Finite Group Databasebeta

← #13154239

Subgroups — #13154239

Order 1728.

1250 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#126C211yesmaximal, characteristic, complemented
2#11721754C211yesmaximal, characteristic, complemented
3#11721752C211yesmaximal, characteristic, complemented
4#11721751C211yesmaximal, characteristic, complemented
5#11721751C211yesmaximal, characteristic, complemented
6#11721750C211yesmaximal, characteristic, complemented
7#11721749C211yesmaximal, characteristic, complemented
8#11721731C211yesmaximal, characteristic, complemented
9#11721730C211yesmaximal, characteristic, complemented
10#11721729C211yesmaximal, characteristic, complemented
11#11721728C211yesmaximal, characteristic, complemented
12#11721728C211yesmaximal, characteristic, complemented
13C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
14#11721712C211yesmaximal, characteristic, complemented
15C4×C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
16#10596175—31nomaximal
17#10589806—33nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×C4⋊(C3⋊D9)C2211yescharacteristic
22C2×C4⋊(C3⋊D9)C2211yescharacteristic
23C2×C4⋊(C3⋊D9)C2211yescharacteristic
24C2×C4⋊(C3⋊D9)C2211yescharacteristic
25C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
26C2×C4×C3⋊D9C2211yescharacteristic
27C2×C4×C3⋊D9C2211yescharacteristic
28C2×C4×C3⋊D9C2211yescharacteristic, complemented
29C2×C4×C3⋊D9C2211yescharacteristic, complemented
30C2×#6226C2211yescharacteristic, complemented
31C3×C9×C4⋊C4C2211yescharacteristic, complemented
32C3×C9×C4⋊C4C2211yescharacteristic, complemented
33C3×C9×C4⋊C4C2211yescharacteristic, complemented
34C3×C9×C22⋊C4C2211yescharacteristic
35C3×C9×C22⋊C4C2211yescharacteristic
36C3×C9×C22⋊C4C2211yescharacteristic
37C3×C42×C9C2211yescharacteristic, complemented
38#88551C2211yescharacteristic
39#88536C2211yescharacteristic
40#88536C2211yescharacteristic
41#88536C2211yescharacteristic
42#88536C2211yescharacteristic
43#88536C2211yescharacteristic
44#88536C2211yescharacteristic
45#88536C2211yescharacteristic, complemented
46#88536C2211yescharacteristic, complemented
47#88536C2211yescharacteristic, complemented
48#88536C2211yescharacteristic, complemented
49C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
50#88534C2211yescharacteristic, complemented
51#88534C2211yescharacteristic, complemented
52C4×C3⋊Dic9C2211yescharacteristic, complemented
53C32×#126D311yescharacteristic
54#64107—31no—
55#64105—31no—
56#64104—31no—
57#64104—31no—
58#64103—31no—
59#64102—31no—
60#64094—31no—
61#64093—31no—
62#64092—31no—
63#64091—31no—
64#64091—31no—
65C22⋊C4×C3⋊D3—31no—
66#64084—31no—
67C4×C4⋊(C3⋊D3)—31no—
68C9×#126D313yescomplemented
69#63460—33no—
70#63458—33no—
71#63457—33no—
72#63457—33no—
73#63456—33no—
74#63455—33no—
75#63447—33no—
76#63446—33no—
77#63445—33no—
78#63444—33no—
79#63444—33no—
80C22⋊C4×D9—33no—
81#63437—33no—
82C4×D36—33no—
83C23×C3×C9C2311yescharacteristic
84C22×C3⋊D9—22no—
85C22×C3⋊D9—41no—
86C22×C3⋊D9—41no—
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97#6233—41no—
98#6233—41no—
99C2×C3⋊Dic9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C4⋊(C3⋊D9)—22no—
104C4⋊(C3⋊D9)—22no—
105C4⋊(C3⋊D9)—41no—
106C4⋊(C3⋊D9)—41no—
107C4⋊(C3⋊D9)—41no—
108C4×C3⋊D9—41no—
109C4×C3⋊D9—41no—
110C4×C3⋊D9—41no—
111C4×C3⋊D9—41no—
112#6226—41no—
113#5704—93no—
114#5704—91no—
115C23×C3⋊D3—31no—
116C2×#638—31no—
117C2×#638—31no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4⋊(C3⋊D3)—31no—
120C2×C4⋊(C3⋊D3)—31no—
121C2×C4⋊(C3⋊D3)—31no—
122C2×C4⋊(C3⋊D3)—31no—
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3—31no—
127C2×#634—31no—
128C23×D9—33no—
129C32×C4⋊C4C2×D311yescharacteristic
130C32×C4⋊C4C2×D311yescharacteristic
131C32×C4⋊C4C2×D311yescharacteristic
132C32×C22⋊C4C2×D311yescharacteristic
133C32×C22⋊C4C2×D311yescharacteristic
134C32×C22⋊C4C2×D311yescharacteristic
135C32×C42C2×D311yescharacteristic
136#3757—31no—
137#3752—31no—
138#3752—31no—
139#3752—31no—
140#3752—31no—
141#3752—31no—
142#3752—31no—
143#3752—31no—
144#3752—31no—
145#3752—31no—
146#3752—31no—
147C4⋊(C3⋊Dic3)—31no—
148#3750—31no—
149#3750—31no—
150C4×C3⋊Dic3—31no—
151C2×#611—33no—
152C2×#611—33no—
153C2×D36—33no—
154C2×D36—33no—
155C2×D36—33no—
156C2×D36—33no—
157C2×D36—33no—
158C2×C4×D9—33no—
159C2×C4×D9—33no—
160C2×C4×D9—33no—
161C2×C4×D9—33no—
162C2×Dic18—33no—
163C9×C4⋊C4C2×D313yescomplemented
164C9×C4⋊C4C2×D313yescomplemented
165C9×C4⋊C4C2×D313yescomplemented
166C9×C22⋊C4C2×D313yes—
167C9×C22⋊C4C2×D313yes—
168C9×C22⋊C4C2×D313yes—
169C42×C9C2×D313yescomplemented
170#3676—33no—
171(C2×D9)⋊C4—33no—
172(C2×D9)⋊C4—33no—
173(C2×D9)⋊C4—33no—
174(C2×D9)⋊C4—33no—
175(C2×D9)⋊C4—33no—
176(C2×D9)⋊C4—33no—
177(C2×D9)⋊C4—33no—
178(C2×D9)⋊C4—33no—
179(C2×D9)⋊C4—33no—
180(C2×D9)⋊C4—33no—
181C4⋊Dic9—33no—
182Dic9⋊C4—33no—
183Dic9⋊C4—33no—
184C4×Dic9—33no—
185C22×C3×C9—21no—
186C22×C3×C9—21no—
187C22×C3×C9—21no—
188C22×C3×C9C2411yescharacteristic
189C2×C3⋊D9—21no—
190C2×C3⋊D9—21no—
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9—21no—
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×C3⋊D9—44no—
201C2×C3⋊D9#4112yes—
202C3×C4×C9—21no—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3×C4×C9—21no—
208C3⋊Dic9—21no—
209C3⋊Dic9—21no—
210C3⋊Dic9—21no—
211C3⋊Dic9—21no—
212C3×#126D913yescomplemented
213C3×#126C3⋊D311yescharacteristic
214#898—93no—
215#898—91no—
216#896—93no—
217#896—91no—
218#895—93no—
219#895—93no—
220#895—91no—
221#895—91no—
222#894—93no—
223#894—91no—
224#893—93no—
225#893—91no—
226#885—93no—
227#885—91no—
228#884—93no—
229#884—91no—
230#883—93no—
231#883—91no—
232#882—93no—
233#882—93no—
234#882—91no—
235#882—91no—
236D3×C22⋊C4—93no—
237D3×C22⋊C4—91no—
238#875—93no—
239#875—91no—
240C4×D12—93no—
241C4×D12—91no—
242C23×C32C22×D311yescharacteristic
243C22×C3⋊D3—31no—
244C22×C3⋊D3—31no—
245C22×C3⋊D3—31no—
246C22×C3⋊D3—31no—
247C22×C3⋊D3—62no—
248C22×C3⋊D3—121no—
249C22×C3⋊D3—121no—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256#638—121no—
257#638—121no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—31no—
262C4⋊(C3⋊D3)—62no—
263C4⋊(C3⋊D3)—62no—
264C4⋊(C3⋊D3)—121no—
265C4⋊(C3⋊D3)—121no—
266C4⋊(C3⋊D3)—121no—
267C4×C3⋊D3—121no—
268C4×C3⋊D3—121no—
269C4×C3⋊D3—121no—
270C4×C3⋊D3—121no—
271#634—121no—
272C23×C9C22×D313yes—
273C22×D9—33no—
274C22×D9—33no—
275C22×D9—33no—
276C22×D9—33no—
277C22×D9—66no—
278C22×D9—123no—
279C22×D9—123no—
280C2×C4×C9C22×D313yes—
281C2×C4×C9C22×D313yes—
282C2×C4×C9C22×D313yes—
283C2×C4×C9C22×D313yes—
284C2×C4×C9C22×D313yes—
285C2×C4×C9C22×D313yes—
286#611—123no—
287#611—123no—
288C2×Dic9—33no—
289C2×Dic9—33no—
290C2×Dic9—33no—
291C2×Dic9—33no—
292D36—66no—
293D36—66no—
294D36—123no—
295D36—123no—
296D36—123no—
297C4×D9—123no—
298C4×D9—123no—
299C4×D9—123no—
300C4×D9—123no—
301Dic18—123no—
302#538—271noSylow
303C2×C3×C9—41no—
304C2×C3×C9C2×#4111yescharacteristic
305C2×C3×C9H(5,𝔽2)11yescharacteristic
306C2×C3×C9H(5,𝔽2)11yescharacteristic
307C3⋊D9—22no—
308C3⋊D9—41no—
309C3⋊D9—41no—
310C3⋊D9—41no—
311C23×D3—93no—
312C23×D3—91no—
313C2×#67—93no—
314C2×#67—93no—
315C2×#67—91no—
316C2×#67—91no—
317C2×D12—93no—
318C2×D12—93no—
319C2×D12—91no—
320C2×D12—91no—
321C2×D12—93no—
322C2×D12—93no—
323C2×D12—93no—
324C2×D12—91no—
325C2×D12—91no—
326C2×D12—91no—
327C2×C4×D3—93no—
328C2×C4×D3—93no—
329C2×C4×D3—93no—
330C2×C4×D3—93no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×Dic6—93no—
336C2×Dic6—91no—
337C3×C4⋊C4C2×D913yescomplemented
338C3×C4⋊C4C2×D913yescomplemented
339C3×C4⋊C4C2×D913yescomplemented
340C3×C4⋊C4C2×C3⋊D311yescharacteristic
341C3×C4⋊C4C2×C3⋊D311yescharacteristic
342C3×C4⋊C4C2×C3⋊D311yescharacteristic
343C3×C22⋊C4C2×D913yes—
344C3×C22⋊C4C2×D913yes—
345C3×C22⋊C4C2×D913yes—
346C3×C22⋊C4C2×C3⋊D311yescharacteristic
347C3×C22⋊C4C2×C3⋊D311yescharacteristic
348C3×C22⋊C4C2×C3⋊D311yescharacteristic
349C3×C42C2×D913yescomplemented
350C3×C42C2×C3⋊D311yescharacteristic
351#217—93no—
352#217—91no—
353(C2×D3)⋊C4—93no—
354(C2×D3)⋊C4—93no—
355(C2×D3)⋊C4—93no—
356(C2×D3)⋊C4—93no—
357(C2×D3)⋊C4—93no—
358(C2×D3)⋊C4—93no—
359(C2×D3)⋊C4—93no—
360(C2×D3)⋊C4—93no—
361(C2×D3)⋊C4—93no—
362(C2×D3)⋊C4—93no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373C4⋊Dic3—93no—
374C4⋊Dic3—91no—
375Dic3⋊C4—93no—
376Dic3⋊C4—93no—
377Dic3⋊C4—91no—
378Dic3⋊C4—91no—
379C4×Dic3—93no—
380C4×Dic3—91no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32C23×D311yescharacteristic
385C2×C3⋊D3—32no—
386C2×C3⋊D3—61no—
387C2×C3⋊D3—61no—
388C2×C3⋊D3—61no—
389C2×C3⋊D3—61no—
390C2×C3⋊D3—61no—
391C2×C3⋊D3—61no—
392C2×C3⋊D3—61no—
393C2×C3⋊D3—61no—
394C2×C3⋊D3—61no—
395C2×C3⋊D3—61no—
396C2×C3⋊D3—61no—
397C2×C3⋊D3—124no—
398C32×C4—21no—
399C32×C4—21no—
400C32×C4—21no—
401C32×C4—21no—
402C32×C4—21no—
403C32×C4—21no—
404C3⋊Dic3—61no—
405C3⋊Dic3—61no—
406C3⋊Dic3—61no—
407C3⋊Dic3—61no—
408C22×C9—23no—
409C22×C9—23no—
410C22×C9—23no—
411C22×C9C23×D313yes—
412C2×D9—36no—
413C2×D9—63no—
414C2×D9—63no—
415C2×D9—63no—
416C2×D9—63no—
417C2×D9—63no—
418C2×D9—63no—
419C2×D9—63no—
420C2×D9—63no—
421C2×D9—63no—
422C2×D9—63no—
423C2×D9—63no—
424C2×D9—1212no—
425C4×C9—23no—
426C4×C9—23no—
427C4×C9—23no—
428C4×C9—23no—
429C4×C9—23no—
430C4×C9—23no—
431Dic9—63no—
432Dic9—63no—
433Dic9—63no—
434Dic9—63no—
435#126—271no—
436#126C3⋊D911yescharacteristic, complemented
437#124—271no—
438#124—271no—
439#123—271no—
440#123—271no—
441C22⋊Q8—271no—
442#121—271no—
443#121—271no—
444#121—271no—
445#120—271no—
446#120—271no—
447C4×D4—271no—
448C4×D4—271no—
449C2×C22⋊C4—271no—
450C3×C9#53811yescharacteristic, complemented, Sylow
451C23×C3C22×D913yes—
452C23×C3C22×C3⋊D311yescharacteristic
453C22×D3—91no—
454C22×D3—93no—
455C22×D3—91no—
456C22×D3—91no—
457C22×D3—91no—
458C22×D3—93no—
459C22×D3—93no—
460C22×D3—93no—
461C22×D3—182no—
462C22×D3—186no—
463C22×D3—361no—
464C22×D3—361no—
465C22×D3—363no—
466C22×D3—363no—
467C2×C3×C4C22×D913yes—
468C2×C3×C4C22×D913yes—
469C2×C3×C4C22×D913yes—
470C2×C3×C4C22×D913yes—
471C2×C3×C4C22×D913yes—
472C2×C3×C4C22×D913yes—
473C2×C3×C4C22×C3⋊D311yescharacteristic
474C2×C3×C4C22×C3⋊D311yescharacteristic
475C2×C3×C4C22×C3⋊D311yescharacteristic
476C2×C3×C4C22×C3⋊D311yescharacteristic
477C2×C3×C4C22×C3⋊D311yescharacteristic
478C2×C3×C4C22×C3⋊D311yescharacteristic
479#67—361no—
480#67—361no—
481#67—363no—
482#67—363no—
483C2×Dic3—91no—
484C2×Dic3—91no—
485C2×Dic3—91no—
486C2×Dic3—91no—
487C2×Dic3—93no—
488C2×Dic3—93no—
489C2×Dic3—93no—
490C2×Dic3—93no—
491D12—182no—
492D12—182no—
493D12—186no—
494D12—186no—
495D12—361no—
496D12—361no—
497D12—361no—
498D12—363no—
499D12—363no—
500D12—363no—
501C4×D3—361no—
502C4×D3—361no—
503C4×D3—361no—
504C4×D3—361no—
505C4×D3—363no—
506C4×D3—363no—
507C4×D3—363no—
508C4×D3—363no—
509Dic6—361no—
510Dic6—363no—
511C2×C32—41no—
512C2×C32D3×#4111yescharacteristic
513C2×C32#100911yescharacteristic
514C2×C32#100911yescharacteristic
515C3⋊D3—62no—
516C3⋊D3—121no—
517C3⋊D3—121no—
518C3⋊D3—121no—
519C2×C9—43no—
520C2×C9D3×#4113yes—
521C2×C9#100913yes—
522C2×C9#100913yes—
523D9—66no—
524D9—123no—
525D9—123no—
526D9—123no—
527C24—271no—
528C2×Q8—271no—
529C2×D4—271no—
530C2×D4—271no—
531C2×D4—271no—
532C2×D4—271no—
533C2×D4—271no—
534C2×D4—271no—
535C2×D4—271no—
536C22×C4—271no—
537C22×C4—271no—
538C22×C4—271no—
539C22×C4—271no—
540C4⋊C4—271no—
541C4⋊C4—271no—
542C4⋊C4—271no—
543C4⋊C4C2×C3⋊D911yescharacteristic, complemented
544C4⋊C4C2×C3⋊D911yescharacteristic, complemented
545C4⋊C4C2×C3⋊D911yescharacteristic, complemented
546C22⋊C4—271no—
547C22⋊C4—271no—
548C22⋊C4—271no—
549C22⋊C4—271no—
550C22⋊C4—271no—
551C22⋊C4—271no—
552C22⋊C4—271no—
553C22⋊C4—271no—
554C22⋊C4—271no—
555C22⋊C4—271no—
556C22⋊C4—271no—
557C22⋊C4C2×C3⋊D911yescharacteristic
558C22⋊C4C2×C3⋊D911yescharacteristic
559C22⋊C4C2×C3⋊D911yescharacteristic
560C42—271no—
561C42C2×C3⋊D911yescharacteristic, complemented
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—23no—
566C22×C3—23no—
567C22×C3—23no—
568C22×C3C23×D913yes—
569C22×C3C23×C3⋊D311yescharacteristic
570C2×D3—92no—
571C2×D3—96no—
572C2×D3—181no—
573C2×D3—181no—
574C2×D3—183no—
575C2×D3—183no—
576C2×D3—181no—
577C2×D3—181no—
578C2×D3—181no—
579C2×D3—181no—
580C2×D3—181no—
581C2×D3—181no—
582C2×D3—181no—
583C2×D3—181no—
584C2×D3—181no—
585C2×D3—183no—
586C2×D3—183no—
587C2×D3—183no—
588C2×D3—183no—
589C2×D3—183no—
590C2×D3—183no—
591C2×D3—183no—
592C2×D3—183no—
593C2×D3—183no—
594C2×D3—364no—
595C2×D3—3612no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—23no—
603C3×C4—23no—
604C3×C4—23no—
605C3×C4—23no—
606C3×C4—23no—
607C3×C4—23no—
608Dic3—181no—
609Dic3—181no—
610Dic3—181no—
611Dic3—181no—
612Dic3—183no—
613Dic3—183no—
614Dic3—183no—
615Dic3—183no—
616C32#570411yescharacteristic
617C9#570413yescomplemented
618C23—271no—
619C23—271no—
620C23—271no—
621C23—271no—
622C23—542no—
623C23—1081no—
624C23—1081no—
625C23C22×C3⋊D911yescharacteristic
626Q8—1081no—
627D4—542no—
628D4—542no—
629D4—1081no—
630D4—1081no—
631D4—1081no—
632D4—1081no—
633D4—1081no—
634C2×C4—271no—
635C2×C4—271no—
636C2×C4—271no—
637C2×C4—271no—
638C2×C4—1081no—
639C2×C4—1081no—
640C2×C4—1081no—
641C2×C4—1081no—
642C2×C4C22×C3⋊D911yescharacteristic
643C2×C4C22×C3⋊D911yescharacteristic
644C2×C4C22×C3⋊D911yescharacteristic
645C2×C4C22×C3⋊D911yescharacteristic
646C2×C4C22×C3⋊D911yescharacteristic
647C2×C4C22×C3⋊D911yescharacteristic
648C2×C3—41no—
649C2×C3—43no—
650C2×C3#41×D913yes—
651C2×C3#6371513yes—
652C2×C3#6371513yes—
653C2×C3#41×C3⋊D311yescharacteristic
654C2×C3#6436611yescharacteristic
655C2×C3#6436611yescharacteristic
656D3—182no—
657D3—186no—
658D3—361no—
659D3—361no—
660D3—361no—
661D3—363no—
662D3—363no—
663D3—363no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—272no—
668C22—541no—
669C22—541no—
670C22—541no—
671C22—541no—
672C22—541no—
673C22—541no—
674C22—541no—
675C22—541no—
676C22—541no—
677C22—541no—
678C22—541no—
679C22—1084no—
680C22C23×C3⋊D911yescharacteristic
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—21no—
686C4—21no—
687C4—541no—
688C4—541no—
689C4—541no—
690C4—541no—
691C3#1058980613yescomplemented
692C3#1059617511yescharacteristic
693C2—41no—
694C2—542no—
695C2—1081no—
696C2—1081no—
697C2—1081no—
698C2#41×C3⋊D911yescharacteristic
699C2#1172267211yescharacteristic
700C2#1172267211yescharacteristic
subgroupG/H
centerC22C23×C3⋊D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C23×C3⋊D3
FittingC3×C9×#126C2
socleC22×C32C23×D3
hypercenter#126C3⋊D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. C3×C9×#126C2semidirect
2. #11721754C2semidirect
3. #11721752C2semidirect
4. #11721751C2semidirect
5. #11721751C2semidirect
6. #11721750C2semidirect
7. #11721749C2semidirect
8. #11721731C2semidirect
9. #11721730C2semidirect
10. #11721729C2semidirect
11. #11721728C2semidirect
12. #11721728C2semidirect
13. C22⋊C4×C3⋊D9C2semidirect
14. #11721712C2semidirect
15. C4×C4⋊(C3⋊D9)C2semidirect
25. C2×C4⋊(C3⋊D9)C22semidirect
28. C2×C4×C3⋊D9C22semidirect
29. C2×C4×C3⋊D9C22semidirect
30. C2×#6226C22semidirect
31. C3×C9×C4⋊C4C22semidirect
32. C3×C9×C4⋊C4C22semidirect
33. C3×C9×C4⋊C4C22semidirect
37. C3×C42×C9C22semidirect
45. #88536C22semidirect
46. #88536C22semidirect
47. #88536C22semidirect
48. #88536C22semidirect
49. C4⋊(C3⋊Dic9)C22semidirect
50. #88534C22semidirect
51. #88534C22semidirect
52. C4×C3⋊Dic9C22semidirect
68. C9×#126D3semidirect
163. C9×C4⋊C4C2×D3semidirect
164. C9×C4⋊C4C2×D3semidirect
165. C9×C4⋊C4C2×D3semidirect
169. C42×C9C2×D3semidirect
212. C3×#126D9semidirect
337. C3×C4⋊C4C2×D9semidirect
338. C3×C4⋊C4C2×D9semidirect
339. C3×C4⋊C4C2×D9semidirect
349. C3×C42C2×D9semidirect
436. #126C3⋊D9semidirect
450. C3×C9#538semidirect
543. C4⋊C4C2×C3⋊D9semidirect
544. C4⋊C4C2×C3⋊D9semidirect
545. C4⋊C4C2×C3⋊D9semidirect
561. C42C2×C3⋊D9semidirect
617. C9#5704semidirect
691. C3#10589806semidirect

Maximal subgroups

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

subgroupindex
C3×C9×#1262
#117217542
#117217522
#117217512
#117217502
#117217492
#117217312
#117217302
#117217292
#117217282
C22⋊C4×C3⋊D92
#117217122
C4×C4⋊(C3⋊D9)2
#105961753
#105898063