Finite Group Databasebeta

← #13147937

Subgroups — #13147937

Order 1728.

946 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×#88658C211yesmaximal, characteristic, complemented
2C2×D9×Dic6C211yesmaximal, characteristic, complemented
3#11721731C211yesmaximal, characteristic, complemented
4C3×#63446C211yesmaximal, characteristic, complemented
5C9×#878C211yesmaximal, characteristic, complemented
6Dic3×#611C211yesmaximal, characteristic, complemented
7#11721271C211yesmaximal, characteristic, complemented
8#11721257C211yesmaximal, characteristic, complemented
9#11721003C211yesmaximal, characteristic, complemented
10#11721002C211yesmaximal, characteristic, complemented
11#11720998C211yesmaximal, characteristic, complemented
12#11720996C211yesmaximal, characteristic, complemented
13#11720994C211yesmaximal, characteristic, complemented
14#11720983C211yesmaximal, characteristic, complemented
15#11720902C211yesmaximal, characteristic, complemented
16#10594074—31nomaximal
17#10589735—31nomaximal
18C2×#6233C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C22×C9×Dic3C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C9×Dic6C2211yescharacteristic
26C2×#6192C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×(C3⋊D9)⋊C4C2211yescharacteristic
29#88658—24no—
30C2×Dic3×D9C2211yescharacteristic
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C2×#6189C2211yescharacteristic
34C2×#6189C2211yescharacteristic
35D9×Dic6—24no—
36C3×C9×C22⋊C4C2211yescharacteristic
37#88551C2211yescharacteristic
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic
40C4×C3⋊Dic9C2211yescharacteristic
41C9×#217C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C9×C4⋊Dic3C2211yescharacteristic
44C9×Dic3⋊C4C2211yescharacteristic
45C9×Dic3⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47#88445C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53Dic3×Dic9C2211yescharacteristic
54Dic3×Dic9C2211yescharacteristic
55C2×#3804—31no—
56C2×D3×Dic6—31no—
57#64094—31no—
58C3×#884—31no—
59C3×#878D311yescharacteristic
60Dic3×#67—31no—
61#63971—31no—
62#63959—31no—
63#63907—31no—
64#63904—31no—
65#63898—31no—
66#63896—31no—
67#63895—31no—
68#63886—31no—
69#63838—31no—
70C2×Q8×D9—31no—
71C2×#3697—31no—
72C9×C22⋊Q8—31no—
73#63509—31no—
74C4×#611—31no—
75#63458—31no—
76#63458—31no—
77#63457—31no—
78#63455—31no—
79#63455—31no—
80#63449—31no—
81#63447—31no—
82#63447—31no—
83#63447—61no—
84#63446—31no—
85#63446D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92#6233—22no—
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96#6226—22no—
97C3×#611—22no—
98C3×#611—22no—
99C2×C9×Dic3—22no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×D36—22no—
107C3×C4×D9—22no—
108C9×Dic6—22no—
109#6192—22no—
110#6192—22no—
111(C3⋊D9)⋊C4—22no—
112Dic3×D9—22no—
113Dic3×D9—22no—
114Dic3×D9—22no—
115#6189—22no—
116#6189D414yescomplemented
117#5633—91no—
118#5598—91no—
119C2×#638—31no—
120C2×#634—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C22×C3×Dic3C2×D311yescharacteristic
124C2×C3×D12—31no—
125C2×C3×C4×D3—31no—
126C2×C3×Dic6C2×D311yescharacteristic
127C2×#627—31no—
128C2×#627—31no—
129C2×#626—31no—
130C2×#626—31no—
131C2×#624—31no—
132#3804—64no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136D3×Dic6—64no—
137C32×C22⋊C4C2×D311yescharacteristic
138#3757—31no—
139#3752—31no—
140#3752—31no—
141C4×C3⋊Dic3—31no—
142C3×#217C2×D311yescharacteristic
143C3×(C2×D3)⋊C4—31no—
144C3×C4⋊Dic3C2×D311yescharacteristic
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4C2×D311yescharacteristic
147C3×Dic3⋊C4C2×D311yescharacteristic
148#3724—31no—
149Dic3⋊Dic3—31no—
150#3722—31no—
151(C2×D3)⋊Dic3—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154Dic32—31no—
155Dic32—31no—
156C2×Q8×C9—31no—
157C22×C4×C9—31no—
158C2×#611—31no—
159C2×#611—61no—
160C2×#611C2×D311yescharacteristic
161C2×#611C2×D311yescharacteristic
162Q8×D9—64no—
163#3697—64no—
164C2×D36—31no—
165C2×D36—31no—
166C2×D36C2×D311yescharacteristic
167C2×C4×D9—31no—
168C2×C4×D9—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9C2×D311yescharacteristic
172C2×Dic18—31no—
173C2×Dic18—31no—
174C2×Dic18—31no—
175C2×Dic18—61no—
176C9×C4⋊C4—31no—
177C9×C4⋊C4—31no—
178C9×C4⋊C4—31no—
179C9×C22⋊C4—21no—
180C9×C22⋊C4—31no—
181C9×C22⋊C4C2×D311yescharacteristic
182#3676—31no—
183#3676—61no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—61no—
191(C2×D9)⋊C4—61no—
192(C2×D9)⋊C4C2×D311yescharacteristic
193Dic9⋊C4—31no—
194Dic9⋊C4—31no—
195Dic9⋊C4C2×D311yescharacteristic
196C4×Dic9—31no—
197C4×Dic9—31no—
198C4×Dic9—31no—
199C4×Dic9—61no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C2×C3×D9—21no—
211C2×C3×D9—21no—
212C2×C3×D9#4112yescomplemented
213C3×C4×C9—21no—
214C3×C4×C9—21no—
215C3⋊Dic9—21no—
216C3⋊Dic9—21no—
217C3⋊Dic9C2×D412yes—
218C9×Dic3—21no—
219C9×Dic3—21no—
220C9×Dic3—21no—
221C9×Dic3C2×D412yes—
222C3×Dic9—21no—
223C3×Dic9C2×D412yes—
224C2×D3×Q8—91no—
225C2×#237—91no—
226C2×#235—91no—
227C22×Dic6—91no—
228C3×C22⋊Q8—31no—
229C3×#121—91no—
230#947—91no—
231#939—91no—
232#939—91no—
233#936—91no—
234D4×Dic3—91no—
235D4×Dic3—91no—
236C4×#67—91no—
237C4×#67—91no—
238#897—91no—
239#896—91no—
240#896—91no—
241#895—91no—
242#893—91no—
243#893—91no—
244#887—91no—
245#887—91no—
246#885—91no—
247#885—91no—
248#885—91no—
249#885—91no—
250#885—181no—
251#884—31no—
252#884—91no—
253#878—91no—
254#878D911yescharacteristic, complemented
255C23×C32C22×D311yescharacteristic
256C22×C3⋊D3—31no—
257C22×C3×D3—31no—
258C22×C3×D3—31no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261#638—62no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265#634—62no—
266C3×#67—62no—
267C3×#67—62no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3C22×D311yescharacteristic
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C3×D12—62no—
276C3×C4×D3—62no—
277C3×Dic6—22no—
278#627—34no—
279#627—62no—
280#626—62no—
281#626—62no—
282#624—62no—
283D3×Dic3—62no—
284D3×Dic3—62no—
285D3×Dic3—62no—
286C23×C9—21no—
287C23×C9C22×D311yescharacteristic
288C22×D9—31no—
289C22×D9—61no—
290C22×D9C22×D311yescharacteristic
291C22×D9C22×D311yescharacteristic
292Q8×C9—62no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—31no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—62no—
300C2×C4×C9C22×D311yescharacteristic
301C2×C4×C9C22×D311yescharacteristic
302#611—22no—
303#611—22no—
304#611—62no—
305#611—122no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—31no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9C22×D311yescharacteristic
313C2×Dic9C22×D311yescharacteristic
314D36—22no—
315D36—62no—
316D36—62no—
317C4×D9—22no—
318C4×D9—62no—
319C4×D9—62no—
320C4×D9—62no—
321C4×D9—62no—
322Dic18—34no—
323Dic18—62no—
324Dic18—62no—
325Dic18—122no—
326#548—271noSylow
327C2×C3×C9—41no—
328C2×C3×C9C22×D411yescharacteristic
329C2×C3×C9C2×#4111yescharacteristic
330C2×C3×C92−1+411yescharacteristic
331C3⋊D9—41no—
332C3×D9—22no—
333C3×D9—41no—
334C2×C3×Q8—31no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C22×C3×C4—31no—
339C22×C3×C4—91no—
340C2×#67—31no—
341C2×#67—31no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—181no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C22×Dic3C2×D911yescharacteristic
351D3×Q8—184no—
352#237—184no—
353#235—184no—
354C2×D12—31no—
355C2×D12—91no—
356C2×D12—91no—
357C2×C4×D3—31no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×Dic6—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C2×Dic6—181no—
370C2×Dic6—184no—
371C2×Dic6C2×D911yescharacteristic
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—91no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4C2×D911yescharacteristic
380C3×C22⋊C4D3211yescharacteristic
381#217—91no—
382#217—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—181no—
387#217C2×D911yescharacteristic
388(C2×D3)⋊C4—31no—
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—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—181no—
399(C2×D3)⋊C4—181no—
400C4⋊Dic3—91no—
401C4⋊Dic3C2×D911yescharacteristic
402Dic3⋊C4—31no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4C2×D911yescharacteristic
407Dic3⋊C4C2×D911yescharacteristic
408C4×Dic3—91no—
409C4×Dic3—91no—
410C4×Dic3—91no—
411C4×Dic3—91no—
412C4×Dic3—91no—
413C4×Dic3—91no—
414C4×Dic3—181no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C23×D311yescharacteristic
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—61no—
422C2×C3×D3—32no—
423C2×C3×D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C2×C3×D3—61no—
428C32×C4—21no—
429C32×C4—21no—
430C3⋊Dic3—32no—
431C3⋊Dic3—61no—
432C3⋊Dic3—61no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—32no—
437C3×Dic3—61no—
438C3×Dic3D3×D412yes—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—41no—
444C22×C9—41no—
445C22×C9—41no—
446C22×C9C23×D311yescharacteristic
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—21no—
452C2×D9—61no—
453C2×D9—61no—
454C2×D9—61no—
455C2×D9—121no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9#23712yescomplemented
459C4×C9—21no—
460C4×C9—21no—
461C4×C9—32no—
462C4×C9—41no—
463C4×C9—41no—
464C4×C9—61no—
465C4×C9—61no—
466C4×C9—61no—
467Dic9—21no—
468Dic9—32no—
469Dic9—62no—
470Dic9—61no—
471Dic9—61no—
472Dic9—121no—
473Dic9—121no—
474Dic9D3×D412yes—
475C2×#41—271no—
476C22×Q8—271no—
477#124—271no—
478#124—271no—
479#124—271no—
480C22⋊Q8—31no—
481C22⋊Q8—271no—
482C22⋊Q8—271no—
483#121—91no—
484#121—271no—
485#121—271no—
486C4×Q8—271no—
487C4×D4—271no—
488C4×D4—271no—
489C4×D4—271no—
490C3×C9#54811yescharacteristic, complemented, Sylow
491C23×C3—21no—
492C23×C3—91no—
493C23×C3—91no—
494C23×C3C22×D911yescharacteristic
495C23×C3C2×D3211yescharacteristic
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—91no—
499C22×D3—91no—
500C22×D3—181no—
501C3×Q8—62no—
502C3×D4—182no—
503C3×D4—182no—
504C3×D4—182no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—62no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—182no—
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519#67—62no—
520#67—62no—
521#67—182no—
522#67—182no—
523#67—182no—
524#67—182no—
525#67—362no—
526C2×Dic3—22no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—181no—
536C2×Dic3—181no—
537C2×Dic3—181no—
538C2×Dic3—182no—
539C2×Dic3—182no—
540C2×Dic3—182no—
541C2×Dic3C22×D911yescharacteristic
542C2×Dic3C22×D911yescharacteristic
543C2×Dic3C22×D911yescharacteristic
544C2×Dic3C22×D911yescharacteristic
545D12—62no—
546D12—182no—
547D12—182no—
548C4×D3—62no—
549C4×D3—182no—
550C4×D3—182no—
551C4×D3—182no—
552C4×D3—182no—
553C4×D3—182no—
554Dic6—22no—
555Dic6—94no—
556Dic6—94no—
557Dic6—182no—
558Dic6—182no—
559Dic6—182no—
560Dic6—182no—
561Dic6—362no—
562C2×C32—41no—
563C2×C32C2×D3×D411yescharacteristic
564C2×C32#100711yescharacteristic
565C2×C32D3×#4111yescharacteristic
566C3⋊D3—121no—
567C3×D3—62no—
568C3×D3—121no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9—21no—
572C2×C9—41no—
573C2×C9—81no—
574C2×C9C2×D3×D411yescharacteristic
575C2×C9C2×#23711yescharacteristic
576C2×C9#101011yescharacteristic
577D9—22no—
578D9—41no—
579D9—121no—
580D9—241no—
581#41—544no—
582C2×Q8—31no—
583C2×Q8—271no—
584C2×Q8—271no—
585C2×Q8—271no—
586C2×Q8—544no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—91no—
590C2×D4—271no—
591C2×D4—271no—
592C2×D4—271no—
593C22×C4—31no—
594C22×C4—91no—
595C22×C4—271no—
596C22×C4—271no—
597C22×C4—271no—
598C22×C4—271no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—271no—
604C4⋊C4—271no—
605C22⋊C4—31no—
606C22⋊C4—91no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4D3×D911yescharacteristic
615C42—271no—
616C42—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—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—92no—
629C22×C3—181no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3—181no—
633C22×C3—181no—
634C22×C3C23×D911yescharacteristic
635C22×C3C22×D3211yescharacteristic
636C2×D3—32no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—361no—
649C2×D3—361no—
650C2×D3—361no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—92no—
662C3×C4—181no—
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—32no—
667Dic3—61no—
668Dic3—92no—
669Dic3—92no—
670Dic3—182no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—361no—
676Dic3—361no—
677Dic3D4×D912yes—
678C32#563311yescharacteristic
679C9—21no—
680C9#559811yescharacteristic, complemented
681C23—91no—
682C23—91no—
683C23—271no—
684C23C2×D3×D911yescharacteristic
685Q8—62no—
686Q8—274no—
687Q8—542no—
688Q8—542no—
689D4—182no—
690D4—182no—
691D4—182no—
692D4—542no—
693D4—542no—
694D4—542no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—62no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—182no—
703C2×C4—271no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—542no—
707C2×C4—542no—
708C2×C4—542no—
709C2×C4—542no—
710C2×C4C2×D3×D911yescharacteristic
711C2×C4C2×D3×D911yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—41no—
716C2×C3—41no—
717C2×C3—81no—
718C2×C3—182no—
719C2×C3—361no—
720C2×C3C2×D4×D911yescharacteristic
721C2×C3#6371311yescharacteristic
722C2×C3#41×D911yescharacteristic
723C2×C3#6429711yescharacteristic
724C2×C3D32×D411yescharacteristic
725C2×C3D3×#23711yescharacteristic
726D3—62no—
727D3—121no—
728D3—361no—
729D3—361no—
730D3—721no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—92no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—181no—
740C22—541no—
741C22—541no—
742C22—541no—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—21no—
746C4—32no—
747C4—61no—
748C4—61no—
749C4—61no—
750C4—92no—
751C4—181no—
752C4—272no—
753C4—541no—
754C4—541no—
755C3—21no—
756C3#1058973511yescharacteristic, complemented
757C3#1059407411yescharacteristic
758C2—41no—
759C2—182no—
760C2—361no—
761C2—1081no—
762C2#1172245811yescharacteristic
763C2D3×D4×D911yescharacteristic
764C2D9×#23711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#548
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×#88658C2semidirect
2. C2×D9×Dic6C2semidirect
3. #11721731C2semidirect
4. C3×#63446C2semidirect
5. C9×#878C2semidirect
6. Dic3×#611C2semidirect
7. #11721271C2semidirect
8. #11721257C2semidirect
9. #11721003C2semidirect
10. #11721002C2semidirect
11. #11720998C2semidirect
12. #11720996C2semidirect
13. #11720994C2semidirect
14. #11720983C2semidirect
15. #11720902C2semidirect
85. #63446D3semidirect
116. #6189D4semidirect
212. C2×C3×D9#41semidirect
254. #878D9semidirect
458. C2×D9#237semidirect
490. C3×C9#548semidirect
680. C9#5598semidirect
756. C3#10589735semidirect

Maximal subgroups

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

subgroupindex
C2×#886582
C2×D9×Dic62
#117217312
C3×#634462
C9×#8782
Dic3×#6112
#117212712
#117212572
#117210032
#117210022
#117209982
#117209962
#117209942
#117209832
#117209022
#105940743
#105897353