Finite Group Databasebeta

← #13148202

Subgroups — #13148202

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×D3×#611C211yesmaximal, characteristic, complemented
2C2×#88639C211yesmaximal, characteristic, complemented
3#11721730C211yesmaximal, characteristic, complemented
4C9×#882C211yesmaximal, characteristic, complemented
5C3×#63447C211yesmaximal, characteristic, complemented
6#11721289C211yesmaximal, characteristic, complemented
7#11721287C211yesmaximal, characteristic, complemented
8#11721282C211yesmaximal, characteristic, complemented
9#11721051C211yesmaximal, characteristic, complemented
10#11721050C211yesmaximal, characteristic, complemented
11#11721041C211yesmaximal, characteristic, complemented
12#11721040C211yesmaximal, characteristic, complemented
13#11721035C211yesmaximal, characteristic, complemented
14#11721016C211yesmaximal, characteristic, complemented
15#11721010C211yesmaximal, characteristic, complemented
16#10594270—31nomaximal
17#10589694—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
23C2×C4×C3⋊D9C2211yescharacteristic, complemented
24C2×C9×#67C2211yescharacteristic, complemented
25C2×C3×#611C2211yescharacteristic
26C2×C9×D12C2211yescharacteristic
27C2×C9×D12C2211yescharacteristic, complemented
28C2×C3×Dic18C2211yescharacteristic, complemented
29D3×#611—24no—
30C2×#6195C2211yescharacteristic
31C2×#6195C2211yescharacteristic
32C2×#6195C2211yescharacteristic, complemented
33C2×#6195C2211yescharacteristic, complemented
34C2×#6195C2211yescharacteristic, complemented
35C2×#6194C2211yescharacteristic
36C2×#6194C2211yescharacteristic, complemented
37C2×D3×Dic9C2211yescharacteristic
38C2×D3×Dic9C2211yescharacteristic, complemented
39C2×#6192C2211yescharacteristic, complemented
40#88639—24no—
41C3×C9×C22⋊C4C2211yescharacteristic, complemented
42#88536C2211yescharacteristic, complemented
43#88534C2211yescharacteristic, complemented
44C3×#3676C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic
46C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
49C3×C4×Dic9C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3796—31no—
57#64093—31no—
58C3×#885—31no—
59C3×#882D311yescharacteristic
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—
70C22×#611—31no—
71C2×#3699—31no—
72C9×#120—31no—
73#63515—31no—
74#63502—31no—
75#63502—31no—
76#63501—31no—
77#63501—31no—
78#63499—31no—
79#63447—31no—
80#63447D311yescharacteristic, complemented
81#63446—31no—
82#63446—31no—
83#63446—61no—
84#63444—31no—
85#63439—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9—22no—
90C22×D3×C9—41no—
91C22×D3×C9—41no—
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×D3×C9C2311yescharacteristic
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—41no—
108C3×#611—22no—
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C9×D12—22no—
114C9×D12—41no—
115C3×Dic18—22no—
116#6195—22no—
117#6195—22no—
118#6195—22no—
119#6195—41no—
120#6195—41no—
121#6194—22no—
122#6194—41no—
123D3×Dic9—22no—
124D3×Dic9D414yescomplemented
125#6192—41no—
126#5674—91no—
127#5592—91no—
128C23×C3×D3C2×D311yescharacteristic
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×D12C2×D311yescharacteristic
137C2×C3×D12C2×D311yescharacteristic
138C2×C3×Dic6—31no—
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—
151C24×C9—31no—
152C23×D9—31no—
153C32×C22⋊C4C2×D311yescharacteristic
154#3752—31no—
155#3750—31no—
156C3×#217—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4C2×D311yescharacteristic
160C3×(C2×D3)⋊C4C2×D311yescharacteristic
161C3×C4×Dic3—31no—
162#3724—31no—
163#3722—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—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—31no—
178C2×#611—31no—
179C2×#611—64no—
180C2×#611—61no—
181C2×#611—61no—
182C2×#611C2×D311yescharacteristic
183C22×Dic9—31no—
184C22×Dic9—31no—
185#3699—64no—
186C2×D36—31no—
187C2×D36—31no—
188C2×D36—61no—
189C2×C4×D9—31no—
190C2×C4×D9—61no—
191C2×Dic18C2×D311yescharacteristic, complemented
192C9×C22⋊C4—21no—
193C9×C22⋊C4—31no—
194C9×C22⋊C4—31no—
195C9×C22⋊C4C2×D311yescharacteristic, complemented
196#3676—31no—
197#3676—31no—
198#3676C2×D311yescharacteristic, complemented
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—61no—
202(C2×D9)⋊C4C2×D311yescharacteristic, complemented
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204Dic9⋊C4—31no—
205Dic9⋊C4—31no—
206Dic9⋊C4—61no—
207C4×Dic9—31no—
208C4×Dic9C2×D311yescharacteristic, complemented
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×D3×C9—21no—
223C2×D3×C9—21no—
224C2×D3×C9—21no—
225C2×D3×C9—21no—
226C2×D3×C9—21no—
227C2×D3×C9—44no—
228C2×D3×C9C2×D412yes—
229C2×C3×D9—21no—
230C2×C3×D9—21no—
231C2×C3×D9—21no—
232D3×D9—44no—
233C3×C4×C9—21no—
234C3×C4×C9—21no—
235C3⋊Dic9—21no—
236C3⋊Dic9C2×D412yes—
237C9×Dic3—21no—
238C3×Dic9—21no—
239C3×Dic9—21no—
240C3×Dic9C2×D412yes—
241C22×#67—91no—
242C2×#239—91no—
243C2×#237—91no—
244C2×D3×D4—91no—
245C3×#124—91no—
246C3×#120—31no—
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—31no—
256#885—91no—
257#884—91no—
258#884—91no—
259#884—91no—
260#884—91no—
261#884—91no—
262#884—91no—
263#884—181no—
264#882—91no—
265#882—91no—
266#882—91no—
267#882—91no—
268#882D911yescharacteristic, complemented
269#877—91no—
270#874—91no—
271#872—91no—
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—31no—
274C22×C3⋊D3—31no—
275C22×C3×D3—22no—
276C22×C3×D3—31no—
277C22×C3×D3—41no—
278C22×C3×D3—41no—
279C22×C3×D3C22×D311yescharacteristic
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—
288#638—121no—
289C2×C3⋊Dic3—31no—
290C2×C3⋊Dic3—31no—
291C4⋊(C3⋊D3)—121no—
292C4×C3⋊D3—62no—
293C3×#67—41no—
294C3×#67—62no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3C22×D311yescharacteristic
299C3×D12—22no—
300C3×D12—41no—
301C3×Dic6—62no—
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×C9—31no—
315C23×C9—31no—
316C23×C9—62no—
317C23×C9—121no—
318C23×C9—121no—
319C23×C9C22×D311yescharacteristic
320C22×D9—31no—
321C22×D9—31no—
322C22×D9—61no—
323C22×D9—61no—
324C22×D9—62no—
325C22×D9—121no—
326C22×D9—121no—
327C22×D9C22×D311yescharacteristic
328D4×C9—62no—
329D4×C9—121no—
330D4×C9—121no—
331C2×C4×C9—21no—
332C2×C4×C9—21no—
333C2×C4×C9—31no—
334C2×C4×C9C22×D311yescharacteristic
335C2×C4×C9C22×D311yescharacteristic
336#611—22no—
337#611—62no—
338#611—62no—
339#611—62no—
340#611—62no—
341#611—62no—
342#611—122no—
343#611—121no—
344#611—121no—
345#611—121no—
346#611—121no—
347#611—122no—
348C2×Dic9—31no—
349C2×Dic9—34no—
350C2×Dic9—31no—
351C2×Dic9—61no—
352C2×Dic9—61no—
353C2×Dic9—62no—
354C2×Dic9C22×D311yescharacteristic
355C2×Dic9C22×D311yescharacteristic
356C2×Dic9C22×D311yescharacteristic
357D36—121no—
358D36—122no—
359D36—121no—
360C4×D9—62no—
361C4×D9—122no—
362Dic18—22no—
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—22no—
371D3×C9—41no—
372D3×C9—41no—
373C3×D9—41no—
374C24×C3—31no—
375C23×D3—91no—
376C23×D3—91no—
377C23×D3C2×D911yescharacteristic
378C2×C3×Q8—91no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—31no—
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, complemented
402C22×Dic3—91no—
403C22×Dic3—91no—
404#239—184no—
405#237—184no—
406D3×D4—184no—
407C2×D12—91no—
408C2×D12—91no—
409C2×D12—91no—
410C2×D12—91no—
411C2×D12—91no—
412C2×D12—91no—
413C2×D12—91no—
414C2×D12—91no—
415C2×D12—181no—
416C2×D12C2×D911yescharacteristic
417C2×D12C2×D911yescharacteristic, complemented
418C2×C4×D3—91no—
419C2×C4×D3—91no—
420C2×C4×D3—91no—
421C2×C4×D3—91no—
422C2×C4×D3—181no—
423C2×Dic6—31no—
424C3×C22⋊C4—21no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4C2×D911yescharacteristic, complemented
431C3×C22⋊C4D3211yescharacteristic
432C3×C42—91no—
433#217—31no—
434#217—91no—
435#217—91no—
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
446(C2×D3)⋊C4C2×D911yescharacteristic, complemented
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—181no—
452C4×Dic3—31no—
453C4×Dic3—91no—
454C4×Dic3—91no—
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—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—44no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3D3×D412yes—
478D32—124no—
479C32×C4—21no—
480C32×C4—21no—
481C3⋊Dic3—32no—
482C3⋊Dic3—61no—
483C3×Dic3—21no—
484C3×Dic3—32no—
485C3×Dic3—61no—
486C3×Dic3—61no—
487C22×C9—21no—
488C22×C9—21no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—32no—
492C22×C9—41no—
493C22×C9—41no—
494C22×C9—41no—
495C22×C9—61no—
496C22×C9—61no—
497C22×C9—61no—
498C22×C9—61no—
499C22×C9—61no—
500C22×C9—61no—
501C22×C9—61no—
502C22×C9—61no—
503C22×C9—124no—
504C22×C9C23×D311yescharacteristic
505C2×D9—21no—
506C2×D9—21no—
507C2×D9—21no—
508C2×D9—62no—
509C2×D9—61no—
510C2×D9—61no—
511C2×D9—61no—
512C2×D9—61no—
513C2×D9—61no—
514C2×D9—61no—
515C2×D9—121no—
516C2×D9—121no—
517C2×D9—121no—
518C2×D9—121no—
519C2×D9—121no—
520C2×D9—124no—
521C4×C9—21no—
522C4×C9—21no—
523C4×C9—41no—
524C4×C9—41no—
525C4×C9—61no—
526Dic9—21no—
527Dic9—21no—
528Dic9—32no—
529Dic9—62no—
530Dic9—61no—
531Dic9—121no—
532Dic9D3×D412yes—
533C2×#41—271no—
534C22×D4—271no—
535#127—271no—
536#127—271no—
537#124—91no—
538#124—271no—
539#121—271no—
540#121—271no—
541#121—271no—
542#121—271no—
543#120—31no—
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—31no—
552C23×C3—31no—
553C23×C3—62no—
554C23×C3—91no—
555C23×C3—121no—
556C23×C3—121no—
557C23×C3C22×D911yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C22×D3—22no—
560C22×D3—31no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—91no—
564C22×D3—91no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—181no—
568C22×D3—181no—
569C22×D3—182no—
570C22×D3—182no—
571C22×D3—361no—
572C22×D3—361no—
573C22×D3—361no—
574C22×D3—361no—
575C22×D3C22×D911yescharacteristic
576C22×D3C22×D911yescharacteristic
577C22×D3C22×D911yescharacteristic
578C3×Q8—182no—
579C3×D4—62no—
580C3×D4—121no—
581C3×D4—121no—
582C3×D4—182no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—31no—
586C2×C3×C4—91no—
587C2×C3×C4—91no—
588C2×C3×C4—91no—
589C2×C3×C4C22×D911yescharacteristic
590C2×C3×C4C22×D911yescharacteristic
591C2×C3×C4C2×D3211yescharacteristic
592C2×C3×C4C2×D3211yescharacteristic
593#67—41no—
594#67—62no—
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—31no—
613C2×Dic3—31no—
614C2×Dic3—94no—
615C2×Dic3—91no—
616C2×Dic3—91no—
617C2×Dic3—91no—
618C2×Dic3—91no—
619C2×Dic3—181no—
620C2×Dic3—181no—
621C2×Dic3—182no—
622C2×Dic3C22×D911yescharacteristic
623D12—22no—
624D12—41no—
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—62no—
640C2×C32—41no—
641C2×C32C2×D3×D411yescharacteristic
642C2×C32#100411yescharacteristic
643C2×C32#100411yescharacteristic
644C3⋊D3—121no—
645C3⋊D3—121no—
646C3×D3—22no—
647C3×D3—41no—
648C3×D3—41no—
649C3×D3—121no—
650C2×C9—21no—
651C2×C9—21no—
652C2×C9—21no—
653C2×C9—41no—
654C2×C9—62no—
655C2×C9—81no—
656C2×C9—121no—
657C2×C9—121no—
658C2×C9C2×D3×D411yescharacteristic
659C2×C9#100911yescharacteristic
660C2×C9#100911yescharacteristic
661D9—41no—
662D9—122no—
663D9—121no—
664D9—121no—
665D9—241no—
666C24—31no—
667C24—271no—
668#41—544no—
669C2×Q8—91no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
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—91no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4D3×D911yescharacteristic, complemented
701C42—91no—
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—32no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—124no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3C23×D911yescharacteristic
727C22×C3C22×D3211yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—44no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—182no—
741C2×D3—181no—
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—361no—
754C2×D3—361no—
755C2×D3—361no—
756C2×D3—361no—
757C2×D3—361no—
758C2×D3—364no—
759C2×D3—364no—
760C2×D3D4×D912yes—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—61no—
768C3×C4—92no—
769C3×C4—181no—
770C3×C4—181no—
771Dic3—21no—
772Dic3—32no—
773Dic3—61no—
774Dic3—61no—
775Dic3—92no—
776Dic3—92no—
777Dic3—182no—
778Dic3—181no—
779Dic3—181no—
780Dic3—361no—
781C32#559211yescharacteristic
782C9—21no—
783C9#567411yescharacteristic, complemented
784C23—31no—
785C23—31no—
786C23—31no—
787C23—62no—
788C23—91no—
789C23—121no—
790C23—121no—
791C23—271no—
792C23—271no—
793C23—542no—
794C23—1081no—
795C23—1081no—
796C23C2×D3×D911yescharacteristic
797Q8—182no—
798D4—62no—
799D4—121no—
800D4—121no—
801D4—182no—
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—91no—
815C2×C4—91no—
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—62no—
830C2×C3—81no—
831C2×C3—121no—
832C2×C3—121no—
833C2×C3—361no—
834C2×C3C2×D4×D911yescharacteristic
835C2×C3#6371011yescharacteristic
836C2×C3#6371011yescharacteristic
837C2×C3#6430711yescharacteristic
838C2×C3D32×D411yescharacteristic
839C2×C3#6431411yescharacteristic
840D3—22no—
841D3—41no—
842D3—41no—
843D3—121no—
844D3—362no—
845D3—361no—
846D3—361no—
847D3—361no—
848D3—361no—
849D3—721no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—32no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—124no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—541no—
867C22—541no—
868C22—541no—
869C22—541no—
870C22—541no—
871C22—541no—
872C22—1084no—
873C22C22×D3×D911yescharacteristic
874C4—21no—
875C4—21no—
876C4—61no—
877C4—92no—
878C4—181no—
879C4—181no—
880C4—272no—
881C4—541no—
882C3—21no—
883C3#1058969411yescharacteristic, complemented
884C3#1059427011yescharacteristic
885C2—41no—
886C2—62no—
887C2—121no—
888C2—121no—
889C2—361no—
890C2—1081no—
891C2—1081no—
892C2#1172247611yescharacteristic
893C2D3×D4×D911yescharacteristic
894C2#1172250011yescharacteristic
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×D3×#611C2semidirect
2. C2×#88639C2semidirect
3. #11721730C2semidirect
4. C9×#882C2semidirect
5. C3×#63447C2semidirect
6. #11721289C2semidirect
7. #11721287C2semidirect
8. #11721282C2semidirect
9. #11721051C2semidirect
10. #11721050C2semidirect
11. #11721041C2semidirect
12. #11721040C2semidirect
13. #11721035C2semidirect
14. #11721016C2semidirect
15. #11721010C2semidirect
21. C2×#6233C22semidirect
22. C2×C4⋊(C3⋊D9)C22semidirect
23. C2×C4×C3⋊D9C22semidirect
24. C2×C9×#67C22semidirect
27. C2×C9×D12C22semidirect
28. C2×C3×Dic18C22semidirect
32. C2×#6195C22semidirect
33. C2×#6195C22semidirect
34. C2×#6195C22semidirect
36. C2×#6194C22semidirect
38. C2×D3×Dic9C22semidirect
39. C2×#6192C22semidirect
41. C3×C9×C22⋊C4C22semidirect
42. #88536C22semidirect
43. #88534C22semidirect
44. C3×#3676C22semidirect
46. C9×(C2×D3)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C3×(C2×D9)⋊C4C22semidirect
49. C3×C4×Dic9C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. #88445C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
80. #63447D3semidirect
124. D3×Dic9D4semidirect
191. C2×Dic18C2×D3semidirect
195. C9×C22⋊C4C2×D3semidirect
198. #3676C2×D3semidirect
202. (C2×D9)⋊C4C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
208. C4×Dic9C2×D3semidirect
268. #882D9semidirect
401. C2×#67C2×D9semidirect
417. C2×D12C2×D9semidirect
430. C3×C22⋊C4C2×D9semidirect
446. (C2×D3)⋊C4C2×D9semidirect
548. C3×C9#535semidirect
700. C22⋊C4D3×D9semidirect
783. C9#5674semidirect
883. C3#10589694semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×#886392
#117217302
C9×#8822
C3×#634472
#117212892
#117212872
#117212822
#117210512
#117210502
#117210412
#117210402
#117210352
#117210162
#117210102
#105942703
#105896943