Finite Group Databasebeta

← #13151287

Subgroups — #13151287

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#237C211yesmaximal, characteristic, complemented
2C2×#88668C211yesmaximal, characteristic, complemented
3#11721837C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#67×Dic9C211yesmaximal, characteristic, complemented
7#11721282C211yesmaximal, characteristic, complemented
8#11721277C211yesmaximal, characteristic, complemented
9C2×#88445C211yesmaximal, characteristic, complemented
10#11721259C211yesmaximal, characteristic, complemented
11#11721240C211yesmaximal, characteristic, complemented
12D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
13#11721003C211yesmaximal, characteristic, complemented
14#11720986C211yesmaximal, characteristic, complemented
15#11720954C211yesmaximal, characteristic, complemented
16#10595305—31nomaximal
17#10589931—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic
24C2×C9×#67C2211yescharacteristic, complemented
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic, complemented
27C22×C9×Dic3C2211yescharacteristic, complemented
28C22×C9×Dic3C2211yescharacteristic, complemented
29C22×C3×Dic9C2211yescharacteristic, complemented
30C9×#237—24no—
31C2×C4×D3×C9C2211yescharacteristic, complemented
32C2×C9×Dic6C2211yescharacteristic, complemented
33#88668—24no—
34C2×#6195C2211yescharacteristic
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic
37C2×(C3⋊D9)⋊C4C2211yescharacteristic
38#88551C2211yescharacteristic, complemented
39#88536C2211yescharacteristic
40#88536C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C3×Dic9⋊C4C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic, complemented
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C3×#237D311yescharacteristic
56C2×#3811—31no—
57#64146—31no—
58C3×#939—31no—
59#63983—31no—
60#63978—31no—
61Dic3×#67—31no—
62#63971—31no—
63C2×#3722—31no—
64#63961—31no—
65#63952—31no—
66D3×(C2×D3)⋊C4—31no—
67#63907—31no—
68#63888—31no—
69#63850—31no—
70C2×C9×#41—31no—
71C2×D4×D9—31no—
72#63509—31no—
73#63508—31no—
74#63501—31no—
75#63501D311yescharacteristic, complemented
76#63499—31no—
77#63499—31no—
78#63499—61no—
79D4×Dic9—31no—
80#63492—31no—
81#63491—31no—
82#63491—31no—
83C4×#611—31no—
84C2×(C2×D9)⋊C4—31no—
85C2×(C2×D9)⋊C4—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9—41no—
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
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#6233—41no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C9×#67—22no—
105C9×#67D414yescomplemented
106C3×#611—22no—
107C3×#611—41no—
108C2×C9×Dic3—22no—
109C2×C9×Dic3—22no—
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C3×Dic9—41no—
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C4×D3×C9—22no—
118C9×Dic6—22no—
119#6195—22no—
120D3×Dic9—41no—
121#6192—22no—
122(C3⋊D9)⋊C4—22no—
123#5829—91no—
124#5610—91no—
125C23×C3⋊D3—31no—
126C22×D32—31no—
127C2×C32×D4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67C2×D311yescharacteristic
133C2×C3×#67C2×D311yescharacteristic
134C22×C3×Dic3—31no—
135C22×C3×Dic3C2×D311yescharacteristic
136C22×C3×Dic3C2×D311yescharacteristic
137C3×#237—24no—
138C2×C3×C4×D3C2×D311yescharacteristic
139C2×C3×Dic6C2×D311yescharacteristic
140#3811—64no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#624—31no—
144C2×D3×Dic3—31no—
145C23×D9—31no—
146C23×D9—31no—
147C23×D9—61no—
148#3757—31no—
149#3752—31no—
150#3752—31no—
151C3×#217—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×Dic3⋊C4—31no—
154#3724—31no—
155#3724—31no—
156Dic3⋊Dic3—31no—
157#3722—31no—
158#3722—31no—
159#3722—31no—
160#3722—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164Dic32—31no—
165C9×#41—64no—
166C2×Q8×C9—31no—
167C2×D4×C9—21no—
168C2×D4×C9—31no—
169C2×D4×C9—31no—
170C2×D4×C9C2×D311yescharacteristic, complemented
171C22×C4×C9—31no—
172C22×C4×C9—31no—
173C22×C4×C9—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—61no—
178C2×#611—61no—
179C2×#611C2×D311yescharacteristic
180C2×#611C2×D311yescharacteristic, complemented
181C22×Dic9—31no—
182C22×Dic9C2×D311yescharacteristic, complemented
183D4×D9—64no—
184C2×D36—31no—
185C2×C4×D9—31no—
186#3676—31no—
187#3676—31no—
188#3676—61no—
189#3676C2×D311yescharacteristic, complemented
190(C2×D9)⋊C4—31no—
191(C2×D9)⋊C4—31no—
192(C2×D9)⋊C4—31no—
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—61no—
199(C2×D9)⋊C4—61no—
200(C2×D9)⋊C4C2×D311yescharacteristic, complemented
201C4⋊Dic9—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4C2×D311yescharacteristic, complemented
205C4×Dic9—31no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9C2×D412yes—
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⋊D9—44no—
219C2×C3⋊D9#4112yescomplemented
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9C2×D412yes—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C9×Dic3C2×D412yes—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C2×C3×#41—31no—
237C2×#237D911yescharacteristic, complemented
238C2×D3×D4—91no—
239C2×D3×D4—91no—
240C3×#121—91no—
241#947—91no—
242#946—91no—
243#939—31no—
244#939—91no—
245#939—91no—
246#937—91no—
247#937—91no—
248#937—91no—
249#937—91no—
250#937—181no—
251#935—91no—
252D4×Dic3—91no—
253#930—91no—
254#929—91no—
255#929—91no—
256C4×#67—91no—
257C4×#67—91no—
258C2×(C2×D3)⋊C4—91no—
259C2×(C2×D3)⋊C4—91no—
260C2×(C2×D3)⋊C4—91no—
261#896—91no—
262#894—91no—
263#885—91no—
264#884—91no—
265#67⋊C4—91no—
266D3×C22⋊C4—91no—
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C22×C3⋊D3—31no—
270C22×C3⋊D3—31no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—62no—
273C22×C3⋊D3—121no—
274C22×C3×D3—31no—
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C32×D4—22no—
280C2×C32×C4C22×D311yescharacteristic
281#638—62no—
282#638—121no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C3×#67—22no—
286C3×#67—62no—
287C3×#67—121no—
288C3×#67#6714yes—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—121no—
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C3×C4×D3—22no—
299C3×Dic6—22no—
300#626—62no—
301#626—62no—
302#624—62no—
303D3×Dic3—121no—
304C23×C9—21no—
305C23×C9—21no—
306C23×C9—31no—
307C23×C9C22×D311yescharacteristic
308C23×C9C22×D311yescharacteristic
309C22×D9—31no—
310C22×D9—31no—
311C22×D9—61no—
312C22×D9—61no—
313C22×D9—62no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—122no—
318C22×D9—122no—
319C22×D9—121no—
320C22×D9—121no—
321C22×D9—122no—
322C22×D9C22×D311yescharacteristic
323Q8×C9—62no—
324D4×C9—22no—
325D4×C9—34no—
326D4×C9—42no—
327D4×C9—62no—
328C2×C4×C9—21no—
329C2×C4×C9—31no—
330C2×C4×C9—31no—
331C2×C4×C9—31no—
332C2×C4×C9—62no—
333C2×C4×C9—62no—
334C2×C4×C9—62no—
335C2×C4×C9C22×D311yescharacteristic
336#611—22no—
337#611—41no—
338#611—62no—
339#611—62no—
340#611—122no—
341#611—121no—
342#611—122no—
343C2×Dic9—31no—
344C2×Dic9—31no—
345C2×Dic9—41no—
346C2×Dic9—61no—
347C2×Dic9—61no—
348C2×Dic9—121no—
349C2×Dic9C22×D311yescharacteristic
350C2×Dic9C22×D311yescharacteristic
351C2×Dic9C22×D311yescharacteristic
352D36—62no—
353C4×D9—62no—
354#546—271noSylow
355C2×C3×C9—22no—
356C2×C3×C9—41no—
357C2×C3×C9C22×D411yescharacteristic
358C2×C3×C9C2×#4111yescharacteristic
359C2×C3×C9H(5,𝔽2)11yescharacteristic
360C3⋊D9—22no—
361C3⋊D9—41no—
362D3×C9—22no—
363C3×D9—41no—
364C23×D3—91no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—181no—
369C3×#41—64no—
370C2×C3×Q8—31no—
371C2×C3×D4—21no—
372C2×C3×D4—31no—
373C2×C3×D4—31no—
374C2×C3×D4—91no—
375C2×C3×D4—91no—
376C2×C3×D4C2×D911yescharacteristic, complemented
377C2×C3×D4D3211yescharacteristic
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—91no—
382C2×#67—31no—
383C2×#67—31no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—181no—
391C2×#67—181no—
392C2×#67C2×D911yescharacteristic
393C2×#67C2×D911yescharacteristic, complemented
394C22×Dic3—31no—
395C22×Dic3—91no—
396C22×Dic3C2×D911yescharacteristic, complemented
397C22×Dic3C2×D911yescharacteristic, complemented
398#237—24no—
399D3×D4—184no—
400D3×D4—184no—
401C2×D12—91no—
402C2×D12—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3C2×D911yescharacteristic, complemented
407C2×Dic6C2×D911yescharacteristic, complemented
408C3×C4⋊C4—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411#217—31no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—181no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—181no—
435(C2×D3)⋊C4—181no—
436C4⋊Dic3—91no—
437Dic3⋊C4—31no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32C2×#6712yes—
451C22×C32C23×D311yescharacteristic
452C2×C3⋊D3—32no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—124no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3C2×#6712yes—
465D32—124no—
466C32×C4—21no—
467C3⋊Dic3—61no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3C2×#6712yes—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—21no—
480C22×C9—21no—
481C22×C9—22no—
482C22×C9—32no—
483C22×C9—41no—
484C22×C9—41no—
485C22×C9—41no—
486C22×C9—41no—
487C22×C9—41no—
488C22×C9—61no—
489C22×C9—61no—
490C22×C9D3×D412yes—
491C22×C9C23×D311yescharacteristic
492C2×D9—21no—
493C2×D9—21no—
494C2×D9—21no—
495C2×D9—32no—
496C2×D9—62no—
497C2×D9—61no—
498C2×D9—61no—
499C2×D9—62no—
500C2×D9—61no—
501C2×D9—61no—
502C2×D9—61no—
503C2×D9—121no—
504C2×D9—121no—
505C2×D9—121no—
506C2×D9—121no—
507C2×D9—124no—
508C2×D9—124no—
509C2×D9—128no—
510C4×C9—21no—
511C4×C9—32no—
512C4×C9—41no—
513C4×C9—61no—
514C4×C9—61no—
515Dic9—21no—
516Dic9—21no—
517Dic9—21no—
518Dic9—61no—
519Dic9—61no—
520Dic9—121no—
521Dic9—121no—
522C2×#41—31no—
523C22×D4—271no—
524#124—271no—
525#123—271no—
526#123—271no—
527C22⋊Q8—271no—
528#121—91no—
529#121—271no—
530#121—271no—
531#120—271no—
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×C3C22×D911yescharacteristic
543C23×C3C22×D911yescharacteristic
544C23×C3C2×D3211yescharacteristic
545C23×C3C2×D3211yescharacteristic
546C22×D3—31no—
547C22×D3—91no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—91no—
551C22×D3—181no—
552C22×D3—181no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—182no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—362no—
562C22×D3—362no—
563C22×D3—361no—
564C22×D3—361no—
565C22×D3—361no—
566C22×D3—361no—
567C22×D3—362no—
568C22×D3C22×D911yescharacteristic
569C3×Q8—62no—
570C3×D4—22no—
571C3×D4—22no—
572C3×D4—34no—
573C3×D4—42no—
574C3×D4—62no—
575C3×D4—182no—
576C3×D4—361no—
577C2×C3×C4—21no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—62no—
582C2×C3×C4—62no—
583C2×C3×C4—62no—
584C2×C3×C4—91no—
585C2×C3×C4—91no—
586C2×C3×C4—91no—
587C2×C3×C4—361no—
588C2×C3×C4C22×D911yescharacteristic
589C2×C3×C4C2×D3211yescharacteristic
590#67—22no—
591#67—62no—
592#67—121no—
593#67—182no—
594#67—182no—
595#67—182no—
596#67—182no—
597#67—362no—
598#67—361no—
599#67—361no—
600#67—362no—
601#67#61114yescomplemented
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—91no—
608C2×Dic3—91no—
609C2×Dic3—91no—
610C2×Dic3—91no—
611C2×Dic3—121no—
612C2×Dic3—181no—
613C2×Dic3—181no—
614C2×Dic3—361no—
615C2×Dic3C22×D911yescharacteristic
616C2×Dic3C22×D911yescharacteristic
617C2×Dic3C22×D911yescharacteristic
618D12—182no—
619D12—182no—
620C4×D3—22no—
621C4×D3—182no—
622C4×D3—182no—
623C4×D3—361no—
624Dic6—22no—
625C2×C32—22no—
626C2×C32—41no—
627C2×C32D3×#4111yescharacteristic
628C2×C32#100911yescharacteristic
629C2×C32C22×#6711yescharacteristic
630C3⋊D3—62no—
631C3⋊D3—121no—
632C3×D3—22no—
633C3×D3—121no—
634C2×C9—22no—
635C2×C9—21no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—42no—
639C2×C9—41no—
640C2×C9—62no—
641C2×C9—81no—
642C2×C9C2×D3×D411yescharacteristic
643C2×C9#100411yescharacteristic
644C2×C9D3×#4111yescharacteristic
645D9—41no—
646D9—62no—
647D9—122no—
648D9—122no—
649D9—121no—
650C24—271no—
651C24—271no—
652#41—64no—
653C2×Q8—31no—
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—31no—
666C22×C4—31no—
667C22×C4—91no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—91no—
671C4⋊C4—271no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—91no—
675C22⋊C4—91no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
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—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—22no—
699C22×C3—32no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—181no—
708C22×C3—181no—
709C22×C3—181no—
710C22×C3C2×#61112yes—
711C22×C3C23×D911yescharacteristic
712C22×C3D3×#6712yes—
713C22×C3C22×D3211yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—61no—
719C2×D3—92no—
720C2×D3—92no—
721C2×D3—182no—
722C2×D3—181no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—182no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C2×D3—181no—
731C2×D3—181no—
732C2×D3—181no—
733C2×D3—361no—
734C2×D3—361no—
735C2×D3—361no—
736C2×D3—361no—
737C2×D3—364no—
738C2×D3—364no—
739C2×D3—364no—
740C2×D3—364no—
741C2×D3—368no—
742C2×D3C2×#61112yes—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—32no—
746C3×C4—41no—
747C3×C4—61no—
748C3×C4—61no—
749C3×C4—181no—
750C3×C4—181no—
751C3×C4—181no—
752Dic3—21no—
753Dic3—21no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—181no—
758Dic3—181no—
759Dic3—181no—
760Dic3—181no—
761Dic3—361no—
762Dic3—361no—
763Dic3C2×#61112yes—
764C32#582911yescharacteristic
765C9—21no—
766C9#561011yescharacteristic, complemented
767C23—31no—
768C23—91no—
769C23—271no—
770C23—271no—
771C23—542no—
772C23—542no—
773C23—542no—
774C23—542no—
775C23—1081no—
776C23—1081no—
777C23C2×D3×D911yescharacteristic
778C23C2×D3×D911yescharacteristic
779Q8—62no—
780D4—22no—
781D4—34no—
782D4—62no—
783D4—182no—
784D4—361no—
785D4—542no—
786D4—542no—
787D4—542no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—91no—
796C2×C4—91no—
797C2×C4—91no—
798C2×C4—271no—
799C2×C4—271no—
800C2×C4—361no—
801C2×C4—542no—
802C2×C4—1081no—
803C2×C4C2×D3×D911yescharacteristic
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—42no—
810C2×C3—41no—
811C2×C3—41no—
812C2×C3—62no—
813C2×C3—81no—
814C2×C3—361no—
815C2×C3#41×D911yescharacteristic
816C2×C3#6371511yescharacteristic
817C2×C3C22×#61111yescharacteristic
818C2×C3#6431211yescharacteristic
819C2×C3#6431411yescharacteristic
820C2×C3C2×D3×#6711yescharacteristic
821D3—22no—
822D3—121no—
823D3—182no—
824D3—182no—
825D3—362no—
826D3—362no—
827D3—361no—
828D3—361no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—32no—
835C22—61no—
836C22—61no—
837C22—181no—
838C22—181no—
839C22—181no—
840C22—272no—
841C22—541no—
842C22—541no—
843C22—541no—
844C22—541no—
845C22—541no—
846C22—1084no—
847C22—1084no—
848C22D3×#61112yes—
849C22C22×D3×D911yescharacteristic
850C4—21no—
851C4—32no—
852C4—61no—
853C4—61no—
854C4—181no—
855C4—181no—
856C4—181no—
857C4—541no—
858C4—541no—
859C3—21no—
860C3#1058993111yescharacteristic, complemented
861C3#1059530511yescharacteristic
862C2—22no—
863C2—41no—
864C2—62no—
865C2—361no—
866C2—542no—
867C2—1081no—
868C2#1172249811yescharacteristic
869C2#1172250111yescharacteristic
870C2C2×D3×#61111yescharacteristic
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×C9×#237C2semidirect
2. C2×#88668C2semidirect
3. #11721837C2semidirect
4. C3×#63501C2semidirect
5. #11721292C2semidirect
6. #67×Dic9C2semidirect
7. #11721282C2semidirect
8. #11721277C2semidirect
9. C2×#88445C2semidirect
10. #11721259C2semidirect
11. #11721240C2semidirect
12. D3×(C2×D9)⋊C4C2semidirect
13. #11721003C2semidirect
14. #11720986C2semidirect
15. #11720954C2semidirect
20. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
24. C2×C9×#67C22semidirect
26. C2×C3×#611C22semidirect
27. C22×C9×Dic3C22semidirect
28. C22×C9×Dic3C22semidirect
29. C22×C3×Dic9C22semidirect
31. C2×C4×D3×C9C22semidirect
32. C2×C9×Dic6C22semidirect
35. C2×D3×Dic9C22semidirect
38. #88551C22semidirect
40. #88536C22semidirect
41. C3×#3676C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C3×Dic9⋊C4C22semidirect
44. (C2×D3)⋊Dic9C22semidirect
47. #88445C22semidirect
48. #88445C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. #88442C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
75. #63501D3semidirect
105. C9×#67D4semidirect
170. C2×D4×C9C2×D3semidirect
180. C2×#611C2×D3semidirect
182. C22×Dic9C2×D3semidirect
189. #3676C2×D3semidirect
200. (C2×D9)⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
219. C2×C3⋊D9#41semidirect
237. C2×#237D9semidirect
376. C2×C3×D4C2×D9semidirect
393. C2×#67C2×D9semidirect
396. C22×Dic3C2×D9semidirect
397. C22×Dic3C2×D9semidirect
406. C2×C4×D3C2×D9semidirect
407. C2×Dic6C2×D9semidirect
537. C3×C9#546semidirect
601. #67#611semidirect
663. C2×D4D3×D9semidirect
766. C9#5610semidirect
860. C3#10589931semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#2372
C2×#886682
#117218372
C3×#635012
#117212922
#67×Dic92
#117212822
#117212772
C2×#884452
#117212592
#117212402
D3×(C2×D9)⋊C42
#117210032
#117209862
#117209542
#105953053
#105899313