Finite Group Databasebeta

← #13150577

Subgroups — #13150577

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
2C4×C9×#67C211yesmaximal, characteristic, complemented
3C3×C4×#611C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic
5#11721280C211yesmaximal, characteristic, complemented
6#11721269C211yesmaximal, characteristic, complemented
7#11721242C211yesmaximal, characteristic, complemented
8D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721010C211yesmaximal, characteristic, complemented
11#11720974C211yesmaximal, characteristic, complemented
12#11720955C211yesmaximal, characteristic, complemented
13#11720939C211yesmaximal, characteristic, complemented
14#11720934C211yesmaximal, characteristic, complemented
15#11720926C211yesmaximal, characteristic, complemented
16#10595087—31nomaximal
17#10589658—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic
27C2×#6189C2211yescharacteristic, complemented
28#88551C2211yescharacteristic, complemented
29#88536C2211yescharacteristic
30#88536C2211yescharacteristic
31#88534C2211yescharacteristic, complemented
32#88534C2211yescharacteristic, complemented
33C9×#217C2211yescharacteristic, complemented
34C3×#3676C2211yescharacteristic, complemented
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C9×Dic3⋊C4C2211yescharacteristic, complemented
38C4×C9×Dic3C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40C3×C4×Dic9C2211yescharacteristic, complemented
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
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—
54C3×C4×#67—31no—
55C3×C4×#67D311yescharacteristic
56#63983—31no—
57#63969—31no—
58#63969—31no—
59#63953—31no—
60D3×(C2×D3)⋊C4—31no—
61D3×(C2×D3)⋊C4—31no—
62#63877—31no—
63#63877—31no—
64#63868—31no—
65#63868—31no—
66#63851—31no—
67#63851—31no—
68C4×D4×C9—31no—
69#63499—31no—
70#63497—31no—
71#63491—31no—
72#63491—61no—
73C4×#611D311yescharacteristic, complemented
74C2×(C2×D9)⋊C4—31no—
75#63486—31no—
76#63460—31no—
77#63458—31no—
78#63447—31no—
79#63445—31no—
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×C9—41no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94#6233—41no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C9×#67—22no—
99C3×#611—22no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C4×D3×C9—41no—
107C3×C4×D9—41no—
108D3×Dic9—22no—
109Dic3×D9—22no—
110#6189—41no—
111#5556—91no—
112#5556—91no—
113C22×D32—31no—
114C22×C32×C4C2×D311yescharacteristic
115C2×#638—31no—
116C2×C3×#67—31no—
117C2×C3×#67C2×D311yescharacteristic
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3C2×D311yescharacteristic
120C2×#627—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C23×D9—31no—
124#3757—31no—
125#3752—31no—
126#3752—31no—
127#3750—31no—
128#3750—31no—
129C3×#217—31no—
130C3×#217C2×D311yescharacteristic
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4C2×D311yescharacteristic
135C3×C4×Dic3—31no—
136C3×C4×Dic3C2×D311yescharacteristic
137#3724—31no—
138#3724—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—21no—
151C22×C4×C9—31no—
152C22×C4×C9C2×D311yescharacteristic, complemented
153C2×#611—31no—
154C2×#611—61no—
155C2×#611C2×D311yescharacteristic
156C22×Dic9—31no—
157C2×C4×D9—31no—
158C2×C4×D9C2×D311yescharacteristic
159C2×Dic18—31no—
160C9×C4⋊C4—31no—
161C9×C22⋊C4—31no—
162C9×C22⋊C4—31no—
163C42×C9—31no—
164#3676—31no—
165#3676—31no—
166#3676—31no—
167#3676—61no—
168#3676C2×D311yescharacteristic, complemented
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—61no—
177(C2×D9)⋊C4—61no—
178(C2×D9)⋊C4C2×D311yescharacteristic
179C4⋊Dic9—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—61no—
186Dic9⋊C4—61no—
187Dic9⋊C4C2×D311yescharacteristic, complemented
188C4×Dic9—31no—
189C4×Dic9C2×D311yescharacteristic, complemented
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×C4×D4—31no—
216C3×C4×D4—91no—
217#937—91no—
218#937—91no—
219#935—91no—
220#935—91no—
221#929—91no—
222#929—91no—
223#929—181no—
224C4×#67—31no—
225C4×#67D911yescharacteristic, complemented
226C2×(C2×D3)⋊C4—91no—
227C2×(C2×D3)⋊C4—91no—
228#924—91no—
229#924—91no—
230#898—91no—
231#898—91no—
232#896—91no—
233#896—91no—
234#885—91no—
235#885—91no—
236#883—91no—
237#883—91no—
238D3×C22⋊C4—91no—
239D3×C22⋊C4—91no—
240#877—91no—
241#877—91no—
242#876—91no—
243#876—91no—
244#872—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×C4—41no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256#638—121no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C3×#67—22no—
261C3×#67—62no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C3×C4×D3—41no—
269C3×C4×D3—121no—
270#627—121no—
271D3×Dic3—62no—
272D3×Dic3—62no—
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—41no—
289C2×C4×C9—42no—
290C2×C4×C9—121no—
291C2×C4×C9C22×D311yescharacteristic
292C2×C4×C9C22×D311yescharacteristic
293#611—22no—
294#611—121no—
295#611—122no—
296C2×Dic9—31no—
297C2×Dic9—31no—
298C2×Dic9—31no—
299C2×Dic9—61no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9—62no—
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306C4×D9—41no—
307C4×D9—62no—
308Dic18—121no—
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—21no—
322C22×C3×C4—31no—
323C22×C3×C4—91no—
324C22×C3×C4C2×D911yescharacteristic, complemented
325C22×C3×C4D3211yescharacteristic
326C2×#67—31no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—181no—
330C2×#67C2×D911yescharacteristic
331C22×Dic3—91no—
332C22×Dic3—91no—
333C2×C4×D3—31no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3C2×D911yescharacteristic
337C2×Dic6—91no—
338C2×Dic6—91no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—91no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C42—31no—
346C3×C42—91no—
347#217—31no—
348#217—91no—
349#217—91no—
350#217—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354#217—181no—
355#217C2×D911yescharacteristic, complemented
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—91no—
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—181no—
372(C2×D3)⋊C4—181no—
373(C2×D3)⋊C4C2×D911yescharacteristic
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376Dic3⋊C4—31no—
377Dic3⋊C4—91no—
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—181no—
388Dic3⋊C4—181no—
389Dic3⋊C4C2×D911yescharacteristic, complemented
390C4×Dic3—31no—
391C4×Dic3—91no—
392C4×Dic3—91no—
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—22no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—21no—
423C22×C9—21no—
424C22×C9—32no—
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#23512yes—
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—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—31no—
466C4×D4—91no—
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—41no—
496C2×C3×C4—41no—
497C2×C3×C4—42no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—121no—
502C2×C3×C4—361no—
503C2×C3×C4C22×D911yescharacteristic
504C2×C3×C4C22×D911yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507#67—22no—
508#67—62no—
509#67—361no—
510#67—361no—
511#67—362no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—181no—
522C2×Dic3—181no—
523C2×Dic3—181no—
524C2×Dic3—182no—
525C2×Dic3—182no—
526C2×Dic3C22×D911yescharacteristic
527C2×Dic3C22×D911yescharacteristic
528C2×Dic3C22×D911yescharacteristic
529C4×D3—41no—
530C4×D3—121no—
531C4×D3—182no—
532C4×D3—182no—
533Dic6—361no—
534Dic6—361no—
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—42no—
546C2×C9—41no—
547C2×C9—62no—
548C2×C9C2×#23511yescharacteristic
549C2×C9#100411yescharacteristic
550C2×C9D3×#4111yescharacteristic
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—91no—
561C22×C4—271no—
562C22×C4—271no—
563C22×C4D3×D911yescharacteristic, complemented
564C4⋊C4—31no—
565C4⋊C4—91no—
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—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⋊C4—271no—
586C42—31no—
587C42—91no—
588C42—271no—
589C22×C3—22no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—32no—
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—181no—
643Dic3—181no—
644Dic3—181no—
645Dic3—181no—
646Dic3—181no—
647Dic3—181no—
648Dic3—361no—
649Dic3—361no—
650Dic3—361no—
651C32#555611yescharacteristic
652C9—21no—
653C9#555611yescharacteristic, 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—41no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—121no—
673C2×C4—271no—
674C2×C4—271no—
675C2×C4—271no—
676C2×C4—361no—
677C2×C4—542no—
678C2×C4—542no—
679C2×C4C2×D3×D911yescharacteristic
680C2×C4C2×D3×D911yescharacteristic
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—42no—
685C2×C3—41no—
686C2×C3—41no—
687C2×C3—62no—
688C2×C3—182no—
689C2×C3C2×#369711yescharacteristic
690C2×C3#6371011yescharacteristic
691C2×C3#41×D911yescharacteristic
692C2×C3D3×#23511yescharacteristic
693C2×C3D3×#23511yescharacteristic
694C2×C3#6433011yescharacteristic
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#1059508711yescharacteristic
728C2—41no—
729C2—62no—
730C2—182no—
731C2—1081no—
732C2D3×#369711yescharacteristic
733C2D9×#23511yescharacteristic
734C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
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. #11721818C2semidirect
2. C4×C9×#67C2semidirect
3. C3×C4×#611C2semidirect
5. #11721280C2semidirect
6. #11721269C2semidirect
7. #11721242C2semidirect
8. D3×(C2×D9)⋊C4C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721010C2semidirect
11. #11720974C2semidirect
12. #11720955C2semidirect
13. #11720939C2semidirect
14. #11720934C2semidirect
15. #11720926C2semidirect
19. C22×C3×C4×C9C22semidirect
27. C2×#6189C22semidirect
28. #88551C22semidirect
31. #88534C22semidirect
32. #88534C22semidirect
33. C9×#217C22semidirect
34. C3×#3676C22semidirect
37. C9×Dic3⋊C4C22semidirect
38. C4×C9×Dic3C22semidirect
39. C3×Dic9⋊C4C22semidirect
40. C3×C4×Dic9C22semidirect
48. Dic3⋊Dic9C22semidirect
49. #88442C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
73. C4×#611D3semidirect
152. C22×C4×C9C2×D3semidirect
168. #3676C2×D3semidirect
187. Dic9⋊C4C2×D3semidirect
189. C4×Dic9C2×D3semidirect
225. C4×#67D9semidirect
324. C22×C3×C4C2×D9semidirect
355. #217C2×D9semidirect
389. Dic3⋊C4C2×D9semidirect
393. C4×Dic3C2×D9semidirect
471. C3×C9#551semidirect
563. C22×C4D3×D9semidirect
653. C9#5556semidirect
726. C3#10589658semidirect

Maximal subgroups

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

subgroupindex
#117218182
C4×C9×#672
C3×C4×#6112
#117212922
#117212802
#117212692
#117212422
D3×(C2×D9)⋊C42
D9×(C2×D3)⋊C42
#117210102
#117209742
#117209552
#117209392
#117209342
#117209262
#105950873
#105896583