Finite Group Databasebeta

← #13147996

Subgroups — #13147996

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D9×#67C211yesmaximal, characteristic, complemented
2C2×#88634C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C9×#885C211yesmaximal, characteristic, complemented
5C3×#63444C211yesmaximal, characteristic, complemented
6#11721289C211yesmaximal, characteristic, complemented
7#11721276C211yesmaximal, characteristic, complemented
8#11721271C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721049C211yesmaximal, characteristic, complemented
11#11721041C211yesmaximal, characteristic, complemented
12#11721006C211yesmaximal, characteristic, complemented
13#11721003C211yesmaximal, characteristic, complemented
14#11720982C211yesmaximal, characteristic, complemented
15#11720974C211yesmaximal, characteristic, complemented
16#10594270—31nomaximal
17#10589776—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C4×C3⋊D9C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic, complemented
26C2×C3×D36C2211yescharacteristic
27C2×C3×D36C2211yescharacteristic, complemented
28C2×C9×Dic6C2211yescharacteristic, complemented
29D9×#67—24no—
30C2×#6195C2211yescharacteristic, complemented
31C2×#6194C2211yescharacteristic
32C2×#6194C2211yescharacteristic, complemented
33C2×#6192C2211yescharacteristic
34C2×#6192C2211yescharacteristic
35C2×#6192C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic, complemented
37C2×#6192C2211yescharacteristic, complemented
38C2×Dic3×D9C2211yescharacteristic
39C2×Dic3×D9C2211yescharacteristic, complemented
40#88634—24no—
41C3×C9×C22⋊C4C2211yescharacteristic, complemented
42#88536C2211yescharacteristic, complemented
43#88534C2211yescharacteristic, complemented
44C9×#217C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic
48C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
49C4×C9×Dic3C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3796—31no—
57#64093—31no—
58C3×#885D311yescharacteristic
59C3×#882—31no—
60#63979—31no—
61#63977—31no—
62#63971—31no—
63#63923—31no—
64#63922—31no—
65#63912—31no—
66#63911—31no—
67#63907—31no—
68#63885—31no—
69#63877—31no—
70C2×#3701—31no—
71C2×D4×D9—31no—
72C9×#124—31no—
73#63509—31no—
74#63502—31no—
75#63446—31no—
76#63446—31no—
77#63446—31no—
78#63446—31no—
79#63446—61no—
80#63444—31no—
81#63444—31no—
82#63444—31no—
83#63444D311yescharacteristic, complemented
84#63436—31no—
85#63434—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×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233—22no—
102#6233—41no—
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C4⋊(C3⋊D9)—41no—
106C4×C3⋊D9—22no—
107C9×#67—22no—
108C3×#611—41no—
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C3×D36—22no—
114C3×D36—41no—
115C9×Dic6—22no—
116#6195—41no—
117#6194—22no—
118#6194—41no—
119#6192—22no—
120#6192—22no—
121#6192—22no—
122#6192—41no—
123#6192—41no—
124Dic3×D9—22no—
125Dic3×D9D414yescomplemented
126#5674—91no—
127#5592—91no—
128C23×C3×D3—31no—
129C22×D32—31no—
130C2×#638—31no—
131C2×#638—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4×C3⋊D3—31no—
134C2×C3×#67—31no—
135C2×C3×#67C2×D311yescharacteristic
136C2×C3×D12—31no—
137C2×C3×D12—31no—
138C2×C3×Dic6C2×D311yescharacteristic
139D3×#67—64no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#625—31no—
147C2×#625—31no—
148C2×D3×Dic3—31no—
149C2×D3×Dic3—31no—
150#3796—64no—
151C23×D9—31no—
152C23×D9C2×D311yescharacteristic
153C32×C22⋊C4C2×D311yescharacteristic
154#3752—31no—
155#3750—31no—
156C3×#217C2×D311yescharacteristic
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4C2×D311yescharacteristic
160C3×(C2×D3)⋊C4C2×D311yescharacteristic
161C3×C4×Dic3C2×D311yescharacteristic
162#3724—31no—
163#3722—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166Dic32—31no—
167C2×Q8×C9—31no—
168C2×D4×C9—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—61no—
175C2×#611—61no—
176C2×#611C2×D311yescharacteristic, complemented
177#3701—64no—
178D4×D9—64no—
179C2×D36—31no—
180C2×D36—31no—
181C2×D36—31no—
182C2×D36—31no—
183C2×D36—31no—
184C2×D36—31no—
185C2×D36—61no—
186C2×D36C2×D311yescharacteristic
187C2×D36C2×D311yescharacteristic, complemented
188C2×C4×D9—31no—
189C2×C4×D9—31no—
190C2×C4×D9—31no—
191C2×C4×D9—61no—
192C9×C22⋊C4—21no—
193C9×C22⋊C4—31no—
194C9×C22⋊C4—31no—
195C9×C22⋊C4—31no—
196C9×C22⋊C4C2×D311yescharacteristic, complemented
197C42×C9—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—61no—
203(C2×D9)⋊C4C2×D311yescharacteristic
204(C2×D9)⋊C4C2×D311yescharacteristic, complemented
205Dic9⋊C4—31no—
206Dic9⋊C4—31no—
207Dic9⋊C4—61no—
208C4×Dic9—31no—
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⋊D9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—21no—
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—
233C3×C4×C9—21no—
234C3×C4×C9—21no—
235C3⋊Dic9—21no—
236C3⋊Dic9C2×D412yes—
237C9×Dic3—21no—
238C9×Dic3—21no—
239C9×Dic3C2×D412yes—
240C3×Dic9—21no—
241C22×#67—91no—
242C2×#239—91no—
243C2×#237—91no—
244C2×D3×D4—91no—
245C3×#124—31no—
246C3×#120—91no—
247#953—91no—
248#947—91no—
249#940—91no—
250#940—91no—
251#940—91no—
252#939—91no—
253#939—91no—
254#937—91no—
255#885—91no—
256#885D911yescharacteristic, complemented
257#884—91no—
258#884—91no—
259#884—91no—
260#884—91no—
261#884—91no—
262#884—91no—
263#884—181no—
264#882—31no—
265#882—91no—
266#882—91no—
267#882—91no—
268#882—91no—
269#877—91no—
270#874—91no—
271#872—91no—
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—31no—
274C22×C3⋊D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—62no—
279C22×C3×D3—121no—
280C22×C3×D3—121no—
281C22×C3×D3C22×D311yescharacteristic
282C2×D32—62no—
283C2×D32—121no—
284C2×D32—121no—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287#638—62no—
288#638—121no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C4⋊(C3⋊D3)—121no—
292C4×C3⋊D3—62no—
293C3×#67—22no—
294C3×#67—121no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299C3×D12—62no—
300C3×D12—121no—
301C3×Dic6—22no—
302#626—62no—
303#626—62no—
304#626—62no—
305#626—121no—
306#626—121no—
307#626—121no—
308#625—62no—
309#625—121no—
310D3×Dic3—34no—
311D3×Dic3—62no—
312C23×C9—21no—
313C23×C9—31no—
314C23×C9C22×D311yescharacteristic
315C22×D9—22no—
316C22×D9—31no—
317C22×D9—31no—
318C22×D9—41no—
319C22×D9—41no—
320C22×D9—61no—
321C22×D9—61no—
322C22×D9—62no—
323C22×D9—121no—
324C22×D9—121no—
325C22×D9C22×D311yescharacteristic
326C22×D9C22×D311yescharacteristic
327C22×D9C22×D311yescharacteristic
328Q8×C9—62no—
329D4×C9—62no—
330C2×C4×C9—21no—
331C2×C4×C9—21no—
332C2×C4×C9—31no—
333C2×C4×C9—31no—
334C2×C4×C9—31no—
335C2×C4×C9C22×D311yescharacteristic
336C2×C4×C9C22×D311yescharacteristic
337#611—41no—
338#611—62no—
339#611—62no—
340#611—122no—
341#611—121no—
342#611—121no—
343#611—121no—
344#611—122no—
345C2×Dic9—31no—
346C2×Dic9—31no—
347C2×Dic9—61no—
348C2×Dic9—61no—
349C2×Dic9C22×D311yescharacteristic
350D36—22no—
351D36—41no—
352D36—62no—
353D36—62no—
354D36—62no—
355D36—121no—
356D36—122no—
357D36—121no—
358D36—121no—
359C4×D9—34no—
360C4×D9—62no—
361C4×D9—62no—
362C4×D9—122no—
363#535—271noSylow
364C2×C3×C9—41no—
365C2×C3×C9C22×D411yescharacteristic
366C2×C3×C9H(5,𝔽2)11yescharacteristic
367C2×C3×C9H(5,𝔽2)11yescharacteristic
368C3⋊D9—41no—
369C3⋊D9—41no—
370D3×C9—41no—
371C3×D9—22no—
372C3×D9—41no—
373C3×D9—41no—
374C24×C3—91no—
375C23×D3—31no—
376C23×D3—91no—
377C23×D3—91no—
378C2×C3×Q8—31no—
379C2×C3×D4—31no—
380C2×C3×D4—91no—
381C2×C3×D4—91no—
382C2×C3×D4—91no—
383C2×#67—31no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
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—91no—
398C2×#67—181no—
399C2×#67—181no—
400C2×#67—184no—
401C2×#67C2×D911yescharacteristic
402C22×Dic3—91no—
403C22×Dic3—91no—
404#239—184no—
405#237—184no—
406D3×D4—184no—
407C2×D12—31no—
408C2×D12—31no—
409C2×D12—91no—
410C2×D12—91no—
411C2×D12—91no—
412C2×D12—91no—
413C2×D12—91no—
414C2×D12—91no—
415C2×D12—91no—
416C2×D12—91no—
417C2×D12—181no—
418C2×C4×D3—91no—
419C2×C4×D3—91no—
420C2×C4×D3—91no—
421C2×C4×D3—91no—
422C2×C4×D3—181no—
423C2×Dic6C2×D911yescharacteristic, complemented
424C3×C22⋊C4—21no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—31no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4C2×D911yescharacteristic, complemented
431C3×C22⋊C4D3211yescharacteristic
432C3×C42—31no—
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—181no—
445(C2×D3)⋊C4C2×D911yescharacteristic, complemented
446(C2×D3)⋊C4C2×D911yescharacteristic, complemented
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—181no—
452C4×Dic3—91no—
453C4×Dic3—91no—
454C4×Dic3C2×D911yescharacteristic, complemented
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32C23×D311yescharacteristic
459C2×C3⋊D3—61no—
460C2×C3⋊D3—61no—
461C2×C3⋊D3—61no—
462C2×C3⋊D3—61no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3×D3—21no—
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—
478D32—124no—
479C32×C4—21no—
480C32×C4—21no—
481C3⋊Dic3—32no—
482C3⋊Dic3—61no—
483C3×Dic3—21no—
484C3×Dic3—21no—
485C3×Dic3—61no—
486C3×Dic3D3×D412yes—
487C22×C9—21no—
488C22×C9—21no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—41no—
492C22×C9—41no—
493C22×C9—41no—
494C22×C9—61no—
495C22×C9—61no—
496C22×C9—61no—
497C22×C9C23×D311yescharacteristic
498C2×D9—21no—
499C2×D9—21no—
500C2×D9—21no—
501C2×D9—21no—
502C2×D9—21no—
503C2×D9—21no—
504C2×D9—21no—
505C2×D9—21no—
506C2×D9—44no—
507C2×D9—62no—
508C2×D9—61no—
509C2×D9—61no—
510C2×D9—61no—
511C2×D9—61no—
512C2×D9—61no—
513C2×D9—61no—
514C2×D9—121no—
515C2×D9—121no—
516C2×D9—121no—
517C2×D9—121no—
518C2×D9—121no—
519C2×D9—124no—
520C2×D9D3×D412yes—
521C4×C9—21no—
522C4×C9—21no—
523C4×C9—32no—
524C4×C9—41no—
525C4×C9—41no—
526C4×C9—61no—
527C4×C9—61no—
528Dic9—21no—
529Dic9—32no—
530Dic9—62no—
531Dic9—61no—
532Dic9—121no—
533C2×#41—271no—
534C22×D4—271no—
535#127—271no—
536#127—271no—
537#124—31no—
538#124—271no—
539#121—271no—
540#121—271no—
541#121—271no—
542#121—271no—
543#120—91no—
544#120—271no—
545#120—271no—
546#120—271no—
547#117—271no—
548C3×C9#53511yescharacteristic, complemented, Sylow
549C23×C3—21no—
550C23×C3—31no—
551C23×C3—91no—
552C23×C3—91no—
553C23×C3—91no—
554C23×C3—182no—
555C23×C3—361no—
556C23×C3—361no—
557C23×C3C22×D911yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—62no—
563C22×D3—91no—
564C22×D3—91no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—181no—
570C22×D3—181no—
571C22×D3—182no—
572C22×D3—182no—
573C22×D3—361no—
574C22×D3—361no—
575C22×D3—361no—
576C22×D3—361no—
577C22×D3C22×D911yescharacteristic
578C3×Q8—62no—
579C3×D4—62no—
580C3×D4—182no—
581C3×D4—361no—
582C3×D4—361no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—91no—
589C2×C3×C4C22×D911yescharacteristic
590C2×C3×C4C22×D911yescharacteristic
591C2×C3×C4C2×D3211yescharacteristic
592C2×C3×C4C2×D3211yescharacteristic
593#67—22no—
594#67—121no—
595#67—182no—
596#67—182no—
597#67—182no—
598#67—182no—
599#67—182no—
600#67—182no—
601#67—182no—
602#67—362no—
603#67—361no—
604#67—361no—
605#67—361no—
606#67—361no—
607#67—361no—
608#67—361no—
609#67—361no—
610#67—362no—
611C2×Dic3—31no—
612C2×Dic3—91no—
613C2×Dic3—91no—
614C2×Dic3—94no—
615C2×Dic3—91no—
616C2×Dic3—91no—
617C2×Dic3—181no—
618C2×Dic3—181no—
619C2×Dic3—182no—
620C2×Dic3C22×D911yescharacteristic
621C2×Dic3C22×D911yescharacteristic
622C2×Dic3C22×D911yescharacteristic
623D12—62no—
624D12—121no—
625D12—182no—
626D12—182no—
627D12—182no—
628D12—361no—
629D12—361no—
630D12—362no—
631D12—361no—
632D12—361no—
633D12—361no—
634C4×D3—94no—
635C4×D3—182no—
636C4×D3—182no—
637C4×D3—182no—
638C4×D3—362no—
639Dic6—22no—
640C2×C32—41no—
641C2×C32C2×D3×D411yescharacteristic
642C2×C32#100911yescharacteristic
643C2×C32#100911yescharacteristic
644C3⋊D3—121no—
645C3⋊D3—121no—
646C3×D3—41no—
647C3×D3—62no—
648C3×D3—121no—
649C3×D3—121no—
650C2×C9—21no—
651C2×C9—21no—
652C2×C9—21no—
653C2×C9—41no—
654C2×C9—81no—
655C2×C9—121no—
656C2×C9C2×D3×D411yescharacteristic
657C2×C9#100411yescharacteristic
658C2×C9#100411yescharacteristic
659D9—22no—
660D9—41no—
661D9—41no—
662D9—122no—
663D9—121no—
664D9—121no—
665D9—241no—
666C24—91no—
667C24—271no—
668#41—544no—
669C2×Q8—31no—
670C2×D4—31no—
671C2×D4—91no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—271no—
675C2×D4—271no—
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—271no—
685C2×D4—544no—
686C22×C4—271no—
687C22×C4—271no—
688C22×C4—271no—
689C4⋊C4—271no—
690C4⋊C4—271no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4D3×D911yescharacteristic, complemented
701C42—31no—
702C42—271no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—92no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—181no—
721C22×C3—181no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—364no—
726C22×C3C23×D911yescharacteristic
727C22×C3C22×D3211yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—32no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—124no—
741C2×D3—182no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
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—361no—
755C2×D3—361no—
756C2×D3—361no—
757C2×D3—361no—
758C2×D3—361no—
759C2×D3—364no—
760C2×D3—364no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—32no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—181no—
771Dic3—21no—
772Dic3—21no—
773Dic3—61no—
774Dic3—92no—
775Dic3—92no—
776Dic3—182no—
777Dic3—181no—
778Dic3—181no—
779Dic3—361no—
780Dic3D4×D912yes—
781C32#567411yescharacteristic
782C9—21no—
783C9#559211yescharacteristic, complemented
784C23—31no—
785C23—91no—
786C23—91no—
787C23—91no—
788C23—182no—
789C23—271no—
790C23—271no—
791C23—361no—
792C23—361no—
793C23—542no—
794C23—1081no—
795C23—1081no—
796C23C2×D3×D911yescharacteristic
797Q8—62no—
798D4—62no—
799D4—182no—
800D4—361no—
801D4—361no—
802D4—542no—
803D4—542no—
804D4—542no—
805D4—542no—
806D4—542no—
807D4—1081no—
808D4—1081no—
809D4—1081no—
810D4—1081no—
811D4—1081no—
812D4—1081no—
813C2×C4—31no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—91no—
817C2×C4—274no—
818C2×C4—271no—
819C2×C4—271no—
820C2×C4—542no—
821C2×C4—542no—
822C2×C4C2×D3×D911yescharacteristic
823C2×C4C2×D3×D911yescharacteristic
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—41no—
828C2×C3—41no—
829C2×C3—81no—
830C2×C3—121no—
831C2×C3—182no—
832C2×C3—361no—
833C2×C3—361no—
834C2×C3C2×D4×D911yescharacteristic
835C2×C3#6371511yescharacteristic
836C2×C3#6371511yescharacteristic
837C2×C3#6430711yescharacteristic
838C2×C3D32×D411yescharacteristic
839C2×C3#6431411yescharacteristic
840D3—41no—
841D3—62no—
842D3—121no—
843D3—121no—
844D3—362no—
845D3—361no—
846D3—361no—
847D3—361no—
848D3—361no—
849D3—721no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—92no—
857C22—181no—
858C22—181no—
859C22—181no—
860C22—181no—
861C22—181no—
862C22—181no—
863C22—181no—
864C22—181no—
865C22—364no—
866C22—541no—
867C22—541no—
868C22—541no—
869C22—541no—
870C22—541no—
871C22—541no—
872C22—1084no—
873C22C22×D3×D911yescharacteristic
874C4—21no—
875C4—21no—
876C4—32no—
877C4—61no—
878C4—61no—
879C4—181no—
880C4—272no—
881C4—541no—
882C3—21no—
883C3#1058977611yescharacteristic, complemented
884C3#1059427011yescharacteristic
885C2—41no—
886C2—121no—
887C2—182no—
888C2—361no—
889C2—361no—
890C2—1081no—
891C2—1081no—
892C2#1172247711yescharacteristic
893C2D3×D4×D911yescharacteristic
894C2#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#535
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×#88634C2semidirect
3. #11721730C2semidirect
4. C9×#885C2semidirect
5. C3×#63444C2semidirect
6. #11721289C2semidirect
7. #11721276C2semidirect
8. #11721271C2semidirect
9. #11721051C2semidirect
10. #11721049C2semidirect
11. #11721041C2semidirect
12. #11721006C2semidirect
13. #11721003C2semidirect
14. #11720982C2semidirect
15. #11720974C2semidirect
21. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
23. C2×C4×C3⋊D9C22semidirect
25. C2×C3×#611C22semidirect
27. C2×C3×D36C22semidirect
28. C2×C9×Dic6C22semidirect
30. C2×#6195C22semidirect
32. C2×#6194C22semidirect
35. C2×#6192C22semidirect
36. C2×#6192C22semidirect
37. C2×#6192C22semidirect
39. C2×Dic3×D9C22semidirect
41. C3×C9×C22⋊C4C22semidirect
42. #88536C22semidirect
43. #88534C22semidirect
44. C9×#217C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C9×(C2×D3)⋊C4C22semidirect
48. C3×(C2×D9)⋊C4C22semidirect
49. C4×C9×Dic3C22semidirect
50. #88445C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
83. #63444D3semidirect
125. Dic3×D9D4semidirect
176. C2×#611C2×D3semidirect
187. C2×D36C2×D3semidirect
196. C9×C22⋊C4C2×D3semidirect
204. (C2×D9)⋊C4C2×D3semidirect
256. #885D9semidirect
423. C2×Dic6C2×D9semidirect
430. C3×C22⋊C4C2×D9semidirect
435. #217C2×D9semidirect
445. (C2×D3)⋊C4C2×D9semidirect
446. (C2×D3)⋊C4C2×D9semidirect
454. C4×Dic3C2×D9semidirect
548. C3×C9#535semidirect
700. C22⋊C4D3×D9semidirect
783. C9#5592semidirect
883. C3#10589776semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×#886342
#117217302
C9×#8852
C3×#634442
#117212892
#117212762
#117212712
#117210512
#117210492
#117210412
#117210062
#117210032
#117209822
#117209742
#105942703
#105897763