Finite Group Databasebeta

← #13147969

Subgroups — #13147969

Order 1728.

650 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721724C211yesmaximal, characteristic
2C9×#879C211yesmaximal, characteristic
3C3×#63441C211yesmaximal, characteristic
4#11721267C211yesmaximal, characteristic
5#11721248C211yesmaximal, characteristic
6#11721247C211yesmaximal, characteristic
7#11721247C211yesmaximal, characteristic
8#11720933C211yesmaximal, characteristic, complemented
9#11720927C211yesmaximal, characteristic, complemented
10#11720919C211yesmaximal, characteristic, complemented
11#11720918C211yesmaximal, characteristic, complemented
12#11720914C211yesmaximal, characteristic, complemented
13#11720913C211yesmaximal, characteristic, complemented
14#11720905C211yesmaximal, characteristic, complemented
15#11720900C211yesmaximal, characteristic, complemented
16#10594031—31nomaximal
17#10589803—31nomaximal
18C22×C3⋊Dic9C2211yescharacteristic
19C2×#6226C2211yescharacteristic
20C2×#6189C2211yescharacteristic
21C3×C9×C22⋊C4C2211yescharacteristic
22#88551C2211yescharacteristic
23C4⋊(C3⋊Dic9)C2211yescharacteristic
24#88534C2211yescharacteristic
25#88534C2211yescharacteristic
26C9×#217C2211yescharacteristic
27C9×#217C2211yescharacteristic
28C3×#3676C2211yescharacteristic
29C3×#3676C2211yescharacteristic
30C9×C4⋊Dic3C2211yescharacteristic
31C9×Dic3⋊C4C2211yescharacteristic
32C9×Dic3⋊C4C2211yescharacteristic
33C4×C9×Dic3C2211yescharacteristic
34C3×C4⋊Dic9C2211yescharacteristic
35C3×Dic9⋊C4C2211yescharacteristic
36C3×Dic9⋊C4C2211yescharacteristic
37C3×C4×Dic9C2211yescharacteristic
38Dic3⋊Dic9C2211yescharacteristic
39Dic3⋊Dic9C2211yescharacteristic
40Dic3⋊Dic9C2211yescharacteristic
41#88442C2211yescharacteristic
42#88442C2211yescharacteristic
43#88442C2211yescharacteristic
44#88442C2211yescharacteristic
45#88442C2211yescharacteristic
46Dic9⋊Dic3C2211yescharacteristic
47Dic9⋊Dic3C2211yescharacteristic
48Dic9⋊Dic3C2211yescharacteristic
49Dic3×Dic9C2211yescharacteristic
50Dic3×Dic9C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64087—31no—
54C3×#879—31no—
55C3×#879D311yescharacteristic
56#63982—31no—
57#63957—31no—
58#63956—31no—
59#63956—31no—
60#63869—31no—
61#63867—31no—
62#63847—31no—
63#63847—31no—
64#63845—31no—
65#63844—31no—
66#63840—31no—
67#63837—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#63441D311yescharacteristic
78#63440—31no—
79#63440—31no—
80#63440—61no—
81#63439—31no—
82#63432—31no—
83C4×Dic18—31no—
84C23×C3×C9C2311yescharacteristic
85C2×C3×C4×C9C2311yescharacteristic
86C2×C3×C4×C9C2311yescharacteristic
87C2×C3⋊Dic9—22no—
88C2×C3⋊Dic9C2311yescharacteristic
89C2×C3⋊Dic9C2311yescharacteristic
90C2×C3⋊Dic9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92#6226—22no—
93C2×C9×Dic3C2311yescharacteristic
94C2×C9×Dic3C2311yescharacteristic
95C2×C9×Dic3C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101#6189—22no—
102#5701—91no—
103#5701—91no—
104C22×C3⋊Dic3—31no—
105C2×#634—31no—
106C2×#627—31no—
107C32×C22⋊C4C2×D311yescharacteristic
108#3757—31no—
109C4⋊(C3⋊Dic3)—31no—
110#3750—31no—
111#3750—31no—
112C3×#217—31no—
113C3×#217—31no—
114C3×#217C2×D311yescharacteristic
115C3×#217C2×D311yescharacteristic
116C3×C4⋊Dic3—31no—
117C3×C4⋊Dic3C2×D311yescharacteristic
118C3×Dic3⋊C4—31no—
119C3×Dic3⋊C4—31no—
120C3×Dic3⋊C4C2×D311yescharacteristic
121C3×Dic3⋊C4C2×D311yescharacteristic
122C3×C4×Dic3—31no—
123C3×C4×Dic3C2×D311yescharacteristic
124#3724—31no—
125#3724—31no—
126#3724—31no—
127#3724—31no—
128#3724—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×Dic9—31no—
140C22×Dic9—61no—
141C2×Dic18—31no—
142C2×Dic18—31no—
143C2×Dic18—61no—
144C9×C4⋊C4—31no—
145C9×C4⋊C4—31no—
146C9×C4⋊C4—31no—
147C9×C22⋊C4—21no—
148C9×C22⋊C4—31no—
149C9×C22⋊C4—31no—
150C9×C22⋊C4C2×D311yescharacteristic
151C42×C9—31no—
152#3676—31no—
153#3676—61no—
154#3676C2×D311yescharacteristic
155#3676C2×D311yescharacteristic
156C4⋊Dic9—31no—
157C4⋊Dic9—31no—
158C4⋊Dic9—31no—
159C4⋊Dic9—31no—
160C4⋊Dic9—61no—
161C4⋊Dic9C2×D311yescharacteristic
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—31no—
172Dic9⋊C4—61no—
173Dic9⋊C4—61no—
174Dic9⋊C4C2×D311yescharacteristic
175Dic9⋊C4C2×D311yescharacteristic
176C4×Dic9—31no—
177C4×Dic9—31no—
178C4×Dic9—31no—
179C4×Dic9—31no—
180C4×Dic9C2×D311yescharacteristic
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#4112yes—
191C9×Dic3—21no—
192C9×Dic3—21no—
193C9×Dic3—21no—
194C9×Dic3—21no—
195C3×Dic9—21no—
196C3×Dic9—21no—
197C3×Dic9—21no—
198C3×Dic9—21no—
199C3×#126—31no—
200C3×#126—91no—
201#890—91no—
202#890—91no—
203#889—91no—
204#889—91no—
205#889—91no—
206#889—91no—
207#889—91no—
208#889—91no—
209#888—91no—
210#888—91no—
211#887—91no—
212#887—91no—
213#879—31no—
214#879—91no—
215#879—91no—
216#879—91no—
217#879—91no—
218#879D911yescharacteristic
219#878—91no—
220#878—91no—
221#878—91no—
222#878—91no—
223#878—181no—
224#877—91no—
225#877—91no—
226#870—91no—
227#870—91no—
228C4×Dic6—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—62no—
238#634—62no—
239C2×C3×Dic3—31no—
240C2×C3×Dic3—31no—
241C2×C3×Dic3—31no—
242C2×C3×Dic3—31no—
243C2×C3×Dic3C22×D311yescharacteristic
244C2×C3×Dic3C22×D311yescharacteristic
245C2×C3×Dic3C22×D311yescharacteristic
246C2×C3×Dic3C22×D311yescharacteristic
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—31no—
259C2×Dic9—31no—
260C2×Dic9—31no—
261C2×Dic9—31no—
262C2×Dic9—61no—
263C2×Dic9—61no—
264C2×Dic9—61no—
265C2×Dic9—61no—
266C2×Dic9—62no—
267C2×Dic9—122no—
268C2×Dic9C22×D311yescharacteristic
269C2×Dic9C22×D311yescharacteristic
270C2×Dic9C22×D311yescharacteristic
271C2×Dic9C22×D311yescharacteristic
272Dic18—62no—
273Dic18—62no—
274Dic18—122no—
275#541—271noSylow
276C2×C3×C9—41no—
277C2×C3×C9C2×#4111yescharacteristic
278C2×C3×C92−1+411yescharacteristic
279C2×C3×C92−1+411yescharacteristic
280C22×Dic3—91no—
281C22×Dic3—91no—
282C22×Dic3—181no—
283C2×Dic6—91no—
284C2×Dic6—91no—
285C2×Dic6—91no—
286C2×Dic6—91no—
287C2×Dic6—181no—
288C3×C4⋊C4—31no—
289C3×C4⋊C4—31no—
290C3×C4⋊C4—31no—
291C3×C4⋊C4—91no—
292C3×C4⋊C4—91no—
293C3×C4⋊C4—91no—
294C3×C22⋊C4—21no—
295C3×C22⋊C4—31no—
296C3×C22⋊C4—31no—
297C3×C22⋊C4—91no—
298C3×C22⋊C4—91no—
299C3×C22⋊C4C2×D911yescharacteristic
300C3×C22⋊C4D3211yescharacteristic
301C3×C42—31no—
302C3×C42—91no—
303#217—31no—
304#217—31no—
305#217—91no—
306#217—91no—
307#217—181no—
308#217C2×D911yescharacteristic
309#217C2×D911yescharacteristic
310C4⋊Dic3—31no—
311C4⋊Dic3—91no—
312C4⋊Dic3—91no—
313C4⋊Dic3—91no—
314C4⋊Dic3—91no—
315C4⋊Dic3—91no—
316C4⋊Dic3—91no—
317C4⋊Dic3—91no—
318C4⋊Dic3—91no—
319C4⋊Dic3—181no—
320C4⋊Dic3C2×D911yescharacteristic
321Dic3⋊C4—31no—
322Dic3⋊C4—31no—
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—91no—
340Dic3⋊C4—91no—
341Dic3⋊C4—91no—
342Dic3⋊C4—91no—
343Dic3⋊C4—181no—
344Dic3⋊C4—181no—
345Dic3⋊C4C2×D911yescharacteristic
346Dic3⋊C4C2×D911yescharacteristic
347C4×Dic3—31no—
348C4×Dic3—91no—
349C4×Dic3—91no—
350C4×Dic3—91no—
351C4×Dic3—91no—
352C4×Dic3—91no—
353C4×Dic3—91no—
354C4×Dic3—91no—
355C4×Dic3—91no—
356C4×Dic3C2×D911yescharacteristic
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32C23×D311yescharacteristic
361C32×C4—21no—
362C32×C4—21no—
363C3⋊Dic3—32no—
364C3⋊Dic3—61no—
365C3⋊Dic3—61no—
366C3⋊Dic3—61no—
367C3×Dic3—21no—
368C3×Dic3—21no—
369C3×Dic3—21no—
370C3×Dic3—21no—
371C3×Dic3—61no—
372C3×Dic3—61no—
373C3×Dic3—61no—
374C3×Dic3—61no—
375C22×C9—22no—
376C22×C9—21no—
377C22×C9—21no—
378C22×C9—21no—
379C22×C9—21no—
380C22×C9—41no—
381C22×C9—41no—
382C22×C9C23×D311yescharacteristic
383C4×C9—21no—
384C4×C9—21no—
385C4×C9—41no—
386C4×C9—41no—
387C4×C9—61no—
388C4×C9—61no—
389C4×C9—61no—
390C4×C9—61no—
391Dic9—21no—
392Dic9—21no—
393Dic9—21no—
394Dic9—21no—
395Dic9—32no—
396Dic9—62no—
397Dic9—61no—
398Dic9—61no—
399Dic9—61no—
400Dic9—121no—
401Dic9—121no—
402Dic9—121no—
403C4⋊Q8—271no—
404#126—31no—
405#126—91no—
406#126—271no—
407#126—271no—
408#125—271no—
409#125—271no—
410#125—271no—
411#125—271no—
412#125—271no—
413C22⋊Q8—271no—
414C22⋊Q8—271no—
415C4×Q8—271no—
416C4×Q8—271no—
417#117—271no—
418C3×C9#54111yescharacteristic, complemented, Sylow
419C23×C3—21no—
420C23×C3C22×D911yescharacteristic
421C23×C3C2×D3211yescharacteristic
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—31no—
425C2×C3×C4—31no—
426C2×C3×C4—31no—
427C2×C3×C4—31no—
428C2×C3×C4—91no—
429C2×C3×C4—91no—
430C2×C3×C4—91no—
431C2×C3×C4—91no—
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—91no—
441C2×Dic3—91no—
442C2×Dic3—91no—
443C2×Dic3—91no—
444C2×Dic3—91no—
445C2×Dic3—91no—
446C2×Dic3—91no—
447C2×Dic3—91no—
448C2×Dic3—181no—
449C2×Dic3—181no—
450C2×Dic3—181no—
451C2×Dic3—181no—
452C2×Dic3—182no—
453C2×Dic3—182no—
454C2×Dic3—362no—
455C2×Dic3C22×D911yescharacteristic
456C2×Dic3C22×D911yescharacteristic
457C2×Dic3C22×D911yescharacteristic
458C2×Dic3C22×D911yescharacteristic
459Dic6—182no—
460Dic6—182no—
461Dic6—182no—
462Dic6—182no—
463Dic6—362no—
464C2×C32—41no—
465C2×C32D3×#4111yescharacteristic
466C2×C32#101011yescharacteristic
467C2×C32#101011yescharacteristic
468C2×C9—21no—
469C2×C9—21no—
470C2×C9—21no—
471C2×C9—42no—
472C2×C9—41no—
473C2×C9D3×#4111yescharacteristic
474C2×C9#101011yescharacteristic
475C2×C9#101011yescharacteristic
476C2×Q8—271no—
477C2×Q8—271no—
478C22×C4—271no—
479C4⋊C4—31no—
480C4⋊C4—31no—
481C4⋊C4—31no—
482C4⋊C4—91no—
483C4⋊C4—91no—
484C4⋊C4—91no—
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—
495C4⋊C4—271no—
496C4⋊C4—271no—
497C4⋊C4—271no—
498C4⋊C4—271no—
499C22⋊C4—31no—
500C22⋊C4—31no—
501C22⋊C4—91no—
502C22⋊C4—91no—
503C22⋊C4—271no—
504C22⋊C4D3×D911yescharacteristic
505C42—31no—
506C42—91no—
507C42—271no—
508C42—271no—
509C42—271no—
510C42—271no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3C23×D911yescharacteristic
522C22×C3C22×D3211yescharacteristic
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—41no—
528C3×C4—41no—
529C3×C4—61no—
530C3×C4—61no—
531C3×C4—61no—
532C3×C4—61no—
533C3×C4—181no—
534C3×C4—181no—
535C3×C4—181no—
536C3×C4—181no—
537Dic3—21no—
538Dic3—21no—
539Dic3—21no—
540Dic3—21no—
541Dic3—61no—
542Dic3—61no—
543Dic3—61no—
544Dic3—61no—
545Dic3—92no—
546Dic3—92no—
547Dic3—182no—
548Dic3—181no—
549Dic3—181no—
550Dic3—181no—
551Dic3—181no—
552Dic3—181no—
553Dic3—181no—
554Dic3—361no—
555Dic3—361no—
556Dic3—361no—
557C32#570111yescharacteristic
558C9—21no—
559C9#570111yescharacteristic, complemented
560C23C2×D3×D911yescharacteristic
561Q8—542no—
562Q8—542no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—91no—
568C2×C4—91no—
569C2×C4—91no—
570C2×C4—91no—
571C2×C4—271no—
572C2×C4—271no—
573C2×C4—271no—
574C2×C4—271no—
575C2×C4—542no—
576C2×C4C2×D3×D911yescharacteristic
577C2×C4C2×D3×D911yescharacteristic
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—42no—
582C2×C3—41no—
583C2×C3—41no—
584C2×C3#41×D911yescharacteristic
585C2×C3#6371611yescharacteristic
586C2×C3#6371611yescharacteristic
587C2×C3#6429811yescharacteristic
588C2×C3#6430911yescharacteristic
589C2×C3#6431211yescharacteristic
590C22—21no—
591C22—21no—
592C22—21no—
593C22C22×D3×D911yescharacteristic
594C4—21no—
595C4—21no—
596C4—61no—
597C4—61no—
598C4—61no—
599C4—61no—
600C4—181no—
601C4—181no—
602C4—181no—
603C4—181no—
604C4—272no—
605C4—541no—
606C4—541no—
607C4—541no—
608C3—21no—
609C3#1058980311yescharacteristic, complemented
610C3#1059403111yescharacteristic
611C2—41no—
612C2#1172246511yescharacteristic
613C2#1172249411yescharacteristic
614C2#1172249811yescharacteristic
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. #11720933C2semidirect
9. #11720927C2semidirect
10. #11720919C2semidirect
11. #11720918C2semidirect
12. #11720914C2semidirect
13. #11720913C2semidirect
14. #11720905C2semidirect
15. #11720900C2semidirect
418. C3×C9#541semidirect
559. C9#5701semidirect
609. C3#10589803semidirect

Maximal subgroups

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

subgroupindex
#117217242
C9×#8792
C3×#634412
#117212672
#117212482
#117212472
#117209332
#117209272
#117209192
#117209182
#117209142
#117209132
#117209052
#117209002
#105940313
#105898033