Finite Group Databasebeta

← #13150975

Subgroups — #13150975

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3#11721837C211yesmaximal, characteristic, complemented
4C9×#939C211yesmaximal, characteristic, complemented
5C3×#63502C211yesmaximal, characteristic, complemented
6#11721292C211yesmaximal, characteristic, complemented
7#11721289C211yesmaximal, characteristic, complemented
8#11721278C211yesmaximal, characteristic, complemented
9#11721277C211yesmaximal, characteristic, complemented
10#11721270C211yesmaximal, characteristic, complemented
11#11721257C211yesmaximal, characteristic, complemented
12#11721049C211yesmaximal, characteristic, complemented
13#11720983C211yesmaximal, characteristic, complemented
14#11720956C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10595299—31nomaximal
17#10589709—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
27C2×C3×#611C2211yescharacteristic, complemented
28C2×C3×#611C2211yescharacteristic, complemented
29C22×C9×Dic3C2211yescharacteristic, complemented
30C2×C3×D36C2211yescharacteristic, complemented
31#88668—24no—
32C2×#6195C2211yescharacteristic
33C2×#6194C2211yescharacteristic, complemented
34C2×#6192C2211yescharacteristic
35C2×#6192C2211yescharacteristic
36C2×#6192C2211yescharacteristic, complemented
37C2×(C3⋊D9)⋊C4C2211yescharacteristic
38#88658—24no—
39C2×Dic3×D9C2211yescharacteristic, complemented
40C2×#6189C2211yescharacteristic, complemented
41#88551C2211yescharacteristic, complemented
42#88536C2211yescharacteristic
43#88536C2211yescharacteristic, complemented
44C9×#217C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47C3×C4×Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×#3804—31no—
57#64146—31no—
58C3×#940—31no—
59C3×#939D311yescharacteristic
60#63983—31no—
61#63981—31no—
62#63979—31no—
63#63978—31no—
64#63970—31no—
65#63959—31no—
66#63922—31no—
67#63886—31no—
68#63852—31no—
69#63836—31no—
70C2×D4×D9—31no—
71C2×#3697—31no—
72C9×#121—31no—
73#63502—31no—
74#63502D311yescharacteristic, complemented
75#63500—31no—
76#63499—31no—
77#63499—31no—
78#63499—61no—
79#63492—31no—
80#63457—31no—
81#63454—31no—
82#63447—31no—
83#63447—31no—
84#63444—31no—
85#63444—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9—22no—
89C22×C3⋊D9—41no—
90C22×C3⋊D9—41no—
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C22×C3×D9C2311yescharacteristic
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×D3×D9—41no—
99C3×D4×C9—41no—
100C2×C3×C4×C9C2311yescharacteristic
101#6233—22no—
102#6233—41no—
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C9×#67—22no—
106C9×#67—41no—
107C3×#611—22no—
108C3×#611—22no—
109C3×#611—41no—
110C3×#611—41no—
111C2×C9×Dic3—22no—
112C2×C9×Dic3C2311yescharacteristic
113C2×C9×Dic3C2311yescharacteristic
114C2×C9×Dic3C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C3×D36—41no—
118#6195—22no—
119#6194—41no—
120#6192—22no—
121#6192—22no—
122#6192—41no—
123(C3⋊D9)⋊C4D414yescomplemented
124Dic3×D9—22no—
125#6189—22no—
126#5715—91no—
127#5607—91no—
128C23×C3⋊D3—31no—
129C22×D32—31no—
130C2×C32×D4C2×D311yescharacteristic
131C2×#638—31no—
132C2×#638—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×#67C2×D311yescharacteristic
139C22×C3×Dic3C2×D311yescharacteristic
140C2×C3×D12—31no—
141#3811—64no—
142C2×#627—31no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#625—31no—
148C2×#624—31no—
149#3804—64no—
150C2×D3×Dic3—31no—
151C23×D9—31no—
152C23×D9—31no—
153C23×D9—61no—
154#3757—31no—
155#3752—31no—
156#3752—31no—
157C3×#217C2×D311yescharacteristic
158C3×(C2×D3)⋊C4C2×D311yescharacteristic
159C3×Dic3⋊C4C2×D311yescharacteristic
160C3×C4×Dic3—31no—
161Dic3⋊Dic3—31no—
162#3722—31no—
163#3722—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166(C2×D3)⋊Dic3—31no—
167Dic32—31no—
168C2×D4×C9—21no—
169C2×D4×C9—31no—
170C2×D4×C9—31no—
171C2×D4×C9C2×D311yescharacteristic, complemented
172C22×C4×C9—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—61no—
178C2×#611—61no—
179C2×#611C2×D311yescharacteristic
180C2×#611C2×D311yescharacteristic, complemented
181C2×#611C2×D311yescharacteristic, complemented
182C2×#611C2×D311yescharacteristic, complemented
183D4×D9—64no—
184#3697—64no—
185C2×D36—31no—
186C2×D36—31no—
187C2×D36—31no—
188C2×D36C2×D311yescharacteristic, complemented
189C2×C4×D9—31no—
190C2×C4×D9—31no—
191C2×Dic18—31no—
192C9×C4⋊C4—31no—
193C9×C22⋊C4—31no—
194C9×C22⋊C4—31no—
195#3676—31no—
196#3676—31no—
197#3676—61no—
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—31no—
204(C2×D9)⋊C4—61no—
205(C2×D9)⋊C4—61no—
206C4⋊Dic9—31no—
207C4×Dic9—31no—
208C4×Dic9C2×D311yescharacteristic, complemented
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9—21no—
214C22×C3×C9—21no—
215C22×C3×C9C2411yescharacteristic
216C2×C3⋊D9—21no—
217C2×C3⋊D9—21no—
218C2×C3⋊D9—21no—
219C2×C3⋊D9—21no—
220C2×C3⋊D9—21no—
221C2×C3⋊D9—44no—
222C2×C3⋊D9C2×D412yes—
223C2×D3×C9—21no—
224C2×D3×C9—21no—
225C2×D3×C9—21no—
226C2×C3×D9—21no—
227C2×C3×D9—21no—
228C2×C3×D9—21no—
229C2×C3×D9—21no—
230C2×C3×D9—21no—
231C2×C3×D9—21no—
232D3×D9—44no—
233C3×C4×C9—21no—
234C3⋊Dic9—21no—
235C3⋊Dic9—21no—
236C9×Dic3—21no—
237C9×Dic3—21no—
238C9×Dic3C2×D412yes—
239C3×Dic9—21no—
240C3×Dic9C2×D412yes—
241C2×#237—91no—
242C2×D3×D4—91no—
243C2×D3×D4—91no—
244C2×#235—91no—
245C3×#127—91no—
246C3×#121—31no—
247#940—31no—
248#940—91no—
249#940—91no—
250#939—91no—
251#939—91no—
252#939—91no—
253#939D911yescharacteristic, complemented
254#938—91no—
255#937—91no—
256#937—91no—
257#937—91no—
258#937—91no—
259#937—91no—
260#937—91no—
261#937—181no—
262#936—91no—
263#930—91no—
264#895—91no—
265#892—91no—
266#885—91no—
267#885—91no—
268#882—91no—
269#882—91no—
270#875—91no—
271#872—91no—
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—62no—
277C22×C3⋊D3—121no—
278C22×C3⋊D3—121no—
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3C22×D311yescharacteristic
282C2×D32—62no—
283C2×D32—121no—
284C2×D32—121no—
285C32×D4—41no—
286C2×C32×C4C22×D311yescharacteristic
287#638—62no—
288#638—121no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C3×#67—22no—
292C3×#67—41no—
293C3×#67—62no—
294C3×#67—62no—
295C3×#67—121no—
296C3×#67—121no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3C22×D311yescharacteristic
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C22×D311yescharacteristic
303C3×D12—121no—
304#627—62no—
305#626—62no—
306#626—62no—
307#626—62no—
308#626—121no—
309#625—121no—
310#624—34no—
311D3×Dic3—62no—
312C23×C9—21no—
313C23×C9—21no—
314C23×C9—31no—
315C23×C9C22×D311yescharacteristic
316C23×C9C22×D311yescharacteristic
317C22×D9—31no—
318C22×D9—31no—
319C22×D9—61no—
320C22×D9—61no—
321C22×D9—62no—
322C22×D9—62no—
323C22×D9—122no—
324C22×D9—121no—
325C22×D9—121no—
326C22×D9—121no—
327C22×D9—121no—
328C22×D9—122no—
329C22×D9—122no—
330C22×D9C22×D311yescharacteristic
331C22×D9C22×D311yescharacteristic
332D4×C9—41no—
333D4×C9—42no—
334D4×C9—62no—
335D4×C9—121no—
336C2×C4×C9—21no—
337C2×C4×C9—31no—
338C2×C4×C9—31no—
339C2×C4×C9—31no—
340C2×C4×C9—62no—
341C2×C4×C9C22×D311yescharacteristic
342#611—22no—
343#611—22no—
344#611—41no—
345#611—41no—
346#611—62no—
347#611—62no—
348#611—122no—
349#611—121no—
350#611—121no—
351#611—122no—
352C2×Dic9—31no—
353C2×Dic9—31no—
354C2×Dic9—61no—
355C2×Dic9—61no—
356C2×Dic9C22×D311yescharacteristic
357C2×Dic9C22×D311yescharacteristic
358D36—41no—
359D36—62no—
360D36—62no—
361D36—121no—
362C4×D9—34no—
363C4×D9—62no—
364Dic18—62no—
365#535—271noSylow
366C2×C3×C9—41no—
367C2×C3×C9—41no—
368C2×C3×C9C22×D411yescharacteristic
369C2×C3×C9H(5,𝔽2)11yescharacteristic
370C2×C3×C9H(5,𝔽2)11yescharacteristic
371C3⋊D9—22no—
372C3⋊D9—41no—
373D3×C9—41no—
374C3×D9—41no—
375C3×D9—41no—
376C23×D3—91no—
377C23×D3—91no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—181no—
381C2×C3×D4—21no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C2×C3×D4—91no—
389C2×C3×D4C2×D911yescharacteristic, complemented
390C2×C3×D4D3211yescharacteristic
391C22×C3×C4—31no—
392C2×#67—31no—
393C2×#67—31no—
394C2×#67—31no—
395C2×#67—31no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—91no—
400C2×#67—91no—
401C2×#67—91no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—91no—
405C2×#67—91no—
406C2×#67—181no—
407C2×#67—181no—
408C2×#67C2×D911yescharacteristic
409C2×#67C2×D911yescharacteristic, complemented
410C22×Dic3—91no—
411C22×Dic3C2×D911yescharacteristic, complemented
412#237—184no—
413D3×D4—184no—
414D3×D4—184no—
415#235—184no—
416C2×D12—31no—
417C2×D12—91no—
418C2×D12—91no—
419C2×D12—91no—
420C2×D12—91no—
421C2×C4×D3—91no—
422C2×C4×D3—91no—
423C2×C4×D3—91no—
424C2×Dic6—91no—
425C2×Dic6—91no—
426C3×C4⋊C4—31no—
427C3×C22⋊C4—31no—
428C3×C22⋊C4—31no—
429C3×C42—91no—
430#217—91no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—91no—
435#217—181no—
436#217C2×D911yescharacteristic, complemented
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—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—91no—
448(C2×D3)⋊C4—181no—
449(C2×D3)⋊C4—181no—
450(C2×D3)⋊C4C2×D911yescharacteristic, complemented
451C4⋊Dic3—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4C2×D911yescharacteristic, complemented
454C4×Dic3—31no—
455C4×Dic3—91no—
456C4×Dic3—91no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32C23×D311yescharacteristic
464C2×C3⋊D3—32no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—61no—
470C2×C3⋊D3—124no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480D32—124no—
481C32×C4—21no—
482C3⋊Dic3—61no—
483C3⋊Dic3—61no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—32no—
487C3×Dic3—61no—
488C3×Dic3D3×D412yes—
489C22×C9—22no—
490C22×C9—21no—
491C22×C9—21no—
492C22×C9—21no—
493C22×C9—21no—
494C22×C9—21no—
495C22×C9—21no—
496C22×C9—21no—
497C22×C9—41no—
498C22×C9—41no—
499C22×C9—41no—
500C22×C9—41no—
501C22×C9—41no—
502C22×C9—61no—
503C22×C9—61no—
504C22×C9—61no—
505C22×C9C23×D311yescharacteristic
506C2×D9—21no—
507C2×D9—21no—
508C2×D9—21no—
509C2×D9—21no—
510C2×D9—21no—
511C2×D9—21no—
512C2×D9—32no—
513C2×D9—62no—
514C2×D9—61no—
515C2×D9—61no—
516C2×D9—62no—
517C2×D9—61no—
518C2×D9—61no—
519C2×D9—61no—
520C2×D9—121no—
521C2×D9—121no—
522C2×D9—121no—
523C2×D9—121no—
524C2×D9—124no—
525C2×D9—124no—
526C2×D9—128no—
527C4×C9—21no—
528C4×C9—32no—
529C4×C9—41no—
530C4×C9—61no—
531C4×C9—61no—
532Dic9—21no—
533Dic9—61no—
534Dic9—61no—
535Dic9—121no—
536Dic9—121no—
537Dic9D3×D412yes—
538C2×#41—271no—
539C22×D4—271no—
540#127—91no—
541#127—271no—
542#124—271no—
543#124—271no—
544#121—31no—
545#121—271no—
546#121—271no—
547#121—271no—
548#120—271no—
549#120—271no—
550#120—271no—
551#120—271no—
552#117—271no—
553C3×C9#53511yescharacteristic, complemented, Sylow
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—31no—
557C23×C3—91no—
558C23×C3—91no—
559C23×C3C22×D911yescharacteristic
560C23×C3C22×D911yescharacteristic
561C23×C3C2×D3211yescharacteristic
562C23×C3C2×D3211yescharacteristic
563C22×D3—31no—
564C22×D3—31no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—91no—
568C22×D3—91no—
569C22×D3—181no—
570C22×D3—181no—
571C22×D3—182no—
572C22×D3—182no—
573C22×D3—182no—
574C22×D3—182no—
575C22×D3—362no—
576C22×D3—361no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—361no—
580C22×D3—361no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3—362no—
585C22×D3—362no—
586C22×D3C22×D911yescharacteristic
587C3×D4—41no—
588C3×D4—41no—
589C3×D4—42no—
590C3×D4—62no—
591C3×D4—121no—
592C3×D4—182no—
593C3×D4—182no—
594C3×D4—361no—
595C3×D4—361no—
596C3×D4—361no—
597C2×C3×C4—21no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—31no—
601C2×C3×C4—62no—
602C2×C3×C4—91no—
603C2×C3×C4—91no—
604C2×C3×C4C22×D911yescharacteristic
605C2×C3×C4C2×D3211yescharacteristic
606#67—22no—
607#67—41no—
608#67—62no—
609#67—62no—
610#67—121no—
611#67—121no—
612#67—182no—
613#67—182no—
614#67—182no—
615#67—182no—
616#67—182no—
617#67—362no—
618#67—361no—
619#67—361no—
620#67—361no—
621#67—361no—
622#67—361no—
623#67—362no—
624C2×Dic3—22no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—91no—
628C2×Dic3—91no—
629C2×Dic3—91no—
630C2×Dic3—91no—
631C2×Dic3—181no—
632C2×Dic3—181no—
633C2×Dic3—182no—
634C2×Dic3C22×D911yescharacteristic
635C2×Dic3C22×D911yescharacteristic
636C2×Dic3C22×D911yescharacteristic
637D12—121no—
638D12—182no—
639D12—182no—
640D12—182no—
641D12—361no—
642C4×D3—94no—
643C4×D3—94no—
644C4×D3—182no—
645Dic6—182no—
646Dic6—182no—
647C2×C32—41no—
648C2×C32—41no—
649C2×C32C2×D3×D411yescharacteristic
650C2×C32#100411yescharacteristic
651C2×C32#100911yescharacteristic
652C3⋊D3—62no—
653C3⋊D3—121no—
654C3×D3—41no—
655C3×D3—121no—
656C3×D3—121no—
657C2×C9—21no—
658C2×C9—21no—
659C2×C9—21no—
660C2×C9—42no—
661C2×C9—41no—
662C2×C9—41no—
663C2×C9—81no—
664C2×C9—121no—
665C2×C9C2×D3×D411yescharacteristic
666C2×C9#100411yescharacteristic
667C2×C9#100411yescharacteristic
668D9—41no—
669D9—41no—
670D9—62no—
671D9—122no—
672D9—122no—
673D9—121no—
674C24—271no—
675C24—271no—
676#41—544no—
677C2×Q8—271no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—91no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—91no—
684C2×D4—91no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—271no—
689C2×D4—271no—
690C2×D4—271no—
691C2×D4—271no—
692C2×D4—544no—
693C2×D4D3×D911yescharacteristic, complemented
694C22×C4—31no—
695C22×C4—271no—
696C22×C4—271no—
697C4⋊C4—31no—
698C4⋊C4—271no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4—271no—
709C42—91no—
710C42—271no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—181no—
734C22×C3—181no—
735C22×C3—181no—
736C22×C3—181no—
737C22×C3—181no—
738C22×C3—181no—
739C22×C3C23×D911yescharacteristic
740C22×C3C22×D3211yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—92no—
751C2×D3—92no—
752C2×D3—182no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—182no—
758C2×D3—181no—
759C2×D3—181no—
760C2×D3—181no—
761C2×D3—181no—
762C2×D3—181no—
763C2×D3—181no—
764C2×D3—361no—
765C2×D3—361no—
766C2×D3—361no—
767C2×D3—361no—
768C2×D3—364no—
769C2×D3—364no—
770C2×D3—364no—
771C2×D3—364no—
772C2×D3—368no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—32no—
776C3×C4—41no—
777C3×C4—61no—
778C3×C4—61no—
779C3×C4—92no—
780C3×C4—181no—
781Dic3—21no—
782Dic3—21no—
783Dic3—32no—
784Dic3—61no—
785Dic3—181no—
786Dic3—181no—
787Dic3—181no—
788Dic3—181no—
789Dic3—361no—
790Dic3—361no—
791Dic3D4×D912yes—
792C32#560711yescharacteristic
793C9—21no—
794C9#571511yescharacteristic, complemented
795C23—31no—
796C23—91no—
797C23—91no—
798C23—271no—
799C23—271no—
800C23—542no—
801C23—542no—
802C23—1081no—
803C23—1081no—
804C23—1081no—
805C23—1081no—
806C23C2×D3×D911yescharacteristic
807C23C2×D3×D911yescharacteristic
808Q8—542no—
809D4—41no—
810D4—62no—
811D4—121no—
812D4—182no—
813D4—182no—
814D4—361no—
815D4—361no—
816D4—361no—
817D4—542no—
818D4—542no—
819D4—542no—
820D4—542no—
821D4—1081no—
822D4—1081no—
823D4—1081no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—31no—
827C2×C4—62no—
828C2×C4—91no—
829C2×C4—91no—
830C2×C4—274no—
831C2×C4—271no—
832C2×C4—271no—
833C2×C4—542no—
834C2×C4C2×D3×D911yescharacteristic
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—42no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—41no—
842C2×C3—41no—
843C2×C3—81no—
844C2×C3—121no—
845C2×C3—361no—
846C2×C3—361no—
847C2×C3C2×D4×D911yescharacteristic
848C2×C3#6371011yescharacteristic
849C2×C3#6371511yescharacteristic
850C2×C3D32×D411yescharacteristic
851C2×C3#6431411yescharacteristic
852C2×C3#6433011yescharacteristic
853D3—41no—
854D3—121no—
855D3—121no—
856D3—182no—
857D3—182no—
858D3—362no—
859D3—362no—
860D3—361no—
861D3—361no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22—181no—
875C22—181no—
876C22—181no—
877C22—272no—
878C22—541no—
879C22—541no—
880C22—541no—
881C22—541no—
882C22—541no—
883C22—1084no—
884C22—1084no—
885C22C22×D3×D911yescharacteristic
886C4—21no—
887C4—32no—
888C4—61no—
889C4—61no—
890C4—92no—
891C4—181no—
892C4—541no—
893C4—541no—
894C3—21no—
895C3#1058970911yescharacteristic, complemented
896C3#1059529911yescharacteristic
897C2—41no—
898C2—41no—
899C2—121no—
900C2—361no—
901C2—361no—
902C2—542no—
903C2—1081no—
904C2D3×D4×D911yescharacteristic
905C2#1172250111yescharacteristic
906C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#535
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×#88668C2semidirect
2. C2×#88658C2semidirect
3. #11721837C2semidirect
4. C9×#939C2semidirect
5. C3×#63502C2semidirect
6. #11721292C2semidirect
7. #11721289C2semidirect
8. #11721278C2semidirect
9. #11721277C2semidirect
10. #11721270C2semidirect
11. #11721257C2semidirect
12. #11721049C2semidirect
13. #11720983C2semidirect
14. #11720956C2semidirect
15. #11720899C2semidirect
20. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
24. C2×C9×#67C22semidirect
26. C2×C3×#611C22semidirect
27. C2×C3×#611C22semidirect
28. C2×C3×#611C22semidirect
29. C22×C9×Dic3C22semidirect
30. C2×C3×D36C22semidirect
33. C2×#6194C22semidirect
36. C2×#6192C22semidirect
39. C2×Dic3×D9C22semidirect
40. C2×#6189C22semidirect
41. #88551C22semidirect
43. #88536C22semidirect
44. C9×#217C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. C3×C4×Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic3⋊Dic9C22semidirect
54. Dic3×Dic9C22semidirect
74. #63502D3semidirect
123. (C3⋊D9)⋊C4D4semidirect
171. C2×D4×C9C2×D3semidirect
180. C2×#611C2×D3semidirect
181. C2×#611C2×D3semidirect
182. C2×#611C2×D3semidirect
188. C2×D36C2×D3semidirect
208. C4×Dic9C2×D3semidirect
253. #939D9semidirect
389. C2×C3×D4C2×D9semidirect
409. C2×#67C2×D9semidirect
411. C22×Dic3C2×D9semidirect
436. #217C2×D9semidirect
450. (C2×D3)⋊C4C2×D9semidirect
453. Dic3⋊C4C2×D9semidirect
553. C3×C9#535semidirect
693. C2×D4D3×D9semidirect
794. C9#5715semidirect
895. C3#10589709semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C2×#886582
#117218372
C9×#9392
C3×#635022
#117212922
#117212892
#117212782
#117212772
#117212702
#117212572
#117210492
#117209832
#117209562
#117208992
#105952993
#105897093