Finite Group Databasebeta

← #13150452

Subgroups — #13150452

Order 1728.

1084 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×C9C211yesmaximal, characteristic, complemented
2C2×#88640C211yesmaximal, characteristic, complemented
3C4×#6233C211yesmaximal, characteristic, complemented
4C3×C4×#611C211yesmaximal, characteristic, complemented
5#11721287C211yesmaximal, characteristic, complemented
6#11721286C211yesmaximal, characteristic, complemented
7#11721277C211yesmaximal, characteristic, complemented
8#11721249C211yesmaximal, characteristic, complemented
9#11721034C211yesmaximal, characteristic, complemented
10#11721032C211yesmaximal, characteristic, complemented
11C4×#6195C211yesmaximal, characteristic, complemented
12C4×#6194C211yesmaximal, characteristic, complemented
13#11720959C211yesmaximal, characteristic, complemented
14#11720955C211yesmaximal, characteristic, complemented
15#11720954C211yesmaximal, characteristic, complemented
16#10595002—31nomaximal
17#10589893—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C4×D3×C9—24no—
25C2×C4×D3×C9C2211yescharacteristic
26C2×C4×D3×C9C2211yescharacteristic
27C2×C4×D3×C9C2211yescharacteristic
28C2×C4×D3×C9C2211yescharacteristic
29C2×C3×C4×D9C2211yescharacteristic, complemented
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic
32C2×#6194C2211yescharacteristic
33C2×#6194C2211yescharacteristic
34C2×#6192C2211yescharacteristic, complemented
35C2×#6189C2211yescharacteristic, complemented
36#88640—24no—
37#88551C2211yescharacteristic
38#88536C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C4×C3⋊Dic9C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C3×Dic9⋊C4C2211yescharacteristic, complemented
44C3×C4×Dic9C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D3)⋊Dic9C2211yescharacteristic
48(C2×D3)⋊Dic9C2211yescharacteristic
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C22×C3×C4×D3D311yescharacteristic
56C2×#3798—31no—
57C4×#638—31no—
58C3×C4×#67—31no—
59#63978—31no—
60#63977—31no—
61#63976—31no—
62#63964—31no—
63#63906—31no—
64#63905—31no—
65C4×#626—31no—
66C4×#625—31no—
67#63855—31no—
68#63851—31no—
69#63850—31no—
70C23×C4×C9—31no—
71C2×#3697—31no—
72#63515—31no—
73#63515—31no—
74#63492—31no—
75#63492—31no—
76#63491—31no—
77#63491—31no—
78C4×#611—31no—
79C4×#611—31no—
80C4×#611—31no—
81C4×#611—61no—
82C4×#611D311yescharacteristic, complemented
83#63488—31no—
84#63486—31no—
85#63486—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9—22no—
89C22×D3×C9—22no—
90C22×D3×C9—22no—
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×C3×C4×C9—22no—
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97#6233—22no—
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C4×C3⋊D9—22no—
102C3×#611—22no—
103C2×C9×Dic3—22no—
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C4×D3×C9—22no—
110C4×D3×C9—22no—
111C4×D3×C9—22no—
112C4×D3×C9D414yescomplemented
113C3×C4×D9—22no—
114#6195—22no—
115#6195—22no—
116#6194—22no—
117#6194—22no—
118#6192—22no—
119#6189—22no—
120#5791—91no—
121#5547—91no—
122C23×C3×D3C2×D311yescharacteristic
123C22×C32×C4C2×D311yescharacteristic
124C2×#638—31no—
125C2×C4×C3⋊D3—31no—
126C2×C3×#67—31no—
127C22×C3×Dic3C2×D311yescharacteristic
128C2×C3×C4×D3—24no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3C2×D311yescharacteristic
131C2×C3×C4×D3C2×D311yescharacteristic
132C2×C3×C4×D3C2×D311yescharacteristic
133C2×C3×C4×D3C2×D311yescharacteristic
134C2×#627—31no—
135C2×#626—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#625—31no—
139C2×#625—31no—
140#3798—64no—
141C24×C9—31no—
142#3757—31no—
143#3752—31no—
144#3750—31no—
145C4×C3⋊Dic3—31no—
146C3×#217—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×C4×Dic3—31no—
150#3724—31no—
151Dic3⋊Dic3—31no—
152Dic3⋊Dic3—31no—
153Dic3⋊Dic3—31no—
154#3722—31no—
155(C2×D3)⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160C22×C4×C9—21no—
161C22×C4×C9—31no—
162C22×C4×C9—31no—
163C22×C4×C9—31no—
164C22×C4×C9—31no—
165C22×C4×C9—31no—
166C22×C4×C9—64no—
167C22×C4×C9C2×D311yescharacteristic
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—61no—
174C2×#611C2×D311yescharacteristic
175#3697—64no—
176C2×D36—31no—
177C2×C4×D9—31no—
178C2×C4×D9—61no—
179C2×C4×D9C2×D311yescharacteristic, complemented
180C2×Dic18—31no—
181#3676—31no—
182#3676—31no—
183#3676—31no—
184#3676—31no—
185#3676—31no—
186#3676—61no—
187#3676C2×D311yescharacteristic
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—61no—
192(C2×D9)⋊C4C2×D311yescharacteristic, complemented
193C4⋊Dic9—31no—
194C4⋊Dic9—31no—
195Dic9⋊C4—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—61no—
199Dic9⋊C4C2×D311yescharacteristic, complemented
200C4×Dic9—31no—
201C4×Dic9—61no—
202C4×Dic9C2×D311yescharacteristic, complemented
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9#4112yescomplemented
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9—21no—
210C2×D3×C9—28no—
211C2×D3×C9—21no—
212C2×D3×C9—21no—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9C2×D412yes—
216C2×D3×C9#4112yescomplemented
217C2×C3×D9—21no—
218C2×C3×D9—21no—
219C2×C3×D9—21no—
220C3×C4×C9—21no—
221C3×C4×C9C2×D412yes—
222C3⋊Dic9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C9×Dic3—21no—
226C9×Dic3C2×D412yes—
227C3×Dic9—21no—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C23×C3×C4—31no—
231C2×#235—91no—
232C2×#235—91no—
233C22×C4×D3D911yescharacteristic, complemented
234C3×C4×D4—91no—
235#953—91no—
236#953—91no—
237#939—91no—
238#937—91no—
239#930—91no—
240#930—91no—
241#929—91no—
242#929—91no—
243C4×#67—31no—
244C4×#67—91no—
245C4×#67—91no—
246C4×#67—91no—
247C4×#67—91no—
248C4×#67—91no—
249C4×#67—181no—
250#926—91no—
251#924—91no—
252#924—91no—
253#896—91no—
254#894—91no—
255#884—91no—
256#883—91no—
257#882—91no—
258#878—91no—
259C4×D12—91no—
260#872—91no—
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3×D3—22no—
264C22×C3×D3—22no—
265C22×C3×D3—22no—
266C22×C3×D3—31no—
267C22×C3×D3C22×D311yescharacteristic
268C22×C3×D3C22×D311yescharacteristic
269C2×C32×C4—22no—
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272#638—62no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C4×C3⋊D3—62no—
277C3×#67—62no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C3×C4×D3—22no—
285C3×C4×D3—22no—
286C3×C4×D3—22no—
287C3×C4×D3—62no—
288C3×C4×D3#6714yes—
289#627—62no—
290#626—62no—
291#626—62no—
292#626—62no—
293#625—62no—
294#625—62no—
295C23×C9—21no—
296C23×C9—31no—
297C23×C9—31no—
298C23×C9—62no—
299C23×C9—62no—
300C23×C9—62no—
301C23×C9C22×D311yescharacteristic
302C22×D9—31no—
303C22×D9—61no—
304C22×D9C22×D311yescharacteristic
305C2×C4×C9—22no—
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—31no—
309C2×C4×C9—34no—
310C2×C4×C9—31no—
311C2×C4×C9—42no—
312C2×C4×C9—62no—
313C2×C4×C9—62no—
314C2×C4×C9—62no—
315C2×C4×C9—62no—
316C2×C4×C9C22×D311yescharacteristic
317C2×C4×C9C22×D311yescharacteristic
318#611—22no—
319#611—62no—
320#611—62no—
321#611—62no—
322#611—62no—
323#611—64no—
324#611—62no—
325C2×Dic9—31no—
326C2×Dic9—31no—
327C2×Dic9—31no—
328C2×Dic9—61no—
329C2×Dic9—61no—
330C2×Dic9—61no—
331C2×Dic9C22×D311yescharacteristic
332C2×Dic9C22×D311yescharacteristic
333C2×Dic9C22×D311yescharacteristic
334D36—62no—
335C4×D9—22no—
336C4×D9—62no—
337C4×D9—122no—
338Dic18—62no—
339#525—271noSylow
340C2×C3×C9—22no—
341C2×C3×C9C22×D411yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343C2×C3×C9C2×#4111yescharacteristic
344C3⋊D9—41no—
345D3×C9—22no—
346D3×C9—22no—
347C3×D9—41no—
348C24×C3—31no—
349C23×D3C2×D911yescharacteristic
350C2×C3×D4—91no—
351C22×C3×C4—21no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—64no—
358C22×C3×C4—91no—
359C22×C3×C4C2×D911yescharacteristic
360C22×C3×C4D3211yescharacteristic
361C2×#67—31no—
362C2×#67—91no—
363C2×#67—91no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—91no—
370C2×#67—91no—
371C2×#67—181no—
372C22×Dic3C2×D911yescharacteristic
373#235—184no—
374#235—184no—
375C2×D12—91no—
376C2×D12—91no—
377C2×D12—91no—
378C2×C4×D3—24no—
379C2×C4×D3—31no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—181no—
383C2×C4×D3C2×D911yescharacteristic
384C2×C4×D3C2×D911yescharacteristic
385C2×C4×D3C2×D911yescharacteristic
386C2×C4×D3C2×D911yescharacteristic
387C2×Dic6—91no—
388C2×Dic6—91no—
389C3×C4⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C42—91no—
393#217—31no—
394#217—91no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—181no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—181no—
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416Dic3⋊C4—31no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—181no—
425C4×Dic3—31no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—181no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32#23512yes—
432C22×C32C23×D311yescharacteristic
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3×D3—28no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C2×C3×D3#23512yes—
445C2×C3×D3C2×#6712yes—
446C32×C4—21no—
447C32×C4C2×#6712yes—
448C3⋊Dic3—61no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3×Dic3—21no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3—61no—
455C3×Dic3C2×#6712yes—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—22no—
460C22×C9—32no—
461C22×C9—32no—
462C22×C9—41no—
463C22×C9—41no—
464C22×C9—68no—
465C22×C9—61no—
466C22×C9—61no—
467C22×C9—61no—
468C22×C9—61no—
469C22×C9#23512yescomplemented
470C22×C9C23×D311yescharacteristic
471C2×D9—21no—
472C2×D9—21no—
473C2×D9—21no—
474C2×D9—62no—
475C2×D9—61no—
476C2×D9—61no—
477C2×D9—61no—
478C2×D9—121no—
479C2×D9—121no—
480C4×C9—21no—
481C4×C9—22no—
482C4×C9—32no—
483C4×C9—41no—
484C4×C9—61no—
485C4×C9D3×D412yes—
486Dic9—21no—
487Dic9—21no—
488Dic9—21no—
489Dic9—62no—
490Dic9—61no—
491Dic9—61no—
492Dic9—61no—
493Dic9—121no—
494Dic9—121no—
495C2×#41—271no—
496C23×C4—31no—
497#123—271no—
498#123—271no—
499C22⋊Q8—271no—
500C22⋊Q8—271no—
501#121—271no—
502#121—271no—
503#120—271no—
504#120—271no—
505C4×D4—91no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509#117—271no—
510C3×C9#52511yescharacteristic, complemented, Sylow
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—31no—
514C23×C3—62no—
515C23×C3—62no—
516C23×C3—62no—
517C23×C3—91no—
518C23×C3C22×D911yescharacteristic
519C23×C3C2×D3211yescharacteristic
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—31no—
524C22×D3—91no—
525C22×D3—91no—
526C22×D3—181no—
527C22×D3C22×D911yescharacteristic
528C22×D3C22×D911yescharacteristic
529C3×D4—182no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—34no—
536C2×C3×C4—31no—
537C2×C3×C4—42no—
538C2×C3×C4—62no—
539C2×C3×C4—62no—
540C2×C3×C4—62no—
541C2×C3×C4—62no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—91no—
545C2×C3×C4—182no—
546C2×C3×C4C22×D911yescharacteristic
547C2×C3×C4C22×D911yescharacteristic
548C2×C3×C4C2×D3211yescharacteristic
549C2×C3×C4C2×D3211yescharacteristic
550#67—62no—
551#67—182no—
552#67—182no—
553#67—182no—
554#67—182no—
555#67—184no—
556#67—182no—
557#67—182no—
558#67—182no—
559#67—182no—
560#67—182no—
561C2×Dic3—22no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—91no—
570C2×Dic3—91no—
571C2×Dic3—181no—
572C2×Dic3—181no—
573C2×Dic3—181no—
574C2×Dic3C22×D911yescharacteristic
575C2×Dic3C22×D911yescharacteristic
576D12—182no—
577D12—182no—
578D12—182no—
579C4×D3—22no—
580C4×D3—22no—
581C4×D3—22no—
582C4×D3—62no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—362no—
586C4×D3#61114yescomplemented
587Dic6—182no—
588Dic6—182no—
589C2×C32—22no—
590C2×C32C2×#23511yescharacteristic
591C2×C32C2×#23511yescharacteristic
592C2×C32C22×#6711yescharacteristic
593C3⋊D3—121no—
594C3×D3—22no—
595C3×D3—22no—
596C3×D3—121no—
597C2×C9—22no—
598C2×C9—21no—
599C2×C9—21no—
600C2×C9—21no—
601C2×C9—42no—
602C2×C9—62no—
603C2×C9—62no—
604C2×C9C2×#23511yescharacteristic
605C2×C9C2×D3×D411yescharacteristic
606C2×C9D3×#4111yescharacteristic
607D9—41no—
608D9—122no—
609D9—121no—
610C24—31no—
611#41—544no—
612C2×Q8—271no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—64no—
626C22×C4—91no—
627C22×C4—271no—
628C22×C4D3×D911yescharacteristic
629C4⋊C4—91no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—91no—
646C42—271no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—32no—
654C22×C3—32no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—68no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—61no—
662C22×C3—181no—
663C22×C3—181no—
664C22×C3—181no—
665C22×C3#369712yescomplemented
666C22×C3C23×D911yescharacteristic
667C22×C3#379812yes—
668C22×C3C22×D3211yescharacteristic
669C2×D3—28no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—182no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—361no—
685C2×D3—361no—
686C2×D3#369712yescomplemented
687C2×D3C2×#61112yes—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—22no—
691C3×C4—32no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—181no—
695C3×C4—181no—
696C3×C4—181no—
697C3×C4C2×#61112yes—
698C3×C4D3×#6712yes—
699Dic3—21no—
700Dic3—61no—
701Dic3—61no—
702Dic3—61no—
703Dic3—182no—
704Dic3—181no—
705Dic3—181no—
706Dic3—181no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—361no—
711Dic3—361no—
712Dic3C2×#61112yes—
713C32#579111yescharacteristic
714C9—21no—
715C9#554711yescharacteristic, complemented
716C23—31no—
717C23—31no—
718C23—62no—
719C23—62no—
720C23—62no—
721C23—91no—
722C23—271no—
723C23C2×D3×D911yescharacteristic
724Q8—542no—
725D4—182no—
726D4—542no—
727D4—542no—
728D4—542no—
729D4—542no—
730D4—542no—
731D4—542no—
732C2×C4—22no—
733C2×C4—31no—
734C2×C4—34no—
735C2×C4—31no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—91no—
741C2×C4—91no—
742C2×C4—91no—
743C2×C4—182no—
744C2×C4—271no—
745C2×C4—271no—
746C2×C4—271no—
747C2×C4—542no—
748C2×C4C2×D3×D911yescharacteristic
749C2×C4C2×D3×D911yescharacteristic
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—42no—
756C2×C3—62no—
757C2×C3—62no—
758C2×C3—361no—
759C2×C3C2×#369711yescharacteristic
760C2×C3C2×#369711yescharacteristic
761C2×C3C22×#61111yescharacteristic
762C2×C3C2×#379811yescharacteristic
763C2×C3D3×#23511yescharacteristic
764C2×C3C2×D3×#6711yescharacteristic
765D3—22no—
766D3—22no—
767D3—121no—
768D3—362no—
769D3—361no—
770D3—361no—
771C22—21no—
772C22—21no—
773C22—32no—
774C22—32no—
775C22—68no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—541no—
784C22—541no—
785C22—541no—
786C22#8864012yescomplemented
787C22C22×D3×D911yescharacteristic
788C4—21no—
789C4—32no—
790C4—61no—
791C4—181no—
792C4—181no—
793C4—181no—
794C4—541no—
795C4—541no—
796C4—541no—
797C4D3×#61112yes—
798C3—21no—
799C3#1058989311yescharacteristic, complemented
800C3#1059500211yescharacteristic
801C2—22no—
802C2—62no—
803C2—62no—
804C2—361no—
805C2—1081no—
806C2C2×#8864011yescharacteristic
807C2D3×#369711yescharacteristic
808C2C2×D3×#61111yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#525
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D3×C9C2semidirect
2. C2×#88640C2semidirect
3. C4×#6233C2semidirect
4. C3×C4×#611C2semidirect
5. #11721287C2semidirect
6. #11721286C2semidirect
7. #11721277C2semidirect
8. #11721249C2semidirect
9. #11721034C2semidirect
10. #11721032C2semidirect
11. C4×#6195C2semidirect
12. C4×#6194C2semidirect
13. #11720959C2semidirect
14. #11720955C2semidirect
15. #11720954C2semidirect
21. C2×C4×C3⋊D9C22semidirect
29. C2×C3×C4×D9C22semidirect
34. C2×#6192C22semidirect
35. C2×#6189C22semidirect
38. #88536C22semidirect
39. #88534C22semidirect
40. C4×C3⋊Dic9C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C3×Dic9⋊C4C22semidirect
44. C3×C4×Dic9C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. Dic3⋊Dic9C22semidirect
53. #88442C22semidirect
54. Dic9⋊Dic3C22semidirect
82. C4×#611D3semidirect
112. C4×D3×C9D4semidirect
179. C2×C4×D9C2×D3semidirect
192. (C2×D9)⋊C4C2×D3semidirect
199. Dic9⋊C4C2×D3semidirect
202. C4×Dic9C2×D3semidirect
205. C22×C3×C9#41semidirect
216. C2×D3×C9#41semidirect
233. C22×C4×D3D9semidirect
469. C22×C9#235semidirect
510. C3×C9#525semidirect
586. C4×D3#611semidirect
665. C22×C3#3697semidirect
686. C2×D3#3697semidirect
715. C9#5547semidirect
786. C22#88640semidirect
799. C3#10589893semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D3×C92
C2×#886402
C4×#62332
C3×C4×#6112
#117212872
#117212862
#117212772
#117212492
#117210342
#117210322
C4×#61952
C4×#61942
#117209592
#117209552
#117209542
#105950023
#105898933