Finite Group Databasebeta

← #13149380

Subgroups — #13149380

Order 1728.

818 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721752C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63455C211yesmaximal, characteristic, complemented
4#11721049C211yesmaximal, characteristic
5#11721048C211yesmaximal, characteristic, complemented
6D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#11721042C211yesmaximal, characteristic, complemented
8#11721031C211yesmaximal, characteristic, complemented
9C4×#6192C211yesmaximal, characteristic, complemented
10#11720981C211yesmaximal, characteristic, complemented
11#11720974C211yesmaximal, characteristic, complemented
12#11720963C211yesmaximal, characteristic, complemented
13#11720945C211yesmaximal, characteristic, complemented
14#11720942C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594645—31nomaximal
17#10589807—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C3×D36C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic, complemented
24C2×#6194C2211yescharacteristic
25C2×#6192C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×Dic3×D9C2211yescharacteristic
28C3×C9×C4⋊C4C2211yescharacteristic, complemented
29#88536C2211yescharacteristic
30#88536C2211yescharacteristic
31#88534C2211yescharacteristic, complemented
32#88534C2211yescharacteristic, complemented
33C9×(C2×D3)⋊C4C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
38C9×C4⋊Dic3C2211yescharacteristic, complemented
39C9×Dic3⋊C4C2211yescharacteristic, complemented
40C4×C9×Dic3C2211yescharacteristic, complemented
41C3×C4×Dic9C2211yescharacteristic, complemented
42(C2×D3)⋊Dic9C2211yescharacteristic
43(C2×D3)⋊Dic9C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64105—31no—
54C3×#898D311yescharacteristic
55C3×#893—31no—
56#63922—31no—
57#63921—31no—
58D3×(C2×D3)⋊C4—31no—
59#63913—31no—
60#63905—31no—
61C4×#626—31no—
62#63884—31no—
63#63877—31no—
64#63859—31no—
65#63857—31no—
66#63854—31no—
67#63836—31no—
68C9×#126—31no—
69#63459—31no—
70#63458—31no—
71#63458—61no—
72#63456—31no—
73#63456—31no—
74#63455D311yescharacteristic, complemented
75#63454—31no—
76#63447—31no—
77#63445—31no—
78#63444—31no—
79C22⋊C4×D9—31no—
80C22⋊C4×D9—31no—
81#63441—31no—
82C4×D36—31no—
83#63434—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×D3×D9—22no—
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C4×C3⋊D9—41no—
98#6226—41no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C3×D36—22no—
105C3×C4×D9—41no—
106C3×C4×D9—41no—
107#6194—41no—
108#6192—22no—
109(C3⋊D9)⋊C4—22no—
110Dic3×D9—22no—
111#5705—91no—
112#5556—91no—
113C22×D32—31no—
114C2×C4×C3⋊D3—31no—
115C2×#634—31no—
116C2×C3×D12—31no—
117C2×C3×C4×D3—31no—
118C2×C3×C4×D3—31no—
119C2×#626—31no—
120C2×#625—31no—
121C2×#624—31no—
122C2×D3×Dic3—31no—
123C23×D9—31no—
124C32×C4⋊C4C2×D311yescharacteristic
125#3752—31no—
126#3752—31no—
127#3750—31no—
128#3750—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4C2×D311yescharacteristic
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×(C2×D3)⋊C4C2×D311yescharacteristic
134C3×C4⋊Dic3C2×D311yescharacteristic
135C3×Dic3⋊C4C2×D311yescharacteristic
136C3×C4×Dic3—31no—
137C3×C4×Dic3C2×D311yescharacteristic
138#3724—31no—
139Dic3⋊Dic3—31no—
140Dic3⋊Dic3—31no—
141#3722—31no—
142(C2×D3)⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148Dic32—31no—
149C2×#611—31no—
150C2×D36—31no—
151C2×D36C2×D311yescharacteristic
152C2×C4×D9—31no—
153C2×C4×D9—31no—
154C2×C4×D9—31no—
155C2×C4×D9—61no—
156C2×C4×D9C2×D311yescharacteristic
157C2×C4×D9C2×D311yescharacteristic, complemented
158C2×Dic18—31no—
159C2×Dic18—61no—
160C9×C4⋊C4—21no—
161C9×C4⋊C4—31no—
162C9×C4⋊C4—31no—
163C9×C4⋊C4C2×D311yescharacteristic, complemented
164C9×C22⋊C4—31no—
165C9×C22⋊C4—31no—
166C9×C22⋊C4—31no—
167C42×C9—31no—
168#3676—31no—
169#3676—31no—
170(C2×D9)⋊C4—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—61no—
178(C2×D9)⋊C4—61no—
179(C2×D9)⋊C4C2×D311yescharacteristic
180(C2×D9)⋊C4C2×D311yescharacteristic, complemented
181C4⋊Dic9—31no—
182C4⋊Dic9—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—61no—
187Dic9⋊C4—61no—
188C4×Dic9—31no—
189C4×Dic9C2×D311yescharacteristic, complemented
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#4112yes—
203D3×D9—44no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C3⋊Dic9—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C9×Dic3—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#126—31no—
216C3×C4×D4—91no—
217#937—91no—
218#935—91no—
219#929—91no—
220C4×#67—91no—
221C2×(C2×D3)⋊C4—91no—
222#924—91no—
223#898D911yescharacteristic, complemented
224#897—91no—
225#896—91no—
226#896—91no—
227#896—181no—
228#894—91no—
229#894—91no—
230#893—31no—
231#892—91no—
232#885—91no—
233#885—91no—
234#883—91no—
235#883—91no—
236#882—91no—
237D3×C22⋊C4—91no—
238D3×C22⋊C4—91no—
239D3×C22⋊C4—91no—
240#879—91no—
241#877—91no—
242#876—91no—
243C4×D12—91no—
244#872—91no—
245#872—91no—
246C22×C3⋊D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3C22×D311yescharacteristic
250C2×D32—62no—
251C2×D32—62no—
252C2×D32—121no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C4×C3⋊D3—121no—
260#634—121no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C3×D12—62no—
267C3×C4×D3—121no—
268C3×C4×D3—121no—
269#626—62no—
270#625—121no—
271#624—62no—
272D3×Dic3—62no—
273C23×C9—31no—
274C22×D9—31no—
275C22×D9—61no—
276C22×D9—62no—
277C22×D9—62no—
278C22×D9—121no—
279C22×D9C22×D311yescharacteristic
280C22×D9C22×D311yescharacteristic
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9C22×D311yescharacteristic
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290#611—121no—
291C2×Dic9—31no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—61no—
295C2×Dic9—61no—
296C2×Dic9—61no—
297C2×Dic9C22×D311yescharacteristic
298C2×Dic9C22×D311yescharacteristic
299D36—22no—
300D36—62no—
301C4×D9—41no—
302C4×D9—41no—
303C4×D9—62no—
304C4×D9—62no—
305C4×D9—121no—
306C4×D9—122no—
307Dic18—121no—
308Dic18—122no—
309#551—271noSylow
310C2×C3×C9C2×#4111yescharacteristic
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9H(5,𝔽2)11yescharacteristic
313C3⋊D9—22no—
314D3×C9—41no—
315C3×D9—22no—
316C3×D9—41no—
317C23×D3—91no—
318C23×D3—91no—
319C2×C3×D4—91no—
320C22×C3×C4—91no—
321C22×C3×C4—91no—
322C2×#67—91no—
323C2×#67—91no—
324C2×#67—91no—
325C22×Dic3—91no—
326C2×D12—31no—
327C2×D12—91no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—181no—
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—181no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4C2×D911yescharacteristic, complemented
343C3×C4⋊C4D3211yescharacteristic
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C42—31no—
350C3×C42—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354#217—91no—
355#217—91no—
356#217—91no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
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—181no—
372(C2×D3)⋊C4—181no—
373(C2×D3)⋊C4C2×D911yescharacteristic
374(C2×D3)⋊C4C2×D911yescharacteristic
375(C2×D3)⋊C4C2×D911yescharacteristic
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3C2×D911yescharacteristic, complemented
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—181no—
388Dic3⋊C4—181no—
389Dic3⋊C4C2×D911yescharacteristic, complemented
390C4×Dic3—31no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3C2×D911yescharacteristic, complemented
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—32no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407D32—124no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—61no—
421C22×C9—61no—
422C22×C9—61no—
423C22×C9C23×D311yescharacteristic
424C2×D9—21no—
425C2×D9—21no—
426C2×D9—21no—
427C2×D9—21no—
428C2×D9—21no—
429C2×D9—32no—
430C2×D9—62no—
431C2×D9—61no—
432C2×D9—61no—
433C2×D9—121no—
434C2×D9—121no—
435C2×D9—124no—
436C2×D9#23512yes—
437C4×C9—21no—
438C4×C9—21no—
439C4×C9—21no—
440C4×C9—41no—
441C4×C9—41no—
442C4×C9—41no—
443C4×C9—61no—
444C4×C9—61no—
445C4×C9—61no—
446Dic9—21no—
447Dic9—21no—
448Dic9—62no—
449Dic9—61no—
450Dic9—61no—
451Dic9—61no—
452Dic9—121no—
453Dic9—121no—
454#126—31no—
455#126—271no—
456#124—271no—
457#123—271no—
458#123—271no—
459#123—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462#120—271no—
463C4×D4—91no—
464C4×D4—271no—
465#117—271no—
466#117—271no—
467C2×C22⋊C4—271no—
468C2×C22⋊C4—271no—
469C3×C9#55111yescharacteristic, complemented, Sylow
470C23×C3—31no—
471C23×C3—91no—
472C23×C3—91no—
473C22×D3—31no—
474C22×D3—31no—
475C22×D3—91no—
476C22×D3—91no—
477C22×D3—181no—
478C22×D3—182no—
479C22×D3—182no—
480C22×D3—182no—
481C22×D3—182no—
482C22×D3—361no—
483C22×D3—361no—
484C22×D3C22×D911yescharacteristic
485C3×D4—182no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—91no—
493C2×C3×C4—91no—
494C2×C3×C4—361no—
495C2×C3×C4—361no—
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C22×D911yescharacteristic
498C2×C3×C4C22×D911yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500C2×C3×C4C2×D3211yescharacteristic
501C2×C3×C4C2×D3211yescharacteristic
502#67—182no—
503#67—361no—
504#67—361no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—181no—
514C2×Dic3—181no—
515C2×Dic3—181no—
516C2×Dic3—182no—
517C2×Dic3C22×D911yescharacteristic
518C2×Dic3C22×D911yescharacteristic
519C2×Dic3C22×D911yescharacteristic
520D12—62no—
521D12—182no—
522C4×D3—121no—
523C4×D3—121no—
524C4×D3—182no—
525C4×D3—182no—
526C4×D3—182no—
527C4×D3—361no—
528C4×D3—361no—
529C4×D3—362no—
530Dic6—361no—
531Dic6—361no—
532Dic6—362no—
533C2×C32D3×#4111yescharacteristic
534C2×C32D3×#4111yescharacteristic
535C2×C32#100911yescharacteristic
536C3⋊D3—62no—
537C3×D3—41no—
538C3×D3—62no—
539C3×D3—121no—
540C2×C9—21no—
541C2×C9—21no—
542C2×C9—21no—
543C2×C9—121no—
544C2×C9C2×#23511yescharacteristic
545C2×C9#100411yescharacteristic
546C2×C9D3×#4111yescharacteristic
547D9—22no—
548D9—41no—
549D9—62no—
550D9—122no—
551C24—271no—
552C2×Q8—271no—
553C2×D4—91no—
554C2×D4—271no—
555C2×D4—271no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4D3×D911yescharacteristic, complemented
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—91no—
573C22⋊C4—91no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C42—31no—
584C42—91no—
585C42—271no—
586C22×C3—21no—
587C22×C3—61no—
588C22×C3—61no—
589C22×C3—61no—
590C22×C3—92no—
591C22×C3—181no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3C23×D911yescharacteristic
597C22×C3C22×D3211yescharacteristic
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—21no—
601C2×D3—32no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—61no—
606C2×D3—61no—
607C2×D3—92no—
608C2×D3—92no—
609C2×D3—182no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—361no—
615C2×D3—361no—
616C2×D3—364no—
617C2×D3—364no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—61no—
630C3×C4—181no—
631C3×C4—181no—
632Dic3—21no—
633Dic3—21no—
634Dic3—21no—
635Dic3—61no—
636Dic3—61no—
637Dic3—182no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—181no—
644Dic3—361no—
645Dic3—361no—
646C32#570511yescharacteristic
647C9—21no—
648C9#555611yescharacteristic, complemented
649C23—31no—
650C23—91no—
651C23—91no—
652C23—271no—
653C23—542no—
654C23—542no—
655C23—1081no—
656Q8—1081no—
657D4—182no—
658D4—542no—
659D4—1081no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—271no—
666C2×C4—271no—
667C2×C4—271no—
668C2×C4—361no—
669C2×C4—361no—
670C2×C4—542no—
671C2×C4—542no—
672C2×C4—1081no—
673C2×C4C2×D3×D911yescharacteristic
674C2×C4C2×D3×D911yescharacteristic
675C2×C4C2×D3×D911yescharacteristic
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—121no—
680C2×C3—182no—
681C2×C3—361no—
682C2×C3#41×D911yescharacteristic
683C2×C3#41×D911yescharacteristic
684C2×C3#6371511yescharacteristic
685C2×C3D3×#23511yescharacteristic
686C2×C3#6431411yescharacteristic
687C2×C3#6431911yescharacteristic
688D3—41no—
689D3—62no—
690D3—121no—
691D3—182no—
692D3—182no—
693D3—362no—
694C22—61no—
695C22—61no—
696C22—61no—
697C22—92no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22—181no—
703C22—272no—
704C22—541no—
705C22—541no—
706C22—1084no—
707C22C22×D3×D911yescharacteristic
708C4—21no—
709C4—21no—
710C4—21no—
711C4—61no—
712C4—61no—
713C4—61no—
714C4—181no—
715C4—181no—
716C4—541no—
717C4—541no—
718C4—541no—
719C3—21no—
720C3#1058980711yescharacteristic, complemented
721C3#1059464511yescharacteristic
722C2—121no—
723C2—182no—
724C2—361no—
725C2—542no—
726C2D9×#23511yescharacteristic
727C2#1172250111yescharacteristic
728C2#1172251411yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
prime radical#11721049C2
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#551
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. #11721752C2semidirect
2. C9×#898C2semidirect
3. C3×#63455C2semidirect
5. #11721048C2semidirect
6. D9×(C2×D3)⋊C4C2semidirect
7. #11721042C2semidirect
8. #11721031C2semidirect
9. C4×#6192C2semidirect
10. #11720981C2semidirect
11. #11720974C2semidirect
12. #11720963C2semidirect
13. #11720945C2semidirect
14. #11720942C2semidirect
15. #11720899C2semidirect
20. C2×#6226C22semidirect
23. C2×C3×C4×D9C22semidirect
28. C3×C9×C4⋊C4C22semidirect
31. #88534C22semidirect
32. #88534C22semidirect
37. C3×(C2×D9)⋊C4C22semidirect
38. C9×C4⋊Dic3C22semidirect
39. C9×Dic3⋊C4C22semidirect
40. C4×C9×Dic3C22semidirect
41. C3×C4×Dic9C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
74. #63455D3semidirect
157. C2×C4×D9C2×D3semidirect
163. C9×C4⋊C4C2×D3semidirect
180. (C2×D9)⋊C4C2×D3semidirect
189. C4×Dic9C2×D3semidirect
223. #898D9semidirect
342. C3×C4⋊C4C2×D9semidirect
378. C4⋊Dic3C2×D9semidirect
389. Dic3⋊C4C2×D9semidirect
393. C4×Dic3C2×D9semidirect
469. C3×C9#551semidirect
568. C4⋊C4D3×D9semidirect
648. C9#5556semidirect
720. C3#10589807semidirect

Maximal subgroups

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

subgroupindex
#117217522
C9×#8982
C3×#634552
#117210492
#117210482
D9×(C2×D3)⋊C42
#117210422
#117210312
C4×#61922
#117209812
#117209742
#117209632
#117209452
#117209422
#117208992
#105946453
#105898073