Finite Group Databasebeta

← #13148063

Subgroups — #13148063

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#11721724C211yesmaximal, characteristic, complemented
2C3×#63444C211yesmaximal, characteristic
3C9×#877C211yesmaximal, characteristic, complemented
4#611⋊Dic3C211yesmaximal, characteristic, complemented
5D9×#217C211yesmaximal, characteristic, complemented
6#11721259C211yesmaximal, characteristic, complemented
7C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
8#11720996C211yesmaximal, characteristic, complemented
9Dic3×D36C211yesmaximal, characteristic, complemented
10#11720981C211yesmaximal, characteristic, complemented
11#11720981C211yesmaximal, characteristic, complemented
12#11720974C211yesmaximal, characteristic, complemented
13#11720949C211yesmaximal, characteristic, complemented
14#11720948C211yesmaximal, characteristic, complemented
15#11720947C211yesmaximal, characteristic, complemented
16#10594117—31nomaximal
17#10589629—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C3×#611C2211yescharacteristic
22C22×C9×Dic3C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic
25C2×Dic3×D9C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic
27C2×Dic3×D9C2211yescharacteristic, complemented
28C3×C9×C22⋊C4C2211yescharacteristic
29#88551C2211yescharacteristic
30C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
31#88534C2211yescharacteristic, complemented
32#88534C2211yescharacteristic, complemented
33C9×#217C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C9×Dic3⋊C4C2211yescharacteristic, complemented
37C9×Dic3⋊C4C2211yescharacteristic, complemented
38C4×C9×Dic3C2211yescharacteristic, complemented
39C4×C9×Dic3C2211yescharacteristic, complemented
40(C2×D9)⋊Dic3C2211yescharacteristic
41(C2×D9)⋊Dic3C2211yescharacteristic
42(C2×D9)⋊Dic3C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic, complemented
47(C2×D9)⋊Dic3C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64087—31no—
54C3×#882—31no—
55C3×#877D311yescharacteristic
56#67⋊Dic3—31no—
57D3×#217—31no—
58#63961—31no—
59C2×(C2×D3)⋊Dic3—31no—
60#63896—31no—
61Dic3×D12—31no—
62#63884—31no—
63#63884—31no—
64#63877—31no—
65#63861—31no—
66#63860—31no—
67#63859—31no—
68C9×#117—31no—
69#63491—31no—
70C2×(C2×D9)⋊C4—31no—
71#63460—31no—
72#63458—31no—
73#63456—31no—
74#63456—31no—
75#63444D311yescharacteristic
76#611⋊C4—31no—
77C22⋊C4×D9—31no—
78#63440—31no—
79#63440—61no—
80#63438—31no—
81#63437—31no—
82C4×D36—31no—
83#63434—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×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9—41no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98#6226—41no—
99C3×#611—22no—
100C2×C9×Dic3—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×D36—22no—
107C3×D36—41no—
108Dic3×D9—22no—
109Dic3×D9—41no—
110Dic3×D9—41no—
111#5587—91no—
112#5527—91no—
113C23×C3×D3—31no—
114C22×C3⋊Dic3—31no—
115C2×#634—31no—
116C2×C3×#67—31no—
117C22×C3×Dic3C2×D311yescharacteristic
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×D3×Dic3—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C23×D9C2×D311yescharacteristic
124C32×C22⋊C4C2×D311yescharacteristic
125#3757—31no—
126C4⋊(C3⋊Dic3)—31no—
127#3750—31no—
128#3750—31no—
129C3×#217C2×D311yescharacteristic
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×Dic3⋊C4C2×D311yescharacteristic
133C3×Dic3⋊C4C2×D311yescharacteristic
134C3×C4×Dic3C2×D311yescharacteristic
135C3×C4×Dic3C2×D311yescharacteristic
136#3724—31no—
137#3724—31no—
138Dic3⋊Dic3—31no—
139(C2×D3)⋊Dic3—31no—
140(C2×D3)⋊Dic3—31no—
141(C2×D3)⋊Dic3—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—
149C22×C4×C9—31no—
150C2×#611C2×D311yescharacteristic
151C22×Dic9—31no—
152C22×Dic9—61no—
153C2×D36C2×D311yescharacteristic
154C2×D36C2×D311yescharacteristic
155C2×C4×D9—31no—
156C2×C4×D9—31no—
157C2×C4×D9—31no—
158C2×Dic18—31no—
159C2×Dic18—61no—
160C9×C4⋊C4—31no—
161C9×C4⋊C4—31no—
162C9×C22⋊C4—21no—
163C9×C22⋊C4—31no—
164C9×C22⋊C4C2×D311yescharacteristic
165C42×C9—31no—
166C42×C9—31no—
167#3676—31no—
168#3676—61no—
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—31no—
178(C2×D9)⋊C4C2×D311yescharacteristic
179(C2×D9)⋊C4C2×D311yescharacteristic
180C4⋊Dic9—31no—
181C4⋊Dic9—61no—
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—
209C3⋊Dic9—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C9×Dic3—21no—
213C9×Dic3—21no—
214C3×Dic9—21no—
215C3×#120—91no—
216C3×#117—31no—
217C2×#217—91no—
218C2×#217—91no—
219#936—91no—
220#935—91no—
221#935—91no—
222#935—91no—
223D4×Dic3—91no—
224D4×Dic3—91no—
225#929—91no—
226C2×(C2×D3)⋊C4—91no—
227#898—91no—
228#896—91no—
229#894—91no—
230#894—91no—
231#882—31no—
232#67⋊C4—91no—
233D3×C22⋊C4—91no—
234#879—91no—
235#879—91no—
236#878—91no—
237#878—91no—
238#878—91no—
239#878—181no—
240#877—91no—
241#877D911yescharacteristic, complemented
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×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—121no—
260#634—121no—
261C3×#67—62no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C3×D12—62no—
269C3×D12—121no—
270D3×Dic3—62no—
271D3×Dic3—121no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9C22×D311yescharacteristic
275C22×D9—22no—
276C22×D9—22no—
277C22×D9—41no—
278C22×D9C22×D311yescharacteristic
279C22×D9C22×D311yescharacteristic
280C22×D9C22×D311yescharacteristic
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9—31no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—62no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290#611—22no—
291C2×Dic9—31no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—61no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—121no—
300C2×Dic9—122no—
301C2×Dic9C22×D311yescharacteristic
302D36—22no—
303D36—41no—
304C4×D9—62no—
305C4×D9—121no—
306C4×D9—121no—
307Dic18—121no—
308Dic18—122no—
309#551—271noSylow
310C2×C3×C9—22no—
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314C3×D9—22no—
315C3×D9—41no—
316C3×D9—41no—
317C24×C3—91no—
318C23×D3—31no—
319C2×C3×D4—91no—
320C2×C3×D4—91no—
321C2×C3×D4—91no—
322C22×C3×C4—31no—
323C2×#67—31no—
324C22×Dic3—91no—
325C22×Dic3—91no—
326C22×Dic3—91no—
327C22×Dic3—91no—
328C22×Dic3—91no—
329C22×Dic3—181no—
330C22×Dic3C2×D911yescharacteristic
331C2×D12—31no—
332C2×D12—31no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—181no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4C2×D911yescharacteristic
346C3×C22⋊C4D3211yescharacteristic
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—91no—
356#217—91no—
357#217—91no—
358#217—91no—
359#217—91no—
360#217—181no—
361#217C2×D911yescharacteristic
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
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—
373C4⋊Dic3—91no—
374C4⋊Dic3—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3—181no—
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—181no—
387Dic3⋊C4—181no—
388Dic3⋊C4C2×D911yescharacteristic, complemented
389Dic3⋊C4C2×D911yescharacteristic, complemented
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—32no—
399C2×C3×D3—61no—
400C2×C3×D3—61no—
401C2×C3×D3—61no—
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—61no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
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—21no—
433C2×D9—21no—
434C2×D9—21no—
435C2×D9—44no—
436C2×D9#23712yes—
437C4×C9—21no—
438C4×C9—21no—
439C4×C9—41no—
440C4×C9—41no—
441C4×C9—61no—
442C4×C9—61no—
443C4×C9—61no—
444C4×C9—61no—
445Dic9—21no—
446Dic9—62no—
447Dic9—61no—
448Dic9—61no—
449Dic9—61no—
450Dic9—61no—
451Dic9—121no—
452Dic9—121no—
453Dic9—121no—
454#126—271no—
455#126—271no—
456#124—271no—
457#123—271no—
458#123—271no—
459#123—271no—
460C22⋊Q8—271no—
461C22⋊Q8—271no—
462#120—91no—
463C4×D4—271no—
464C4×D4—271no—
465#117—31no—
466#117—271no—
467C2×C22⋊C4—271no—
468C2×C22⋊C4—271no—
469C3×C9#55111yescharacteristic, complemented, Sylow
470C23×C3—21no—
471C23×C3—91no—
472C23×C3—91no—
473C23×C3—91no—
474C23×C3—182no—
475C23×C3—182no—
476C23×C3—361no—
477C23×C3C22×D911yescharacteristic
478C23×C3C2×D3211yescharacteristic
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—121no—
485C3×D4—182no—
486C3×D4—182no—
487C3×D4—361no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—62no—
495C2×C3×C4—91no—
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C22×D911yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500#67—62no—
501C2×Dic3—22no—
502C2×Dic3—31no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—181no—
512C2×Dic3—181no—
513C2×Dic3—181no—
514C2×Dic3—181no—
515C2×Dic3—182no—
516C2×Dic3—361no—
517C2×Dic3—361no—
518C2×Dic3—361no—
519C2×Dic3—361no—
520C2×Dic3—362no—
521C2×Dic3C22×D911yescharacteristic
522C2×Dic3C22×D911yescharacteristic
523C2×Dic3C22×D911yescharacteristic
524C2×Dic3C22×D911yescharacteristic
525D12—62no—
526D12—121no—
527C4×D3—182no—
528C4×D3—361no—
529C4×D3—361no—
530Dic6—361no—
531Dic6—361no—
532Dic6—362no—
533C2×C32—22no—
534C2×C32C2×#23511yescharacteristic
535C2×C32D3×#4111yescharacteristic
536C2×C32#100911yescharacteristic
537C3×D3—62no—
538C3×D3—121no—
539C3×D3—121no—
540C2×C9—22no—
541C2×C9—21no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—42no—
545C2×C9C2×#23711yescharacteristic
546C2×C9C2×#23711yescharacteristic
547C2×C9#100411yescharacteristic
548D9—22no—
549D9—41no—
550D9—41no—
551C24—91no—
552C2×Q8—271no—
553C2×D4—91no—
554C2×D4—91no—
555C2×D4—91no—
556C22×C4—31no—
557C22×C4—271no—
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⋊C4—271no—
569C22⋊C4—31no—
570C22⋊C4—91no—
571C22⋊C4—91no—
572C22⋊C4—271no—
573C22⋊C4—271no—
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⋊C4D3×D911yescharacteristic
583C42—31no—
584C42—31no—
585C42—271no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—22no—
591C22×C3—21no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—92no—
595C22×C3—181no—
596C22×C3—181no—
597C22×C3—181no—
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#379512yes—
607C22×C3C22×D3211yescharacteristic
608C2×D3—32no—
609C2×D3—61no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—124no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—61no—
627C3×C4—61no—
628C3×C4—181no—
629Dic3—21no—
630Dic3—21no—
631Dic3—21no—
632Dic3—21no—
633Dic3—61no—
634Dic3—182no—
635Dic3—181no—
636Dic3—181no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—361no—
644Dic3—361no—
645Dic3—361no—
646C32#552711yescharacteristic
647C9—21no—
648C9#558711yescharacteristic, complemented
649C23—91no—
650C23—91no—
651C23—91no—
652C23—182no—
653C23—182no—
654C23—361no—
655C23C2×D3×D911yescharacteristic
656Q8—1081no—
657D4—182no—
658D4—182no—
659D4—361no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—62no—
665C2×C4—91no—
666C2×C4—271no—
667C2×C4—271no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—542no—
671C2×C4—1081no—
672C2×C4—1081no—
673C2×C4—1081no—
674C2×C4C2×D3×D911yescharacteristic
675C2×C4C2×D3×D911yescharacteristic
676C2×C3—22no—
677C2×C3—22no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—42no—
682C2×C3—182no—
683C2×C3—361no—
684C2×C3—361no—
685C2×C3C2×#369711yescharacteristic
686C2×C3#41×D911yescharacteristic
687C2×C3#6371511yescharacteristic
688C2×C3C2×#379511yescharacteristic
689C2×C3D3×#23711yescharacteristic
690C2×C3#6431411yescharacteristic
691D3—62no—
692D3—121no—
693D3—121no—
694C22—21no—
695C22—21no—
696C22—92no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22—181no—
703C22—181no—
704C22—181no—
705C22—364no—
706C22#8864112yes—
707C22C22×D3×D911yescharacteristic
708C4—21no—
709C4—21no—
710C4—61no—
711C4—61no—
712C4—61no—
713C4—61no—
714C4—181no—
715C4—541no—
716C4—541no—
717C4—541no—
718C4—541no—
719C3—21no—
720C3#1058962911yescharacteristic, complemented
721C3#1059411711yescharacteristic
722C2—22no—
723C2—182no—
724C2—361no—
725C2—361no—
726C2C2×#8864111yescharacteristic
727C2D9×#23711yescharacteristic
728C2#1172250111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC3×#63444C2
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. #11721724C2semidirect
3. C9×#877C2semidirect
4. #611⋊Dic3C2semidirect
5. D9×#217C2semidirect
6. #11721259C2semidirect
7. C2×(C2×D9)⋊Dic3C2semidirect
8. #11720996C2semidirect
9. Dic3×D36C2semidirect
10. #11720981C2semidirect
11. #11720981C2semidirect
12. #11720974C2semidirect
13. #11720949C2semidirect
14. #11720948C2semidirect
15. #11720947C2semidirect
20. C2×#6226C22semidirect
27. C2×Dic3×D9C22semidirect
30. C4⋊(C3⋊Dic9)C22semidirect
31. #88534C22semidirect
32. #88534C22semidirect
36. C9×Dic3⋊C4C22semidirect
37. C9×Dic3⋊C4C22semidirect
38. C4×C9×Dic3C22semidirect
39. C4×C9×Dic3C22semidirect
46. (C2×D9)⋊Dic3C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. #88442C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
241. #877D9semidirect
388. Dic3⋊C4C2×D9semidirect
389. Dic3⋊C4C2×D9semidirect
392. C4×Dic3C2×D9semidirect
393. C4×Dic3C2×D9semidirect
469. C3×C9#551semidirect
648. C9#5587semidirect
720. C3#10589629semidirect

Maximal subgroups

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

subgroupindex
#117217242
C3×#634442
C9×#8772
#611⋊Dic32
D9×#2172
#117212592
C2×(C2×D9)⋊Dic32
#117209962
Dic3×D362
#117209812
#117209742
#117209492
#117209482
#117209472
#105941173
#105896293