Finite Group Databasebeta

← C3×#10589780 #13153092

Subgroups — C3×#10589780 #13153092

Order 1728.

826 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#124C211yesmaximal, characteristic, complemented
2C3×#63509C211yesmaximal, characteristic, complemented
3C3×#63508C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic, complemented
5C3×#63499C211yesmaximal, characteristic, complemented
6C3×#63448C211yesmaximal, characteristic, complemented
7C3×#63446C211yesmaximal, characteristic, complemented
8C3×#63446C211yesmaximal, characteristic, complemented
9C3×#63445C211yesmaximal, characteristic, complemented
10C3×#63444C211yesmaximal, characteristic, complemented
11C3×#611⋊C4C211yesmaximal, characteristic, complemented
12C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
13C3×#63441C211yesmaximal, characteristic, complemented
14C3×#63438C211yesmaximal, characteristic, complemented
15C3×C4×D36C211yesmaximal, characteristic, complemented
16C3×#5678—31nomaximal
17#10589780C311yesmaximal, characteristic, direct product factor
18C23×C3×D9C2211yescharacteristic
19C2×C3×Q8×C9C2211yescharacteristic, complemented
20C2×C3×D4×C9C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic, complemented
25C22×C3×Dic9C2211yescharacteristic, complemented
26C2×C3×D36C2211yescharacteristic
27C2×C3×D36C2211yescharacteristic
28C2×C3×C4×D9C2211yescharacteristic
29C2×C3×C4×D9C2211yescharacteristic
30C2×C3×C4×D9C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32C3×C9×C22⋊C4C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic, complemented
34C3×C9×C22⋊C4C2211yescharacteristic, complemented
35C3×C42×C9C2211yescharacteristic, complemented
36C3×#3676C2211yescharacteristic
37C3×#3676C2211yescharacteristic
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×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×C4⋊Dic9C2211yescharacteristic, complemented
47C3×C4⋊Dic9C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49C3×Dic9⋊C4C2211yescharacteristic, complemented
50C3×Dic9⋊C4C2211yescharacteristic, complemented
51C3×Dic9⋊C4C2211yescharacteristic, complemented
52C3×C4×Dic9C2211yescharacteristic, complemented
53C32×#124D311yescharacteristic
54C3×#947—31no—
55C3×#946—31no—
56C3×#939—31no—
57C3×#937—31no—
58C3×#886—31no—
59C3×#884—31no—
60C3×#884—31no—
61C3×#883—31no—
62C3×#882—31no—
63C3×#67⋊C4—31no—
64C3×D3×C22⋊C4—31no—
65C3×#879—31no—
66C3×#876—31no—
67C3×C4×D12—31no—
68C9×#124—21no—
69C9×#124C2×C311yescharacteristic, complemented
70#63509C2×C311yescharacteristic, complemented
71#63508C2×C311yescharacteristic, complemented
72#63501C2×C311yescharacteristic, complemented
73#63499C2×C311yescharacteristic, complemented
74#63448C2×C311yescharacteristic, complemented
75#63446C2×C311yescharacteristic, complemented
76#63446C2×C311yescharacteristic, complemented
77#63445C2×C311yescharacteristic, complemented
78#63444C2×C311yescharacteristic, complemented
79#611⋊C4C2×C311yescharacteristic, complemented
80C22⋊C4×D9C2×C311yescharacteristic, complemented
81#63441C2×C311yescharacteristic, complemented
82#63438C2×C311yescharacteristic, complemented
83C4×D36C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C23×C3×C9C2311yescharacteristic
86C22×C3×D9—22no—
87C22×C3×D9—41no—
88C22×C3×D9—41no—
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C3×Q8×C9—41no—
93C3×D4×C9—41no—
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C3×#611—22no—
100C3×#611—41no—
101C3×#611—41no—
102C3×#611—41no—
103C2×C3×Dic9—41no—
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C3×D36—22no—
110C3×D36—41no—
111C3×C4×D9—41no—
112C3×C4×D9—41no—
113C3×C4×D9—41no—
114C3×#538—91no—
115#5678—31no—
116C23×C3×D3—31no—
117C2×C32×Q8C2×D311yescharacteristic
118C2×C32×D4C2×D311yescharacteristic
119C2×C3×#67—31no—
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C22×C3×Dic3—31no—
124C2×C3×D12—31no—
125C2×C3×D12—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—31no—
129C23×D9C22×C311yescharacteristic
130C32×C22⋊C4C2×D311yescharacteristic
131C32×C22⋊C4C2×D311yescharacteristic
132C32×C22⋊C4C2×D311yescharacteristic
133C32×C22⋊C4C2×D311yescharacteristic
134C32×C42C2×D311yescharacteristic
135C3×#217—31no—
136C3×#217—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×(C2×D3)⋊C4—31no—
143C3×(C2×D3)⋊C4—31no—
144C3×(C2×D3)⋊C4—31no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—31no—
147C3×Dic3⋊C4—31no—
148C3×Dic3⋊C4—31no—
149C3×Dic3⋊C4—31no—
150C3×Dic3⋊C4—31no—
151C3×C4×Dic3—31no—
152C2×Q8×C9—21no—
153C2×Q8×C9C22×C311yescharacteristic, complemented
154C2×D4×C9—21no—
155C2×D4×C9C22×C311yescharacteristic
156C2×#611C22×C311yescharacteristic
157C2×#611C22×C311yescharacteristic
158C2×#611C22×C311yescharacteristic
159C2×#611C22×C311yescharacteristic, complemented
160C22×Dic9C22×C311yescharacteristic, complemented
161C2×D36C22×C311yescharacteristic
162C2×D36C22×C311yescharacteristic
163C2×C4×D9C22×C311yescharacteristic
164C2×C4×D9C22×C311yescharacteristic
165C2×C4×D9C22×C311yescharacteristic, complemented
166C9×C22⋊C4—21no—
167C9×C22⋊C4—21no—
168C9×C22⋊C4—21no—
169C9×C22⋊C4—21no—
170C9×C22⋊C4C22×C311yescharacteristic
171C9×C22⋊C4C22×C311yescharacteristic
172C9×C22⋊C4C22×C311yescharacteristic, complemented
173C9×C22⋊C4C22×C311yescharacteristic, complemented
174C42×C9—21no—
175C42×C9C22×C311yescharacteristic, complemented
176#3676C22×C311yescharacteristic
177#3676C22×C311yescharacteristic
178(C2×D9)⋊C4C22×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, complemented
185(C2×D9)⋊C4C22×C311yescharacteristic, complemented
186C4⋊Dic9C22×C311yescharacteristic, complemented
187C4⋊Dic9C22×C311yescharacteristic, complemented
188Dic9⋊C4C22×C311yescharacteristic, complemented
189Dic9⋊C4C22×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×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9C2411yescharacteristic
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×Dic9—21no—
216C3×Dic9—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#126—91no—
221C3×#126—91no—
222C3×#124—21no—
223C3×#124—91no—
224C3×#124D911yescharacteristic, complemented
225C3×#124C3×D311yescharacteristic
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#947—31no—
238#946—31no—
239#939—31no—
240#937—31no—
241#886—31no—
242#884—31no—
243#884—31no—
244#883—31no—
245#882—31no—
246#67⋊C4—31no—
247D3×C22⋊C4—31no—
248#879—31no—
249#876—31no—
250C4×D12—31no—
251C23×C32C22×D311yescharacteristic
252C23×C32C22×D311yescharacteristic
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3—31no—
256C22×C3×D3—62no—
257C22×C3×D3—121no—
258C22×C3×D3—121no—
259C32×Q8—41no—
260C32×D4—41no—
261C2×C32×C4C22×D311yescharacteristic
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C3×#67—62no—
267C3×#67—121no—
268C3×#67—121no—
269C3×#67—121no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—121no—
276C3×D12—62no—
277C3×D12—121no—
278C3×C4×D3—121no—
279C3×C4×D3—121no—
280C3×C4×D3—121no—
281C23×C9—21no—
282C23×C9—21no—
283C23×C9C23×C311yescharacteristic
284C23×C9C23×C311yescharacteristic
285C22×D9—22no—
286C22×D9—41no—
287C22×D9—41no—
288C22×D9C23×C311yescharacteristic
289C22×D9C23×C311yescharacteristic
290C22×D9C23×C311yescharacteristic
291Q8×C9—41no—
292Q8×C9—42no—
293D4×C9—41no—
294D4×C9—42no—
295C2×C4×C9—21no—
296C2×C4×C9—21no—
297C2×C4×C9—21no—
298C2×C4×C9—21no—
299C2×C4×C9—21no—
300C2×C4×C9C23×C311yescharacteristic
301C2×C4×C9C23×C311yescharacteristic
302C2×C4×C9C23×C311yescharacteristic
303C2×C4×C9C23×C311yescharacteristic
304C2×C4×C9C23×C311yescharacteristic
305#611—22no—
306#611—41no—
307#611—41no—
308#611—41no—
309C2×Dic9—41no—
310C2×Dic9C23×C311yescharacteristic
311C2×Dic9C23×C311yescharacteristic
312C2×Dic9C23×C311yescharacteristic
313C2×Dic9C23×C311yescharacteristic
314C2×Dic9C23×C311yescharacteristic
315D36—22no—
316D36—41no—
317C4×D9—41no—
318C4×D9—41no—
319C4×D9—41no—
320#538—91noSylow
321C2×C3×C9—41no—
322C2×C3×C9—41no—
323C2×C3×C9C2×#4111yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C2×C3×C9H(5,𝔽2)11yescharacteristic
326C3×D9—22no—
327C3×D9—41no—
328C3×D9—41no—
329C24×C3—91no—
330C23×D3—31no—
331C2×C3×Q8—21no—
332C2×C3×Q8C2×D911yescharacteristic, complemented
333C2×C3×Q8C2×C3×D311yescharacteristic
334C2×C3×D4—21no—
335C2×C3×D4—91no—
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C2×C3×D4—91no—
340C2×C3×D4—91no—
341C2×C3×D4C2×D911yescharacteristic
342C2×C3×D4C2×C3×D311yescharacteristic
343C22×C3×C4—91no—
344C22×C3×C4—91no—
345C22×C3×C4—91no—
346C22×C3×C4—91no—
347C2×#67—31no—
348C2×#67—31no—
349C2×#67—31no—
350C2×#67—31no—
351C22×Dic3—31no—
352C2×D12—31no—
353C2×D12—31no—
354C2×C4×D3—31no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4—91no—
359C3×C4⋊C4—91no—
360C3×C4⋊C4—91no—
361C3×C4⋊C4—91no—
362C3×C4⋊C4—91no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—91no—
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⋊C4C2×D911yescharacteristic
378C3×C22⋊C4C2×D911yescharacteristic
379C3×C22⋊C4C2×D911yescharacteristic, complemented
380C3×C22⋊C4C2×D911yescharacteristic, complemented
381C3×C22⋊C4C2×C3×D311yescharacteristic
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#217—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—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405C4×Dic3—31no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C23×D311yescharacteristic
413C2×C3×D3—32no—
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—61no—
421C2×C3×D3—61no—
422C2×C3×D3—124no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C3×Dic3—61no—
429C3×Dic3—61no—
430C3×Dic3—61no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C22×C9—21no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—21no—
440C22×C9—41no—
441C22×C9—41no—
442C22×C9—41no—
443C22×C9—41no—
444C22×C9—41no—
445C22×C9—41no—
446C22×C9C24×C311yescharacteristic
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—21no—
450C2×D9—21no—
451C2×D9—21no—
452C2×D9—21no—
453C2×D9—21no—
454C2×D9—21no—
455C2×D9—44no—
456C2×D9C3×#4112yes—
457C4×C9—22no—
458C4×C9—21no—
459C4×C9—21no—
460C4×C9—21no—
461C4×C9—21no—
462C4×C9—21no—
463C4×C9—41no—
464C4×C9—41no—
465C4×C9—41no—
466C4×C9—41no—
467Dic9—21no—
468Dic9—21no—
469Dic9—21no—
470Dic9—21no—
471Dic9—21no—
472#126—91no—
473#126—91no—
474#124—91no—
475#124C3×D911yescharacteristic, complemented
476#123—91no—
477#123—91no—
478C22⋊Q8—91no—
479#121—91no—
480#121—91no—
481#121—91no—
482#120—91no—
483#120—91no—
484C4×D4—91no—
485C4×D4—91no—
486C2×C22⋊C4—91no—
487C3×C9#53811yescharacteristic, complemented, Sylow
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—91no—
491C23×C3—91no—
492C23×C3—91no—
493C23×C3—182no—
494C23×C3—361no—
495C23×C3—361no—
496C23×C3C22×D911yescharacteristic
497C23×C3C22×D911yescharacteristic
498C23×C3C22×C3×D311yescharacteristic
499C23×C3C22×C3×D311yescharacteristic
500C22×D3—31no—
501C22×D3—31no—
502C22×D3—31no—
503C22×D3—62no—
504C22×D3—121no—
505C22×D3—121no—
506C3×Q8—41no—
507C3×Q8—41no—
508C3×Q8—42no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—42no—
512C3×D4—182no—
513C3×D4—182no—
514C3×D4—361no—
515C3×D4—361no—
516C3×D4—361no—
517C3×D4—361no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—91no—
524C2×C3×C4—91no—
525C2×C3×C4—91no—
526C2×C3×C4—91no—
527C2×C3×C4—91no—
528C2×C3×C4—361no—
529C2×C3×C4—361no—
530C2×C3×C4—361no—
531C2×C3×C4—361no—
532C2×C3×C4C22×D911yescharacteristic
533C2×C3×C4C22×D911yescharacteristic
534C2×C3×C4C22×D911yescharacteristic
535C2×C3×C4C22×D911yescharacteristic
536C2×C3×C4C22×D911yescharacteristic
537C2×C3×C4C22×C3×D311yescharacteristic
538C2×C3×C4C22×C3×D311yescharacteristic
539C2×C3×C4C22×C3×D311yescharacteristic
540C2×C3×C4C22×C3×D311yescharacteristic
541C2×C3×C4C22×C3×D311yescharacteristic
542#67—62no—
543#67—121no—
544#67—121no—
545#67—121no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—121no—
552D12—62no—
553D12—121no—
554C4×D3—121no—
555C4×D3—121no—
556C4×D3—121no—
557C2×C32—41no—
558C2×C32—41no—
559C2×C32#100411yescharacteristic
560C2×C32D3×#4111yescharacteristic
561C2×C32#100911yescharacteristic
562C3×D3—62no—
563C3×D3—121no—
564C3×D3—121no—
565C2×C9—21no—
566C2×C9—21no—
567C2×C9—21no—
568C2×C9—41no—
569C2×C9—41no—
570C2×C9—81no—
571C2×C9—81no—
572C2×C9C2×C3×#4111yescharacteristic
573C2×C9C3×H(5,𝔽2)11yescharacteristic
574C2×C9C3×H(5,𝔽2)11yescharacteristic
575D9—22no—
576D9—41no—
577D9—41no—
578C24—91no—
579C2×Q8C2×C3×D911yescharacteristic, complemented
580C2×D4—91no—
581C2×D4—91no—
582C2×D4—91no—
583C2×D4—91no—
584C2×D4—91no—
585C2×D4—91no—
586C2×D4C2×C3×D911yescharacteristic
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—91no—
591C4⋊C4—91no—
592C4⋊C4—91no—
593C4⋊C4—91no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—91no—
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—91no—
602C22⋊C4—91no—
603C22⋊C4—91no—
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4C2×C3×D911yescharacteristic
608C22⋊C4C2×C3×D911yescharacteristic
609C22⋊C4C2×C3×D911yescharacteristic, complemented
610C22⋊C4C2×C3×D911yescharacteristic, complemented
611C42—91no—
612C42C2×C3×D911yescharacteristic, complemented
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—92no—
633C22×C3—181no—
634C22×C3—181no—
635C22×C3—181no—
636C22×C3—181no—
637C22×C3—181no—
638C22×C3—181no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3—364no—
642C22×C3C23×D911yescharacteristic
643C22×C3C23×C3×D311yescharacteristic
644C2×D3—32no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—124no—
654C3×C4—22no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—181no—
670C3×C4—181no—
671C3×C4—181no—
672C3×C4—181no—
673C3×C4—181no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679C32#567811yescharacteristic
680C9—21no—
681C9C3×#53811yescharacteristic, complemented
682C23—91no—
683C23—91no—
684C23—91no—
685C23—182no—
686C23—361no—
687C23—361no—
688C23C22×C3×D911yescharacteristic
689C23C22×C3×D911yescharacteristic
690Q8—41no—
691D4—41no—
692D4—182no—
693D4—182no—
694D4—361no—
695D4—361no—
696D4—361no—
697D4—361no—
698C2×C4—91no—
699C2×C4—91no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—361no—
704C2×C4—361no—
705C2×C4—361no—
706C2×C4—361no—
707C2×C4C22×C3×D911yescharacteristic
708C2×C4C22×C3×D911yescharacteristic
709C2×C4C22×C3×D911yescharacteristic
710C2×C4C22×C3×D911yescharacteristic
711C2×C4C22×C3×D911yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—41no—
716C2×C3—41no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—81no—
720C2×C3—81no—
721C2×C3—182no—
722C2×C3—361no—
723C2×C3—361no—
724C2×C3#6371011yescharacteristic
725C2×C3#41×D911yescharacteristic
726C2×C3#6371511yescharacteristic
727C2×C3C3×#100411yescharacteristic
728C2×C3C3×D3×#4111yescharacteristic
729C2×C3C3×#100911yescharacteristic
730D3—62no—
731D3—121no—
732D3—121no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—92no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—181no—
745C22—181no—
746C22—181no—
747C22—181no—
748C22—364no—
749C22C23×C3×D911yescharacteristic
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—181no—
756C4—181no—
757C4—181no—
758C4—181no—
759C4—181no—
760C3—21no—
761C3#1058978011yescharacteristic, direct product factor
762C3C3×#567811yescharacteristic
763C2—41no—
764C2—41no—
765C2—182no—
766C2—361no—
767C2—361no—
768C2C3×#6371011yescharacteristic
769C2C3×#41×D911yescharacteristic
770C2C3×#6371511yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#124C2
socleC22×C32C23×D3
hypercenterC3×#124D9
hypocenterC9C3×#538
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#124

Complements

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

NH ≅ G/Ntype
1. C3×C9×#124C2semidirect
2. C3×#63509C2semidirect
3. C3×#63508C2semidirect
4. C3×#63501C2semidirect
5. C3×#63499C2semidirect
6. C3×#63448C2semidirect
7. C3×#63446C2semidirect
8. C3×#63446C2semidirect
9. C3×#63445C2semidirect
10. C3×#63444C2semidirect
11. C3×#611⋊C4C2semidirect
12. C3×C22⋊C4×D9C2semidirect
13. C3×#63441C2semidirect
14. C3×#63438C2semidirect
15. C3×C4×D36C2semidirect
17. #10589780C3direct (N × H)
19. C2×C3×Q8×C9C22semidirect
24. C2×C3×#611C22semidirect
25. C22×C3×Dic9C22semidirect
30. C2×C3×C4×D9C22semidirect
33. C3×C9×C22⋊C4C22semidirect
34. C3×C9×C22⋊C4C22semidirect
35. C3×C42×C9C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×C4⋊Dic9C22semidirect
47. C3×C4⋊Dic9C22semidirect
48. C3×Dic9⋊C4C22semidirect
49. C3×Dic9⋊C4C22semidirect
50. C3×Dic9⋊C4C22semidirect
51. C3×Dic9⋊C4C22semidirect
52. C3×C4×Dic9C22semidirect
69. C9×#124C2×C3semidirect
70. #63509C2×C3semidirect
71. #63508C2×C3semidirect
72. #63501C2×C3semidirect
73. #63499C2×C3semidirect
74. #63448C2×C3semidirect
75. #63446C2×C3semidirect
76. #63446C2×C3semidirect
77. #63445C2×C3semidirect
78. #63444C2×C3semidirect
79. #611⋊C4C2×C3semidirect
80. C22⋊C4×D9C2×C3semidirect
81. #63441C2×C3semidirect
82. #63438C2×C3semidirect
83. C4×D36C2×C3semidirect
153. C2×Q8×C9C22×C3semidirect
159. C2×#611C22×C3semidirect
160. C22×Dic9C22×C3semidirect
165. C2×C4×D9C22×C3semidirect
172. C9×C22⋊C4C22×C3semidirect
173. C9×C22⋊C4C22×C3semidirect
175. C42×C9C22×C3semidirect
184. (C2×D9)⋊C4C22×C3semidirect
185. (C2×D9)⋊C4C22×C3semidirect
186. C4⋊Dic9C22×C3semidirect
187. C4⋊Dic9C22×C3semidirect
188. Dic9⋊C4C22×C3semidirect
189. Dic9⋊C4C22×C3semidirect
190. Dic9⋊C4C22×C3semidirect
191. Dic9⋊C4C22×C3semidirect
192. C4×Dic9C22×C3semidirect
224. C3×#124D9semidirect
332. C2×C3×Q8C2×D9semidirect
379. C3×C22⋊C4C2×D9semidirect
380. C3×C22⋊C4C2×D9semidirect
387. C3×C42C2×D9semidirect
475. #124C3×D9semidirect
487. C3×C9#538semidirect
579. C2×Q8C2×C3×D9semidirect
609. C22⋊C4C2×C3×D9semidirect
610. C22⋊C4C2×C3×D9semidirect
612. C42C2×C3×D9semidirect
681. C9C3×#538semidirect
761. C3#10589780direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1242
C3×#635092
C3×#635082
C3×#635012
C3×#634992
C3×#634482
C3×#634462
C3×#634452
C3×#634442
C3×#611⋊C42
C3×C22⋊C4×D92
C3×#634412
C3×#634382
C3×C4×D362
C3×#56783
#105897803