no—
540C2×Dic3—181no—
541C2×Dic3—181no—
542C2×Dic3—182no—
543C2×Dic3—182no—
544C2×Dic3—182no—
545C2×Dic3—182no—
546C2×Dic3—184no—
547C2×Dic3—182no—
548C2×Dic3—182no—
549C2×Dic3—182no—
550C2×Dic3—362no—
551C2×Dic3C22×D911yescharacteristic
552C2×Dic3C22×D911yescharacteristic
553D12—22no—
554C4×D3—22no—
555C4×D3—22no—
556C4×D3—182no—
557C4×D3—182no—
558C4×D3—182no—
559Dic6—22no—
560Dic6—182no—
561Dic6—182no—
562C2×C32—22no—
563C2×C32D3×#4111yescharacteristic
564C2×C32#101011yescharacteristic
565C2×C32C22×#6711yescharacteristic
566C3×D3—22no—
567C3×D3—41no—
568C3×D3—121no—
569C2×C9—24no—
570C2×C9—22no—
571C2×C9—21no—
572C2×C9—21no—
573C2×C9—21no—
574C2×C9—62no—
575C2×C9—121no—
576C2×C9C2×D3×D411yescharacteristic
577C2×C9D3×#4111yescharacteristic
578C2×C9#101011yescharacteristic
579D9—41no—
580#41—64no—
581#41—544no—
582C2×Q8—31no—
583C2×Q8—271no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—91no—
588C2×D4—271no—
589C2×D4—271no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—271no—
593C22×C4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4D3×D911yescharacteristic
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C22⋊C4—91no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C42—271no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—32no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3C2×#61112yes—
635C22×C3C23×D911yescharacteristic
636C22×C3D3×#6712yes—
637C22×C3C22×D3211yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3C2×#61112yes—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—181no—
656C3×C4—181no—
657C3×C4—181no—
658Dic3—21no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—92no—
663Dic3—92no—
664Dic3—182no—
665Dic3—182no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—361no—
673Dic3—361no—
674Dic3C2×#61112yes—
675C32#582411yescharacteristic
676C9—21no—
677C9#565511yescharacteristic, complemented
678C23—31no—
679C23—31no—
680C23—91no—
681C23C2×D3×D911yescharacteristic
682Q8—62no—
683Q8—542no—
684D4—34no—
685D4—62no—
686D4—62no—
687D4—182no—
688D4—542no—
689D4—542no—
690C2×C4—22no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—91no—
696C2×C4—91no—
697C2×C4—91no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—271no—
701C2×C4—271no—
702C2×C4—542no—
703C2×C4—542no—
704C2×C4—542no—
705C2×C4—542no—
706C2×C4—542no—
707C2×C4C2×D3×D911yescharacteristic
708C2×C4C2×D3×D911yescharacteristic
709C2×C3—24no—
710C2×C3—22no—
711C2×C3—22no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—62no—
716C2×C3—121no—
717C2×C3—361no—
718C2×C3#41×D911yescharacteristic
719C2×C3#6371611yescharacteristic
720C2×C3C22×#61111yescharacteristic
721C2×C3#6429811yescharacteristic
722C2×C3#6430611yescharacteristic
723C2×C3C2×D3×#6711yescharacteristic
724D3—22no—
725D3—41no—
726D3—121no—
727C22—21no—
728C22—21no—
729C22—32no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22D3×#61112yes—
739C22C22×D3×D911yescharacteristic
740C4—21no—
741C4—21no—
742C4—32no—
743C4—61no—
744C4—181no—
745C4—181no—
746C4—181no—
747C4—272no—
748C4—541no—
749C4—541no—
750C4—541no—
751C3—21no—
752C3#1058992611yescharacteristic, complemented
753C3#1059488811yescharacteristic
754C2—22no—
755C2—62no—
756C2—121no—
757C2—361no—
758C2#1172246511yescharacteristic
759C2#1172247511yescharacteristic
760C2C2×D3×#61111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#547
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C9×#235C2semidirect
2. C2×#88663C2semidirect
3. C2×#88534C2semidirect
4. C3×#63491C2semidirect
5. #11721290C2semidirect
6. #67⋊Dic9C2semidirect
7. #11721266C2semidirect
8. #11721032C2semidirect
9. #11721016C2semidirect
10. #11721015C2semidirect
11. D3×Dic9⋊C4C2semidirect
12. #11720984C2semidirect
13. #11720976C2semidirect
14. #11720955C2semidirect
15. #11720903C2semidirect
80. #63491D3semidirect
100. C9×#67D4semidirect
218. C3⋊Dic9#41semidirect
227. C2×#235D9semidirect
489. C3×C9#547semidirect
526. #67#611semidirect
677. C9#5655semidirect
752. C3#10589926semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#2352
C2×#886632
C2×#885342
C3×#634912
#117212902
#67⋊Dic92
#117212662
#117210322
#117210162
#117210152
D3×Dic9⋊C42
#117209842
#117209762
#117209552
#117209032
#105948883
#105899263