Finite Group Databasebeta

← C3×#10589597 #13152343

Subgroups — C3×#10589597 #13152343

Order 1728.

876 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
2C3×#63515C211yesmaximal, characteristic
3C2×C3×#3676C211yesmaximal, characteristic, complemented
4C3×#63491C211yesmaximal, characteristic, complemented
5C3×C4×#611C211yesmaximal, characteristic, complemented
6C3×#63488C211yesmaximal, characteristic, complemented
7C3×#63486C211yesmaximal, characteristic, complemented
8C3×#63448C211yesmaximal, characteristic, complemented
9C3×#63447C211yesmaximal, characteristic, complemented
10C3×#63445C211yesmaximal, characteristic, complemented
11C3×#611⋊C4C211yesmaximal, characteristic, complemented
12C3×#63441C211yesmaximal, characteristic, complemented
13C3×#63441C211yesmaximal, characteristic, complemented
14C3×#63440C211yesmaximal, characteristic, complemented
15C3×#63439C211yesmaximal, characteristic, complemented
16C3×#5495—31nomaximal
17#10589597C311yesmaximal, characteristic, direct product factor
18C24×C3×C9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C22×C3×Dic9C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic, complemented
27C2×C3×Dic18C2211yescharacteristic, complemented
28C3×C9×C22⋊C4C2211yescharacteristic
29C3×C9×C22⋊C4C2211yescharacteristic
30C3×C9×C22⋊C4C2211yescharacteristic
31C3×C9×C22⋊C4C2211yescharacteristic
32C3×#3676C2211yescharacteristic
33C3×#3676C2211yescharacteristic
34C3×#3676C2211yescharacteristic
35C3×#3676C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C3×#3676C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C3×C4⋊Dic9C2211yescharacteristic, complemented
43C3×C4⋊Dic9C2211yescharacteristic, complemented
44C3×C4⋊Dic9C2211yescharacteristic, complemented
45C3×Dic9⋊C4C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49C3×Dic9⋊C4C2211yescharacteristic, complemented
50C3×C4×Dic9C2211yescharacteristic, complemented
51C3×C4×Dic9C2211yescharacteristic, complemented
52C3×C4×Dic9C2211yescharacteristic, complemented
53C2×C32×C22⋊C4D311yescharacteristic
54C3×#953—31no—
55C2×C3×#217—31no—
56C3×#929—31no—
57C3×C4×#67—31no—
58C3×#926—31no—
59C3×#924—31no—
60C3×#886—31no—
61C3×#885—31no—
62C3×#883—31no—
63C3×#67⋊C4—31no—
64C3×#879—31no—
65C3×#879—31no—
66C3×#878—31no—
67C3×#877—31no—
68C2×C9×C22⋊C4—21no—
69C2×C9×C22⋊C4C2×C311yescharacteristic, complemented
70#63515C2×C311yescharacteristic
71C2×#3676C2×C311yescharacteristic, complemented
72#63491C2×C311yescharacteristic, complemented
73C4×#611C2×C311yescharacteristic, complemented
74#63488C2×C311yescharacteristic, complemented
75#63486C2×C311yescharacteristic, complemented
76#63448C2×C311yescharacteristic, complemented
77#63447C2×C311yescharacteristic, complemented
78#63445C2×C311yescharacteristic, complemented
79#611⋊C4C2×C311yescharacteristic, complemented
80#63441C2×C311yescharacteristic, complemented
81#63441C2×C311yescharacteristic, complemented
82#63440C2×C311yescharacteristic, complemented
83#63439C2×C311yescharacteristic, complemented
84C23×C3×C9—22no—
85C23×C3×C9—22no—
86C23×C3×C9—41no—
87C23×C3×C9C2311yescharacteristic
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9—22no—
92C2×C3×C4×C9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C3×#611—22no—
98C3×#611—22no—
99C3×#611—41no—
100C2×C3×Dic9—22no—
101C2×C3×Dic9—41no—
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C3×C4×D9—41no—
110C3×Dic18—41no—
111C3×#551—91no—
112#5495—31no—
113C24×C32C2×D311yescharacteristic
114C22×C32×C4C2×D311yescharacteristic
115C22×C32×C4C2×D311yescharacteristic
116C2×C3×#67—31no—
117C2×C3×#67—31no—
118C2×C3×#67—31no—
119C22×C3×Dic3—31no—
120C22×C3×Dic3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×Dic6—31no—
123C24×C9—21no—
124C24×C9C22×C311yescharacteristic
125C32×C22⋊C4C2×D311yescharacteristic
126C32×C22⋊C4C2×D311yescharacteristic
127C32×C22⋊C4C2×D311yescharacteristic
128C32×C22⋊C4C2×D311yescharacteristic
129C3×#217—31no—
130C3×#217—31no—
131C3×#217—31no—
132C3×#217—31no—
133C3×#217—31no—
134C3×#217—31no—
135C3×#217—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×C4⋊Dic3—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×Dic3⋊C4—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C22×C4×C9—21no—
151C22×C4×C9—21no—
152C22×C4×C9C22×C311yescharacteristic
153C22×C4×C9C22×C311yescharacteristic
154C2×#611C22×C311yescharacteristic
155C2×#611C22×C311yescharacteristic
156C2×#611C22×C311yescharacteristic
157C22×Dic9C22×C311yescharacteristic
158C22×Dic9C22×C311yescharacteristic
159C2×C4×D9C22×C311yescharacteristic, complemented
160C2×Dic18C22×C311yescharacteristic, complemented
161C9×C22⋊C4—21no—
162C9×C22⋊C4—21no—
163C9×C22⋊C4—21no—
164C9×C22⋊C4—21no—
165C9×C22⋊C4C22×C311yescharacteristic
166C9×C22⋊C4C22×C311yescharacteristic
167C9×C22⋊C4C22×C311yescharacteristic
168C9×C22⋊C4C22×C311yescharacteristic
169#3676C22×C311yescharacteristic
170#3676C22×C311yescharacteristic
171#3676C22×C311yescharacteristic
172#3676C22×C311yescharacteristic
173#3676C22×C311yescharacteristic
174#3676C22×C311yescharacteristic
175#3676C22×C311yescharacteristic
176(C2×D9)⋊C4C22×C311yescharacteristic, complemented
177(C2×D9)⋊C4C22×C311yescharacteristic, complemented
178(C2×D9)⋊C4C22×C311yescharacteristic, complemented
179C4⋊Dic9C22×C311yescharacteristic, complemented
180C4⋊Dic9C22×C311yescharacteristic, complemented
181C4⋊Dic9C22×C311yescharacteristic, complemented
182Dic9⋊C4C22×C311yescharacteristic, complemented
183Dic9⋊C4C22×C311yescharacteristic, complemented
184Dic9⋊C4C22×C311yescharacteristic, complemented
185Dic9⋊C4C22×C311yescharacteristic, complemented
186Dic9⋊C4C22×C311yescharacteristic, complemented
187C4×Dic9C22×C311yescharacteristic, complemented
188C4×Dic9C22×C311yescharacteristic, complemented
189C4×Dic9C22×C311yescharacteristic, complemented
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9—21no—
197C22×C3×C9—44no—
198C22×C3×C9#4112yes—
199C22×C3×C9#4112yes—
200C22×C3×C9C2411yescharacteristic
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C2×C3×D9—21no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3×C4×C9—21no—
207C3×C4×C9—21no—
208C3×Dic9—21no—
209C3×Dic9—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—91no—
227C3×#117—91no—
228C2×C3×C22⋊C4—21no—
229C2×C3×C22⋊C4—91no—
230C2×C3×C22⋊C4D911yescharacteristic, complemented
231C2×C3×C22⋊C4C3×D311yescharacteristic
232#953—31no—
233C2×#217—31no—
234#929—31no—
235C4×#67—31no—
236#926—31no—
237#924—31no—
238#886—31no—
239#885—31no—
240#883—31no—
241#67⋊C4—31no—
242#879—31no—
243#879—31no—
244#878—31no—
245#877—31no—
246C23×C32—22no—
247C23×C32—22no—
248C23×C32—41no—
249C23×C32C22×D311yescharacteristic
250C23×C32C22×D311yescharacteristic
251C23×C32C22×D311yescharacteristic
252C22×C3×D3—31no—
253C2×C32×C4—22no—
254C2×C32×C4—41no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C3×#67—62no—
260C3×#67—62no—
261C3×#67—121no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—62no—
270C2×C3×Dic3—121no—
271C3×C4×D3—121no—
272C3×Dic6—121no—
273C23×C9—24no—
274C23×C9—22no—
275C23×C9—22no—
276C23×C9—21no—
277C23×C9—21no—
278C23×C9—21no—
279C23×C9—42no—
280C23×C9—41no—
281C23×C9—42no—
282C23×C9C23×C311yescharacteristic
283C23×C9C23×C311yescharacteristic
284C23×C9C23×C311yescharacteristic
285C22×D9C23×C311yescharacteristic
286C2×C4×C9—22no—
287C2×C4×C9—21no—
288C2×C4×C9—21no—
289C2×C4×C9—21no—
290C2×C4×C9—21no—
291C2×C4×C9—42no—
292C2×C4×C9—41no—
293C2×C4×C9—42no—
294C2×C4×C9C23×C311yescharacteristic
295C2×C4×C9C23×C311yescharacteristic
296C2×C4×C9C23×C311yescharacteristic
297C2×C4×C9C23×C311yescharacteristic
298#611—22no—
299#611—22no—
300#611—41no—
301C2×Dic9—22no—
302C2×Dic9—41no—
303C2×Dic9C23×C311yescharacteristic
304C2×Dic9C23×C311yescharacteristic
305C2×Dic9C23×C311yescharacteristic
306C2×Dic9C23×C311yescharacteristic
307C2×Dic9C23×C311yescharacteristic
308C2×Dic9C23×C311yescharacteristic
309C2×Dic9C23×C311yescharacteristic
310C4×D9—41no—
311Dic18—41no—
312#551—91noSylow
313C2×C3×C9—22no—
314C2×C3×C9—22no—
315C2×C3×C9—41no—
316C2×C3×C9C2×#4111yescharacteristic
317C2×C3×C9C2×#4111yescharacteristic
318C2×C3×C9H(5,𝔽2)11yescharacteristic
319C3×D9—41no—
320C24×C3—21no—
321C24×C3C2×D911yescharacteristic
322C24×C3C2×C3×D311yescharacteristic
323C2×C3×Q8—91no—
324C2×C3×D4—91no—
325C2×C3×D4—91no—
326C2×C3×D4—91no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—91no—
330C22×C3×C4—91no—
331C22×C3×C4—91no—
332C22×C3×C4C2×D911yescharacteristic
333C22×C3×C4C2×D911yescharacteristic
334C22×C3×C4C2×C3×D311yescharacteristic
335C22×C3×C4C2×C3×D311yescharacteristic
336C2×#67—31no—
337C2×#67—31no—
338C2×#67—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C2×C4×D3—31no—
342C2×Dic6—31no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4—91no—
348C3×C4⋊C4—91no—
349C3×C4⋊C4—91no—
350C3×C4⋊C4—91no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
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⋊C4—91no—
364C3×C22⋊C4—91no—
365C3×C22⋊C4C2×D911yescharacteristic
366C3×C22⋊C4C2×D911yescharacteristic
367C3×C22⋊C4C2×D911yescharacteristic
368C3×C22⋊C4C2×D911yescharacteristic
369C3×C22⋊C4C2×C3×D311yescharacteristic
370C3×C22⋊C4C2×C3×D311yescharacteristic
371C3×C22⋊C4C2×C3×D311yescharacteristic
372C3×C22⋊C4C2×C3×D311yescharacteristic
373C3×C42—91no—
374C3×C42—91no—
375C3×C42—91no—
376#217—31no—
377#217—31no—
378#217—31no—
379#217—31no—
380#217—31no—
381#217—31no—
382#217—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—31no—
385(C2×D3)⋊C4—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—44no—
405C22×C32#23512yes—
406C22×C32#23712yes—
407C22×C32C23×D311yescharacteristic
408C2×C3×D3—61no—
409C2×C3×D3—61no—
410C2×C3×D3—61no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C3×Dic3—61no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C3×Dic3—61no—
420C3×Dic3—61no—
421C3×Dic3—61no—
422C22×C9—22no—
423C22×C9—22no—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—21no—
427C22×C9—21no—
428C22×C9—22no—
429C22×C9—21no—
430C22×C9—21no—
431C22×C9—21no—
432C22×C9—21no—
433C22×C9—22no—
434C22×C9—22no—
435C22×C9—41no—
436C22×C9—41no—
437C22×C9—41no—
438C22×C9—41no—
439C22×C9—44no—
440C22×C9—48no—
441C22×C9C3×#4112yes—
442C22×C9C3×#4112yes—
443C22×C9C24×C311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C4×C9—21no—
448C4×C9—21no—
449C4×C9—21no—
450C4×C9—21no—
451C4×C9—41no—
452C4×C9—41no—
453C4×C9—41no—
454C4×C9—41no—
455Dic9—21no—
456Dic9—21no—
457Dic9—21no—
458Dic9—21no—
459Dic9—21no—
460Dic9—21no—
461Dic9—21no—
462#126—91no—
463#126—91no—
464#124—91no—
465#123—91no—
466#123—91no—
467#123—91no—
468C22⋊Q8—91no—
469C22⋊Q8—91no—
470#120—91no—
471C4×D4—91no—
472C4×D4—91no—
473#117—91no—
474#117—91no—
475C2×C22⋊C4—91no—
476C2×C22⋊C4C3×D911yescharacteristic, complemented
477C3×C9#55111yescharacteristic, complemented, Sylow
478C23×C3—24no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—42no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—42no—
490C23×C3—91no—
491C23×C3C22×D911yescharacteristic
492C23×C3C22×D911yescharacteristic
493C23×C3C22×D911yescharacteristic
494C23×C3C22×C3×D311yescharacteristic
495C23×C3C22×C3×D311yescharacteristic
496C23×C3C22×C3×D311yescharacteristic
497C22×D3—31no—
498C3×Q8—361no—
499C3×D4—182no—
500C3×D4—182no—
501C3×D4—361no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—42no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—42no—
512C2×C3×C4—91no—
513C2×C3×C4—91no—
514C2×C3×C4—91no—
515C2×C3×C4—91no—
516C2×C3×C4—91no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—182no—
520C2×C3×C4—361no—
521C2×C3×C4—361no—
522C2×C3×C4C22×D911yescharacteristic
523C2×C3×C4C22×D911yescharacteristic
524C2×C3×C4C22×D911yescharacteristic
525C2×C3×C4C22×D911yescharacteristic
526C2×C3×C4C22×C3×D311yescharacteristic
527C2×C3×C4C22×C3×D311yescharacteristic
528C2×C3×C4C22×C3×D311yescharacteristic
529C2×C3×C4C22×C3×D311yescharacteristic
530#67—62no—
531#67—62no—
532#67—121no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—62no—
541C2×Dic3—121no—
542C4×D3—121no—
543Dic6—121no—
544C2×C32—22no—
545C2×C32—22no—
546C2×C32—41no—
547C2×C32C2×#23511yescharacteristic
548C2×C32C2×#23711yescharacteristic
549C2×C32#100411yescharacteristic
550C3×D3—121no—
551C2×C9—24no—
552C2×C9—22no—
553C2×C9—22no—
554C2×C9—21no—
555C2×C9—21no—
556C2×C9—21no—
557C2×C9—42no—
558C2×C9—42no—
559C2×C9—41no—
560C2×C9C2×C3×#4111yescharacteristic
561C2×C9C2×C3×#4111yescharacteristic
562C2×C9C3×H(5,𝔽2)11yescharacteristic
563D9—41no—
564C24C2×C3×D911yescharacteristic
565C2×Q8—91no—
566C2×D4—91no—
567C2×D4—91no—
568C2×D4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4—91no—
572C22×C4C2×C3×D911yescharacteristic
573C22×C4C2×C3×D911yescharacteristic
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C22⋊C4—91no—
583C22⋊C4—91no—
584C22⋊C4—91no—
585C22⋊C4—91no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4C2×C3×D911yescharacteristic
593C22⋊C4C2×C3×D911yescharacteristic
594C22⋊C4C2×C3×D911yescharacteristic
595C22⋊C4C2×C3×D911yescharacteristic
596C42—91no—
597C42—91no—
598C42—91no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—22no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—44no—
624C22×C3—44no—
625C22×C3—48no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3#369712yes—
630C22×C3#369912yes—
631C22×C3C23×D911yescharacteristic
632C22×C3C3×#23512yes—
633C22×C3C3×#23712yes—
634C22×C3C23×C3×D311yescharacteristic
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—181no—
651C3×C4—181no—
652C3×C4—181no—
653C3×C4—181no—
654C3×C4—181no—
655C3×C4—181no—
656C3×C4—181no—
657Dic3—61no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664C32#549511yescharacteristic
665C9—21no—
666C9C3×#55111yescharacteristic, complemented
667C23—22no—
668C23—22no—
669C23—41no—
670C23—91no—
671C23C22×C3×D911yescharacteristic
672C23C22×C3×D911yescharacteristic
673C23C22×C3×D911yescharacteristic
674Q8—361no—
675D4—182no—
676D4—182no—
677D4—361no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—91no—
681C2×C4—91no—
682C2×C4—91no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—91no—
687C2×C4—182no—
688C2×C4—361no—
689C2×C4—361no—
690C2×C4C22×C3×D911yescharacteristic
691C2×C4C22×C3×D911yescharacteristic
692C2×C4C22×C3×D911yescharacteristic
693C2×C4C22×C3×D911yescharacteristic
694C2×C3—24no—
695C2×C3—22no—
696C2×C3—22no—
697C2×C3—22no—
698C2×C3—22no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—42no—
703C2×C3—42no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3—361no—
707C2×C3C2×#369711yescharacteristic
708C2×C3C2×#369911yescharacteristic
709C2×C3#6371011yescharacteristic
710C2×C3C2×C3×#23511yescharacteristic
711C2×C3C2×C3×#23711yescharacteristic
712C2×C3C3×#100411yescharacteristic
713D3—121no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—44no—
722C22—181no—
723C22—181no—
724C22—181no—
725C22C3×#369712yes—
726C22C3×#369912yes—
727C22C23×C3×D911yescharacteristic
728C4—21no—
729C4—21no—
730C4—21no—
731C4—21no—
732C4—181no—
733C4—181no—
734C4—181no—
735C4—181no—
736C4—181no—
737C4—181no—
738C4—181no—
739C3—21no—
740C3#1058959711yescharacteristic, direct product factor
741C3C3×#549511yescharacteristic
742C2—22no—
743C2—22no—
744C2—41no—
745C2—361no—
746C2C2×C3×#369711yescharacteristic
747C2C2×C3×#369911yescharacteristic
748C2C3×#6371011yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC2×C3×C9×C22⋊C4C2
socleC22×C32C23×D3
prime radicalC3×#63515C2
hypercenterC2×C3×C22⋊C4D9
hypocenterC9C3×#551
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C2×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C9×C22⋊C4C2semidirect
3. C2×C3×#3676C2semidirect
4. C3×#63491C2semidirect
5. C3×C4×#611C2semidirect
6. C3×#63488C2semidirect
7. C3×#63486C2semidirect
8. C3×#63448C2semidirect
9. C3×#63447C2semidirect
10. C3×#63445C2semidirect
11. C3×#611⋊C4C2semidirect
12. C3×#63441C2semidirect
13. C3×#63441C2semidirect
14. C3×#63440C2semidirect
15. C3×#63439C2semidirect
17. #10589597C3direct (N × H)
26. C2×C3×C4×D9C22semidirect
27. C2×C3×Dic18C22semidirect
39. C3×(C2×D9)⋊C4C22semidirect
40. C3×(C2×D9)⋊C4C22semidirect
41. C3×(C2×D9)⋊C4C22semidirect
42. C3×C4⋊Dic9C22semidirect
43. C3×C4⋊Dic9C22semidirect
44. C3×C4⋊Dic9C22semidirect
45. C3×Dic9⋊C4C22semidirect
46. C3×Dic9⋊C4C22semidirect
47. C3×Dic9⋊C4C22semidirect
48. C3×Dic9⋊C4C22semidirect
49. C3×Dic9⋊C4C22semidirect
50. C3×C4×Dic9C22semidirect
51. C3×C4×Dic9C22semidirect
52. C3×C4×Dic9C22semidirect
69. C2×C9×C22⋊C4C2×C3semidirect
71. C2×#3676C2×C3semidirect
72. #63491C2×C3semidirect
73. C4×#611C2×C3semidirect
74. #63488C2×C3semidirect
75. #63486C2×C3semidirect
76. #63448C2×C3semidirect
77. #63447C2×C3semidirect
78. #63445C2×C3semidirect
79. #611⋊C4C2×C3semidirect
80. #63441C2×C3semidirect
81. #63441C2×C3semidirect
82. #63440C2×C3semidirect
83. #63439C2×C3semidirect
159. C2×C4×D9C22×C3semidirect
160. C2×Dic18C22×C3semidirect
176. (C2×D9)⋊C4C22×C3semidirect
177. (C2×D9)⋊C4C22×C3semidirect
178. (C2×D9)⋊C4C22×C3semidirect
179. C4⋊Dic9C22×C3semidirect
180. C4⋊Dic9C22×C3semidirect
181. C4⋊Dic9C22×C3semidirect
182. Dic9⋊C4C22×C3semidirect
183. Dic9⋊C4C22×C3semidirect
184. Dic9⋊C4C22×C3semidirect
185. Dic9⋊C4C22×C3semidirect
186. Dic9⋊C4C22×C3semidirect
187. C4×Dic9C22×C3semidirect
188. C4×Dic9C22×C3semidirect
189. C4×Dic9C22×C3semidirect
230. C2×C3×C22⋊C4D9semidirect
476. C2×C22⋊C4C3×D9semidirect
477. C3×C9#551semidirect
666. C9C3×#551semidirect
740. C3#10589597direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C9×C22⋊C42
C3×#635152
C2×C3×#36762
C3×#634912
C3×C4×#6112
C3×#634882
C3×#634862
C3×#634482
C3×#634472
C3×#634452
C3×#611⋊C42
C3×#634412
C3×#634402
C3×#634392
C3×#54953
#105895973