Finite Group Databasebeta

← #13148862

Subgroups — #13148862

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
2C3×#63454C211yesmaximal, characteristic, complemented
3C9×#889C211yesmaximal, characteristic, complemented
4#11720995C211yesmaximal, characteristic, complemented
5#11720991C211yesmaximal, characteristic, complemented
6#11720988C211yesmaximal, characteristic
7#11720977C211yesmaximal, characteristic
8#11720975C211yesmaximal, characteristic, complemented
9D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
10C4×#6189C211yesmaximal, characteristic, complemented
11#11720938C211yesmaximal, characteristic
12#11720935C211yesmaximal, characteristic, complemented
13#11720934C211yesmaximal, characteristic, complemented
14#11720916C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594412—31nomaximal
17#10589796—31nomaximal
18C2×C3×C4×D9C2211yescharacteristic
19C2×#6192C2211yescharacteristic
20C2×(C3⋊D9)⋊C4C2211yescharacteristic
21C2×Dic3×D9C2211yescharacteristic
22C2×Dic3×D9C2211yescharacteristic
23C2×#6189C2211yescharacteristic
24C3×C9×C4⋊C4C2211yescharacteristic
25#88536C2211yescharacteristic
26#88536C2211yescharacteristic
27#88536C2211yescharacteristic
28C4⋊(C3⋊Dic9)C2211yescharacteristic
29#88534C2211yescharacteristic
30C4×C3⋊Dic9C2211yescharacteristic
31C3×(C2×D9)⋊C4C2211yescharacteristic
32C3×(C2×D9)⋊C4C2211yescharacteristic
33C9×C4⋊Dic3C2211yescharacteristic
34C9×Dic3⋊C4C2211yescharacteristic
35C9×Dic3⋊C4C2211yescharacteristic
36C9×Dic3⋊C4C2211yescharacteristic
37C9×Dic3⋊C4C2211yescharacteristic
38C4×C9×Dic3C2211yescharacteristic
39C3×C4⋊Dic9C2211yescharacteristic
40C3×C4×Dic9C2211yescharacteristic
41C3×C4×Dic9C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45Dic3⋊Dic9C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49#88442C2211yescharacteristic
50#88442C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64107—31no—
54C3×#892—31no—
55C3×#889D311yescharacteristic
56C4×#627—31no—
57#63895—31no—
58#63893—31no—
59#63890—31no—
60#63880—31no—
61#63878—31no—
62D3×Dic3⋊C4—31no—
63#63869—31no—
64#63868—31no—
65#63850—31no—
66#63846—31no—
67#63836—31no—
68C9×#125—31no—
69#63460—31no—
70#63460—31no—
71#63460—61no—
72#63459—31no—
73#63459—31no—
74#63456—31no—
75#63456—31no—
76#63454—31no—
77#63454—31no—
78#63454D311yescharacteristic, complemented
79C4⋊C4×D9—31no—
80#63452—31no—
81#63452—31no—
82C4×D36—31no—
83C4×Dic18—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
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×C9×Dic3C2311yescharacteristic
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C3×C4×D9—22no—
100#6192—22no—
101(C3⋊D9)⋊C4—22no—
102Dic3×D9—22no—
103Dic3×D9—22no—
104#6189—22no—
105#5694—91no—
106#5531—91no—
107C2×C3×C4×D3—31no—
108C2×#627—31no—
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)⋊C4—31no—
121C3×(C2×D3)⋊C4—31no—
122C3×C4⋊Dic3—31no—
123C3×C4⋊Dic3C2×D311yescharacteristic
124C3×Dic3⋊C4C2×D311yescharacteristic
125C3×Dic3⋊C4C2×D311yescharacteristic
126C3×Dic3⋊C4C2×D311yescharacteristic
127C3×Dic3⋊C4C2×D311yescharacteristic
128C3×C4×Dic3—31no—
129C3×C4×Dic3—31no—
130C3×C4×Dic3C2×D311yescharacteristic
131#3724—31no—
132#3724—31no—
133Dic3⋊Dic3—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—31no—
138#3722—31no—
139#3722—31no—
140(C2×D3)⋊Dic3—31no—
141Dic32—31no—
142C2×D36—31no—
143C2×C4×D9—31no—
144C2×C4×D9—31no—
145C2×C4×D9—31no—
146C2×C4×D9C2×D311yescharacteristic
147C2×Dic18—31no—
148C9×C4⋊C4—21no—
149C9×C4⋊C4—31no—
150C9×C4⋊C4—31no—
151C9×C4⋊C4—31no—
152C9×C4⋊C4—31no—
153C9×C4⋊C4—31no—
154C9×C4⋊C4C2×D311yescharacteristic
155C42×C9—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—31no—
161(C2×D9)⋊C4—31no—
162(C2×D9)⋊C4—61no—
163(C2×D9)⋊C4—61no—
164(C2×D9)⋊C4—61no—
165(C2×D9)⋊C4C2×D311yescharacteristic
166(C2×D9)⋊C4C2×D311yescharacteristic
167C4⋊Dic9—31no—
168C4⋊Dic9—31no—
169C4⋊Dic9—31no—
170C4⋊Dic9—31no—
171C4⋊Dic9—31no—
172C4⋊Dic9—61no—
173C4⋊Dic9C2×D311yescharacteristic
174Dic9⋊C4—31no—
175Dic9⋊C4—31no—
176Dic9⋊C4—31no—
177Dic9⋊C4—31no—
178Dic9⋊C4—61no—
179C4×Dic9—31no—
180C4×Dic9—31no—
181C4×Dic9—61no—
182C4×Dic9C2×D311yescharacteristic
183C4×Dic9C2×D311yescharacteristic
184C22×C3×C9C2411yescharacteristic
185C2×C3⋊D9—21no—
186C2×C3⋊D9—21no—
187C2×C3⋊D9—21no—
188C2×C3×D9—21no—
189C2×C3×D9—21no—
190C2×C3×D9#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—21no—
200C9×Dic3#4112yes—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×#125—31no—
205C3×#117—91no—
206#929—91no—
207C2×Dic3⋊C4—91no—
208#898—91no—
209#898—91no—
210#898—91no—
211#898—181no—
212#897—91no—
213#897—91no—
214#896—91no—
215#894—91no—
216#894—91no—
217#892—31no—
218#892—91no—
219#892—91no—
220D3×C4⋊C4—91no—
221#890—91no—
222#890—91no—
223#889—91no—
224#889D911yescharacteristic, complemented
225#886—91no—
226#67⋊C4—91no—
227#878—91no—
228#877—91no—
229#876—91no—
230C4×D12—91no—
231#872—91no—
232#870—91no—
233C4×Dic6—91no—
234C4×Dic6—91no—
235C22×C3⋊D3—31no—
236C22×C3×D3—31no—
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×Dic3C22×D311yescharacteristic
247C2×C3×Dic3C22×D311yescharacteristic
248C2×C3×Dic3C22×D311yescharacteristic
249C2×C3×Dic3C22×D311yescharacteristic
250C3×C4×D3—62no—
251#627—62no—
252#626—62no—
253#624—62no—
254D3×Dic3—62no—
255D3×Dic3—62no—
256C22×D9—31no—
257C22×D9—61no—
258C22×D9C22×D311yescharacteristic
259C2×C4×C9—21no—
260C2×C4×C9—21no—
261C2×C4×C9—21no—
262C2×C4×C9—31no—
263C2×C4×C9—31no—
264C2×C4×C9—31no—
265C2×C4×C9—31no—
266C2×C4×C9C22×D311yescharacteristic
267C2×C4×C9C22×D311yescharacteristic
268C2×C4×C9C22×D311yescharacteristic
269C2×Dic9—31no—
270C2×Dic9—31no—
271C2×Dic9—31no—
272C2×Dic9—61no—
273C2×Dic9—61no—
274C2×Dic9—61no—
275C2×Dic9C22×D311yescharacteristic
276C2×Dic9C22×D311yescharacteristic
277C2×Dic9C22×D311yescharacteristic
278D36—62no—
279C4×D9—22no—
280C4×D9—62no—
281C4×D9—62no—
282C4×D9—62no—
283Dic18—62no—
284#552—271noSylow
285C2×C3×C9C2×#4111yescharacteristic
286C2×C3×C9C2×#4111yescharacteristic
287C2×C3×C92−1+411yescharacteristic
288C3⋊D9—41no—
289C3×D9—22no—
290C22×C3×C4—91no—
291C2×#67—91no—
292C22×Dic3—91no—
293C22×Dic3—91no—
294C2×D12—91no—
295C2×C4×D3—31no—
296C2×C4×D3—91no—
297C2×C4×D3—91no—
298C2×C4×D3—91no—
299C2×C4×D3—91no—
300C2×Dic6—91no—
301C2×Dic6—91no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—91no—
309C3×C4⋊C4C2×D911yescharacteristic
310C3×C4⋊C4D3211yescharacteristic
311C3×C22⋊C4—91no—
312C3×C22⋊C4—91no—
313C3×C42—31no—
314C3×C42—91no—
315C3×C42—91no—
316#217—91no—
317(C2×D3)⋊C4—31no—
318(C2×D3)⋊C4—31no—
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—91no—
328(C2×D3)⋊C4—91no—
329(C2×D3)⋊C4—91no—
330(C2×D3)⋊C4—181no—
331(C2×D3)⋊C4—181no—
332(C2×D3)⋊C4—181no—
333C4⋊Dic3—31no—
334C4⋊Dic3—91no—
335C4⋊Dic3—91no—
336C4⋊Dic3—91no—
337C4⋊Dic3—91no—
338C4⋊Dic3—91no—
339C4⋊Dic3—91no—
340C4⋊Dic3—91no—
341C4⋊Dic3—181no—
342C4⋊Dic3C2×D911yescharacteristic
343Dic3⋊C4—91no—
344Dic3⋊C4—91no—
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
357Dic3⋊C4C2×D911yescharacteristic
358Dic3⋊C4C2×D911yescharacteristic
359C4×Dic3—31no—
360C4×Dic3—31no—
361C4×Dic3—91no—
362C4×Dic3—91no—
363C4×Dic3—91no—
364C4×Dic3—91no—
365C4×Dic3—181no—
366C4×Dic3C2×D911yescharacteristic
367C22×C32C23×D311yescharacteristic
368C2×C3⋊D3—61no—
369C2×C3⋊D3—61no—
370C2×C3⋊D3—61no—
371C2×C3×D3—32no—
372C2×C3×D3—61no—
373C2×C3×D3—61no—
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—21no—
383C3×Dic3—61no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3#23912yes—
387C22×C9—21no—
388C22×C9C23×D311yescharacteristic
389C2×D9—21no—
390C2×D9—21no—
391C2×D9—61no—
392C2×D9—61no—
393C2×D9—61no—
394C2×D9—121no—
395C2×D9—121no—
396C2×D9—121no—
397C2×D9#23512yes—
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—
407C4×C9—61no—
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—31no—
420#125—271no—
421#125—271no—
422#123—271no—
423#123—271no—
424C22⋊Q8—271no—
425C22⋊Q8—271no—
426C4×Q8—271no—
427C4×D4—271no—
428#117—91no—
429#117—271no—
430#117—271no—
431C2×C4⋊C4—271no—
432C3×C9#55211yescharacteristic, complemented, Sylow
433C23×C3—91no—
434C22×D3—31no—
435C22×D3—91no—
436C22×D3—91no—
437C22×D3—181no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—31no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—31no—
445C2×C3×C4—91no—
446C2×C3×C4—91no—
447C2×C3×C4—91no—
448C2×C3×C4—182no—
449C2×C3×C4C22×D911yescharacteristic
450C2×C3×C4C22×D911yescharacteristic
451C2×C3×C4C22×D911yescharacteristic
452C2×C3×C4C2×D3211yescharacteristic
453C2×C3×C4C2×D3211yescharacteristic
454C2×C3×C4C2×D3211yescharacteristic
455#67—182no—
456C2×Dic3—31no—
457C2×Dic3—31no—
458C2×Dic3—31no—
459C2×Dic3—91no—
460C2×Dic3—91no—
461C2×Dic3—91no—
462C2×Dic3—91no—
463C2×Dic3—91no—
464C2×Dic3—91no—
465C2×Dic3—181no—
466C2×Dic3—181no—
467C2×Dic3—181no—
468C2×Dic3—182no—
469C2×Dic3—182no—
470C2×Dic3C22×D911yescharacteristic
471C2×Dic3C22×D911yescharacteristic
472C2×Dic3C22×D911yescharacteristic
473C2×Dic3C22×D911yescharacteristic
474D12—182no—
475C4×D3—62no—
476C4×D3—182no—
477C4×D3—182no—
478C4×D3—182no—
479C4×D3—182no—
480Dic6—182no—
481Dic6—182no—
482C2×C32C2×#23911yescharacteristic
483C2×C32D3×#4111yescharacteristic
484C2×C32#101011yescharacteristic
485C3⋊D3—121no—
486C3×D3—62no—
487C2×C9—21no—
488C2×C9—21no—
489C2×C9—21no—
490C2×C9C2×#23511yescharacteristic
491C2×C9D3×#4111yescharacteristic
492C2×C9#101011yescharacteristic
493D9—22no—
494D9—121no—
495D9—241no—
496C2×Q8—271no—
497C2×D4—271no—
498C22×C4—91no—
499C22×C4—271no—
500C22×C4—271no—
501C22×C4—271no—
502C4⋊C4—31no—
503C4⋊C4—31no—
504C4⋊C4—31no—
505C4⋊C4—31no—
506C4⋊C4—31no—
507C4⋊C4—91no—
508C4⋊C4—271no—
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—91no—
519C22⋊C4—91no—
520C22⋊C4—271no—
521C22⋊C4—271no—
522C22⋊C4—271no—
523C22⋊C4—271no—
524C22⋊C4—271no—
525C22⋊C4—271no—
526C42—31no—
527C42—91no—
528C42—91no—
529C42—271no—
530C42—271no—
531C22×C3—21no—
532C22×C3—92no—
533C22×C3—181no—
534C22×C3—181no—
535C22×C3C23×D911yescharacteristic
536C22×C3C22×D3211yescharacteristic
537C2×D3—32no—
538C2×D3—61no—
539C2×D3—61no—
540C2×D3—181no—
541C2×D3—181no—
542C2×D3—181no—
543C2×D3—181no—
544C2×D3—181no—
545C2×D3—181no—
546C2×D3—361no—
547C2×D3—361no—
548C2×D3—361no—
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—61no—
562C3×C4—181no—
563C3×C4—181no—
564C3×C4—181no—
565Dic3—21no—
566Dic3—21no—
567Dic3—21no—
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#370112yes—
581C32#569411yescharacteristic
582C9—21no—
583C9#553111yescharacteristic, complemented
584C23—91no—
585C23—271no—
586Q8—542no—
587D4—542no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—31no—
591C2×C4—31no—
592C2×C4—91no—
593C2×C4—91no—
594C2×C4—91no—
595C2×C4—182no—
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—182no—
609C2×C3C2×#370111yescharacteristic
610C2×C3#41×D911yescharacteristic
611C2×C3#6371611yescharacteristic
612C2×C3D3×#23511yescharacteristic
613C2×C3#6430911yescharacteristic
614C2×C3D3×#23911yescharacteristic
615D3—62no—
616D3—361no—
617D3—361no—
618D3—721no—
619C22—92no—
620C22—181no—
621C22—181no—
622C22—541no—
623C22—541no—
624C22—541no—
625C22C22×D3×D911yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—32no—
630C4—61no—
631C4—61no—
632C4—61no—
633C4—181no—
634C4—181no—
635C4—181no—
636C4—541no—
637C4—541no—
638C4—541no—
639C3—21no—
640C3#1058979611yescharacteristic, complemented
641C3#1059441211yescharacteristic
642C2—182no—
643C2—1081no—
644C2D9×#23511yescharacteristic
645C2#1172249411yescharacteristic
646C2D3×#370111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#6192C22
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. C3×#63454C2semidirect
3. C9×#889C2semidirect
4. #11720995C2semidirect
5. #11720991C2semidirect
8. #11720975C2semidirect
9. D9×Dic3⋊C4C2semidirect
10. C4×#6189C2semidirect
12. #11720935C2semidirect
13. #11720934C2semidirect
14. #11720916C2semidirect
15. #11720899C2semidirect
78. #63454D3semidirect
224. #889D9semidirect
432. C3×C9#552semidirect
583. C9#5531semidirect
640. C3#10589796semidirect

Maximal subgroups

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

subgroupindex
#117217542
C3×#634542
C9×#8892
#117209952
#117209912
#117209882
#117209772
#117209752
D9×Dic3⋊C42
C4×#61892
#117209382
#117209352
#117209342
#117209162
#117208992
#105944123
#105897963