Finite Group Databasebeta

← #13148936

Subgroups — #13148936

Order 1728.

806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63456C211yesmaximal, characteristic, complemented
4#11721041C211yesmaximal, characteristic, complemented
5#11721041C211yesmaximal, characteristic, complemented
6#11721021C211yesmaximal, characteristic, complemented
7#11721014C211yesmaximal, characteristic, complemented
8#11721012C211yesmaximal, characteristic, complemented
9#11721007C211yesmaximal, characteristic, complemented
10C4×#6192C211yesmaximal, characteristic, complemented
11#11720982C211yesmaximal, characteristic, complemented
12#11720978C211yesmaximal, characteristic, complemented
13#11720974C211yesmaximal, characteristic, complemented
14#11720949C211yesmaximal, characteristic, complemented
15#11720918C211yesmaximal, characteristic, complemented
16#10594473—31nomaximal
17#10589811—31nomaximal
18C2×C4×C3⋊D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×#6195C2211yescharacteristic
24C2×#6194C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26C2×D3×Dic9C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×Dic3×D9C2211yescharacteristic
30C3×C9×C4⋊C4C2211yescharacteristic
31C4⋊(C3⋊Dic9)C2211yescharacteristic
32#88534C2211yescharacteristic
33#88534C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C9×C4⋊Dic3C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C4×C9×Dic3C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic
49#88442C2211yescharacteristic
50#88442C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53C4⋊C4×C3⋊D3—31no—
54C3×#898D311yescharacteristic
55C3×#894—31no—
56#63916—31no—
57#63912—31no—
58#63912—31no—
59C4×#626—31no—
60#63891—31no—
61#63885—31no—
62#63881—31no—
63#63881—31no—
64#63879—31no—
65#63877—31no—
66#63861—31no—
67#63847—31no—
68C9×#126—31no—
69#63460—31no—
70#63457—31no—
71#63456D311yescharacteristic, complemented
72#63455—31no—
73C4⋊C4×D9—31no—
74C4⋊C4×D9—61no—
75#63451—31no—
76#63448—31no—
77#63446—31no—
78#63446—31no—
79#63446—31no—
80#611⋊C4—31no—
81#611⋊C4—31no—
82C4×D36—31no—
83#63434—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C4×C3⋊D9—22no—
95C4×C3⋊D9—41no—
96C4×C3⋊D9—41no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C3×D36—41no—
103C3×C4×D9—41no—
104#6195—22no—
105#6194—22no—
106#6194—41no—
107D3×Dic9—41no—
108#6192—22no—
109#6192—22no—
110Dic3×D9—22no—
111#5709—91no—
112#5661—91no—
113C2×C4×C3⋊D3—31no—
114C2×C4×C3⋊D3—31no—
115C2×C4×C3⋊D3—31no—
116C2×C3×D12—31no—
117C2×C3×C4×D3—31no—
118C2×#626—31no—
119C2×#626—31no—
120C2×#626—31no—
121C2×#625—31no—
122C2×#625—31no—
123C2×D3×Dic3—31no—
124C2×D3×Dic3—31no—
125C32×C4⋊C4C2×D311yescharacteristic
126C4⋊(C3⋊Dic3)—31no—
127#3750—31no—
128#3750—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×(C2×D3)⋊C4C2×D311yescharacteristic
134C3×(C2×D3)⋊C4C2×D311yescharacteristic
135C3×C4⋊Dic3C2×D311yescharacteristic
136C3×Dic3⋊C4—31no—
137C3×Dic3⋊C4C2×D311yescharacteristic
138C3×C4×Dic3C2×D311yescharacteristic
139#3724—31no—
140#3724—31no—
141Dic3⋊Dic3—31no—
142#3722—31no—
143(C2×D3)⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146Dic32—31no—
147Dic32—31no—
148C2×#611—31no—
149C2×#611—31no—
150C2×#611—31no—
151C22×Dic9—31no—
152C2×D36—31no—
153C2×D36—31no—
154C2×D36C2×D311yescharacteristic
155C2×C4×D9—31no—
156C2×C4×D9—31no—
157C2×C4×D9—31no—
158C2×C4×D9—31no—
159C2×C4×D9—61no—
160C2×C4×D9—61no—
161C2×C4×D9—61no—
162C2×C4×D9C2×D311yescharacteristic
163C9×C4⋊C4—21no—
164C9×C4⋊C4—31no—
165C9×C4⋊C4—31no—
166C9×C4⋊C4C2×D311yescharacteristic
167C9×C22⋊C4—31no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4—31no—
170C42×C9—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4C2×D311yescharacteristic
176(C2×D9)⋊C4C2×D311yescharacteristic
177(C2×D9)⋊C4C2×D311yescharacteristic
178C4⋊Dic9—31no—
179C4⋊Dic9—31no—
180C4⋊Dic9—61no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—61no—
186Dic9⋊C4—61no—
187Dic9⋊C4C2×D311yescharacteristic
188C4×Dic9—31no—
189C4×Dic9—31no—
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9#4112yes—
194C2×D3×C9—21no—
195C2×D3×C9—21no—
196C2×D3×C9—21no—
197C2×C3×D9—21no—
198C2×C3×D9—21no—
199C2×C3×D9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9#4112yes—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×#126—31no—
215C3×#123—91no—
216#939—91no—
217#938—91no—
218C4×#67—91no—
219C4×#67—91no—
220#898—91no—
221#898D911yescharacteristic, complemented
222#895—91no—
223#894—31no—
224#893—91no—
225#893—91no—
226D3×C4⋊C4—91no—
227D3×C4⋊C4—91no—
228D3×C4⋊C4—181no—
229#889—91no—
230#889—91no—
231#886—91no—
232#884—91no—
233#884—91no—
234#884—91no—
235#884—91no—
236#884—91no—
237#883—91no—
238#67⋊C4—91no—
239#67⋊C4—91no—
240#67⋊C4—91no—
241#879—91no—
242#877—91no—
243C4×D12—91no—
244#872—91no—
245C22×C3⋊D3—31no—
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C4×C3⋊D3—62no—
256C4×C3⋊D3—121no—
257C4×C3⋊D3—121no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3C22×D311yescharacteristic
261C2×C3×Dic3C22×D311yescharacteristic
262C2×C3×Dic3C22×D311yescharacteristic
263C3×D12—121no—
264C3×C4×D3—121no—
265#626—62no—
266#626—62no—
267#626—62no—
268#625—62no—
269#625—121no—
270D3×Dic3—62no—
271D3×Dic3—121no—
272C23×C9—31no—
273C22×D9—31no—
274C22×D9—61no—
275C22×D9C22×D311yescharacteristic
276C22×D9C22×D311yescharacteristic
277C2×C4×C9—21no—
278C2×C4×C9—21no—
279C2×C4×C9—21no—
280C2×C4×C9—31no—
281C2×C4×C9—31no—
282C2×C4×C9—31no—
283C2×C4×C9C22×D311yescharacteristic
284C2×C4×C9C22×D311yescharacteristic
285C2×C4×C9C22×D311yescharacteristic
286#611—62no—
287#611—62no—
288#611—121no—
289C2×Dic9—31no—
290C2×Dic9—31no—
291C2×Dic9—31no—
292C2×Dic9—61no—
293C2×Dic9—61no—
294C2×Dic9—61no—
295C2×Dic9—121no—
296C2×Dic9C22×D311yescharacteristic
297C2×Dic9C22×D311yescharacteristic
298D36—41no—
299D36—62no—
300D36—62no—
301C4×D9—41no—
302C4×D9—62no—
303C4×D9—62no—
304C4×D9—64no—
305C4×D9—121no—
306C4×D9—121no—
307C4×D9—122no—
308C4×D9—122no—
309#553—271noSylow
310C2×C3×C9C2×#4111yescharacteristic
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9H(5,𝔽2)11yescharacteristic
313C3⋊D9—22no—
314D3×C9—41no—
315C3×D9—41no—
316C3×D9—41no—
317C2×C3×D4—91no—
318C22×C3×C4—91no—
319C2×#67—91no—
320C2×#67—91no—
321C2×#67—91no—
322C2×#67—91no—
323C2×#67—91no—
324C2×#67—91no—
325C2×#67—91no—
326C22×Dic3—91no—
327C22×Dic3—91no—
328C2×D12—31no—
329C2×D12—91no—
330C2×D12—91no—
331C2×D12—91no—
332C2×C4×D3—31no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—181no—
342C2×C4×D3—181no—
343C2×C4×D3—181no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4C2×D911yescharacteristic
349C3×C4⋊C4D3211yescharacteristic
350C3×C22⋊C4—31no—
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—91no—
354C3×C22⋊C4—91no—
355C3×C22⋊C4—91no—
356C3×C42—31no—
357#217—91no—
358#217—91no—
359#217—91no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
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)⋊C4C2×D911yescharacteristic
369(C2×D3)⋊C4C2×D911yescharacteristic
370(C2×D3)⋊C4C2×D911yescharacteristic
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3—91no—
374C4⋊Dic3—181no—
375C4⋊Dic3C2×D911yescharacteristic
376Dic3⋊C4—31no—
377Dic3⋊C4—91no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—181no—
387Dic3⋊C4—181no—
388Dic3⋊C4C2×D911yescharacteristic
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3C2×D911yescharacteristic
394C22×C32C23×D311yescharacteristic
395C2×C3⋊D3—32no—
396C2×C3⋊D3—61no—
397C2×C3⋊D3—61no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C3⋊Dic3—32no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C22×C9—21no—
419C22×C9—61no—
420C22×C9—61no—
421C22×C9—61no—
422C22×C9C23×D311yescharacteristic
423C2×D9—21no—
424C2×D9—21no—
425C2×D9—21no—
426C2×D9—21no—
427C2×D9—21no—
428C2×D9—21no—
429C2×D9—32no—
430C2×D9—62no—
431C2×D9—62no—
432C2×D9—62no—
433C2×D9—61no—
434C2×D9—61no—
435C4×C9—22no—
436C4×C9—21no—
437C4×C9—21no—
438C4×C9—21no—
439C4×C9—41no—
440C4×C9—41no—
441C4×C9—61no—
442C4×C9—61no—
443C4×C9—61no—
444Dic9—21no—
445Dic9—21no—
446Dic9—32no—
447Dic9—62no—
448Dic9—61no—
449Dic9—61no—
450Dic9—121no—
451Dic9—121no—
452#126—31no—
453#126—271no—
454#125—271no—
455#123—91no—
456#123—271no—
457#121—271no—
458#121—271no—
459#121—271no—
460#121—271no—
461C4×D4—271no—
462C4×D4—271no—
463C4×D4—271no—
464C4×D4—271no—
465#117—271no—
466C2×C4⋊C4—271no—
467C3×C9#55311yescharacteristic, complemented, Sylow
468C23×C3—31no—
469C23×C3—91no—
470C23×C3—91no—
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—91no—
474C22×D3—91no—
475C22×D3—181no—
476C22×D3C22×D911yescharacteristic
477C3×D4—361no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—361no—
487C2×C3×C4C22×D911yescharacteristic
488C2×C3×C4C22×D911yescharacteristic
489C2×C3×C4C22×D911yescharacteristic
490C2×C3×C4C2×D3211yescharacteristic
491C2×C3×C4C2×D3211yescharacteristic
492C2×C3×C4C2×D3211yescharacteristic
493#67—182no—
494#67—182no—
495#67—182no—
496#67—182no—
497#67—182no—
498#67—361no—
499#67—361no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—91no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—181no—
509C2×Dic3—181no—
510C2×Dic3—181no—
511C2×Dic3—182no—
512C2×Dic3—361no—
513C2×Dic3C22×D911yescharacteristic
514C2×Dic3C22×D911yescharacteristic
515C2×Dic3C22×D911yescharacteristic
516D12—121no—
517D12—182no—
518D12—182no—
519D12—182no—
520C4×D3—121no—
521C4×D3—182no—
522C4×D3—182no—
523C4×D3—182no—
524C4×D3—184no—
525C4×D3—361no—
526C4×D3—361no—
527C4×D3—361no—
528C4×D3—361no—
529C4×D3—361no—
530C4×D3—362no—
531C4×D3—362no—
532C2×C32D3×#4111yescharacteristic
533C2×C32D3×#4111yescharacteristic
534C2×C32#100911yescharacteristic
535C3⋊D3—62no—
536C3×D3—41no—
537C3×D3—121no—
538C3×D3—121no—
539C2×C9—21no—
540C2×C9—21no—
541C2×C9—21no—
542C2×C9—121no—
543C2×C9#100411yescharacteristic
544C2×C9D3×#4111yescharacteristic
545C2×C9D3×#4111yescharacteristic
546D9—41no—
547D9—41no—
548D9—64no—
549D9—62no—
550C2×D4—91no—
551C2×D4—271no—
552C2×D4—271no—
553C2×D4—271no—
554C2×D4—271no—
555C2×D4—271no—
556C22×C4—91no—
557C22×C4—271no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4—271no—
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—91no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4D3×D911yescharacteristic
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—91no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C42—31no—
583C42—271no—
584C42—271no—
585C22×C3—21no—
586C22×C3—61no—
587C22×C3—61no—
588C22×C3—61no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3—181no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3C23×D911yescharacteristic
596C22×C3C22×D3211yescharacteristic
597C2×D3—21no—
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—61no—
601C2×D3—61no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—61no—
606C2×D3—92no—
607C2×D3—92no—
608C2×D3—182no—
609C2×D3—182no—
610C2×D3—182no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—181no—
615C3×C4—22no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—61no—
627C3×C4—181no—
628C3×C4—181no—
629Dic3—21no—
630Dic3—21no—
631Dic3—21no—
632Dic3—61no—
633Dic3—61no—
634Dic3—92no—
635Dic3—92no—
636Dic3—182no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—361no—
642Dic3—361no—
643C32#570911yescharacteristic
644C9—21no—
645C9#566111yescharacteristic, complemented
646C23—31no—
647C23—91no—
648C23—91no—
649C23—271no—
650D4—361no—
651D4—542no—
652D4—542no—
653D4—542no—
654D4—542no—
655D4—1081no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—271no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—361no—
665C2×C4—542no—
666C2×C4—542no—
667C2×C4—1081no—
668C2×C4—1081no—
669C2×C4—1081no—
670C2×C4C2×D3×D911yescharacteristic
671C2×C4C2×D3×D911yescharacteristic
672C2×C4C2×D3×D911yescharacteristic
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—121no—
677C2×C3—361no—
678C2×C3—361no—
679C2×C3#41×D911yescharacteristic
680C2×C3#41×D911yescharacteristic
681C2×C3#6371511yescharacteristic
682C2×C3#6430611yescharacteristic
683C2×C3#6431411yescharacteristic
684C2×C3#6431911yescharacteristic
685D3—41no—
686D3—121no—
687D3—121no—
688D3—184no—
689D3—182no—
690D3—182no—
691C22—61no—
692C22—61no—
693C22—61no—
694C22—181no—
695C22—181no—
696C22—181no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—272no—
701C22—541no—
702C22—541no—
703C22C22×D3×D911yescharacteristic
704C4—21no—
705C4—21no—
706C4—21no—
707C4—61no—
708C4—61no—
709C4—61no—
710C4—181no—
711C4—181no—
712C4—272no—
713C4—541no—
714C4—541no—
715C3—21no—
716C3#1058981111yescharacteristic, complemented
717C3#1059447311yescharacteristic
718C2—121no—
719C2—361no—
720C2—361no—
721C2—542no—
722C2#1172247511yescharacteristic
723C2#1172250111yescharacteristic
724C2#1172251411yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#553
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. C4⋊C4×C3⋊D9C2semidirect
2. C9×#898C2semidirect
3. C3×#63456C2semidirect
4. #11721041C2semidirect
5. #11721041C2semidirect
6. #11721021C2semidirect
7. #11721014C2semidirect
8. #11721012C2semidirect
9. #11721007C2semidirect
10. C4×#6192C2semidirect
11. #11720982C2semidirect
12. #11720978C2semidirect
13. #11720974C2semidirect
14. #11720949C2semidirect
15. #11720918C2semidirect
71. #63456D3semidirect
221. #898D9semidirect
467. C3×C9#553semidirect
645. C9#5661semidirect
716. C3#10589811semidirect

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×#8982
C3×#634562
#117210412
#117210212
#117210142
#117210122
#117210072
C4×#61922
#117209822
#117209782
#117209742
#117209492
#117209182
#105944733
#105898113