Finite Group Databasebeta

← #13148095

Subgroups — #13148095

Order 1728.

870 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊C4×C3⋊D9C211yesmaximal, characteristic
2C9×#879C211yesmaximal, characteristic, complemented
3C3×#63441C211yesmaximal, characteristic, complemented
4#11721274C211yesmaximal, characteristic
5#11721274C211yesmaximal, characteristic
6#11721247C211yesmaximal, characteristic, complemented
7#11721246C211yesmaximal, characteristic, complemented
8#11721000C211yesmaximal, characteristic, complemented
9#11720980C211yesmaximal, characteristic, complemented
10#11720980C211yesmaximal, characteristic, complemented
11C4×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
12#11720934C211yesmaximal, characteristic, complemented
13#11720926C211yesmaximal, characteristic, complemented
14#11720921C211yesmaximal, characteristic, complemented
15#11720920C211yesmaximal, characteristic, complemented
16#10594154—31nomaximal
17D9×#126—31nomaximal
18C23×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×C22⋊C4C2211yescharacteristic
26#88551C2211yescharacteristic
27#88536C2211yescharacteristic
28#88536C2211yescharacteristic
29C9×#217C2211yescharacteristic
30C9×#217C2211yescharacteristic
31C3×#3676C2211yescharacteristic
32C3×#3676C2211yescharacteristic
33C9×C4⋊Dic3C2211yescharacteristic, complemented
34C9×Dic3⋊C4C2211yescharacteristic, complemented
35C9×Dic3⋊C4C2211yescharacteristic, complemented
36C4×C9×Dic3C2211yescharacteristic, complemented
37C3×C4⋊Dic9C2211yescharacteristic, complemented
38C3×Dic9⋊C4C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic9C2211yescharacteristic, complemented
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45Dic3⋊Dic9C2211yescharacteristic, complemented
46Dic3⋊Dic9C2211yescharacteristic, complemented
47#88442C2211yescharacteristic, complemented
48#88442C2211yescharacteristic, complemented
49Dic9⋊Dic3C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C22⋊C4×C3⋊D3—31no—
54C3×#879—31no—
55C3×#879D311yescharacteristic
56#63974—31no—
57#63974—31no—
58#63956—31no—
59#63956—31no—
60#63900—31no—
61#63883—31no—
62#63883—31no—
63C4×#624—31no—
64#63868—31no—
65#63868—31no—
66#63848—31no—
67#63848—31no—
68C9×#126—31no—
69#63460—31no—
70#63460—31no—
71#63460—31no—
72C4⋊C4×D9—31no—
73C4⋊C4×D9—31no—
74C4⋊C4×D9—31no—
75C22⋊C4×D9—31no—
76C22⋊C4×D9—31no—
77C22⋊C4×D9—31no—
78C22⋊C4×D9—61no—
79#63441—31no—
80#63441—31no—
81#63441D311yescharacteristic, complemented
82#63438—31no—
83C42×D9—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9—22no—
86C22×C3⋊D9—22no—
87C22×C3⋊D9—22no—
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C4×C3⋊D9—22no—
95C4×C3⋊D9—22no—
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104(C3⋊D9)⋊C4—22no—
105(C3⋊D9)⋊C4—22no—
106(C3⋊D9)⋊C4—22no—
107(C3⋊D9)⋊C4—22no—
108D3×#126—91no—
109D3×#126—91no—
110C23×C3⋊D3—31no—
111C2×C4×C3⋊D3—31no—
112C2×C4×C3⋊D3—31no—
113C2×#624—31no—
114C2×#624—31no—
115C2×#624—31no—
116C2×#624—31no—
117C23×D9—31no—
118C23×D9—61no—
119C32×C22⋊C4C2×D311yescharacteristic
120#3757—31no—
121#3752—31no—
122#3752—31no—
123C3×#217—31no—
124C3×#217—31no—
125C3×#217C2×D311yescharacteristic
126C3×#217C2×D311yescharacteristic
127C3×C4⋊Dic3—31no—
128C3×C4⋊Dic3C2×D311yescharacteristic
129C3×Dic3⋊C4—31no—
130C3×Dic3⋊C4—31no—
131C3×Dic3⋊C4C2×D311yescharacteristic
132C3×Dic3⋊C4C2×D311yescharacteristic
133C3×C4×Dic3—31no—
134C3×C4×Dic3C2×D311yescharacteristic
135#3724—31no—
136#3724—31no—
137Dic3⋊Dic3—31no—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140Dic3⋊Dic3—31no—
141#3722—31no—
142#3722—31no—
143#3722—31no—
144#3722—31no—
145Dic32—31no—
146Dic32—31no—
147C2×C4×D9—31no—
148C2×C4×D9—31no—
149C2×C4×D9—31no—
150C2×C4×D9—31no—
151C2×C4×D9—31no—
152C2×C4×D9—31no—
153C2×C4×D9—61no—
154C2×C4×D9—61no—
155C9×C4⋊C4—31no—
156C9×C4⋊C4—31no—
157C9×C4⋊C4—31no—
158C9×C22⋊C4—21no—
159C9×C22⋊C4—31no—
160C9×C22⋊C4—31no—
161C9×C22⋊C4C2×D311yescharacteristic
162C42×C9—31no—
163#3676—31no—
164#3676—61no—
165#3676C2×D311yescharacteristic
166#3676C2×D311yescharacteristic
167(C2×D9)⋊C4—31no—
168(C2×D9)⋊C4—31no—
169(C2×D9)⋊C4—31no—
170(C2×D9)⋊C4—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—61no—
174(C2×D9)⋊C4—61no—
175C4⋊Dic9—31no—
176C4⋊Dic9—31no—
177C4⋊Dic9C2×D311yescharacteristic, complemented
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4C2×D311yescharacteristic, complemented
183Dic9⋊C4C2×D311yescharacteristic, complemented
184C4×Dic9—31no—
185C4×Dic9—31no—
186C4×Dic9C2×D311yescharacteristic, complemented
187C22×C3×C9—21no—
188C22×C3×C9—21no—
189C22×C3×C9—21no—
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9—21no—
194C2×C3⋊D9—44no—
195C2×C3⋊D9#4112yes—
196C2×C3⋊D9#4112yes—
197C2×C3⋊D9#4112yes—
198C3×C4×C9—21no—
199C3×C4×C9—21no—
200C3⋊Dic9—21no—
201C3⋊Dic9—21no—
202C9×Dic3—21no—
203C9×Dic3—21no—
204C9×Dic3—21no—
205C9×Dic3—21no—
206C3×Dic9—21no—
207C3×Dic9—21no—
208C3×Dic9—21no—
209C3×Dic9—21no—
210C3×#126—31no—
211C3×#126—91no—
212#898—91no—
213#898—91no—
214#898—91no—
215#898—91no—
216#898—91no—
217#898—91no—
218D3×C4⋊C4—91no—
219D3×C4⋊C4—91no—
220D3×C4⋊C4—91no—
221D3×C4⋊C4—91no—
222D3×C4⋊C4—91no—
223D3×C4⋊C4—91no—
224D3×C22⋊C4—91no—
225D3×C22⋊C4—91no—
226D3×C22⋊C4—91no—
227D3×C22⋊C4—91no—
228D3×C22⋊C4—91no—
229D3×C22⋊C4—91no—
230D3×C22⋊C4—181no—
231#879—31no—
232#879—91no—
233#879—91no—
234#879—91no—
235#879—91no—
236#879D911yescharacteristic, complemented
237#876—91no—
238#876—91no—
239C42×D3—91no—
240C42×D3—91no—
241C23×C32C22×D311yescharacteristic
242C22×C3⋊D3—31no—
243C22×C3⋊D3—31no—
244C22×C3⋊D3—62no—
245C22×C3⋊D3—62no—
246C22×C3⋊D3—62no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C3⋊Dic3—31no—
250C2×C3⋊Dic3—31no—
251C4×C3⋊D3—62no—
252C4×C3⋊D3—62no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3—31no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3C22×D311yescharacteristic
258C2×C3×Dic3C22×D311yescharacteristic
259C2×C3×Dic3C22×D311yescharacteristic
260C2×C3×Dic3C22×D311yescharacteristic
261#624—62no—
262#624—62no—
263#624—62no—
264#624—62no—
265C23×C9—21no—
266C23×C9C22×D311yescharacteristic
267C22×D9—31no—
268C22×D9—31no—
269C22×D9—61no—
270C22×D9—61no—
271C22×D9—62no—
272C22×D9—62no—
273C22×D9—62no—
274C22×D9—64no—
275C22×D9—122no—
276C22×D9—122no—
277C2×C4×C9—21no—
278C2×C4×C9—21no—
279C2×C4×C9—31no—
280C2×C4×C9—31no—
281C2×C4×C9—31no—
282C2×C4×C9—31no—
283C2×C4×C9C22×D311yescharacteristic
284C2×C4×C9C22×D311yescharacteristic
285C2×Dic9—31no—
286C2×Dic9—31no—
287C2×Dic9—61no—
288C2×Dic9—61no—
289C2×Dic9C22×D311yescharacteristic
290C2×Dic9C22×D311yescharacteristic
291C2×Dic9C22×D311yescharacteristic
292C2×Dic9C22×D311yescharacteristic
293C4×D9—62no—
294C4×D9—62no—
295C4×D9—62no—
296C4×D9—62no—
297C4×D9—62no—
298C4×D9—62no—
299C4×D9—122no—
300C4×D9—122no—
301C2×#126—271noSylow
302C2×C3×C9—41no—
303C2×C3×C9C2×#4111yescharacteristic
304C2×C3×C9C2×#4111yescharacteristic
305C2×C3×C9C2×#4111yescharacteristic
306C3⋊D9—41no—
307C3⋊D9#12614yescomplemented
308C23×D3—91no—
309C23×D3—91no—
310C23×D3—181no—
311C2×C4×D3—91no—
312C2×C4×D3—91no—
313C2×C4×D3—91no—
314C2×C4×D3—91no—
315C2×C4×D3—91no—
316C2×C4×D3—91no—
317C2×C4×D3—91no—
318C2×C4×D3—91no—
319C2×C4×D3—91no—
320C2×C4×D3—91no—
321C2×C4×D3—91no—
322C2×C4×D3—91no—
323C2×C4×D3—181no—
324C2×C4×D3—181no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C22⋊C4—21no—
332C3×C22⋊C4—31no—
333C3×C22⋊C4—31no—
334C3×C22⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C22⋊C4C2×D911yescharacteristic
337C3×C22⋊C4D3211yescharacteristic
338C3×C42—31no—
339C3×C42—91no—
340#217—31no—
341#217—31no—
342#217—91no—
343#217—91no—
344#217—181no—
345#217C2×D911yescharacteristic
346#217C2×D911yescharacteristic
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—91no—
351(C2×D3)⋊C4—91no—
352(C2×D3)⋊C4—91no—
353(C2×D3)⋊C4—91no—
354(C2×D3)⋊C4—91no—
355(C2×D3)⋊C4—91no—
356(C2×D3)⋊C4—91no—
357(C2×D3)⋊C4—91no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—181no—
360(C2×D3)⋊C4—181no—
361C4⋊Dic3—31no—
362C4⋊Dic3—91no—
363C4⋊Dic3—91no—
364C4⋊Dic3—91no—
365C4⋊Dic3—91no—
366C4⋊Dic3C2×D911yescharacteristic, complemented
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4C2×D911yescharacteristic, complemented
378Dic3⋊C4C2×D911yescharacteristic, complemented
379C4×Dic3—31no—
380C4×Dic3—91no—
381C4×Dic3—91no—
382C4×Dic3—91no—
383C4×Dic3—91no—
384C4×Dic3C2×D911yescharacteristic, complemented
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32C23×D311yescharacteristic
389C2×C3⋊D3—32no—
390C2×C3⋊D3—32no—
391C2×C3⋊D3—32no—
392C2×C3⋊D3—61no—
393C2×C3⋊D3—61no—
394C2×C3⋊D3—61no—
395C2×C3⋊D3—124no—
396C32×C4—21no—
397C32×C4—21no—
398C3⋊Dic3—61no—
399C3⋊Dic3—61no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—21no—
403C3×Dic3—21no—
404C3×Dic3—61no—
405C3×Dic3—61no—
406C3×Dic3—61no—
407C3×Dic3—61no—
408C22×C9—22no—
409C22×C9—21no—
410C22×C9—21no—
411C22×C9—21no—
412C22×C9—21no—
413C22×C9—41no—
414C22×C9—41no—
415C22×C9C23×D311yescharacteristic
416C2×D9—32no—
417C2×D9—32no—
418C2×D9—32no—
419C2×D9—62no—
420C2×D9—62no—
421C2×D9—62no—
422C2×D9—62no—
423C2×D9—61no—
424C2×D9—61no—
425C2×D9—61no—
426C2×D9—121no—
427C2×D9—121no—
428C2×D9—124no—
429C2×D9—128no—
430C4×C9—21no—
431C4×C9—21no—
432C4×C9—41no—
433C4×C9—41no—
434C4×C9—61no—
435C4×C9—61no—
436C4×C9—61no—
437C4×C9—61no—
438Dic9—21no—
439Dic9—21no—
440Dic9—21no—
441Dic9—21no—
442Dic9—61no—
443Dic9—61no—
444Dic9—121no—
445Dic9—121no—
446#126—31no—
447#126—91no—
448#126—271no—
449#126—271no—
450#126—271no—
451#126—271no—
452#126—271no—
453#126—271no—
454C2×C4⋊C4—271no—
455C2×C4⋊C4—271no—
456C2×C4⋊C4—271no—
457C2×C22⋊C4—271no—
458C2×C22⋊C4—271no—
459C2×C22⋊C4—271no—
460C2×C42—271no—
461C3×C9C2×#12611yescharacteristic, complemented, Sylow
462C23×C3—21no—
463C23×C3C22×D911yescharacteristic
464C23×C3C2×D3211yescharacteristic
465C22×D3—91no—
466C22×D3—91no—
467C22×D3—91no—
468C22×D3—91no—
469C22×D3—181no—
470C22×D3—181no—
471C22×D3—182no—
472C22×D3—182no—
473C22×D3—182no—
474C22×D3—182no—
475C22×D3—182no—
476C22×D3—182no—
477C22×D3—184no—
478C22×D3—362no—
479C22×D3—362no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—91no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4C22×D911yescharacteristic
491C2×C3×C4C22×D911yescharacteristic
492C2×C3×C4C2×D3211yescharacteristic
493C2×C3×C4C2×D3211yescharacteristic
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—91no—
499C2×Dic3—91no—
500C2×Dic3—91no—
501C2×Dic3—91no—
502C2×Dic3—181no—
503C2×Dic3—181no—
504C2×Dic3C22×D911yescharacteristic
505C2×Dic3C22×D911yescharacteristic
506C2×Dic3C22×D911yescharacteristic
507C2×Dic3C22×D911yescharacteristic
508C4×D3—182no—
509C4×D3—182no—
510C4×D3—182no—
511C4×D3—182no—
512C4×D3—182no—
513C4×D3—182no—
514C4×D3—182no—
515C4×D3—182no—
516C4×D3—182no—
517C4×D3—182no—
518C4×D3—182no—
519C4×D3—182no—
520C4×D3—362no—
521C4×D3—362no—
522C2×C32—41no—
523C2×C32D3×#4111yescharacteristic
524C2×C32D3×#4111yescharacteristic
525C2×C32D3×#4111yescharacteristic
526C3⋊D3—34no—
527C3⋊D3—121no—
528C2×C9—21no—
529C2×C9—21no—
530C2×C9—21no—
531C2×C9—42no—
532C2×C9—41no—
533C2×C9D3×#4111yescharacteristic
534C2×C9D3×#4111yescharacteristic
535C2×C9D3×#4111yescharacteristic
536D9—34no—
537D9—64no—
538D9—122no—
539D9—121no—
540C24—271no—
541C22×C4—271no—
542C22×C4—271no—
543C22×C4—271no—
544C22×C4—271no—
545C22×C4—271no—
546C22×C4—271no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—91no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—271no—
554C4⋊C4—271no—
555C4⋊C4—271no—
556C4⋊C4—271no—
557C4⋊C4—271no—
558C4⋊C4—271no—
559C22⋊C4—31no—
560C22⋊C4—31no—
561C22⋊C4—91no—
562C22⋊C4—91no—
563C22⋊C4—271no—
564C22⋊C4—271no—
565C22⋊C4—271no—
566C22⋊C4—271no—
567C22⋊C4—271no—
568C22⋊C4—271no—
569C22⋊C4—271no—
570C22⋊C4D3×D911yescharacteristic
571C42—31no—
572C42—91no—
573C42—271no—
574C42—271no—
575C22×C3—22no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3C23×D911yescharacteristic
586C22×C3C22×D3211yescharacteristic
587C2×D3—92no—
588C2×D3—92no—
589C2×D3—92no—
590C2×D3—92no—
591C2×D3—92no—
592C2×D3—92no—
593C2×D3—182no—
594C2×D3—182no—
595C2×D3—182no—
596C2×D3—182no—
597C2×D3—181no—
598C2×D3—181no—
599C2×D3—181no—
600C2×D3—181no—
601C2×D3—181no—
602C2×D3—181no—
603C2×D3—361no—
604C2×D3—361no—
605C2×D3—364no—
606C2×D3—364no—
607C2×D3—368no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—61no—
615C3×C4—61no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—181no—
619C3×C4—181no—
620C3×C4—181no—
621C3×C4—181no—
622Dic3—21no—
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—61no—
627Dic3—61no—
628Dic3—61no—
629Dic3—61no—
630Dic3—181no—
631Dic3—181no—
632Dic3—181no—
633Dic3—181no—
634Dic3—361no—
635Dic3—361no—
636C32D3×#12611yescharacteristic
637C9—21no—
638C9D3×#12611yescharacteristic, complemented
639C23—271no—
640C23—271no—
641C23—542no—
642C23—542no—
643C23—542no—
644C23C2×D3×D911yescharacteristic
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—91no—
653C2×C4—271no—
654C2×C4—271no—
655C2×C4—542no—
656C2×C4—542no—
657C2×C4—542no—
658C2×C4—542no—
659C2×C4—542no—
660C2×C4—542no—
661C2×C4C2×D3×D911yescharacteristic
662C2×C4C2×D3×D911yescharacteristic
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—42no—
667C2×C3—41no—
668C2×C3—41no—
669C2×C3#41×D911yescharacteristic
670C2×C3#41×D911yescharacteristic
671C2×C3#41×D911yescharacteristic
672C2×C3#6430611yescharacteristic
673C2×C3#6431211yescharacteristic
674C2×C3#6431211yescharacteristic
675D3—94no—
676D3—94no—
677D3—184no—
678D3—362no—
679D3—361no—
680D3—361no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—272no—
685C22—272no—
686C22—272no—
687C22—541no—
688C22—541no—
689C22—541no—
690C22—1084no—
691C22C22×D3×D911yescharacteristic
692C4—21no—
693C4—21no—
694C4—61no—
695C4—61no—
696C4—61no—
697C4—61no—
698C4—181no—
699C4—181no—
700C4—181no—
701C4—181no—
702C4—541no—
703C4—541no—
704C3—21no—
705C3D9×#12611yescharacteristic, complemented
706C3#1059415411yescharacteristic
707C2—41no—
708C2—274no—
709C2—1081no—
710C2#1172247511yescharacteristic
711C2#1172249811yescharacteristic
712C2#1172249811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC23×C3⋊D9C22
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×#126
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C9×#879C2semidirect
3. C3×#63441C2semidirect
6. #11721247C2semidirect
7. #11721246C2semidirect
8. #11721000C2semidirect
9. #11720980C2semidirect
10. #11720980C2semidirect
11. C4×(C3⋊D9)⋊C4C2semidirect
12. #11720934C2semidirect
13. #11720926C2semidirect
14. #11720921C2semidirect
15. #11720920C2semidirect
33. C9×C4⋊Dic3C22semidirect
34. C9×Dic3⋊C4C22semidirect
35. C9×Dic3⋊C4C22semidirect
36. C4×C9×Dic3C22semidirect
37. C3×C4⋊Dic9C22semidirect
38. C3×Dic9⋊C4C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. C3×C4×Dic9C22semidirect
45. Dic3⋊Dic9C22semidirect
46. Dic3⋊Dic9C22semidirect
47. #88442C22semidirect
48. #88442C22semidirect
49. Dic9⋊Dic3C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
81. #63441D3semidirect
177. C4⋊Dic9C2×D3semidirect
182. Dic9⋊C4C2×D3semidirect
183. Dic9⋊C4C2×D3semidirect
186. C4×Dic9C2×D3semidirect
236. #879D9semidirect
307. C3⋊D9#126semidirect
366. C4⋊Dic3C2×D9semidirect
377. Dic3⋊C4C2×D9semidirect
378. Dic3⋊C4C2×D9semidirect
384. C4×Dic3C2×D9semidirect
461. C3×C9C2×#126semidirect
638. C9D3×#126semidirect
705. C3D9×#126semidirect

Maximal subgroups

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

subgroupindex
C22⋊C4×C3⋊D92
C9×#8792
C3×#634412
#117212742
#117212472
#117212462
#117210002
#117209802
C4×(C3⋊D9)⋊C42
#117209342
#117209262
#117209212
#117209202
#105941543
D9×#1263