Finite Group Databasebeta

← #13151289

Subgroups — #13151289

Order 1728.

1166 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88742C211yesmaximal, characteristic, complemented
2C2×D9×#67C211yesmaximal, characteristic, complemented
3C9×#939C211yesmaximal, characteristic, complemented
4C3×#63499C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#611⋊Dic3C211yesmaximal, characteristic, complemented
8#11721266C211yesmaximal, characteristic, complemented
9C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
10#11721256C211yesmaximal, characteristic, complemented
11#11721240C211yesmaximal, characteristic, complemented
12#11721048C211yesmaximal, characteristic, complemented
13#11721042C211yesmaximal, characteristic, complemented
14#11720996C211yesmaximal, characteristic, complemented
15#11720941C211yesmaximal, characteristic, complemented
16#10595307—31nomaximal
17#10589712—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic, complemented
23C22×C3⋊Dic9C2211yescharacteristic, complemented
24C22×C3⋊Dic9C2211yescharacteristic, complemented
25#88742—24no—
26C2×C4×C3⋊D9C2211yescharacteristic, complemented
27C2×#6226C2211yescharacteristic, complemented
28C2×C9×#67C2211yescharacteristic
29C2×C9×#67C2211yescharacteristic, complemented
30C2×C3×#611C2211yescharacteristic
31C2×C3×#611C2211yescharacteristic, complemented
32C22×C9×Dic3C2211yescharacteristic, complemented
33D9×#67—24no—
34C2×#6194C2211yescharacteristic
35C2×#6192C2211yescharacteristic
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37C2×Dic3×D9C2211yescharacteristic
38C9×#217C2211yescharacteristic, complemented
39C3×#3676C2211yescharacteristic, complemented
40C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C9×Dic3⋊C4C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46#88445C2211yescharacteristic, complemented
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3830—31no—
56C2×D3×#67—31no—
57C3×#939D311yescharacteristic
58C3×#937—31no—
59#63983—31no—
60#63980—31no—
61#67⋊Dic3—31no—
62#63962—31no—
63C2×(C2×D3)⋊Dic3—31no—
64#63958—31no—
65#63952—31no—
66#63921—31no—
67#63913—31no—
68#63896—31no—
69#63853—31no—
70C2×#3699—31no—
71C2×#3699—61no—
72C2×D4×D9—31no—
73C9×#121—31no—
74#63501—31no—
75#63499—31no—
76#63499D311yescharacteristic, complemented
77#63497—31no—
78C4×#611—31no—
79C2×(C2×D9)⋊C4—31no—
80#63458—31no—
81#63456—31no—
82#63447—31no—
83#63446—31no—
84#611⋊C4—31no—
85C22⋊C4×D9—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9—22no—
91C22×C3×D9—22no—
92C22×C3×D9—41no—
93C22×C3×D9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C3×D4×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100#6233—22no—
101#6233D414yescomplemented
102C2×C3⋊Dic9—22no—
103C2×C3⋊Dic9—22no—
104C2×C3⋊Dic9C2311yescharacteristic
105C2×C3⋊Dic9C2311yescharacteristic
106C2×C3⋊Dic9C2311yescharacteristic
107C4×C3⋊D9—22no—
108#6226—22no—
109C9×#67—22no—
110C9×#67—41no—
111C3×#611—22no—
112C3×#611—41no—
113C2×C9×Dic3—41no—
114C2×C9×Dic3C2311yescharacteristic
115C2×C9×Dic3C2311yescharacteristic
116C2×C9×Dic3C2311yescharacteristic
117C2×C3×Dic9C2311yescharacteristic
118C2×C3×Dic9C2311yescharacteristic
119#6194—22no—
120#6192—22no—
121(C3⋊D9)⋊C4—41no—
122Dic3×D9—22no—
123#5610—91no—
124#5591—91no—
125C23×C3×D3—31no—
126C22×D32—31no—
127C2×C32×D4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—31no—
132#3830—64no—
133C2×C4×C3⋊D3—31no—
134C2×#634—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×#67C2×D311yescharacteristic
139C22×C3×Dic3C2×D311yescharacteristic
140D3×#67—64no—
141C2×#626—31no—
142C2×#625—31no—
143C2×#624—31no—
144C2×D3×Dic3—31no—
145C23×D9—31no—
146C23×D9C2×D311yescharacteristic
147C3×#217—31no—
148C3×#217C2×D311yescharacteristic
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4—31no—
151C3×(C2×D3)⋊C4C2×D311yescharacteristic
152C3×Dic3⋊C4C2×D311yescharacteristic
153#3724—31no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—31no—
156#3722—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163Dic32—31no—
164C2×D4×C9—21no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C2×D4×C9C2×D311yescharacteristic, complemented
168C22×C4×C9—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—61no—
173C2×#611—61no—
174C2×#611C2×D311yescharacteristic
175C2×#611C2×D311yescharacteristic, complemented
176C22×Dic9—31no—
177C22×Dic9—31no—
178C22×Dic9—61no—
179C22×Dic9—61no—
180#3699—64no—
181#3699—68no—
182D4×D9—64no—
183C2×D36—31no—
184C2×C4×D9—31no—
185C2×C4×D9—31no—
186C2×C4×D9—31no—
187C2×C4×D9—61no—
188C2×Dic18—31no—
189C2×Dic18—61no—
190C9×C4⋊C4—31no—
191C9×C22⋊C4—31no—
192C9×C22⋊C4—31no—
193#3676—31no—
194#3676—31no—
195#3676C2×D311yescharacteristic, complemented
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4C2×D311yescharacteristic
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
205Dic9⋊C4—31no—
206C4×Dic9—31no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9C2×D412yes—
213C22×C3×C9C2411yescharacteristic
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3⋊D9C2×D412yes—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—44no—
226C2×C3×D9#4112yescomplemented
227D3×D9—44no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9C2×D412yes—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C9×Dic3—21no—
235C3×Dic9—21no—
236C3×Dic9—21no—
237C22×#67—91no—
238C2×#237—91no—
239C2×#237—91no—
240C2×#237—181no—
241C2×D3×D4—91no—
242C3×#121—31no—
243C3×#120—91no—
244C2×#217—91no—
245#939—91no—
246#939—91no—
247#939D911yescharacteristic, complemented
248#938—91no—
249#937—31no—
250#937—91no—
251#937—91no—
252#935—91no—
253D4×Dic3—91no—
254C4×#67—91no—
255C2×(C2×D3)⋊C4—91no—
256#896—91no—
257#894—91no—
258#886—91no—
259#885—91no—
260#885—91no—
261#884—91no—
262#883—91no—
263#67⋊C4—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—91no—
267#878—91no—
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—62no—
274C22×C3×D3—62no—
275C22×C3×D3—121no—
276C22×C3×D3C22×D311yescharacteristic
277C2×D32—62no—
278C2×D32—62no—
279C2×D32—121no—
280C32×D4—22no—
281C2×C32×C4C22×D311yescharacteristic
282#638—34no—
283#638—62no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—31no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—62no—
289C4×C3⋊D3—62no—
290#634—62no—
291C3×#67—22no—
292C3×#67—41no—
293C3×#67—62no—
294C3×#67—121no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—41no—
298C2×C3×Dic3C22×D311yescharacteristic
299C2×C3×Dic3C22×D311yescharacteristic
300C2×C3×Dic3C22×D311yescharacteristic
301#626—62no—
302#625—62no—
303#624—121no—
304D3×Dic3—62no—
305C23×C9—21no—
306C23×C9—21no—
307C23×C9—31no—
308C23×C9C22×D311yescharacteristic
309C23×C9C22×D311yescharacteristic
310C22×D9—22no—
311C22×D9—22no—
312C22×D9—31no—
313C22×D9—41no—
314C22×D9—61no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—121no—
318C22×D9C22×D311yescharacteristic
319C22×D9C22×D311yescharacteristic
320D4×C9—24no—
321D4×C9—22no—
322D4×C9—62no—
323D4×C9—121no—
324C2×C4×C9—21no—
325C2×C4×C9—31no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9—121no—
329C2×C4×C9C22×D311yescharacteristic
330#611—22no—
331#611—34no—
332#611—41no—
333#611—64no—
334#611—62no—
335#611—62no—
336#611—64no—
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—31no—
340C2×Dic9—61no—
341C2×Dic9—61no—
342C2×Dic9—61no—
343C2×Dic9—62no—
344C2×Dic9—64no—
345C2×Dic9—64no—
346C2×Dic9—62no—
347C2×Dic9C22×D311yescharacteristic
348C2×Dic9C22×D311yescharacteristic
349D36—62no—
350C4×D9—62no—
351C4×D9—62no—
352C4×D9—64no—
353C4×D9—121no—
354Dic18—62no—
355Dic18—64no—
356#546—271noSylow
357C2×C3×C9—22no—
358C2×C3×C9—41no—
359C2×C3×C9C22×D411yescharacteristic
360C2×C3×C9C2×#4111yescharacteristic
361C2×C3×C9H(5,𝔽2)11yescharacteristic
362C3⋊D9—22no—
363D3×C9—41no—
364C3×D9—22no—
365C3×D9—41no—
366C24×C3—91no—
367C23×D3—31no—
368C23×D3—91no—
369C23×D3—91no—
370C2×C3×D4—21no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—91no—
374C2×C3×D4—91no—
375C2×C3×D4C2×D911yescharacteristic, complemented
376C2×C3×D4D3211yescharacteristic
377C22×C3×C4—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—181no—
388C2×#67—181no—
389C2×#67—184no—
390C2×#67C2×D911yescharacteristic
391C2×#67C2×D911yescharacteristic, complemented
392C22×Dic3—91no—
393C22×Dic3—91no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3—91no—
397C22×Dic3—181no—
398C22×Dic3—181no—
399C22×Dic3C2×D911yescharacteristic, complemented
400#237—184no—
401#237—184no—
402#237—188no—
403D3×D4—184no—
404C2×D12—91no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×C4×D3—91no—
408C2×C4×D3—91no—
409C2×C4×D3—91no—
410C2×C4×D3—181no—
411C2×Dic6—91no—
412C2×Dic6—91no—
413C2×Dic6—181no—
414C3×C4⋊C4—31no—
415C3×C22⋊C4—31no—
416C3×C22⋊C4—31no—
417C3×C22⋊C4—91no—
418C3×C22⋊C4—91no—
419C3×C22⋊C4—91no—
420#217—31no—
421#217—91no—
422#217—91no—
423#217—91no—
424#217—91no—
425#217—91no—
426#217—91no—
427#217C2×D911yescharacteristic, complemented
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4C2×D911yescharacteristic, complemented
439C4⋊Dic3—91no—
440C4⋊Dic3—91no—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443Dic3⋊C4—91no—
444Dic3⋊C4—91no—
445Dic3⋊C4C2×D911yescharacteristic, complemented
446C4×Dic3—91no—
447C4×Dic3—91no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32D3×D412yes—
454C22×C32C23×D311yescharacteristic
455C2×C3⋊D3—32no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—32no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—124no—
468D32—124no—
469C32×C4—21no—
470C3⋊Dic3—32no—
471C3⋊Dic3—61no—
472C3⋊Dic3—61no—
473C3×Dic3—21no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—61no—
477C3×Dic3—61no—
478C22×C9—21no—
479C22×C9—21no—
480C22×C9—22no—
481C22×C9—21no—
482C22×C9—21no—
483C22×C9—21no—
484C22×C9—21no—
485C22×C9—22no—
486C22×C9—41no—
487C22×C9—41no—
488C22×C9—41no—
489C22×C9—41no—
490C22×C9—61no—
491C22×C9—61no—
492C22×C9—61no—
493C22×C9D3×D412yes—
494C22×C9C23×D311yescharacteristic
495C2×D9—21no—
496C2×D9—21no—
497C2×D9—21no—
498C2×D9—21no—
499C2×D9—21no—
500C2×D9—32no—
501C2×D9—44no—
502C2×D9—62no—
503C2×D9—61no—
504C2×D9—61no—
505C2×D9—121no—
506C2×D9—121no—
507C2×D9—124no—
508C2×D9#23712yescomplemented
509C4×C9—22no—
510C4×C9—21no—
511C4×C9—61no—
512C4×C9—61no—
513C4×C9—61no—
514Dic9—21no—
515Dic9—21no—
516Dic9—32no—
517Dic9—62no—
518Dic9—62no—
519Dic9—62no—
520Dic9—61no—
521Dic9—61no—
522C2×#41—271no—
523C22×D4—271no—
524#124—271no—
525#123—271no—
526#123—271no—
527C22⋊Q8—271no—
528#121—31no—
529#121—271no—
530#121—271no—
531#120—91no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—271no—
536C2×C22⋊C4—271no—
537C3×C9#54611yescharacteristic, complemented, Sylow
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—91no—
542C23×C3—91no—
543C23×C3—182no—
544C23×C3—182no—
545C23×C3—361no—
546C23×C3C22×D911yescharacteristic
547C23×C3C22×D911yescharacteristic
548C23×C3C2×D3211yescharacteristic
549C23×C3C2×D3211yescharacteristic
550C22×D3—31no—
551C22×D3—31no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—91no—
555C22×D3—91no—
556C22×D3—121no—
557C22×D3—181no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—182no—
562C22×D3—361no—
563C22×D3—361no—
564C22×D3C22×D911yescharacteristic
565C3×D4—24no—
566C3×D4—22no—
567C3×D4—22no—
568C3×D4—62no—
569C3×D4—121no—
570C3×D4—182no—
571C3×D4—361no—
572C2×C3×C4—21no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578C2×C3×C4—121no—
579C2×C3×C4C22×D911yescharacteristic
580C2×C3×C4C2×D3211yescharacteristic
581#67—22no—
582#67—41no—
583#67—62no—
584#67—94no—
585#67—94no—
586#67—121no—
587#67—184no—
588#67—182no—
589#67—182no—
590#67—182no—
591#67—182no—
592#67—182no—
593#67—184no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—41no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—91no—
603C2×Dic3—181no—
604C2×Dic3—181no—
605C2×Dic3—181no—
606C2×Dic3—182no—
607C2×Dic3—182no—
608C2×Dic3—182no—
609C2×Dic3—184no—
610C2×Dic3—184no—
611C2×Dic3—182no—
612C2×Dic3—182no—
613C2×Dic3C22×D911yescharacteristic
614C2×Dic3C22×D911yescharacteristic
615C2×Dic3C22×D911yescharacteristic
616D12—182no—
617C4×D3—182no—
618C4×D3—182no—
619C4×D3—182no—
620C4×D3—184no—
621C4×D3—361no—
622C4×D3—361no—
623Dic6—182no—
624Dic6—182no—
625Dic6—184no—
626C2×C32—22no—
627C2×C32—41no—
628C2×C32C2×D3×D411yescharacteristic
629C2×C32#100411yescharacteristic
630C2×C32D3×#4111yescharacteristic
631C3⋊D3—62no—
632C3×D3—41no—
633C3×D3—62no—
634C3×D3—121no—
635C2×C9—22no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—21no—
639C2×C9—42no—
640C2×C9—42no—
641C2×C9—41no—
642C2×C9—121no—
643C2×C9C2×D3×D411yescharacteristic
644C2×C9C2×#23711yescharacteristic
645C2×C9#100411yescharacteristic
646D9—22no—
647D9—41no—
648D9—62no—
649D9—122no—
650C24—91no—
651C24—271no—
652#41—544no—
653C2×Q8—271no—
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—271no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—544no—
663C2×D4D3×D911yescharacteristic, complemented
664C22×C4—31no—
665C22×C4—271no—
666C22×C4—271no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—31no—
671C4⋊C4—271no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—91no—
677C22⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4—271no—
686C42—271no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—22no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—22no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—92no—
708C22×C3—181no—
709C22×C3—181no—
710C22×C3—181no—
711C22×C3—181no—
712C22×C3—181no—
713C22×C3—364no—
714C22×C3D4×D912yes—
715C22×C3C23×D911yescharacteristic
716C22×C3#381112yes—
717C22×C3C22×D3211yescharacteristic
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—32no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—92no—
728C2×D3—92no—
729C2×D3—124no—
730C2×D3—182no—
731C2×D3—181no—
732C2×D3—181no—
733C2×D3—181no—
734C2×D3—181no—
735C2×D3—361no—
736C2×D3—361no—
737C2×D3—364no—
738C2×D3—364no—
739C3×C4—22no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—61no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—181no—
746C3×C4—181no—
747Dic3—21no—
748Dic3—21no—
749Dic3—21no—
750Dic3—61no—
751Dic3—61no—
752Dic3—92no—
753Dic3—92no—
754Dic3—182no—
755Dic3—182no—
756Dic3—182no—
757Dic3—181no—
758Dic3—181no—
759Dic3—181no—
760Dic3—181no—
761C32#561011yescharacteristic
762C9—21no—
763C9#559111yescharacteristic, complemented
764C23—31no—
765C23—91no—
766C23—91no—
767C23—182no—
768C23—182no—
769C23—271no—
770C23—361no—
771C23—542no—
772C23—542no—
773C23—1081no—
774C23C2×D3×D911yescharacteristic
775C23C2×D3×D911yescharacteristic
776Q8—542no—
777D4—22no—
778D4—62no—
779D4—121no—
780D4—182no—
781D4—274no—
782D4—361no—
783D4—542no—
784D4—542no—
785D4—542no—
786C2×C4—31no—
787C2×C4—31no—
788C2×C4—31no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—121no—
792C2×C4—271no—
793C2×C4—271no—
794C2×C4—271no—
795C2×C4—542no—
796C2×C4—542no—
797C2×C4—542no—
798C2×C4—542no—
799C2×C4—1081no—
800C2×C4C2×D3×D911yescharacteristic
801C2×C3—22no—
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—42no—
807C2×C3—42no—
808C2×C3—41no—
809C2×C3—41no—
810C2×C3—121no—
811C2×C3—182no—
812C2×C3—361no—
813C2×C3C2×D4×D911yescharacteristic
814C2×C3#6371011yescharacteristic
815C2×C3#41×D911yescharacteristic
816C2×C3D3×#23711yescharacteristic
817C2×C3#6431311yescharacteristic
818C2×C3C2×#381111yescharacteristic
819D3—41no—
820D3—62no—
821D3—121no—
822D3—182no—
823D3—182no—
824D3—362no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—92no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—181no—
838C22—181no—
839C22—272no—
840C22—364no—
841C22—541no—
842C22—541no—
843C22—1084no—
844C22#8866812yes—
845C22C22×D3×D911yescharacteristic
846C4—21no—
847C4—61no—
848C4—61no—
849C4—61no—
850C4—181no—
851C4—181no—
852C4—272no—
853C4—541no—
854C4—541no—
855C3—21no—
856C3#1058971211yescharacteristic, complemented
857C3#1059530711yescharacteristic
858C2—22no—
859C2—41no—
860C2—121no—
861C2—182no—
862C2—361no—
863C2—542no—
864C2D9×#23711yescharacteristic
865C2#1172249911yescharacteristic
866C2C2×#8866811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#546
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×#88742C2semidirect
2. C2×D9×#67C2semidirect
3. C9×#939C2semidirect
4. C3×#63499C2semidirect
5. #11721292C2semidirect
6. #11721290C2semidirect
7. #611⋊Dic3C2semidirect
8. #11721266C2semidirect
9. C2×(C2×D9)⋊Dic3C2semidirect
10. #11721256C2semidirect
11. #11721240C2semidirect
12. #11721048C2semidirect
13. #11721042C2semidirect
14. #11720996C2semidirect
15. #11720941C2semidirect
20. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C22×C3⋊Dic9C22semidirect
24. C22×C3⋊Dic9C22semidirect
26. C2×C4×C3⋊D9C22semidirect
27. C2×#6226C22semidirect
29. C2×C9×#67C22semidirect
31. C2×C3×#611C22semidirect
32. C22×C9×Dic3C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
38. C9×#217C22semidirect
39. C3×#3676C22semidirect
40. C9×(C2×D3)⋊C4C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C9×Dic3⋊C4C22semidirect
44. (C2×D3)⋊Dic9C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
46. #88445C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
76. #63499D3semidirect
101. #6233D4semidirect
167. C2×D4×C9C2×D3semidirect
175. C2×#611C2×D3semidirect
195. #3676C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
226. C2×C3×D9#41semidirect
247. #939D9semidirect
375. C2×C3×D4C2×D9semidirect
391. C2×#67C2×D9semidirect
399. C22×Dic3C2×D9semidirect
427. #217C2×D9semidirect
438. (C2×D3)⋊C4C2×D9semidirect
445. Dic3⋊C4C2×D9semidirect
508. C2×D9#237semidirect
537. C3×C9#546semidirect
663. C2×D4D3×D9semidirect
763. C9#5591semidirect
856. C3#10589712semidirect

Maximal subgroups

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

subgroupindex
C2×#887422
C2×D9×#672
C9×#9392
C3×#634992
#117212922
#117212902
#611⋊Dic32
#117212662
C2×(C2×D9)⋊Dic32
#117212562
#117212402
#117210482
#117210422
#117209962
#117209412
#105953073
#105897123