Finite Group Databasebeta

← C3×#10589811 #13153219

Subgroups — C3×#10589811 #13153219

Order 1728.

774 conjugacy classes of subgroups.

The subgroup lattice has 720 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×#63457C211yesmaximal, characteristic, complemented
4C3×#63456C211yesmaximal, characteristic, complemented
5C3×#63455C211yesmaximal, characteristic, complemented
6C3×C4⋊C4×D9C211yesmaximal, characteristic, complemented
7C3×#63451C211yesmaximal, characteristic, complemented
8C3×#63448C211yesmaximal, characteristic, complemented
9C3×#63446C211yesmaximal, characteristic, complemented
10C3×#63446C211yesmaximal, characteristic, complemented
11C3×#63446C211yesmaximal, characteristic, complemented
12C3×#611⋊C4C211yesmaximal, characteristic, complemented
13C3×#611⋊C4C211yesmaximal, characteristic, complemented
14C3×C4×D36C211yesmaximal, characteristic, complemented
15C3×#63434C211yesmaximal, characteristic, complemented
16C3×#5709—31nomaximal
17#10589811C311yesmaximal, characteristic, direct product factor
18C2×C3×#611C2211yescharacteristic
19C2×C3×#611C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C22×C3×Dic9C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28C2×C3×C4×D9C2211yescharacteristic
29C2×C3×C4×D9C2211yescharacteristic
30C3×C9×C4⋊C4C2211yescharacteristic
31C3×C9×C4⋊C4C2211yescharacteristic
32C3×C9×C4⋊C4C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic
34C3×C9×C22⋊C4C2211yescharacteristic
35C3×C9×C22⋊C4C2211yescharacteristic
36C3×C42×C9C2211yescharacteristic
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
45C3×C4⋊Dic9C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×Dic9⋊C4C2211yescharacteristic
50C3×Dic9⋊C4C2211yescharacteristic
51C3×C4×Dic9C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×#126D311yescharacteristic
54C3×#898—31no—
55C3×#895—31no—
56C3×#894—31no—
57C3×#893—31no—
58C3×D3×C4⋊C4—31no—
59C3×#889—31no—
60C3×#886—31no—
61C3×#884—31no—
62C3×#884—31no—
63C3×#884—31no—
64C3×#67⋊C4—31no—
65C3×#67⋊C4—31no—
66C3×C4×D12—31no—
67C3×#872—31no—
68C9×#126—21no—
69C9×#126C2×C311yescharacteristic, complemented
70#63460C2×C311yescharacteristic, complemented
71#63457C2×C311yescharacteristic, complemented
72#63456C2×C311yescharacteristic, complemented
73#63455C2×C311yescharacteristic, complemented
74C4⋊C4×D9C2×C311yescharacteristic, complemented
75#63451C2×C311yescharacteristic, complemented
76#63448C2×C311yescharacteristic, complemented
77#63446C2×C311yescharacteristic, complemented
78#63446C2×C311yescharacteristic, complemented
79#63446C2×C311yescharacteristic, complemented
80#611⋊C4C2×C311yescharacteristic, complemented
81#611⋊C4C2×C311yescharacteristic, complemented
82C4×D36C2×C311yescharacteristic, complemented
83#63434C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C3×#611—22no—
95C3×#611—22no—
96C3×#611—41no—
97C2×C3×Dic9—41no—
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C3×D36—22no—
104C3×D36—22no—
105C3×D36—41no—
106C3×C4×D9—22no—
107C3×C4×D9—22no—
108C3×C4×D9—41no—
109C3×C4×D9—41no—
110C3×C4×D9—41no—
111C3×#553—91no—
112#5709—31no—
113C2×C3×#67—31no—
114C2×C3×#67—31no—
115C2×C3×#67—31no—
116C22×C3×Dic3—31no—
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—31no—
124C2×C3×C4×D3—31no—
125C32×C4⋊C4C2×D311yescharacteristic
126C32×C4⋊C4C2×D311yescharacteristic
127C32×C4⋊C4C2×D311yescharacteristic
128C32×C22⋊C4C2×D311yescharacteristic
129C32×C22⋊C4C2×D311yescharacteristic
130C32×C22⋊C4C2×D311yescharacteristic
131C32×C42C2×D311yescharacteristic
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×C4⋊Dic3—31no—
140C3×C4⋊Dic3—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C2×#611C22×C311yescharacteristic
149C2×#611C22×C311yescharacteristic
150C2×#611C22×C311yescharacteristic
151C22×Dic9C22×C311yescharacteristic
152C2×D36C22×C311yescharacteristic
153C2×D36C22×C311yescharacteristic
154C2×D36C22×C311yescharacteristic
155C2×C4×D9C22×C311yescharacteristic
156C2×C4×D9C22×C311yescharacteristic
157C2×C4×D9C22×C311yescharacteristic
158C2×C4×D9C22×C311yescharacteristic
159C2×C4×D9C22×C311yescharacteristic
160C9×C4⋊C4—21no—
161C9×C4⋊C4—21no—
162C9×C4⋊C4—21no—
163C9×C4⋊C4C22×C311yescharacteristic
164C9×C4⋊C4C22×C311yescharacteristic
165C9×C4⋊C4C22×C311yescharacteristic
166C9×C22⋊C4—21no—
167C9×C22⋊C4—21no—
168C9×C22⋊C4—21no—
169C9×C22⋊C4C22×C311yescharacteristic
170C9×C22⋊C4C22×C311yescharacteristic
171C9×C22⋊C4C22×C311yescharacteristic
172C42×C9—21no—
173C42×C9C22×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
182C4⋊Dic9C22×C311yescharacteristic
183Dic9⋊C4C22×C311yescharacteristic
184Dic9⋊C4C22×C311yescharacteristic
185Dic9⋊C4C22×C311yescharacteristic
186Dic9⋊C4C22×C311yescharacteristic
187Dic9⋊C4C22×C311yescharacteristic
188C4×Dic9C22×C311yescharacteristic
189C4×Dic9C22×C311yescharacteristic
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
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#4112yes—
203C3×C4×C9—21no—
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#4112yes—
214C3×#126—21no—
215C3×#126—91no—
216C3×#126D911yescharacteristic, complemented
217C3×#126C3×D311yescharacteristic
218C3×#125—91no—
219C3×#123—91no—
220C3×#123—91no—
221C3×#121—91no—
222C3×#121—91no—
223C3×#121—91no—
224C3×#121—91no—
225C3×C4×D4—91no—
226C3×C4×D4—91no—
227C3×C4×D4—91no—
228C3×C4×D4—91no—
229C3×#117—91no—
230C2×C3×C4⋊C4—91no—
231#898—31no—
232#895—31no—
233#894—31no—
234#893—31no—
235D3×C4⋊C4—31no—
236#889—31no—
237#886—31no—
238#884—31no—
239#884—31no—
240#884—31no—
241#67⋊C4—31no—
242#67⋊C4—31no—
243C4×D12—31no—
244#872—31no—
245C23×C32C22×D311yescharacteristic
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C3×#67—62no—
256C3×#67—62no—
257C3×#67—121no—
258C2×C3×Dic3—31no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—121no—
264C3×D12—62no—
265C3×D12—62no—
266C3×D12—121no—
267C3×C4×D3—62no—
268C3×C4×D3—62no—
269C3×C4×D3—121no—
270C3×C4×D3—121no—
271C3×C4×D3—121no—
272C23×C9—21no—
273C23×C9C23×C311yescharacteristic
274C22×D9C23×C311yescharacteristic
275C22×D9C23×C311yescharacteristic
276C22×D9C23×C311yescharacteristic
277C2×C4×C9—21no—
278C2×C4×C9—21no—
279C2×C4×C9—21no—
280C2×C4×C9—21no—
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9C23×C311yescharacteristic
284C2×C4×C9C23×C311yescharacteristic
285C2×C4×C9C23×C311yescharacteristic
286C2×C4×C9C23×C311yescharacteristic
287C2×C4×C9C23×C311yescharacteristic
288C2×C4×C9C23×C311yescharacteristic
289#611—22no—
290#611—22no—
291#611—41no—
292C2×Dic9—41no—
293C2×Dic9C23×C311yescharacteristic
294C2×Dic9C23×C311yescharacteristic
295C2×Dic9C23×C311yescharacteristic
296C2×Dic9C23×C311yescharacteristic
297C2×Dic9C23×C311yescharacteristic
298D36—22no—
299D36—22no—
300D36—41no—
301C4×D9—22no—
302C4×D9—22no—
303C4×D9—41no—
304C4×D9—41no—
305C4×D9—41no—
306#553—91noSylow
307C2×C3×C9—41no—
308C2×C3×C9C2×#4111yescharacteristic
309C2×C3×C9C2×#4111yescharacteristic
310C2×C3×C9H(5,𝔽2)11yescharacteristic
311C3×D9—22no—
312C3×D9—41no—
313C3×D9—41no—
314C2×C3×D4—91no—
315C2×C3×D4—91no—
316C2×C3×D4—91no—
317C2×C3×D4—91no—
318C2×C3×D4—91no—
319C2×C3×D4—91no—
320C22×C3×C4—91no—
321C22×C3×C4—91no—
322C22×C3×C4—91no—
323C22×C3×C4—91no—
324C22×C3×C4—91no—
325C22×C3×C4—91no—
326C2×#67—31no—
327C2×#67—31no—
328C2×#67—31no—
329C22×Dic3—31no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—31no—
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C3×C4⋊C4—21no—
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⋊C4—91no—
348C3×C4⋊C4C2×D911yescharacteristic
349C3×C4⋊C4C2×D911yescharacteristic
350C3×C4⋊C4C2×D911yescharacteristic
351C3×C4⋊C4C2×C3×D311yescharacteristic
352C3×C4⋊C4C2×C3×D311yescharacteristic
353C3×C4⋊C4C2×C3×D311yescharacteristic
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
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⋊C4C2×D911yescharacteristic
365C3×C22⋊C4C2×D911yescharacteristic
366C3×C22⋊C4C2×D911yescharacteristic
367C3×C22⋊C4C2×C3×D311yescharacteristic
368C3×C22⋊C4C2×C3×D311yescharacteristic
369C3×C22⋊C4C2×C3×D311yescharacteristic
370C3×C42—21no—
371C3×C42—91no—
372C3×C42—91no—
373C3×C42C2×D911yescharacteristic
374C3×C42C2×C3×D311yescharacteristic
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—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32C23×D311yescharacteristic
395C2×C3×D3—32no—
396C2×C3×D3—61no—
397C2×C3×D3—61no—
398C2×C3×D3—61no—
399C2×C3×D3—61no—
400C2×C3×D3—61no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C3×Dic3—32no—
411C3×Dic3—61no—
412C3×Dic3—61no—
413C3×Dic3—61no—
414C3×Dic3—61no—
415C22×C9—21no—
416C22×C9—21no—
417C22×C9—21no—
418C22×C9—21no—
419C22×C9—41no—
420C22×C9—41no—
421C22×C9—41no—
422C22×C9C24×C311yescharacteristic
423C2×D9—21no—
424C2×D9—21no—
425C2×D9—21no—
426C2×D9—21no—
427C2×D9—21no—
428C2×D9—21no—
429C2×D9—21no—
430C2×D9—21no—
431C2×D9C3×#4112yes—
432C4×C9—21no—
433C4×C9—21no—
434C4×C9—21no—
435C4×C9—21no—
436C4×C9—21no—
437C4×C9—21no—
438C4×C9—41no—
439C4×C9—41no—
440C4×C9—41no—
441C4×C9—41no—
442C4×C9—41no—
443C4×C9—41no—
444Dic9—21no—
445Dic9—21no—
446Dic9—21no—
447Dic9—21no—
448Dic9C3×#4112yes—
449#126—91no—
450#126C3×D911yescharacteristic, complemented
451#125—91no—
452#123—91no—
453#123—91no—
454#121—91no—
455#121—91no—
456#121—91no—
457#121—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462#117—91no—
463C2×C4⋊C4—91no—
464C3×C9#55311yescharacteristic, complemented, Sylow
465C23×C3—21no—
466C23×C3—91no—
467C23×C3—91no—
468C23×C3—91no—
469C23×C3C22×D911yescharacteristic
470C23×C3C22×C3×D311yescharacteristic
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—31no—
474C3×D4—182no—
475C3×D4—182no—
476C3×D4—182no—
477C3×D4—182no—
478C3×D4—361no—
479C3×D4—361no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—91no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—182no—
492C2×C3×C4—182no—
493C2×C3×C4—361no—
494C2×C3×C4—361no—
495C2×C3×C4—361no—
496C2×C3×C4—361no—
497C2×C3×C4C22×D911yescharacteristic
498C2×C3×C4C22×D911yescharacteristic
499C2×C3×C4C22×D911yescharacteristic
500C2×C3×C4C22×D911yescharacteristic
501C2×C3×C4C22×D911yescharacteristic
502C2×C3×C4C22×D911yescharacteristic
503C2×C3×C4C22×C3×D311yescharacteristic
504C2×C3×C4C22×C3×D311yescharacteristic
505C2×C3×C4C22×C3×D311yescharacteristic
506C2×C3×C4C22×C3×D311yescharacteristic
507C2×C3×C4C22×C3×D311yescharacteristic
508C2×C3×C4C22×C3×D311yescharacteristic
509#67—62no—
510#67—62no—
511#67—121no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—121no—
518D12—62no—
519D12—62no—
520D12—121no—
521C4×D3—62no—
522C4×D3—62no—
523C4×D3—121no—
524C4×D3—121no—
525C4×D3—121no—
526C2×C32—41no—
527C2×C32D3×#4111yescharacteristic
528C2×C32D3×#4111yescharacteristic
529C2×C32#100911yescharacteristic
530C3×D3—62no—
531C3×D3—121no—
532C3×D3—121no—
533C2×C9—21no—
534C2×C9—21no—
535C2×C9—21no—
536C2×C9—41no—
537C2×C9—81no—
538C2×C9C2×C3×#4111yescharacteristic
539C2×C9C2×C3×#4111yescharacteristic
540C2×C9C3×H(5,𝔽2)11yescharacteristic
541D9—22no—
542D9—41no—
543D9—41no—
544C2×D4—91no—
545C2×D4—91no—
546C2×D4—91no—
547C2×D4—91no—
548C2×D4—91no—
549C2×D4—91no—
550C22×C4—91no—
551C22×C4—91no—
552C22×C4—91no—
553C22×C4—91no—
554C22×C4—91no—
555C22×C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—91no—
563C4⋊C4C2×C3×D911yescharacteristic
564C4⋊C4C2×C3×D911yescharacteristic
565C4⋊C4C2×C3×D911yescharacteristic
566C22⋊C4—91no—
567C22⋊C4—91no—
568C22⋊C4—91no—
569C22⋊C4—91no—
570C22⋊C4—91no—
571C22⋊C4—91no—
572C22⋊C4—91no—
573C22⋊C4C2×C3×D911yescharacteristic
574C22⋊C4C2×C3×D911yescharacteristic
575C22⋊C4C2×C3×D911yescharacteristic
576C42—91no—
577C42—91no—
578C42C2×C3×D911yescharacteristic
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—92no—
590C22×C3—181no—
591C22×C3—181no—
592C22×C3—181no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3C23×D911yescharacteristic
599C22×C3C23×C3×D311yescharacteristic
600C2×D3—32no—
601C2×D3—61no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—61no—
606C2×D3—61no—
607C2×D3—61no—
608C2×D3—61no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—92no—
628C3×C4—181no—
629C3×C4—181no—
630C3×C4—181no—
631C3×C4—181no—
632Dic3—32no—
633Dic3—61no—
634Dic3—61no—
635Dic3—61no—
636Dic3—61no—
637C32#570911yescharacteristic
638C9—21no—
639C9C3×#55311yescharacteristic, complemented
640C23—91no—
641C23—91no—
642C23—91no—
643C23C22×C3×D911yescharacteristic
644D4—182no—
645D4—182no—
646D4—182no—
647D4—182no—
648D4—361no—
649D4—361no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—91no—
655C2×C4—182no—
656C2×C4—182no—
657C2×C4—361no—
658C2×C4—361no—
659C2×C4—361no—
660C2×C4—361no—
661C2×C4C22×C3×D911yescharacteristic
662C2×C4C22×C3×D911yescharacteristic
663C2×C4C22×C3×D911yescharacteristic
664C2×C4C22×C3×D911yescharacteristic
665C2×C4C22×C3×D911yescharacteristic
666C2×C4C22×C3×D911yescharacteristic
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—41no—
671C2×C3—41no—
672C2×C3—81no—
673C2×C3—182no—
674C2×C3—361no—
675C2×C3—361no—
676C2×C3#41×D911yescharacteristic
677C2×C3#41×D911yescharacteristic
678C2×C3#6371511yescharacteristic
679C2×C3C3×D3×#4111yescharacteristic
680C2×C3C3×D3×#4111yescharacteristic
681C2×C3C3×#100911yescharacteristic
682D3—62no—
683D3—121no—
684D3—121no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—92no—
689C22—181no—
690C22—181no—
691C22—181no—
692C22—181no—
693C22—181no—
694C22—181no—
695C22—181no—
696C22—181no—
697C22C23×C3×D911yescharacteristic
698C4—21no—
699C4—21no—
700C4—21no—
701C4—21no—
702C4—21no—
703C4—21no—
704C4—92no—
705C4—181no—
706C4—181no—
707C4—181no—
708C4—181no—
709C3—21no—
710C3#1058981111yescharacteristic, direct product factor
711C3C3×#570911yescharacteristic
712C2—41no—
713C2—182no—
714C2—361no—
715C2—361no—
716C2C3×#41×D911yescharacteristic
717C2C3×#41×D911yescharacteristic
718C2C3×#6371511yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#126C2
socleC22×C32C23×D3
hypercenterC3×#126D9
hypocenterC9C3×#553
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×#63457C2semidirect
4. C3×#63456C2semidirect
5. C3×#63455C2semidirect
6. C3×C4⋊C4×D9C2semidirect
7. C3×#63451C2semidirect
8. C3×#63448C2semidirect
9. C3×#63446C2semidirect
10. C3×#63446C2semidirect
11. C3×#63446C2semidirect
12. C3×#611⋊C4C2semidirect
13. C3×#611⋊C4C2semidirect
14. C3×C4×D36C2semidirect
15. C3×#63434C2semidirect
17. #10589811C3direct (N × H)
69. C9×#126C2×C3semidirect
70. #63460C2×C3semidirect
71. #63457C2×C3semidirect
72. #63456C2×C3semidirect
73. #63455C2×C3semidirect
74. C4⋊C4×D9C2×C3semidirect
75. #63451C2×C3semidirect
76. #63448C2×C3semidirect
77. #63446C2×C3semidirect
78. #63446C2×C3semidirect
79. #63446C2×C3semidirect
80. #611⋊C4C2×C3semidirect
81. #611⋊C4C2×C3semidirect
82. C4×D36C2×C3semidirect
83. #63434C2×C3semidirect
216. C3×#126D9semidirect
450. #126C3×D9semidirect
464. C3×C9#553semidirect
639. C9C3×#553semidirect
710. C3#10589811direct (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×#634572
C3×#634562
C3×#634552
C3×C4⋊C4×D92
C3×#634512
C3×#634482
C3×#634462
C3×#611⋊C42
C3×C4×D362
C3×#634342
C3×#57093
#105898113