Finite Group Databasebeta

← #13149367

Subgroups — #13149367

Order 1728.

830 conjugacy classes of subgroups.

The subgroup lattice has 696 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×#63460C211yesmaximal, characteristic, complemented
4#11721048C211yesmaximal, characteristic
5#11721048C211yesmaximal, characteristic
6#11721048C211yesmaximal, characteristic
7#11721000C211yesmaximal, characteristic, complemented
8#11720980C211yesmaximal, characteristic, complemented
9C4×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
10#11720965C211yesmaximal, characteristic, complemented
11#11720963C211yesmaximal, characteristic, complemented
12#11720962C211yesmaximal, characteristic, complemented
13#11720949C211yesmaximal, characteristic, complemented
14#11720947C211yesmaximal, characteristic, complemented
15#11720946C211yesmaximal, characteristic, complemented
16#10594656—31nomaximal
17D9×#126—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×(C3⋊D9)⋊C4C2211yescharacteristic
23C2×(C3⋊D9)⋊C4C2211yescharacteristic
24C2×(C3⋊D9)⋊C4C2211yescharacteristic
25C3×C9×C4⋊C4C2211yescharacteristic, complemented
26C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
27#88534C2211yescharacteristic, complemented
28#88534C2211yescharacteristic, complemented
29C9×(C2×D3)⋊C4C2211yescharacteristic
30C9×(C2×D3)⋊C4C2211yescharacteristic
31C9×(C2×D3)⋊C4C2211yescharacteristic
32C3×(C2×D9)⋊C4C2211yescharacteristic
33C3×(C2×D9)⋊C4C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C9×C4⋊Dic3C2211yescharacteristic, complemented
36C9×Dic3⋊C4C2211yescharacteristic, complemented
37C4×C9×Dic3C2211yescharacteristic, complemented
38C3×C4⋊Dic9C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic9C2211yescharacteristic, complemented
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic, complemented
48#88442C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C4⋊C4×C3⋊D3—31no—
54C3×#898—31no—
55C3×#898D311yescharacteristic
56#63921—31no—
57#63921—31no—
58#63921—31no—
59#63900—31no—
60#63883—31no—
61C4×#624—31no—
62#63861—31no—
63#63861—31no—
64#63859—31no—
65#63859—31no—
66#63858—31no—
67#63858—31no—
68C9×#126—31no—
69#63460—31no—
70#63460—31no—
71#63460D311yescharacteristic, complemented
72C4⋊C4×D9—31no—
73C4⋊C4×D9—31no—
74C4⋊C4×D9—31no—
75C4⋊C4×D9—61no—
76C22⋊C4×D9—31no—
77C22⋊C4×D9—31no—
78C22⋊C4×D9—31no—
79#63441—31no—
80#63441—31no—
81#63441—31no—
82#63438—31no—
83C42×D9—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C2×D3×D9—22no—
88C2×D3×D9—22no—
89C2×D3×D9—22no—
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C4×C3⋊D9—22no—
97C4×C3⋊D9—22no—
98C4×C3⋊D9—22no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105(C3⋊D9)⋊C4—22no—
106(C3⋊D9)⋊C4—22no—
107(C3⋊D9)⋊C4—22no—
108D3×#126—91no—
109D3×#126—91no—
110C22×D32—31no—
111C2×C4×C3⋊D3—31no—
112C2×C4×C3⋊D3—31no—
113C2×C4×C3⋊D3—31no—
114C2×#624—31no—
115C2×#624—31no—
116C2×#624—31no—
117C23×D9—31no—
118C32×C4⋊C4C2×D311yescharacteristic
119C4⋊(C3⋊Dic3)—31no—
120#3750—31no—
121#3750—31no—
122C3×(C2×D3)⋊C4—31no—
123C3×(C2×D3)⋊C4—31no—
124C3×(C2×D3)⋊C4—31no—
125C3×(C2×D3)⋊C4C2×D311yescharacteristic
126C3×(C2×D3)⋊C4C2×D311yescharacteristic
127C3×(C2×D3)⋊C4C2×D311yescharacteristic
128C3×C4⋊Dic3—31no—
129C3×C4⋊Dic3C2×D311yescharacteristic
130C3×Dic3⋊C4—31no—
131C3×Dic3⋊C4C2×D311yescharacteristic
132C3×C4×Dic3—31no—
133C3×C4×Dic3C2×D311yescharacteristic
134#3724—31no—
135#3724—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—
142(C2×D3)⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144Dic32—31no—
145Dic32—31no—
146C2×C4×D9—31no—
147C2×C4×D9—31no—
148C2×C4×D9—31no—
149C2×C4×D9—31no—
150C2×C4×D9—31no—
151C2×C4×D9—31no—
152C2×C4×D9—61no—
153C2×C4×D9—61no—
154C2×C4×D9—61no—
155C9×C4⋊C4—21no—
156C9×C4⋊C4—31no—
157C9×C4⋊C4—31no—
158C9×C4⋊C4C2×D311yescharacteristic, complemented
159C9×C22⋊C4—31no—
160C9×C22⋊C4—31no—
161C9×C22⋊C4—31no—
162C42×C9—31no—
163#3676—31no—
164#3676—31no—
165#3676—31no—
166(C2×D9)⋊C4—31no—
167(C2×D9)⋊C4—31no—
168(C2×D9)⋊C4—31no—
169(C2×D9)⋊C4C2×D311yescharacteristic
170(C2×D9)⋊C4C2×D311yescharacteristic
171(C2×D9)⋊C4C2×D311yescharacteristic
172C4⋊Dic9—31no—
173C4⋊Dic9—31no—
174C4⋊Dic9—61no—
175C4⋊Dic9C2×D311yescharacteristic, complemented
176Dic9⋊C4—31no—
177Dic9⋊C4—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—61no—
182Dic9⋊C4—61no—
183Dic9⋊C4C2×D311yescharacteristic, complemented
184C4×Dic9—31no—
185C4×Dic9—31no—
186C4×Dic9C2×D311yescharacteristic, complemented
187C22×C3×C9C2411yescharacteristic
188C2×C3⋊D9#4112yes—
189C2×C3⋊D9#4112yes—
190C2×C3⋊D9#4112yes—
191C2×D3×C9—21no—
192C2×D3×C9—21no—
193C2×D3×C9—21no—
194C2×C3×D9—21no—
195C2×C3×D9—21no—
196C2×C3×D9—21no—
197D3×D9—44no—
198C3×C4×C9—21no—
199C3×C4×C9—21no—
200C3×C4×C9—21no—
201C3⋊Dic9—21no—
202C3⋊Dic9—21no—
203C3⋊Dic9—21no—
204C9×Dic3—21no—
205C9×Dic3—21no—
206C9×Dic3—21no—
207C3×Dic9—21no—
208C3×Dic9—21no—
209C3×Dic9—21no—
210C3×#126—31no—
211C3×#126—91no—
212#898—31no—
213#898—91no—
214#898—91no—
215#898—91no—
216#898—91no—
217#898D911yescharacteristic, complemented
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×C4⋊C4—181no—
225D3×C22⋊C4—91no—
226D3×C22⋊C4—91no—
227D3×C22⋊C4—91no—
228D3×C22⋊C4—91no—
229D3×C22⋊C4—91no—
230D3×C22⋊C4—91no—
231#879—91no—
232#879—91no—
233#879—91no—
234#879—91no—
235#879—91no—
236#879—91no—
237#876—91no—
238#876—91no—
239C42×D3—91no—
240C42×D3—91no—
241C22×C3⋊D3—31no—
242C22×C3×D3—31no—
243C22×C3×D3C22×D311yescharacteristic
244C2×D32—62no—
245C2×D32—62no—
246C2×D32—62no—
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C3⋊Dic3—31no—
251C2×C3⋊Dic3—31no—
252C2×C3⋊Dic3—31no—
253C4×C3⋊D3—62no—
254C4×C3⋊D3—62no—
255C4×C3⋊D3—62no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—31no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3C22×D311yescharacteristic
260C2×C3×Dic3C22×D311yescharacteristic
261C2×C3×Dic3C22×D311yescharacteristic
262#624—62no—
263#624—62no—
264#624—62no—
265C23×C9—31no—
266C22×D9—31no—
267C22×D9—61no—
268C22×D9—62no—
269C22×D9—62no—
270C22×D9—62no—
271C22×D9C22×D311yescharacteristic
272C2×C4×C9—21no—
273C2×C4×C9—21no—
274C2×C4×C9—21no—
275C2×C4×C9—31no—
276C2×C4×C9—31no—
277C2×C4×C9—31no—
278C2×C4×C9C22×D311yescharacteristic
279C2×C4×C9C22×D311yescharacteristic
280C2×C4×C9C22×D311yescharacteristic
281C2×Dic9—31no—
282C2×Dic9—31no—
283C2×Dic9—31no—
284C2×Dic9—61no—
285C2×Dic9—61no—
286C2×Dic9—61no—
287C2×Dic9C22×D311yescharacteristic
288C2×Dic9C22×D311yescharacteristic
289C2×Dic9C22×D311yescharacteristic
290C4×D9—62no—
291C4×D9—62no—
292C4×D9—62no—
293C4×D9—62no—
294C4×D9—62no—
295C4×D9—62no—
296C4×D9—64no—
297C4×D9—122no—
298C4×D9—122no—
299C2×#126—271noSylow
300C2×C3×C9C2×#4111yescharacteristic
301C2×C3×C9C2×#4111yescharacteristic
302C2×C3×C9C2×#4111yescharacteristic
303C3⋊D9#12614yescomplemented
304D3×C9—41no—
305C3×D9—41no—
306C23×D3—91no—
307C23×D3—91no—
308C2×C4×D3—91no—
309C2×C4×D3—91no—
310C2×C4×D3—91no—
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—181no—
321C2×C4×D3—181no—
322C2×C4×D3—181no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4C2×D911yescharacteristic, complemented
329C3×C4⋊C4D3211yescharacteristic
330C3×C22⋊C4—31no—
331C3×C22⋊C4—31no—
332C3×C22⋊C4—31no—
333C3×C22⋊C4—91no—
334C3×C22⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C42—31no—
337C3×C42—91no—
338#217—91no—
339#217—91no—
340#217—91no—
341#217—91no—
342#217—91no—
343#217—91no—
344(C2×D3)⋊C4—31no—
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—31no—
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)⋊C4C2×D911yescharacteristic
354(C2×D3)⋊C4C2×D911yescharacteristic
355(C2×D3)⋊C4C2×D911yescharacteristic
356C4⋊Dic3—31no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—91no—
360C4⋊Dic3—91no—
361C4⋊Dic3—181no—
362C4⋊Dic3C2×D911yescharacteristic, complemented
363Dic3⋊C4—31no—
364Dic3⋊C4—91no—
365Dic3⋊C4—91no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—181no—
375Dic3⋊C4—181no—
376Dic3⋊C4C2×D911yescharacteristic, complemented
377C4×Dic3—31no—
378C4×Dic3—91no—
379C4×Dic3—91no—
380C4×Dic3—91no—
381C4×Dic3—91no—
382C4×Dic3C2×D911yescharacteristic, complemented
383C22×C32C23×D311yescharacteristic
384C2×C3⋊D3—32no—
385C2×C3⋊D3—32no—
386C2×C3⋊D3—32no—
387C2×C3×D3—21no—
388C2×C3×D3—21no—
389C2×C3×D3—21no—
390C2×C3×D3—61no—
391C2×C3×D3—61no—
392C2×C3×D3—61no—
393D32—124no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C3⋊Dic3—61no—
398C3⋊Dic3—61no—
399C3⋊Dic3—61no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—21no—
403C3×Dic3—61no—
404C3×Dic3—61no—
405C3×Dic3—61no—
406C22×C9—21no—
407C22×C9—61no—
408C22×C9—61no—
409C22×C9—61no—
410C22×C9C23×D311yescharacteristic
411C2×D9—21no—
412C2×D9—21no—
413C2×D9—21no—
414C2×D9—32no—
415C2×D9—32no—
416C2×D9—32no—
417C2×D9—62no—
418C2×D9—62no—
419C2×D9—62no—
420C2×D9—124no—
421C4×C9—22no—
422C4×C9—21no—
423C4×C9—21no—
424C4×C9—21no—
425C4×C9—41no—
426C4×C9—41no—
427C4×C9—61no—
428C4×C9—61no—
429C4×C9—61no—
430Dic9—21no—
431Dic9—21no—
432Dic9—21no—
433Dic9—62no—
434Dic9—61no—
435Dic9—61no—
436Dic9—61no—
437Dic9—121no—
438Dic9—121no—
439#126—31no—
440#126—91no—
441#126—271no—
442#126—271no—
443#126—271no—
444#126—271no—
445#126—271no—
446#126—271no—
447C2×C4⋊C4—271no—
448C2×C4⋊C4—271no—
449C2×C4⋊C4—271no—
450C2×C22⋊C4—271no—
451C2×C22⋊C4—271no—
452C2×C22⋊C4—271no—
453C2×C42—271no—
454C3×C9C2×#12611yescharacteristic, complemented, Sylow
455C23×C3—31no—
456C23×C3—91no—
457C22×D3—31no—
458C22×D3—91no—
459C22×D3—91no—
460C22×D3—181no—
461C22×D3—182no—
462C22×D3—182no—
463C22×D3—182no—
464C22×D3—182no—
465C22×D3—182no—
466C22×D3—182no—
467C22×D3C22×D911yescharacteristic
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—91no—
475C2×C3×C4—91no—
476C2×C3×C4—91no—
477C2×C3×C4C22×D911yescharacteristic
478C2×C3×C4C22×D911yescharacteristic
479C2×C3×C4C22×D911yescharacteristic
480C2×C3×C4C2×D3211yescharacteristic
481C2×C3×C4C2×D3211yescharacteristic
482C2×C3×C4C2×D3211yescharacteristic
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—91no—
487C2×Dic3—91no—
488C2×Dic3—91no—
489C2×Dic3—91no—
490C2×Dic3—91no—
491C2×Dic3—91no—
492C2×Dic3—181no—
493C2×Dic3—181no—
494C2×Dic3—181no—
495C2×Dic3C22×D911yescharacteristic
496C2×Dic3C22×D911yescharacteristic
497C2×Dic3C22×D911yescharacteristic
498C4×D3—182no—
499C4×D3—182no—
500C4×D3—182no—
501C4×D3—182no—
502C4×D3—182no—
503C4×D3—182no—
504C4×D3—182no—
505C4×D3—182no—
506C4×D3—182no—
507C4×D3—182no—
508C4×D3—182no—
509C4×D3—182no—
510C4×D3—184no—
511C4×D3—362no—
512C4×D3—362no—
513C2×C32D3×#4111yescharacteristic
514C2×C32D3×#4111yescharacteristic
515C2×C32D3×#4111yescharacteristic
516C3⋊D3—34no—
517C3×D3—41no—
518C3×D3—121no—
519C2×C9—21no—
520C2×C9—21no—
521C2×C9—21no—
522C2×C9—121no—
523C2×C9D3×#4111yescharacteristic
524C2×C9D3×#4111yescharacteristic
525C2×C9D3×#4111yescharacteristic
526D9—34no—
527D9—41no—
528D9—64no—
529C24—271no—
530C22×C4—271no—
531C22×C4—271no—
532C22×C4—271no—
533C22×C4—271no—
534C22×C4—271no—
535C22×C4—271no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4—271no—
541C4⋊C4—271no—
542C4⋊C4—271no—
543C4⋊C4—271no—
544C4⋊C4—271no—
545C4⋊C4—271no—
546C4⋊C4—271no—
547C4⋊C4D3×D911yescharacteristic, complemented
548C22⋊C4—31no—
549C22⋊C4—31no—
550C22⋊C4—31no—
551C22⋊C4—91no—
552C22⋊C4—91no—
553C22⋊C4—91no—
554C22⋊C4—271no—
555C22⋊C4—271no—
556C22⋊C4—271no—
557C22⋊C4—271no—
558C22⋊C4—271no—
559C22⋊C4—271no—
560C42—31no—
561C42—91no—
562C42—271no—
563C42—271no—
564C22×C3—21no—
565C22×C3—61no—
566C22×C3—61no—
567C22×C3—61no—
568C22×C3—181no—
569C22×C3—181no—
570C22×C3—181no—
571C22×C3C23×D911yescharacteristic
572C22×C3C22×D3211yescharacteristic
573C2×D3—21no—
574C2×D3—21no—
575C2×D3—21no—
576C2×D3—61no—
577C2×D3—61no—
578C2×D3—61no—
579C2×D3—92no—
580C2×D3—92no—
581C2×D3—92no—
582C2×D3—92no—
583C2×D3—92no—
584C2×D3—92no—
585C2×D3—182no—
586C2×D3—182no—
587C2×D3—182no—
588C2×D3—364no—
589C2×D3—364no—
590C3×C4—22no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—181no—
603C3×C4—181no—
604C3×C4—181no—
605Dic3—21no—
606Dic3—21no—
607Dic3—21no—
608Dic3—61no—
609Dic3—61no—
610Dic3—61no—
611Dic3—182no—
612Dic3—181no—
613Dic3—181no—
614Dic3—181no—
615Dic3—181no—
616Dic3—181no—
617Dic3—181no—
618Dic3—361no—
619Dic3—361no—
620C32D3×#12611yescharacteristic
621C9—21no—
622C9D3×#12611yescharacteristic, complemented
623C23—31no—
624C23—91no—
625C23—271no—
626C23—542no—
627C23—542no—
628C23—542no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—91no—
633C2×C4—91no—
634C2×C4—91no—
635C2×C4—271no—
636C2×C4—271no—
637C2×C4—271no—
638C2×C4—542no—
639C2×C4—542no—
640C2×C4—542no—
641C2×C4—542no—
642C2×C4—542no—
643C2×C4—542no—
644C2×C4C2×D3×D911yescharacteristic
645C2×C4C2×D3×D911yescharacteristic
646C2×C4C2×D3×D911yescharacteristic
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—121no—
651C2×C3—361no—
652C2×C3#41×D911yescharacteristic
653C2×C3#41×D911yescharacteristic
654C2×C3#41×D911yescharacteristic
655C2×C3#6430611yescharacteristic
656C2×C3#6431211yescharacteristic
657C2×C3#6431911yescharacteristic
658D3—41no—
659D3—94no—
660D3—94no—
661D3—121no—
662D3—184no—
663C22—61no—
664C22—61no—
665C22—61no—
666C22—181no—
667C22—181no—
668C22—181no—
669C22—272no—
670C22—272no—
671C22—272no—
672C22—1084no—
673C22C22×D3×D911yescharacteristic
674C4—21no—
675C4—21no—
676C4—21no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—181no—
681C4—181no—
682C4—181no—
683C4—541no—
684C4—541no—
685C4—541no—
686C3—21no—
687C3D9×#12611yescharacteristic, complemented
688C3#1059465611yescharacteristic
689C2—121no—
690C2—274no—
691C2—361no—
692C2#1172247511yescharacteristic
693C2#1172249811yescharacteristic
694C2#1172251411yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radicalC22×D3×D9C22
hypercenterC4⋊C4D3×D9
hypocenterC3×C9C2×#126
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×#63460C2semidirect
7. #11721000C2semidirect
8. #11720980C2semidirect
9. C4×(C3⋊D9)⋊C4C2semidirect
10. #11720965C2semidirect
11. #11720963C2semidirect
12. #11720962C2semidirect
13. #11720949C2semidirect
14. #11720947C2semidirect
15. #11720946C2semidirect
25. C3×C9×C4⋊C4C22semidirect
26. C4⋊(C3⋊Dic9)C22semidirect
27. #88534C22semidirect
28. #88534C22semidirect
35. C9×C4⋊Dic3C22semidirect
36. C9×Dic3⋊C4C22semidirect
37. C4×C9×Dic3C22semidirect
38. C3×C4⋊Dic9C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. C3×C4×Dic9C22semidirect
47. Dic3⋊Dic9C22semidirect
48. #88442C22semidirect
49. #88442C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
71. #63460D3semidirect
158. C9×C4⋊C4C2×D3semidirect
175. C4⋊Dic9C2×D3semidirect
183. Dic9⋊C4C2×D3semidirect
186. C4×Dic9C2×D3semidirect
217. #898D9semidirect
303. C3⋊D9#126semidirect
328. C3×C4⋊C4C2×D9semidirect
362. C4⋊Dic3C2×D9semidirect
376. Dic3⋊C4C2×D9semidirect
382. C4×Dic3C2×D9semidirect
454. C3×C9C2×#126semidirect
547. C4⋊C4D3×D9semidirect
622. C9D3×#126semidirect
687. C3D9×#126semidirect

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×#634602
#117210482
#117210002
#117209802
C4×(C3⋊D9)⋊C42
#117209652
#117209632
#117209622
#117209492
#117209472
#117209462
#105946563
D9×#1263