Finite Group Databasebeta

← #13147978

Subgroups — #13147978

Order 1728.

636 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721725C211yesmaximal, characteristic
2C9×#879C211yesmaximal, characteristic
3C3×#63440C211yesmaximal, characteristic
4#11721253C211yesmaximal, characteristic
5#11721247C211yesmaximal, characteristic
6#11721247C211yesmaximal, characteristic
7#11721245C211yesmaximal, characteristic
8#11720937C211yesmaximal, characteristic, complemented
9#11720925C211yesmaximal, characteristic, complemented
10#11720919C211yesmaximal, characteristic, complemented
11#11720917C211yesmaximal, characteristic, complemented
12#11720915C211yesmaximal, characteristic, complemented
13Dic3×Dic18C211yesmaximal, characteristic, complemented
14#11720904C211yesmaximal, characteristic, complemented
15#11720902C211yesmaximal, characteristic, complemented
16#10594028—31nomaximal
17#10589803—31nomaximal
18C22×C3×Dic9C2211yescharacteristic
19C2×C3×Dic18C2211yescharacteristic
20C2×#6189C2211yescharacteristic
21C3×C9×C22⋊C4C2211yescharacteristic
22#88551C2211yescharacteristic
23#88551C2211yescharacteristic
24C4⋊(C3⋊Dic9)C2211yescharacteristic
25#88534C2211yescharacteristic
26#88534C2211yescharacteristic
27C4×C3⋊Dic9C2211yescharacteristic
28C9×#217C2211yescharacteristic
29C9×#217C2211yescharacteristic
30C3×#3676C2211yescharacteristic
31C9×C4⋊Dic3C2211yescharacteristic
32C9×Dic3⋊C4C2211yescharacteristic
33C9×Dic3⋊C4C2211yescharacteristic
34C4×C9×Dic3C2211yescharacteristic
35C3×C4⋊Dic9C2211yescharacteristic
36C3×Dic9⋊C4C2211yescharacteristic
37C3×Dic9⋊C4C2211yescharacteristic
38Dic3⋊Dic9C2211yescharacteristic
39Dic3⋊Dic9C2211yescharacteristic
40Dic3⋊Dic9C2211yescharacteristic
41#88442C2211yescharacteristic
42#88442C2211yescharacteristic
43#88442C2211yescharacteristic
44Dic9⋊Dic3C2211yescharacteristic
45Dic9⋊Dic3C2211yescharacteristic
46Dic9⋊Dic3C2211yescharacteristic
47Dic9⋊Dic3C2211yescharacteristic
48Dic9⋊Dic3C2211yescharacteristic
49Dic3×Dic9C2211yescharacteristic
50Dic3×Dic9C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64088—31no—
54C3×#879D311yescharacteristic
55C3×#878—31no—
56#63964—31no—
57#63956—31no—
58#63956—31no—
59#63955—31no—
60#63872—31no—
61#63867—31no—
62#63847—31no—
63#63846—31no—
64#63845—31no—
65Dic3×Dic6—31no—
66#63839—31no—
67#63838—31no—
68C9×#126—31no—
69#63452—31no—
70#63451—31no—
71#63451—31no—
72#63451—31no—
73#63450—31no—
74#63449—31no—
75#63441—31no—
76#63441—31no—
77#63441—31no—
78#63441—61no—
79#63440—31no—
80#63440D311yescharacteristic
81#63439—31no—
82#63432—31no—
83C4×Dic18—31no—
84C23×C3×C9C2311yescharacteristic
85C2×C3×C4×C9C2311yescharacteristic
86C2×C3×C4×C9C2311yescharacteristic
87C2×C3⋊Dic9C2311yescharacteristic
88C2×C3⋊Dic9C2311yescharacteristic
89C2×C3⋊Dic9C2311yescharacteristic
90C2×C3⋊Dic9C2311yescharacteristic
91C2×C9×Dic3C2311yescharacteristic
92C2×C9×Dic3C2311yescharacteristic
93C2×C9×Dic3C2311yescharacteristic
94C2×C9×Dic3C2311yescharacteristic
95C2×C3×Dic9—22no—
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C3×Dic18—22no—
101#6189—22no—
102#5701—91no—
103#5625—91no—
104C22×C3×Dic3—31no—
105C2×C3×Dic6—31no—
106C2×#627—31no—
107C32×C22⋊C4C2×D311yescharacteristic
108#3757—31no—
109#3757—31no—
110C4⋊(C3⋊Dic3)—31no—
111#3750—31no—
112#3750—31no—
113C4×C3⋊Dic3—31no—
114C3×#217—31no—
115C3×#217C2×D311yescharacteristic
116C3×#217C2×D311yescharacteristic
117C3×C4⋊Dic3—31no—
118C3×C4⋊Dic3C2×D311yescharacteristic
119C3×Dic3⋊C4—31no—
120C3×Dic3⋊C4—31no—
121C3×Dic3⋊C4C2×D311yescharacteristic
122C3×Dic3⋊C4C2×D311yescharacteristic
123C3×C4×Dic3C2×D311yescharacteristic
124#3724—31no—
125#3724—31no—
126#3724—31no—
127Dic3⋊Dic3—31no—
128Dic3⋊Dic3—31no—
129Dic3⋊Dic3—31no—
130Dic3⋊Dic3—31no—
131Dic3⋊Dic3—31no—
132Dic3⋊Dic3—31no—
133Dic3⋊Dic3—31no—
134Dic3⋊Dic3—31no—
135Dic32—31no—
136Dic32—31no—
137Dic32—31no—
138Dic32—31no—
139C22×Dic9C2×D311yescharacteristic
140C2×Dic18—31no—
141C2×Dic18C2×D311yescharacteristic
142C9×C4⋊C4—31no—
143C9×C4⋊C4—31no—
144C9×C4⋊C4—31no—
145C9×C22⋊C4—21no—
146C9×C22⋊C4—31no—
147C9×C22⋊C4—31no—
148C9×C22⋊C4C2×D311yescharacteristic
149C42×C9—31no—
150#3676—31no—
151#3676—31no—
152#3676—61no—
153#3676—61no—
154#3676C2×D311yescharacteristic
155C4⋊Dic9—31no—
156C4⋊Dic9—31no—
157C4⋊Dic9—31no—
158C4⋊Dic9—31no—
159C4⋊Dic9—61no—
160C4⋊Dic9C2×D311yescharacteristic
161Dic9⋊C4—31no—
162Dic9⋊C4—31no—
163Dic9⋊C4—31no—
164Dic9⋊C4—31no—
165Dic9⋊C4—31no—
166Dic9⋊C4—31no—
167Dic9⋊C4—31no—
168Dic9⋊C4—31no—
169Dic9⋊C4—31no—
170Dic9⋊C4—31no—
171Dic9⋊C4—61no—
172Dic9⋊C4—61no—
173Dic9⋊C4C2×D311yescharacteristic
174Dic9⋊C4C2×D311yescharacteristic
175C4×Dic9—31no—
176C4×Dic9—31no—
177C4×Dic9—31no—
178C4×Dic9—31no—
179C4×Dic9—31no—
180C4×Dic9—61no—
181C22×C3×C9—21no—
182C22×C3×C9—21no—
183C22×C3×C9—21no—
184C22×C3×C9C2411yescharacteristic
185C3×C4×C9—21no—
186C3×C4×C9—21no—
187C3⋊Dic9—21no—
188C3⋊Dic9—21no—
189C3⋊Dic9—21no—
190C3⋊Dic9—21no—
191C9×Dic3—21no—
192C9×Dic3—21no—
193C9×Dic3—21no—
194C9×Dic3—21no—
195C3×Dic9—21no—
196C3×Dic9—21no—
197C3×Dic9—21no—
198C3×Dic9#4112yes—
199C3×#126—31no—
200C3×C22⋊Q8—91no—
201Q8×Dic3—91no—
202#944—91no—
203#926—91no—
204#924—91no—
205#890—91no—
206#890—91no—
207#890—91no—
208#890—91no—
209#889—91no—
210#889—91no—
211#889—91no—
212#889—91no—
213#889—91no—
214#888—91no—
215#887—91no—
216#887—91no—
217#879—91no—
218#879—91no—
219#879—91no—
220#879—91no—
221#879—91no—
222#879—91no—
223#879—181no—
224#879D911yescharacteristic
225#878—31no—
226#878—91no—
227#877—91no—
228#870—91no—
229C4×Dic6—91no—
230C23×C32C22×D311yescharacteristic
231C2×C32×C4C22×D311yescharacteristic
232C2×C32×C4C22×D311yescharacteristic
233C2×C3⋊Dic3—31no—
234C2×C3⋊Dic3—31no—
235C2×C3⋊Dic3—31no—
236C2×C3⋊Dic3—31no—
237C2×C3×Dic3—31no—
238C2×C3×Dic3—31no—
239C2×C3×Dic3—31no—
240C2×C3×Dic3—31no—
241C2×C3×Dic3—62no—
242C2×C3×Dic3C22×D311yescharacteristic
243C2×C3×Dic3C22×D311yescharacteristic
244C2×C3×Dic3C22×D311yescharacteristic
245C2×C3×Dic3C22×D311yescharacteristic
246C3×Dic6—62no—
247#627—62no—
248C23×C9—21no—
249C23×C9C22×D311yescharacteristic
250C2×C4×C9—21no—
251C2×C4×C9—21no—
252C2×C4×C9—31no—
253C2×C4×C9—31no—
254C2×C4×C9—31no—
255C2×C4×C9—31no—
256C2×C4×C9C22×D311yescharacteristic
257C2×C4×C9C22×D311yescharacteristic
258C2×Dic9—22no—
259C2×Dic9—31no—
260C2×Dic9—31no—
261C2×Dic9—31no—
262C2×Dic9—31no—
263C2×Dic9—61no—
264C2×Dic9—61no—
265C2×Dic9—61no—
266C2×Dic9—61no—
267C2×Dic9C22×D311yescharacteristic
268C2×Dic9C22×D311yescharacteristic
269C2×Dic9C22×D311yescharacteristic
270C2×Dic9C22×D311yescharacteristic
271Dic18—22no—
272Dic18—62no—
273#541—271noSylow
274C2×C3×C9—41no—
275C2×C3×C9C2×#4111yescharacteristic
276C2×C3×C92−1+411yescharacteristic
277C2×C3×C92−1+411yescharacteristic
278C2×C3×Q8—91no—
279C22×C3×C4—91no—
280C22×Dic3—31no—
281C2×Dic6—31no—
282C2×Dic6—91no—
283C2×Dic6—91no—
284C3×C4⋊C4—31no—
285C3×C4⋊C4—31no—
286C3×C4⋊C4—31no—
287C3×C4⋊C4—91no—
288C3×C4⋊C4—91no—
289C3×C4⋊C4—91no—
290C3×C22⋊C4—21no—
291C3×C22⋊C4—31no—
292C3×C22⋊C4—31no—
293C3×C22⋊C4—91no—
294C3×C22⋊C4C2×D911yescharacteristic
295C3×C22⋊C4D3211yescharacteristic
296C3×C42—31no—
297#217—31no—
298#217—91no—
299#217—91no—
300#217—91no—
301#217—91no—
302#217—181no—
303#217—181no—
304#217C2×D911yescharacteristic
305#217C2×D911yescharacteristic
306C4⋊Dic3—31no—
307C4⋊Dic3—91no—
308C4⋊Dic3—91no—
309C4⋊Dic3—91no—
310C4⋊Dic3—91no—
311C4⋊Dic3—91no—
312C4⋊Dic3—91no—
313C4⋊Dic3—91no—
314C4⋊Dic3—91no—
315C4⋊Dic3—91no—
316C4⋊Dic3—91no—
317C4⋊Dic3—181no—
318C4⋊Dic3C2×D911yescharacteristic
319Dic3⋊C4—31no—
320Dic3⋊C4—31no—
321Dic3⋊C4—91no—
322Dic3⋊C4—91no—
323Dic3⋊C4—91no—
324Dic3⋊C4—91no—
325Dic3⋊C4—91no—
326Dic3⋊C4—91no—
327Dic3⋊C4—91no—
328Dic3⋊C4—91no—
329Dic3⋊C4—91no—
330Dic3⋊C4—91no—
331Dic3⋊C4—91no—
332Dic3⋊C4—91no—
333Dic3⋊C4—91no—
334Dic3⋊C4—91no—
335Dic3⋊C4—91no—
336Dic3⋊C4—91no—
337Dic3⋊C4—91no—
338Dic3⋊C4—91no—
339Dic3⋊C4—181no—
340Dic3⋊C4—181no—
341Dic3⋊C4C2×D911yescharacteristic
342Dic3⋊C4C2×D911yescharacteristic
343C4×Dic3—91no—
344C4×Dic3—91no—
345C4×Dic3—91no—
346C4×Dic3—91no—
347C4×Dic3—91no—
348C4×Dic3—91no—
349C4×Dic3—91no—
350C4×Dic3—91no—
351C4×Dic3—91no—
352C4×Dic3—91no—
353C4×Dic3—181no—
354C4×Dic3C2×D911yescharacteristic
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32C23×D311yescharacteristic
359C32×C4—21no—
360C32×C4—21no—
361C3⋊Dic3—61no—
362C3⋊Dic3—61no—
363C3⋊Dic3—61no—
364C3⋊Dic3—61no—
365C3×Dic3—21no—
366C3×Dic3—21no—
367C3×Dic3—21no—
368C3×Dic3—21no—
369C3×Dic3—32no—
370C3×Dic3—61no—
371C3×Dic3—61no—
372C3×Dic3—61no—
373C22×C9—21no—
374C22×C9—21no—
375C22×C9—21no—
376C22×C9—21no—
377C22×C9—41no—
378C22×C9—41no—
379C22×C9—41no—
380C22×C9C23×D311yescharacteristic
381C4×C9—21no—
382C4×C9—21no—
383C4×C9—41no—
384C4×C9—41no—
385C4×C9—61no—
386C4×C9—61no—
387C4×C9—61no—
388C4×C9—61no—
389Dic9—21no—
390Dic9—21no—
391Dic9—21no—
392Dic9—61no—
393Dic9—61no—
394Dic9—61no—
395Dic9—61no—
396Dic9—121no—
397Dic9—121no—
398Dic9—121no—
399Dic9—121no—
400Dic9#23712yes—
401C4⋊Q8—271no—
402#126—31no—
403#126—271no—
404#126—271no—
405#126—271no—
406#125—271no—
407#125—271no—
408#125—271no—
409#125—271no—
410#125—271no—
411C22⋊Q8—91no—
412C22⋊Q8—271no—
413C4×Q8—271no—
414C4×Q8—271no—
415#117—271no—
416C3×C9#54111yescharacteristic, complemented, Sylow
417C23×C3—21no—
418C23×C3C22×D911yescharacteristic
419C23×C3C2×D3211yescharacteristic
420C3×Q8—182no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—31no—
424C2×C3×C4—31no—
425C2×C3×C4—31no—
426C2×C3×C4—31no—
427C2×C3×C4—91no—
428C2×C3×C4—91no—
429C2×C3×C4—91no—
430C2×C3×C4—91no—
431C2×C3×C4—182no—
432C2×C3×C4C22×D911yescharacteristic
433C2×C3×C4C22×D911yescharacteristic
434C2×C3×C4C2×D3211yescharacteristic
435C2×C3×C4C2×D3211yescharacteristic
436C2×Dic3—31no—
437C2×Dic3—31no—
438C2×Dic3—31no—
439C2×Dic3—31no—
440C2×Dic3—62no—
441C2×Dic3—91no—
442C2×Dic3—91no—
443C2×Dic3—91no—
444C2×Dic3—91no—
445C2×Dic3—91no—
446C2×Dic3—91no—
447C2×Dic3—91no—
448C2×Dic3—91no—
449C2×Dic3—181no—
450C2×Dic3—181no—
451C2×Dic3—181no—
452C2×Dic3—181no—
453C2×Dic3C22×D911yescharacteristic
454C2×Dic3C22×D911yescharacteristic
455C2×Dic3C22×D911yescharacteristic
456C2×Dic3C22×D911yescharacteristic
457Dic6—62no—
458Dic6—182no—
459Dic6—182no—
460C2×C32—41no—
461C2×C32D3×#4111yescharacteristic
462C2×C32#101011yescharacteristic
463C2×C32#101011yescharacteristic
464C2×C9—21no—
465C2×C9—21no—
466C2×C9—21no—
467C2×C9—41no—
468C2×C9—81no—
469C2×C9C2×#23711yescharacteristic
470C2×C9#100711yescharacteristic
471C2×C9#101011yescharacteristic
472C2×Q8—91no—
473C2×Q8—271no—
474C22×C4—91no—
475C4⋊C4—31no—
476C4⋊C4—31no—
477C4⋊C4—31no—
478C4⋊C4—91no—
479C4⋊C4—91no—
480C4⋊C4—91no—
481C4⋊C4—271no—
482C4⋊C4—271no—
483C4⋊C4—271no—
484C4⋊C4—271no—
485C4⋊C4—271no—
486C4⋊C4—271no—
487C4⋊C4—271no—
488C4⋊C4—271no—
489C4⋊C4—271no—
490C4⋊C4—271no—
491C4⋊C4—271no—
492C4⋊C4—271no—
493C4⋊C4—271no—
494C4⋊C4—271no—
495C22⋊C4—31no—
496C22⋊C4—31no—
497C22⋊C4—91no—
498C22⋊C4—271no—
499C22⋊C4—271no—
500C22⋊C4D3×D911yescharacteristic
501C42—31no—
502C42—271no—
503C42—271no—
504C42—271no—
505C42—271no—
506C42—271no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3C23×D911yescharacteristic
518C22×C3C22×D3211yescharacteristic
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—41no—
524C3×C4—41no—
525C3×C4—61no—
526C3×C4—61no—
527C3×C4—61no—
528C3×C4—61no—
529C3×C4—92no—
530C3×C4—181no—
531C3×C4—181no—
532C3×C4—181no—
533Dic3—21no—
534Dic3—21no—
535Dic3—21no—
536Dic3—21no—
537Dic3—32no—
538Dic3—61no—
539Dic3—61no—
540Dic3—61no—
541Dic3—181no—
542Dic3—181no—
543Dic3—181no—
544Dic3—181no—
545Dic3—181no—
546Dic3—181no—
547Dic3—181no—
548Dic3—181no—
549Dic3—361no—
550Dic3—361no—
551Dic3—361no—
552Dic3—361no—
553C32#570111yescharacteristic
554C9—21no—
555C9#562511yescharacteristic, complemented
556C23C2×D3×D911yescharacteristic
557Q8—182no—
558Q8—542no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—31no—
562C2×C4—31no—
563C2×C4—91no—
564C2×C4—91no—
565C2×C4—91no—
566C2×C4—91no—
567C2×C4—182no—
568C2×C4—271no—
569C2×C4—271no—
570C2×C4—271no—
571C2×C4—271no—
572C2×C4C2×D3×D911yescharacteristic
573C2×C4C2×D3×D911yescharacteristic
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—41no—
578C2×C3—41no—
579C2×C3—81no—
580C2×C3#41×D911yescharacteristic
581C2×C3#6371611yescharacteristic
582C2×C3#6371611yescharacteristic
583C2×C3#6429711yescharacteristic
584C2×C3#6430911yescharacteristic
585C2×C3D3×#23711yescharacteristic
586C22—21no—
587C22—21no—
588C22—21no—
589C22C22×D3×D911yescharacteristic
590C4—21no—
591C4—21no—
592C4—61no—
593C4—61no—
594C4—61no—
595C4—61no—
596C4—92no—
597C4—181no—
598C4—181no—
599C4—181no—
600C4—541no—
601C4—541no—
602C4—541no—
603C4—541no—
604C3—21no—
605C3#1058980311yescharacteristic, complemented
606C3#1059402811yescharacteristic
607C2—41no—
608C2#1172246411yescharacteristic
609C2#1172249411yescharacteristic
610C2D9×#23711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC23×C32C22×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#541
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
8. #11720937C2semidirect
9. #11720925C2semidirect
10. #11720919C2semidirect
11. #11720917C2semidirect
12. #11720915C2semidirect
13. Dic3×Dic18C2semidirect
14. #11720904C2semidirect
15. #11720902C2semidirect
416. C3×C9#541semidirect
555. C9#5625semidirect
605. C3#10589803semidirect

Maximal subgroups

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

subgroupindex
#117217252
C9×#8792
C3×#634402
#117212532
#117212472
#117212452
#117209372
#117209252
#117209192
#117209172
#117209152
Dic3×Dic182
#117209042
#117209022
#105940283
#105898033