Finite Group Databasebeta

← #13150339

Subgroups — #13150339

Order 1728.

876 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88536C211yesmaximal, characteristic, complemented
2C3×C4×#611C211yesmaximal, characteristic, complemented
3C9×#924C211yesmaximal, characteristic, complemented
4#11721278C211yesmaximal, characteristic
5#11721274C211yesmaximal, characteristic, complemented
6#11721260C211yesmaximal, characteristic, complemented
7#11721248C211yesmaximal, characteristic, complemented
8#11721003C211yesmaximal, characteristic, complemented
9#11721002C211yesmaximal, characteristic, complemented
10#11720986C211yesmaximal, characteristic, complemented
11#11720942C211yesmaximal, characteristic, complemented
12#11720938C211yesmaximal, characteristic, complemented
13#11720934C211yesmaximal, characteristic, complemented
14#11720920C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10595035—31nomaximal
17#10589739—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic, complemented
23C2×C9×Dic6C2211yescharacteristic, complemented
24C2×#6192C2211yescharacteristic
25C2×#6192C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic
28#88536C2211yescharacteristic
29#88536C2211yescharacteristic
30#88536C2211yescharacteristic
31#88536C2211yescharacteristic
32C9×#217C2211yescharacteristic
33C9×#217C2211yescharacteristic
34C3×#3676C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
36C9×C4⋊Dic3C2211yescharacteristic, complemented
37C9×Dic3⋊C4C2211yescharacteristic, complemented
38C9×Dic3⋊C4C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic9C2211yescharacteristic, complemented
41#88445C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic, complemented
46(C2×D9)⋊Dic3C2211yescharacteristic, complemented
47Dic3⋊Dic9C2211yescharacteristic, complemented
48Dic3⋊Dic9C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C2×#3752—31no—
54C3×C4×#67—31no—
55C3×#924D311yescharacteristic
56#63981—31no—
57#63974—31no—
58#63962—31no—
59#63957—31no—
60#63907—31no—
61#63904—31no—
62#63888—31no—
63#63868—31no—
64#63854—31no—
65#63850—31no—
66#63848—31no—
67#63836—31no—
68C9×C22⋊Q8—31no—
69#63509—31no—
70#63508—31no—
71C4×#611D311yescharacteristic, complemented
72C2×(C2×D9)⋊C4—31no—
73C2×(C2×D9)⋊C4—61no—
74#63460—31no—
75#63460—31no—
76#63456—31no—
77#63456—31no—
78#63455—31no—
79#63454—31no—
80#63448—31no—
81#63444—31no—
82C22⋊C4×D9—31no—
83#63439—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9—22no—
86C22×C3⋊D9—22no—
87C22×C3⋊D9—41no—
88C22×C3⋊D9C2311yescharacteristic
89C22×C3⋊D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9—41no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3⋊Dic9—22no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C3×#611—22no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C3×C4×D9—41no—
106C9×Dic6—41no—
107#6192—22no—
108#6192—41no—
109(C3⋊D9)⋊C4—22no—
110(C3⋊D9)⋊C4—41no—
111#5637—91no—
112#5556—91no—
113C23×C3⋊D3—31no—
114C22×C32×C4C2×D311yescharacteristic
115C22×C3⋊Dic3—31no—
116C2×C3×#67—31no—
117C2×C3×C4×D3—31no—
118C2×C3×Dic6C2×D311yescharacteristic
119C2×#626—31no—
120C2×#626—31no—
121C2×#624—31no—
122C2×#624—31no—
123C23×D9—31no—
124C23×D9—61no—
125#3752—31no—
126#3752—31no—
127#3752—31no—
128#3752—31no—
129C3×#217—31no—
130C3×#217C2×D311yescharacteristic
131C3×#217C2×D311yescharacteristic
132C3×(C2×D3)⋊C4—31no—
133C3×C4⋊Dic3C2×D311yescharacteristic
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4C2×D311yescharacteristic
136C3×Dic3⋊C4C2×D311yescharacteristic
137C3×C4×Dic3—31no—
138#3724—31no—
139#3724—31no—
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142#3722—31no—
143#3722—31no—
144#3722—31no—
145#3722—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148Dic32—31no—
149Dic32—31no—
150C2×Q8×C9—31no—
151C22×C4×C9—21no—
152C22×C4×C9C2×D311yescharacteristic
153C2×#611C2×D311yescharacteristic
154C22×Dic9—31no—
155C22×Dic9—61no—
156C2×D36—31no—
157C2×D36—31no—
158C2×C4×D9—31no—
159C2×C4×D9—31no—
160C2×C4×D9C2×D311yescharacteristic, complemented
161C9×C4⋊C4—31no—
162C9×C4⋊C4—31no—
163C9×C4⋊C4—31no—
164C9×C22⋊C4—31no—
165C9×C22⋊C4—31no—
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—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)⋊C4—61no—
180(C2×D9)⋊C4—61no—
181(C2×D9)⋊C4C2×D311yescharacteristic, complemented
182C4⋊Dic9—31no—
183C4⋊Dic9—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4C2×D311yescharacteristic, complemented
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9C2×D311yescharacteristic, complemented
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—44no—
200C2×C3⋊D9#4112yes—
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C2×C3×D9—21no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×C22⋊Q8—31no—
216C3×C4×D4—91no—
217#947—91no—
218#946—91no—
219#937—91no—
220#935—91no—
221#929—91no—
222C4×#67—31no—
223C4×#67—91no—
224C2×(C2×D3)⋊C4—91no—
225C2×(C2×D3)⋊C4—91no—
226C2×(C2×D3)⋊C4—181no—
227#924D911yescharacteristic, complemented
228#898—91no—
229#898—91no—
230#898—91no—
231#896—91no—
232#894—91no—
233#894—91no—
234#893—91no—
235#892—91no—
236#886—91no—
237#885—91no—
238#883—91no—
239#882—91no—
240D3×C22⋊C4—91no—
241D3×C22⋊C4—91no—
242#877—91no—
243#877—91no—
244#876—91no—
245#872—91no—
246C23×C32C22×D311yescharacteristic
247C22×C3⋊D3—31no—
248C22×C3⋊D3—31no—
249C22×C3⋊D3—62no—
250C22×C3⋊D3—62no—
251C22×C3⋊D3—121no—
252C22×C3×D3—31no—
253C2×C32×C4—41no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—62no—
259C3×#67—62no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C3×C4×D3—121no—
268C3×Dic6—41no—
269#626—62no—
270#626—121no—
271#624—62no—
272#624—121no—
273C23×C9—21no—
274C23×C9C22×D311yescharacteristic
275C22×D9—31no—
276C22×D9—31no—
277C22×D9—61no—
278C22×D9—61no—
279C22×D9—62no—
280C22×D9—64no—
281C22×D9—62no—
282C22×D9—122no—
283C22×D9—121no—
284C22×D9—122no—
285C22×D9C22×D311yescharacteristic
286Q8×C9—121no—
287C2×C4×C9—21no—
288C2×C4×C9—21no—
289C2×C4×C9—31no—
290C2×C4×C9—31no—
291C2×C4×C9—31no—
292C2×C4×C9—31no—
293C2×C4×C9—41no—
294C2×C4×C9—42no—
295C2×C4×C9C22×D311yescharacteristic
296C2×C4×C9C22×D311yescharacteristic
297#611—22no—
298C2×Dic9—31no—
299C2×Dic9—31no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9—62no—
303C2×Dic9—122no—
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C2×Dic9C22×D311yescharacteristic
307D36—62no—
308D36—121no—
309C4×D9—41no—
310C4×D9—62no—
311C4×D9—121no—
312#551—271noSylow
313C2×C3×C9—22no—
314C2×C3×C9C2×#4111yescharacteristic
315C2×C3×C9C2×#4111yescharacteristic
316C2×C3×C9H(5,𝔽2)11yescharacteristic
317C3⋊D9—22no—
318C3⋊D9—41no—
319C3×D9—41no—
320C23×D3—91no—
321C23×D3—91no—
322C23×D3—181no—
323C2×C3×Q8—31no—
324C2×C3×D4—91no—
325C22×C3×C4—21no—
326C22×C3×C4—91no—
327C22×C3×C4C2×D911yescharacteristic
328C22×C3×C4D3211yescharacteristic
329C2×#67—31no—
330C2×#67—91no—
331C2×#67—91no—
332C22×Dic3—91no—
333C22×Dic3—91no—
334C22×Dic3—181no—
335C2×D12—91no—
336C2×D12—91no—
337C2×C4×D3—31no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×Dic6C2×D911yescharacteristic, complemented
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—91no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C42—91no—
352#217—31no—
353#217—91no—
354#217—91no—
355#217C2×D911yescharacteristic
356#217C2×D911yescharacteristic
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—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—181no—
377(C2×D3)⋊C4—181no—
378(C2×D3)⋊C4—181no—
379(C2×D3)⋊C4—181no—
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382C4⋊Dic3C2×D911yescharacteristic, complemented
383Dic3⋊C4—31no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4C2×D911yescharacteristic, complemented
391Dic3⋊C4C2×D911yescharacteristic, complemented
392C4×Dic3—31no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32#23912yes—
400C22×C32C23×D311yescharacteristic
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—
408C2×C3×D3—61no—
409C2×C3×D3—61no—
410C2×C3×D3—61no—
411C32×C4—21no—
412C32×C4—21no—
413C3⋊Dic3—61no—
414C3⋊Dic3—61no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—61no—
420C3×Dic3—61no—
421C3×Dic3—61no—
422C22×C9—22no—
423C22×C9—22no—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—21no—
427C22×C9—22no—
428C22×C9#23512yes—
429C22×C9C23×D311yescharacteristic
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—21no—
433C2×D9—32no—
434C2×D9—62no—
435C2×D9—61no—
436C2×D9—61no—
437C2×D9—62no—
438C2×D9—61no—
439C2×D9—61no—
440C2×D9—61no—
441C2×D9—121no—
442C2×D9—121no—
443C2×D9—121no—
444C2×D9—121no—
445C2×D9—124no—
446C2×D9—128no—
447C4×C9—21no—
448C4×C9—21no—
449C4×C9—41no—
450C4×C9—41no—
451C4×C9—61no—
452C4×C9—61no—
453C4×C9—61no—
454C4×C9—61no—
455Dic9—21no—
456Dic9—21no—
457Dic9—21no—
458Dic9—61no—
459Dic9—61no—
460Dic9—121no—
461Dic9—121no—
462#126—271no—
463#126—271no—
464#124—271no—
465#123—271no—
466#123—271no—
467#123—271no—
468C22⋊Q8—31no—
469C22⋊Q8—271no—
470#120—271no—
471C4×D4—91no—
472C4×D4—271no—
473#117—271no—
474#117—271no—
475C2×C22⋊C4—271no—
476C2×C22⋊C4—271no—
477C3×C9#55111yescharacteristic, complemented, Sylow
478C23×C3—21no—
479C23×C3—91no—
480C23×C3C22×D911yescharacteristic
481C23×C3C2×D3211yescharacteristic
482C22×D3—31no—
483C22×D3—91no—
484C22×D3—91no—
485C22×D3—91no—
486C22×D3—91no—
487C22×D3—181no—
488C22×D3—181no—
489C22×D3—182no—
490C22×D3—182no—
491C22×D3—184no—
492C22×D3—182no—
493C22×D3—182no—
494C22×D3—362no—
495C22×D3—361no—
496C22×D3—361no—
497C22×D3—362no—
498C3×Q8—121no—
499C3×D4—182no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—42no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—361no—
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517#67—62no—
518#67—182no—
519#67—361no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—91no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—181no—
528C2×Dic3—181no—
529C2×Dic3—182no—
530C2×Dic3—182no—
531C2×Dic3—362no—
532C2×Dic3C22×D911yescharacteristic
533C2×Dic3C22×D911yescharacteristic
534C2×Dic3C22×D911yescharacteristic
535C2×Dic3C22×D911yescharacteristic
536D12—182no—
537D12—361no—
538C4×D3—121no—
539C4×D3—182no—
540C4×D3—182no—
541C4×D3—361no—
542C4×D3—361no—
543Dic6—41no—
544C2×C32—22no—
545C2×C32#100411yescharacteristic
546C2×C32C2×#23911yescharacteristic
547C2×C32D3×#4111yescharacteristic
548C3⋊D3—62no—
549C3⋊D3—121no—
550C3×D3—121no—
551C2×C9—24no—
552C2×C9—22no—
553C2×C9—21no—
554C2×C9—21no—
555C2×C9—21no—
556C2×C9C2×#23511yescharacteristic
557C2×C9#100411yescharacteristic
558C2×C9D3×#4111yescharacteristic
559D9—41no—
560D9—62no—
561D9—122no—
562D9—122no—
563D9—121no—
564C24—271no—
565C2×Q8—31no—
566C2×D4—91no—
567C2×D4—271no—
568C2×D4—271no—
569C22×C4—91no—
570C22×C4—271no—
571C22×C4—271no—
572C22×C4—271no—
573C22×C4D3×D911yescharacteristic
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—91no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—91no—
585C22⋊C4—91no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4—271no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C22⋊C4—271no—
595C22⋊C4—271no—
596C42—91no—
597C42—271no—
598C42—271no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—22no—
606C22×C3—21no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3#370112yes—
611C22×C3C23×D911yescharacteristic
612C22×C3#379912yes—
613C22×C3C22×D3211yescharacteristic
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—92no—
618C2×D3—92no—
619C2×D3—182no—
620C2×D3—181no—
621C2×D3—181no—
622C2×D3—181no—
623C2×D3—181no—
624C2×D3—182no—
625C2×D3—181no—
626C2×D3—181no—
627C2×D3—181no—
628C2×D3—181no—
629C2×D3—181no—
630C2×D3—181no—
631C2×D3—361no—
632C2×D3—361no—
633C2×D3—361no—
634C2×D3—361no—
635C2×D3—364no—
636C2×D3—364no—
637C2×D3—368no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—181no—
649C3×C4—181no—
650C3×C4—181no—
651Dic3—21no—
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—181no—
659Dic3—181no—
660Dic3—181no—
661Dic3—181no—
662Dic3—361no—
663Dic3—361no—
664C32#563711yescharacteristic
665C9—21no—
666C9#555611yescharacteristic, complemented
667C23—91no—
668C23—271no—
669C23—271no—
670C23—542no—
671C23—542no—
672C23—1081no—
673C23C2×D3×D911yescharacteristic
674Q8—121no—
675D4—182no—
676D4—542no—
677D4—1081no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—41no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—271no—
687C2×C4—271no—
688C2×C4—361no—
689C2×C4—542no—
690C2×C4—542no—
691C2×C4—1081no—
692C2×C4C2×D3×D911yescharacteristic
693C2×C4C2×D3×D911yescharacteristic
694C2×C3—24no—
695C2×C3—22no—
696C2×C3—22no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—361no—
701C2×C3#6371011yescharacteristic
702C2×C3C2×#370111yescharacteristic
703C2×C3#41×D911yescharacteristic
704C2×C3C2×#379911yescharacteristic
705C2×C3#6430611yescharacteristic
706C2×C3#6433011yescharacteristic
707D3—121no—
708D3—182no—
709D3—182no—
710D3—362no—
711D3—362no—
712D3—361no—
713D3—361no—
714C22—21no—
715C22—21no—
716C22—181no—
717C22—181no—
718C22—181no—
719C22—272no—
720C22—541no—
721C22—541no—
722C22—541no—
723C22—541no—
724C22—541no—
725C22—1084no—
726C22#8863512yes—
727C22C22×D3×D911yescharacteristic
728C4—21no—
729C4—21no—
730C4—61no—
731C4—61no—
732C4—61no—
733C4—61no—
734C4—181no—
735C4—181no—
736C4—181no—
737C4—541no—
738C4—541no—
739C3—21no—
740C3#1058973911yescharacteristic, complemented
741C3#1059503511yescharacteristic
742C2—22no—
743C2—361no—
744C2—542no—
745C2—1081no—
746C2C2×#8863511yescharacteristic
747C2#1172247511yescharacteristic
748C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
prime radical#11721278C2
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. C2×#88536C2semidirect
2. C3×C4×#611C2semidirect
3. C9×#924C2semidirect
5. #11721274C2semidirect
6. #11721260C2semidirect
7. #11721248C2semidirect
8. #11721003C2semidirect
9. #11721002C2semidirect
10. #11720986C2semidirect
11. #11720942C2semidirect
12. #11720938C2semidirect
13. #11720934C2semidirect
14. #11720920C2semidirect
15. #11720899C2semidirect
22. C2×C3×C4×D9C22semidirect
23. C2×C9×Dic6C22semidirect
35. C3×(C2×D9)⋊C4C22semidirect
36. C9×C4⋊Dic3C22semidirect
37. C9×Dic3⋊C4C22semidirect
38. C9×Dic3⋊C4C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. C3×C4×Dic9C22semidirect
45. (C2×D9)⋊Dic3C22semidirect
46. (C2×D9)⋊Dic3C22semidirect
47. Dic3⋊Dic9C22semidirect
48. Dic3⋊Dic9C22semidirect
49. #88442C22semidirect
50. #88442C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
71. C4×#611D3semidirect
160. C2×C4×D9C2×D3semidirect
181. (C2×D9)⋊C4C2×D3semidirect
186. Dic9⋊C4C2×D3semidirect
189. C4×Dic9C2×D3semidirect
227. #924D9semidirect
342. C2×Dic6C2×D9semidirect
382. C4⋊Dic3C2×D9semidirect
390. Dic3⋊C4C2×D9semidirect
391. Dic3⋊C4C2×D9semidirect
477. C3×C9#551semidirect
666. C9#5556semidirect
740. C3#10589739semidirect

Maximal subgroups

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

subgroupindex
C2×#885362
C3×C4×#6112
C9×#9242
#117212782
#117212742
#117212602
#117212482
#117210032
#117210022
#117209862
#117209422
#117209382
#117209342
#117209202
#117208992
#105950353
#105897393