Finite Group Databasebeta

← #13148902

Subgroups — #13148902

Order 1728.

702 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721754C211yesmaximal, characteristic, complemented
2C9×#896C211yesmaximal, characteristic, complemented
3C3×#63452C211yesmaximal, characteristic, complemented
4#11721030C211yesmaximal, characteristic
5#11721020C211yesmaximal, characteristic
6#11721020C211yesmaximal, characteristic
7D3×C4⋊Dic9C211yesmaximal, characteristic, complemented
8#11721011C211yesmaximal, characteristic, complemented
9#11721010C211yesmaximal, characteristic, complemented
10#11720986C211yesmaximal, characteristic, complemented
11#11720921C211yesmaximal, characteristic, complemented
12#11720916C211yesmaximal, characteristic, complemented
13#11720914C211yesmaximal, characteristic, complemented
14#11720911C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594449—31nomaximal
17#10589744—31nomaximal
18C2×C4×D3×C9C2211yescharacteristic
19C2×C9×Dic6C2211yescharacteristic
20C2×#6195C2211yescharacteristic
21C2×D3×Dic9C2211yescharacteristic
22C2×D3×Dic9C2211yescharacteristic
23C2×(C3⋊D9)⋊C4C2211yescharacteristic
24C3×C9×C4⋊C4C2211yescharacteristic
25#88536C2211yescharacteristic
26#88536C2211yescharacteristic
27#88536C2211yescharacteristic
28C4⋊(C3⋊Dic9)C2211yescharacteristic
29#88534C2211yescharacteristic
30C4×C3⋊Dic9C2211yescharacteristic
31C9×(C2×D3)⋊C4C2211yescharacteristic
32C9×(C2×D3)⋊C4C2211yescharacteristic
33C9×Dic3⋊C4C2211yescharacteristic
34C9×Dic3⋊C4C2211yescharacteristic
35C3×C4⋊Dic9C2211yescharacteristic
36C3×C4⋊Dic9C2211yescharacteristic
37C3×C4⋊Dic9C2211yescharacteristic
38C3×Dic9⋊C4C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40C3×C4×Dic9C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44Dic3⋊Dic9C2211yescharacteristic
45Dic3⋊Dic9C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic3×Dic9C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64107—31no—
54C3×#896D311yescharacteristic
55C3×#890—31no—
56#63904—31no—
57#63890—31no—
58#63890—31no—
59D3×C4⋊Dic3—31no—
60#63888—31no—
61#63878—31no—
62#63877—31no—
63#63848—31no—
64#63846—31no—
65#63845—31no—
66#63843—31no—
67#63836—31no—
68C9×C22⋊Q8—31no—
69#63508—31no—
70Q8×Dic9—31no—
71C4×#611—31no—
72C2×C4⋊Dic9—31no—
73#63460—31no—
74#63460—31no—
75#63460—61no—
76#63454—31no—
77#63452—31no—
78#63452—31no—
79#63452D311yescharacteristic, complemented
80#63448—31no—
81#63448—31no—
82#63439—31no—
83#63439—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C2×C3×C4×C9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3⋊Dic9C2311yescharacteristic
90C2×C3⋊Dic9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C9×Dic3C2311yescharacteristic
93C2×C9×Dic3C2311yescharacteristic
94C2×C9×Dic3C2311yescharacteristic
95C2×C3×Dic9C2311yescharacteristic
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C4×D3×C9—22no—
100C9×Dic6—22no—
101#6195—22no—
102D3×Dic9—22no—
103D3×Dic9—22no—
104(C3⋊D9)⋊C4—22no—
105#5693—91no—
106#5642—91no—
107C2×C3×C4×D3C2×D311yescharacteristic
108C2×C3×Dic6C2×D311yescharacteristic
109C2×#626—31no—
110C2×#624—31no—
111C2×D3×Dic3—31no—
112C2×D3×Dic3—31no—
113C32×C4⋊C4C2×D311yescharacteristic
114#3752—31no—
115#3752—31no—
116#3752—31no—
117C4⋊(C3⋊Dic3)—31no—
118#3750—31no—
119C4×C3⋊Dic3—31no—
120C3×(C2×D3)⋊C4C2×D311yescharacteristic
121C3×(C2×D3)⋊C4C2×D311yescharacteristic
122C3×C4⋊Dic3—31no—
123C3×C4⋊Dic3—31no—
124C3×C4⋊Dic3—31no—
125C3×Dic3⋊C4—31no—
126C3×Dic3⋊C4—31no—
127C3×Dic3⋊C4C2×D311yescharacteristic
128C3×Dic3⋊C4C2×D311yescharacteristic
129C3×C4×Dic3—31no—
130#3724—31no—
131Dic3⋊Dic3—31no—
132Dic3⋊Dic3—31no—
133Dic3⋊Dic3—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136#3722—31no—
137#3722—31no—
138(C2×D3)⋊Dic3—31no—
139Dic32—31no—
140Dic32—31no—
141Dic32—31no—
142C2×Q8×C9—31no—
143C22×C4×C9—31no—
144C2×#611—31no—
145C22×Dic9—31no—
146C22×Dic9—31no—
147C2×C4×D9—31no—
148C9×C4⋊C4—21no—
149C9×C4⋊C4—31no—
150C9×C4⋊C4—31no—
151C9×C4⋊C4C2×D311yescharacteristic
152C9×C22⋊C4—31no—
153C9×C22⋊C4—31no—
154#3676—31no—
155(C2×D9)⋊C4—31no—
156(C2×D9)⋊C4—31no—
157(C2×D9)⋊C4—31no—
158(C2×D9)⋊C4—31no—
159(C2×D9)⋊C4—31no—
160(C2×D9)⋊C4—61no—
161(C2×D9)⋊C4—61no—
162(C2×D9)⋊C4—61no—
163C4⋊Dic9—31no—
164C4⋊Dic9—31no—
165C4⋊Dic9—31no—
166C4⋊Dic9—31no—
167C4⋊Dic9—31no—
168C4⋊Dic9—61no—
169C4⋊Dic9C2×D311yescharacteristic
170C4⋊Dic9C2×D311yescharacteristic
171C4⋊Dic9C2×D311yescharacteristic
172Dic9⋊C4—31no—
173Dic9⋊C4—31no—
174Dic9⋊C4—31no—
175Dic9⋊C4—61no—
176Dic9⋊C4C2×D311yescharacteristic
177Dic9⋊C4C2×D311yescharacteristic
178C4×Dic9—31no—
179C4×Dic9—31no—
180C4×Dic9—31no—
181C4×Dic9—31no—
182C4×Dic9—61no—
183C4×Dic9C2×D311yescharacteristic
184C22×C3×C9C2411yescharacteristic
185C2×C3⋊D9—21no—
186C2×C3⋊D9—21no—
187C2×C3⋊D9—21no—
188C2×D3×C9—21no—
189C2×D3×C9—21no—
190C2×D3×C9#4112yes—
191C3×C4×C9—21no—
192C3×C4×C9—21no—
193C3×C4×C9—21no—
194C3⋊Dic9—21no—
195C3⋊Dic9—21no—
196C3⋊Dic9—21no—
197C9×Dic3—21no—
198C9×Dic3—21no—
199C9×Dic3#4112yes—
200C3×Dic9—21no—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×#125—91no—
205C3×C22⋊Q8—31no—
206#946—91no—
207Q8×Dic3—91no—
208C4×#67—91no—
209C2×C4⋊Dic3—91no—
210#898—91no—
211#898—91no—
212#898—91no—
213#898—91no—
214#898—181no—
215#896—91no—
216#896D911yescharacteristic, complemented
217#894—91no—
218#894—91no—
219#893—91no—
220#892—91no—
221#892—91no—
222D3×C4⋊C4—91no—
223#890—31no—
224#890—91no—
225#890—91no—
226#889—91no—
227#889—91no—
228#887—91no—
229#886—91no—
230#886—91no—
231#877—91no—
232#877—91no—
233#872—91no—
234#872—91no—
235C22×C3⋊D3—31no—
236C22×C3×D3C22×D311yescharacteristic
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240C2×C3⋊Dic3—31no—
241C2×C3⋊Dic3—31no—
242C2×C3⋊Dic3—31no—
243C2×C3×Dic3—31no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3C22×D311yescharacteristic
248C2×C3×Dic3C22×D311yescharacteristic
249C2×C3×Dic3C22×D311yescharacteristic
250C3×C4×D3—22no—
251C3×Dic6—22no—
252#626—62no—
253#624—62no—
254D3×Dic3—62no—
255D3×Dic3—62no—
256C23×C9—31no—
257C22×D9—31no—
258C22×D9—61no—
259Q8×C9—62no—
260C2×C4×C9—21no—
261C2×C4×C9—21no—
262C2×C4×C9—21no—
263C2×C4×C9—31no—
264C2×C4×C9—31no—
265C2×C4×C9—31no—
266C2×C4×C9—62no—
267C2×C4×C9C22×D311yescharacteristic
268C2×C4×C9C22×D311yescharacteristic
269C2×C4×C9C22×D311yescharacteristic
270#611—62no—
271C2×Dic9—31no—
272C2×Dic9—31no—
273C2×Dic9—31no—
274C2×Dic9—61no—
275C2×Dic9—61no—
276C2×Dic9—61no—
277C2×Dic9—62no—
278C2×Dic9—62no—
279C2×Dic9C22×D311yescharacteristic
280C2×Dic9C22×D311yescharacteristic
281C2×Dic9C22×D311yescharacteristic
282C2×Dic9C22×D311yescharacteristic
283C4×D9—62no—
284#552—271noSylow
285C2×C3×C9C2×#4111yescharacteristic
286C2×C3×C9C2×#4111yescharacteristic
287C2×C3×C92−1+411yescharacteristic
288C3⋊D9—41no—
289D3×C9—22no—
290C2×C3×Q8—31no—
291C22×C3×C4—31no—
292C2×#67—91no—
293C22×Dic3—91no—
294C22×Dic3—91no—
295C2×D12—91no—
296C2×C4×D3—91no—
297C2×C4×D3—91no—
298C2×C4×D3—91no—
299C2×C4×D3—91no—
300C2×C4×D3C2×D911yescharacteristic
301C2×Dic6C2×D911yescharacteristic
302C3×C4⋊C4—21no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—91no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4—91no—
308C3×C4⋊C4—91no—
309C3×C4⋊C4—91no—
310C3×C4⋊C4C2×D911yescharacteristic
311C3×C4⋊C4D3211yescharacteristic
312C3×C22⋊C4—31no—
313C3×C22⋊C4—31no—
314C3×C42—91no—
315#217—91no—
316(C2×D3)⋊C4—91no—
317(C2×D3)⋊C4—91no—
318(C2×D3)⋊C4—91no—
319(C2×D3)⋊C4—91no—
320(C2×D3)⋊C4—91no—
321(C2×D3)⋊C4—91no—
322(C2×D3)⋊C4—91no—
323(C2×D3)⋊C4—91no—
324(C2×D3)⋊C4—91no—
325(C2×D3)⋊C4—91no—
326(C2×D3)⋊C4—91no—
327(C2×D3)⋊C4—181no—
328(C2×D3)⋊C4—181no—
329(C2×D3)⋊C4—181no—
330(C2×D3)⋊C4C2×D911yescharacteristic
331(C2×D3)⋊C4C2×D911yescharacteristic
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—91no—
336C4⋊Dic3—91no—
337C4⋊Dic3—91no—
338C4⋊Dic3—91no—
339C4⋊Dic3—91no—
340C4⋊Dic3—91no—
341C4⋊Dic3—91no—
342C4⋊Dic3—181no—
343Dic3⋊C4—31no—
344Dic3⋊C4—31no—
345Dic3⋊C4—91no—
346Dic3⋊C4—91no—
347Dic3⋊C4—91no—
348Dic3⋊C4—91no—
349Dic3⋊C4—91no—
350Dic3⋊C4—91no—
351Dic3⋊C4—91no—
352Dic3⋊C4—91no—
353Dic3⋊C4—91no—
354Dic3⋊C4—181no—
355Dic3⋊C4C2×D911yescharacteristic
356Dic3⋊C4C2×D911yescharacteristic
357C4×Dic3—31no—
358C4×Dic3—91no—
359C4×Dic3—91no—
360C4×Dic3—91no—
361C4×Dic3—91no—
362C4×Dic3—91no—
363C4×Dic3—91no—
364C4×Dic3—91no—
365C4×Dic3—91no—
366C4×Dic3—181no—
367C22×C32C23×D311yescharacteristic
368C2×C3⋊D3—61no—
369C2×C3⋊D3—61no—
370C2×C3⋊D3—61no—
371C2×C3×D3—21no—
372C2×C3×D3—21no—
373C2×C3×D3#23912yes—
374C32×C4—21no—
375C32×C4—21no—
376C32×C4—21no—
377C3⋊Dic3—61no—
378C3⋊Dic3—61no—
379C3⋊Dic3—61no—
380C3×Dic3—21no—
381C3×Dic3—21no—
382C3×Dic3—61no—
383C3×Dic3—61no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3#23712yes—
387C22×C9—21no—
388C22×C9—32no—
389C22×C9—61no—
390C22×C9—61no—
391C22×C9C23×D311yescharacteristic
392C2×D9—61no—
393C2×D9—61no—
394C2×D9—61no—
395C2×D9—121no—
396C2×D9—121no—
397C2×D9—121no—
398C4×C9—21no—
399C4×C9—21no—
400C4×C9—21no—
401C4×C9—32no—
402C4×C9—41no—
403C4×C9—41no—
404C4×C9—41no—
405C4×C9—61no—
406C4×C9—61no—
407Dic9—21no—
408Dic9—21no—
409Dic9—21no—
410Dic9—21no—
411Dic9—61no—
412Dic9—61no—
413Dic9—61no—
414Dic9—121no—
415Dic9—121no—
416Dic9—121no—
417#126—271no—
418#126—271no—
419#125—91no—
420#125—271no—
421#125—271no—
422#123—271no—
423#123—271no—
424C22⋊Q8—31no—
425C22⋊Q8—271no—
426C4×Q8—271no—
427C4×D4—271no—
428#117—271no—
429#117—271no—
430#117—271no—
431C2×C4⋊C4—271no—
432C3×C9#55211yescharacteristic, complemented, Sylow
433C23×C3—31no—
434C22×D3—91no—
435C22×D3—91no—
436C22×D3—181no—
437C22×D3C22×D911yescharacteristic
438C3×Q8—62no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—31no—
445C2×C3×C4—62no—
446C2×C3×C4—91no—
447C2×C3×C4—91no—
448C2×C3×C4—91no—
449C2×C3×C4—91no—
450C2×C3×C4C22×D911yescharacteristic
451C2×C3×C4C22×D911yescharacteristic
452C2×C3×C4C22×D911yescharacteristic
453C2×C3×C4C2×D3211yescharacteristic
454C2×C3×C4C2×D3211yescharacteristic
455C2×C3×C4C2×D3211yescharacteristic
456#67—182no—
457C2×Dic3—31no—
458C2×Dic3—31no—
459C2×Dic3—31no—
460C2×Dic3—31no—
461C2×Dic3—91no—
462C2×Dic3—91no—
463C2×Dic3—91no—
464C2×Dic3—91no—
465C2×Dic3—91no—
466C2×Dic3—91no—
467C2×Dic3—181no—
468C2×Dic3—181no—
469C2×Dic3—181no—
470C2×Dic3—182no—
471C2×Dic3—182no—
472C2×Dic3C22×D911yescharacteristic
473C2×Dic3C22×D911yescharacteristic
474C2×Dic3C22×D911yescharacteristic
475D12—182no—
476C4×D3—22no—
477C4×D3—182no—
478C4×D3—182no—
479C4×D3—182no—
480C4×D3—182no—
481Dic6—22no—
482C2×C32C2×#23711yescharacteristic
483C2×C32C2×#23911yescharacteristic
484C2×C32#101011yescharacteristic
485C3⋊D3—121no—
486C3×D3—22no—
487C2×C9—21no—
488C2×C9—21no—
489C2×C9—21no—
490C2×C9—62no—
491C2×C9#100711yescharacteristic
492C2×C9D3×#4111yescharacteristic
493C2×C9D3×#4111yescharacteristic
494D9—121no—
495D9—241no—
496C2×Q8—31no—
497C2×D4—271no—
498C22×C4—31no—
499C22×C4—271no—
500C22×C4—271no—
501C22×C4—271no—
502C4⋊C4—31no—
503C4⋊C4—31no—
504C4⋊C4—91no—
505C4⋊C4—91no—
506C4⋊C4—91no—
507C4⋊C4—91no—
508C4⋊C4—91no—
509C4⋊C4—271no—
510C4⋊C4—271no—
511C4⋊C4—271no—
512C4⋊C4—271no—
513C4⋊C4—271no—
514C4⋊C4—271no—
515C4⋊C4—271no—
516C4⋊C4—271no—
517C4⋊C4D3×D911yescharacteristic
518C22⋊C4—31no—
519C22⋊C4—31no—
520C22⋊C4—271no—
521C22⋊C4—271no—
522C22⋊C4—271no—
523C22⋊C4—271no—
524C22⋊C4—271no—
525C22⋊C4—271no—
526C42—91no—
527C42—271no—
528C42—271no—
529C42—271no—
530C42—271no—
531C22×C3—21no—
532C22×C3—32no—
533C22×C3—61no—
534C22×C3—61no—
535C22×C3C23×D911yescharacteristic
536C22×C3C22×D3211yescharacteristic
537C2×D3—21no—
538C2×D3—21no—
539C2×D3—181no—
540C2×D3—181no—
541C2×D3—181no—
542C2×D3—181no—
543C2×D3—181no—
544C2×D3—181no—
545C2×D3—361no—
546C2×D3—361no—
547C2×D3—361no—
548C2×D3#370112yes—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—32no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—41no—
559C3×C4—61no—
560C3×C4—61no—
561C3×C4—181no—
562C3×C4—181no—
563C3×C4—181no—
564C3×C4—181no—
565Dic3—21no—
566Dic3—21no—
567Dic3—61no—
568Dic3—61no—
569Dic3—61no—
570Dic3—61no—
571Dic3—181no—
572Dic3—181no—
573Dic3—181no—
574Dic3—181no—
575Dic3—181no—
576Dic3—181no—
577Dic3—361no—
578Dic3—361no—
579Dic3—361no—
580Dic3#369912yes—
581C32#564211yescharacteristic
582C9—21no—
583C9#569311yescharacteristic, complemented
584C23—31no—
585C23—271no—
586Q8—62no—
587D4—542no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—62no—
592C2×C4—91no—
593C2×C4—91no—
594C2×C4—91no—
595C2×C4—91no—
596C2×C4—271no—
597C2×C4—271no—
598C2×C4—271no—
599C2×C4—542no—
600C2×C4—542no—
601C2×C4—542no—
602C2×C4C2×D3×D911yescharacteristic
603C2×C4C2×D3×D911yescharacteristic
604C2×C4C2×D3×D911yescharacteristic
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—62no—
609C2×C3C2×#369911yescharacteristic
610C2×C3C2×#370111yescharacteristic
611C2×C3#6371611yescharacteristic
612C2×C3#6429711yescharacteristic
613C2×C3D3×#23711yescharacteristic
614C2×C3D3×#23911yescharacteristic
615D3—22no—
616D3—361no—
617D3—361no—
618D3—721no—
619C22—32no—
620C22—61no—
621C22—61no—
622C22—541no—
623C22—541no—
624C22—541no—
625C22C22×D3×D911yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—32no—
630C4—61no—
631C4—61no—
632C4—181no—
633C4—181no—
634C4—181no—
635C4—181no—
636C4—541no—
637C4—541no—
638C4—541no—
639C3—21no—
640C3#1058974411yescharacteristic, complemented
641C3#1059444911yescharacteristic
642C2—62no—
643C2—1081no—
644C2#1172246411yescharacteristic
645C2D3×#369911yescharacteristic
646C2D3×#370111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#6195C22
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#552
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721754C2semidirect
2. C9×#896C2semidirect
3. C3×#63452C2semidirect
7. D3×C4⋊Dic9C2semidirect
8. #11721011C2semidirect
9. #11721010C2semidirect
10. #11720986C2semidirect
11. #11720921C2semidirect
12. #11720916C2semidirect
13. #11720914C2semidirect
14. #11720911C2semidirect
15. #11720899C2semidirect
79. #63452D3semidirect
216. #896D9semidirect
432. C3×C9#552semidirect
583. C9#5693semidirect
640. C3#10589744semidirect

Maximal subgroups

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

subgroupindex
#117217542
C9×#8962
C3×#634522
#117210302
#117210202
D3×C4⋊Dic92
#117210112
#117210102
#117209862
#117209212
#117209162
#117209142
#117209112
#117208992
#105944493
#105897443