Finite Group Databasebeta

← #13148848

Subgroups — #13148848

Order 1728.

770 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×C3⋊D9C211yesmaximal, characteristic
2C9×#889C211yesmaximal, characteristic, complemented
3C3×#63451C211yesmaximal, characteristic, complemented
4#11721000C211yesmaximal, characteristic
5#11720980C211yesmaximal, characteristic
6#11720980C211yesmaximal, characteristic
7#11720980C211yesmaximal, characteristic
8#11720980C211yesmaximal, characteristic
9C4×(C3⋊D9)⋊C4C211yesmaximal, characteristic
10#11720933C211yesmaximal, characteristic, complemented
11#11720925C211yesmaximal, characteristic, complemented
12#11720917C211yesmaximal, characteristic, complemented
13#11720916C211yesmaximal, characteristic, complemented
14#11720915C211yesmaximal, characteristic, complemented
15#11720914C211yesmaximal, characteristic, complemented
16#10594399—31nomaximal
17D9×#125—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×(C3⋊D9)⋊C4C2211yescharacteristic
22C2×(C3⋊D9)⋊C4C2211yescharacteristic
23C2×(C3⋊D9)⋊C4C2211yescharacteristic
24C2×(C3⋊D9)⋊C4C2211yescharacteristic
25C3×C9×C4⋊C4C2211yescharacteristic
26C4⋊(C3⋊Dic9)C2211yescharacteristic
27#88534C2211yescharacteristic
28#88534C2211yescharacteristic
29C9×C4⋊Dic3C2211yescharacteristic
30C9×Dic3⋊C4C2211yescharacteristic
31C9×Dic3⋊C4C2211yescharacteristic
32C9×Dic3⋊C4C2211yescharacteristic
33C9×Dic3⋊C4C2211yescharacteristic
34C4×C9×Dic3C2211yescharacteristic
35C3×C4⋊Dic9C2211yescharacteristic
36C3×Dic9⋊C4C2211yescharacteristic
37C3×Dic9⋊C4C2211yescharacteristic
38C3×Dic9⋊C4C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40C3×C4×Dic9C2211yescharacteristic
41Dic3⋊Dic9C2211yescharacteristic
42Dic3⋊Dic9C2211yescharacteristic
43Dic3⋊Dic9C2211yescharacteristic
44Dic3⋊Dic9C2211yescharacteristic
45#88442C2211yescharacteristic
46#88442C2211yescharacteristic
47Dic9⋊Dic3C2211yescharacteristic
48Dic9⋊Dic3C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53C4⋊C4×C3⋊D3—31no—
54C3×#889—31no—
55C3×#889D311yescharacteristic
56#63900—31no—
57#63883—31no—
58#63883—31no—
59#63883—31no—
60#63883—31no—
61C4×#624—31no—
62#63867—31no—
63#63867—31no—
64#63846—31no—
65#63846—31no—
66#63845—31no—
67#63845—31no—
68C9×#125—31no—
69C4⋊C4×D9—31no—
70C4⋊C4×D9—31no—
71C4⋊C4×D9—31no—
72C4⋊C4×D9—31no—
73C4⋊C4×D9—31no—
74C4⋊C4×D9—31no—
75C4⋊C4×D9—61no—
76#63452—31no—
77#63452—31no—
78#63451—31no—
79#63451—31no—
80#63451—31no—
81#63451D311yescharacteristic, complemented
82C42×D9—31no—
83#63432—31no—
84C22×C3⋊D9C2311yescharacteristic
85C2×C3×C4×C9C2311yescharacteristic
86C2×C3×C4×C9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3⋊Dic9C2311yescharacteristic
89C2×C3⋊Dic9C2311yescharacteristic
90C2×C3⋊Dic9C2311yescharacteristic
91C4×C3⋊D9—22no—
92C4×C3⋊D9—22no—
93C4×C3⋊D9—22no—
94C2×C9×Dic3C2311yescharacteristic
95C2×C9×Dic3C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102(C3⋊D9)⋊C4—22no—
103(C3⋊D9)⋊C4—22no—
104(C3⋊D9)⋊C4—22no—
105(C3⋊D9)⋊C4Q814yes—
106D3×#125—91no—
107D3×#125—91no—
108C2×C4×C3⋊D3—31no—
109C2×C4×C3⋊D3—31no—
110C2×C4×C3⋊D3—31no—
111C2×#624—31no—
112C2×#624—31no—
113C2×#624—31no—
114C2×#624—31no—
115C32×C4⋊C4C2×D311yescharacteristic
116C4⋊(C3⋊Dic3)—31no—
117#3750—31no—
118#3750—31no—
119C3×C4⋊Dic3—31no—
120C3×C4⋊Dic3C2×D311yescharacteristic
121C3×Dic3⋊C4—31no—
122C3×Dic3⋊C4—31no—
123C3×Dic3⋊C4—31no—
124C3×Dic3⋊C4—31no—
125C3×Dic3⋊C4C2×D311yescharacteristic
126C3×Dic3⋊C4C2×D311yescharacteristic
127C3×Dic3⋊C4C2×D311yescharacteristic
128C3×Dic3⋊C4C2×D311yescharacteristic
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—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140Dic3⋊Dic3—31no—
141Dic32—31no—
142Dic32—31no—
143C2×C4×D9—31no—
144C2×C4×D9—31no—
145C2×C4×D9—31no—
146C2×C4×D9—31no—
147C2×C4×D9—31no—
148C2×C4×D9—31no—
149C2×C4×D9—31no—
150C2×C4×D9—61no—
151C2×C4×D9—61no—
152C2×C4×D9—61no—
153C9×C4⋊C4—21no—
154C9×C4⋊C4—31no—
155C9×C4⋊C4—31no—
156C9×C4⋊C4—31no—
157C9×C4⋊C4—31no—
158C9×C4⋊C4—31no—
159C9×C4⋊C4C2×D311yescharacteristic
160C42×C9—31no—
161C4⋊Dic9—31no—
162C4⋊Dic9—31no—
163C4⋊Dic9—31no—
164C4⋊Dic9—31no—
165C4⋊Dic9—31no—
166C4⋊Dic9—61no—
167C4⋊Dic9C2×D311yescharacteristic
168Dic9⋊C4—31no—
169Dic9⋊C4—31no—
170Dic9⋊C4—31no—
171Dic9⋊C4—31no—
172Dic9⋊C4—31no—
173Dic9⋊C4—31no—
174Dic9⋊C4—31no—
175Dic9⋊C4—31no—
176Dic9⋊C4—61no—
177Dic9⋊C4—61no—
178Dic9⋊C4C2×D311yescharacteristic
179Dic9⋊C4C2×D311yescharacteristic
180Dic9⋊C4C2×D311yescharacteristic
181Dic9⋊C4C2×D311yescharacteristic
182C4×Dic9—31no—
183C4×Dic9—31no—
184C4×Dic9C2×D311yescharacteristic
185C22×C3×C9C2411yescharacteristic
186C2×C3⋊D9C2×Q812yes—
187C2×C3⋊D9#4112yes—
188C2×C3⋊D9#4112yes—
189C3×C4×C9—21no—
190C3×C4×C9—21no—
191C3×C4×C9—21no—
192C3⋊Dic9—21no—
193C3⋊Dic9—21no—
194C3⋊Dic9—21no—
195C9×Dic3—21no—
196C9×Dic3—21no—
197C9×Dic3—21no—
198C9×Dic3C2×Q812yes—
199C3×Dic9—21no—
200C3×Dic9—21no—
201C3×Dic9—21no—
202C3×Dic9C2×Q812yes—
203C3×#125—31no—
204C3×#125—91no—
205D3×C4⋊C4—91no—
206D3×C4⋊C4—91no—
207D3×C4⋊C4—91no—
208D3×C4⋊C4—91no—
209D3×C4⋊C4—91no—
210D3×C4⋊C4—91no—
211D3×C4⋊C4—91no—
212D3×C4⋊C4—91no—
213D3×C4⋊C4—91no—
214D3×C4⋊C4—91no—
215D3×C4⋊C4—91no—
216D3×C4⋊C4—91no—
217D3×C4⋊C4—181no—
218#890—91no—
219#890—91no—
220#890—91no—
221#890—91no—
222#889—31no—
223#889—91no—
224#889—91no—
225#889—91no—
226#889—91no—
227#889—91no—
228#889—91no—
229#889D911yescharacteristic, complemented
230C42×D3—91no—
231C42×D3—91no—
232#870—91no—
233#870—91no—
234C22×C3⋊D3—31no—
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C22×D311yescharacteristic
237C2×C32×C4C22×D311yescharacteristic
238C2×C3⋊Dic3—31no—
239C2×C3⋊Dic3—31no—
240C2×C3⋊Dic3—31no—
241C4×C3⋊D3—62no—
242C4×C3⋊D3—62no—
243C4×C3⋊D3—62no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3C22×D311yescharacteristic
249C2×C3×Dic3C22×D311yescharacteristic
250C2×C3×Dic3C22×D311yescharacteristic
251C2×C3×Dic3C22×D311yescharacteristic
252#624—34no—
253#624—62no—
254#624—62no—
255#624—62no—
256C22×D9—31no—
257C22×D9—61no—
258C2×C4×C9—21no—
259C2×C4×C9—21no—
260C2×C4×C9—21no—
261C2×C4×C9—31no—
262C2×C4×C9—31no—
263C2×C4×C9—31no—
264C2×C4×C9—31no—
265C2×C4×C9C22×D311yescharacteristic
266C2×C4×C9C22×D311yescharacteristic
267C2×C4×C9C22×D311yescharacteristic
268C2×Dic9—31no—
269C2×Dic9—31no—
270C2×Dic9—31no—
271C2×Dic9—61no—
272C2×Dic9—61no—
273C2×Dic9—61no—
274C2×Dic9C22×D311yescharacteristic
275C2×Dic9C22×D311yescharacteristic
276C2×Dic9C22×D311yescharacteristic
277C2×Dic9C22×D311yescharacteristic
278C4×D9—34no—
279C4×D9—62no—
280C4×D9—62no—
281C4×D9—62no—
282C4×D9—62no—
283C4×D9—62no—
284C4×D9—62no—
285C4×D9—64no—
286C4×D9—122no—
287C4×D9—122no—
288C2×#125—271noSylow
289C2×C3×C9C22×Q811yescharacteristic
290C2×C3×C9C2×#4111yescharacteristic
291C2×C3×C9C2×#4111yescharacteristic
292C3⋊D9#12514yescomplemented
293C2×C4×D3—91no—
294C2×C4×D3—91no—
295C2×C4×D3—91no—
296C2×C4×D3—91no—
297C2×C4×D3—91no—
298C2×C4×D3—91no—
299C2×C4×D3—91no—
300C2×C4×D3—91no—
301C2×C4×D3—91no—
302C2×C4×D3—91no—
303C2×C4×D3—91no—
304C2×C4×D3—91no—
305C2×C4×D3—91no—
306C2×C4×D3—91no—
307C2×C4×D3—181no—
308C2×C4×D3—181no—
309C2×C4×D3—181no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4—91no—
319C3×C4⋊C4—91no—
320C3×C4⋊C4—91no—
321C3×C4⋊C4C2×D911yescharacteristic
322C3×C4⋊C4D3211yescharacteristic
323C3×C42—31no—
324C3×C42—91no—
325C4⋊Dic3—31no—
326C4⋊Dic3—91no—
327C4⋊Dic3—91no—
328C4⋊Dic3—91no—
329C4⋊Dic3—91no—
330C4⋊Dic3—91no—
331C4⋊Dic3—91no—
332C4⋊Dic3—91no—
333C4⋊Dic3—91no—
334C4⋊Dic3—91no—
335C4⋊Dic3—91no—
336C4⋊Dic3—181no—
337C4⋊Dic3C2×D911yescharacteristic
338Dic3⋊C4—31no—
339Dic3⋊C4—31no—
340Dic3⋊C4—31no—
341Dic3⋊C4—31no—
342Dic3⋊C4—91no—
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—91no—
355Dic3⋊C4—91no—
356Dic3⋊C4—91no—
357Dic3⋊C4—91no—
358Dic3⋊C4—181no—
359Dic3⋊C4—181no—
360Dic3⋊C4C2×D911yescharacteristic
361Dic3⋊C4C2×D911yescharacteristic
362Dic3⋊C4C2×D911yescharacteristic
363Dic3⋊C4C2×D911yescharacteristic
364C4×Dic3—31no—
365C4×Dic3—91no—
366C4×Dic3—91no—
367C4×Dic3—91no—
368C4×Dic3—91no—
369C4×Dic3C2×D911yescharacteristic
370C22×C32C23×D311yescharacteristic
371C2×C3⋊D3—32no—
372C2×C3⋊D3—32no—
373C2×C3⋊D3—32no—
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—32no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3—61no—
387C3×Dic3D3×Q812yes—
388C22×C9—21no—
389C22×C9C23×D311yescharacteristic
390C2×D9—32no—
391C2×D9—32no—
392C2×D9—32no—
393C2×D9—62no—
394C2×D9—62no—
395C2×D9—62no—
396C4×C9—22no—
397C4×C9—21no—
398C4×C9—21no—
399C4×C9—21no—
400C4×C9—32no—
401C4×C9—41no—
402C4×C9—41no—
403C4×C9—61no—
404C4×C9—61no—
405C4×C9—61no—
406Dic9—21no—
407Dic9—21no—
408Dic9—21no—
409Dic9—62no—
410Dic9—61no—
411Dic9—61no—
412Dic9—61no—
413Dic9—121no—
414Dic9—121no—
415Dic9D3×Q812yes—
416#125—31no—
417#125—91no—
418#125—271no—
419#125—271no—
420#125—271no—
421#125—271no—
422#125—271no—
423#125—271no—
424C2×C4⋊C4—271no—
425C2×C4⋊C4—271no—
426C2×C4⋊C4—271no—
427C2×C4⋊C4—271no—
428C2×C4⋊C4—271no—
429C2×C4⋊C4—271no—
430C2×C42—271no—
431C3×C9C2×#12511yescharacteristic, complemented, Sylow
432C22×D3—91no—
433C22×D3—91no—
434C22×D3—181no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—31no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—91no—
443C2×C3×C4—91no—
444C2×C3×C4—91no—
445C2×C3×C4—91no—
446C2×C3×C4C22×D911yescharacteristic
447C2×C3×C4C22×D911yescharacteristic
448C2×C3×C4C22×D911yescharacteristic
449C2×C3×C4C2×D3211yescharacteristic
450C2×C3×C4C2×D3211yescharacteristic
451C2×C3×C4C2×D3211yescharacteristic
452C2×Dic3—31no—
453C2×Dic3—31no—
454C2×Dic3—31no—
455C2×Dic3—31no—
456C2×Dic3—91no—
457C2×Dic3—91no—
458C2×Dic3—91no—
459C2×Dic3—91no—
460C2×Dic3—91no—
461C2×Dic3—91no—
462C2×Dic3—181no—
463C2×Dic3—181no—
464C2×Dic3—181no—
465C2×Dic3C22×D911yescharacteristic
466C2×Dic3C22×D911yescharacteristic
467C2×Dic3C22×D911yescharacteristic
468C2×Dic3C22×D911yescharacteristic
469C4×D3—94no—
470C4×D3—94no—
471C4×D3—182no—
472C4×D3—182no—
473C4×D3—182no—
474C4×D3—182no—
475C4×D3—182no—
476C4×D3—182no—
477C4×D3—182no—
478C4×D3—182no—
479C4×D3—182no—
480C4×D3—182no—
481C4×D3—182no—
482C4×D3—182no—
483C4×D3—184no—
484C4×D3—362no—
485C4×D3—362no—
486C2×C32C2×D3×Q811yescharacteristic
487C2×C32D3×#4111yescharacteristic
488C2×C32D3×#4111yescharacteristic
489C3⋊D3—34no—
490C2×C9—21no—
491C2×C9—21no—
492C2×C9—21no—
493C2×C9C2×D3×Q811yescharacteristic
494C2×C9D3×#4111yescharacteristic
495C2×C9D3×#4111yescharacteristic
496D9—34no—
497D9—64no—
498C22×C4—271no—
499C22×C4—271no—
500C22×C4—271no—
501C22×C4—271no—
502C22×C4—271no—
503C22×C4—271no—
504C22×C4—271no—
505C4⋊C4—31no—
506C4⋊C4—31no—
507C4⋊C4—31no—
508C4⋊C4—31no—
509C4⋊C4—31no—
510C4⋊C4—91no—
511C4⋊C4—91no—
512C4⋊C4—91no—
513C4⋊C4—91no—
514C4⋊C4—91no—
515C4⋊C4—271no—
516C4⋊C4—271no—
517C4⋊C4—271no—
518C4⋊C4—271no—
519C4⋊C4—271no—
520C4⋊C4—271no—
521C4⋊C4—271no—
522C4⋊C4—271no—
523C4⋊C4—271no—
524C4⋊C4—271no—
525C4⋊C4—271no—
526C4⋊C4—271no—
527C4⋊C4—271no—
528C4⋊C4D3×D911yescharacteristic
529C42—31no—
530C42—91no—
531C42—271no—
532C42—271no—
533C22×C3—21no—
534C22×C3C23×D911yescharacteristic
535C22×C3C22×D3211yescharacteristic
536C2×D3—92no—
537C2×D3—92no—
538C2×D3—92no—
539C2×D3—92no—
540C2×D3—92no—
541C2×D3—92no—
542C2×D3—182no—
543C2×D3—182no—
544C2×D3—182no—
545C3×C4—22no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—32no—
553C3×C4—41no—
554C3×C4—41no—
555C3×C4—61no—
556C3×C4—61no—
557C3×C4—61no—
558C3×C4—92no—
559C3×C4—181no—
560C3×C4—181no—
561C3×C4—181no—
562Dic3—21no—
563Dic3—21no—
564Dic3—21no—
565Dic3—32no—
566Dic3—61no—
567Dic3—61no—
568Dic3—61no—
569Dic3—182no—
570Dic3—181no—
571Dic3—181no—
572Dic3—181no—
573Dic3—181no—
574Dic3—181no—
575Dic3—181no—
576Dic3—361no—
577Dic3—361no—
578Dic3Q8×D912yes—
579C32D3×#12511yescharacteristic
580C9—21no—
581C9D3×#12511yescharacteristic, complemented
582C23—271no—
583C2×C4—31no—
584C2×C4—31no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—91no—
588C2×C4—91no—
589C2×C4—91no—
590C2×C4—91no—
591C2×C4—274no—
592C2×C4—271no—
593C2×C4—271no—
594C2×C4—271no—
595C2×C4—542no—
596C2×C4—542no—
597C2×C4—542no—
598C2×C4—542no—
599C2×C4—542no—
600C2×C4—542no—
601C2×C4C2×D3×D911yescharacteristic
602C2×C4C2×D3×D911yescharacteristic
603C2×C4C2×D3×D911yescharacteristic
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3C2×Q8×D911yescharacteristic
608C2×C3#41×D911yescharacteristic
609C2×C3#41×D911yescharacteristic
610C2×C3#6430611yescharacteristic
611C2×C3#6431211yescharacteristic
612C2×C3D32×Q811yescharacteristic
613D3—94no—
614D3—94no—
615D3—184no—
616C22—272no—
617C22—272no—
618C22—272no—
619C22C22×D3×D911yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—32no—
624C4—61no—
625C4—61no—
626C4—61no—
627C4—92no—
628C4—181no—
629C4—181no—
630C4—181no—
631C4—541no—
632C4—541no—
633C4—541no—
634C3—21no—
635C3D9×#12511yescharacteristic, complemented
636C3#1059439911yescharacteristic
637C2—274no—
638C2#1172247511yescharacteristic
639C2#1172249811yescharacteristic
640C2D3×Q8×D911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC22×C3⋊D9C23
hypercenterC4⋊C4D3×D9
hypocenterC3×C9C2×#125
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C9×#889C2semidirect
3. C3×#63451C2semidirect
10. #11720933C2semidirect
11. #11720925C2semidirect
12. #11720917C2semidirect
13. #11720916C2semidirect
14. #11720915C2semidirect
15. #11720914C2semidirect
81. #63451D3semidirect
229. #889D9semidirect
292. C3⋊D9#125semidirect
431. C3×C9C2×#125semidirect
581. C9D3×#125semidirect
635. C3D9×#125semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C3⋊D92
C9×#8892
C3×#634512
#117210002
#117209802
C4×(C3⋊D9)⋊C42
#117209332
#117209252
#117209172
#117209162
#117209152
#117209142
#105943993
D9×#1253