Finite Group Databasebeta

← C3×#10589629 #13152488

Subgroups — C3×#10589629 #13152488

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
1C3×C9×#117C211yesmaximal, characteristic, complemented
2C3×#63491C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
4C3×#63460C211yesmaximal, characteristic, complemented
5C3×#63458C211yesmaximal, characteristic, complemented
6C3×#63456C211yesmaximal, characteristic, complemented
7C3×#63456C211yesmaximal, characteristic, complemented
8C3×#63444C211yesmaximal, characteristic
9C3×#611⋊C4C211yesmaximal, characteristic, complemented
10C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
11C3×#63440C211yesmaximal, characteristic, complemented
12C3×#63438C211yesmaximal, characteristic, complemented
13C3×#63437C211yesmaximal, characteristic, complemented
14C3×C4×D36C211yesmaximal, characteristic, complemented
15C3×#63434C211yesmaximal, characteristic, complemented
16C3×#5527—31nomaximal
17#10589629C311yesmaximal, characteristic, direct product factor
18C23×C3×D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C22×C3×Dic9C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic, complemented
27C2×C3×Dic18C2211yescharacteristic, complemented
28C3×C9×C4⋊C4C2211yescharacteristic, complemented
29C3×C9×C4⋊C4C2211yescharacteristic, complemented
30C3×C9×C22⋊C4C2211yescharacteristic
31C3×C9×C22⋊C4C2211yescharacteristic
32C3×C42×C9C2211yescharacteristic, complemented
33C3×C42×C9C2211yescharacteristic, complemented
34C3×#3676C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
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, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×C4⋊Dic9C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49C3×Dic9⋊C4C2211yescharacteristic, complemented
50C3×Dic9⋊C4C2211yescharacteristic, complemented
51C3×Dic9⋊C4C2211yescharacteristic, complemented
52C3×C4×Dic9C2211yescharacteristic, complemented
53C32×#117D311yescharacteristic
54C3×#929—31no—
55C2×C3×(C2×D3)⋊C4—31no—
56C3×#898—31no—
57C3×#896—31no—
58C3×#894—31no—
59C3×#894—31no—
60C3×#882—31no—
61C3×#67⋊C4—31no—
62C3×D3×C22⋊C4—31no—
63C3×#878—31no—
64C3×#876—31no—
65C3×#875—31no—
66C3×C4×D12—31no—
67C3×#872—31no—
68C9×#117—21no—
69C9×#117C2×C311yescharacteristic, complemented
70#63491C2×C311yescharacteristic, complemented
71C2×(C2×D9)⋊C4C2×C311yescharacteristic, complemented
72#63460C2×C311yescharacteristic, complemented
73#63458C2×C311yescharacteristic, complemented
74#63456C2×C311yescharacteristic, complemented
75#63456C2×C311yescharacteristic, complemented
76#63444C2×C311yescharacteristic
77#611⋊C4C2×C311yescharacteristic, complemented
78C22⋊C4×D9C2×C311yescharacteristic, complemented
79#63440C2×C311yescharacteristic, complemented
80#63438C2×C311yescharacteristic, complemented
81#63437C2×C311yescharacteristic, complemented
82C4×D36C2×C311yescharacteristic, complemented
83#63434C2×C311yescharacteristic, complemented
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×C9—22no—
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—22no—
99C2×C3×Dic9—41no—
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C3×D36—22no—
106C3×D36—41no—
107C3×C4×D9—22no—
108C3×C4×D9—41no—
109C3×C4×D9—41no—
110C3×Dic18—41no—
111C3×#551—91no—
112#5527—31no—
113C23×C3×D3—31no—
114C22×C32×C4C2×D311yescharacteristic
115C2×C3×#67—31no—
116C22×C3×Dic3—31no—
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×C4×D3—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×C42C2×D311yescharacteristic
129C32×C42C2×D311yescharacteristic
130C3×#217—31no—
131C3×(C2×D3)⋊C4—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×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4—31no—
142C3×C4⋊Dic3—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×Dic3⋊C4—31no—
148C3×C4×Dic3—31no—
149C22×C4×C9—21no—
150C22×C4×C9C22×C311yescharacteristic
151C2×#611C22×C311yescharacteristic
152C22×Dic9C22×C311yescharacteristic
153C2×D36C22×C311yescharacteristic
154C2×D36C22×C311yescharacteristic
155C2×C4×D9C22×C311yescharacteristic
156C2×C4×D9C22×C311yescharacteristic
157C2×C4×D9C22×C311yescharacteristic, complemented
158C2×Dic18C22×C311yescharacteristic, complemented
159C9×C4⋊C4—21no—
160C9×C4⋊C4—21no—
161C9×C4⋊C4C22×C311yescharacteristic, complemented
162C9×C4⋊C4C22×C311yescharacteristic, complemented
163C9×C22⋊C4—21no—
164C9×C22⋊C4—21no—
165C9×C22⋊C4C22×C311yescharacteristic
166C9×C22⋊C4C22×C311yescharacteristic
167C42×C9—21no—
168C42×C9—21no—
169C42×C9C22×C311yescharacteristic, complemented
170C42×C9C22×C311yescharacteristic, complemented
171#3676C22×C311yescharacteristic
172(C2×D9)⋊C4C22×C311yescharacteristic
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, complemented
181(C2×D9)⋊C4C22×C311yescharacteristic, complemented
182(C2×D9)⋊C4C22×C311yescharacteristic, complemented
183C4⋊Dic9C22×C311yescharacteristic, complemented
184Dic9⋊C4C22×C311yescharacteristic, complemented
185Dic9⋊C4C22×C311yescharacteristic, complemented
186Dic9⋊C4C22×C311yescharacteristic, complemented
187Dic9⋊C4C22×C311yescharacteristic, complemented
188Dic9⋊C4C22×C311yescharacteristic, complemented
189C4×Dic9C22×C311yescharacteristic, complemented
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×C4×C9—21no—
207C3×C4×C9—21no—
208C3×C4×C9—21no—
209C3×C4×C9—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—91no—
219C3×#123—91no—
220C3×#123—91no—
221C3×C22⋊Q8—91no—
222C3×C22⋊Q8—91no—
223C3×#120—91no—
224C3×C4×D4—91no—
225C3×C4×D4—91no—
226C3×#117—21no—
227C3×#117—91no—
228C3×#117D911yescharacteristic, complemented
229C3×#117C3×D311yescharacteristic
230C2×C3×C22⋊C4—91no—
231C2×C3×C22⋊C4—91no—
232#929—31no—
233C2×(C2×D3)⋊C4—31no—
234#898—31no—
235#896—31no—
236#894—31no—
237#894—31no—
238#882—31no—
239#67⋊C4—31no—
240D3×C22⋊C4—31no—
241#878—31no—
242#876—31no—
243#875—31no—
244C4×D12—31no—
245#872—31no—
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×C4—22no—
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C3×#67—62no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—121no—
267C3×D12—62no—
268C3×D12—121no—
269C3×C4×D3—62no—
270C3×C4×D3—121no—
271C3×C4×D3—121no—
272C3×Dic6—121no—
273C23×C9—21no—
274C23×C9C23×C311yescharacteristic
275C22×D9—22no—
276C22×D9—22no—
277C22×D9—41no—
278C22×D9C23×C311yescharacteristic
279C22×D9C23×C311yescharacteristic
280C22×D9C23×C311yescharacteristic
281C2×C4×C9—24no—
282C2×C4×C9—22no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—21no—
286C2×C4×C9—21no—
287C2×C4×C9—21no—
288C2×C4×C9—21no—
289C2×C4×C9C23×C311yescharacteristic
290C2×C4×C9C23×C311yescharacteristic
291C2×C4×C9C23×C311yescharacteristic
292C2×C4×C9C23×C311yescharacteristic
293C2×C4×C9C23×C311yescharacteristic
294C2×C4×C9C23×C311yescharacteristic
295#611—22no—
296C2×Dic9—41no—
297C2×Dic9C23×C311yescharacteristic
298C2×Dic9C23×C311yescharacteristic
299C2×Dic9C23×C311yescharacteristic
300C2×Dic9C23×C311yescharacteristic
301C2×Dic9C23×C311yescharacteristic
302D36—22no—
303D36—41no—
304C4×D9—22no—
305C4×D9—41no—
306C4×D9—41no—
307Dic18—41no—
308#551—91noSylow
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—91no—
319C2×C3×D4—91no—
320C2×C3×D4—91no—
321C2×C3×D4—91no—
322C22×C3×C4—21no—
323C22×C3×C4—91no—
324C22×C3×C4—91no—
325C22×C3×C4—91no—
326C22×C3×C4—91no—
327C22×C3×C4C2×D911yescharacteristic
328C22×C3×C4C2×C3×D311yescharacteristic
329C2×#67—31no—
330C22×Dic3—31no—
331C2×D12—31no—
332C2×D12—31no—
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×Dic6—31no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—91no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4C2×D911yescharacteristic, complemented
346C3×C4⋊C4C2×D911yescharacteristic, complemented
347C3×C4⋊C4C2×C3×D311yescharacteristic
348C3×C4⋊C4C2×C3×D311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4—91no—
353C3×C22⋊C4—91no—
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⋊C4C2×D911yescharacteristic
364C3×C22⋊C4C2×D911yescharacteristic
365C3×C22⋊C4C2×C3×D311yescharacteristic
366C3×C22⋊C4C2×C3×D311yescharacteristic
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—91no—
370C3×C42C2×D911yescharacteristic, complemented
371C3×C42C2×D911yescharacteristic, complemented
372C3×C42C2×C3×D311yescharacteristic
373C3×C42C2×C3×D311yescharacteristic
374#217—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—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—
385(C2×D3)⋊C4—31no—
386C4⋊Dic3—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392C4×Dic3—31no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32#23512yes—
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—
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—
418C22×C9—21no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—22no—
422C22×C9—41no—
423C22×C9—41no—
424C22×C9C3×#4112yes—
425C22×C9C24×C311yescharacteristic
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×D9C3×#4112yes—
436C4×C9—22no—
437C4×C9—22no—
438C4×C9—21no—
439C4×C9—21no—
440C4×C9—21no—
441C4×C9—21no—
442C4×C9—21no—
443C4×C9—21no—
444C4×C9—41no—
445C4×C9—41no—
446C4×C9—41no—
447C4×C9—41no—
448Dic9—21no—
449Dic9—21no—
450Dic9—21no—
451Dic9—21no—
452Dic9—21no—
453#126—91no—
454#126—91no—
455#124—91no—
456#123—91no—
457#123—91no—
458#123—91no—
459C22⋊Q8—91no—
460C22⋊Q8—91no—
461#120—91no—
462C4×D4—91no—
463C4×D4—91no—
464#117—91no—
465#117C3×D911yescharacteristic, complemented
466C2×C22⋊C4—91no—
467C2×C22⋊C4—91no—
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×C3C22×C3×D311yescharacteristic
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—121no—
484C3×Q8—361no—
485C3×D4—182no—
486C3×D4—182no—
487C3×D4—361no—
488C2×C3×C4—24no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—182no—
503C2×C3×C4—361no—
504C2×C3×C4—361no—
505C2×C3×C4—361no—
506C2×C3×C4C22×D911yescharacteristic
507C2×C3×C4C22×D911yescharacteristic
508C2×C3×C4C22×D911yescharacteristic
509C2×C3×C4C22×D911yescharacteristic
510C2×C3×C4C22×D911yescharacteristic
511C2×C3×C4C22×D911yescharacteristic
512C2×C3×C4C22×C3×D311yescharacteristic
513C2×C3×C4C22×C3×D311yescharacteristic
514C2×C3×C4C22×C3×D311yescharacteristic
515C2×C3×C4C22×C3×D311yescharacteristic
516C2×C3×C4C22×C3×D311yescharacteristic
517C2×C3×C4C22×C3×D311yescharacteristic
518#67—62no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—121no—
525D12—62no—
526D12—121no—
527C4×D3—62no—
528C4×D3—121no—
529C4×D3—121no—
530Dic6—121no—
531C2×C32—22no—
532C2×C32C2×#23511yescharacteristic
533C2×C32D3×#4111yescharacteristic
534C2×C32#100911yescharacteristic
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×C3×#4111yescharacteristic
544C2×C9C2×C3×#4111yescharacteristic
545C2×C9C3×H(5,𝔽2)11yescharacteristic
546D9—22no—
547D9—41no—
548D9—41no—
549C24—91no—
550C2×Q8—91no—
551C2×D4—91no—
552C2×D4—91no—
553C2×D4—91no—
554C22×C4—91no—
555C22×C4—91no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4C2×C3×D911yescharacteristic
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—91no—
563C4⋊C4—91no—
564C4⋊C4—91no—
565C4⋊C4C2×C3×D911yescharacteristic, complemented
566C4⋊C4C2×C3×D911yescharacteristic, complemented
567C22⋊C4—91no—
568C22⋊C4—91no—
569C22⋊C4—91no—
570C22⋊C4—91no—
571C22⋊C4—91no—
572C22⋊C4—91no—
573C22⋊C4—91no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—91no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4C2×C3×D911yescharacteristic
580C22⋊C4C2×C3×D911yescharacteristic
581C42—91no—
582C42C2×C3×D911yescharacteristic, complemented
583C42C2×C3×D911yescharacteristic, complemented
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—22no—
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#369712yes—
603C22×C3C23×D911yescharacteristic
604C22×C3C3×#23512yes—
605C22×C3C23×C3×D311yescharacteristic
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—22no—
617C3×C4—22no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—181no—
635C3×C4—181no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—181no—
639Dic3—61no—
640Dic3—61no—
641Dic3—61no—
642Dic3—61no—
643Dic3—61no—
644C32#552711yescharacteristic
645C9—21no—
646C9C3×#55111yescharacteristic, complemented
647C23—91no—
648C23—91no—
649C23—91no—
650C23—182no—
651C23—182no—
652C23—361no—
653C23C22×C3×D911yescharacteristic
654Q8—361no—
655D4—182no—
656D4—182no—
657D4—361no—
658C2×C4—22no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—91no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—182no—
665C2×C4—361no—
666C2×C4—361no—
667C2×C4—361no—
668C2×C4C22×C3×D911yescharacteristic
669C2×C4C22×C3×D911yescharacteristic
670C2×C4C22×C3×D911yescharacteristic
671C2×C4C22×C3×D911yescharacteristic
672C2×C4C22×C3×D911yescharacteristic
673C2×C4C22×C3×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×C3C2×#369711yescharacteristic
684C2×C3#41×D911yescharacteristic
685C2×C3#6371511yescharacteristic
686C2×C3C2×C3×#23511yescharacteristic
687C2×C3C3×D3×#4111yescharacteristic
688C2×C3C3×#100911yescharacteristic
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—
704C22C3×#369712yes—
705C22C23×C3×D911yescharacteristic
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—181no—
713C4—181no—
714C4—181no—
715C4—181no—
716C4—181no—
717C3—21no—
718C3#1058962911yescharacteristic, direct product factor
719C3C3×#552711yescharacteristic
720C2—22no—
721C2—182no—
722C2—361no—
723C2—361no—
724C2C2×C3×#369711yescharacteristic
725C2C3×#41×D911yescharacteristic
726C2C3×#6371511yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#117C2
socleC22×C32C23×D3
prime radicalC3×#63444C2
hypercenterC3×#117D9
hypocenterC9C3×#551
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#117

Complements

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

NH ≅ G/Ntype
1. C3×C9×#117C2semidirect
2. C3×#63491C2semidirect
3. C2×C3×(C2×D9)⋊C4C2semidirect
4. C3×#63460C2semidirect
5. C3×#63458C2semidirect
6. C3×#63456C2semidirect
7. C3×#63456C2semidirect
9. C3×#611⋊C4C2semidirect
10. C3×C22⋊C4×D9C2semidirect
11. C3×#63440C2semidirect
12. C3×#63438C2semidirect
13. C3×#63437C2semidirect
14. C3×C4×D36C2semidirect
15. C3×#63434C2semidirect
17. #10589629C3direct (N × H)
26. C2×C3×C4×D9C22semidirect
27. C2×C3×Dic18C22semidirect
28. C3×C9×C4⋊C4C22semidirect
29. C3×C9×C4⋊C4C22semidirect
32. C3×C42×C9C22semidirect
33. C3×C42×C9C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×C4⋊Dic9C22semidirect
47. C3×Dic9⋊C4C22semidirect
48. C3×Dic9⋊C4C22semidirect
49. C3×Dic9⋊C4C22semidirect
50. C3×Dic9⋊C4C22semidirect
51. C3×Dic9⋊C4C22semidirect
52. C3×C4×Dic9C22semidirect
69. C9×#117C2×C3semidirect
70. #63491C2×C3semidirect
71. C2×(C2×D9)⋊C4C2×C3semidirect
72. #63460C2×C3semidirect
73. #63458C2×C3semidirect
74. #63456C2×C3semidirect
75. #63456C2×C3semidirect
77. #611⋊C4C2×C3semidirect
78. C22⋊C4×D9C2×C3semidirect
79. #63440C2×C3semidirect
80. #63438C2×C3semidirect
81. #63437C2×C3semidirect
82. C4×D36C2×C3semidirect
83. #63434C2×C3semidirect
157. C2×C4×D9C22×C3semidirect
158. C2×Dic18C22×C3semidirect
161. C9×C4⋊C4C22×C3semidirect
162. C9×C4⋊C4C22×C3semidirect
169. C42×C9C22×C3semidirect
170. C42×C9C22×C3semidirect
180. (C2×D9)⋊C4C22×C3semidirect
181. (C2×D9)⋊C4C22×C3semidirect
182. (C2×D9)⋊C4C22×C3semidirect
183. C4⋊Dic9C22×C3semidirect
184. Dic9⋊C4C22×C3semidirect
185. Dic9⋊C4C22×C3semidirect
186. Dic9⋊C4C22×C3semidirect
187. Dic9⋊C4C22×C3semidirect
188. Dic9⋊C4C22×C3semidirect
189. C4×Dic9C22×C3semidirect
228. C3×#117D9semidirect
345. C3×C4⋊C4C2×D9semidirect
346. C3×C4⋊C4C2×D9semidirect
370. C3×C42C2×D9semidirect
371. C3×C42C2×D9semidirect
465. #117C3×D9semidirect
468. C3×C9#551semidirect
565. C4⋊C4C2×C3×D9semidirect
566. C4⋊C4C2×C3×D9semidirect
582. C42C2×C3×D9semidirect
583. C42C2×C3×D9semidirect
646. C9C3×#551semidirect
718. C3#10589629direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1172
C3×#634912
C2×C3×(C2×D9)⋊C42
C3×#634602
C3×#634582
C3×#634562
C3×#634442
C3×#611⋊C42
C3×C22⋊C4×D92
C3×#634402
C3×#634382
C3×#634372
C3×C4×D362
C3×#634342
C3×#55273
#105896293