Finite Group Databasebeta

← D9×#883 #13148400

Subgroups — D9×#883 #13148400

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D9×#67C211yesmaximal, characteristic
2C2×C4×D3×D9C211yesmaximal, characteristic, complemented
3#11721729C211yesmaximal, characteristic, complemented
4C9×#883C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
6#11721280C211yesmaximal, characteristic, complemented
7#11721275C211yesmaximal, characteristic, complemented
8D9×#217C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721032C211yesmaximal, characteristic, complemented
11#11721021C211yesmaximal, characteristic, complemented
12D9×C4⋊Dic3C211yesmaximal, characteristic, complemented
13D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
14#11720942C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16D3×#883—31nomaximal
17D9×#123—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic, complemented
24C2×C3×C4×D9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26D9×#67—24no—
27C2×#6194C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic, complemented
29C2×#6192C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C4×D3×D9—24no—
35C3×C9×C22⋊C4C2211yescharacteristic, complemented
36#88551C2211yescharacteristic, complemented
37#88536C2211yescharacteristic, complemented
38C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
39#88534C2211yescharacteristic, complemented
40C9×#217C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C9×C4⋊Dic3C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×C4×D32—31no—
57#64092—31no—
58C3×#883D311yescharacteristic
59C3×D3×C22⋊C4—31no—
60#63975—31no—
61#63969—31no—
62D3×#217—31no—
63D3×(C2×D3)⋊C4—31no—
64#63905—31no—
65#63891—31no—
66D3×C4⋊Dic3—31no—
67D3×Dic3⋊C4—31no—
68#63854—31no—
69#63853—31no—
70C2×D4×D9—31no—
71C22×C4×D9—31no—
72C9×#123—31no—
73#63497—31no—
74#63491—31no—
75#63456—31no—
76#63456—31no—
77C4⋊C4×D9—31no—
78C4⋊C4×D9—31no—
79#63448—31no—
80#63445—31no—
81#63445—31no—
82#63445—61no—
83C22⋊C4×D9—31no—
84C22⋊C4×D9—31no—
85C22⋊C4×D9D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9—22no—
90C22×C3×D9—22no—
91C22×C3×D9—22no—
92C22×C3×D9C2311yescharacteristic
93C22×C3×D9C2311yescharacteristic
94C2×D3×D9—22no—
95C2×D3×D9—22no—
96C2×D3×D9D414yes—
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99#6233—22no—
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C4×C3⋊D9—22no—
104C9×#67—22no—
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C9×Dic3C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C4×D3×C9—22no—
111C3×C4×D9—22no—
112C3×C4×D9—22no—
113#6194—22no—
114D3×Dic9—22no—
115#6192—22no—
116(C3⋊D9)⋊C4—22no—
117Dic3×D9—22no—
118Dic3×D9—22no—
119Dic3×D9—22no—
120D3×#123—91no—
121C2×#883—91no—
122C23×C3×D3—31no—
123C22×D32—31no—
124C2×#638—31no—
125C2×C4×C3⋊D3—31no—
126C2×C3×#67C2×D311yescharacteristic
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3C2×D311yescharacteristic
130D3×#67—64no—
131C2×#626—31no—
132C2×#625—31no—
133C2×#624—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C4×D32—64no—
139C23×D9—31no—
140C23×D9C2×D311yescharacteristic
141C32×C22⋊C4C2×D311yescharacteristic
142#3757—31no—
143#3752—31no—
144C4⋊(C3⋊Dic3)—31no—
145#3750—31no—
146C3×#217—31no—
147C3×#217C2×D311yescharacteristic
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×C4⋊Dic3C2×D311yescharacteristic
152C3×Dic3⋊C4C2×D311yescharacteristic
153#3724—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156Dic3⋊Dic3—31no—
157#3722—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161C2×D4×C9—31no—
162C22×C4×C9—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—61no—
166C22×Dic9—31no—
167D4×D9—64no—
168C2×D36—31no—
169C2×C4×D9—31no—
170C2×C4×D9—31no—
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—64no—
175C2×C4×D9—61no—
176C2×C4×D9C2×D311yescharacteristic
177C2×C4×D9C2×D311yescharacteristic
178C9×C4⋊C4—31no—
179C9×C4⋊C4—31no—
180C9×C22⋊C4—21no—
181C9×C22⋊C4—31no—
182C9×C22⋊C4—31no—
183C9×C22⋊C4C2×D311yescharacteristic, complemented
184#3676—31no—
185#3676—31no—
186#3676—61no—
187#3676C2×D311yescharacteristic, complemented
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—61no—
193(C2×D9)⋊C4C2×D311yescharacteristic, complemented
194(C2×D9)⋊C4C2×D311yescharacteristic, complemented
195C4⋊Dic9—31no—
196C4⋊Dic9—31no—
197C4⋊Dic9—61no—
198Dic9⋊C4—31no—
199Dic9⋊C4—31no—
200Dic9⋊C4—31no—
201Dic9⋊C4—31no—
202Dic9⋊C4—61no—
203C22×C3×C9—21no—
204C22×C3×C9—21no—
205C22×C3×C9—21no—
206C22×C3×C9C2411yescharacteristic
207C2×C3⋊D9—21no—
208C2×C3⋊D9—21no—
209C2×C3⋊D9C2×D412yes—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9C2×D412yes—
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C2×C3×D9—44no—
217C2×C3×D9C2×D412yes—
218C2×C3×D9#4112yes—
219C2×C3×D9#4112yes—
220D3×D9—28no—
221C3×C4×C9—21no—
222C3×C4×C9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C3⋊Dic9—21no—
226C9×Dic3—21no—
227C9×Dic3—21no—
228C9×Dic3—21no—
229C3×Dic9—21no—
230C3×Dic9—21no—
231C22×#67—91no—
232C2×D3×D4—91no—
233C22×C4×D3—91no—
234C22×C4×D3—91no—
235C3×#123—31no—
236C2×C3×C22⋊C4—91no—
237C2×#217—91no—
238#935—91no—
239#929—91no—
240C2×(C2×D3)⋊C4—91no—
241C2×C4⋊Dic3—91no—
242C2×Dic3⋊C4—91no—
243#894—91no—
244#894—91no—
245D3×C4⋊C4—91no—
246D3×C4⋊C4—91no—
247#886—91no—
248#883—91no—
249#883—91no—
250#883—91no—
251#883—91no—
252#883—91no—
253#883—91no—
254#883—91no—
255#883—91no—
256#883—91no—
257#883—181no—
258#883D911yescharacteristic, direct product factor
259D3×C22⋊C4—31no—
260D3×C22⋊C4—91no—
261D3×C22⋊C4—91no—
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—
269C22×C3×D3C22×D311yescharacteristic
270C2×D32—34no—
271C2×D32—62no—
272C2×D32—62no—
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275#638—62no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—31no—
279C4×C3⋊D3—62no—
280C3×#67—22no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C2×C3×Dic3C22×D311yescharacteristic
286C3×C4×D3—22no—
287C3×C4×D3—62no—
288C3×C4×D3—62no—
289#626—62no—
290#625—62no—
291#624—62no—
292D3×Dic3—62no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295D3×Dic3—62no—
296C23×C9—21no—
297C23×C9—31no—
298C23×C9C22×D311yescharacteristic
299C22×D9—22no—
300C22×D9—22no—
301C22×D9—22no—
302C22×D9—31no—
303C22×D9—34no—
304C22×D9—61no—
305C22×D9—62no—
306C22×D9—62no—
307C22×D9C22×D311yescharacteristic
308C22×D9C22×D311yescharacteristic
309D4×C9—62no—
310C2×C4×C9—21no—
311C2×C4×C9—21no—
312C2×C4×C9—31no—
313C2×C4×C9—31no—
314C2×C4×C9—31no—
315C2×C4×C9—62no—
316C2×C4×C9C22×D311yescharacteristic
317C2×C4×C9C22×D311yescharacteristic
318#611—62no—
319#611—62no—
320#611—122no—
321C2×Dic9—31no—
322C2×Dic9—31no—
323C2×Dic9—31no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9—61no—
327C2×Dic9—62no—
328C2×Dic9C22×D311yescharacteristic
329C2×Dic9C22×D311yescharacteristic
330D36—62no—
331C4×D9—22no—
332C4×D9—22no—
333C4×D9—62no—
334C4×D9—62no—
335C4×D9—62no—
336C4×D9—62no—
337C4×D9—62no—
338C4×D9—122no—
339C2×#123—271noSylow
340C2×C3×C9—41no—
341C2×C3×C9C22×D411yescharacteristic
342C2×C3×C9C2×#4111yescharacteristic
343C2×C3×C9C2×#4111yescharacteristic
344C3⋊D9—22no—
345D3×C9—22no—
346C3×D9—41no—
347C3×D9#12314yescomplemented
348C24×C3—91no—
349C23×D3—31no—
350C23×D3—91no—
351C23×D3—91no—
352C2×C3×D4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—91no—
355C22×C3×C4—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—181no—
362C2×#67—184no—
363C2×#67C2×D911yescharacteristic
364C22×Dic3—91no—
365C22×Dic3—91no—
366C22×Dic3—91no—
367C22×Dic3—91no—
368D3×D4—184no—
369C2×D12—91no—
370C2×C4×D3—31no—
371C2×C4×D3—31no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—181no—
381C2×C4×D3—184no—
382C2×C4×D3—184no—
383C2×C4×D3C2×D911yescharacteristic, complemented
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—31no—
388C3×C22⋊C4—31no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4C2×D911yescharacteristic, complemented
393C3×C22⋊C4D3211yescharacteristic
394#217—31no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—181no—
401#217C2×D911yescharacteristic, complemented
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
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—181no—
412(C2×D3)⋊C4C2×D911yescharacteristic, complemented
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416C4⋊Dic3—91no—
417C4⋊Dic3—91no—
418C4⋊Dic3—181no—
419C4⋊Dic3C2×D911yescharacteristic, complemented
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—181no—
428Dic3⋊C4C2×D911yescharacteristic, complemented
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32C23×D311yescharacteristic
433C2×C3⋊D3—32no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—32no—
439C2×C3×D3—32no—
440C2×C3×D3—32no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3—61no—
444C2×C3×D3—124no—
445C2×C3×D3D3×D412yes—
446D32—68no—
447C32×C4—21no—
448C32×C4—21no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3⋊Dic3—61no—
452C3×Dic3—21no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—61no—
456C3×Dic3—61no—
457C22×C9—21no—
458C22×C9—21no—
459C22×C9—21no—
460C22×C9—21no—
461C22×C9—32no—
462C22×C9—41no—
463C22×C9—41no—
464C22×C9—41no—
465C22×C9—61no—
466C22×C9—61no—
467C22×C9C23×D311yescharacteristic
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—21no—
471C2×D9—32no—
472C2×D9—44no—
473C2×D9—62no—
474C2×D9—61no—
475C2×D9—61no—
476C2×D9—68no—
477C2×D9—121no—
478C2×D9—121no—
479C2×D9#23512yes—
480C2×D9D3×D412yes—
481C2×D9#23712yes—
482C4×C9—21no—
483C4×C9—21no—
484C4×C9—41no—
485C4×C9—41no—
486C4×C9—61no—
487C4×C9—61no—
488C4×C9—61no—
489Dic9—21no—
490Dic9—21no—
491Dic9—61no—
492Dic9—61no—
493Dic9—61no—
494Dic9—121no—
495Dic9—121no—
496Dic9—121no—
497C22×D4—271no—
498C23×C4—271no—
499#123—31no—
500#123—271no—
501#123—271no—
502#123—271no—
503#123—271no—
504#123—271no—
505#123—271no—
506#123—271no—
507C2×C4⋊C4—271no—
508C2×C4⋊C4—271no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—271no—
511C2×C22⋊C4—271no—
512C3×C9C2×#12311yescharacteristic, complemented, Sylow
513C23×C3—21no—
514C23×C3—31no—
515C23×C3—91no—
516C23×C3—91no—
517C23×C3—182no—
518C23×C3—182no—
519C23×C3—182no—
520C23×C3C22×D911yescharacteristic
521C23×C3C2×D3211yescharacteristic
522C22×D3—31no—
523C22×D3—31no—
524C22×D3—62no—
525C22×D3—62no—
526C22×D3—62no—
527C22×D3—94no—
528C22×D3—91no—
529C22×D3—91no—
530C22×D3—94no—
531C22×D3—181no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3C22×D911yescharacteristic
537C3×D4—62no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—31no—
543C2×C3×C4—62no—
544C2×C3×C4—91no—
545C2×C3×C4—91no—
546C2×C3×C4—182no—
547C2×C3×C4—182no—
548C2×C3×C4C22×D911yescharacteristic
549C2×C3×C4C22×D911yescharacteristic
550C2×C3×C4C2×D3211yescharacteristic
551C2×C3×C4C2×D3211yescharacteristic
552#67—22no—
553#67—182no—
554#67—182no—
555#67—182no—
556#67—182no—
557#67—182no—
558#67—362no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—181no—
568C2×Dic3—181no—
569C2×Dic3—181no—
570C2×Dic3—182no—
571C2×Dic3—182no—
572C2×Dic3—182no—
573C2×Dic3—182no—
574C2×Dic3C22×D911yescharacteristic
575C2×Dic3C22×D911yescharacteristic
576C2×Dic3C22×D911yescharacteristic
577D12—182no—
578C4×D3—22no—
579C4×D3—62no—
580C4×D3—62no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—182no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—362no—
590C2×C32—41no—
591C2×C32C2×D3×D411yescharacteristic
592C2×C32D3×#4111yescharacteristic
593C2×C32D3×#4111yescharacteristic
594C3⋊D3—62no—
595C3×D3—22no—
596C3×D3—34no—
597C3×D3—121no—
598C2×C9—21no—
599C2×C9—21no—
600C2×C9—21no—
601C2×C9—41no—
602C2×C9—62no—
603C2×C9—81no—
604C2×C9C2×#23511yescharacteristic
605C2×C9C2×D3×D411yescharacteristic
606C2×C9C2×#23711yescharacteristic
607D9—41no—
608D9—62no—
609D9—122no—
610D9#88314yesdirect product factor
611C24—91no—
612C24—271no—
613C2×D4—31no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—544no—
618C22×C4—31no—
619C22×C4—91no—
620C22×C4—91no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—544no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4D3×D911yescharacteristic, complemented
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—61no—
660C22×C3—61no—
661C22×C3—92no—
662C22×C3—92no—
663C22×C3—92no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3—181no—
667C22×C3—364no—
668C22×C3C23×D911yescharacteristic
669C22×C3C22×D3211yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—32no—
673C2×D3—32no—
674C2×D3—32no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—92no—
679C2×D3—92no—
680C2×D3—124no—
681C2×D3—182no—
682C2×D3—188no—
683C2×D3—188no—
684C2×D3—181no—
685C2×D3—181no—
686C2×D3—181no—
687C2×D3—181no—
688C2×D3—361no—
689C2×D3—361no—
690C2×D3D4×D912yes—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—181no—
701C3×C4—181no—
702Dic3—21no—
703Dic3—21no—
704Dic3—21no—
705Dic3—61no—
706Dic3—61no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—181no—
712Dic3—181no—
713Dic3—361no—
714Dic3—361no—
715Dic3—361no—
716C32D3×#12311yescharacteristic
717C9—21no—
718C9C2×#88311yescharacteristic, complemented
719C23—31no—
720C23—91no—
721C23—91no—
722C23—182no—
723C23—182no—
724C23—182no—
725C23—274no—
726C23—271no—
727C23—542no—
728C23—542no—
729C23C2×D3×D911yescharacteristic
730D4—62no—
731D4—542no—
732D4—542no—
733D4—542no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—62no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—182no—
741C2×C4—182no—
742C2×C4—271no—
743C2×C4—271no—
744C2×C4—271no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4—542no—
748C2×C4—542no—
749C2×C4—542no—
750C2×C4—542no—
751C2×C4C2×D3×D911yescharacteristic
752C2×C4C2×D3×D911yescharacteristic
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—62no—
759C2×C3—81no—
760C2×C3—94no—
761C2×C3—361no—
762C2×C3C2×D4×D911yescharacteristic
763C2×C3#41×D911yescharacteristic
764C2×C3#41×D911yescharacteristic
765C2×C3D3×#23511yescharacteristic
766C2×C3D32×D411yescharacteristic
767C2×C3D3×#23711yescharacteristic
768D3—22no—
769D3—34no—
770D3—121no—
771D3—182no—
772D3—182no—
773D3—362no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—32no—
778C22—61no—
779C22—61no—
780C22—92no—
781C22—92no—
782C22—92no—
783C22—181no—
784C22—181no—
785C22—181no—
786C22—272no—
787C22—364no—
788C22—548no—
789C22—541no—
790C22—541no—
791C22C22×D3×D911yescharacteristic
792C4—21no—
793C4—21no—
794C4—61no—
795C4—61no—
796C4—61no—
797C4—181no—
798C4—181no—
799C4—541no—
800C4—541no—
801C4—541no—
802C3—21no—
803C3D9×#12311yescharacteristic, complemented
804C3D3×#88311yescharacteristic
805C2—41no—
806C2—62no—
807C2—94no—
808C2—361no—
809C2—542no—
810C2D9×#23511yescharacteristic
811C2D3×D4×D911yescharacteristic
812C2D9×#23711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×D9×#67C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×#123
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×D9C2semidirect
3. #11721729C2semidirect
4. C9×#883C2semidirect
5. C3×C22⋊C4×D9C2semidirect
6. #11721280C2semidirect
7. #11721275C2semidirect
8. D9×#217C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721032C2semidirect
11. #11721021C2semidirect
12. D9×C4⋊Dic3C2semidirect
13. D9×Dic3⋊C4C2semidirect
14. #11720942C2semidirect
15. #11720941C2semidirect
21. C2×C4×C3⋊D9C22semidirect
23. C2×C4×D3×C9C22semidirect
28. C2×D3×Dic9C22semidirect
30. C2×(C3⋊D9)⋊C4C22semidirect
35. C3×C9×C22⋊C4C22semidirect
36. #88551C22semidirect
37. #88536C22semidirect
38. C4⋊(C3⋊Dic9)C22semidirect
39. #88534C22semidirect
40. C9×#217C22semidirect
41. C3×#3676C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C9×C4⋊Dic3C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. #88445C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic9⋊Dic3C22semidirect
85. C22⋊C4×D9D3semidirect
183. C9×C22⋊C4C2×D3semidirect
187. #3676C2×D3semidirect
193. (C2×D9)⋊C4C2×D3semidirect
194. (C2×D9)⋊C4C2×D3semidirect
258. #883D9direct (N × H)
347. C3×D9#123semidirect
383. C2×C4×D3C2×D9semidirect
392. C3×C22⋊C4C2×D9semidirect
401. #217C2×D9semidirect
412. (C2×D3)⋊C4C2×D9semidirect
419. C4⋊Dic3C2×D9semidirect
428. Dic3⋊C4C2×D9semidirect
512. C3×C9C2×#123semidirect
610. D9#883direct (N × H)
647. C22⋊C4D3×D9semidirect
718. C9C2×#883semidirect
803. C3D9×#123semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×C4×D3×D92
#117217292
C9×#8832
C3×C22⋊C4×D92
#117212802
#117212752
D9×#2172
D9×(C2×D3)⋊C42
#117210322
#117210212
D9×C4⋊Dic32
D9×Dic3⋊C42
#117209422
#117209412
D3×#8833
D9×#1233