Finite Group Databasebeta

← C3×#10589760 #13153016

Subgroups — C3×#10589760 #13153016

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
1C3×C9×#123C211yesmaximal, characteristic, complemented
2C3×#63499C211yesmaximal, characteristic
3C3×D4×Dic9C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
5C3×#63488C211yesmaximal, characteristic, complemented
6C3×#63460C211yesmaximal, characteristic, complemented
7C3×#63460C211yesmaximal, characteristic, complemented
8C3×#63459C211yesmaximal, characteristic, complemented
9C3×#63454C211yesmaximal, characteristic, complemented
10C3×#63448C211yesmaximal, characteristic, complemented
11C3×#63447C211yesmaximal, characteristic, complemented
12C3×#63445C211yesmaximal, characteristic, complemented
13C3×#611⋊C4C211yesmaximal, characteristic, complemented
14C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
15C3×#63440C211yesmaximal, characteristic, complemented
16C3×#5658—31nomaximal
17#10589760C311yesmaximal, characteristic, direct product factor
18C23×C3×D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C3×Dic9C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic, complemented
25C2×C3×C4×D9C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×C3×Dic18C2211yescharacteristic, complemented
28C3×C9×C4⋊C4C2211yescharacteristic, complemented
29C3×C9×C4⋊C4C2211yescharacteristic, complemented
30C3×C9×C22⋊C4C2211yescharacteristic
31C3×C9×C22⋊C4C2211yescharacteristic, complemented
32C3×C9×C22⋊C4C2211yescharacteristic, complemented
33C3×#3676C2211yescharacteristic
34C3×#3676C2211yescharacteristic
35C3×#3676C2211yescharacteristic, complemented
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45C3×C4⋊Dic9C2211yescharacteristic, complemented
46C3×C4⋊Dic9C2211yescharacteristic, complemented
47C3×C4⋊Dic9C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49C3×Dic9⋊C4C2211yescharacteristic, complemented
50C3×C4×Dic9C2211yescharacteristic, complemented
51C3×C4×Dic9C2211yescharacteristic, complemented
52C3×C4×Dic9C2211yescharacteristic, complemented
53C32×#123D311yescharacteristic
54C3×#937—31no—
55C3×D4×Dic3—31no—
56C2×C3×(C2×D3)⋊C4—31no—
57C3×#926—31no—
58C3×#898—31no—
59C3×#898—31no—
60C3×#897—31no—
61C3×#892—31no—
62C3×#886—31no—
63C3×#885—31no—
64C3×#883—31no—
65C3×#67⋊C4—31no—
66C3×D3×C22⋊C4—31no—
67C3×#878—31no—
68C9×#123—21no—
69C9×#123C2×C311yescharacteristic, complemented
70#63499C2×C311yescharacteristic
71D4×Dic9C2×C311yescharacteristic, complemented
72C2×(C2×D9)⋊C4C2×C311yescharacteristic, complemented
73#63488C2×C311yescharacteristic, complemented
74#63460C2×C311yescharacteristic, complemented
75#63460C2×C311yescharacteristic, complemented
76#63459C2×C311yescharacteristic, complemented
77#63454C2×C311yescharacteristic, complemented
78#63448C2×C311yescharacteristic, complemented
79#63447C2×C311yescharacteristic, complemented
80#63445C2×C311yescharacteristic, complemented
81#611⋊C4C2×C311yescharacteristic, complemented
82C22⋊C4×D9C2×C311yescharacteristic, complemented
83#63440C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×C3×D9—22no—
87C22×C3×D9—22no—
88C22×C3×D9—41no—
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C3×D4×C9—22no—
92C2×C3×C4×C9—22no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98C3×#611—22no—
99C3×#611—41no—
100C2×C3×Dic9—41no—
101C2×C3×Dic9—41no—
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C3×C4×D9—22no—
109C3×C4×D9—41no—
110C3×Dic18—41no—
111C3×#551—91no—
112#5658—31no—
113C23×C3×D3—31no—
114C2×C32×D4C2×D311yescharacteristic
115C22×C32×C4C2×D311yescharacteristic
116C2×C3×#67—31no—
117C2×C3×#67—31no—
118C22×C3×Dic3—31no—
119C22×C3×Dic3—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×Dic6—31no—
123C23×D9C22×C311yescharacteristic
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C2×D311yescharacteristic
126C32×C22⋊C4C2×D311yescharacteristic
127C32×C22⋊C4C2×D311yescharacteristic
128C32×C22⋊C4C2×D311yescharacteristic
129C3×#217—31no—
130C3×#217—31no—
131C3×#217—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×C4⋊Dic3—31no—
141C3×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×C4⋊Dic3—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C2×D4×C9—21no—
150C2×D4×C9C22×C311yescharacteristic
151C22×C4×C9—21no—
152C22×C4×C9C22×C311yescharacteristic
153C2×#611C22×C311yescharacteristic
154C2×#611C22×C311yescharacteristic
155C22×Dic9C22×C311yescharacteristic
156C22×Dic9C22×C311yescharacteristic, complemented
157C2×C4×D9C22×C311yescharacteristic
158C2×C4×D9C22×C311yescharacteristic
159C2×Dic18C22×C311yescharacteristic, complemented
160C9×C4⋊C4—21no—
161C9×C4⋊C4—21no—
162C9×C4⋊C4C22×C311yescharacteristic, complemented
163C9×C4⋊C4C22×C311yescharacteristic, complemented
164C9×C22⋊C4—21no—
165C9×C22⋊C4—21no—
166C9×C22⋊C4—21no—
167C9×C22⋊C4C22×C311yescharacteristic
168C9×C22⋊C4C22×C311yescharacteristic, complemented
169C9×C22⋊C4C22×C311yescharacteristic, complemented
170#3676C22×C311yescharacteristic
171#3676C22×C311yescharacteristic
172#3676C22×C311yescharacteristic, complemented
173(C2×D9)⋊C4C22×C311yescharacteristic
174(C2×D9)⋊C4C22×C311yescharacteristic
175(C2×D9)⋊C4C22×C311yescharacteristic
176(C2×D9)⋊C4C22×C311yescharacteristic
177(C2×D9)⋊C4C22×C311yescharacteristic
178(C2×D9)⋊C4C22×C311yescharacteristic
179(C2×D9)⋊C4C22×C311yescharacteristic
180(C2×D9)⋊C4C22×C311yescharacteristic
181C4⋊Dic9C22×C311yescharacteristic, complemented
182C4⋊Dic9C22×C311yescharacteristic, complemented
183C4⋊Dic9C22×C311yescharacteristic, complemented
184C4⋊Dic9C22×C311yescharacteristic, complemented
185Dic9⋊C4C22×C311yescharacteristic, complemented
186Dic9⋊C4C22×C311yescharacteristic, complemented
187C4×Dic9C22×C311yescharacteristic, complemented
188C4×Dic9C22×C311yescharacteristic, complemented
189C4×Dic9C22×C311yescharacteristic, complemented
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9#4112yes—
196C22×C3×C9C2411yescharacteristic
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×C4×C9—21no—
207C3×C4×C9—21no—
208C3×C4×C9—21no—
209C3×Dic9—21no—
210C3×Dic9—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#126—91no—
216C3×#126—91no—
217C3×#124—91no—
218C3×#123—21no—
219C3×#123—91no—
220C3×#123—91no—
221C3×#123D911yescharacteristic, complemented
222C3×#123C3×D311yescharacteristic
223C3×C22⋊Q8—91no—
224C3×C22⋊Q8—91no—
225C3×#120—91no—
226C3×C4×D4—91no—
227C3×C4×D4—91no—
228C3×#117—91no—
229C3×#117—91no—
230C2×C3×C22⋊C4—91no—
231C2×C3×C22⋊C4—91no—
232#937—31no—
233D4×Dic3—31no—
234C2×(C2×D3)⋊C4—31no—
235#926—31no—
236#898—31no—
237#898—31no—
238#897—31no—
239#892—31no—
240#886—31no—
241#885—31no—
242#883—31no—
243#67⋊C4—31no—
244D3×C22⋊C4—31no—
245#878—31no—
246C23×C32C22×D311yescharacteristic
247C23×C32C22×D311yescharacteristic
248C22×C3×D3—31no—
249C22×C3×D3—31no—
250C22×C3×D3—62no—
251C22×C3×D3—62no—
252C22×C3×D3—121no—
253C32×D4—22no—
254C2×C32×C4—22no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C3×#67—62no—
261C3×#67—121no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—121no—
269C2×C3×Dic3—121no—
270C3×C4×D3—62no—
271C3×C4×D3—121no—
272C3×Dic6—121no—
273C23×C9—21no—
274C23×C9—21no—
275C23×C9C23×C311yescharacteristic
276C23×C9C23×C311yescharacteristic
277C22×D9—22no—
278C22×D9—22no—
279C22×D9—41no—
280C22×D9C23×C311yescharacteristic
281C22×D9C23×C311yescharacteristic
282D4×C9—22no—
283D4×C9—42no—
284C2×C4×C9—22no—
285C2×C4×C9—21no—
286C2×C4×C9—21no—
287C2×C4×C9—21no—
288C2×C4×C9—21no—
289C2×C4×C9—21no—
290C2×C4×C9—42no—
291C2×C4×C9C23×C311yescharacteristic
292C2×C4×C9C23×C311yescharacteristic
293C2×C4×C9C23×C311yescharacteristic
294C2×C4×C9C23×C311yescharacteristic
295C2×C4×C9C23×C311yescharacteristic
296#611—22no—
297#611—41no—
298C2×Dic9—41no—
299C2×Dic9—41no—
300C2×Dic9C23×C311yescharacteristic
301C2×Dic9C23×C311yescharacteristic
302C2×Dic9C23×C311yescharacteristic
303C2×Dic9C23×C311yescharacteristic
304C2×Dic9C23×C311yescharacteristic
305C2×Dic9C23×C311yescharacteristic
306C4×D9—22no—
307C4×D9—41no—
308Dic18—41no—
309#551—91noSylow
310C2×C3×C9—22no—
311C2×C3×C9—41no—
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9C2×#4111yescharacteristic
314C2×C3×C9H(5,𝔽2)11yescharacteristic
315C3×D9—22no—
316C3×D9—41no—
317C24×C3—91no—
318C23×D3—31no—
319C2×C3×Q8—91no—
320C2×C3×D4—21no—
321C2×C3×D4—91no—
322C2×C3×D4—91no—
323C2×C3×D4C2×D911yescharacteristic
324C2×C3×D4C2×C3×D311yescharacteristic
325C22×C3×C4—21no—
326C22×C3×C4—91no—
327C22×C3×C4—91no—
328C22×C3×C4—91no—
329C22×C3×C4—91no—
330C22×C3×C4C2×D911yescharacteristic
331C22×C3×C4C2×C3×D311yescharacteristic
332C2×#67—31no—
333C2×#67—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×Dic6—31no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4C2×D911yescharacteristic, complemented
348C3×C4⋊C4C2×D911yescharacteristic, complemented
349C3×C4⋊C4C2×C3×D311yescharacteristic
350C3×C4⋊C4C2×C3×D311yescharacteristic
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—91no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4—91no—
357C3×C22⋊C4—91no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4—91no—
360C3×C22⋊C4—91no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4C2×D911yescharacteristic
366C3×C22⋊C4C2×D911yescharacteristic, complemented
367C3×C22⋊C4C2×D911yescharacteristic, complemented
368C3×C22⋊C4C2×C3×D311yescharacteristic
369C3×C22⋊C4C2×C3×D311yescharacteristic
370C3×C22⋊C4C2×C3×D311yescharacteristic
371C3×C42—91no—
372C3×C42—91no—
373C3×C42—91no—
374#217—31no—
375#217—31no—
376#217—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32#23712yes—
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—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—21no—
413C3×Dic3—61no—
414C3×Dic3—61no—
415C3×Dic3—61no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—21no—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—22no—
426C22×C9—41no—
427C22×C9—41no—
428C22×C9—41no—
429C22×C9—41no—
430C22×C9—41no—
431C22×C9C3×#4112yes—
432C22×C9C24×C311yescharacteristic
433C2×D9—21no—
434C2×D9—21no—
435C2×D9—21no—
436C2×D9—21no—
437C2×D9—21no—
438C2×D9—44no—
439C2×D9C3×#4112yes—
440C4×C9—21no—
441C4×C9—21no—
442C4×C9—21no—
443C4×C9—21no—
444C4×C9—21no—
445C4×C9—41no—
446C4×C9—41no—
447C4×C9—41no—
448C4×C9—41no—
449C4×C9—41no—
450Dic9—21no—
451Dic9—21no—
452Dic9—21no—
453Dic9—21no—
454Dic9—21no—
455Dic9—21no—
456#126—91no—
457#126—91no—
458#124—91no—
459#123—91no—
460#123—91no—
461#123C3×D911yescharacteristic, complemented
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464#120—91no—
465C4×D4—91no—
466C4×D4—91no—
467#117—91no—
468#117—91no—
469C2×C22⋊C4—91no—
470C2×C22⋊C4—91no—
471C3×C9#55111yescharacteristic, complemented, Sylow
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—91no—
475C23×C3—91no—
476C23×C3—182no—
477C23×C3—182no—
478C23×C3—361no—
479C23×C3C22×D911yescharacteristic
480C23×C3C22×D911yescharacteristic
481C23×C3C22×C3×D311yescharacteristic
482C23×C3C22×C3×D311yescharacteristic
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—62no—
486C22×D3—62no—
487C22×D3—121no—
488C3×Q8—361no—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—42no—
492C3×D4—182no—
493C3×D4—361no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—42no—
502C2×C3×C4—91no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—91no—
506C2×C3×C4—91no—
507C2×C3×C4—91no—
508C2×C3×C4—182no—
509C2×C3×C4—361no—
510C2×C3×C4—361no—
511C2×C3×C4—361no—
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C22×C3×D311yescharacteristic
518C2×C3×C4C22×C3×D311yescharacteristic
519C2×C3×C4C22×C3×D311yescharacteristic
520C2×C3×C4C22×C3×D311yescharacteristic
521C2×C3×C4C22×C3×D311yescharacteristic
522#67—62no—
523#67—121no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C4×D3—62no—
533C4×D3—121no—
534Dic6—121no—
535C2×C32—22no—
536C2×C32—41no—
537C2×C32C2×#23711yescharacteristic
538C2×C32D3×#4111yescharacteristic
539C2×C32#100911yescharacteristic
540C3×D3—62no—
541C3×D3—121no—
542C2×C9—22no—
543C2×C9—21no—
544C2×C9—21no—
545C2×C9—21no—
546C2×C9—42no—
547C2×C9—41no—
548C2×C9—81no—
549C2×C9C2×C3×#4111yescharacteristic
550C2×C9C2×C3×#4111yescharacteristic
551C2×C9C3×H(5,𝔽2)11yescharacteristic
552D9—22no—
553D9—41no—
554C24—91no—
555C2×Q8—91no—
556C2×D4—91no—
557C2×D4—91no—
558C2×D4C2×C3×D911yescharacteristic
559C22×C4—91no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4C2×C3×D911yescharacteristic
564C4⋊C4—91no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4C2×C3×D911yescharacteristic, complemented
571C4⋊C4C2×C3×D911yescharacteristic, complemented
572C22⋊C4—91no—
573C22⋊C4—91no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—91no—
581C22⋊C4—91no—
582C22⋊C4—91no—
583C22⋊C4C2×C3×D911yescharacteristic
584C22⋊C4C2×C3×D911yescharacteristic, complemented
585C22⋊C4C2×C3×D911yescharacteristic, complemented
586C42—91no—
587C42—91no—
588C42—91no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—22no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—92no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3—181no—
611C22×C3—181no—
612C22×C3—364no—
613C22×C3#369912yes—
614C22×C3C23×D911yescharacteristic
615C22×C3C3×#23712yes—
616C22×C3C23×C3×D311yescharacteristic
617C2×D3—32no—
618C2×D3—61no—
619C2×D3—61no—
620C2×D3—61no—
621C2×D3—61no—
622C2×D3—61no—
623C2×D3—124no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—181no—
640C3×C4—181no—
641C3×C4—181no—
642C3×C4—181no—
643C3×C4—181no—
644C3×C4—181no—
645Dic3—61no—
646Dic3—61no—
647Dic3—61no—
648Dic3—61no—
649Dic3—61no—
650Dic3—61no—
651C32#565811yescharacteristic
652C9—21no—
653C9C3×#55111yescharacteristic, complemented
654C23—91no—
655C23—91no—
656C23—182no—
657C23—182no—
658C23—361no—
659C23C22×C3×D911yescharacteristic
660C23C22×C3×D911yescharacteristic
661Q8—361no—
662D4—22no—
663D4—182no—
664D4—361no—
665C2×C4—22no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—182no—
673C2×C4—361no—
674C2×C4—361no—
675C2×C4—361no—
676C2×C4C22×C3×D911yescharacteristic
677C2×C4C22×C3×D911yescharacteristic
678C2×C4C22×C3×D911yescharacteristic
679C2×C4C22×C3×D911yescharacteristic
680C2×C4C22×C3×D911yescharacteristic
681C2×C3—22no—
682C2×C3—22no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—42no—
687C2×C3—41no—
688C2×C3—41no—
689C2×C3—81no—
690C2×C3—182no—
691C2×C3—361no—
692C2×C3C2×#369911yescharacteristic
693C2×C3#41×D911yescharacteristic
694C2×C3#6371511yescharacteristic
695C2×C3C2×C3×#23711yescharacteristic
696C2×C3C3×D3×#4111yescharacteristic
697C2×C3C3×#100911yescharacteristic
698D3—62no—
699D3—121no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—92no—
706C22—181no—
707C22—181no—
708C22—181no—
709C22—181no—
710C22—181no—
711C22—364no—
712C22C3×#369912yes—
713C22C23×C3×D911yescharacteristic
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—181no—
720C4—181no—
721C4—181no—
722C4—181no—
723C4—181no—
724C4—181no—
725C3—21no—
726C3#1058976011yescharacteristic, direct product factor
727C3C3×#565811yescharacteristic
728C2—22no—
729C2—41no—
730C2—182no—
731C2—361no—
732C2C2×C3×#369911yescharacteristic
733C2C3×#41×D911yescharacteristic
734C2C3×#6371511yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#123C2
socleC22×C32C23×D3
prime radicalC3×#63499C2
hypercenterC3×#123D9
hypocenterC9C3×#551
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C9×#123C2semidirect
3. C3×D4×Dic9C2semidirect
4. C2×C3×(C2×D9)⋊C4C2semidirect
5. C3×#63488C2semidirect
6. C3×#63460C2semidirect
7. C3×#63460C2semidirect
8. C3×#63459C2semidirect
9. C3×#63454C2semidirect
10. C3×#63448C2semidirect
11. C3×#63447C2semidirect
12. C3×#63445C2semidirect
13. C3×#611⋊C4C2semidirect
14. C3×C22⋊C4×D9C2semidirect
15. C3×#63440C2semidirect
17. #10589760C3direct (N × H)
24. C22×C3×Dic9C22semidirect
27. C2×C3×Dic18C22semidirect
28. C3×C9×C4⋊C4C22semidirect
29. C3×C9×C4⋊C4C22semidirect
31. C3×C9×C22⋊C4C22semidirect
32. C3×C9×C22⋊C4C22semidirect
35. C3×#3676C22semidirect
44. C3×C4⋊Dic9C22semidirect
45. C3×C4⋊Dic9C22semidirect
46. C3×C4⋊Dic9C22semidirect
47. C3×C4⋊Dic9C22semidirect
48. C3×Dic9⋊C4C22semidirect
49. C3×Dic9⋊C4C22semidirect
50. C3×C4×Dic9C22semidirect
51. C3×C4×Dic9C22semidirect
52. C3×C4×Dic9C22semidirect
69. C9×#123C2×C3semidirect
71. D4×Dic9C2×C3semidirect
72. C2×(C2×D9)⋊C4C2×C3semidirect
73. #63488C2×C3semidirect
74. #63460C2×C3semidirect
75. #63460C2×C3semidirect
76. #63459C2×C3semidirect
77. #63454C2×C3semidirect
78. #63448C2×C3semidirect
79. #63447C2×C3semidirect
80. #63445C2×C3semidirect
81. #611⋊C4C2×C3semidirect
82. C22⋊C4×D9C2×C3semidirect
83. #63440C2×C3semidirect
156. C22×Dic9C22×C3semidirect
159. C2×Dic18C22×C3semidirect
162. C9×C4⋊C4C22×C3semidirect
163. C9×C4⋊C4C22×C3semidirect
168. C9×C22⋊C4C22×C3semidirect
169. C9×C22⋊C4C22×C3semidirect
172. #3676C22×C3semidirect
181. C4⋊Dic9C22×C3semidirect
182. C4⋊Dic9C22×C3semidirect
183. C4⋊Dic9C22×C3semidirect
184. C4⋊Dic9C22×C3semidirect
185. Dic9⋊C4C22×C3semidirect
186. Dic9⋊C4C22×C3semidirect
187. C4×Dic9C22×C3semidirect
188. C4×Dic9C22×C3semidirect
189. C4×Dic9C22×C3semidirect
221. C3×#123D9semidirect
347. C3×C4⋊C4C2×D9semidirect
348. C3×C4⋊C4C2×D9semidirect
366. C3×C22⋊C4C2×D9semidirect
367. C3×C22⋊C4C2×D9semidirect
461. #123C3×D9semidirect
471. C3×C9#551semidirect
570. C4⋊C4C2×C3×D9semidirect
571. C4⋊C4C2×C3×D9semidirect
584. C22⋊C4C2×C3×D9semidirect
585. C22⋊C4C2×C3×D9semidirect
653. C9C3×#551semidirect
726. C3#10589760direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1232
C3×#634992
C3×D4×Dic92
C2×C3×(C2×D9)⋊C42
C3×#634882
C3×#634602
C3×#634592
C3×#634542
C3×#634482
C3×#634472
C3×#634452
C3×#611⋊C42
C3×C22⋊C4×D92
C3×#634402
C3×#56583
#105897603