Finite Group Databasebeta

← #13148066

Subgroups — #13148066

Order 1728.

820 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721723C211yesmaximal, characteristic, complemented
2C3×#63444C211yesmaximal, characteristic
3C9×#878C211yesmaximal, characteristic, complemented
4Dic3×#611C211yesmaximal, characteristic, complemented
5D9×#217C211yesmaximal, characteristic, complemented
6#11721260C211yesmaximal, characteristic, complemented
7C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
8#11720998C211yesmaximal, characteristic, complemented
9#11720984C211yesmaximal, characteristic, complemented
10#11720981C211yesmaximal, characteristic, complemented
11#11720981C211yesmaximal, characteristic, complemented
12#11720975C211yesmaximal, characteristic, complemented
13#11720951C211yesmaximal, characteristic, complemented
14#11720950C211yesmaximal, characteristic, complemented
15#11720946C211yesmaximal, characteristic, complemented
16#10594119—31nomaximal
17#10589739—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C22×C9×Dic3C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C9×Dic6C2211yescharacteristic, complemented
25C2×Dic3×D9C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic
27C2×Dic3×D9C2211yescharacteristic, complemented
28C3×C9×C22⋊C4C2211yescharacteristic
29#88551C2211yescharacteristic
30#88534C2211yescharacteristic, complemented
31#88534C2211yescharacteristic, complemented
32C4×C3⋊Dic9C2211yescharacteristic, complemented
33C4×C3⋊Dic9C2211yescharacteristic, complemented
34C9×#217C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C9×C4⋊Dic3C2211yescharacteristic, complemented
38C9×Dic3⋊C4C2211yescharacteristic, complemented
39C9×Dic3⋊C4C2211yescharacteristic, 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
49Dic3⋊Dic9C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64086—31no—
54C3×#882—31no—
55C3×#878D311yescharacteristic
56Dic3×#67—31no—
57D3×#217—31no—
58#63962—31no—
59C2×(C2×D3)⋊Dic3—31no—
60#63898—31no—
61#63887—31no—
62#63884—31no—
63#63884—31no—
64#63878—31no—
65#63863—31no—
66#63862—31no—
67#63858—31no—
68C9×C22⋊Q8—31no—
69#63509—31no—
70#63508—31no—
71C4×#611—31no—
72C2×(C2×D9)⋊C4—31no—
73#63460—31no—
74#63460—31no—
75#63456—31no—
76#63456—31no—
77#63455—31no—
78#63454—31no—
79#63448—31no—
80#63444D311yescharacteristic
81C22⋊C4×D9—31no—
82#63439—31no—
83#63439—61no—
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—22no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C3×#611—22no—
99C2×C9×Dic3—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C3×D36—22no—
106C3×D36—41no—
107C9×Dic6—41no—
108Dic3×D9—22no—
109Dic3×D9—41no—
110Dic3×D9—41no—
111#5637—91no—
112#5587—91no—
113C23×C3×D3—31no—
114C22×C3⋊Dic3—31no—
115C2×C3×#67—31no—
116C22×C3×Dic3C2×D311yescharacteristic
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×Dic6C2×D311yescharacteristic
120C2×D3×Dic3—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C23×D9C2×D311yescharacteristic
124C32×C22⋊C4C2×D311yescharacteristic
125#3757—31no—
126#3750—31no—
127#3750—31no—
128C4×C3⋊Dic3—31no—
129C4×C3⋊Dic3—31no—
130C3×#217C2×D311yescharacteristic
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×C4⋊Dic3C2×D311yescharacteristic
134C3×Dic3⋊C4C2×D311yescharacteristic
135C3×Dic3⋊C4C2×D311yescharacteristic
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—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—
149C2×Q8×C9—31no—
150C22×C4×C9—31no—
151C2×#611C2×D311yescharacteristic
152C22×Dic9—31no—
153C22×Dic9—61no—
154C2×D36C2×D311yescharacteristic
155C2×D36C2×D311yescharacteristic
156C2×C4×D9—31no—
157C2×C4×D9—31no—
158C2×C4×D9—31no—
159C9×C4⋊C4—31no—
160C9×C4⋊C4—31no—
161C9×C4⋊C4—31no—
162C9×C22⋊C4—21no—
163C9×C22⋊C4—31no—
164C9×C22⋊C4C2×D311yescharacteristic
165#3676—31no—
166#3676—61no—
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)⋊C4C2×D311yescharacteristic
177(C2×D9)⋊C4C2×D311yescharacteristic
178C4⋊Dic9—31no—
179C4⋊Dic9—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—61no—
184Dic9⋊C4—61no—
185C4×Dic9—31no—
186C4×Dic9—31no—
187C4×Dic9—31no—
188C4×Dic9—61no—
189C4×Dic9—61no—
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×C22⋊Q8—31no—
216C3×#120—91no—
217C2×#217—91no—
218C2×#217—91no—
219#947—91no—
220#946—91no—
221#936—91no—
222#935—91no—
223#935—91no—
224#935—91no—
225D4×Dic3—91no—
226D4×Dic3—91no—
227C4×#67—91no—
228C2×(C2×D3)⋊C4—91no—
229#898—91no—
230#898—91no—
231#894—91no—
232#894—91no—
233#893—91no—
234#892—91no—
235#886—91no—
236#882—31no—
237D3×C22⋊C4—91no—
238#879—91no—
239#879—91no—
240#878—91no—
241#878D911yescharacteristic, complemented
242#877—91no—
243#877—91no—
244#877—91no—
245#877—181no—
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—62no—
260C3×#67—62no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—41no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C3×D12—62no—
268C3×D12—121no—
269C3×Dic6—41no—
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
281Q8×C9—121no—
282C2×C4×C9—21no—
283C2×C4×C9—21no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9—121no—
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291#611—22no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—64no—
301C2×Dic9—62no—
302C2×Dic9C22×D311yescharacteristic
303D36—22no—
304D36—41no—
305C4×D9—62no—
306C4×D9—121no—
307C4×D9—121no—
308#551—271noSylow
309C2×C3×C9—22no—
310C2×C3×C9C2×#4111yescharacteristic
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9H(5,𝔽2)11yescharacteristic
313C3×D9—22no—
314C3×D9—41no—
315C3×D9—41no—
316C24×C3—91no—
317C23×D3—31no—
318C2×C3×Q8—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×Dic6C2×D911yescharacteristic, complemented
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4C2×D911yescharacteristic
345C3×C22⋊C4D3211yescharacteristic
346#217—91no—
347#217—91no—
348#217—91no—
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—181no—
358#217C2×D911yescharacteristic
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
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—
370C4⋊Dic3—91no—
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3C2×D911yescharacteristic, complemented
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—91no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—181no—
382Dic3⋊C4—181no—
383Dic3⋊C4C2×D911yescharacteristic, complemented
384Dic3⋊C4C2×D911yescharacteristic, complemented
385C4×Dic3—91no—
386C4×Dic3—91no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—181no—
392C4×Dic3—181no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32#23912yes—
396C22×C32C23×D311yescharacteristic
397C2×C3×D3—32no—
398C2×C3×D3—61no—
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—124no—
407C32×C4—21no—
408C32×C4—21no—
409C3⋊Dic3—61no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—61no—
418C22×C9—21no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—22no—
422C22×C9—41no—
423C22×C9—41no—
424C22×C9#23712yes—
425C22×C9C23×D311yescharacteristic
426C2×D9—21no—
427C2×D9—21no—
428C2×D9—21no—
429C2×D9—21no—
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—21no—
433C2×D9—21no—
434C2×D9—44no—
435C2×D9#23712yes—
436C4×C9—21no—
437C4×C9—21no—
438C4×C9—41no—
439C4×C9—41no—
440C4×C9—61no—
441C4×C9—61no—
442C4×C9—61no—
443C4×C9—61no—
444Dic9—21no—
445Dic9—62no—
446Dic9—62no—
447Dic9—61no—
448Dic9—61no—
449Dic9—61no—
450Dic9—61no—
451Dic9—121no—
452Dic9—121no—
453#126—271no—
454#126—271no—
455#124—271no—
456#123—271no—
457#123—271no—
458#123—271no—
459C22⋊Q8—31no—
460C22⋊Q8—271no—
461#120—91no—
462C4×D4—271no—
463C4×D4—271no—
464#117—271no—
465#117—271no—
466C2×C22⋊C4—271no—
467C2×C22⋊C4—271no—
468C3×C9#55111yescharacteristic, complemented, Sylow
469C23×C3—21no—
470C23×C3—91no—
471C23×C3—91no—
472C23×C3—91no—
473C23×C3—182no—
474C23×C3—182no—
475C23×C3—361no—
476C23×C3C22×D911yescharacteristic
477C23×C3C2×D3211yescharacteristic
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—121no—
484C3×Q8—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—91no—
495C2×C3×C4—121no—
496C2×C3×C4C22×D911yescharacteristic
497C2×C3×C4C22×D911yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500#67—62no—
501C2×Dic3—31no—
502C2×Dic3—41no—
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—184no—
517C2×Dic3—182no—
518C2×Dic3—182no—
519C2×Dic3—361no—
520C2×Dic3—361no—
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—41no—
531C2×C32—22no—
532C2×C32#100411yescharacteristic
533C2×C32C2×#23911yescharacteristic
534C2×C32D3×#4111yescharacteristic
535C3×D3—62no—
536C3×D3—121no—
537C3×D3—121no—
538C2×C9—22no—
539C2×C9—21no—
540C2×C9—21no—
541C2×C9—21no—
542C2×C9—42no—
543C2×C9C2×#23711yescharacteristic
544C2×C9C2×#23711yescharacteristic
545C2×C9#100411yescharacteristic
546D9—22no—
547D9—41no—
548D9—41no—
549C24—91no—
550C2×Q8—31no—
551C2×D4—91no—
552C2×D4—91no—
553C2×D4—91no—
554C22×C4—31no—
555C22×C4—271no—
556C22×C4—271no—
557C22×C4—271no—
558C22×C4—271no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C22⋊C4—31no—
568C22⋊C4—91no—
569C22⋊C4—91no—
570C22⋊C4—271no—
571C22⋊C4—271no—
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⋊C4D3×D911yescharacteristic
581C42—271no—
582C42—271no—
583C42—271no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—92no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3—181no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—364no—
602C22×C3#370112yes—
603C22×C3C23×D911yescharacteristic
604C22×C3#379612yes—
605C22×C3C22×D3211yescharacteristic
606C2×D3—32no—
607C2×D3—61no—
608C2×D3—61no—
609C2×D3—61no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—124no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—61no—
623C3×C4—61no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—181no—
627Dic3—21no—
628Dic3—21no—
629Dic3—21no—
630Dic3—21no—
631Dic3—61no—
632Dic3—182no—
633Dic3—182no—
634Dic3—181no—
635Dic3—181no—
636Dic3—181no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—361no—
643Dic3—361no—
644C32#563711yescharacteristic
645C9—21no—
646C9#558711yescharacteristic, complemented
647C23—91no—
648C23—91no—
649C23—91no—
650C23—182no—
651C23—182no—
652C23—361no—
653C23C2×D3×D911yescharacteristic
654Q8—121no—
655D4—182no—
656D4—182no—
657D4—361no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—91no—
663C2×C4—121no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—271no—
667C2×C4—271no—
668C2×C4—542no—
669C2×C4—542no—
670C2×C4—1081no—
671C2×C4—1081no—
672C2×C4C2×D3×D911yescharacteristic
673C2×C4C2×D3×D911yescharacteristic
674C2×C3—22no—
675C2×C3—22no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—42no—
680C2×C3—182no—
681C2×C3—361no—
682C2×C3—361no—
683C2×C3#6371011yescharacteristic
684C2×C3C2×#370111yescharacteristic
685C2×C3#41×D911yescharacteristic
686C2×C3C2×#379611yescharacteristic
687C2×C3D3×#23711yescharacteristic
688C2×C3#6431311yescharacteristic
689D3—62no—
690D3—121no—
691D3—121no—
692C22—21no—
693C22—21no—
694C22—92no—
695C22—181no—
696C22—181no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22—181no—
703C22—364no—
704C22#8863412yes—
705C22C22×D3×D911yescharacteristic
706C4—21no—
707C4—21no—
708C4—61no—
709C4—61no—
710C4—61no—
711C4—61no—
712C4—181no—
713C4—541no—
714C4—541no—
715C4—541no—
716C4—541no—
717C3—21no—
718C3#1058973911yescharacteristic, complemented
719C3#1059411911yescharacteristic
720C2—22no—
721C2—182no—
722C2—361no—
723C2—361no—
724C2C2×#8863411yescharacteristic
725C2D9×#23711yescharacteristic
726C2#1172249911yescharacteristic
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. #11721723C2semidirect
3. C9×#878C2semidirect
4. Dic3×#611C2semidirect
5. D9×#217C2semidirect
6. #11721260C2semidirect
7. C2×(C2×D9)⋊Dic3C2semidirect
8. #11720998C2semidirect
9. #11720984C2semidirect
10. #11720981C2semidirect
11. #11720981C2semidirect
12. #11720975C2semidirect
13. #11720951C2semidirect
14. #11720950C2semidirect
15. #11720946C2semidirect
24. C2×C9×Dic6C22semidirect
27. C2×Dic3×D9C22semidirect
30. #88534C22semidirect
31. #88534C22semidirect
32. C4×C3⋊Dic9C22semidirect
33. C4×C3⋊Dic9C22semidirect
37. C9×C4⋊Dic3C22semidirect
38. C9×Dic3⋊C4C22semidirect
39. C9×Dic3⋊C4C22semidirect
46. (C2×D9)⋊Dic3C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. Dic3⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
241. #878D9semidirect
336. C2×Dic6C2×D9semidirect
373. C4⋊Dic3C2×D9semidirect
383. Dic3⋊C4C2×D9semidirect
384. Dic3⋊C4C2×D9semidirect
468. C3×C9#551semidirect
646. C9#5587semidirect
718. C3#10589739semidirect

Maximal subgroups

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

subgroupindex
#117217232
C3×#634442
C9×#8782
Dic3×#6112
D9×#2172
#117212602
C2×(C2×D9)⋊Dic32
#117209982
#117209842
#117209812
#117209752
#117209512
#117209502
#117209462
#105941193
#105897393