Finite Group Databasebeta

← #13150959

Subgroups — #13150959

Order 1728.

1084 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88658C211yesmaximal, characteristic, complemented
2C22×Dic3×D9C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C3×#63499C211yesmaximal, characteristic, complemented
5D4×C9×Dic3C211yesmaximal, characteristic, complemented
6#11721276C211yesmaximal, characteristic, complemented
7Dic3×#611C211yesmaximal, characteristic, complemented
8#11721271C211yesmaximal, characteristic, complemented
9#11721269C211yesmaximal, characteristic, complemented
10#11721267C211yesmaximal, characteristic, complemented
11#11721240C211yesmaximal, characteristic, complemented
12#11720999C211yesmaximal, characteristic, complemented
13#11720988C211yesmaximal, characteristic, complemented
14#11720977C211yesmaximal, characteristic, complemented
15#11720974C211yesmaximal, characteristic, complemented
16#10595129—31nomaximal
17#10589649—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C22×C3⋊Dic9C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic
26C22×C9×Dic3C2211yescharacteristic, complemented
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
30#88658—24no—
31C2×Dic3×D9—24no—
32C2×Dic3×D9C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic
35C2×Dic3×D9C2211yescharacteristic
36C2×#6189C2211yescharacteristic, complemented
37#88551C2211yescharacteristic, complemented
38#88536C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C9×#217C2211yescharacteristic
41C9×#217C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C9×C4⋊Dic3C2211yescharacteristic, complemented
46C4×C9×Dic3C2211yescharacteristic, complemented
47#88445C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3804—31no—
56C22×D3×Dic3—31no—
57#64148—31no—
58C3×#937—31no—
59C3×D4×Dic3D311yescharacteristic
60#63982—31no—
61#63977—31no—
62Dic3×#67—31no—
63#63971—31no—
64#63969—31no—
65#63952—31no—
66#63899—31no—
67#63890—31no—
68#63880—31no—
69#63877—31no—
70C2×#3697—31no—
71C22×C4×D9—31no—
72C4×D4×C9—31no—
73#63501—31no—
74#63501—61no—
75#63499D311yescharacteristic, complemented
76C4×#611—31no—
77C4×#611—31no—
78#63458—31no—
79#63456—31no—
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#63440—31no—
84C4×D36—31no—
85#63434—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×C3×D9—22no—
90C22×C3×D9—22no—
91C22×C3×D9—22no—
92C22×C3×D9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C3×D4×C9—22no—
95C2×C3×C4×C9C2311yescharacteristic
96#6233—22no—
97#6233—22no—
98C2×C3⋊Dic9—22no—
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C3×#611—22no—
103C3×#611—22no—
104C2×C9×Dic3—22no—
105C2×C9×Dic3—22no—
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112#6192—22no—
113#6192—22no—
114(C3⋊D9)⋊C4—22no—
115Dic3×D9—22no—
116Dic3×D9—22no—
117Dic3×D9—22no—
118Dic3×D9D414yescomplemented
119#6189—22no—
120#5586—91no—
121#5547—91no—
122C23×C3×D3—31no—
123C2×C32×D4C2×D311yescharacteristic
124C2×#638—31no—
125C2×#638—31no—
126C22×C3⋊Dic3—31no—
127C2×C3×#67—31no—
128C2×C3×#67—31no—
129C22×C3×Dic3C2×D311yescharacteristic
130C22×C3×Dic3C2×D311yescharacteristic
131C2×#627—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×#624—31no—
135#3804—64no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—31no—
140C2×D3×Dic3—64no—
141C23×D9C2×D311yescharacteristic
142#3757—31no—
143#3752—31no—
144#3750—31no—
145C3×#217—31no—
146C3×#217C2×D311yescharacteristic
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×C4⋊Dic3C2×D311yescharacteristic
151C3×C4×Dic3C2×D311yescharacteristic
152#3724—31no—
153#3724—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156#3722—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159Dic32—31no—
160C2×D4×C9—21no—
161C2×D4×C9C2×D311yescharacteristic
162C22×C4×C9—31no—
163C22×C4×C9—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—61no—
167C2×#611—61no—
168C2×#611C2×D311yescharacteristic
169C2×#611C2×D311yescharacteristic
170C22×Dic9—31no—
171C22×Dic9—61no—
172#3697—64no—
173C2×D36—31no—
174C2×D36—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—64no—
181C2×Dic18—31no—
182C9×C4⋊C4—31no—
183C9×C22⋊C4—31no—
184C9×C22⋊C4—31no—
185C42×C9—31no—
186#3676—31no—
187#3676—61no—
188#3676C2×D311yescharacteristic
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—61no—
194(C2×D9)⋊C4C2×D311yescharacteristic
195(C2×D9)⋊C4C2×D311yescharacteristic
196C4⋊Dic9—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—61no—
202C4×Dic9—31no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9#4112yescomplemented
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9—21no—
213C2×C3×D9—28no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9C2×D412yes—
219C2×C3×D9#4112yescomplemented
220C3×C4×C9—21no—
221C3⋊Dic9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9C2×D412yes—
224C9×Dic3—21no—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C9×Dic3C2×D412yes—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C23×Dic3—91no—
231C2×#237—91no—
232C2×#235—91no—
233C22×C4×D3—91no—
234C3×#120—91no—
235C3×C4×D4—31no—
236#953—91no—
237#939—91no—
238#939—91no—
239#939—91no—
240#939—181no—
241#937—31no—
242#935—91no—
243D4×Dic3—91no—
244D4×Dic3D911yescharacteristic, complemented
245C4×#67—91no—
246C4×#67—91no—
247#896—91no—
248#894—91no—
249#886—91no—
250#884—91no—
251#883—91no—
252#882—91no—
253#67⋊C4—91no—
254#67⋊C4—91no—
255#878—91no—
256#878—91no—
257#878—91no—
258#877—91no—
259C4×D12—91no—
260#872—91no—
261C23×C32C22×D311yescharacteristic
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—62no—
267C22×C3×D3—62no—
268C22×C3×D3—62no—
269C32×D4—22no—
270C2×C32×C4C22×D311yescharacteristic
271#638—62no—
272#638—62no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—62no—
277C3×#67—62no—
278C3×#67—62no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C2×C3×Dic3C22×D311yescharacteristic
287#627—62no—
288#626—62no—
289#626—62no—
290#624—62no—
291D3×Dic3—34no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—21no—
296C23×C9—21no—
297C23×C9C22×D311yescharacteristic
298C23×C9C22×D311yescharacteristic
299C22×D9—22no—
300C22×D9—22no—
301C22×D9—22no—
302C22×D9—31no—
303C22×D9—61no—
304C22×D9C22×D311yescharacteristic
305C22×D9C22×D311yescharacteristic
306D4×C9—22no—
307D4×C9—42no—
308C2×C4×C9—21no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9—31no—
313C2×C4×C9—62no—
314C2×C4×C9—62no—
315C2×C4×C9C22×D311yescharacteristic
316#611—22no—
317#611—22no—
318#611—62no—
319#611—62no—
320#611—122no—
321#611—122no—
322C2×Dic9—31no—
323C2×Dic9—31no—
324C2×Dic9—31no—
325C2×Dic9—61no—
326C2×Dic9—61no—
327C2×Dic9—61no—
328C2×Dic9—62no—
329C2×Dic9—122no—
330C2×Dic9C22×D311yescharacteristic
331C2×Dic9C22×D311yescharacteristic
332D36—62no—
333D36—62no—
334C4×D9—34no—
335C4×D9—62no—
336C4×D9—62no—
337C4×D9—62no—
338C4×D9—62no—
339Dic18—62no—
340#525—271noSylow
341C2×C3×C9—22no—
342C2×C3×C9—41no—
343C2×C3×C9C22×D411yescharacteristic
344C2×C3×C9C2×#4111yescharacteristic
345C2×C3×C9C2×#4111yescharacteristic
346C3⋊D9—41no—
347C3×D9—22no—
348C3×D9—22no—
349C24×C3—91no—
350C23×D3—31no—
351C2×C3×D4—21no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C2×C3×D4C2×D911yescharacteristic
355C2×C3×D4D3211yescharacteristic
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C2×#67—31no—
359C2×#67—31no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—181no—
367C2×#67—181no—
368C22×Dic3—91no—
369C22×Dic3—91no—
370C22×Dic3—91no—
371C22×Dic3—91no—
372C22×Dic3—91no—
373C22×Dic3—91no—
374C22×Dic3—181no—
375C22×Dic3—184no—
376C22×Dic3C2×D911yescharacteristic
377C22×Dic3C2×D911yescharacteristic, complemented
378#237—184no—
379#235—184no—
380C2×D12—91no—
381C2×D12—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—184no—
389C2×Dic6—91no—
390C2×Dic6—91no—
391C3×C4⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C42—31no—
398#217—31no—
399#217—91no—
400#217—91no—
401#217—91no—
402#217—91no—
403#217—181no—
404#217C2×D911yescharacteristic
405#217C2×D911yescharacteristic, complemented
406(C2×D3)⋊C4—31no—
407(C2×D3)⋊C4—31no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—181no—
415C4⋊Dic3—91no—
416C4⋊Dic3—91no—
417C4⋊Dic3C2×D911yescharacteristic, complemented
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—181no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3C2×D911yescharacteristic, complemented
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32#23512yes—
436C22×C32C23×D311yescharacteristic
437C2×C3⋊D3—61no—
438C2×C3⋊D3—61no—
439C2×C3⋊D3—61no—
440C2×C3×D3—32no—
441C2×C3×D3—32no—
442C2×C3×D3—68no—
443C2×C3×D3—61no—
444C2×C3×D3—61no—
445C2×C3×D3—61no—
446C2×C3×D3—61no—
447C32×C4—21no—
448C3⋊Dic3—32no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3×Dic3—21no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—61no—
455C3×Dic3—61no—
456C3×Dic3D3×D412yes—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—21no—
462C22×C9—21no—
463C22×C9—22no—
464C22×C9—41no—
465C22×C9—41no—
466C22×C9—41no—
467C22×C9—41no—
468C22×C9—41no—
469C22×C9#23712yescomplemented
470C22×C9C23×D311yescharacteristic
471C2×D9—28no—
472C2×D9—21no—
473C2×D9—21no—
474C2×D9—21no—
475C2×D9—21no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—61no—
479C2×D9—121no—
480C2×D9—121no—
481C2×D9—121no—
482C2×D9D3×D412yes—
483C2×D9#23712yescomplemented
484C4×C9—21no—
485C4×C9—32no—
486C4×C9—41no—
487C4×C9—61no—
488C4×C9—61no—
489C4×C9—61no—
490Dic9—21no—
491Dic9—21no—
492Dic9—32no—
493Dic9—62no—
494Dic9—61no—
495Dic9—61no—
496Dic9—121no—
497Dic9—121no—
498C2×#41—271no—
499C23×C4—271no—
500#123—271no—
501#123—271no—
502C22⋊Q8—271no—
503C22⋊Q8—271no—
504#121—271no—
505#121—271no—
506#120—91no—
507#120—271no—
508C4×D4—31no—
509C4×D4—271no—
510C4×D4—271no—
511C4×D4—271no—
512#117—271no—
513C3×C9#52511yescharacteristic, complemented, Sylow
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—91no—
517C23×C3—91no—
518C23×C3—182no—
519C23×C3—182no—
520C23×C3—182no—
521C23×C3C22×D911yescharacteristic
522C23×C3C22×D911yescharacteristic
523C23×C3C2×D3211yescharacteristic
524C23×C3C2×D3211yescharacteristic
525C22×D3—31no—
526C22×D3—31no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3—91no—
531C22×D3—91no—
532C22×D3—181no—
533C3×D4—22no—
534C3×D4—22no—
535C3×D4—42no—
536C3×D4—182no—
537C3×D4—182no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—62no—
544C2×C3×C4—62no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4C22×D911yescharacteristic
548C2×C3×C4C2×D3211yescharacteristic
549#67—62no—
550#67—62no—
551#67—182no—
552#67—182no—
553#67—182no—
554#67—182no—
555#67—182no—
556#67—182no—
557#67—362no—
558#67—362no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—94no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—91no—
570C2×Dic3—181no—
571C2×Dic3—181no—
572C2×Dic3—181no—
573C2×Dic3—182no—
574C2×Dic3—182no—
575C2×Dic3—182no—
576C2×Dic3—182no—
577C2×Dic3—182no—
578C2×Dic3—362no—
579C2×Dic3C22×D911yescharacteristic
580C2×Dic3C22×D911yescharacteristic
581C2×Dic3C22×D911yescharacteristic
582C2×Dic3C22×D911yescharacteristic
583D12—182no—
584D12—182no—
585C4×D3—94no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—182no—
590C4×D3—182no—
591Dic6—182no—
592Dic6—182no—
593C2×C32—22no—
594C2×C32—41no—
595C2×C32C2×#23511yescharacteristic
596C2×C32C2×D3×D411yescharacteristic
597C2×C32D3×#4111yescharacteristic
598C3⋊D3—121no—
599C3×D3—62no—
600C3×D3—62no—
601C2×C9—22no—
602C2×C9—21no—
603C2×C9—21no—
604C2×C9—21no—
605C2×C9—42no—
606C2×C9—41no—
607C2×C9—81no—
608C2×C9C2×D3×D411yescharacteristic
609C2×C9C2×#23711yescharacteristic
610C2×C9C2×#23711yescharacteristic
611D9—22no—
612D9—22no—
613D9—121no—
614D9—241no—
615C24—91no—
616#41—544no—
617C2×Q8—271no—
618C2×D4—91no—
619C2×D4—91no—
620C2×D4—271no—
621C2×D4—271no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4D3×D911yescharacteristic
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—271no—
628C22×C4—271no—
629C22×C4—271no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C22×C4—544no—
634C4⋊C4—31no—
635C4⋊C4—271no—
636C4⋊C4—271no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C4⋊C4—271no—
640C22⋊C4—31no—
641C22⋊C4—31no—
642C22⋊C4—91no—
643C22⋊C4—91no—
644C22⋊C4—91no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4—271no—
650C42—31no—
651C42—271no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—22no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—92no—
670C22×C3—92no—
671C22×C3—188no—
672C22×C3—181no—
673C22×C3—181no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3#369712yescomplemented
677C22×C3C23×D911yescharacteristic
678C22×C3#380412yes—
679C22×C3C22×D3211yescharacteristic
680C2×D3—32no—
681C2×D3—32no—
682C2×D3—68no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—181no—
688C2×D3—181no—
689C2×D3—181no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—361no—
694C2×D3—361no—
695C2×D3—361no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—32no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—61no—
703C3×C4—181no—
704C3×C4—181no—
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—61no—
709Dic3—61no—
710Dic3—92no—
711Dic3—92no—
712Dic3—182no—
713Dic3—181no—
714Dic3—181no—
715Dic3—181no—
716Dic3—181no—
717Dic3—361no—
718Dic3—361no—
719Dic3D4×D912yes—
720C32#554711yescharacteristic
721C9—21no—
722C9#558611yescharacteristic, complemented
723C23—91no—
724C23—91no—
725C23—182no—
726C23—182no—
727C23—182no—
728C23—271no—
729C23C2×D3×D911yescharacteristic
730C23C2×D3×D911yescharacteristic
731Q8—542no—
732D4—22no—
733D4—182no—
734D4—182no—
735D4—542no—
736D4—542no—
737D4—542no—
738D4—542no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—274no—
748C2×C4—271no—
749C2×C4—271no—
750C2×C4—271no—
751C2×C4—542no—
752C2×C4—542no—
753C2×C4—542no—
754C2×C4—542no—
755C2×C4—542no—
756C2×C4C2×D3×D911yescharacteristic
757C2×C3—22no—
758C2×C3—22no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—42no—
763C2×C3—41no—
764C2×C3—41no—
765C2×C3—81no—
766C2×C3—182no—
767C2×C3—182no—
768C2×C3C2×#369711yescharacteristic
769C2×C3C2×D4×D911yescharacteristic
770C2×C3#41×D911yescharacteristic
771C2×C3D32×D411yescharacteristic
772C2×C3D3×#23711yescharacteristic
773C2×C3C2×#380411yescharacteristic
774D3—62no—
775D3—62no—
776D3—361no—
777D3—361no—
778D3—721no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—92no—
785C22—92no—
786C22—188no—
787C22—181no—
788C22—181no—
789C22—181no—
790C22—181no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22#8865812yescomplemented
795C22C22×D3×D911yescharacteristic
796C4—21no—
797C4—32no—
798C4—61no—
799C4—61no—
800C4—61no—
801C4—181no—
802C4—181no—
803C4—272no—
804C4—541no—
805C4—541no—
806C3—21no—
807C3#1058964911yescharacteristic, complemented
808C3#1059512911yescharacteristic
809C2—22no—
810C2—41no—
811C2—182no—
812C2—182no—
813C2—1081no—
814C2D3×D4×D911yescharacteristic
815C2D9×#23711yescharacteristic
816C2C2×#8865811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#525
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×#88658C2semidirect
2. C22×Dic3×D9C2semidirect
3. #11721839C2semidirect
4. C3×#63499C2semidirect
5. D4×C9×Dic3C2semidirect
6. #11721276C2semidirect
7. Dic3×#611C2semidirect
8. #11721271C2semidirect
9. #11721269C2semidirect
10. #11721267C2semidirect
11. #11721240C2semidirect
12. #11720999C2semidirect
13. #11720988C2semidirect
14. #11720977C2semidirect
15. #11720974C2semidirect
21. C2×#6233C22semidirect
26. C22×C9×Dic3C22semidirect
29. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×#6189C22semidirect
37. #88551C22semidirect
38. #88536C22semidirect
39. #88534C22semidirect
41. C9×#217C22semidirect
45. C9×C4⋊Dic3C22semidirect
46. C4×C9×Dic3C22semidirect
47. #88445C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
75. #63499D3semidirect
118. Dic3×D9D4semidirect
208. C22×C3×C9#41semidirect
219. C2×C3×D9#41semidirect
244. D4×Dic3D9semidirect
377. C22×Dic3C2×D9semidirect
405. #217C2×D9semidirect
417. C4⋊Dic3C2×D9semidirect
429. C4×Dic3C2×D9semidirect
469. C22×C9#237semidirect
483. C2×D9#237semidirect
513. C3×C9#525semidirect
676. C22×C3#3697semidirect
722. C9#5586semidirect
794. C22#88658semidirect
807. C3#10589649semidirect

Maximal subgroups

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

subgroupindex
C2×#886582
C22×Dic3×D92
#117218392
C3×#634992
D4×C9×Dic32
#117212762
Dic3×#6112
#117212712
#117212692
#117212672
#117212402
#117209992
#117209882
#117209772
#117209742
#105951293
#105896493