Finite Group Databasebeta

← #13150239

Subgroups — #13150239

Order 1728.

822 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#11721818C211yesmaximal, characteristic, complemented
2C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
3C9×#926C211yesmaximal, characteristic, complemented
4#11721276C211yesmaximal, characteristic
5D9×#217C211yesmaximal, characteristic, complemented
6#11721253C211yesmaximal, characteristic, complemented
7#11721241C211yesmaximal, characteristic, complemented
8#11720999C211yesmaximal, characteristic, complemented
9#11720988C211yesmaximal, characteristic, complemented
10#11720977C211yesmaximal, characteristic, complemented
11#11720974C211yesmaximal, characteristic, complemented
12#11720947C211yesmaximal, characteristic, complemented
13#11720946C211yesmaximal, characteristic, complemented
14#11720942C211yesmaximal, characteristic, complemented
15#11720940C211yesmaximal, characteristic, complemented
16#10594937—31nomaximal
17#10589629—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C22×C3×Dic9C2211yescharacteristic
22C2×#6192C2211yescharacteristic
23C2×#6192C2211yescharacteristic
24C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
25C2×Dic3×D9C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic
27C2×#6189C2211yescharacteristic, complemented
28#88551C2211yescharacteristic
29#88536C2211yescharacteristic, complemented
30#88536C2211yescharacteristic, complemented
31#88534C2211yescharacteristic, complemented
32#88534C2211yescharacteristic, complemented
33C9×#217C2211yescharacteristic
34C9×#217C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C9×C4⋊Dic3C2211yescharacteristic, complemented
40C9×C4⋊Dic3C2211yescharacteristic, complemented
41C4×C9×Dic3C2211yescharacteristic, complemented
42C4×C9×Dic3C2211yescharacteristic, complemented
43#88445C2211yescharacteristic, complemented
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48Dic3⋊Dic9C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64138—31no—
54C2×C3×(C2×D3)⋊C4—31no—
55C3×#926D311yescharacteristic
56#63977—31no—
57D3×#217—31no—
58#63964—31no—
59#63952—31no—
60#63899—31no—
61#63890—31no—
62#63880—31no—
63#63877—31no—
64#63859—31no—
65#63858—31no—
66#63854—31no—
67#63852—31no—
68C9×#117—31no—
69#63491—31no—
70#63491—61no—
71C2×(C2×D9)⋊C4D311yescharacteristic, complemented
72#63460—31no—
73#63458—31no—
74#63456—31no—
75#63456—31no—
76#63444—31no—
77#611⋊C4—31no—
78C22⋊C4×D9—31no—
79#63440—31no—
80#63438—31no—
81#63437—31no—
82C4×D36—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3×D9—22no—
87C22×C3×D9—22no—
88C22×C3×D9—41no—
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9—22no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—22no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9—41no—
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105#6192—22no—
106#6192—41no—
107(C3⋊D9)⋊C4—41no—
108Dic3×D9—22no—
109Dic3×D9—41no—
110#6189—41no—
111#5527—91no—
112#5495—91no—
113C23×C3×D3—31no—
114C22×C32×C4C2×D311yescharacteristic
115C2×#638—31no—
116C22×C3×Dic3—31no—
117C2×#627—31no—
118C2×#626—31no—
119C2×#626—31no—
120C2×#624—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C23×D9C2×D311yescharacteristic
124#3757—31no—
125#3752—31no—
126#3752—31no—
127#3750—31no—
128#3750—31no—
129C3×#217C2×D311yescharacteristic
130C3×#217C2×D311yescharacteristic
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×C4⋊Dic3C2×D311yescharacteristic
136C3×C4⋊Dic3C2×D311yescharacteristic
137C3×C4×Dic3C2×D311yescharacteristic
138C3×C4×Dic3C2×D311yescharacteristic
139#3724—31no—
140#3724—31no—
141Dic3⋊Dic3—31no—
142Dic3⋊Dic3—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—
149C22×C4×C9—21no—
150C22×C4×C9C2×D311yescharacteristic
151C2×#611—31no—
152C2×#611—61no—
153C22×Dic9C2×D311yescharacteristic
154C2×D36—31no—
155C2×D36—31no—
156C2×C4×D9—31no—
157C2×C4×D9—31no—
158C2×C4×D9—31no—
159C2×Dic18—31no—
160C9×C4⋊C4—31no—
161C9×C4⋊C4—31no—
162C9×C22⋊C4—31no—
163C9×C22⋊C4—31no—
164C42×C9—31no—
165C42×C9—31no—
166#3676—31no—
167#3676—61no—
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—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—61no—
176(C2×D9)⋊C4—61no—
177(C2×D9)⋊C4C2×D311yescharacteristic
178(C2×D9)⋊C4C2×D311yescharacteristic
179(C2×D9)⋊C4C2×D311yescharacteristic
180(C2×D9)⋊C4C2×D311yescharacteristic
181C4⋊Dic9—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—61no—
188Dic9⋊C4—61no—
189C4×Dic9—31no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9#4112yes—
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×C3×D9—21no—
198C2×C3×D9—21no—
199C2×C3×D9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9—44no—
203C2×C3×D9#4112yes—
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—
212C9×Dic3—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#117—31no—
216C2×C3×C22⋊C4—91no—
217#953—91no—
218C2×#217—91no—
219#929—91no—
220#929—91no—
221#929—181no—
222C4×#67—91no—
223C2×(C2×D3)⋊C4—31no—
224#926D911yescharacteristic, complemented
225#924—91no—
226#898—91no—
227#896—91no—
228#894—91no—
229#894—91no—
230#886—91no—
231#885—91no—
232#883—91no—
233#882—91no—
234#67⋊C4—91no—
235#67⋊C4—91no—
236D3×C22⋊C4—91no—
237#879—91no—
238#879—91no—
239#878—91no—
240#878—91no—
241#877—91no—
242#876—91no—
243#875—91no—
244C4×D12—91no—
245#872—91no—
246C23×C32C22×D311yescharacteristic
247C22×C3⋊D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—31no—
250C22×C3×D3—62no—
251C22×C3×D3—62no—
252C22×C3×D3—121no—
253C2×C32×C4—22no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256#638—62no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—121no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267#627—121no—
268#626—62no—
269#626—121no—
270#624—121no—
271D3×Dic3—62no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9C22×D311yescharacteristic
275C22×D9—22no—
276C22×D9—22no—
277C22×D9—31no—
278C22×D9—41no—
279C22×D9—61no—
280C22×D9C22×D311yescharacteristic
281C22×D9C22×D311yescharacteristic
282C2×C4×C9—22no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9—31no—
289C2×C4×C9—42no—
290C2×C4×C9C22×D311yescharacteristic
291C2×C4×C9C22×D311yescharacteristic
292#611—62no—
293#611—122no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—31no—
297C2×Dic9—41no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—61no—
301C2×Dic9C22×D311yescharacteristic
302C2×Dic9C22×D311yescharacteristic
303D36—62no—
304D36—121no—
305C4×D9—62no—
306C4×D9—121no—
307C4×D9—121no—
308Dic18—121no—
309#551—271noSylow
310C2×C3×C9—22no—
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314C3⋊D9—41no—
315C3×D9—22no—
316C3×D9—41no—
317C24×C3—91no—
318C23×D3—31no—
319C22×C3×C4—21no—
320C22×C3×C4—91no—
321C22×C3×C4C2×D911yescharacteristic
322C22×C3×C4D3211yescharacteristic
323C2×#67—91no—
324C2×#67—91no—
325C2×#67—91no—
326C2×#67—91no—
327C2×#67—181no—
328C22×Dic3—31no—
329C22×Dic3—91no—
330C22×Dic3—91no—
331C2×D12—91no—
332C2×D12—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×Dic6—91no—
338C2×Dic6—91no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C42—31no—
348C3×C42—31no—
349#217—91no—
350#217—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354#217—91no—
355#217—181no—
356#217C2×D911yescharacteristic
357#217C2×D911yescharacteristic
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
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—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3C2×D911yescharacteristic, complemented
377C4⋊Dic3C2×D911yescharacteristic, complemented
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—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—181no—
389Dic3⋊C4—181no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3C2×D911yescharacteristic, complemented
393C4×Dic3C2×D911yescharacteristic, complemented
394C22×C32—21no—
395C22×C32—21no—
396C22×C32#23512yes—
397C22×C32C23×D311yescharacteristic
398C2×C3⋊D3—61no—
399C2×C3⋊D3—61no—
400C2×C3⋊D3—61no—
401C2×C3×D3—32no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407C2×C3×D3—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—21no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—22no—
423C22×C9—41no—
424C22×C9—41no—
425C22×C9#23712yes—
426C22×C9C23×D311yescharacteristic
427C2×D9—21no—
428C2×D9—21no—
429C2×D9—21no—
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—44no—
433C2×D9—61no—
434C2×D9—61no—
435C2×D9—61no—
436C2×D9—121no—
437C2×D9—121no—
438C2×D9—121no—
439C2×D9#23512yes—
440C4×C9—21no—
441C4×C9—21no—
442C4×C9—41no—
443C4×C9—41no—
444C4×C9—61no—
445C4×C9—61no—
446C4×C9—61no—
447C4×C9—61no—
448Dic9—21no—
449Dic9—21no—
450Dic9—61no—
451Dic9—61no—
452Dic9—61no—
453Dic9—121no—
454Dic9—121no—
455Dic9—121no—
456#126—271no—
457#126—271no—
458#124—271no—
459#123—271no—
460#123—271no—
461#123—271no—
462C22⋊Q8—271no—
463C22⋊Q8—271no—
464#120—271no—
465C4×D4—271no—
466C4×D4—271no—
467#117—31no—
468#117—271no—
469C2×C22⋊C4—91no—
470C2×C22⋊C4—271no—
471C3×C9#55111yescharacteristic, complemented, Sylow
472C23×C3—21no—
473C23×C3—91no—
474C23×C3—91no—
475C23×C3—182no—
476C23×C3—182no—
477C23×C3—361no—
478C23×C3C22×D911yescharacteristic
479C23×C3C2×D3211yescharacteristic
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—91no—
485C22×D3—91no—
486C22×D3—121no—
487C22×D3—181no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—42no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—361no—
500C2×C3×C4C22×D911yescharacteristic
501C2×C3×C4C22×D911yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504#67—182no—
505#67—182no—
506#67—182no—
507#67—362no—
508#67—361no—
509C2×Dic3—31no—
510C2×Dic3—31no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—121no—
518C2×Dic3—181no—
519C2×Dic3—181no—
520C2×Dic3—181no—
521C2×Dic3—182no—
522C2×Dic3—361no—
523C2×Dic3C22×D911yescharacteristic
524C2×Dic3C22×D911yescharacteristic
525C2×Dic3C22×D911yescharacteristic
526C2×Dic3C22×D911yescharacteristic
527D12—182no—
528D12—361no—
529C4×D3—182no—
530C4×D3—361no—
531C4×D3—361no—
532C4×D3—361no—
533Dic6—361no—
534Dic6—361no—
535C2×C32—22no—
536C2×C32C2×#23511yescharacteristic
537C2×C32D3×#4111yescharacteristic
538C2×C32#100911yescharacteristic
539C3⋊D3—121no—
540C3×D3—62no—
541C3×D3—121no—
542C2×C9—22no—
543C2×C9—21no—
544C2×C9—21no—
545C2×C9—21no—
546C2×C9—42no—
547C2×C9C2×#23511yescharacteristic
548C2×C9C2×#23711yescharacteristic
549C2×C9#100411yescharacteristic
550D9—22no—
551D9—41no—
552D9—121no—
553D9—241no—
554C24—91no—
555C2×Q8—271no—
556C2×D4—271no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—91no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4D3×D911yescharacteristic
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—91no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C42—31no—
587C42—31no—
588C42—271no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—22no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—92no—
598C22×C3—181no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3—181no—
603C22×C3—364no—
604C22×C3#369712yes—
605C22×C3C23×D911yescharacteristic
606C22×C3#380412yes—
607C22×C3C22×D3211yescharacteristic
608C2×D3—32no—
609C2×D3—61no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—124no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—181no—
620C2×D3—181no—
621C2×D3—361no—
622C2×D3—361no—
623C2×D3—361no—
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—61no—
634C3×C4—181no—
635C3×C4—181no—
636Dic3—21no—
637Dic3—21no—
638Dic3—21no—
639Dic3—21no—
640Dic3—61no—
641Dic3—61no—
642Dic3—181no—
643Dic3—181no—
644Dic3—181no—
645Dic3—181no—
646Dic3—181no—
647Dic3—181no—
648Dic3—361no—
649Dic3—361no—
650Dic3—361no—
651C32#552711yescharacteristic
652C9—21no—
653C9#549511yescharacteristic, complemented
654C23—91no—
655C23—91no—
656C23—182no—
657C23—182no—
658C23—271no—
659C23—361no—
660C23C2×D3×D911yescharacteristic
661Q8—1081no—
662D4—542no—
663D4—542no—
664D4—1081no—
665C2×C4—22no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—271no—
673C2×C4—271no—
674C2×C4—271no—
675C2×C4—361no—
676C2×C4—542no—
677C2×C4—1081no—
678C2×C4—1081no—
679C2×C4C2×D3×D911yescharacteristic
680C2×C4C2×D3×D911yescharacteristic
681C2×C3—22no—
682C2×C3—22no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—42no—
687C2×C3—182no—
688C2×C3—361no—
689C2×C3C2×#369711yescharacteristic
690C2×C3#41×D911yescharacteristic
691C2×C3#6371511yescharacteristic
692C2×C3D3×#23511yescharacteristic
693C2×C3#6430711yescharacteristic
694C2×C3C2×#380411yescharacteristic
695D3—62no—
696D3—121no—
697D3—361no—
698D3—361no—
699D3—721no—
700C22—21no—
701C22—21no—
702C22—92no—
703C22—181no—
704C22—181no—
705C22—181no—
706C22—181no—
707C22—181no—
708C22—364no—
709C22—541no—
710C22—541no—
711C22—541no—
712C22#8865812yes—
713C22C22×D3×D911yescharacteristic
714C4—21no—
715C4—21no—
716C4—61no—
717C4—61no—
718C4—61no—
719C4—61no—
720C4—181no—
721C4—181no—
722C4—541no—
723C4—541no—
724C4—541no—
725C3—21no—
726C3#1058962911yescharacteristic, complemented
727C3#1059493711yescharacteristic
728C2—22no—
729C2—182no—
730C2—361no—
731C2—1081no—
732C2D9×#23511yescharacteristic
733C2#1172247711yescharacteristic
734C2C2×#8865811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
prime radical#11721276C2
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. #11721818C2semidirect
2. C2×C3×(C2×D9)⋊C4C2semidirect
3. C9×#926C2semidirect
5. D9×#217C2semidirect
6. #11721253C2semidirect
7. #11721241C2semidirect
8. #11720999C2semidirect
9. #11720988C2semidirect
10. #11720977C2semidirect
11. #11720974C2semidirect
12. #11720947C2semidirect
13. #11720946C2semidirect
14. #11720942C2semidirect
15. #11720940C2semidirect
24. C2×(C3⋊D9)⋊C4C22semidirect
27. C2×#6189C22semidirect
29. #88536C22semidirect
30. #88536C22semidirect
31. #88534C22semidirect
32. #88534C22semidirect
39. C9×C4⋊Dic3C22semidirect
40. C9×C4⋊Dic3C22semidirect
41. C4×C9×Dic3C22semidirect
42. C4×C9×Dic3C22semidirect
43. #88445C22semidirect
48. Dic3⋊Dic9C22semidirect
49. #88442C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
71. C2×(C2×D9)⋊C4D3semidirect
224. #926D9semidirect
376. C4⋊Dic3C2×D9semidirect
377. C4⋊Dic3C2×D9semidirect
392. C4×Dic3C2×D9semidirect
393. C4×Dic3C2×D9semidirect
471. C3×C9#551semidirect
653. C9#5495semidirect
726. C3#10589629semidirect

Maximal subgroups

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

subgroupindex
#117218182
C2×C3×(C2×D9)⋊C42
C9×#9262
#117212762
D9×#2172
#117212532
#117212412
#117209992
#117209882
#117209772
#117209742
#117209472
#117209462
#117209422
#117209402
#105949373
#105896293