Finite Group Databasebeta

← #13148966

Subgroups — #13148966

Order 1728.

644 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
1#11721746C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63460C211yesmaximal, characteristic, complemented
4#11721044C211yesmaximal, characteristic
5#11721026C211yesmaximal, characteristic, complemented
6#11721023C211yesmaximal, characteristic, complemented
7#11721021C211yesmaximal, characteristic
8#11720999C211yesmaximal, characteristic, complemented
9#11720991C211yesmaximal, characteristic, complemented
10#11720989C211yesmaximal, characteristic
11#11720970C211yesmaximal, characteristic, complemented
12#11720969C211yesmaximal, characteristic, complemented
13#11720963C211yesmaximal, characteristic, complemented
14#11720947C211yesmaximal, characteristic, complemented
15#11720928C211yesmaximal, characteristic, complemented
16#10594507—31nomaximal
17#10589814—31nomaximal
18C2×#6194C2211yescharacteristic
19C2×D3×Dic9C2211yescharacteristic
20C2×Dic3×D9C2211yescharacteristic
21C2×#6189C2211yescharacteristic
22C2×#6189C2211yescharacteristic
23C2×#6189C2211yescharacteristic
24C3×C9×C4⋊C4C2211yescharacteristic
25C4⋊(C3⋊Dic9)C2211yescharacteristic
26C4⋊(C3⋊Dic9)C2211yescharacteristic
27C4⋊(C3⋊Dic9)C2211yescharacteristic
28#88534C2211yescharacteristic
29#88534C2211yescharacteristic
30C4×C3⋊Dic9C2211yescharacteristic
31C9×(C2×D3)⋊C4C2211yescharacteristic
32C9×(C2×D3)⋊C4C2211yescharacteristic
33C9×(C2×D3)⋊C4C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C9×C4⋊Dic3C2211yescharacteristic
38C9×Dic3⋊C4C2211yescharacteristic
39C4×C9×Dic3C2211yescharacteristic
40C3×C4⋊Dic9C2211yescharacteristic
41C3×Dic9⋊C4C2211yescharacteristic
42C3×C4×Dic9C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49#88442C2211yescharacteristic
50#88442C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53#64099—31no—
54C3×#898—31no—
55C3×#898D311yescharacteristic
56#63918—31no—
57#63918—31no—
58#63915—31no—
59#63899—31no—
60#63899—31no—
61#63893—31no—
62#63893—31no—
63#63891—31no—
64#63891—31no—
65#63870—31no—
66#63859—31no—
67#63859—31no—
68C9×#126—31no—
69#63460D311yescharacteristic, complemented
70#63459—31no—
71#63458—31no—
72#63452—31no—
73#63452—61no—
74#63451—31no—
75#63450—31no—
76#63448—31no—
77#63447—31no—
78#63445—31no—
79#63441—31no—
80#63440—31no—
81#63440—31no—
82#63438—31no—
83#63431—31no—
84C22×D3×C9C2311yescharacteristic
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×C3⋊Dic9C2311yescharacteristic
93C2×C9×Dic3C2311yescharacteristic
94C2×C9×Dic3C2311yescharacteristic
95C2×C9×Dic3C2311yescharacteristic
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99#6194—41no—
100D3×Dic9—41no—
101Dic3×D9—41no—
102#6189—41no—
103#6189—41no—
104#6189—41no—
105#5712—91no—
106#5712—91no—
107C2×#627—31no—
108C2×#627—31no—
109C2×#627—31no—
110C2×#625—31no—
111C2×D3×Dic3—31no—
112C2×D3×Dic3—31no—
113C32×C4⋊C4C2×D311yescharacteristic
114C4⋊(C3⋊Dic3)—31no—
115C4⋊(C3⋊Dic3)—31no—
116C4⋊(C3⋊Dic3)—31no—
117#3750—31no—
118#3750—31no—
119C4×C3⋊Dic3—31no—
120C3×(C2×D3)⋊C4—31no—
121C3×(C2×D3)⋊C4—31no—
122C3×(C2×D3)⋊C4—31no—
123C3×(C2×D3)⋊C4C2×D311yescharacteristic
124C3×(C2×D3)⋊C4C2×D311yescharacteristic
125C3×(C2×D3)⋊C4C2×D311yescharacteristic
126C3×C4⋊Dic3—31no—
127C3×C4⋊Dic3C2×D311yescharacteristic
128C3×Dic3⋊C4—31no—
129C3×Dic3⋊C4C2×D311yescharacteristic
130C3×C4×Dic3—31no—
131C3×C4×Dic3C2×D311yescharacteristic
132#3724—31no—
133#3724—31no—
134Dic3⋊Dic3—31no—
135Dic3⋊Dic3—31no—
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—31no—
138(C2×D3)⋊Dic3—31no—
139(C2×D3)⋊Dic3—31no—
140(C2×D3)⋊Dic3—31no—
141(C2×D3)⋊Dic3—31no—
142C2×#611—31no—
143C22×Dic9—31no—
144C2×C4×D9—31no—
145C2×Dic18—31no—
146C2×Dic18—31no—
147C2×Dic18—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—
154C9×C22⋊C4—31no—
155C42×C9—31no—
156#3676—31no—
157#3676—31no—
158(C2×D9)⋊C4—31no—
159(C2×D9)⋊C4—31no—
160(C2×D9)⋊C4C2×D311yescharacteristic
161(C2×D9)⋊C4C2×D311yescharacteristic
162(C2×D9)⋊C4C2×D311yescharacteristic
163C4⋊Dic9—31no—
164C4⋊Dic9—31no—
165C4⋊Dic9—31no—
166C4⋊Dic9—31no—
167C4⋊Dic9—31no—
168C4⋊Dic9—61no—
169C4⋊Dic9—61no—
170C4⋊Dic9—61no—
171C4⋊Dic9C2×D311yescharacteristic
172Dic9⋊C4—31no—
173Dic9⋊C4—31no—
174Dic9⋊C4—31no—
175Dic9⋊C4—31no—
176Dic9⋊C4—31no—
177Dic9⋊C4—31no—
178Dic9⋊C4—61no—
179Dic9⋊C4—61no—
180Dic9⋊C4C2×D311yescharacteristic
181C4×Dic9—31no—
182C4×Dic9—61no—
183C4×Dic9C2×D311yescharacteristic
184C22×C3×C9C2411yescharacteristic
185C2×D3×C9—21no—
186C2×D3×C9—21no—
187C2×D3×C9—21no—
188C2×C3×D9—21no—
189C2×C3×D9—21no—
190C2×C3×D9—21no—
191C3×C4×C9—21no—
192C3×C4×C9—21no—
193C3×C4×C9—21no—
194C3⋊Dic9—21no—
195C3⋊Dic9—21no—
196C3⋊Dic9—21no—
197C3⋊Dic9—21no—
198C9×Dic3—21no—
199C9×Dic3—21no—
200C9×Dic3—21no—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×#126—31no—
205C3×#126—91no—
206#898—31no—
207#898D911yescharacteristic, complemented
208#897—91no—
209#897—91no—
210#896—91no—
211#896—91no—
212#890—91no—
213#890—91no—
214#890—181no—
215#889—91no—
216#889—91no—
217#888—91no—
218#888—91no—
219#886—91no—
220#886—91no—
221#885—91no—
222#885—91no—
223#883—91no—
224#883—91no—
225#879—91no—
226#879—91no—
227#878—91no—
228#878—91no—
229#878—91no—
230#878—91no—
231#876—91no—
232#876—91no—
233#869—91no—
234#869—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
250#627—121no—
251#627—121no—
252#627—121no—
253#625—121no—
254D3×Dic3—121no—
255D3×Dic3—121no—
256C23×C9—31no—
257C22×D9C22×D311yescharacteristic
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×C9C22×D311yescharacteristic
265C2×C4×C9C22×D311yescharacteristic
266C2×C4×C9C22×D311yescharacteristic
267#611—121no—
268C2×Dic9—31no—
269C2×Dic9—31no—
270C2×Dic9—31no—
271C2×Dic9—31no—
272C2×Dic9—61no—
273C2×Dic9—61no—
274C2×Dic9—61no—
275C2×Dic9—61no—
276C2×Dic9—121no—
277C2×Dic9C22×D311yescharacteristic
278C2×Dic9C22×D311yescharacteristic
279C2×Dic9C22×D311yescharacteristic
280C4×D9—121no—
281Dic18—121no—
282Dic18—121no—
283Dic18—121no—
284#563—271noSylow
285C2×C3×C9H(5,𝔽2)11yescharacteristic
286C2×C3×C92−1+411yescharacteristic
287C2×C3×C92−1+411yescharacteristic
288D3×C9—41no—
289C3×D9—41no—
290C2×#67—91no—
291C2×#67—91no—
292C22×Dic3—91no—
293C22×Dic3—91no—
294C2×C4×D3—91no—
295C2×C4×D3—91no—
296C2×Dic6—91no—
297C2×Dic6—91no—
298C2×Dic6—91no—
299C2×Dic6—91no—
300C2×Dic6—91no—
301C2×Dic6—91no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—91no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4C2×D911yescharacteristic
308C3×C4⋊C4D3211yescharacteristic
309C3×C22⋊C4—31no—
310C3×C22⋊C4—31no—
311C3×C22⋊C4—31no—
312C3×C22⋊C4—91no—
313C3×C22⋊C4—91no—
314C3×C22⋊C4—91no—
315C3×C42—31no—
316C3×C42—91no—
317#217—91no—
318#217—91no—
319#217—91no—
320#217—91no—
321(C2×D3)⋊C4—31no—
322(C2×D3)⋊C4—31no—
323(C2×D3)⋊C4—31no—
324(C2×D3)⋊C4—91no—
325(C2×D3)⋊C4—91no—
326(C2×D3)⋊C4—91no—
327(C2×D3)⋊C4—91no—
328(C2×D3)⋊C4C2×D911yescharacteristic
329(C2×D3)⋊C4C2×D911yescharacteristic
330(C2×D3)⋊C4C2×D911yescharacteristic
331C4⋊Dic3—31no—
332C4⋊Dic3—91no—
333C4⋊Dic3—91no—
334C4⋊Dic3—91no—
335C4⋊Dic3—91no—
336C4⋊Dic3—91no—
337C4⋊Dic3—91no—
338C4⋊Dic3—91no—
339C4⋊Dic3—91no—
340C4⋊Dic3—91no—
341C4⋊Dic3—91no—
342C4⋊Dic3—181no—
343C4⋊Dic3—181no—
344C4⋊Dic3—181no—
345C4⋊Dic3C2×D911yescharacteristic
346Dic3⋊C4—31no—
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—91no—
359Dic3⋊C4—181no—
360Dic3⋊C4—181no—
361Dic3⋊C4C2×D911yescharacteristic
362C4×Dic3—31no—
363C4×Dic3—91no—
364C4×Dic3—91no—
365C4×Dic3—181no—
366C4×Dic3C2×D911yescharacteristic
367C22×C32C23×D311yescharacteristic
368C2×C3×D3—21no—
369C2×C3×D3—21no—
370C2×C3×D3—21no—
371C2×C3×D3—61no—
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—61no—
381C3×Dic3—21no—
382C3×Dic3—21no—
383C3×Dic3—21no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3—61no—
387C22×C9—21no—
388C22×C9—61no—
389C22×C9—61no—
390C22×C9—61no—
391C22×C9C23×D311yescharacteristic
392C2×D9—21no—
393C2×D9—21no—
394C2×D9—21no—
395C4×C9—22no—
396C4×C9—21no—
397C4×C9—21no—
398C4×C9—21no—
399C4×C9—41no—
400C4×C9—41no—
401C4×C9—61no—
402C4×C9—61no—
403C4×C9—61no—
404Dic9—21no—
405Dic9—21no—
406Dic9—21no—
407Dic9—61no—
408Dic9—61no—
409Dic9—61no—
410Dic9—61no—
411Dic9—121no—
412Dic9—121no—
413Dic9—121no—
414Dic9—121no—
415C4⋊Q8—271no—
416C4⋊Q8—271no—
417#126—31no—
418#126—91no—
419#126—271no—
420#126—271no—
421#125—271no—
422#125—271no—
423#124—271no—
424#123—271no—
425#123—271no—
426C22⋊Q8—271no—
427C22⋊Q8—271no—
428C22⋊Q8—271no—
429C22⋊Q8—271no—
430C3×C9#56311yescharacteristic, complemented, Sylow
431C23×C3—31no—
432C23×C3—91no—
433C22×D3—31no—
434C22×D3C22×D911yescharacteristic
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—91no—
442C2×C3×C4—91no—
443C2×C3×C4—91no—
444C2×C3×C4C22×D911yescharacteristic
445C2×C3×C4C22×D911yescharacteristic
446C2×C3×C4C22×D911yescharacteristic
447C2×C3×C4C2×D3211yescharacteristic
448C2×C3×C4C2×D3211yescharacteristic
449C2×C3×C4C2×D3211yescharacteristic
450#67—361no—
451#67—361no—
452C2×Dic3—31no—
453C2×Dic3—31no—
454C2×Dic3—31no—
455C2×Dic3—91no—
456C2×Dic3—91no—
457C2×Dic3—91no—
458C2×Dic3—91no—
459C2×Dic3—91no—
460C2×Dic3—91no—
461C2×Dic3—91no—
462C2×Dic3—91no—
463C2×Dic3—181no—
464C2×Dic3—181no—
465C2×Dic3—181no—
466C2×Dic3—181no—
467C2×Dic3—361no—
468C2×Dic3—361no—
469C2×Dic3C22×D911yescharacteristic
470C2×Dic3C22×D911yescharacteristic
471C2×Dic3C22×D911yescharacteristic
472C4×D3—361no—
473C4×D3—361no—
474Dic6—361no—
475Dic6—361no—
476Dic6—361no—
477Dic6—361no—
478Dic6—361no—
479Dic6—361no—
480C2×C32#100911yescharacteristic
481C2×C32#101011yescharacteristic
482C2×C32#101011yescharacteristic
483C3×D3—41no—
484C3×D3—121no—
485C2×C9—21no—
486C2×C9—21no—
487C2×C9—21no—
488C2×C9—121no—
489C2×C9#100911yescharacteristic
490C2×C9#101011yescharacteristic
491C2×C9#101011yescharacteristic
492D9—41no—
493C2×Q8—271no—
494C2×Q8—271no—
495C2×Q8—271no—
496C2×D4—271no—
497C22×C4—271no—
498C22×C4—271no—
499C4⋊C4—31no—
500C4⋊C4—31no—
501C4⋊C4—91no—
502C4⋊C4—91no—
503C4⋊C4—271no—
504C4⋊C4—271no—
505C4⋊C4—271no—
506C4⋊C4—271no—
507C4⋊C4—271no—
508C4⋊C4—271no—
509C4⋊C4—271no—
510C4⋊C4—271no—
511C4⋊C4—271no—
512C4⋊C4—271no—
513C4⋊C4—271no—
514C4⋊C4D3×D911yescharacteristic
515C22⋊C4—31no—
516C22⋊C4—31no—
517C22⋊C4—31no—
518C22⋊C4—91no—
519C22⋊C4—91no—
520C22⋊C4—91no—
521C22⋊C4—271no—
522C22⋊C4—271no—
523C22⋊C4—271no—
524C22⋊C4—271no—
525C42—31no—
526C42—91no—
527C42—271no—
528C22×C3—21no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—181no—
533C22×C3—181no—
534C22×C3—181no—
535C22×C3C23×D911yescharacteristic
536C22×C3C22×D3211yescharacteristic
537C2×D3—21no—
538C2×D3—21no—
539C2×D3—21no—
540C2×D3—61no—
541C2×D3—61no—
542C2×D3—61no—
543C3×C4—22no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—41no—
551C3×C4—41no—
552C3×C4—61no—
553C3×C4—61no—
554C3×C4—61no—
555C3×C4—181no—
556C3×C4—181no—
557C3×C4—181no—
558Dic3—21no—
559Dic3—21no—
560Dic3—21no—
561Dic3—61no—
562Dic3—61no—
563Dic3—61no—
564Dic3—181no—
565Dic3—181no—
566Dic3—181no—
567Dic3—181no—
568Dic3—181no—
569Dic3—181no—
570Dic3—181no—
571Dic3—181no—
572Dic3—361no—
573Dic3—361no—
574Dic3—361no—
575Dic3—361no—
576C32#571211yescharacteristic
577C9—21no—
578C9#571211yescharacteristic, complemented
579C23—31no—
580C23—91no—
581Q8—1081no—
582Q8—1081no—
583Q8—1081no—
584D4—1081no—
585C2×C4—31no—
586C2×C4—31no—
587C2×C4—31no—
588C2×C4—91no—
589C2×C4—91no—
590C2×C4—91no—
591C2×C4—271no—
592C2×C4—271no—
593C2×C4—271no—
594C2×C4—271no—
595C2×C4—1081no—
596C2×C4—1081no—
597C2×C4C2×D3×D911yescharacteristic
598C2×C4C2×D3×D911yescharacteristic
599C2×C4C2×D3×D911yescharacteristic
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—121no—
604C2×C3—361no—
605C2×C3#6371511yescharacteristic
606C2×C3#6371611yescharacteristic
607C2×C3#6371611yescharacteristic
608C2×C3#6429811yescharacteristic
609C2×C3#6430911yescharacteristic
610C2×C3#6432011yescharacteristic
611D3—41no—
612D3—121no—
613C22—61no—
614C22—61no—
615C22—61no—
616C22—181no—
617C22—181no—
618C22—181no—
619C22C22×D3×D911yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—61no—
624C4—61no—
625C4—61no—
626C4—181no—
627C4—181no—
628C4—181no—
629C4—541no—
630C4—541no—
631C4—541no—
632C4—541no—
633C3—21no—
634C3#1058981411yescharacteristic, complemented
635C3#1059450711yescharacteristic
636C2—121no—
637C2—361no—
638C2#1172246511yescharacteristic
639C2#1172249411yescharacteristic
640C2#1172251511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#6194C22
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#563
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. #11721746C2semidirect
2. C9×#898C2semidirect
3. C3×#63460C2semidirect
5. #11721026C2semidirect
6. #11721023C2semidirect
8. #11720999C2semidirect
9. #11720991C2semidirect
11. #11720970C2semidirect
12. #11720969C2semidirect
13. #11720963C2semidirect
14. #11720947C2semidirect
15. #11720928C2semidirect
69. #63460D3semidirect
207. #898D9semidirect
430. C3×C9#563semidirect
578. C9#5712semidirect
634. C3#10589814semidirect

Maximal subgroups

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

subgroupindex
#117217462
C9×#8982
C3×#634602
#117210442
#117210262
#117210232
#117210212
#117209992
#117209912
#117209892
#117209702
#117209692
#117209632
#117209472
#117209282
#105945073
#105898143