Finite Group Databasebeta

← #13147991

Subgroups — #13147991

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×Dic3×D9C211yesmaximal, characteristic, complemented
2C2×#88634C211yesmaximal, characteristic, complemented
3#11721727C211yesmaximal, characteristic, complemented
4C3×#63444C211yesmaximal, characteristic, complemented
5C9×#878C211yesmaximal, characteristic, complemented
6#11721277C211yesmaximal, characteristic, complemented
7#11721276C211yesmaximal, characteristic, complemented
8#611⋊Dic3C211yesmaximal, characteristic, complemented
9#11720998C211yesmaximal, characteristic, complemented
10#11720988C211yesmaximal, characteristic, complemented
11#11720984C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720981C211yesmaximal, characteristic, complemented
14#11720978C211yesmaximal, characteristic, complemented
15#11720975C211yesmaximal, characteristic, complemented
16#10594055—31nomaximal
17#10589729—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic
26C2×C9×Dic6C2211yescharacteristic, complemented
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic, complemented
30C2×Dic3×D9—24no—
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic
35C2×Dic3×D9C2211yescharacteristic, complemented
36#88634—24no—
37C3×C9×C22⋊C4C2211yescharacteristic
38#88536C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C4×C3⋊Dic9C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C9×C4⋊Dic3C2211yescharacteristic, complemented
45C9×Dic3⋊C4C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47#88445C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×D3×Dic3—31no—
56C2×#3796—31no—
57#64090—31no—
58C3×#882—31no—
59C3×#878D311yescharacteristic
60#63978—31no—
61#63977—31no—
62#67⋊Dic3—31no—
63#63898—31no—
64#63890—31no—
65#63887—31no—
66#63886—31no—
67#63884—31no—
68#63881—31no—
69#63878—31no—
70C2×#3701—31no—
71C22×C4×D9—31no—
72C9×C22⋊Q8—31no—
73#63508—31no—
74#63492—31no—
75#63457—31no—
76#63456—31no—
77#63456—31no—
78#63455—31no—
79#63455—31no—
80#63454—31no—
81#63444—31no—
82#63444D311yescharacteristic, complemented
83#611⋊C4—31no—
84#611⋊C4—31no—
85#611⋊C4—61no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3×D9—22no—
89C22×C3×D9—22no—
90C22×C3×D9—22no—
91C22×C3×D9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96#6233—22no—
97C2×C3⋊Dic9—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×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C3×D36—22no—
110C3×D36—22no—
111C9×Dic6—22no—
112#6192—22no—
113#6192—22no—
114#6192—22no—
115Dic3×D9—22no—
116Dic3×D9—22no—
117Dic3×D9—22no—
118Dic3×D9—22no—
119Dic3×D9D414yescomplemented
120#5627—91no—
121#5586—91no—
122C23×C3×D3—31no—
123C2×#638—31no—
124C22×C3⋊Dic3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C3×#67—31no—
127C22×C3×Dic3C2×D311yescharacteristic
128C2×C3×D12—31no—
129C2×C3×D12—31no—
130C2×C3×Dic6C2×D311yescharacteristic
131C2×#626—31no—
132C2×#626—31no—
133C2×#626—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C2×D3×Dic3—64no—
140#3796—64no—
141C23×D9C2×D311yescharacteristic
142C32×C22⋊C4C2×D311yescharacteristic
143#3752—31no—
144#3750—31no—
145C4×C3⋊Dic3—31no—
146C3×#217C2×D311yescharacteristic
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×C4⋊Dic3C2×D311yescharacteristic
150C3×Dic3⋊C4C2×D311yescharacteristic
151C3×Dic3⋊C4C2×D311yescharacteristic
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—
159Dic32—31no—
160C2×Q8×C9—31no—
161C22×C4×C9—31no—
162C2×#611—31no—
163C2×#611—61no—
164C2×#611C2×D311yescharacteristic
165C22×Dic9—31no—
166C22×Dic9—61no—
167#3701—64no—
168C2×D36—31no—
169C2×D36—31no—
170C2×D36—31no—
171C2×D36C2×D311yescharacteristic
172C2×D36C2×D311yescharacteristic
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—31no—
178C2×C4×D9—31no—
179C2×C4×D9—64no—
180C2×C4×D9—61no—
181C9×C4⋊C4—31no—
182C9×C4⋊C4—31no—
183C9×C4⋊C4—31no—
184C9×C22⋊C4—21no—
185C9×C22⋊C4—31no—
186C9×C22⋊C4C2×D311yescharacteristic
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
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—61no—
200C4×Dic9—31no—
201C4×Dic9—31no—
202C4×Dic9—61no—
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×C3×D9—28no—
211C2×C3×D9—21no—
212C2×C3×D9—21no—
213C2×C3×D9—21no—
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×C4×C9—21no—
222C3⋊Dic9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9C2×D412yes—
225C9×Dic3—21no—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C9×Dic3C2×D412yes—
229C3×Dic9—21no—
230C23×Dic3—91no—
231C2×#239—91no—
232C2×#237—91no—
233C22×C4×D3—91no—
234C3×C22⋊Q8—31no—
235C3×#120—91no—
236#953—91no—
237#946—91no—
238#939—91no—
239#939—91no—
240#935—91no—
241D4×Dic3—91no—
242D4×Dic3—91no—
243#930—91no—
244#895—91no—
245#894—91no—
246#894—91no—
247#893—91no—
248#893—91no—
249#892—91no—
250#886—91no—
251#882—31no—
252#882—91no—
253#67⋊C4—91no—
254#67⋊C4—91no—
255#67⋊C4—91no—
256#67⋊C4—91no—
257#67⋊C4—181no—
258#878—91no—
259#878D911yescharacteristic, complemented
260#877—91no—
261C23×C32C22×D311yescharacteristic
262C22×C3⋊D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—62no—
267C22×C3×D3—62no—
268C22×C3×D3—62no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271#638—62no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—62no—
276C4×C3⋊D3—62no—
277C3×#67—62no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3C22×D311yescharacteristic
281C2×C3×Dic3C22×D311yescharacteristic
282C2×C3×Dic3C22×D311yescharacteristic
283C2×C3×Dic3C22×D311yescharacteristic
284C3×D12—62no—
285C3×D12—62no—
286C3×Dic6—22no—
287#626—62no—
288#626—62no—
289#626—62no—
290D3×Dic3—34no—
291D3×Dic3—62no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—21no—
296C23×C9C22×D311yescharacteristic
297C22×D9—22no—
298C22×D9—22no—
299C22×D9—22no—
300C22×D9—31no—
301C22×D9—61no—
302C22×D9C22×D311yescharacteristic
303C22×D9C22×D311yescharacteristic
304C22×D9C22×D311yescharacteristic
305Q8×C9—62no—
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—31no—
311C2×C4×C9—31no—
312C2×C4×C9—62no—
313C2×C4×C9C22×D311yescharacteristic
314C2×C4×C9C22×D311yescharacteristic
315#611—22no—
316#611—64no—
317#611—62no—
318C2×Dic9—31no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—61no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—62no—
325C2×Dic9—122no—
326C2×Dic9C22×D311yescharacteristic
327D36—22no—
328D36—22no—
329D36—62no—
330D36—62no—
331D36—62no—
332C4×D9—34no—
333C4×D9—62no—
334C4×D9—62no—
335C4×D9—62no—
336C4×D9—62no—
337C4×D9—62no—
338C4×D9—122no—
339#525—271noSylow
340C2×C3×C9—22no—
341C2×C3×C9C22×D411yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343C2×C3×C9C2×#4111yescharacteristic
344C3⋊D9—41no—
345C3×D9—22no—
346C3×D9—22no—
347C3×D9—41no—
348C24×C3—91no—
349C23×D3—31no—
350C2×C3×Q8—31no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4—91no—
354C22×C3×C4—31no—
355C2×#67—31no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—181no—
362C22×Dic3—91no—
363C22×Dic3—91no—
364C22×Dic3—91no—
365C22×Dic3—91no—
366C22×Dic3—91no—
367C22×Dic3—91no—
368C22×Dic3—91no—
369C22×Dic3—181no—
370C22×Dic3—184no—
371C22×Dic3C2×D911yescharacteristic
372#239—184no—
373#237—184no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—91no—
377C2×D12—91no—
378C2×D12—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—181no—
387C2×C4×D3—184no—
388C2×Dic6C2×D911yescharacteristic, complemented
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4C2×D911yescharacteristic
397C3×C22⋊C4D3211yescharacteristic
398#217—91no—
399#217—91no—
400#217—91no—
401#217—91no—
402#217C2×D911yescharacteristic
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—31no—
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—91no—
413(C2×D3)⋊C4—181no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416C4⋊Dic3C2×D911yescharacteristic, complemented
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—181no—
422Dic3⋊C4C2×D911yescharacteristic, complemented
423Dic3⋊C4C2×D911yescharacteristic, complemented
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—181no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32#23912yes—
432C22×C32C23×D311yescharacteristic
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3×D3—32no—
437C2×C3×D3—32no—
438C2×C3×D3—68no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C2×C3×D3—61no—
445C2×C3×D3—61no—
446C32×C4—21no—
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×Dic3D3×D412yes—
456C22×C9—21no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—22no—
460C22×C9—41no—
461C22×C9—41no—
462C22×C9#23712yescomplemented
463C22×C9C23×D311yescharacteristic
464C2×D9—28no—
465C2×D9—21no—
466C2×D9—21no—
467C2×D9—21no—
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—21no—
471C2×D9—21no—
472C2×D9—62no—
473C2×D9—61no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—121no—
477C2×D9—121no—
478C2×D9D3×D412yes—
479C2×D9#23712yescomplemented
480C4×C9—21no—
481C4×C9—21no—
482C4×C9—32no—
483C4×C9—41no—
484C4×C9—41no—
485C4×C9—61no—
486C4×C9—61no—
487C4×C9—61no—
488Dic9—21no—
489Dic9—32no—
490Dic9—62no—
491Dic9—62no—
492Dic9—61no—
493Dic9—61no—
494Dic9—121no—
495C2×#41—271no—
496C23×C4—271no—
497#123—271no—
498#123—271no—
499C22⋊Q8—31no—
500C22⋊Q8—271no—
501#121—271no—
502#121—271no—
503#120—91no—
504#120—271no—
505C4×D4—271no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509#117—271no—
510C3×C9#52511yescharacteristic, complemented, Sylow
511C23×C3—21no—
512C23×C3—91no—
513C23×C3—91no—
514C23×C3—91no—
515C23×C3—182no—
516C23×C3—182no—
517C23×C3—182no—
518C23×C3C22×D911yescharacteristic
519C23×C3C2×D3211yescharacteristic
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—31no—
523C22×D3—62no—
524C22×D3—62no—
525C22×D3—62no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—181no—
529C3×Q8—62no—
530C3×D4—182no—
531C3×D4—182no—
532C3×D4—182no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—62no—
540C2×C3×C4—91no—
541C2×C3×C4C22×D911yescharacteristic
542C2×C3×C4C22×D911yescharacteristic
543C2×C3×C4C2×D3211yescharacteristic
544C2×C3×C4C2×D3211yescharacteristic
545#67—62no—
546#67—182no—
547#67—182no—
548#67—184no—
549#67—182no—
550#67—182no—
551#67—182no—
552C2×Dic3—22no—
553C2×Dic3—31no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—94no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—91no—
560C2×Dic3—91no—
561C2×Dic3—181no—
562C2×Dic3—181no—
563C2×Dic3—181no—
564C2×Dic3—182no—
565C2×Dic3—182no—
566C2×Dic3—182no—
567C2×Dic3—182no—
568C2×Dic3—182no—
569C2×Dic3—182no—
570C2×Dic3—362no—
571C2×Dic3C22×D911yescharacteristic
572C2×Dic3C22×D911yescharacteristic
573C2×Dic3C22×D911yescharacteristic
574C2×Dic3C22×D911yescharacteristic
575D12—62no—
576D12—62no—
577D12—182no—
578D12—182no—
579D12—182no—
580C4×D3—94no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—182no—
587C4×D3—362no—
588Dic6—22no—
589C2×C32—22no—
590C2×C32C2×D3×D411yescharacteristic
591C2×C32C2×#23911yescharacteristic
592C2×C32D3×#4111yescharacteristic
593C3⋊D3—121no—
594C3×D3—62no—
595C3×D3—62no—
596C3×D3—121no—
597C2×C9—22no—
598C2×C9—21no—
599C2×C9—21no—
600C2×C9—21no—
601C2×C9—42no—
602C2×C9C2×D3×D411yescharacteristic
603C2×C9C2×#23711yescharacteristic
604C2×C9C2×#23711yescharacteristic
605D9—22no—
606D9—22no—
607D9—41no—
608D9—122no—
609D9—121no—
610C24—91no—
611#41—544no—
612C2×Q8—31no—
613C2×D4—91no—
614C2×D4—91no—
615C2×D4—91no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C22×C4—31no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—271no—
628C22×C4—544no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C22⋊C4—31no—
636C22⋊C4—91no—
637C22⋊C4—91no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4D3×D911yescharacteristic
645C42—271no—
646C42—271no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—92no—
656C22×C3—92no—
657C22×C3—188no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3—181no—
663C22×C3—181no—
664C22×C3—181no—
665C22×C3#370112yescomplemented
666C22×C3C23×D911yescharacteristic
667C22×C3#379612yes—
668C22×C3C22×D3211yescharacteristic
669C2×D3—32no—
670C2×D3—32no—
671C2×D3—68no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—182no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—361no—
687C2×D3—361no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—32no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—181no—
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—61no—
703Dic3—92no—
704Dic3—92no—
705Dic3—182no—
706Dic3—182no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—361no—
712Dic3D4×D912yes—
713C32#562711yescharacteristic
714C9—21no—
715C9#558611yescharacteristic, complemented
716C23—91no—
717C23—91no—
718C23—91no—
719C23—182no—
720C23—182no—
721C23—182no—
722C23—271no—
723C23C2×D3×D911yescharacteristic
724Q8—62no—
725D4—182no—
726D4—182no—
727D4—182no—
728D4—542no—
729D4—542no—
730D4—542no—
731D4—542no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—62no—
737C2×C4—91no—
738C2×C4—274no—
739C2×C4—271no—
740C2×C4—271no—
741C2×C4—271no—
742C2×C4—542no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
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—182no—
757C2×C3—182no—
758C2×C3—361no—
759C2×C3C2×D4×D911yescharacteristic
760C2×C3C2×#370111yescharacteristic
761C2×C3#41×D911yescharacteristic
762C2×C3C2×#379611yescharacteristic
763C2×C3D32×D411yescharacteristic
764C2×C3D3×#23711yescharacteristic
765D3—62no—
766D3—62no—
767D3—121no—
768D3—362no—
769D3—361no—
770D3—361no—
771C22—21no—
772C22—21no—
773C22—92no—
774C22—92no—
775C22—188no—
776C22—181no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—541no—
784C22—541no—
785C22—541no—
786C22#8863412yescomplemented
787C22C22×D3×D911yescharacteristic
788C4—21no—
789C4—21no—
790C4—32no—
791C4—61no—
792C4—61no—
793C4—61no—
794C4—181no—
795C4—272no—
796C4—541no—
797C4—541no—
798C3—21no—
799C3#1058972911yescharacteristic, complemented
800C3#1059405511yescharacteristic
801C2—22no—
802C2—182no—
803C2—182no—
804C2—361no—
805C2—1081no—
806C2C2×#8863411yescharacteristic
807C2D3×D4×D911yescharacteristic
808C2D9×#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#525
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. C22×Dic3×D9C2semidirect
2. C2×#88634C2semidirect
3. #11721727C2semidirect
4. C3×#63444C2semidirect
5. C9×#878C2semidirect
6. #11721277C2semidirect
7. #11721276C2semidirect
8. #611⋊Dic3C2semidirect
9. #11720998C2semidirect
10. #11720988C2semidirect
11. #11720984C2semidirect
12. #11720983C2semidirect
13. #11720981C2semidirect
14. #11720978C2semidirect
15. #11720975C2semidirect
21. C2×C4×C3⋊D9C22semidirect
26. C2×C9×Dic6C22semidirect
29. C2×#6192C22semidirect
35. C2×Dic3×D9C22semidirect
38. #88536C22semidirect
39. #88534C22semidirect
40. C4×C3⋊Dic9C22semidirect
44. C9×C4⋊Dic3C22semidirect
45. C9×Dic3⋊C4C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
82. #63444D3semidirect
119. Dic3×D9D4semidirect
205. C22×C3×C9#41semidirect
219. C2×C3×D9#41semidirect
259. #878D9semidirect
388. C2×Dic6C2×D9semidirect
416. C4⋊Dic3C2×D9semidirect
422. Dic3⋊C4C2×D9semidirect
423. Dic3⋊C4C2×D9semidirect
462. C22×C9#237semidirect
479. C2×D9#237semidirect
510. C3×C9#525semidirect
665. C22×C3#3701semidirect
715. C9#5586semidirect
786. C22#88634semidirect
799. C3#10589729semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3×D92
C2×#886342
#117217272
C3×#634442
C9×#8782
#117212772
#117212762
#611⋊Dic32
#117209982
#117209882
#117209842
#117209832
#117209812
#117209782
#117209752
#105940553
#105897293