Finite Group Databasebeta

← C3×#10589739 #13152916

Subgroups — C3×#10589739 #13152916

Order 1728.

818 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×C22⋊Q8C211yesmaximal, characteristic, complemented
2C3×#63509C211yesmaximal, characteristic, complemented
3C3×#63508C211yesmaximal, characteristic, complemented
4C3×C4×#611C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
6C3×#63460C211yesmaximal, characteristic, complemented
7C3×#63460C211yesmaximal, characteristic, complemented
8C3×#63456C211yesmaximal, characteristic, complemented
9C3×#63456C211yesmaximal, characteristic, complemented
10C3×#63455C211yesmaximal, characteristic, complemented
11C3×#63454C211yesmaximal, characteristic, complemented
12C3×#63448C211yesmaximal, characteristic, complemented
13C3×#63444C211yesmaximal, characteristic
14C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
15C3×#63439C211yesmaximal, characteristic, complemented
16C3×#5637—31nomaximal
17#10589739C311yesmaximal, characteristic, direct product factor
18C23×C3×D9C2211yescharacteristic
19C2×C3×Q8×C9C2211yescharacteristic, complemented
20C22×C3×C4×C9C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C22×C3×Dic9C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic
24C2×C3×D36C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic, complemented
28C3×C9×C4⋊C4C2211yescharacteristic, complemented
29C3×C9×C4⋊C4C2211yescharacteristic, complemented
30C3×C9×C4⋊C4C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32C3×C9×C22⋊C4C2211yescharacteristic
33C3×#3676C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
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, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×C4⋊Dic9C2211yescharacteristic, complemented
46C3×C4⋊Dic9C2211yescharacteristic, 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
53C32×C22⋊Q8D311yescharacteristic
54C3×#947—31no—
55C3×#946—31no—
56C3×C4×#67—31no—
57C2×C3×(C2×D3)⋊C4—31no—
58C3×#898—31no—
59C3×#898—31no—
60C3×#894—31no—
61C3×#894—31no—
62C3×#893—31no—
63C3×#892—31no—
64C3×#886—31no—
65C3×#882—31no—
66C3×D3×C22⋊C4—31no—
67C3×#877—31no—
68C9×C22⋊Q8—21no—
69C9×C22⋊Q8C2×C311yescharacteristic, complemented
70#63509C2×C311yescharacteristic, complemented
71#63508C2×C311yescharacteristic, complemented
72C4×#611C2×C311yescharacteristic, complemented
73C2×(C2×D9)⋊C4C2×C311yescharacteristic, complemented
74#63460C2×C311yescharacteristic, complemented
75#63460C2×C311yescharacteristic, complemented
76#63456C2×C311yescharacteristic, complemented
77#63456C2×C311yescharacteristic, complemented
78#63455C2×C311yescharacteristic, complemented
79#63454C2×C311yescharacteristic, complemented
80#63448C2×C311yescharacteristic, complemented
81#63444C2×C311yescharacteristic
82C22⋊C4×D9C2×C311yescharacteristic, complemented
83#63439C2×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
91C3×Q8×C9—41no—
92C2×C3×C4×C9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98C2×C3×C4×C9C2311yescharacteristic
99C3×#611—22no—
100C2×C3×Dic9—22no—
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C3×D36—22no—
107C3×D36—41no—
108C3×C4×D9—22no—
109C3×C4×D9—41no—
110C3×C4×D9—41no—
111C3×#551—91no—
112#5637—31no—
113C23×C3×D3—31no—
114C2×C32×Q8C2×D311yescharacteristic
115C22×C32×C4C2×D311yescharacteristic
116C2×C3×#67—31no—
117C22×C3×Dic3—31no—
118C2×C3×D12—31no—
119C2×C3×D12—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C23×D9C22×C311yescharacteristic
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C4⋊C4C2×D311yescharacteristic
126C32×C4⋊C4C2×D311yescharacteristic
127C32×C22⋊C4C2×D311yescharacteristic
128C32×C22⋊C4C2×D311yescharacteristic
129C3×#217—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×(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×C4⋊Dic3—31no—
142C3×C4⋊Dic3—31no—
143C3×Dic3⋊C4—31no—
144C3×Dic3⋊C4—31no—
145C3×Dic3⋊C4—31no—
146C3×C4×Dic3—31no—
147C3×C4×Dic3—31no—
148C3×C4×Dic3—31no—
149C2×Q8×C9—21no—
150C2×Q8×C9C22×C311yescharacteristic, complemented
151C22×C4×C9—21no—
152C22×C4×C9C22×C311yescharacteristic
153C2×#611C22×C311yescharacteristic
154C22×Dic9C22×C311yescharacteristic
155C2×D36C22×C311yescharacteristic
156C2×D36C22×C311yescharacteristic
157C2×C4×D9C22×C311yescharacteristic
158C2×C4×D9C22×C311yescharacteristic
159C2×C4×D9C22×C311yescharacteristic, complemented
160C9×C4⋊C4—21no—
161C9×C4⋊C4—21no—
162C9×C4⋊C4—21no—
163C9×C4⋊C4C22×C311yescharacteristic, complemented
164C9×C4⋊C4C22×C311yescharacteristic, complemented
165C9×C4⋊C4C22×C311yescharacteristic, complemented
166C9×C22⋊C4—21no—
167C9×C22⋊C4—21no—
168C9×C22⋊C4C22×C311yescharacteristic
169C9×C22⋊C4C22×C311yescharacteristic
170#3676C22×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
177(C2×D9)⋊C4C22×C311yescharacteristic
178(C2×D9)⋊C4C22×C311yescharacteristic
179(C2×D9)⋊C4C22×C311yescharacteristic, complemented
180(C2×D9)⋊C4C22×C311yescharacteristic, complemented
181(C2×D9)⋊C4C22×C311yescharacteristic, complemented
182C4⋊Dic9C22×C311yescharacteristic, complemented
183C4⋊Dic9C22×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#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—21no—
222C3×C22⋊Q8—91no—
223C3×C22⋊Q8D911yescharacteristic, complemented
224C3×C22⋊Q8C3×D311yescharacteristic
225C3×#120—91no—
226C3×C4×D4—91no—
227C3×C4×D4—91no—
228C3×#117—91no—
229C3×#117—91no—
230C2×C3×C22⋊C4—91no—
231C2×C3×C22⋊C4—91no—
232#947—31no—
233#946—31no—
234C4×#67—31no—
235C2×(C2×D3)⋊C4—31no—
236#898—31no—
237#898—31no—
238#894—31no—
239#894—31no—
240#893—31no—
241#892—31no—
242#886—31no—
243#882—31no—
244D3×C22⋊C4—31no—
245#877—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—
253C32×Q8—41no—
254C2×C32×C4—41no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C32×C4C22×D311yescharacteristic
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C3×#67—62no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3—62no—
268C3×D12—62no—
269C3×D12—121no—
270C3×C4×D3—62no—
271C3×C4×D3—121no—
272C3×C4×D3—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
281Q8×C9—41no—
282Q8×C9—42no—
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×C9—41no—
290C2×C4×C9—42no—
291C2×C4×C9C23×C311yescharacteristic
292C2×C4×C9C23×C311yescharacteristic
293C2×C4×C9C23×C311yescharacteristic
294C2×C4×C9C23×C311yescharacteristic
295C2×C4×C9C23×C311yescharacteristic
296C2×C4×C9C23×C311yescharacteristic
297#611—22no—
298C2×Dic9—22no—
299C2×Dic9C23×C311yescharacteristic
300C2×Dic9C23×C311yescharacteristic
301C2×Dic9C23×C311yescharacteristic
302C2×Dic9C23×C311yescharacteristic
303C2×Dic9C23×C311yescharacteristic
304D36—22no—
305D36—41no—
306C4×D9—22no—
307C4×D9—41no—
308C4×D9—41no—
309#551—91noSylow
310C2×C3×C9—22no—
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314C3×D9—22no—
315C3×D9—41no—
316C3×D9—41no—
317C24×C3—91no—
318C23×D3—31no—
319C2×C3×Q8—21no—
320C2×C3×Q8C2×D911yescharacteristic, complemented
321C2×C3×Q8C2×C3×D311yescharacteristic
322C2×C3×D4—91no—
323C2×C3×D4—91no—
324C2×C3×D4—91no—
325C22×C3×C4—21no—
326C22×C3×C4—91no—
327C22×C3×C4—91no—
328C22×C3×C4—91no—
329C22×C3×C4—91no—
330C22×C3×C4C2×D911yescharacteristic
331C22×C3×C4C2×C3×D311yescharacteristic
332C2×#67—31no—
333C22×Dic3—31no—
334C2×D12—31no—
335C2×D12—31no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C4⋊C4—91no—
347C3×C4⋊C4C2×D911yescharacteristic, complemented
348C3×C4⋊C4C2×D911yescharacteristic, complemented
349C3×C4⋊C4C2×D911yescharacteristic, complemented
350C3×C4⋊C4C2×C3×D311yescharacteristic
351C3×C4⋊C4C2×C3×D311yescharacteristic
352C3×C4⋊C4C2×C3×D311yescharacteristic
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⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4C2×D911yescharacteristic
368C3×C22⋊C4C2×D911yescharacteristic
369C3×C22⋊C4C2×C3×D311yescharacteristic
370C3×C22⋊C4C2×C3×D311yescharacteristic
371C3×C42—91no—
372C3×C42—91no—
373C3×C42—91no—
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—
387C4⋊Dic3—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390Dic3⋊C4—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32#23912yes—
397C22×C32C23×D311yescharacteristic
398C2×C3×D3—32no—
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—61no—
407C2×C3×D3—124no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—21no—
414C3×Dic3—61no—
415C3×Dic3—61no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—22no—
423C22×C9—41no—
424C22×C9—41no—
425C22×C9C3×#4112yes—
426C22×C9C24×C311yescharacteristic
427C2×D9—21no—
428C2×D9—21no—
429C2×D9—21no—
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—21no—
433C2×D9—21no—
434C2×D9—21no—
435C2×D9—44no—
436C2×D9C3×#4112yes—
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—
448C4×C9—41no—
449Dic9—21no—
450Dic9—21no—
451Dic9—21no—
452Dic9—21no—
453Dic9—21no—
454#126—91no—
455#126—91no—
456#124—91no—
457#123—91no—
458#123—91no—
459#123—91no—
460C22⋊Q8—91no—
461C22⋊Q8C3×D911yescharacteristic, complemented
462#120—91no—
463C4×D4—91no—
464C4×D4—91no—
465#117—91no—
466#117—91no—
467C2×C22⋊C4—91no—
468C2×C22⋊C4—91no—
469C3×C9#55111yescharacteristic, complemented, Sylow
470C23×C3—21no—
471C23×C3—91no—
472C23×C3—91no—
473C23×C3—91no—
474C23×C3—182no—
475C23×C3—182no—
476C23×C3—361no—
477C23×C3C22×D911yescharacteristic
478C23×C3C22×C3×D311yescharacteristic
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—31no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3—121no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—42no—
488C3×D4—182no—
489C3×D4—182no—
490C3×D4—361no—
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—41no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—91no—
501C2×C3×C4—91no—
502C2×C3×C4—91no—
503C2×C3×C4—91no—
504C2×C3×C4—91no—
505C2×C3×C4—182no—
506C2×C3×C4—182no—
507C2×C3×C4—361no—
508C2×C3×C4—361no—
509C2×C3×C4C22×D911yescharacteristic
510C2×C3×C4C22×D911yescharacteristic
511C2×C3×C4C22×D911yescharacteristic
512C2×C3×C4C22×D911yescharacteristic
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C22×C3×D311yescharacteristic
516C2×C3×C4C22×C3×D311yescharacteristic
517C2×C3×C4C22×C3×D311yescharacteristic
518C2×C3×C4C22×C3×D311yescharacteristic
519C2×C3×C4C22×C3×D311yescharacteristic
520C2×C3×C4C22×C3×D311yescharacteristic
521#67—62no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—62no—
528D12—62no—
529D12—121no—
530C4×D3—62no—
531C4×D3—121no—
532C4×D3—121no—
533C2×C32—22no—
534C2×C32#100411yescharacteristic
535C2×C32C2×#23911yescharacteristic
536C2×C32D3×#4111yescharacteristic
537C3×D3—62no—
538C3×D3—121no—
539C3×D3—121no—
540C2×C9—22no—
541C2×C9—21no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—42no—
545C2×C9C2×C3×#4111yescharacteristic
546C2×C9C2×C3×#4111yescharacteristic
547C2×C9C3×H(5,𝔽2)11yescharacteristic
548D9—22no—
549D9—41no—
550D9—41no—
551C24—91no—
552C2×Q8C2×C3×D911yescharacteristic, complemented
553C2×D4—91no—
554C2×D4—91no—
555C2×D4—91no—
556C22×C4—91no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—91no—
560C22×C4C2×C3×D911yescharacteristic
561C4⋊C4—91no—
562C4⋊C4—91no—
563C4⋊C4—91no—
564C4⋊C4—91no—
565C4⋊C4—91no—
566C4⋊C4C2×C3×D911yescharacteristic, complemented
567C4⋊C4C2×C3×D911yescharacteristic, complemented
568C4⋊C4C2×C3×D911yescharacteristic, complemented
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⋊C4—91no—
580C22⋊C4—91no—
581C22⋊C4C2×C3×D911yescharacteristic
582C22⋊C4C2×C3×D911yescharacteristic
583C42—91no—
584C42—91no—
585C42—91no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—22no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—92no—
595C22×C3—181no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3—181no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3—181no—
603C22×C3—364no—
604C22×C3#370112yes—
605C22×C3C23×D911yescharacteristic
606C22×C3C3×#23912yes—
607C22×C3C23×C3×D311yescharacteristic
608C2×D3—32no—
609C2×D3—61no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—124no—
618C3×C4—22no—
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—21no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—181no—
637C3×C4—181no—
638C3×C4—181no—
639C3×C4—181no—
640C3×C4—181no—
641Dic3—61no—
642Dic3—61no—
643Dic3—61no—
644Dic3—61no—
645Dic3—61no—
646C32#563711yescharacteristic
647C9—21no—
648C9C3×#55111yescharacteristic, complemented
649C23—91no—
650C23—91no—
651C23—91no—
652C23—182no—
653C23—182no—
654C23—361no—
655C23C22×C3×D911yescharacteristic
656Q8—41no—
657D4—182no—
658D4—182no—
659D4—361no—
660C2×C4—41no—
661C2×C4—91no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—182no—
667C2×C4—182no—
668C2×C4—361no—
669C2×C4—361no—
670C2×C4C22×C3×D911yescharacteristic
671C2×C4C22×C3×D911yescharacteristic
672C2×C4C22×C3×D911yescharacteristic
673C2×C4C22×C3×D911yescharacteristic
674C2×C4C22×C3×D911yescharacteristic
675C2×C4C22×C3×D911yescharacteristic
676C2×C3—22no—
677C2×C3—22no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—42no—
682C2×C3—182no—
683C2×C3—361no—
684C2×C3—361no—
685C2×C3#6371011yescharacteristic
686C2×C3C2×#370111yescharacteristic
687C2×C3#41×D911yescharacteristic
688C2×C3C3×#100411yescharacteristic
689C2×C3C2×C3×#23911yescharacteristic
690C2×C3C3×D3×#4111yescharacteristic
691D3—62no—
692D3—121no—
693D3—121no—
694C22—21no—
695C22—21no—
696C22—92no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22—181no—
703C22—181no—
704C22—181no—
705C22—364no—
706C22C3×#370112yes—
707C22C23×C3×D911yescharacteristic
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—21no—
713C4—21no—
714C4—181no—
715C4—181no—
716C4—181no—
717C4—181no—
718C4—181no—
719C3—21no—
720C3#1058973911yescharacteristic, direct product factor
721C3C3×#563711yescharacteristic
722C2—22no—
723C2—182no—
724C2—361no—
725C2—361no—
726C2C3×#6371011yescharacteristic
727C2C2×C3×#370111yescharacteristic
728C2C3×#41×D911yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×C22⋊Q8C2
socleC22×C32C23×D3
prime radicalC3×#63444C2
hypercenterC3×C22⋊Q8D9
hypocenterC9C3×#551
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×C9×C22⋊Q8C2semidirect
2. C3×#63509C2semidirect
3. C3×#63508C2semidirect
4. C3×C4×#611C2semidirect
5. C2×C3×(C2×D9)⋊C4C2semidirect
6. C3×#63460C2semidirect
7. C3×#63460C2semidirect
8. C3×#63456C2semidirect
9. C3×#63456C2semidirect
10. C3×#63455C2semidirect
11. C3×#63454C2semidirect
12. C3×#63448C2semidirect
14. C3×C22⋊C4×D9C2semidirect
15. C3×#63439C2semidirect
17. #10589739C3direct (N × H)
19. C2×C3×Q8×C9C22semidirect
27. C2×C3×C4×D9C22semidirect
28. C3×C9×C4⋊C4C22semidirect
29. C3×C9×C4⋊C4C22semidirect
30. C3×C9×C4⋊C4C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×C4⋊Dic9C22semidirect
46. C3×C4⋊Dic9C22semidirect
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. C9×C22⋊Q8C2×C3semidirect
70. #63509C2×C3semidirect
71. #63508C2×C3semidirect
72. C4×#611C2×C3semidirect
73. C2×(C2×D9)⋊C4C2×C3semidirect
74. #63460C2×C3semidirect
75. #63460C2×C3semidirect
76. #63456C2×C3semidirect
77. #63456C2×C3semidirect
78. #63455C2×C3semidirect
79. #63454C2×C3semidirect
80. #63448C2×C3semidirect
82. C22⋊C4×D9C2×C3semidirect
83. #63439C2×C3semidirect
150. C2×Q8×C9C22×C3semidirect
159. C2×C4×D9C22×C3semidirect
163. C9×C4⋊C4C22×C3semidirect
164. C9×C4⋊C4C22×C3semidirect
165. C9×C4⋊C4C22×C3semidirect
179. (C2×D9)⋊C4C22×C3semidirect
180. (C2×D9)⋊C4C22×C3semidirect
181. (C2×D9)⋊C4C22×C3semidirect
182. C4⋊Dic9C22×C3semidirect
183. C4⋊Dic9C22×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
223. C3×C22⋊Q8D9semidirect
320. C2×C3×Q8C2×D9semidirect
347. C3×C4⋊C4C2×D9semidirect
348. C3×C4⋊C4C2×D9semidirect
349. C3×C4⋊C4C2×D9semidirect
461. C22⋊Q8C3×D9semidirect
469. C3×C9#551semidirect
552. C2×Q8C2×C3×D9semidirect
566. C4⋊C4C2×C3×D9semidirect
567. C4⋊C4C2×C3×D9semidirect
568. C4⋊C4C2×C3×D9semidirect
648. C9C3×#551semidirect
720. C3#10589739direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×C22⋊Q82
C3×#635092
C3×#635082
C3×C4×#6112
C2×C3×(C2×D9)⋊C42
C3×#634602
C3×#634562
C3×#634552
C3×#634542
C3×#634482
C3×#634442
C3×C22⋊C4×D92
C3×#634392
C3×#56373
#105897393