Finite Group Databasebeta

← C3×#10589806 #13153214

Subgroups — C3×#10589806 #13153214

Order 1728.

810 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#126C211yesmaximal, characteristic, complemented
2C3×#63460C211yesmaximal, characteristic, complemented
3C3×#63458C211yesmaximal, characteristic, complemented
4C3×#63457C211yesmaximal, characteristic, complemented
5C3×#63457C211yesmaximal, characteristic, complemented
6C3×#63456C211yesmaximal, characteristic, complemented
7C3×#63455C211yesmaximal, characteristic, complemented
8C3×#63447C211yesmaximal, characteristic, complemented
9C3×#63446C211yesmaximal, characteristic, complemented
10C3×#63445C211yesmaximal, characteristic, complemented
11C3×#63444C211yesmaximal, characteristic, complemented
12C3×#63444C211yesmaximal, characteristic, complemented
13C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
14C3×#63437C211yesmaximal, characteristic, complemented
15C3×C4×D36C211yesmaximal, characteristic, complemented
16C3×#5704—31nomaximal
17#10589806C311yesmaximal, characteristic, direct product factor
18C23×C3×D9C2211yescharacteristic
19C2×C3×#611C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic, complemented
26C2×C3×C4×D9C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28C2×C3×C4×D9C2211yescharacteristic, complemented
29C2×C3×C4×D9C2211yescharacteristic, complemented
30C2×C3×Dic18C2211yescharacteristic, complemented
31C3×C9×C4⋊C4C2211yescharacteristic, complemented
32C3×C9×C4⋊C4C2211yescharacteristic, complemented
33C3×C9×C4⋊C4C2211yescharacteristic, complemented
34C3×C9×C22⋊C4C2211yescharacteristic
35C3×C9×C22⋊C4C2211yescharacteristic
36C3×C9×C22⋊C4C2211yescharacteristic
37C3×C42×C9C2211yescharacteristic, complemented
38C3×#3676C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
49C3×C4⋊Dic9C2211yescharacteristic, complemented
50C3×Dic9⋊C4C2211yescharacteristic, complemented
51C3×Dic9⋊C4C2211yescharacteristic, complemented
52C3×C4×Dic9C2211yescharacteristic, complemented
53C32×#126D311yescharacteristic
54C3×#898—31no—
55C3×#896—31no—
56C3×#895—31no—
57C3×#895—31no—
58C3×#894—31no—
59C3×#893—31no—
60C3×#885—31no—
61C3×#884—31no—
62C3×#883—31no—
63C3×#882—31no—
64C3×#882—31no—
65C3×D3×C22⋊C4—31no—
66C3×#875—31no—
67C3×C4×D12—31no—
68C9×#126—21no—
69C9×#126C2×C311yescharacteristic, complemented
70#63460C2×C311yescharacteristic, complemented
71#63458C2×C311yescharacteristic, complemented
72#63457C2×C311yescharacteristic, complemented
73#63457C2×C311yescharacteristic, complemented
74#63456C2×C311yescharacteristic, complemented
75#63455C2×C311yescharacteristic, complemented
76#63447C2×C311yescharacteristic, complemented
77#63446C2×C311yescharacteristic, complemented
78#63445C2×C311yescharacteristic, complemented
79#63444C2×C311yescharacteristic, complemented
80#63444C2×C311yescharacteristic, complemented
81C22⋊C4×D9C2×C311yescharacteristic, complemented
82#63437C2×C311yescharacteristic, complemented
83C4×D36C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9—22no—
86C22×C3×D9—41no—
87C22×C3×D9—41no—
88C22×C3×D9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98C3×#611—41no—
99C3×#611—41no—
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C3×D36—22no—
105C3×D36—22no—
106C3×D36—41no—
107C3×D36—41no—
108C3×D36—41no—
109C3×C4×D9—41no—
110C3×C4×D9—41no—
111C3×C4×D9—41no—
112C3×C4×D9—41no—
113C3×Dic18—41no—
114C3×#538—91no—
115#5704—31no—
116C23×C3×D3—31no—
117C2×C3×#67—31no—
118C2×C3×#67—31no—
119C2×C3×D12—31no—
120C2×C3×D12—31no—
121C2×C3×D12—31no—
122C2×C3×D12—31no—
123C2×C3×D12—31no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×Dic6—31no—
129C23×D9C22×C311yescharacteristic
130C32×C4⋊C4C2×D311yescharacteristic
131C32×C4⋊C4C2×D311yescharacteristic
132C32×C4⋊C4C2×D311yescharacteristic
133C32×C22⋊C4C2×D311yescharacteristic
134C32×C22⋊C4C2×D311yescharacteristic
135C32×C22⋊C4C2×D311yescharacteristic
136C32×C42C2×D311yescharacteristic
137C3×#217—31no—
138C3×(C2×D3)⋊C4—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×(C2×D3)⋊C4—31no—
146C3×(C2×D3)⋊C4—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×C4⋊Dic3—31no—
149C3×Dic3⋊C4—31no—
150C3×Dic3⋊C4—31no—
151C3×C4×Dic3—31no—
152C2×#611C22×C311yescharacteristic
153C2×#611C22×C311yescharacteristic
154C2×D36C22×C311yescharacteristic
155C2×D36C22×C311yescharacteristic
156C2×D36C22×C311yescharacteristic
157C2×D36C22×C311yescharacteristic
158C2×D36C22×C311yescharacteristic, complemented
159C2×C4×D9C22×C311yescharacteristic
160C2×C4×D9C22×C311yescharacteristic
161C2×C4×D9C22×C311yescharacteristic, complemented
162C2×C4×D9C22×C311yescharacteristic, complemented
163C2×Dic18C22×C311yescharacteristic, complemented
164C9×C4⋊C4—21no—
165C9×C4⋊C4—21no—
166C9×C4⋊C4—21no—
167C9×C4⋊C4C22×C311yescharacteristic, complemented
168C9×C4⋊C4C22×C311yescharacteristic, complemented
169C9×C4⋊C4C22×C311yescharacteristic, complemented
170C9×C22⋊C4—21no—
171C9×C22⋊C4—21no—
172C9×C22⋊C4—21no—
173C9×C22⋊C4C22×C311yescharacteristic
174C9×C22⋊C4C22×C311yescharacteristic
175C9×C22⋊C4C22×C311yescharacteristic
176C42×C9—21no—
177C42×C9C22×C311yescharacteristic, complemented
178#3676C22×C311yescharacteristic
179(C2×D9)⋊C4C22×C311yescharacteristic
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, complemented
186(C2×D9)⋊C4C22×C311yescharacteristic, complemented
187(C2×D9)⋊C4C22×C311yescharacteristic, complemented
188(C2×D9)⋊C4C22×C311yescharacteristic, complemented
189C4⋊Dic9C22×C311yescharacteristic, complemented
190Dic9⋊C4C22×C311yescharacteristic, complemented
191Dic9⋊C4C22×C311yescharacteristic, complemented
192C4×Dic9C22×C311yescharacteristic, complemented
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
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—21no—
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×C4×C9—21no—
215C3×C4×C9—21no—
216C3×Dic9—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#126—21no—
221C3×#126—91no—
222C3×#126D911yescharacteristic, complemented
223C3×#126C3×D311yescharacteristic
224C3×#124—91no—
225C3×#124—91no—
226C3×#123—91no—
227C3×#123—91no—
228C3×C22⋊Q8—91no—
229C3×#121—91no—
230C3×#121—91no—
231C3×#121—91no—
232C3×#120—91no—
233C3×#120—91no—
234C3×C4×D4—91no—
235C3×C4×D4—91no—
236C2×C3×C22⋊C4—91no—
237#898—31no—
238#896—31no—
239#895—31no—
240#895—31no—
241#894—31no—
242#893—31no—
243#885—31no—
244#884—31no—
245#883—31no—
246#882—31no—
247#882—31no—
248D3×C22⋊C4—31no—
249#875—31no—
250C4×D12—31no—
251C23×C32C22×D311yescharacteristic
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—31no—
256C22×C3×D3—62no—
257C22×C3×D3—121no—
258C22×C3×D3—121no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C3×#67—121no—
266C3×#67—121no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C3×D12—62no—
272C3×D12—62no—
273C3×D12—121no—
274C3×D12—121no—
275C3×D12—121no—
276C3×C4×D3—121no—
277C3×C4×D3—121no—
278C3×C4×D3—121no—
279C3×C4×D3—121no—
280C3×Dic6—121no—
281C23×C9—21no—
282C23×C9C23×C311yescharacteristic
283C22×D9—22no—
284C22×D9—41no—
285C22×D9—41no—
286C22×D9C23×C311yescharacteristic
287C22×D9C23×C311yescharacteristic
288C22×D9C23×C311yescharacteristic
289C22×D9C23×C311yescharacteristic
290C2×C4×C9—21no—
291C2×C4×C9—21no—
292C2×C4×C9—21no—
293C2×C4×C9—21no—
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9C23×C311yescharacteristic
297C2×C4×C9C23×C311yescharacteristic
298C2×C4×C9C23×C311yescharacteristic
299C2×C4×C9C23×C311yescharacteristic
300C2×C4×C9C23×C311yescharacteristic
301C2×C4×C9C23×C311yescharacteristic
302#611—41no—
303#611—41no—
304C2×Dic9C23×C311yescharacteristic
305C2×Dic9C23×C311yescharacteristic
306C2×Dic9C23×C311yescharacteristic
307C2×Dic9C23×C311yescharacteristic
308D36—22no—
309D36—22no—
310D36—41no—
311D36—41no—
312D36—41no—
313C4×D9—41no—
314C4×D9—41no—
315C4×D9—41no—
316C4×D9—41no—
317Dic18—41no—
318#538—91noSylow
319C2×C3×C9—41no—
320C2×C3×C9C2×#4111yescharacteristic
321C2×C3×C9H(5,𝔽2)11yescharacteristic
322C2×C3×C9H(5,𝔽2)11yescharacteristic
323C3×D9—22no—
324C3×D9—41no—
325C3×D9—41no—
326C3×D9—41no—
327C24×C3—91no—
328C23×D3—31no—
329C2×C3×Q8—91no—
330C2×C3×D4—91no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C2×C3×D4—91no—
334C2×C3×D4—91no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C22×C3×C4—91no—
338C22×C3×C4—91no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C2×#67—31no—
342C2×#67—31no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—31no—
348C2×C4×D3—31no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×Dic6—31no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—91no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4C2×D911yescharacteristic, complemented
360C3×C4⋊C4C2×D911yescharacteristic, complemented
361C3×C4⋊C4C2×D911yescharacteristic, complemented
362C3×C4⋊C4C2×C3×D311yescharacteristic
363C3×C4⋊C4C2×C3×D311yescharacteristic
364C3×C4⋊C4C2×C3×D311yescharacteristic
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4—91no—
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⋊C4C2×D911yescharacteristic
380C3×C22⋊C4C2×D911yescharacteristic
381C3×C22⋊C4C2×D911yescharacteristic
382C3×C22⋊C4C2×C3×D311yescharacteristic
383C3×C22⋊C4C2×C3×D311yescharacteristic
384C3×C22⋊C4C2×C3×D311yescharacteristic
385C3×C42—21no—
386C3×C42—91no—
387C3×C42C2×D911yescharacteristic, complemented
388C3×C42C2×C3×D311yescharacteristic
389#217—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—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—
400C4⋊Dic3—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403C4×Dic3—31no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32C23×D311yescharacteristic
408C2×C3×D3—32no—
409C2×C3×D3—61no—
410C2×C3×D3—61no—
411C2×C3×D3—61no—
412C2×C3×D3—61no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—124no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C3×Dic3—61no—
428C3×Dic3—61no—
429C3×Dic3—61no—
430C3×Dic3—61no—
431C22×C9—21no—
432C22×C9—21no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—41no—
436C22×C9—41no—
437C22×C9—41no—
438C22×C9C24×C311yescharacteristic
439C2×D9—21no—
440C2×D9—21no—
441C2×D9—21no—
442C2×D9—21no—
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—44no—
451C2×D9C3×#4112yes—
452C4×C9—21no—
453C4×C9—21no—
454C4×C9—21no—
455C4×C9—21no—
456C4×C9—21no—
457C4×C9—21no—
458C4×C9—41no—
459C4×C9—41no—
460C4×C9—41no—
461C4×C9—41no—
462C4×C9—41no—
463C4×C9—41no—
464Dic9—21no—
465Dic9—21no—
466Dic9—21no—
467Dic9—21no—
468#126—91no—
469#126C3×D911yescharacteristic, complemented
470#124—91no—
471#124—91no—
472#123—91no—
473#123—91no—
474C22⋊Q8—91no—
475#121—91no—
476#121—91no—
477#121—91no—
478#120—91no—
479#120—91no—
480C4×D4—91no—
481C4×D4—91no—
482C2×C22⋊C4—91no—
483C3×C9#53811yescharacteristic, complemented, Sylow
484C23×C3—21no—
485C23×C3—91no—
486C23×C3—91no—
487C23×C3—91no—
488C23×C3—91no—
489C23×C3—182no—
490C23×C3—361no—
491C23×C3—361no—
492C23×C3C22×D911yescharacteristic
493C23×C3C22×C3×D311yescharacteristic
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—62no—
499C22×D3—121no—
500C22×D3—121no—
501C3×Q8—361no—
502C3×D4—182no—
503C3×D4—182no—
504C3×D4—361no—
505C3×D4—361no—
506C3×D4—361no—
507C3×D4—361no—
508C3×D4—361no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—361no—
520C2×C3×C4—361no—
521C2×C3×C4—361no—
522C2×C3×C4—361no—
523C2×C3×C4C22×D911yescharacteristic
524C2×C3×C4C22×D911yescharacteristic
525C2×C3×C4C22×D911yescharacteristic
526C2×C3×C4C22×D911yescharacteristic
527C2×C3×C4C22×D911yescharacteristic
528C2×C3×C4C22×D911yescharacteristic
529C2×C3×C4C22×C3×D311yescharacteristic
530C2×C3×C4C22×C3×D311yescharacteristic
531C2×C3×C4C22×C3×D311yescharacteristic
532C2×C3×C4C22×C3×D311yescharacteristic
533C2×C3×C4C22×C3×D311yescharacteristic
534C2×C3×C4C22×C3×D311yescharacteristic
535#67—121no—
536#67—121no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541D12—62no—
542D12—62no—
543D12—121no—
544D12—121no—
545D12—121no—
546C4×D3—121no—
547C4×D3—121no—
548C4×D3—121no—
549C4×D3—121no—
550Dic6—121no—
551C2×C32—41no—
552C2×C32D3×#4111yescharacteristic
553C2×C32#100911yescharacteristic
554C2×C32#100911yescharacteristic
555C3×D3—62no—
556C3×D3—121no—
557C3×D3—121no—
558C3×D3—121no—
559C2×C9—21no—
560C2×C9—21no—
561C2×C9—21no—
562C2×C9—41no—
563C2×C9—81no—
564C2×C9C2×C3×#4111yescharacteristic
565C2×C9C3×H(5,𝔽2)11yescharacteristic
566C2×C9C3×H(5,𝔽2)11yescharacteristic
567D9—22no—
568D9—41no—
569D9—41no—
570D9—41no—
571C24—91no—
572C2×Q8—91no—
573C2×D4—91no—
574C2×D4—91no—
575C2×D4—91no—
576C2×D4—91no—
577C2×D4—91no—
578C2×D4—91no—
579C2×D4—91no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—91no—
583C22×C4—91no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C4⋊C4C2×C3×D911yescharacteristic, complemented
588C4⋊C4C2×C3×D911yescharacteristic, complemented
589C4⋊C4C2×C3×D911yescharacteristic, complemented
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—91no—
596C22⋊C4—91no—
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4C2×C3×D911yescharacteristic
602C22⋊C4C2×C3×D911yescharacteristic
603C22⋊C4C2×C3×D911yescharacteristic
604C42—91no—
605C42C2×C3×D911yescharacteristic, complemented
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—92no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3—181no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—364no—
629C22×C3C23×D911yescharacteristic
630C22×C3C23×C3×D311yescharacteristic
631C2×D3—32no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—61no—
639C2×D3—61no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—124no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—181no—
663C3×C4—181no—
664C3×C4—181no—
665C3×C4—181no—
666Dic3—61no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670C32#570411yescharacteristic
671C9—21no—
672C9C3×#53811yescharacteristic, complemented
673C23—91no—
674C23—91no—
675C23—91no—
676C23—91no—
677C23—182no—
678C23—361no—
679C23—361no—
680C23C22×C3×D911yescharacteristic
681Q8—361no—
682D4—182no—
683D4—182no—
684D4—361no—
685D4—361no—
686D4—361no—
687D4—361no—
688D4—361no—
689C2×C4—91no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—361no—
694C2×C4—361no—
695C2×C4—361no—
696C2×C4—361no—
697C2×C4C22×C3×D911yescharacteristic
698C2×C4C22×C3×D911yescharacteristic
699C2×C4C22×C3×D911yescharacteristic
700C2×C4C22×C3×D911yescharacteristic
701C2×C4C22×C3×D911yescharacteristic
702C2×C4C22×C3×D911yescharacteristic
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—81no—
709C2×C3—182no—
710C2×C3—361no—
711C2×C3—361no—
712C2×C3—361no—
713C2×C3#41×D911yescharacteristic
714C2×C3#6371511yescharacteristic
715C2×C3#6371511yescharacteristic
716C2×C3C3×D3×#4111yescharacteristic
717C2×C3C3×#100911yescharacteristic
718C2×C3C3×#100911yescharacteristic
719D3—62no—
720D3—121no—
721D3—121no—
722D3—121no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—92no—
727C22—181no—
728C22—181no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22—364no—
739C22C23×C3×D911yescharacteristic
740C4—21no—
741C4—21no—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—181no—
747C4—181no—
748C4—181no—
749C4—181no—
750C3—21no—
751C3#1058980611yescharacteristic, direct product factor
752C3C3×#570411yescharacteristic
753C2—41no—
754C2—182no—
755C2—361no—
756C2—361no—
757C2—361no—
758C2C3×#41×D911yescharacteristic
759C2C3×#6371511yescharacteristic
760C2C3×#6371511yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#126C2
socleC22×C32C23×D3
hypercenterC3×#126D9
hypocenterC9C3×#538
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#126

Complements

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

NH ≅ G/Ntype
1. C3×C9×#126C2semidirect
2. C3×#63460C2semidirect
3. C3×#63458C2semidirect
4. C3×#63457C2semidirect
5. C3×#63457C2semidirect
6. C3×#63456C2semidirect
7. C3×#63455C2semidirect
8. C3×#63447C2semidirect
9. C3×#63446C2semidirect
10. C3×#63445C2semidirect
11. C3×#63444C2semidirect
12. C3×#63444C2semidirect
13. C3×C22⋊C4×D9C2semidirect
14. C3×#63437C2semidirect
15. C3×C4×D36C2semidirect
17. #10589806C3direct (N × H)
25. C2×C3×D36C22semidirect
28. C2×C3×C4×D9C22semidirect
29. C2×C3×C4×D9C22semidirect
30. C2×C3×Dic18C22semidirect
31. C3×C9×C4⋊C4C22semidirect
32. C3×C9×C4⋊C4C22semidirect
33. C3×C9×C4⋊C4C22semidirect
37. C3×C42×C9C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C3×(C2×D9)⋊C4C22semidirect
49. C3×C4⋊Dic9C22semidirect
50. C3×Dic9⋊C4C22semidirect
51. C3×Dic9⋊C4C22semidirect
52. C3×C4×Dic9C22semidirect
69. C9×#126C2×C3semidirect
70. #63460C2×C3semidirect
71. #63458C2×C3semidirect
72. #63457C2×C3semidirect
73. #63457C2×C3semidirect
74. #63456C2×C3semidirect
75. #63455C2×C3semidirect
76. #63447C2×C3semidirect
77. #63446C2×C3semidirect
78. #63445C2×C3semidirect
79. #63444C2×C3semidirect
80. #63444C2×C3semidirect
81. C22⋊C4×D9C2×C3semidirect
82. #63437C2×C3semidirect
83. C4×D36C2×C3semidirect
158. C2×D36C22×C3semidirect
161. C2×C4×D9C22×C3semidirect
162. C2×C4×D9C22×C3semidirect
163. C2×Dic18C22×C3semidirect
167. C9×C4⋊C4C22×C3semidirect
168. C9×C4⋊C4C22×C3semidirect
169. C9×C4⋊C4C22×C3semidirect
177. C42×C9C22×C3semidirect
185. (C2×D9)⋊C4C22×C3semidirect
186. (C2×D9)⋊C4C22×C3semidirect
187. (C2×D9)⋊C4C22×C3semidirect
188. (C2×D9)⋊C4C22×C3semidirect
189. C4⋊Dic9C22×C3semidirect
190. Dic9⋊C4C22×C3semidirect
191. Dic9⋊C4C22×C3semidirect
192. C4×Dic9C22×C3semidirect
222. C3×#126D9semidirect
359. C3×C4⋊C4C2×D9semidirect
360. C3×C4⋊C4C2×D9semidirect
361. C3×C4⋊C4C2×D9semidirect
387. C3×C42C2×D9semidirect
469. #126C3×D9semidirect
483. C3×C9#538semidirect
587. C4⋊C4C2×C3×D9semidirect
588. C4⋊C4C2×C3×D9semidirect
589. C4⋊C4C2×C3×D9semidirect
605. C42C2×C3×D9semidirect
672. C9C3×#538semidirect
751. C3#10589806direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1262
C3×#634602
C3×#634582
C3×#634572
C3×#634562
C3×#634552
C3×#634472
C3×#634462
C3×#634452
C3×#634442
C3×C22⋊C4×D92
C3×#634372
C3×C4×D362
C3×#57043
#105898063