Finite Group Databasebeta

← #13148432

Subgroups — #13148432

Order 1728.

820 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721731C211yesmaximal, characteristic, complemented
2C9×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#63445C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic
5#11721280C211yesmaximal, characteristic, complemented
6Dic3×#611C211yesmaximal, characteristic, complemented
7#11721251C211yesmaximal, characteristic, complemented
8D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721011C211yesmaximal, characteristic, complemented
11#11720996C211yesmaximal, characteristic, complemented
12#11720961C211yesmaximal, characteristic, complemented
13#11720943C211yesmaximal, characteristic, complemented
14#11720926C211yesmaximal, characteristic, complemented
15#11720921C211yesmaximal, characteristic, complemented
16#10594299—31nomaximal
17#10589658—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic, complemented
24C2×C4×D3×C9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×D3×Dic9C2211yescharacteristic
27C2×Dic3×D9C2211yescharacteristic
28C3×C9×C22⋊C4C2211yescharacteristic, complemented
29#88551C2211yescharacteristic, complemented
30#88536C2211yescharacteristic
31#88536C2211yescharacteristic
32C4×C3⋊Dic9C2211yescharacteristic, complemented
33C3×#3676C2211yescharacteristic, complemented
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C9×Dic3⋊C4C2211yescharacteristic, complemented
37C4×C9×Dic3C2211yescharacteristic, complemented
38C3×C4⋊Dic9C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40(C2×D3)⋊Dic9C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47#88442C2211yescharacteristic, complemented
48Dic9⋊Dic3C2211yescharacteristic, complemented
49Dic9⋊Dic3C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64094—31no—
54C3×#883—31no—
55C3×#67⋊C4D311yescharacteristic
56#63983—31no—
57Dic3×#67—31no—
58#63969—31no—
59#63966—31no—
60D3×(C2×D3)⋊C4—31no—
61D3×(C2×D3)⋊C4—31no—
62#63896—31no—
63#63878—31no—
64#63868—31no—
65#63857—31no—
66#63855—31no—
67#63848—31no—
68C4×D4×C9—31no—
69#63499—31no—
70#63497—31no—
71#63491—31no—
72C4×#611—31no—
73C2×(C2×D9)⋊C4—31no—
74#63486—31no—
75#63460—31no—
76#63458—31no—
77#63447—31no—
78#63447—61no—
79#63445D311yescharacteristic, complemented
80C22⋊C4×D9—31no—
81#63439—31no—
82#63438—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×D3×D9—22no—
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93#6233—41no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97#6226—41no—
98C9×#67—22no—
99C3×#611—22no—
100C2×C9×Dic3—41no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C4×D3×C9—41no—
108C3×C4×D9—22no—
109D3×Dic9—22no—
110Dic3×D9—41no—
111#5658—91no—
112#5556—91no—
113C22×D32—31no—
114C2×#638—31no—
115C2×#634—31no—
116C2×C3×#67—31no—
117C2×C3×#67C2×D311yescharacteristic
118C22×C3×Dic3C2×D311yescharacteristic
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C23×D9—31no—
124C32×C22⋊C4C2×D311yescharacteristic
125#3757—31no—
126#3752—31no—
127#3752—31no—
128C4×C3⋊Dic3—31no—
129C3×#217—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4C2×D311yescharacteristic
132C3×C4⋊Dic3—31no—
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4C2×D311yescharacteristic
135C3×C4×Dic3C2×D311yescharacteristic
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(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148Dic32—31no—
149C2×D4×C9—31no—
150C22×C4×C9—31no—
151C22×C4×C9—31no—
152C2×#611—31no—
153C2×#611—61no—
154C2×#611C2×D311yescharacteristic
155C22×Dic9—31no—
156C2×C4×D9—31no—
157C2×C4×D9C2×D311yescharacteristic
158C2×Dic18—31no—
159C2×Dic18—61no—
160C9×C4⋊C4—31no—
161C9×C22⋊C4—21no—
162C9×C22⋊C4—31no—
163C9×C22⋊C4C2×D311yescharacteristic, complemented
164C42×C9—31no—
165#3676—31no—
166#3676—31no—
167#3676—31no—
168#3676—61no—
169#3676C2×D311yescharacteristic, complemented
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
180C4⋊Dic9C2×D311yescharacteristic, complemented
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4C2×D311yescharacteristic, complemented
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9—61no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9#4112yes—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9#4112yes—
203D3×D9—44no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#123—91no—
216C3×C4×D4—31no—
217#937—91no—
218#937—91no—
219#935—91no—
220D4×Dic3—91no—
221#929—91no—
222C4×#67—91no—
223C2×(C2×D3)⋊C4—91no—
224C2×(C2×D3)⋊C4—91no—
225#926—91no—
226#924—91no—
227#898—91no—
228#898—91no—
229#898—91no—
230#897—91no—
231#896—91no—
232#892—91no—
233#886—91no—
234#885—91no—
235#885—91no—
236#885—181no—
237#883—31no—
238#883—91no—
239#67⋊C4D911yescharacteristic, complemented
240D3×C22⋊C4—91no—
241D3×C22⋊C4—91no—
242#878—91no—
243#877—91no—
244#876—91no—
245#872—91no—
246C23×C32C22×D311yescharacteristic
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
255#638—121no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259#634—121no—
260C3×#67—22no—
261C3×#67—62no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×C4×D3—41no—
270C3×C4×D3—62no—
271D3×Dic3—62no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9—31no—
275C23×C9C22×D311yescharacteristic
276C22×D9—31no—
277C22×D9—61no—
278C22×D9—62no—
279C22×D9—62no—
280C22×D9—121no—
281C22×D9C22×D311yescharacteristic
282D4×C9—62no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9—121no—
289C2×C4×C9—121no—
290C2×C4×C9C22×D311yescharacteristic
291C2×C4×C9C22×D311yescharacteristic
292#611—22no—
293#611—121no—
294#611—122no—
295C2×Dic9—31no—
296C2×Dic9—31no—
297C2×Dic9—31no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—61no—
301C2×Dic9—62no—
302C2×Dic9C22×D311yescharacteristic
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C4×D9—22no—
306C4×D9—121no—
307Dic18—121no—
308Dic18—122no—
309#551—271noSylow
310C2×C3×C9—41no—
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314C3⋊D9—41no—
315D3×C9—22no—
316C3×D9—22no—
317C23×D3—91no—
318C23×D3—91no—
319C2×C3×D4—31no—
320C2×C3×D4—91no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—91no—
324C2×#67—31no—
325C2×#67—91no—
326C2×#67—91no—
327C2×#67—181no—
328C2×#67C2×D911yescharacteristic
329C22×Dic3—91no—
330C22×Dic3—91no—
331C22×Dic3C2×D911yescharacteristic, complemented
332C2×C4×D3—31no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3C2×D911yescharacteristic
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—181no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4—91no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4C2×D911yescharacteristic, complemented
347C3×C22⋊C4D3211yescharacteristic
348C3×C42—31no—
349#217—31no—
350#217—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354#217—91no—
355#217—91no—
356#217—181no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—91no—
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—91no—
372(C2×D3)⋊C4—181no—
373(C2×D3)⋊C4—181no—
374(C2×D3)⋊C4C2×D911yescharacteristic
375C4⋊Dic3—31no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380Dic3⋊C4—31no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4C2×D911yescharacteristic, complemented
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—181no—
393C4×Dic3C2×D911yescharacteristic, complemented
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32C23×D311yescharacteristic
398C2×C3⋊D3—61no—
399C2×C3⋊D3—61no—
400C2×C3⋊D3—61no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—32no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3#23512yes—
407D32—124no—
408C32×C4—21no—
409C32×C4—21no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—21no—
423C22×C9—32no—
424C22×C9—41no—
425C22×C9—41no—
426C22×C9—41no—
427C22×C9—61no—
428C22×C9—61no—
429C22×C9C23×D311yescharacteristic
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—61no—
433C2×D9—61no—
434C2×D9—61no—
435C2×D9—121no—
436C2×D9—121no—
437C2×D9—121no—
438C2×D9—124no—
439C2×D9#23712yes—
440C4×C9—21no—
441C4×C9—21no—
442C4×C9—41no—
443C4×C9—41no—
444C4×C9—61no—
445C4×C9—61no—
446C4×C9—61no—
447Dic9—21no—
448Dic9—21no—
449Dic9—21no—
450Dic9—62no—
451Dic9—61no—
452Dic9—61no—
453Dic9—61no—
454Dic9—121no—
455Dic9—121no—
456#126—271no—
457#126—271no—
458#124—271no—
459#123—91no—
460#123—271no—
461#123—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464#120—271no—
465C4×D4—31no—
466C4×D4—271no—
467#117—271no—
468#117—271no—
469C2×C22⋊C4—271no—
470C2×C22⋊C4—271no—
471C3×C9#55111yescharacteristic, complemented, Sylow
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—91no—
475C23×C3C22×D911yescharacteristic
476C23×C3C2×D3211yescharacteristic
477C22×D3—31no—
478C22×D3—91no—
479C22×D3—91no—
480C22×D3—181no—
481C22×D3—182no—
482C22×D3—182no—
483C22×D3—182no—
484C22×D3—182no—
485C22×D3—361no—
486C22×D3—361no—
487C22×D3C22×D911yescharacteristic
488C3×D4—62no—
489C3×D4—182no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—91no—
496C2×C3×C4—91no—
497C2×C3×C4—91no—
498C2×C3×C4—121no—
499C2×C3×C4—121no—
500C2×C3×C4—182no—
501C2×C3×C4C22×D911yescharacteristic
502C2×C3×C4C22×D911yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505#67—22no—
506#67—62no—
507#67—361no—
508#67—361no—
509#67—362no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—41no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—181no—
521C2×Dic3—181no—
522C2×Dic3—181no—
523C2×Dic3—182no—
524C2×Dic3—361no—
525C2×Dic3C22×D911yescharacteristic
526C2×Dic3C22×D911yescharacteristic
527C2×Dic3C22×D911yescharacteristic
528C4×D3—41no—
529C4×D3—62no—
530C4×D3—182no—
531C4×D3—361no—
532Dic6—361no—
533Dic6—361no—
534Dic6—362no—
535C2×C32—41no—
536C2×C32C2×#23511yescharacteristic
537C2×C32#100411yescharacteristic
538C2×C32D3×#4111yescharacteristic
539C3⋊D3—121no—
540C3×D3—22no—
541C3×D3—62no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—21no—
545C2×C9—41no—
546C2×C9—62no—
547C2×C9—81no—
548C2×C9C2×#23711yescharacteristic
549C2×C9D3×#4111yescharacteristic
550C2×C9#100911yescharacteristic
551D9—22no—
552D9—121no—
553D9—241no—
554C24—271no—
555C2×Q8—271no—
556C2×D4—31no—
557C2×D4—91no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—91no—
562C22×C4—271no—
563C22×C4—271no—
564C4⋊C4—31no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C22⋊C4—31no—
573C22⋊C4—91no—
574C22⋊C4—91no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4D3×D911yescharacteristic, complemented
586C42—31no—
587C42—271no—
588C42—271no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—32no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—92no—
603C22×C3—181no—
604C22×C3—181no—
605C22×C3C23×D911yescharacteristic
606C22×C3C22×D3211yescharacteristic
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—32no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—361no—
619C2×D3—361no—
620C2×D3—361no—
621C2×D3—364no—
622C2×D3—364no—
623C2×D3#369712yes—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—61no—
631C3×C4—61no—
632C3×C4—61no—
633C3×C4—181no—
634C3×C4—181no—
635C3×C4—181no—
636Dic3—21no—
637Dic3—21no—
638Dic3—21no—
639Dic3—61no—
640Dic3—61no—
641Dic3—61no—
642Dic3—182no—
643Dic3—181no—
644Dic3—181no—
645Dic3—181no—
646Dic3—181no—
647Dic3—181no—
648Dic3—181no—
649Dic3—361no—
650Dic3—361no—
651C32#555611yescharacteristic
652C9—21no—
653C9#565811yescharacteristic, complemented
654C23—31no—
655C23—91no—
656C23—271no—
657C23—542no—
658C23—542no—
659C23—1081no—
660C23C2×D3×D911yescharacteristic
661Q8—1081no—
662D4—62no—
663D4—182no—
664D4—1081no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—182no—
674C2×C4—271no—
675C2×C4—271no—
676C2×C4—271no—
677C2×C4—542no—
678C2×C4—1081no—
679C2×C4C2×D3×D911yescharacteristic
680C2×C4C2×D3×D911yescharacteristic
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—41no—
685C2×C3—41no—
686C2×C3—62no—
687C2×C3—81no—
688C2×C3—182no—
689C2×C3C2×#369711yescharacteristic
690C2×C3#6371011yescharacteristic
691C2×C3#41×D911yescharacteristic
692C2×C3D3×#23511yescharacteristic
693C2×C3D3×#23711yescharacteristic
694C2×C3#6431411yescharacteristic
695D3—22no—
696D3—62no—
697D3—361no—
698D3—361no—
699D3—721no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—32no—
704C22—61no—
705C22—61no—
706C22—92no—
707C22—181no—
708C22—181no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22—1084no—
713C22C22×D3×D911yescharacteristic
714C4—21no—
715C4—21no—
716C4—61no—
717C4—61no—
718C4—61no—
719C4—181no—
720C4—181no—
721C4—181no—
722C4—541no—
723C4—541no—
724C4—541no—
725C3—21no—
726C3#1058965811yescharacteristic, complemented
727C3#1059429911yescharacteristic
728C2—41no—
729C2—62no—
730C2—182no—
731C2—1081no—
732C2D3×#369711yescharacteristic
733C2D9×#23711yescharacteristic
734C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radical#11721292C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#551
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721731C2semidirect
2. C9×#67⋊C4C2semidirect
3. C3×#63445C2semidirect
5. #11721280C2semidirect
6. Dic3×#611C2semidirect
7. #11721251C2semidirect
8. D3×(C2×D9)⋊C4C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721011C2semidirect
11. #11720996C2semidirect
12. #11720961C2semidirect
13. #11720943C2semidirect
14. #11720926C2semidirect
15. #11720921C2semidirect
20. C2×#6226C22semidirect
23. C22×C9×Dic3C22semidirect
28. C3×C9×C22⋊C4C22semidirect
29. #88551C22semidirect
32. C4×C3⋊Dic9C22semidirect
33. C3×#3676C22semidirect
36. C9×Dic3⋊C4C22semidirect
37. C4×C9×Dic3C22semidirect
38. C3×C4⋊Dic9C22semidirect
39. C3×Dic9⋊C4C22semidirect
47. #88442C22semidirect
48. Dic9⋊Dic3C22semidirect
49. Dic9⋊Dic3C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
79. #63445D3semidirect
163. C9×C22⋊C4C2×D3semidirect
169. #3676C2×D3semidirect
180. C4⋊Dic9C2×D3semidirect
186. Dic9⋊C4C2×D3semidirect
239. #67⋊C4D9semidirect
331. C22×Dic3C2×D9semidirect
346. C3×C22⋊C4C2×D9semidirect
387. Dic3⋊C4C2×D9semidirect
393. C4×Dic3C2×D9semidirect
471. C3×C9#551semidirect
585. C22⋊C4D3×D9semidirect
653. C9#5658semidirect
726. C3#10589658semidirect

Maximal subgroups

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

subgroupindex
#117217312
C9×#67⋊C42
C3×#634452
#117212922
#117212802
Dic3×#6112
#117212512
D3×(C2×D9)⋊C42
D9×(C2×D3)⋊C42
#117210112
#117209962
#117209612
#117209432
#117209262
#117209212
#105942993
#105896583