Finite Group Databasebeta

← #13148405

Subgroups — #13148405

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D9×#67C211yesmaximal, characteristic, complemented
2C2×D3×D36C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C9×#883C211yesmaximal, characteristic, complemented
5C3×#63444C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721276C211yesmaximal, characteristic, complemented
8#11721256C211yesmaximal, characteristic, complemented
9#11721049C211yesmaximal, characteristic, complemented
10#11721048C211yesmaximal, characteristic, complemented
11#11721032C211yesmaximal, characteristic, complemented
12#11721007C211yesmaximal, characteristic, complemented
13#11721005C211yesmaximal, characteristic, complemented
14#11720988C211yesmaximal, characteristic, complemented
15#11720981C211yesmaximal, characteristic, complemented
16#10594262—31nomaximal
17#10589755—31nomaximal
18C23×C3×D9C2211yescharacteristic, complemented
19C22×D3×D9C2211yescharacteristic
20C22×D3×D9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
24C2×C4×C3⋊D9C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic, complemented
27C2×C4×D3×C9C2211yescharacteristic, complemented
28C2×C3×D36C2211yescharacteristic
29C2×C3×D36C2211yescharacteristic, complemented
30D9×#67—24no—
31C2×#6194C2211yescharacteristic
32C2×#6192C2211yescharacteristic
33C2×#6192C2211yescharacteristic, complemented
34C2×#6192C2211yescharacteristic, complemented
35C2×#6192C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37C2×Dic3×D9C2211yescharacteristic, complemented
38D3×D36—24no—
39C3×C9×C22⋊C4C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C9×#217C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C9×C4⋊Dic3C2211yescharacteristic, complemented
47C9×Dic3⋊C4C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×D3×D12—31no—
57#64093—31no—
58C3×#883D311yescharacteristic
59C3×#882—31no—
60#63983—31no—
61#63977—31no—
62#63958—31no—
63#63922—31no—
64#63921—31no—
65#63916—31no—
66#63910—31no—
67#63905—31no—
68#63890—31no—
69#63884—31no—
70C2×D4×D9—31no—
71C22×D36—31no—
72C9×#123—31no—
73#63499—31no—
74#63491—31no—
75#63457—31no—
76#63457—31no—
77#63456—31no—
78#63456—31no—
79#63446—31no—
80#63446—31no—
81#63446—61no—
82#63444—31no—
83#63444—31no—
84#63444D311yescharacteristic, complemented
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9—22no—
91C22×C3×D9—41no—
92C22×C3×D9—41no—
93C22×C3×D9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C22×C3×D9C2311yescharacteristic
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×D3×D9—41no—
99C2×D3×D9—41no—
100C2×D3×D9—41no—
101C2×D3×D9D414yescomplemented
102C2×C3×C4×C9C2311yescharacteristic
103C2×C3×C4×C9C2311yescharacteristic
104#6233—22no—
105#6233—41no—
106C2×C3⋊Dic9C2311yescharacteristic
107C2×C3⋊Dic9C2311yescharacteristic
108C4⋊(C3⋊D9)—22no—
109C4×C3⋊D9—41no—
110C9×#67—22no—
111C3×#611—41no—
112C2×C9×Dic3C2311yescharacteristic
113C2×C9×Dic3C2311yescharacteristic
114C2×C9×Dic3C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C4×D3×C9—22no—
117C3×D36—22no—
118C3×D36—41no—
119#6194—22no—
120#6192—22no—
121#6192—22no—
122#6192—22no—
123#6192—41no—
124(C3⋊D9)⋊C4—41no—
125Dic3×D9—22no—
126#5653—91no—
127#5589—91no—
128C23×C3×D3—31no—
129C22×D32—31no—
130C22×D32—31no—
131C2×#638—31no—
132C2×#638—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4×C3⋊D3—31no—
135C2×C3×#67—31no—
136C2×C3×#67C2×D311yescharacteristic
137C2×C3×D12—31no—
138C2×C3×D12—31no—
139C2×C3×C4×D3C2×D311yescharacteristic
140D3×#67—64no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#625—31no—
146C2×#624—31no—
147C2×D3×Dic3—31no—
148D3×D12—64no—
149C23×D9—31no—
150C23×D9—31no—
151C23×D9C2×D311yescharacteristic, complemented
152C32×C22⋊C4C2×D311yescharacteristic
153#3752—31no—
154#3750—31no—
155C3×#217C2×D311yescharacteristic
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4C2×D311yescharacteristic
159C3×C4⋊Dic3C2×D311yescharacteristic
160C3×Dic3⋊C4C2×D311yescharacteristic
161Dic3⋊Dic3—31no—
162#3722—31no—
163(C2×D3)⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166(C2×D3)⋊Dic3—31no—
167(C2×D3)⋊Dic3—31no—
168C2×D4×C9—31no—
169C22×C4×C9—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—61no—
174C2×#611—61no—
175C2×#611C2×D311yescharacteristic, complemented
176D4×D9—64no—
177C2×D36—31no—
178C2×D36—31no—
179C2×D36—31no—
180C2×D36—31no—
181C2×D36—31no—
182C2×D36—64no—
183C2×D36—61no—
184C2×D36C2×D311yescharacteristic
185C2×D36C2×D311yescharacteristic, complemented
186C2×C4×D9—31no—
187C2×C4×D9—31no—
188C2×C4×D9—31no—
189C2×C4×D9—61no—
190C9×C4⋊C4—31no—
191C9×C4⋊C4—31no—
192C9×C22⋊C4—21no—
193C9×C22⋊C4—31no—
194C9×C22⋊C4—31no—
195C9×C22⋊C4C2×D311yescharacteristic, complemented
196#3676—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—31no—
203(C2×D9)⋊C4—61no—
204(C2×D9)⋊C4C2×D311yescharacteristic, complemented
205(C2×D9)⋊C4C2×D311yescharacteristic, complemented
206Dic9⋊C4—31no—
207Dic9⋊C4—31no—
208Dic9⋊C4—61no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9C2411yescharacteristic
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×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9C2×D412yes—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226C2×C3×D9—21no—
227C2×C3×D9—21no—
228C2×C3×D9—21no—
229C2×C3×D9—21no—
230C2×C3×D9—44no—
231C2×C3×D9C2×D412yes—
232D3×D9—44no—
233D3×D9—44no—
234C3×C4×C9—21no—
235C3×C4×C9—21no—
236C3⋊Dic9—21no—
237C3⋊Dic9—21no—
238C9×Dic3—21no—
239C9×Dic3—21no—
240C9×Dic3—21no—
241C3×Dic9—21no—
242C22×#67—91no—
243C2×D3×D4—91no—
244C2×D3×D4—91no—
245C22×D12—91no—
246C3×#123—31no—
247C3×#120—91no—
248#953—91no—
249#938—91no—
250#938—91no—
251#937—91no—
252#937—91no—
253#937—91no—
254#935—91no—
255#929—91no—
256#895—91no—
257#895—91no—
258#894—91no—
259#894—91no—
260#886—91no—
261#884—91no—
262#884—91no—
263#884—91no—
264#884—91no—
265#884—181no—
266#883—91no—
267#883D911yescharacteristic, complemented
268#882—31no—
269#882—91no—
270#882—91no—
271D3×C22⋊C4—91no—
272D3×C22⋊C4—91no—
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—31no—
279C22×C3×D3—62no—
280C22×C3×D3—121no—
281C22×C3×D3—121no—
282C22×C3×D3C22×D311yescharacteristic
283C2×D32—34no—
284C2×D32—62no—
285C2×D32—121no—
286C2×D32—121no—
287C2×D32—121no—
288C2×D32—121no—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—62no—
292#638—121no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C4⋊(C3⋊D3)—62no—
296C4×C3⋊D3—121no—
297C3×#67—22no—
298C3×#67—121no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3C22×D311yescharacteristic
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C3×D12—62no—
304C3×D12—121no—
305C3×C4×D3—22no—
306#626—62no—
307#626—62no—
308#626—62no—
309#626—121no—
310#625—62no—
311#624—121no—
312D3×Dic3—62no—
313C23×C9—21no—
314C23×C9—31no—
315C23×C9C22×D311yescharacteristic
316C22×D9—22no—
317C22×D9—31no—
318C22×D9—34no—
319C22×D9—31no—
320C22×D9—41no—
321C22×D9—41no—
322C22×D9—61no—
323C22×D9—61no—
324C22×D9—62no—
325C22×D9—121no—
326C22×D9—121no—
327C22×D9—121no—
328C22×D9—121no—
329C22×D9C22×D311yescharacteristic
330C22×D9C22×D311yescharacteristic
331C22×D9C22×D311yescharacteristic
332D4×C9—62no—
333C2×C4×C9—21no—
334C2×C4×C9—21no—
335C2×C4×C9—31no—
336C2×C4×C9—31no—
337C2×C4×C9—31no—
338C2×C4×C9—62no—
339C2×C4×C9C22×D311yescharacteristic
340C2×C4×C9C22×D311yescharacteristic
341#611—41no—
342#611—62no—
343#611—62no—
344#611—122no—
345#611—121no—
346#611—122no—
347C2×Dic9—31no—
348C2×Dic9—31no—
349C2×Dic9—61no—
350C2×Dic9—61no—
351C2×Dic9C22×D311yescharacteristic
352D36—22no—
353D36—41no—
354D36—62no—
355D36—62no—
356D36—62no—
357D36—62no—
358D36—122no—
359D36—121no—
360C4×D9—62no—
361C4×D9—121no—
362C4×D9—121no—
363C4×D9—122no—
364#534—271noSylow
365C2×C3×C9—41no—
366C2×C3×C9C22×D411yescharacteristic
367C2×C3×C9H(5,𝔽2)11yescharacteristic
368C2×C3×C9H(5,𝔽2)11yescharacteristic
369C3⋊D9—22no—
370C3⋊D9—41no—
371D3×C9—22no—
372C3×D9—22no—
373C3×D9—41no—
374C3×D9—41no—
375C24×C3—91no—
376C23×D3—31no—
377C23×D3—91no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—91no—
381C2×C3×D4—31no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C22×C3×C4—31no—
386C2×#67—31no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—91no—
393C2×#67—91no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—181no—
398C2×#67—181no—
399C2×#67—184no—
400C2×#67C2×D911yescharacteristic
401C22×Dic3—91no—
402D3×D4—184no—
403D3×D4—184no—
404C2×D12—31no—
405C2×D12—31no—
406C2×D12—91no—
407C2×D12—91no—
408C2×D12—91no—
409C2×D12—91no—
410C2×D12—91no—
411C2×D12—91no—
412C2×D12—181no—
413C2×D12—184no—
414C2×C4×D3—91no—
415C2×C4×D3—91no—
416C2×C4×D3—91no—
417C2×C4×D3—91no—
418C2×C4×D3—91no—
419C2×C4×D3—181no—
420C2×C4×D3C2×D911yescharacteristic, complemented
421C3×C4⋊C4—31no—
422C3×C4⋊C4—31no—
423C3×C22⋊C4—21no—
424C3×C22⋊C4—31no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—91no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4C2×D911yescharacteristic, complemented
429C3×C22⋊C4D3211yescharacteristic
430#217—91no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—91no—
435#217C2×D911yescharacteristic, complemented
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—181no—
448(C2×D3)⋊C4C2×D911yescharacteristic, complemented
449C4⋊Dic3—91no—
450C4⋊Dic3C2×D911yescharacteristic, complemented
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454Dic3⋊C4—181no—
455Dic3⋊C4C2×D911yescharacteristic, complemented
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32C23×D311yescharacteristic
460C2×C3⋊D3—32no—
461C2×C3⋊D3—61no—
462C2×C3⋊D3—61no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—32no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—124no—
478C2×C3×D3D3×D412yes—
479D32—124no—
480D32—124no—
481C32×C4—21no—
482C32×C4—21no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—61no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—21no—
492C22×C9—21no—
493C22×C9—32no—
494C22×C9—41no—
495C22×C9—41no—
496C22×C9—41no—
497C22×C9—61no—
498C22×C9—61no—
499C22×C9C23×D311yescharacteristic
500C2×D9—21no—
501C2×D9—21no—
502C2×D9—21no—
503C2×D9—21no—
504C2×D9—21no—
505C2×D9—21no—
506C2×D9—21no—
507C2×D9—21no—
508C2×D9—32no—
509C2×D9—44no—
510C2×D9—62no—
511C2×D9—61no—
512C2×D9—61no—
513C2×D9—61no—
514C2×D9—61no—
515C2×D9—61no—
516C2×D9—121no—
517C2×D9—121no—
518C2×D9—121no—
519C2×D9—121no—
520C2×D9—121no—
521C2×D9—124no—
522C2×D9—124no—
523C2×D9D3×D412yes—
524C4×C9—21no—
525C4×C9—21no—
526C4×C9—41no—
527C4×C9—41no—
528C4×C9—61no—
529C4×C9—61no—
530C4×C9—61no—
531Dic9—21no—
532Dic9—62no—
533Dic9—61no—
534Dic9—61no—
535Dic9—121no—
536C22×D4—271no—
537C22×D4—271no—
538#123—31no—
539#123—271no—
540#123—271no—
541#123—271no—
542#121—271no—
543#121—271no—
544#121—271no—
545#121—271no—
546#120—91no—
547#120—271no—
548#120—271no—
549#120—271no—
550C2×C22⋊C4—271no—
551C3×C9#53411yescharacteristic, complemented, Sylow
552C23×C3—21no—
553C23×C3—31no—
554C23×C3—91no—
555C23×C3—91no—
556C23×C3—91no—
557C23×C3—182no—
558C23×C3—361no—
559C23×C3—361no—
560C23×C3C22×D911yescharacteristic
561C23×C3C2×D3211yescharacteristic
562C22×D3—31no—
563C22×D3—31no—
564C22×D3—31no—
565C22×D3—62no—
566C22×D3—94no—
567C22×D3—91no—
568C22×D3—91no—
569C22×D3—94no—
570C22×D3—91no—
571C22×D3—91no—
572C22×D3—121no—
573C22×D3—121no—
574C22×D3—181no—
575C22×D3—181no—
576C22×D3—182no—
577C22×D3—182no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3—361no—
585C22×D3—361no—
586C22×D3C22×D911yescharacteristic
587C3×D4—62no—
588C3×D4—182no—
589C3×D4—361no—
590C3×D4—361no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—62no—
597C2×C3×C4—91no—
598C2×C3×C4C22×D911yescharacteristic
599C2×C3×C4C22×D911yescharacteristic
600C2×C3×C4C2×D3211yescharacteristic
601C2×C3×C4C2×D3211yescharacteristic
602#67—22no—
603#67—121no—
604#67—182no—
605#67—182no—
606#67—182no—
607#67—182no—
608#67—182no—
609#67—182no—
610#67—182no—
611#67—362no—
612#67—361no—
613#67—361no—
614#67—361no—
615#67—362no—
616C2×Dic3—31no—
617C2×Dic3—91no—
618C2×Dic3—91no—
619C2×Dic3—91no—
620C2×Dic3—91no—
621C2×Dic3—181no—
622C2×Dic3—181no—
623C2×Dic3—182no—
624C2×Dic3C22×D911yescharacteristic
625C2×Dic3C22×D911yescharacteristic
626C2×Dic3C22×D911yescharacteristic
627D12—62no—
628D12—121no—
629D12—182no—
630D12—182no—
631D12—182no—
632D12—182no—
633D12—182no—
634D12—362no—
635D12—361no—
636C4×D3—22no—
637C4×D3—182no—
638C4×D3—361no—
639C4×D3—361no—
640C4×D3—361no—
641C4×D3—361no—
642C4×D3—362no—
643C2×C32—41no—
644C2×C32C2×D3×D411yescharacteristic
645C2×C32#100911yescharacteristic
646C2×C32#100911yescharacteristic
647C3⋊D3—62no—
648C3⋊D3—121no—
649C3×D3—22no—
650C3×D3—62no—
651C3×D3—121no—
652C3×D3—121no—
653C2×C9—21no—
654C2×C9—21no—
655C2×C9—21no—
656C2×C9—41no—
657C2×C9—62no—
658C2×C9—81no—
659C2×C9C2×D3×D411yescharacteristic
660C2×C9#100411yescharacteristic
661C2×C9#100411yescharacteristic
662D9—22no—
663D9—41no—
664D9—41no—
665D9—62no—
666D9—122no—
667D9—121no—
668D9—241no—
669C24—91no—
670C24—271no—
671C24—271no—
672C2×D4—31no—
673C2×D4—91no—
674C2×D4—91no—
675C2×D4—91no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—544no—
685C2×D4—544no—
686C22×C4—31no—
687C22×C4—271no—
688C22×C4—271no—
689C22×C4—271no—
690C4⋊C4—31no—
691C4⋊C4—31no—
692C4⋊C4—271no—
693C4⋊C4—271no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—91no—
697C22⋊C4—91no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4D3×D911yescharacteristic, complemented
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—92no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3—181no—
727C22×C3—181no—
728C22×C3—364no—
729C22×C3C23×D911yescharacteristic
730C22×C3C22×D3211yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—32no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—92no—
743C2×D3—92no—
744C2×D3—124no—
745C2×D3—182no—
746C2×D3—181no—
747C2×D3—181no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—181no—
751C2×D3—181no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—361no—
757C2×D3—361no—
758C2×D3—361no—
759C2×D3—361no—
760C2×D3—361no—
761C2×D3—364no—
762C2×D3—364no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3D4×D912yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—61no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—181no—
776Dic3—21no—
777Dic3—21no—
778Dic3—21no—
779Dic3—61no—
780Dic3—182no—
781Dic3—181no—
782Dic3—181no—
783Dic3—181no—
784Dic3—181no—
785Dic3—361no—
786C32#565311yescharacteristic
787C9—21no—
788C9#558911yescharacteristic, complemented
789C23—31no—
790C23—91no—
791C23—91no—
792C23—91no—
793C23—182no—
794C23—274no—
795C23—271no—
796C23—271no—
797C23—361no—
798C23—361no—
799C23—542no—
800C23—1081no—
801C23—1081no—
802C23—1081no—
803C23—1081no—
804C23C2×D3×D911yescharacteristic
805D4—62no—
806D4—182no—
807D4—361no—
808D4—361no—
809D4—542no—
810D4—542no—
811D4—542no—
812D4—542no—
813D4—542no—
814D4—542no—
815D4—1081no—
816D4—1081no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—62no—
821C2×C4—91no—
822C2×C4—271no—
823C2×C4—271no—
824C2×C4—542no—
825C2×C4—1081no—
826C2×C4—1081no—
827C2×C4C2×D3×D911yescharacteristic
828C2×C4C2×D3×D911yescharacteristic
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—41no—
833C2×C3—41no—
834C2×C3—62no—
835C2×C3—81no—
836C2×C3—182no—
837C2×C3—361no—
838C2×C3—361no—
839C2×C3C2×D4×D911yescharacteristic
840C2×C3#6371511yescharacteristic
841C2×C3#6371511yescharacteristic
842C2×C3#6430711yescharacteristic
843C2×C3D32×D411yescharacteristic
844C2×C3#6431411yescharacteristic
845D3—22no—
846D3—62no—
847D3—121no—
848D3—121no—
849D3—182no—
850D3—182no—
851D3—362no—
852D3—361no—
853D3—361no—
854D3—721no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—32no—
859C22—61no—
860C22—61no—
861C22—92no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—181no—
868C22—181no—
869C22—181no—
870C22—272no—
871C22—364no—
872C22—541no—
873C22—541no—
874C22—541no—
875C22—541no—
876C22—541no—
877C22—1084no—
878C22—1084no—
879C22C22×D3×D911yescharacteristic
880C4—21no—
881C4—21no—
882C4—61no—
883C4—61no—
884C4—61no—
885C4—181no—
886C4—541no—
887C4—541no—
888C3—21no—
889C3#1058975511yescharacteristic, complemented
890C3#1059426211yescharacteristic
891C2—41no—
892C2—62no—
893C2—182no—
894C2—361no—
895C2—361no—
896C2—542no—
897C2—1081no—
898C2#1172247711yescharacteristic
899C2D3×D4×D911yescharacteristic
900C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#534
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×D9×#67C2semidirect
2. C2×D3×D36C2semidirect
3. #11721730C2semidirect
4. C9×#883C2semidirect
5. C3×#63444C2semidirect
6. #11721292C2semidirect
7. #11721276C2semidirect
8. #11721256C2semidirect
9. #11721049C2semidirect
10. #11721048C2semidirect
11. #11721032C2semidirect
12. #11721007C2semidirect
13. #11721005C2semidirect
14. #11720988C2semidirect
15. #11720981C2semidirect
18. C23×C3×D9C22semidirect
20. C22×D3×D9C22semidirect
21. C2×#6233C22semidirect
22. C2×#6233C22semidirect
23. C2×C4⋊(C3⋊D9)C22semidirect
24. C2×C4×C3⋊D9C22semidirect
26. C2×C3×#611C22semidirect
27. C2×C4×D3×C9C22semidirect
29. C2×C3×D36C22semidirect
33. C2×#6192C22semidirect
34. C2×#6192C22semidirect
35. C2×#6192C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
37. C2×Dic3×D9C22semidirect
39. C3×C9×C22⋊C4C22semidirect
40. #88536C22semidirect
41. #88534C22semidirect
42. C9×#217C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C9×C4⋊Dic3C22semidirect
47. C9×Dic3⋊C4C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. Dic9⋊Dic3C22semidirect
84. #63444D3semidirect
101. C2×D3×D9D4semidirect
151. C23×D9C2×D3semidirect
175. C2×#611C2×D3semidirect
185. C2×D36C2×D3semidirect
195. C9×C22⋊C4C2×D3semidirect
204. (C2×D9)⋊C4C2×D3semidirect
205. (C2×D9)⋊C4C2×D3semidirect
267. #883D9semidirect
420. C2×C4×D3C2×D9semidirect
428. C3×C22⋊C4C2×D9semidirect
435. #217C2×D9semidirect
448. (C2×D3)⋊C4C2×D9semidirect
450. C4⋊Dic3C2×D9semidirect
455. Dic3⋊C4C2×D9semidirect
551. C3×C9#534semidirect
705. C22⋊C4D3×D9semidirect
788. C9#5589semidirect
889. C3#10589755semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×D3×D362
#117217302
C9×#8832
C3×#634442
#117212922
#117212762
#117212562
#117210492
#117210482
#117210322
#117210072
#117210052
#117209882
#117209812
#105942623
#105897553