Finite Group Databasebeta

← C3×#10589812 #13153209

Subgroups — C3×#10589812 #13153209

Order 1728.

708 conjugacy classes of subgroups.

The subgroup lattice has 684 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×#63459C211yesmaximal, characteristic, complemented
4C3×#63458C211yesmaximal, characteristic, complemented
5C3×#63456C211yesmaximal, characteristic, complemented
6C3×#63454C211yesmaximal, characteristic, complemented
7C3×#63450C211yesmaximal, characteristic, complemented
8C3×#63448C211yesmaximal, characteristic, complemented
9C3×#63447C211yesmaximal, characteristic, complemented
10C3×#63447C211yesmaximal, characteristic, complemented
11C3×#63446C211yesmaximal, characteristic
12C3×#611⋊C4C211yesmaximal, characteristic, complemented
13C3×#63440C211yesmaximal, characteristic, complemented
14C3×#63437C211yesmaximal, characteristic, complemented
15C3×C4×Dic18C211yesmaximal, characteristic, complemented
16C3×#5710—31nomaximal
17#10589812C311yesmaximal, characteristic, direct product factor
18C2×C3×#611C2211yescharacteristic
19C2×C3×#611C2211yescharacteristic
20C22×C3×Dic9C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C3×Dic18C2211yescharacteristic
25C2×C3×Dic18C2211yescharacteristic
26C2×C3×Dic18C2211yescharacteristic
27C3×C9×C4⋊C4C2211yescharacteristic
28C3×C9×C4⋊C4C2211yescharacteristic
29C3×C9×C4⋊C4C2211yescharacteristic
30C3×C9×C22⋊C4C2211yescharacteristic
31C3×C9×C22⋊C4C2211yescharacteristic
32C3×C9×C22⋊C4C2211yescharacteristic
33C3×C42×C9C2211yescharacteristic
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×C4⋊Dic9C2211yescharacteristic
44C3×C4⋊Dic9C2211yescharacteristic
45C3×C4⋊Dic9C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×Dic9⋊C4C2211yescharacteristic
50C3×C4×Dic9C2211yescharacteristic
51C3×C4×Dic9C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×#126D311yescharacteristic
54C3×#898—31no—
55C3×#897—31no—
56C3×#896—31no—
57C3×#894—31no—
58C3×#892—31no—
59C3×#888—31no—
60C3×#886—31no—
61C3×#885—31no—
62C3×#885—31no—
63C3×#884—31no—
64C3×#67⋊C4—31no—
65C3×#878—31no—
66C3×#875—31no—
67C3×C4×Dic6—31no—
68C9×#126—21no—
69C9×#126C2×C311yescharacteristic, complemented
70#63460C2×C311yescharacteristic, complemented
71#63459C2×C311yescharacteristic, complemented
72#63458C2×C311yescharacteristic, complemented
73#63456C2×C311yescharacteristic, complemented
74#63454C2×C311yescharacteristic, complemented
75#63450C2×C311yescharacteristic, complemented
76#63448C2×C311yescharacteristic, complemented
77#63447C2×C311yescharacteristic, complemented
78#63447C2×C311yescharacteristic, complemented
79#63446C2×C311yescharacteristic
80#611⋊C4C2×C311yescharacteristic, complemented
81#63440C2×C311yescharacteristic, complemented
82#63437C2×C311yescharacteristic, complemented
83C4×Dic18C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C3×#611—22no—
94C3×#611—41no—
95C2×C3×Dic9—41no—
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C3×D36—41no—
103C3×C4×D9—22no—
104C3×C4×D9—41no—
105C3×Dic18—22no—
106C3×Dic18—41no—
107C3×Dic18—41no—
108C3×#542—91no—
109#5710—31no—
110C2×C3×#67—31no—
111C2×C3×#67—31no—
112C22×C3×Dic3—31no—
113C2×C3×D12—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×Dic6—31no—
117C2×C3×Dic6—31no—
118C2×C3×Dic6—31no—
119C32×C4⋊C4C2×D311yescharacteristic
120C32×C4⋊C4C2×D311yescharacteristic
121C32×C4⋊C4C2×D311yescharacteristic
122C32×C22⋊C4C2×D311yescharacteristic
123C32×C22⋊C4C2×D311yescharacteristic
124C32×C22⋊C4C2×D311yescharacteristic
125C32×C42C2×D311yescharacteristic
126C3×#217—31no—
127C3×(C2×D3)⋊C4—31no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×C4⋊Dic3—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4—31no—
141C3×Dic3⋊C4—31no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C2×#611C22×C311yescharacteristic
146C2×#611C22×C311yescharacteristic
147C22×Dic9C22×C311yescharacteristic
148C2×D36C22×C311yescharacteristic
149C2×C4×D9C22×C311yescharacteristic
150C2×C4×D9C22×C311yescharacteristic
151C2×Dic18C22×C311yescharacteristic
152C2×Dic18C22×C311yescharacteristic
153C2×Dic18C22×C311yescharacteristic
154C9×C4⋊C4—21no—
155C9×C4⋊C4—21no—
156C9×C4⋊C4—21no—
157C9×C4⋊C4C22×C311yescharacteristic
158C9×C4⋊C4C22×C311yescharacteristic
159C9×C4⋊C4C22×C311yescharacteristic
160C9×C22⋊C4—21no—
161C9×C22⋊C4—21no—
162C9×C22⋊C4—21no—
163C9×C22⋊C4C22×C311yescharacteristic
164C9×C22⋊C4C22×C311yescharacteristic
165C9×C22⋊C4C22×C311yescharacteristic
166C42×C9—21no—
167C42×C9C22×C311yescharacteristic
168#3676C22×C311yescharacteristic
169(C2×D9)⋊C4C22×C311yescharacteristic
170(C2×D9)⋊C4C22×C311yescharacteristic
171(C2×D9)⋊C4C22×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
177C4⋊Dic9C22×C311yescharacteristic
178C4⋊Dic9C22×C311yescharacteristic
179C4⋊Dic9C22×C311yescharacteristic
180Dic9⋊C4C22×C311yescharacteristic
181Dic9⋊C4C22×C311yescharacteristic
182Dic9⋊C4C22×C311yescharacteristic
183Dic9⋊C4C22×C311yescharacteristic
184C4×Dic9C22×C311yescharacteristic
185C4×Dic9C22×C311yescharacteristic
186C4×Dic9C22×C311yescharacteristic
187C22×C3×C9—21no—
188C22×C3×C9—21no—
189C22×C3×C9—21no—
190C22×C3×C9C2411yescharacteristic
191C2×C3×D9—21no—
192C2×C3×D9—21no—
193C2×C3×D9—21no—
194C2×C3×D9—21no—
195C2×C3×D9—21no—
196C2×C3×D9—21no—
197C3×C4×C9—21no—
198C3×C4×C9—21no—
199C3×C4×C9—21no—
200C3×C4×C9—21no—
201C3×C4×C9—21no—
202C3×C4×C9—21no—
203C3×Dic9—21no—
204C3×Dic9—21no—
205C3×Dic9—21no—
206C3×Dic9—21no—
207C3×Dic9—21no—
208C3×Dic9#4112yes—
209C3×C4⋊Q8—91no—
210C3×#126—21no—
211C3×#126—91no—
212C3×#126D911yescharacteristic, complemented
213C3×#126C3×D311yescharacteristic
214C3×#124—91no—
215C3×#124—91no—
216C3×#124—91no—
217C3×#123—91no—
218C3×#123—91no—
219C3×C22⋊Q8—91no—
220C3×C22⋊Q8—91no—
221C3×C22⋊Q8—91no—
222C3×#121—91no—
223C3×C4×Q8—91no—
224C3×C4×D4—91no—
225C3×#117—91no—
226#898—31no—
227#897—31no—
228#896—31no—
229#894—31no—
230#892—31no—
231#888—31no—
232#886—31no—
233#885—31no—
234#885—31no—
235#884—31no—
236#67⋊C4—31no—
237#878—31no—
238#875—31no—
239C4×Dic6—31no—
240C23×C32C22×D311yescharacteristic
241C22×C3×D3—31no—
242C22×C3×D3—31no—
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C3×#67—62no—
250C3×#67—121no—
251C2×C3×Dic3—31no—
252C2×C3×Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3—31no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—121no—
258C3×D12—121no—
259C3×C4×D3—62no—
260C3×C4×D3—121no—
261C3×Dic6—62no—
262C3×Dic6—121no—
263C3×Dic6—121no—
264C23×C9—21no—
265C23×C9C23×C311yescharacteristic
266C22×D9C23×C311yescharacteristic
267C22×D9C23×C311yescharacteristic
268C2×C4×C9—21no—
269C2×C4×C9—21no—
270C2×C4×C9—21no—
271C2×C4×C9—21no—
272C2×C4×C9—21no—
273C2×C4×C9—21no—
274C2×C4×C9C23×C311yescharacteristic
275C2×C4×C9C23×C311yescharacteristic
276C2×C4×C9C23×C311yescharacteristic
277C2×C4×C9C23×C311yescharacteristic
278C2×C4×C9C23×C311yescharacteristic
279C2×C4×C9C23×C311yescharacteristic
280#611—22no—
281#611—41no—
282C2×Dic9—41no—
283C2×Dic9C23×C311yescharacteristic
284C2×Dic9C23×C311yescharacteristic
285C2×Dic9C23×C311yescharacteristic
286C2×Dic9C23×C311yescharacteristic
287C2×Dic9C23×C311yescharacteristic
288C2×Dic9C23×C311yescharacteristic
289D36—41no—
290C4×D9—22no—
291C4×D9—41no—
292Dic18—22no—
293Dic18—41no—
294Dic18—41no—
295#542—91noSylow
296C2×C3×C9—41no—
297C2×C3×C9C2×#4111yescharacteristic
298C2×C3×C9H(5,𝔽2)11yescharacteristic
299C2×C3×C92−1+411yescharacteristic
300C3×D9—41no—
301C3×D9—41no—
302C2×C3×Q8—91no—
303C2×C3×Q8—91no—
304C2×C3×Q8—91no—
305C2×C3×D4—91no—
306C2×C3×D4—91no—
307C2×C3×D4—91no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C22×C3×C4—91no—
311C2×#67—31no—
312C2×#67—31no—
313C22×Dic3—31no—
314C2×D12—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—91no—
324C3×C4⋊C4—91no—
325C3×C4⋊C4—91no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4C2×D911yescharacteristic
331C3×C4⋊C4C2×D911yescharacteristic
332C3×C4⋊C4C2×D911yescharacteristic
333C3×C4⋊C4C2×C3×D311yescharacteristic
334C3×C4⋊C4C2×C3×D311yescharacteristic
335C3×C4⋊C4C2×C3×D311yescharacteristic
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—91no—
340C3×C22⋊C4—91no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4C2×D911yescharacteristic
349C3×C22⋊C4C2×D911yescharacteristic
350C3×C22⋊C4C2×D911yescharacteristic
351C3×C22⋊C4C2×C3×D311yescharacteristic
352C3×C22⋊C4C2×C3×D311yescharacteristic
353C3×C22⋊C4C2×C3×D311yescharacteristic
354C3×C42—21no—
355C3×C42—91no—
356C3×C42—91no—
357C3×C42—91no—
358C3×C42C2×D911yescharacteristic
359C3×C42C2×C3×D311yescharacteristic
360#217—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32C23×D311yescharacteristic
383C2×C3×D3—61no—
384C2×C3×D3—61no—
385C2×C3×D3—61no—
386C2×C3×D3—61no—
387C2×C3×D3—61no—
388C2×C3×D3—61no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C3×Dic3—32no—
396C3×Dic3—61no—
397C3×Dic3—61no—
398C3×Dic3—61no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C22×C9—21no—
402C22×C9—21no—
403C22×C9—21no—
404C22×C9—21no—
405C22×C9—41no—
406C22×C9—41no—
407C22×C9—41no—
408C22×C9C24×C311yescharacteristic
409C2×D9—21no—
410C2×D9—21no—
411C2×D9—21no—
412C2×D9—21no—
413C2×D9—21no—
414C2×D9—21no—
415C4×C9—21no—
416C4×C9—21no—
417C4×C9—21no—
418C4×C9—21no—
419C4×C9—21no—
420C4×C9—21no—
421C4×C9—41no—
422C4×C9—41no—
423C4×C9—41no—
424C4×C9—41no—
425C4×C9—41no—
426C4×C9—41no—
427Dic9—21no—
428Dic9—21no—
429Dic9—21no—
430Dic9—21no—
431Dic9—21no—
432Dic9C3×#4112yes—
433C4⋊Q8—91no—
434#126—91no—
435#126C3×D911yescharacteristic, complemented
436#124—91no—
437#124—91no—
438#124—91no—
439#123—91no—
440#123—91no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444#121—91no—
445C4×Q8—91no—
446C4×D4—91no—
447#117—91no—
448C3×C9#54211yescharacteristic, complemented, Sylow
449C23×C3—21no—
450C23×C3—91no—
451C23×C3—91no—
452C23×C3C22×D911yescharacteristic
453C23×C3C22×C3×D311yescharacteristic
454C22×D3—31no—
455C22×D3—31no—
456C3×Q8—182no—
457C3×Q8—361no—
458C3×Q8—361no—
459C3×D4—182no—
460C3×D4—361no—
461C3×D4—361no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—91no—
469C2×C3×C4—91no—
470C2×C3×C4—91no—
471C2×C3×C4—91no—
472C2×C3×C4—91no—
473C2×C3×C4—91no—
474C2×C3×C4—182no—
475C2×C3×C4—361no—
476C2×C3×C4—361no—
477C2×C3×C4C22×D911yescharacteristic
478C2×C3×C4C22×D911yescharacteristic
479C2×C3×C4C22×D911yescharacteristic
480C2×C3×C4C22×D911yescharacteristic
481C2×C3×C4C22×D911yescharacteristic
482C2×C3×C4C22×D911yescharacteristic
483C2×C3×C4C22×C3×D311yescharacteristic
484C2×C3×C4C22×C3×D311yescharacteristic
485C2×C3×C4C22×C3×D311yescharacteristic
486C2×C3×C4C22×C3×D311yescharacteristic
487C2×C3×C4C22×C3×D311yescharacteristic
488C2×C3×C4C22×C3×D311yescharacteristic
489#67—62no—
490#67—121no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—121no—
498D12—121no—
499C4×D3—62no—
500C4×D3—121no—
501Dic6—62no—
502Dic6—121no—
503Dic6—121no—
504C2×C32—41no—
505C2×C32D3×#4111yescharacteristic
506C2×C32#100911yescharacteristic
507C2×C32#101011yescharacteristic
508C3×D3—121no—
509C3×D3—121no—
510C2×C9—21no—
511C2×C9—21no—
512C2×C9—21no—
513C2×C9—41no—
514C2×C9—81no—
515C2×C9C2×C3×#4111yescharacteristic
516C2×C9C3×H(5,𝔽2)11yescharacteristic
517C2×C9C3×2−1+411yescharacteristic
518D9—41no—
519D9—41no—
520C2×Q8—91no—
521C2×Q8—91no—
522C2×Q8—91no—
523C2×D4—91no—
524C2×D4—91no—
525C2×D4—91no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C4⋊C4—91no—
530C4⋊C4—91no—
531C4⋊C4—91no—
532C4⋊C4—91no—
533C4⋊C4—91no—
534C4⋊C4—91no—
535C4⋊C4—91no—
536C4⋊C4C2×C3×D911yescharacteristic
537C4⋊C4C2×C3×D911yescharacteristic
538C4⋊C4C2×C3×D911yescharacteristic
539C22⋊C4—91no—
540C22⋊C4—91no—
541C22⋊C4—91no—
542C22⋊C4—91no—
543C22⋊C4—91no—
544C22⋊C4—91no—
545C22⋊C4—91no—
546C22⋊C4—91no—
547C22⋊C4—91no—
548C22⋊C4C2×C3×D911yescharacteristic
549C22⋊C4C2×C3×D911yescharacteristic
550C22⋊C4C2×C3×D911yescharacteristic
551C42—91no—
552C42—91no—
553C42—91no—
554C42C2×C3×D911yescharacteristic
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—181no—
566C22×C3—181no—
567C22×C3—181no—
568C22×C3—181no—
569C22×C3—181no—
570C22×C3—181no—
571C22×C3C23×D911yescharacteristic
572C22×C3C23×C3×D311yescharacteristic
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—61no—
576C2×D3—61no—
577C2×D3—61no—
578C2×D3—61no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—92no—
598C3×C4—181no—
599C3×C4—181no—
600C3×C4—181no—
601C3×C4—181no—
602C3×C4—181no—
603Dic3—32no—
604Dic3—61no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608Dic3—61no—
609C32#571011yescharacteristic
610C9—21no—
611C9C3×#54211yescharacteristic, complemented
612C23—91no—
613C23—91no—
614C23C22×C3×D911yescharacteristic
615Q8—182no—
616Q8—361no—
617Q8—361no—
618D4—182no—
619D4—361no—
620D4—361no—
621C2×C4—91no—
622C2×C4—91no—
623C2×C4—91no—
624C2×C4—91no—
625C2×C4—91no—
626C2×C4—91no—
627C2×C4—182no—
628C2×C4—361no—
629C2×C4—361no—
630C2×C4C22×C3×D911yescharacteristic
631C2×C4C22×C3×D911yescharacteristic
632C2×C4C22×C3×D911yescharacteristic
633C2×C4C22×C3×D911yescharacteristic
634C2×C4C22×C3×D911yescharacteristic
635C2×C4C22×C3×D911yescharacteristic
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—41no—
640C2×C3—41no—
641C2×C3—81no—
642C2×C3—361no—
643C2×C3—361no—
644C2×C3#41×D911yescharacteristic
645C2×C3#6371511yescharacteristic
646C2×C3#6371611yescharacteristic
647C2×C3C3×D3×#4111yescharacteristic
648C2×C3C3×#100911yescharacteristic
649C2×C3C3×#101011yescharacteristic
650D3—121no—
651D3—121no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—181no—
656C22—181no—
657C22—181no—
658C22—181no—
659C22—181no—
660C22—181no—
661C22C23×C3×D911yescharacteristic
662C4—21no—
663C4—21no—
664C4—21no—
665C4—21no—
666C4—21no—
667C4—21no—
668C4—92no—
669C4—181no—
670C4—181no—
671C4—181no—
672C4—181no—
673C4—181no—
674C3—21no—
675C3#1058981211yescharacteristic, direct product factor
676C3C3×#571011yescharacteristic
677C2—41no—
678C2—361no—
679C2—361no—
680C2C3×#41×D911yescharacteristic
681C2C3×#6371511yescharacteristic
682C2C3×#6371611yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#126C2
socleC22×C32C23×D3
prime radicalC3×#63446C2
hypercenterC3×#126D9
hypocenterC9C3×#542
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×#63459C2semidirect
4. C3×#63458C2semidirect
5. C3×#63456C2semidirect
6. C3×#63454C2semidirect
7. C3×#63450C2semidirect
8. C3×#63448C2semidirect
9. C3×#63447C2semidirect
10. C3×#63447C2semidirect
12. C3×#611⋊C4C2semidirect
13. C3×#63440C2semidirect
14. C3×#63437C2semidirect
15. C3×C4×Dic18C2semidirect
17. #10589812C3direct (N × H)
69. C9×#126C2×C3semidirect
70. #63460C2×C3semidirect
71. #63459C2×C3semidirect
72. #63458C2×C3semidirect
73. #63456C2×C3semidirect
74. #63454C2×C3semidirect
75. #63450C2×C3semidirect
76. #63448C2×C3semidirect
77. #63447C2×C3semidirect
78. #63447C2×C3semidirect
80. #611⋊C4C2×C3semidirect
81. #63440C2×C3semidirect
82. #63437C2×C3semidirect
83. C4×Dic18C2×C3semidirect
212. C3×#126D9semidirect
435. #126C3×D9semidirect
448. C3×C9#542semidirect
611. C9C3×#542semidirect
675. C3#10589812direct (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×#634592
C3×#634582
C3×#634562
C3×#634542
C3×#634502
C3×#634482
C3×#634472
C3×#634462
C3×#611⋊C42
C3×#634402
C3×#634372
C3×C4×Dic182
C3×#57103
#105898123