Finite Group Databasebeta

← C3×#10589715 #13152816

Subgroups — C3×#10589715 #13152816

Order 1728.

844 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#121C211yesmaximal, characteristic, complemented
2C3×#63501C211yesmaximal, characteristic, complemented
3C3×#63500C211yesmaximal, characteristic, complemented
4C3×#63499C211yesmaximal, characteristic, complemented
5C3×#63499C211yesmaximal, characteristic, complemented
6C3×#63498C211yesmaximal, characteristic, complemented
7C3×#63497C211yesmaximal, characteristic, complemented
8C3×#63491C211yesmaximal, characteristic, complemented
9C3×C4×#611C211yesmaximal, characteristic, complemented
10C3×#63460C211yesmaximal, characteristic, complemented
11C3×#63458C211yesmaximal, characteristic, complemented
12C3×#63447C211yesmaximal, characteristic, complemented
13C3×#611⋊C4C211yesmaximal, characteristic, complemented
14C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
15C3×#63441C211yesmaximal, characteristic, complemented
16C3×#5613—31nomaximal
17#10589715C311yesmaximal, characteristic, direct product factor
18C23×C3×D9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C2×C3×D4×C9C2211yescharacteristic, complemented
22C22×C3×C4×C9C2211yescharacteristic, complemented
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C22×C3×Dic9C2211yescharacteristic, complemented
28C2×C3×C4×D9C2211yescharacteristic
29C2×C3×C4×D9C2211yescharacteristic
30C2×C3×Dic18C2211yescharacteristic, complemented
31C3×C9×C4⋊C4C2211yescharacteristic, complemented
32C3×C9×C22⋊C4C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic, complemented
34C3×#3676C2211yescharacteristic
35C3×#3676C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C3×#3676C2211yescharacteristic, complemented
38C3×#3676C2211yescharacteristic, complemented
39C3×#3676C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic
46C3×C4⋊Dic9C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49C3×Dic9⋊C4C2211yescharacteristic, complemented
50C3×Dic9⋊C4C2211yescharacteristic, complemented
51C3×C4×Dic9C2211yescharacteristic, complemented
52C3×C4×Dic9C2211yescharacteristic, complemented
53C32×#121D311yescharacteristic
54C3×#939—31no—
55C3×#938—31no—
56C3×#937—31no—
57C3×#937—31no—
58C3×#936—31no—
59C3×#935—31no—
60C3×#929—31no—
61C3×C4×#67—31no—
62C3×#898—31no—
63C3×#896—31no—
64C3×#885—31no—
65C3×#67⋊C4—31no—
66C3×D3×C22⋊C4—31no—
67C3×#879—31no—
68C9×#121—21no—
69C9×#121C2×C311yescharacteristic, complemented
70#63501C2×C311yescharacteristic, complemented
71#63500C2×C311yescharacteristic, complemented
72#63499C2×C311yescharacteristic, complemented
73#63499C2×C311yescharacteristic, complemented
74#63498C2×C311yescharacteristic, complemented
75#63497C2×C311yescharacteristic, complemented
76#63491C2×C311yescharacteristic, complemented
77C4×#611C2×C311yescharacteristic, complemented
78#63460C2×C311yescharacteristic, complemented
79#63458C2×C311yescharacteristic, complemented
80#63447C2×C311yescharacteristic, complemented
81#611⋊C4C2×C311yescharacteristic, complemented
82C22⋊C4×D9C2×C311yescharacteristic, complemented
83#63441C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C23×C3×C9C2311yescharacteristic
87C22×C3×D9—22no—
88C22×C3×D9—41no—
89C22×C3×D9—41no—
90C22×C3×D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C3×D4×C9—41no—
93C3×D4×C9—41no—
94C3×D4×C9—41no—
95C2×C3×C4×C9—41no—
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100C3×#611—22no—
101C3×#611—22no—
102C3×#611—41no—
103C3×#611—41no—
104C2×C3×Dic9—41no—
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C3×C4×D9—41no—
112C3×C4×D9—41no—
113C3×Dic18—41no—
114C3×#538—91no—
115#5613—31no—
116C23×C3×D3—31no—
117C2×C32×D4C2×D311yescharacteristic
118C2×C32×D4C2×D311yescharacteristic
119C2×C32×D4C2×D311yescharacteristic
120C22×C32×C4C2×D311yescharacteristic
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×#67—31no—
125C22×C3×Dic3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×Dic6—31no—
129C23×D9C22×C311yescharacteristic
130C32×C4⋊C4C2×D311yescharacteristic
131C32×C22⋊C4C2×D311yescharacteristic
132C32×C22⋊C4C2×D311yescharacteristic
133C3×#217—31no—
134C3×#217—31no—
135C3×#217—31no—
136C3×#217—31no—
137C3×#217—31no—
138C3×#217—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4—31no—
145C3×C4⋊Dic3—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C2×D4×C9—21no—
153C2×D4×C9—21no—
154C2×D4×C9—21no—
155C2×D4×C9C22×C311yescharacteristic
156C2×D4×C9C22×C311yescharacteristic
157C2×D4×C9C22×C311yescharacteristic, complemented
158C22×C4×C9—21no—
159C22×C4×C9C22×C311yescharacteristic, complemented
160C2×#611C22×C311yescharacteristic
161C2×#611C22×C311yescharacteristic
162C2×#611C22×C311yescharacteristic
163C2×#611C22×C311yescharacteristic
164C22×Dic9C22×C311yescharacteristic, complemented
165C2×C4×D9C22×C311yescharacteristic
166C2×C4×D9C22×C311yescharacteristic
167C2×Dic18C22×C311yescharacteristic, complemented
168C9×C4⋊C4—21no—
169C9×C4⋊C4C22×C311yescharacteristic, complemented
170C9×C22⋊C4—21no—
171C9×C22⋊C4—21no—
172C9×C22⋊C4C22×C311yescharacteristic
173C9×C22⋊C4C22×C311yescharacteristic, complemented
174#3676C22×C311yescharacteristic
175#3676C22×C311yescharacteristic
176#3676C22×C311yescharacteristic
177#3676C22×C311yescharacteristic, complemented
178#3676C22×C311yescharacteristic, complemented
179#3676C22×C311yescharacteristic, complemented
180(C2×D9)⋊C4C22×C311yescharacteristic
181(C2×D9)⋊C4C22×C311yescharacteristic
182(C2×D9)⋊C4C22×C311yescharacteristic
183(C2×D9)⋊C4C22×C311yescharacteristic
184(C2×D9)⋊C4C22×C311yescharacteristic
185(C2×D9)⋊C4C22×C311yescharacteristic
186C4⋊Dic9C22×C311yescharacteristic, complemented
187Dic9⋊C4C22×C311yescharacteristic, complemented
188Dic9⋊C4C22×C311yescharacteristic, complemented
189Dic9⋊C4C22×C311yescharacteristic, complemented
190Dic9⋊C4C22×C311yescharacteristic, complemented
191C4×Dic9C22×C311yescharacteristic, complemented
192C4×Dic9C22×C311yescharacteristic, complemented
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9C2411yescharacteristic
203C2×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—44no—
209C2×C3×D9#4112yes—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3×C4×C9—21no—
213C3×C4×C9—21no—
214C3×Dic9—21no—
215C3×Dic9—21no—
216C3×Dic9—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#126—91no—
221C3×#126—91no—
222C3×#124—91no—
223C3×#124—91no—
224C3×#123—91no—
225C3×#123—91no—
226C3×C22⋊Q8—91no—
227C3×#121—21no—
228C3×#121—91no—
229C3×#121—91no—
230C3×#121D911yescharacteristic, complemented
231C3×#121C3×D311yescharacteristic
232C3×#120—91no—
233C3×#120—91no—
234C3×C4×D4—91no—
235C3×C4×D4—91no—
236C2×C3×C22⋊C4—91no—
237#939—31no—
238#938—31no—
239#937—31no—
240#937—31no—
241#936—31no—
242#935—31no—
243#929—31no—
244C4×#67—31no—
245#898—31no—
246#896—31no—
247#885—31no—
248#67⋊C4—31no—
249D3×C22⋊C4—31no—
250#879—31no—
251C23×C32C22×D311yescharacteristic
252C23×C32C22×D311yescharacteristic
253C23×C32C22×D311yescharacteristic
254C22×C3×D3—31no—
255C22×C3×D3—31no—
256C22×C3×D3—62no—
257C22×C3×D3—121no—
258C22×C3×D3—121no—
259C32×D4—41no—
260C32×D4—41no—
261C32×D4—41no—
262C2×C32×C4—41no—
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C3×#67—62no—
268C3×#67—62no—
269C3×#67—121no—
270C3×#67—121no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—121no—
278C3×C4×D3—121no—
279C3×C4×D3—121no—
280C3×Dic6—121no—
281C23×C9—21no—
282C23×C9—21no—
283C23×C9—21no—
284C23×C9C23×C311yescharacteristic
285C23×C9C23×C311yescharacteristic
286C23×C9C23×C311yescharacteristic
287C22×D9—22no—
288C22×D9—41no—
289C22×D9—41no—
290C22×D9C23×C311yescharacteristic
291C22×D9C23×C311yescharacteristic
292D4×C9—41no—
293D4×C9—41no—
294D4×C9—41no—
295D4×C9—42no—
296D4×C9—42no—
297D4×C9—42no—
298C2×C4×C9—21no—
299C2×C4×C9—21no—
300C2×C4×C9—21no—
301C2×C4×C9—21no—
302C2×C4×C9—41no—
303C2×C4×C9—42no—
304C2×C4×C9C23×C311yescharacteristic
305C2×C4×C9C23×C311yescharacteristic
306C2×C4×C9C23×C311yescharacteristic
307C2×C4×C9C23×C311yescharacteristic
308#611—22no—
309#611—22no—
310#611—41no—
311#611—41no—
312C2×Dic9—41no—
313C2×Dic9C23×C311yescharacteristic
314C2×Dic9C23×C311yescharacteristic
315C2×Dic9C23×C311yescharacteristic
316C2×Dic9C23×C311yescharacteristic
317C2×Dic9C23×C311yescharacteristic
318C2×Dic9C23×C311yescharacteristic
319C4×D9—41no—
320C4×D9—41no—
321Dic18—41no—
322#538—91noSylow
323C2×C3×C9—41no—
324C2×C3×C9—41no—
325C2×C3×C9—41no—
326C2×C3×C9C2×#4111yescharacteristic
327C2×C3×C9H(5,𝔽2)11yescharacteristic
328C2×C3×C9H(5,𝔽2)11yescharacteristic
329C3×D9—22no—
330C3×D9—41no—
331C24×C3—91no—
332C23×D3—31no—
333C2×C3×Q8—91no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C2×C3×D4—91no—
341C2×C3×D4C2×D911yescharacteristic
342C2×C3×D4C2×D911yescharacteristic
343C2×C3×D4C2×D911yescharacteristic, complemented
344C2×C3×D4C2×C3×D311yescharacteristic
345C2×C3×D4C2×C3×D311yescharacteristic
346C2×C3×D4C2×C3×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—91no—
349C22×C3×C4—91no—
350C22×C3×C4—91no—
351C22×C3×C4C2×D911yescharacteristic, complemented
352C22×C3×C4C2×C3×D311yescharacteristic
353C2×#67—31no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—31no—
357C22×Dic3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×Dic6—31no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—91no—
363C3×C4⋊C4—91no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4C2×D911yescharacteristic, complemented
368C3×C4⋊C4C2×C3×D311yescharacteristic
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4C2×D911yescharacteristic
384C3×C22⋊C4C2×D911yescharacteristic, complemented
385C3×C22⋊C4C2×C3×D311yescharacteristic
386C3×C22⋊C4C2×C3×D311yescharacteristic
387C3×C42—91no—
388C3×C42—91no—
389#217—31no—
390#217—31no—
391#217—31no—
392#217—31no—
393#217—31no—
394#217—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401C4⋊Dic3—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C23×D311yescharacteristic
418C2×C3×D3—32no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C2×C3×D3—61no—
424C2×C3×D3—124no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C3×Dic3—61no—
430C3×Dic3—61no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C3×Dic3—61no—
435C22×C9—22no—
436C22×C9—21no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—21no—
440C22×C9—21no—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—21no—
446C22×C9—41no—
447C22×C9—41no—
448C22×C9—41no—
449C22×C9—41no—
450C22×C9—41no—
451C22×C9—41no—
452C22×C9—41no—
453C22×C9—41no—
454C22×C9C24×C311yescharacteristic
455C2×D9—21no—
456C2×D9—21no—
457C2×D9—21no—
458C2×D9—21no—
459C2×D9—21no—
460C2×D9—44no—
461C2×D9C3×#4112yes—
462C4×C9—22no—
463C4×C9—21no—
464C4×C9—21no—
465C4×C9—21no—
466C4×C9—21no—
467C4×C9—41no—
468C4×C9—41no—
469C4×C9—41no—
470Dic9—21no—
471Dic9—21no—
472Dic9—21no—
473Dic9—21no—
474Dic9—21no—
475Dic9—21no—
476#126—91no—
477#126—91no—
478#124—91no—
479#124—91no—
480#123—91no—
481#123—91no—
482C22⋊Q8—91no—
483#121—91no—
484#121—91no—
485#121C3×D911yescharacteristic, complemented
486#120—91no—
487#120—91no—
488C4×D4—91no—
489C4×D4—91no—
490C2×C22⋊C4—91no—
491C3×C9#53811yescharacteristic, complemented, Sylow
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—91no—
496C23×C3—91no—
497C23×C3—182no—
498C23×C3—361no—
499C23×C3—361no—
500C23×C3C22×D911yescharacteristic
501C23×C3C22×D911yescharacteristic
502C23×C3C22×D911yescharacteristic
503C23×C3C22×C3×D311yescharacteristic
504C23×C3C22×C3×D311yescharacteristic
505C23×C3C22×C3×D311yescharacteristic
506C22×D3—31no—
507C22×D3—31no—
508C22×D3—62no—
509C22×D3—121no—
510C22×D3—121no—
511C3×Q8—361no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—42no—
519C3×D4—42no—
520C3×D4—42no—
521C3×D4—182no—
522C3×D4—182no—
523C3×D4—361no—
524C3×D4—361no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—42no—
532C2×C3×C4—91no—
533C2×C3×C4—91no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—91no—
537C2×C3×C4—91no—
538C2×C3×C4—361no—
539C2×C3×C4—361no—
540C2×C3×C4—361no—
541C2×C3×C4C22×D911yescharacteristic
542C2×C3×C4C22×D911yescharacteristic
543C2×C3×C4C22×D911yescharacteristic
544C2×C3×C4C22×D911yescharacteristic
545C2×C3×C4C22×C3×D311yescharacteristic
546C2×C3×C4C22×C3×D311yescharacteristic
547C2×C3×C4C22×C3×D311yescharacteristic
548C2×C3×C4C22×C3×D311yescharacteristic
549#67—62no—
550#67—62no—
551#67—121no—
552#67—121no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—121no—
560C4×D3—121no—
561C4×D3—121no—
562Dic6—121no—
563C2×C32—41no—
564C2×C32—41no—
565C2×C32—41no—
566C2×C32#100411yescharacteristic
567C2×C32#100411yescharacteristic
568C2×C32D3×#4111yescharacteristic
569C3×D3—62no—
570C3×D3—121no—
571C2×C9—21no—
572C2×C9—21no—
573C2×C9—21no—
574C2×C9—42no—
575C2×C9—41no—
576C2×C9—41no—
577C2×C9—41no—
578C2×C9—81no—
579C2×C9—81no—
580C2×C9C2×C3×#4111yescharacteristic
581C2×C9C3×H(5,𝔽2)11yescharacteristic
582C2×C9C3×H(5,𝔽2)11yescharacteristic
583D9—22no—
584D9—41no—
585C24—91no—
586C2×Q8—91no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—91no—
590C2×D4—91no—
591C2×D4C2×C3×D911yescharacteristic
592C2×D4C2×C3×D911yescharacteristic
593C2×D4C2×C3×D911yescharacteristic, complemented
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4C2×C3×D911yescharacteristic, complemented
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4C2×C3×D911yescharacteristic, complemented
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—91no—
612C22⋊C4—91no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4C2×C3×D911yescharacteristic
617C22⋊C4C2×C3×D911yescharacteristic, complemented
618C42—91no—
619C42—91no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—92no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3—364no—
655C22×C3C23×D911yescharacteristic
656C22×C3C23×C3×D311yescharacteristic
657C2×D3—32no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—124no—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—181no—
677C3×C4—181no—
678C3×C4—181no—
679C3×C4—181no—
680C3×C4—181no—
681C3×C4—181no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688C32#561311yescharacteristic
689C9—21no—
690C9C3×#53811yescharacteristic, complemented
691C23—91no—
692C23—91no—
693C23—182no—
694C23—361no—
695C23—361no—
696C23C22×C3×D911yescharacteristic
697C23C22×C3×D911yescharacteristic
698C23C22×C3×D911yescharacteristic
699Q8—361no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—182no—
704D4—182no—
705D4—361no—
706D4—361no—
707C2×C4—41no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—361no—
715C2×C4—361no—
716C2×C4—361no—
717C2×C4C22×C3×D911yescharacteristic
718C2×C4C22×C3×D911yescharacteristic
719C2×C4C22×C3×D911yescharacteristic
720C2×C4C22×C3×D911yescharacteristic
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—42no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—41no—
728C2×C3—41no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—81no—
732C2×C3—81no—
733C2×C3—182no—
734C2×C3—361no—
735C2×C3#6371011yescharacteristic
736C2×C3#6371011yescharacteristic
737C2×C3#41×D911yescharacteristic
738C2×C3C3×#100411yescharacteristic
739C2×C3C3×#100411yescharacteristic
740C2×C3C3×D3×#4111yescharacteristic
741D3—62no—
742D3—121no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—92no—
753C22—181no—
754C22—181no—
755C22—181no—
756C22—181no—
757C22—181no—
758C22—364no—
759C22C23×C3×D911yescharacteristic
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—181no—
765C4—181no—
766C4—181no—
767C4—181no—
768C4—181no—
769C4—181no—
770C3—21no—
771C3#1058971511yescharacteristic, direct product factor
772C3C3×#561311yescharacteristic
773C2—41no—
774C2—41no—
775C2—41no—
776C2—182no—
777C2—361no—
778C2C3×#6371011yescharacteristic
779C2C3×#6371011yescharacteristic
780C2C3×#41×D911yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#121C2
socleC22×C32C23×D3
hypercenterC3×#121D9
hypocenterC9C3×#538
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#121

Complements

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

NH ≅ G/Ntype
1. C3×C9×#121C2semidirect
2. C3×#63501C2semidirect
3. C3×#63500C2semidirect
4. C3×#63499C2semidirect
5. C3×#63499C2semidirect
6. C3×#63498C2semidirect
7. C3×#63497C2semidirect
8. C3×#63491C2semidirect
9. C3×C4×#611C2semidirect
10. C3×#63460C2semidirect
11. C3×#63458C2semidirect
12. C3×#63447C2semidirect
13. C3×#611⋊C4C2semidirect
14. C3×C22⋊C4×D9C2semidirect
15. C3×#63441C2semidirect
17. #10589715C3direct (N × H)
21. C2×C3×D4×C9C22semidirect
22. C22×C3×C4×C9C22semidirect
27. C22×C3×Dic9C22semidirect
30. C2×C3×Dic18C22semidirect
31. C3×C9×C4⋊C4C22semidirect
33. C3×C9×C22⋊C4C22semidirect
37. C3×#3676C22semidirect
38. C3×#3676C22semidirect
39. C3×#3676C22semidirect
46. C3×C4⋊Dic9C22semidirect
47. C3×Dic9⋊C4C22semidirect
48. C3×Dic9⋊C4C22semidirect
49. C3×Dic9⋊C4C22semidirect
50. C3×Dic9⋊C4C22semidirect
51. C3×C4×Dic9C22semidirect
52. C3×C4×Dic9C22semidirect
69. C9×#121C2×C3semidirect
70. #63501C2×C3semidirect
71. #63500C2×C3semidirect
72. #63499C2×C3semidirect
73. #63499C2×C3semidirect
74. #63498C2×C3semidirect
75. #63497C2×C3semidirect
76. #63491C2×C3semidirect
77. C4×#611C2×C3semidirect
78. #63460C2×C3semidirect
79. #63458C2×C3semidirect
80. #63447C2×C3semidirect
81. #611⋊C4C2×C3semidirect
82. C22⋊C4×D9C2×C3semidirect
83. #63441C2×C3semidirect
157. C2×D4×C9C22×C3semidirect
159. C22×C4×C9C22×C3semidirect
164. C22×Dic9C22×C3semidirect
167. C2×Dic18C22×C3semidirect
169. C9×C4⋊C4C22×C3semidirect
173. C9×C22⋊C4C22×C3semidirect
177. #3676C22×C3semidirect
178. #3676C22×C3semidirect
179. #3676C22×C3semidirect
186. C4⋊Dic9C22×C3semidirect
187. Dic9⋊C4C22×C3semidirect
188. Dic9⋊C4C22×C3semidirect
189. Dic9⋊C4C22×C3semidirect
190. Dic9⋊C4C22×C3semidirect
191. C4×Dic9C22×C3semidirect
192. C4×Dic9C22×C3semidirect
230. C3×#121D9semidirect
343. C2×C3×D4C2×D9semidirect
351. C22×C3×C4C2×D9semidirect
367. C3×C4⋊C4C2×D9semidirect
384. C3×C22⋊C4C2×D9semidirect
485. #121C3×D9semidirect
491. C3×C9#538semidirect
593. C2×D4C2×C3×D9semidirect
597. C22×C4C2×C3×D9semidirect
603. C4⋊C4C2×C3×D9semidirect
617. C22⋊C4C2×C3×D9semidirect
690. C9C3×#538semidirect
771. C3#10589715direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1212
C3×#635012
C3×#635002
C3×#634992
C3×#634982
C3×#634972
C3×#634912
C3×C4×#6112
C3×#634602
C3×#634582
C3×#634472
C3×#611⋊C42
C3×C22⋊C4×D92
C3×#634412
C3×#56133
#105897153