Finite Group Databasebeta

← #13150984

Subgroups — #13150984

Order 1728.

954 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3699C211yesmaximal, characteristic, complemented
2C2×#88663C211yesmaximal, characteristic, complemented
3#11721835C211yesmaximal, characteristic, complemented
4C9×#939C211yesmaximal, characteristic, complemented
5#67×Dic9C211yesmaximal, characteristic, complemented
6Dic3×#611C211yesmaximal, characteristic, complemented
7#11721270C211yesmaximal, characteristic, complemented
8#11721269C211yesmaximal, characteristic, complemented
9#11721265C211yesmaximal, characteristic, complemented
10C2×Dic3⋊Dic9C211yesmaximal, characteristic, complemented
11#11721253C211yesmaximal, characteristic, complemented
12#11721031C211yesmaximal, characteristic, complemented
13#11721018C211yesmaximal, characteristic, complemented
14D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#11720904C211yesmaximal, characteristic, complemented
16#10595151—31nomaximal
17#10589713—31nomaximal
18C2×C3×D4×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C22×C9×Dic3C2211yescharacteristic
25C22×C3×Dic9C2211yescharacteristic
26C22×C3×Dic9C2211yescharacteristic
27C3×#3699—24no—
28C2×C3×C4×D9C2211yescharacteristic
29C2×C3×Dic18C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31#88663—24no—
32C2×D3×Dic9C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic
35C2×#6189C2211yescharacteristic
36#88551C2211yescharacteristic
37#88551C2211yescharacteristic
38#88551C2211yescharacteristic
39#88534C2211yescharacteristic
40#88534C2211yescharacteristic
41C9×#217C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52#88442C2211yescharacteristic
53Dic9⋊Dic3C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×C3×#237—31no—
56C2×#3805—31no—
57#64144—31no—
58C3×#939D311yescharacteristic
59Dic3×#67—31no—
60Dic3×#67—31no—
61#63970—31no—
62#63969—31no—
63C2×Dic3⋊Dic3—31no—
64#63964—31no—
65#63961—31no—
66#63905—31no—
67#63887—31no—
68D3×Dic3⋊C4—31no—
69#63839—31no—
70C2×#3699—31no—
71C2×#3699D311yescharacteristic, complemented
72C9×#121—31no—
73#63500—31no—
74#63497—31no—
75#63497—31no—
76#63497—61no—
77D4×Dic9—31no—
78C4×#611—31no—
79C2×C4⋊Dic9—31no—
80C4⋊C4×D9—31no—
81#63450—31no—
82#63445—31no—
83#63445—31no—
84#63440—31no—
85#63440—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C3×D4×C9—22no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3⋊Dic9—22no—
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C9×#67—22no—
98C9×#67—22no—
99C3×#611—22no—
100C3×#611D414yescomplemented
101C2×C9×Dic3—22no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C3×Dic9—22no—
106C2×C3×Dic9—22no—
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C3×C4×D9—22no—
111C3×Dic18—22no—
112#6194—22no—
113D3×Dic9—22no—
114Dic3×D9—22no—
115Dic3×D9—22no—
116#6189—22no—
117#5824—91no—
118#5611—91no—
119C2×C32×D4C2×D311yescharacteristic
120C22×C3⋊Dic3—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67C2×D311yescharacteristic
124C2×C3×#67C2×D311yescharacteristic
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3C2×D311yescharacteristic
128C3×#237—64no—
129C2×C3×C4×D3—31no—
130C2×C3×Dic6—31no—
131C2×#627—31no—
132C2×#625—31no—
133#3805—64no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137#3757—31no—
138#3757—31no—
139#3757—31no—
140#3750—31no—
141#3750—31no—
142C3×#217C2×D311yescharacteristic
143C3×(C2×D3)⋊C4C2×D311yescharacteristic
144C3×Dic3⋊C4C2×D311yescharacteristic
145#3724—31no—
146#3724—31no—
147Dic3⋊Dic3—31no—
148Dic3⋊Dic3—31no—
149Dic3⋊Dic3—31no—
150Dic3⋊Dic3—31no—
151Dic3⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155Dic32—31no—
156C2×D4×C9—21no—
157C2×D4×C9—31no—
158C2×D4×C9—31no—
159C2×D4×C9C2×D311yescharacteristic
160C22×C4×C9—31no—
161C2×#611—31no—
162C2×#611C2×D311yescharacteristic
163C2×#611C2×D311yescharacteristic
164C22×Dic9—31no—
165C22×Dic9—31no—
166C22×Dic9—61no—
167C22×Dic9C2×D311yescharacteristic
168C22×Dic9C2×D311yescharacteristic
169#3699—24no—
170#3699—64no—
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9C2×D311yescharacteristic
174C2×Dic18—31no—
175C2×Dic18C2×D311yescharacteristic
176C9×C4⋊C4—31no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179#3676—31no—
180#3676—31no—
181#3676—31no—
182#3676—31no—
183#3676—31no—
184#3676—61no—
185#3676—61no—
186#3676—61no—
187(C2×D9)⋊C4—31no—
188C4⋊Dic9—31no—
189C4⋊Dic9—31no—
190C4⋊Dic9—31no—
191C4⋊Dic9—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—61no—
198Dic9⋊C4—61no—
199C4×Dic9—31no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9C2×D412yes—
206C22×C3×C9C2411yescharacteristic
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9C2×D412yes—
213C3×C4×C9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9—21no—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3#4112yescomplemented
221C3×Dic9—21no—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×C3×#41—91no—
225C2×#237—31no—
226C2×#237—91no—
227C2×#237—91no—
228C3×#121—31no—
229#946—91no—
230#944—91no—
231#939—91no—
232#939D911yescharacteristic, complemented
233#938—91no—
234#935—91no—
235#935—91no—
236#935—91no—
237#935—91no—
238#935—181no—
239D4×Dic3—91no—
240D4×Dic3—91no—
241#929—91no—
242#929—91no—
243C4×#67—91no—
244C4×#67—91no—
245C2×C4⋊Dic3—91no—
246#924—91no—
247C2×Dic3⋊C4—91no—
248C2×Dic3⋊C4—91no—
249D3×C4⋊C4—91no—
250#888—91no—
251#883—91no—
252#883—91no—
253#878—91no—
254#878—91no—
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3×D3—31no—
258C22×C3×D3C22×D311yescharacteristic
259C32×D4—22no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C3⋊Dic3—31no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—62no—
266C3×#67—22no—
267C3×#67—22no—
268C3×#67—34no—
269C3×#67—62no—
270C2×C3×Dic3—22no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3—62no—
276C2×C3×Dic3C22×D311yescharacteristic
277C2×C3×Dic3C22×D311yescharacteristic
278C2×C3×Dic3C22×D311yescharacteristic
279C3×C4×D3—62no—
280C3×Dic6—62no—
281#627—62no—
282#625—62no—
283D3×Dic3—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—21no—
287C23×C9—21no—
288C23×C9—31no—
289C23×C9C22×D311yescharacteristic
290C23×C9C22×D311yescharacteristic
291C22×D9C22×D311yescharacteristic
292D4×C9—22no—
293D4×C9—42no—
294D4×C9—62no—
295D4×C9—62no—
296C2×C4×C9—21no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—62no—
301C2×C4×C9C22×D311yescharacteristic
302#611—22no—
303#611—62no—
304#611#6714yescomplemented
305C2×Dic9—22no—
306C2×Dic9—22no—
307C2×Dic9—31no—
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—31no—
311C2×Dic9—61no—
312C2×Dic9—61no—
313C2×Dic9—61no—
314C2×Dic9—61no—
315C2×Dic9—62no—
316C2×Dic9—62no—
317C2×Dic9—122no—
318C2×Dic9C22×D311yescharacteristic
319C2×Dic9C22×D311yescharacteristic
320C2×Dic9C22×D311yescharacteristic
321C4×D9—22no—
322C4×D9—62no—
323C4×D9—62no—
324Dic18—22no—
325Dic18—62no—
326#547—271noSylow
327C2×C3×C9—22no—
328C2×C3×C9—41no—
329C2×C3×C9C22×D411yescharacteristic
330C2×C3×C9C2×#4111yescharacteristic
331C2×C3×C92−1+411yescharacteristic
332D3×C9—41no—
333C3×D9—22no—
334C3×#41—184no—
335C2×C3×Q8—91no—
336C2×C3×D4—21no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—91no—
340C2×C3×D4—91no—
341C2×C3×D4C2×D911yescharacteristic
342C2×C3×D4D3211yescharacteristic
343C22×C3×C4—31no—
344C22×C3×C4—91no—
345C22×C3×C4—91no—
346C22×C3×C4—91no—
347C2×#67—31no—
348C2×#67—31no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67C2×D911yescharacteristic
352C2×#67C2×D911yescharacteristic
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—91no—
356C22×Dic3—91no—
357C22×Dic3—91no—
358C22×Dic3—91no—
359C22×Dic3—91no—
360C22×Dic3—181no—
361C22×Dic3C2×D911yescharacteristic
362#237—64no—
363#237—184no—
364#237—184no—
365C2×C4×D3—31no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×C4×D3—91no—
369C2×Dic6—31no—
370C2×Dic6—91no—
371C2×Dic6—91no—
372C3×C4⋊C4—31no—
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375#217—91no—
376#217—91no—
377#217—91no—
378#217—91no—
379#217—91no—
380#217—91no—
381#217—91no—
382#217—91no—
383#217—91no—
384#217—181no—
385#217—181no—
386#217—181no—
387#217C2×D911yescharacteristic
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4C2×D911yescharacteristic
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
396C4⋊Dic3—91no—
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⋊C4C2×D911yescharacteristic
413C4×Dic3—91no—
414C4×Dic3—91no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32D3×D412yes—
421C22×C32C23×D311yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—32no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C32×C4—21no—
429C3⋊Dic3—61no—
430C3⋊Dic3—61no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—32no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C3×Dic3#23712yes—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—22no—
446C22×C9—41no—
447C22×C9—41no—
448C22×C9—41no—
449C22×C9—41no—
450C22×C9—41no—
451C22×C9—61no—
452C22×C9—61no—
453C22×C9—61no—
454C22×C9C2×#6712yes—
455C22×C9C23×D311yescharacteristic
456C2×D9—21no—
457C2×D9—21no—
458C2×D9C2×#6712yes—
459C4×C9—21no—
460C4×C9—32no—
461C4×C9—41no—
462C4×C9—61no—
463C4×C9—61no—
464Dic9—21no—
465Dic9—21no—
466Dic9—61no—
467Dic9—61no—
468Dic9—61no—
469Dic9—61no—
470Dic9—121no—
471Dic9—121no—
472Dic9—121no—
473Dic9—121no—
474Dic9C2×#6712yes—
475C2×#41—91no—
476C2×#41—271no—
477C4⋊Q8—271no—
478#123—271no—
479#123—271no—
480#123—271no—
481#123—271no—
482C22⋊Q8—271no—
483C22⋊Q8—271no—
484#121—31no—
485#121—271no—
486C4×D4—271no—
487C4×D4—271no—
488C2×C4⋊C4—271no—
489C2×C4⋊C4—271no—
490C3×C9#54711yescharacteristic, complemented, Sylow
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—31no—
494C23×C3—91no—
495C23×C3C22×D911yescharacteristic
496C23×C3C22×D911yescharacteristic
497C23×C3C2×D3211yescharacteristic
498C23×C3C2×D3211yescharacteristic
499C22×D3—31no—
500C22×D3C22×D911yescharacteristic
501C3×Q8—182no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—42no—
505C3×D4—62no—
506C3×D4—62no—
507C3×D4—94no—
508C3×D4—182no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—62no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—182no—
518C2×C3×C4—182no—
519C2×C3×C4—182no—
520C2×C3×C4C22×D911yescharacteristic
521C2×C3×C4C2×D3211yescharacteristic
522#67—22no—
523#67—22no—
524#67—34no—
525#67—62no—
526#67—182no—
527#67—182no—
528C2×Dic3—22no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—62no—
533C2×Dic3—62no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—91no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—181no—
543C2×Dic3—181no—
544C2×Dic3—181no—
545C2×Dic3—181no—
546C2×Dic3—182no—
547C2×Dic3—182no—
548C2×Dic3—182no—
549C2×Dic3—182no—
550C2×Dic3—182no—
551C2×Dic3—362no—
552C2×Dic3C22×D911yescharacteristic
553C2×Dic3C22×D911yescharacteristic
554C2×Dic3C22×D911yescharacteristic
555C4×D3—62no—
556C4×D3—182no—
557C4×D3—182no—
558C4×D3—182no—
559Dic6—62no—
560Dic6—182no—
561Dic6—182no—
562C2×C32—22no—
563C2×C32—41no—
564C2×C32C2×D3×D411yescharacteristic
565C2×C32C2×#23711yescharacteristic
566C2×C32#101011yescharacteristic
567C3×D3—41no—
568C3×D3—62no—
569C2×C9—22no—
570C2×C9—21no—
571C2×C9—21no—
572C2×C9—21no—
573C2×C9—42no—
574C2×C9—41no—
575C2×C9—81no—
576C2×C9—121no—
577C2×C9D3×#4111yescharacteristic
578C2×C9#101011yescharacteristic
579C2×C9C22×#6711yescharacteristic
580D9—22no—
581#41—184no—
582#41—544no—
583C2×Q8—91no—
584C2×Q8—271no—
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—271no—
590C2×D4D3×D911yescharacteristic
591C22×C4—31no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C22×C4—271no—
599C4⋊C4—31no—
600C4⋊C4—271no—
601C4⋊C4—271no—
602C4⋊C4—271no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C4⋊C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C4⋊C4—271no—
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C22⋊C4—271no—
616C22⋊C4—271no—
617C42—271no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—92no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3D4×D912yes—
642C22×C3C23×D911yescharacteristic
643C22×C3D3×#6712yes—
644C22×C3C22×D3211yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—32no—
649C2×D3—61no—
650C2×D3—61no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—32no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—92no—
658C3×C4—181no—
659C3×C4—181no—
660Dic3—21no—
661Dic3—21no—
662Dic3—32no—
663Dic3—61no—
664Dic3—61no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—361no—
674Dic3—361no—
675Dic3—361no—
676Dic3—361no—
677Dic3#369912yescomplemented
678C32#561111yescharacteristic
679C9—21no—
680C9#582411yescharacteristic, complemented
681C23—31no—
682C23—91no—
683C23C2×D3×D911yescharacteristic
684C23C2×D3×D911yescharacteristic
685Q8—182no—
686Q8—542no—
687D4—22no—
688D4—62no—
689D4—62no—
690D4—94no—
691D4—182no—
692D4—542no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—62no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—182no—
701C2×C4—182no—
702C2×C4—182no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4—542no—
710C2×C4—542no—
711C2×C4C2×D3×D911yescharacteristic
712C2×C3—22no—
713C2×C3—22no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—42no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—81no—
721C2×C3—121no—
722C2×C3—182no—
723C2×C3C2×D4×D911yescharacteristic
724C2×C3C2×#369911yescharacteristic
725C2×C3#6371611yescharacteristic
726C2×C3#6430911yescharacteristic
727C2×C3D3×#23711yescharacteristic
728C2×C3C2×D3×#6711yescharacteristic
729D3—41no—
730D3—62no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—92no—
740C22—181no—
741C22—181no—
742C22D9×#6712yes—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—32no—
746C4—61no—
747C4—61no—
748C4—92no—
749C4—181no—
750C4—181no—
751C4—541no—
752C4—541no—
753C4—541no—
754C4—541no—
755C3—21no—
756C3#1058971311yescharacteristic, complemented
757C3#1059515111yescharacteristic
758C2—22no—
759C2—41no—
760C2—121no—
761C2—182no—
762C2#1172249411yescharacteristic
763C2D3×#369911yescharacteristic
764C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#547
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3699C2semidirect
2. C2×#88663C2semidirect
3. #11721835C2semidirect
4. C9×#939C2semidirect
5. #67×Dic9C2semidirect
6. Dic3×#611C2semidirect
7. #11721270C2semidirect
8. #11721269C2semidirect
9. #11721265C2semidirect
10. C2×Dic3⋊Dic9C2semidirect
11. #11721253C2semidirect
12. #11721031C2semidirect
13. #11721018C2semidirect
14. D9×Dic3⋊C4C2semidirect
15. #11720904C2semidirect
71. C2×#3699D3semidirect
100. C3×#611D4semidirect
220. C9×Dic3#41semidirect
232. #939D9semidirect
304. #611#67semidirect
490. C3×C9#547semidirect
677. Dic3#3699semidirect
680. C9#5824semidirect
756. C3#10589713semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#36992
C2×#886632
#117218352
C9×#9392
#67×Dic92
Dic3×#6112
#117212702
#117212692
#117212652
C2×Dic3⋊Dic92
#117212532
#117210312
#117210182
D9×Dic3⋊C42
#117209042
#105951513
#105897133