Finite Group Databasebeta

← #13147995

Subgroups — #13147995

Order 1728.

1078 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D9×#67C211yesmaximal, characteristic, complemented
2C2×#88641C211yesmaximal, characteristic, complemented
3#11721731C211yesmaximal, characteristic, complemented
4C9×#884C211yesmaximal, characteristic, complemented
5C3×#63444C211yesmaximal, characteristic, complemented
6#11721289C211yesmaximal, characteristic, complemented
7#11721285C211yesmaximal, characteristic, complemented
8#11721270C211yesmaximal, characteristic, complemented
9#11721050C211yesmaximal, characteristic, complemented
10#11721049C211yesmaximal, characteristic, complemented
11#11721043C211yesmaximal, characteristic, complemented
12#11721042C211yesmaximal, characteristic, complemented
13#11721034C211yesmaximal, characteristic, complemented
14#11720983C211yesmaximal, characteristic, complemented
15#11720975C211yesmaximal, characteristic, complemented
16#10594269—31nomaximal
17#10589709—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6226C2211yescharacteristic, complemented
22C2×C9×#67C2211yescharacteristic
23C2×C9×#67C2211yescharacteristic, complemented
24C2×C3×#611C2211yescharacteristic, complemented
25C2×C9×D12C2211yescharacteristic, complemented
26C2×C4×D3×C9C2211yescharacteristic, complemented
27C2×C3×D36C2211yescharacteristic
28C2×C3×D36C2211yescharacteristic, complemented
29D9×#67—24no—
30C2×#6195C2211yescharacteristic, complemented
31C2×#6194C2211yescharacteristic
32C2×#6194C2211yescharacteristic
33C2×#6194C2211yescharacteristic, complemented
34C2×#6194C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic
37C2×#6192C2211yescharacteristic, complemented
38C2×Dic3×D9C2211yescharacteristic
39C2×Dic3×D9C2211yescharacteristic, complemented
40#88641—24no—
41C3×C9×C22⋊C4C2211yescharacteristic, complemented
42#88551C2211yescharacteristic, complemented
43#88536C2211yescharacteristic, complemented
44#88536C2211yescharacteristic, complemented
45C4×C3⋊Dic9C2211yescharacteristic, complemented
46C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic
48C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
49C9×Dic3⋊C4C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3795—31no—
57#64094—31no—
58C3×#884D311yescharacteristic
59C3×#882—31no—
60#63979—31no—
61#63976—31no—
62#63970—31no—
63#63922—31no—
64#63922—31no—
65#63914—31no—
66#63913—31no—
67#63906—31no—
68#63886—31no—
69#63878—31no—
70C2×D4×D9—31no—
71C2×#3697—31no—
72C9×#121—31no—
73#63502—31no—
74#63502—31no—
75#63500—31no—
76#63499—31no—
77#63499—31no—
78#63492—31no—
79#63457—31no—
80#63454—31no—
81#63447—31no—
82#63447—31no—
83#63447—61no—
84#63444—31no—
85#63444D311yescharacteristic, complemented
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
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—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105#6226—22no—
106C9×#67—22no—
107C9×#67—41no—
108C3×#611—41no—
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C9×D12—41no—
113C4×D3×C9—22no—
114C3×D36—22no—
115C3×D36—41no—
116#6195—41no—
117#6194—22no—
118#6194—22no—
119#6194—22no—
120#6194—41no—
121#6194—41no—
122#6192—22no—
123#6192—41no—
124Dic3×D9—22no—
125Dic3×D9D414yescomplemented
126#5607—91no—
127#5592—91no—
128C23×C3×D3—31no—
129C22×D32—31no—
130C2×#638—31no—
131C2×#634—31no—
132C2×C3×#67—31no—
133C2×C3×#67C2×D311yescharacteristic
134C2×C3×#67C2×D311yescharacteristic
135C2×C3×D12—31no—
136C2×C3×D12—31no—
137C2×C3×D12C2×D311yescharacteristic
138C2×C3×C4×D3C2×D311yescharacteristic
139D3×#67—64no—
140C2×#626—31no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#625—31no—
144C2×#625—31no—
145C2×#625—31no—
146C2×#625—31no—
147C2×#625—31no—
148C2×D3×Dic3—31no—
149C2×D3×Dic3—31no—
150#3795—64no—
151C23×D9—31no—
152C23×D9C2×D311yescharacteristic
153C32×C22⋊C4C2×D311yescharacteristic
154#3757—31no—
155#3752—31no—
156#3752—31no—
157C4×C3⋊Dic3—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4C2×D311yescharacteristic
161C3×Dic3⋊C4C2×D311yescharacteristic
162Dic3⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166Dic32—31no—
167C2×D4×C9—31no—
168C2×D4×C9—31no—
169C2×D4×C9—31no—
170C22×C4×C9—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—31no—
178C2×#611—61no—
179C2×#611C2×D311yescharacteristic, complemented
180D4×D9—64no—
181#3697—64no—
182C2×D36—31no—
183C2×D36—31no—
184C2×D36C2×D311yescharacteristic
185C2×D36C2×D311yescharacteristic, complemented
186C2×C4×D9—31no—
187C2×C4×D9—31no—
188C2×Dic18—31no—
189C2×Dic18—61no—
190C9×C4⋊C4—31no—
191C9×C22⋊C4—21no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4C2×D311yescharacteristic, complemented
194#3676—31no—
195#3676—31no—
196#3676—61no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—61no—
202(C2×D9)⋊C4—61no—
203(C2×D9)⋊C4C2×D311yescharacteristic
204(C2×D9)⋊C4C2×D311yescharacteristic, complemented
205C4⋊Dic9—31no—
206C4×Dic9—31no—
207C4×Dic9—31no—
208C4×Dic9—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×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—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⋊Dic9—21no—
237C3⋊Dic9C2×D412yes—
238C9×Dic3—21no—
239C9×Dic3C2×D412yes—
240C3×Dic9—21no—
241C22×#67—91no—
242C2×#237—91no—
243C2×D3×D4—91no—
244C2×#235—91no—
245C3×#121—31no—
246C3×#120—91no—
247#953—91no—
248#940—91no—
249#940—91no—
250#940—91no—
251#940—91no—
252#939—91no—
253#939—91no—
254#938—91no—
255#937—91no—
256#937—91no—
257#937—91no—
258#930—91no—
259#895—91no—
260#892—91no—
261#885—91no—
262#885—91no—
263#885—91no—
264#885—91no—
265#885—181no—
266#884—91no—
267#884D911yescharacteristic, complemented
268#882—31no—
269#882—91no—
270#882—91no—
271#877—91no—
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—31no—
277C22×C3×D3—62no—
278C22×C3×D3—121no—
279C22×C3×D3—121no—
280C22×C3×D3C22×D311yescharacteristic
281C22×C3×D3C22×D311yescharacteristic
282C2×D32—62no—
283C2×D32—121no—
284C2×D32—121no—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287#638—62no—
288C2×C3⋊Dic3—31no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291#634—62no—
292C3×#67—22no—
293C3×#67—41no—
294C3×#67—121no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C3×D12—41no—
299C3×D12—62no—
300C3×D12—121no—
301C3×C4×D3—22no—
302#626—62no—
303#626—121no—
304#626—121no—
305#625—62no—
306#625—62no—
307#625—62no—
308#625—121no—
309#625—121no—
310D3×Dic3—34no—
311D3×Dic3—62no—
312C23×C9—21no—
313C23×C9—31no—
314C23×C9—31no—
315C23×C9C22×D311yescharacteristic
316C22×D9—22no—
317C22×D9—31no—
318C22×D9—41no—
319C22×D9—41no—
320C22×D9—61no—
321C22×D9—62no—
322C22×D9—121no—
323C22×D9—121no—
324C22×D9C22×D311yescharacteristic
325C22×D9C22×D311yescharacteristic
326C22×D9C22×D311yescharacteristic
327D4×C9—62no—
328D4×C9—121no—
329D4×C9—121no—
330C2×C4×C9—21no—
331C2×C4×C9—21no—
332C2×C4×C9—31no—
333C2×C4×C9—31no—
334C2×C4×C9—62no—
335C2×C4×C9C22×D311yescharacteristic
336C2×C4×C9C22×D311yescharacteristic
337#611—41no—
338#611—62no—
339#611—62no—
340#611—62no—
341#611—62no—
342#611—122no—
343#611—121no—
344#611—121no—
345#611—121no—
346C2×Dic9—31no—
347C2×Dic9—31no—
348C2×Dic9—31no—
349C2×Dic9—61no—
350C2×Dic9—61no—
351C2×Dic9—61no—
352C2×Dic9C22×D311yescharacteristic
353D36—22no—
354D36—41no—
355D36—62no—
356D36—121no—
357C4×D9—34no—
358C4×D9—62no—
359Dic18—62no—
360Dic18—122no—
361#535—271noSylow
362C2×C3×C9—41no—
363C2×C3×C9C22×D411yescharacteristic
364C2×C3×C9H(5,𝔽2)11yescharacteristic
365C2×C3×C9H(5,𝔽2)11yescharacteristic
366C3⋊D9—41no—
367D3×C9—41no—
368D3×C9—41no—
369C3×D9—22no—
370C3×D9—41no—
371C3×D9—41no—
372C24×C3—91no—
373C23×D3—31no—
374C23×D3—91no—
375C23×D3—91no—
376C2×C3×D4—31no—
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—91no—
380C2×C3×D4—91no—
381C2×C3×D4—91no—
382C22×C3×C4—31no—
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—91no—
399C2×#67—181no—
400C2×#67—184no—
401C2×#67C2×D911yescharacteristic
402C2×#67C2×D911yescharacteristic, complemented
403C22×Dic3—91no—
404C22×Dic3—91no—
405#237—184no—
406D3×D4—184no—
407#235—184no—
408C2×D12—31no—
409C2×D12—31no—
410C2×D12—91no—
411C2×D12—91no—
412C2×D12—91no—
413C2×D12C2×D911yescharacteristic, complemented
414C2×C4×D3—91no—
415C2×C4×D3—91no—
416C2×C4×D3C2×D911yescharacteristic, complemented
417C2×Dic6—91no—
418C2×Dic6—91no—
419C2×Dic6—181no—
420C3×C4⋊C4—31no—
421C3×C22⋊C4—21no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—91no—
424C3×C22⋊C4—91no—
425C3×C22⋊C4C2×D911yescharacteristic, complemented
426C3×C22⋊C4D3211yescharacteristic
427#217—91no—
428#217—91no—
429#217—91no—
430#217—91no—
431#217—91no—
432#217—181no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—181no—
443(C2×D3)⋊C4—181no—
444(C2×D3)⋊C4C2×D911yescharacteristic, complemented
445C4⋊Dic3—91no—
446Dic3⋊C4—91no—
447Dic3⋊C4C2×D911yescharacteristic, complemented
448C4×Dic3—91no—
449C4×Dic3—91no—
450C4×Dic3—91no—
451C4×Dic3—91no—
452C4×Dic3—181no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32C23×D311yescharacteristic
457C2×C3⋊D3—61no—
458C2×C3⋊D3—61no—
459C2×C3⋊D3—61no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—32no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
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—124no—
476D32—124no—
477C32×C4—21no—
478C32×C4—21no—
479C3⋊Dic3—32no—
480C3⋊Dic3—61no—
481C3⋊Dic3—61no—
482C3×Dic3—21no—
483C3×Dic3—61no—
484C3×Dic3D3×D412yes—
485C22×C9—21no—
486C22×C9—21no—
487C22×C9—21no—
488C22×C9—21no—
489C22×C9—41no—
490C22×C9—41no—
491C22×C9—41no—
492C22×C9—61no—
493C22×C9—61no—
494C22×C9—61no—
495C22×C9—61no—
496C22×C9—61no—
497C22×C9—61no—
498C22×C9C23×D311yescharacteristic
499C2×D9—21no—
500C2×D9—21no—
501C2×D9—21no—
502C2×D9—21no—
503C2×D9—21no—
504C2×D9—21no—
505C2×D9—21no—
506C2×D9—21no—
507C2×D9—44no—
508C2×D9—61no—
509C2×D9—61no—
510C2×D9—61no—
511C2×D9—121no—
512C2×D9—121no—
513C2×D9—121no—
514C2×D9—124no—
515C2×D9D3×D412yes—
516C4×C9—21no—
517C4×C9—21no—
518C4×C9—32no—
519C4×C9—41no—
520C4×C9—41no—
521C4×C9—61no—
522Dic9—21no—
523Dic9—32no—
524Dic9—62no—
525Dic9—61no—
526Dic9—61no—
527Dic9—121no—
528Dic9—121no—
529C2×#41—271no—
530C22×D4—271no—
531#127—271no—
532#127—271no—
533#124—271no—
534#124—271no—
535#121—31no—
536#121—271no—
537#121—271no—
538#121—271no—
539#120—91no—
540#120—271no—
541#120—271no—
542#120—271no—
543#117—271no—
544C3×C9#53511yescharacteristic, complemented, Sylow
545C23×C3—21no—
546C23×C3—31no—
547C23×C3—31no—
548C23×C3—91no—
549C23×C3—91no—
550C23×C3—91no—
551C23×C3—182no—
552C23×C3—361no—
553C23×C3—361no—
554C23×C3C22×D911yescharacteristic
555C23×C3C2×D3211yescharacteristic
556C22×D3—31no—
557C22×D3—31no—
558C22×D3—31no—
559C22×D3—62no—
560C22×D3—91no—
561C22×D3—91no—
562C22×D3—121no—
563C22×D3—121no—
564C22×D3—181no—
565C22×D3—182no—
566C22×D3—182no—
567C22×D3—361no—
568C22×D3—361no—
569C22×D3—361no—
570C22×D3—361no—
571C22×D3C22×D911yescharacteristic
572C22×D3C22×D911yescharacteristic
573C3×D4—62no—
574C3×D4—121no—
575C3×D4—121no—
576C3×D4—182no—
577C3×D4—361no—
578C3×D4—361no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—62no—
584C2×C3×C4—91no—
585C2×C3×C4C22×D911yescharacteristic
586C2×C3×C4C22×D911yescharacteristic
587C2×C3×C4C2×D3211yescharacteristic
588C2×C3×C4C2×D3211yescharacteristic
589#67—22no—
590#67—41no—
591#67—121no—
592#67—182no—
593#67—182no—
594#67—182no—
595#67—182no—
596#67—182no—
597#67—182no—
598#67—182no—
599#67—182no—
600#67—182no—
601#67—362no—
602#67—361no—
603#67—361no—
604#67—361no—
605#67—361no—
606#67—361no—
607#67—361no—
608C2×Dic3—31no—
609C2×Dic3—91no—
610C2×Dic3—91no—
611C2×Dic3—94no—
612C2×Dic3—91no—
613C2×Dic3—91no—
614C2×Dic3—91no—
615C2×Dic3—91no—
616C2×Dic3—181no—
617C2×Dic3—181no—
618C2×Dic3—181no—
619C2×Dic3—182no—
620C2×Dic3C22×D911yescharacteristic
621C2×Dic3C22×D911yescharacteristic
622D12—41no—
623D12—62no—
624D12—121no—
625D12—182no—
626D12—361no—
627D12—361no—
628C4×D3—22no—
629C4×D3—94no—
630C4×D3—182no—
631Dic6—182no—
632Dic6—182no—
633Dic6—362no—
634C2×C32—41no—
635C2×C32C2×D3×D411yescharacteristic
636C2×C32#100411yescharacteristic
637C2×C32#100911yescharacteristic
638C3⋊D3—121no—
639C3×D3—41no—
640C3×D3—41no—
641C3×D3—62no—
642C3×D3—121no—
643C3×D3—121no—
644C2×C9—21no—
645C2×C9—21no—
646C2×C9—21no—
647C2×C9—41no—
648C2×C9—81no—
649C2×C9—121no—
650C2×C9—121no—
651C2×C9C2×D3×D411yescharacteristic
652C2×C9#100411yescharacteristic
653C2×C9#100411yescharacteristic
654D9—22no—
655D9—41no—
656D9—41no—
657D9—121no—
658D9—241no—
659C24—91no—
660C24—271no—
661#41—544no—
662C2×Q8—271no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—31no—
666C2×D4—91no—
667C2×D4—91no—
668C2×D4—91no—
669C2×D4—271no—
670C2×D4—271no—
671C2×D4—271no—
672C2×D4—271no—
673C2×D4—271no—
674C2×D4—271no—
675C2×D4—271no—
676C2×D4—271no—
677C2×D4—271no—
678C2×D4—544no—
679C22×C4—31no—
680C22×C4—271no—
681C22×C4—271no—
682C4⋊C4—31no—
683C4⋊C4—271no—
684C22⋊C4—31no—
685C22⋊C4—91no—
686C22⋊C4—91no—
687C22⋊C4—271no—
688C22⋊C4—271no—
689C22⋊C4—271no—
690C22⋊C4—271no—
691C22⋊C4—271no—
692C22⋊C4—271no—
693C22⋊C4D3×D911yescharacteristic, complemented
694C42—271no—
695C42—271no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—92no—
713C22×C3—181no—
714C22×C3—181no—
715C22×C3—181no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—181no—
721C22×C3—364no—
722C22×C3C23×D911yescharacteristic
723C22×C3C22×D3211yescharacteristic
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—32no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—61no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—124no—
740C2×D3—181no—
741C2×D3—181no—
742C2×D3—181no—
743C2×D3—181no—
744C2×D3—181no—
745C2×D3—181no—
746C2×D3—361no—
747C2×D3—361no—
748C2×D3—361no—
749C2×D3—364no—
750C2×D3—364no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—32no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—181no—
760Dic3—21no—
761Dic3—61no—
762Dic3—92no—
763Dic3—92no—
764Dic3—182no—
765Dic3—181no—
766Dic3—181no—
767Dic3—181no—
768Dic3—181no—
769Dic3—361no—
770Dic3—361no—
771Dic3D4×D912yes—
772C32#560711yescharacteristic
773C9—21no—
774C9#559211yescharacteristic, complemented
775C23—31no—
776C23—31no—
777C23—91no—
778C23—91no—
779C23—91no—
780C23—182no—
781C23—271no—
782C23—361no—
783C23—361no—
784C23—542no—
785C23—1081no—
786C23—1081no—
787C23C2×D3×D911yescharacteristic
788Q8—542no—
789D4—62no—
790D4—121no—
791D4—121no—
792D4—182no—
793D4—361no—
794D4—361no—
795D4—542no—
796D4—542no—
797D4—542no—
798D4—542no—
799D4—542no—
800D4—1081no—
801D4—1081no—
802D4—1081no—
803D4—1081no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—62no—
807C2×C4—91no—
808C2×C4—274no—
809C2×C4—271no—
810C2×C4—271no—
811C2×C4—271no—
812C2×C4—542no—
813C2×C4C2×D3×D911yescharacteristic
814C2×C4C2×D3×D911yescharacteristic
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—41no—
819C2×C3—41no—
820C2×C3—81no—
821C2×C3—121no—
822C2×C3—121no—
823C2×C3—182no—
824C2×C3—361no—
825C2×C3—361no—
826C2×C3C2×D4×D911yescharacteristic
827C2×C3#6371011yescharacteristic
828C2×C3#6371511yescharacteristic
829C2×C3#6430711yescharacteristic
830C2×C3D32×D411yescharacteristic
831C2×C3#6431311yescharacteristic
832D3—41no—
833D3—41no—
834D3—62no—
835D3—121no—
836D3—121no—
837D3—361no—
838D3—361no—
839D3—721no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—61no—
847C22—61no—
848C22—61no—
849C22—92no—
850C22—181no—
851C22—181no—
852C22—181no—
853C22—181no—
854C22—181no—
855C22—181no—
856C22—181no—
857C22—181no—
858C22—364no—
859C22—541no—
860C22—541no—
861C22—541no—
862C22—1084no—
863C22C22×D3×D911yescharacteristic
864C4—21no—
865C4—21no—
866C4—32no—
867C4—61no—
868C4—181no—
869C4—272no—
870C4—541no—
871C4—541no—
872C3—21no—
873C3#1058970911yescharacteristic, complemented
874C3#1059426911yescharacteristic
875C2—41no—
876C2—121no—
877C2—121no—
878C2—182no—
879C2—361no—
880C2—361no—
881C2—1081no—
882C2#1172247711yescharacteristic
883C2D3×D4×D911yescharacteristic
884C2#1172249911yescharacteristic
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×#88641C2semidirect
3. #11721731C2semidirect
4. C9×#884C2semidirect
5. C3×#63444C2semidirect
6. #11721289C2semidirect
7. #11721285C2semidirect
8. #11721270C2semidirect
9. #11721050C2semidirect
10. #11721049C2semidirect
11. #11721043C2semidirect
12. #11721042C2semidirect
13. #11721034C2semidirect
14. #11720983C2semidirect
15. #11720975C2semidirect
21. C2×#6226C22semidirect
23. C2×C9×#67C22semidirect
24. C2×C3×#611C22semidirect
25. C2×C9×D12C22semidirect
26. C2×C4×D3×C9C22semidirect
28. C2×C3×D36C22semidirect
30. C2×#6195C22semidirect
33. C2×#6194C22semidirect
34. C2×#6194C22semidirect
35. C2×#6194C22semidirect
37. C2×#6192C22semidirect
39. C2×Dic3×D9C22semidirect
41. C3×C9×C22⋊C4C22semidirect
42. #88551C22semidirect
43. #88536C22semidirect
44. #88536C22semidirect
45. C4×C3⋊Dic9C22semidirect
46. C9×(C2×D3)⋊C4C22semidirect
48. C3×(C2×D9)⋊C4C22semidirect
49. C9×Dic3⋊C4C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic3×Dic9C22semidirect
85. #63444D3semidirect
125. Dic3×D9D4semidirect
179. C2×#611C2×D3semidirect
185. C2×D36C2×D3semidirect
193. C9×C22⋊C4C2×D3semidirect
204. (C2×D9)⋊C4C2×D3semidirect
267. #884D9semidirect
402. C2×#67C2×D9semidirect
413. C2×D12C2×D9semidirect
416. C2×C4×D3C2×D9semidirect
425. C3×C22⋊C4C2×D9semidirect
444. (C2×D3)⋊C4C2×D9semidirect
447. Dic3⋊C4C2×D9semidirect
544. C3×C9#535semidirect
693. C22⋊C4D3×D9semidirect
774. C9#5592semidirect
873. C3#10589709semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C2×#886412
#117217312
C9×#8842
C3×#634442
#117212892
#117212852
#117212702
#117210502
#117210492
#117210432
#117210422
#117210342
#117209832
#117209752
#105942693
#105897093