Finite Group Databasebeta

← C3×#10589748 #13152923

Subgroups — C3×#10589748 #13152923

Order 1728.

662 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×C22⋊Q8C211yesmaximal, characteristic, complemented
2C3×#63508C211yesmaximal, characteristic, complemented
3C3×#63506C211yesmaximal, characteristic, complemented
4C3×#63491C211yesmaximal, characteristic
5C3×#63486C211yesmaximal, characteristic, complemented
6C3×#63460C211yesmaximal, characteristic, complemented
7C3×#63460C211yesmaximal, characteristic, complemented
8C3×#63458C211yesmaximal, characteristic, complemented
9C3×#63452C211yesmaximal, characteristic, complemented
10C3×#63451C211yesmaximal, characteristic, complemented
11C3×#63450C211yesmaximal, characteristic, complemented
12C3×#63447C211yesmaximal, characteristic
13C3×#63445C211yesmaximal, characteristic
14C3×#63441C211yesmaximal, characteristic, complemented
15C3×#63441C211yesmaximal, characteristic, complemented
16C3×#5646—31nomaximal
17#10589748C311yesmaximal, characteristic, direct product factor
18C2×C3×Q8×C9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C3×Dic18C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic
24C3×C9×C4⋊C4C2211yescharacteristic
25C3×C9×C4⋊C4C2211yescharacteristic
26C3×C9×C4⋊C4C2211yescharacteristic
27C3×C9×C22⋊C4C2211yescharacteristic
28C3×C9×C22⋊C4C2211yescharacteristic
29C3×#3676C2211yescharacteristic
30C3×#3676C2211yescharacteristic
31C3×#3676C2211yescharacteristic
32C3×(C2×D9)⋊C4C2211yescharacteristic
33C3×(C2×D9)⋊C4C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×C4⋊Dic9C2211yescharacteristic
38C3×C4⋊Dic9C2211yescharacteristic
39C3×C4⋊Dic9C2211yescharacteristic
40C3×C4⋊Dic9C2211yescharacteristic
41C3×Dic9⋊C4C2211yescharacteristic
42C3×Dic9⋊C4C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×Dic9⋊C4C2211yescharacteristic
50C3×C4×Dic9C2211yescharacteristic
51C3×C4×Dic9C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×C22⋊Q8D311yescharacteristic
54C3×#946—31no—
55C3×#944—31no—
56C3×#929—31no—
57C3×#924—31no—
58C3×#898—31no—
59C3×#898—31no—
60C3×#896—31no—
61C3×#890—31no—
62C3×#889—31no—
63C3×#888—31no—
64C3×#885—31no—
65C3×#883—31no—
66C3×#879—31no—
67C3×#879—31no—
68C9×C22⋊Q8—21no—
69C9×C22⋊Q8C2×C311yescharacteristic, complemented
70#63508C2×C311yescharacteristic, complemented
71#63506C2×C311yescharacteristic, complemented
72#63491C2×C311yescharacteristic
73#63486C2×C311yescharacteristic, complemented
74#63460C2×C311yescharacteristic, complemented
75#63460C2×C311yescharacteristic, complemented
76#63458C2×C311yescharacteristic, complemented
77#63452C2×C311yescharacteristic, complemented
78#63451C2×C311yescharacteristic, complemented
79#63450C2×C311yescharacteristic, complemented
80#63447C2×C311yescharacteristic
81#63445C2×C311yescharacteristic
82#63441C2×C311yescharacteristic, complemented
83#63441C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C3×Q8×C9—41no—
87C2×C3×C4×C9—41no—
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—41no—
95C2×C3×Dic9C2311yescharacteristic
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C3×C4×D9—41no—
103C3×Dic18—41no—
104C3×Dic18—41no—
105C3×#563—91no—
106#5646—31no—
107C2×C32×Q8C2×D311yescharacteristic
108C22×C32×C4C2×D311yescharacteristic
109C2×C3×#67—31no—
110C2×C3×C4×D3—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—31no—
113C32×C4⋊C4C2×D311yescharacteristic
114C32×C4⋊C4C2×D311yescharacteristic
115C32×C4⋊C4C2×D311yescharacteristic
116C32×C22⋊C4C2×D311yescharacteristic
117C32×C22⋊C4C2×D311yescharacteristic
118C3×#217—31no—
119C3×#217—31no—
120C3×#217—31no—
121C3×(C2×D3)⋊C4—31no—
122C3×(C2×D3)⋊C4—31no—
123C3×(C2×D3)⋊C4—31no—
124C3×(C2×D3)⋊C4—31no—
125C3×(C2×D3)⋊C4—31no—
126C3×C4⋊Dic3—31no—
127C3×C4⋊Dic3—31no—
128C3×C4⋊Dic3—31no—
129C3×C4⋊Dic3—31no—
130C3×Dic3⋊C4—31no—
131C3×Dic3⋊C4—31no—
132C3×Dic3⋊C4—31no—
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137C3×Dic3⋊C4—31no—
138C3×Dic3⋊C4—31no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3—31no—
141C3×C4×Dic3—31no—
142C2×Q8×C9—21no—
143C2×Q8×C9C22×C311yescharacteristic
144C22×C4×C9—21no—
145C22×C4×C9C22×C311yescharacteristic
146C2×#611C22×C311yescharacteristic
147C2×C4×D9C22×C311yescharacteristic
148C2×Dic18C22×C311yescharacteristic
149C2×Dic18C22×C311yescharacteristic
150C9×C4⋊C4—21no—
151C9×C4⋊C4—21no—
152C9×C4⋊C4—21no—
153C9×C4⋊C4C22×C311yescharacteristic
154C9×C4⋊C4C22×C311yescharacteristic
155C9×C4⋊C4C22×C311yescharacteristic
156C9×C22⋊C4—21no—
157C9×C22⋊C4—21no—
158C9×C22⋊C4C22×C311yescharacteristic
159C9×C22⋊C4C22×C311yescharacteristic
160#3676C22×C311yescharacteristic
161#3676C22×C311yescharacteristic
162#3676C22×C311yescharacteristic
163(C2×D9)⋊C4C22×C311yescharacteristic
164(C2×D9)⋊C4C22×C311yescharacteristic
165(C2×D9)⋊C4C22×C311yescharacteristic
166(C2×D9)⋊C4C22×C311yescharacteristic
167(C2×D9)⋊C4C22×C311yescharacteristic
168C4⋊Dic9C22×C311yescharacteristic
169C4⋊Dic9C22×C311yescharacteristic
170C4⋊Dic9C22×C311yescharacteristic
171C4⋊Dic9C22×C311yescharacteristic
172Dic9⋊C4C22×C311yescharacteristic
173Dic9⋊C4C22×C311yescharacteristic
174Dic9⋊C4C22×C311yescharacteristic
175Dic9⋊C4C22×C311yescharacteristic
176Dic9⋊C4C22×C311yescharacteristic
177Dic9⋊C4C22×C311yescharacteristic
178Dic9⋊C4C22×C311yescharacteristic
179Dic9⋊C4C22×C311yescharacteristic
180Dic9⋊C4C22×C311yescharacteristic
181C4×Dic9C22×C311yescharacteristic
182C4×Dic9C22×C311yescharacteristic
183C4×Dic9C22×C311yescharacteristic
184C22×C3×C9—21no—
185C22×C3×C9—21no—
186C22×C3×C9—21no—
187C22×C3×C9C2411yescharacteristic
188C2×C3×D9—21no—
189C2×C3×D9—21no—
190C2×C3×D9—21no—
191C3×C4×C9—21no—
192C3×C4×C9—21no—
193C3×C4×C9—21no—
194C3×C4×C9—21no—
195C3×C4×C9—21no—
196C3×C4×C9—21no—
197C3×Dic9—21no—
198C3×Dic9—21no—
199C3×Dic9—21no—
200C3×Dic9—21no—
201C3×Dic9—21no—
202C3×Dic9—21no—
203C3×Dic9—21no—
204C3×C4⋊Q8—91no—
205C3×C4⋊Q8—91no—
206C3×#126—91no—
207C3×#126—91no—
208C3×#126—91no—
209C3×#126—91no—
210C3×#125—91no—
211C3×#125—91no—
212C3×#124—91no—
213C3×#123—91no—
214C3×#123—91no—
215C3×C22⋊Q8—21no—
216C3×C22⋊Q8—91no—
217C3×C22⋊Q8—91no—
218C3×C22⋊Q8—91no—
219C3×C22⋊Q8D911yescharacteristic, complemented
220C3×C22⋊Q8C3×D311yescharacteristic
221#946—31no—
222#944—31no—
223#929—31no—
224#924—31no—
225#898—31no—
226#898—31no—
227#896—31no—
228#890—31no—
229#889—31no—
230#888—31no—
231#885—31no—
232#883—31no—
233#879—31no—
234#879—31no—
235C23×C32C22×D311yescharacteristic
236C22×C3×D3—31no—
237C32×Q8—41no—
238C2×C32×C4—41no—
239C2×C32×C4C22×D311yescharacteristic
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C3×#67—121no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3—31no—
249C2×C3×Dic3—31no—
250C2×C3×Dic3—31no—
251C2×C3×Dic3—31no—
252C2×C3×Dic3—31no—
253C3×C4×D3—121no—
254C3×Dic6—121no—
255C3×Dic6—121no—
256C23×C9—21no—
257C23×C9C23×C311yescharacteristic
258C22×D9C23×C311yescharacteristic
259Q8×C9—41no—
260Q8×C9—42no—
261C2×C4×C9—21no—
262C2×C4×C9—21no—
263C2×C4×C9—21no—
264C2×C4×C9—21no—
265C2×C4×C9—21no—
266C2×C4×C9—21no—
267C2×C4×C9—41no—
268C2×C4×C9—42no—
269C2×C4×C9C23×C311yescharacteristic
270C2×C4×C9C23×C311yescharacteristic
271C2×C4×C9C23×C311yescharacteristic
272C2×C4×C9C23×C311yescharacteristic
273C2×C4×C9C23×C311yescharacteristic
274C2×C4×C9C23×C311yescharacteristic
275#611—41no—
276C2×Dic9C23×C311yescharacteristic
277C2×Dic9C23×C311yescharacteristic
278C2×Dic9C23×C311yescharacteristic
279C2×Dic9C23×C311yescharacteristic
280C2×Dic9C23×C311yescharacteristic
281C2×Dic9C23×C311yescharacteristic
282C2×Dic9C23×C311yescharacteristic
283C4×D9—41no—
284Dic18—41no—
285Dic18—41no—
286#563—91noSylow
287C2×C3×C9—41no—
288C2×C3×C9H(5,𝔽2)11yescharacteristic
289C2×C3×C92−1+411yescharacteristic
290C2×C3×C92−1+411yescharacteristic
291C3×D9—41no—
292C2×C3×Q8—21no—
293C2×C3×Q8—91no—
294C2×C3×Q8—91no—
295C2×C3×Q8C2×D911yescharacteristic
296C2×C3×Q8C2×C3×D311yescharacteristic
297C2×C3×D4—91no—
298C22×C3×C4—21no—
299C22×C3×C4—91no—
300C22×C3×C4C2×D911yescharacteristic
301C22×C3×C4C2×C3×D311yescharacteristic
302C2×#67—31no—
303C2×C4×D3—31no—
304C2×Dic6—31no—
305C2×Dic6—31no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—91no—
310C3×C4⋊C4—91no—
311C3×C4⋊C4—91no—
312C3×C4⋊C4—91no—
313C3×C4⋊C4—91no—
314C3×C4⋊C4—91no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4—91no—
319C3×C4⋊C4—91no—
320C3×C4⋊C4—91no—
321C3×C4⋊C4—91no—
322C3×C4⋊C4C2×D911yescharacteristic
323C3×C4⋊C4C2×D911yescharacteristic
324C3×C4⋊C4C2×D911yescharacteristic
325C3×C4⋊C4C2×C3×D311yescharacteristic
326C3×C4⋊C4C2×C3×D311yescharacteristic
327C3×C4⋊C4C2×C3×D311yescharacteristic
328C3×C22⋊C4—21no—
329C3×C22⋊C4—21no—
330C3×C22⋊C4—91no—
331C3×C22⋊C4—91no—
332C3×C22⋊C4—91no—
333C3×C22⋊C4—91no—
334C3×C22⋊C4—91no—
335C3×C22⋊C4—91no—
336C3×C22⋊C4—91no—
337C3×C22⋊C4—91no—
338C3×C22⋊C4C2×D911yescharacteristic
339C3×C22⋊C4C2×D911yescharacteristic
340C3×C22⋊C4C2×C3×D311yescharacteristic
341C3×C22⋊C4C2×C3×D311yescharacteristic
342C3×C42—91no—
343C3×C42—91no—
344C3×C42—91no—
345#217—31no—
346#217—31no—
347#217—31no—
348(C2×D3)⋊C4—31no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32C23×D311yescharacteristic
373C2×C3×D3—61no—
374C2×C3×D3—61no—
375C2×C3×D3—61no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—21no—
379C32×C4—21no—
380C32×C4—21no—
381C32×C4—21no—
382C3×Dic3—61no—
383C3×Dic3—61no—
384C3×Dic3—61no—
385C3×Dic3—61no—
386C3×Dic3—61no—
387C3×Dic3—61no—
388C3×Dic3—61no—
389C22×C9—22no—
390C22×C9—21no—
391C22×C9—21no—
392C22×C9—21no—
393C22×C9—21no—
394C22×C9—41no—
395C22×C9—41no—
396C22×C9C24×C311yescharacteristic
397C2×D9—21no—
398C2×D9—21no—
399C2×D9—21no—
400C4×C9—22no—
401C4×C9—21no—
402C4×C9—21no—
403C4×C9—21no—
404C4×C9—21no—
405C4×C9—21no—
406C4×C9—21no—
407C4×C9—41no—
408C4×C9—41no—
409C4×C9—41no—
410C4×C9—41no—
411C4×C9—41no—
412Dic9—21no—
413Dic9—21no—
414Dic9—21no—
415Dic9—21no—
416Dic9—21no—
417Dic9—21no—
418Dic9—21no—
419C4⋊Q8—91no—
420C4⋊Q8—91no—
421#126—91no—
422#126—91no—
423#126—91no—
424#126—91no—
425#125—91no—
426#125—91no—
427#124—91no—
428#123—91no—
429#123—91no—
430C22⋊Q8—91no—
431C22⋊Q8—91no—
432C22⋊Q8—91no—
433C22⋊Q8C3×D911yescharacteristic, complemented
434C3×C9#56311yescharacteristic, complemented, Sylow
435C23×C3—21no—
436C23×C3—91no—
437C23×C3C22×D911yescharacteristic
438C23×C3C22×C3×D311yescharacteristic
439C22×D3—31no—
440C3×Q8—41no—
441C3×Q8—41no—
442C3×Q8—42no—
443C3×Q8—361no—
444C3×Q8—361no—
445C3×D4—361no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—42no—
455C2×C3×C4—91no—
456C2×C3×C4—91no—
457C2×C3×C4—91no—
458C2×C3×C4—91no—
459C2×C3×C4—91no—
460C2×C3×C4—91no—
461C2×C3×C4—91no—
462C2×C3×C4—361no—
463C2×C3×C4C22×D911yescharacteristic
464C2×C3×C4C22×D911yescharacteristic
465C2×C3×C4C22×D911yescharacteristic
466C2×C3×C4C22×D911yescharacteristic
467C2×C3×C4C22×D911yescharacteristic
468C2×C3×C4C22×D911yescharacteristic
469C2×C3×C4C22×C3×D311yescharacteristic
470C2×C3×C4C22×C3×D311yescharacteristic
471C2×C3×C4C22×C3×D311yescharacteristic
472C2×C3×C4C22×C3×D311yescharacteristic
473C2×C3×C4C22×C3×D311yescharacteristic
474C2×C3×C4C22×C3×D311yescharacteristic
475#67—121no—
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C4×D3—121no—
484Dic6—121no—
485Dic6—121no—
486C2×C32—41no—
487C2×C32#100411yescharacteristic
488C2×C32#100711yescharacteristic
489C2×C32#101011yescharacteristic
490C3×D3—121no—
491C2×C9—21no—
492C2×C9—21no—
493C2×C9—21no—
494C2×C9—42no—
495C2×C9—41no—
496C2×C9C3×H(5,𝔽2)11yescharacteristic
497C2×C9C3×2−1+411yescharacteristic
498C2×C9C3×2−1+411yescharacteristic
499D9—41no—
500C2×Q8—91no—
501C2×Q8—91no—
502C2×Q8C2×C3×D911yescharacteristic
503C2×D4—91no—
504C22×C4—91no—
505C22×C4C2×C3×D911yescharacteristic
506C4⋊C4—91no—
507C4⋊C4—91no—
508C4⋊C4—91no—
509C4⋊C4—91no—
510C4⋊C4—91no—
511C4⋊C4—91no—
512C4⋊C4—91no—
513C4⋊C4—91no—
514C4⋊C4—91no—
515C4⋊C4—91no—
516C4⋊C4—91no—
517C4⋊C4—91no—
518C4⋊C4—91no—
519C4⋊C4C2×C3×D911yescharacteristic
520C4⋊C4C2×C3×D911yescharacteristic
521C4⋊C4C2×C3×D911yescharacteristic
522C22⋊C4—91no—
523C22⋊C4—91no—
524C22⋊C4—91no—
525C22⋊C4—91no—
526C22⋊C4—91no—
527C22⋊C4—91no—
528C22⋊C4—91no—
529C22⋊C4—91no—
530C22⋊C4C2×C3×D911yescharacteristic
531C22⋊C4C2×C3×D911yescharacteristic
532C42—91no—
533C42—91no—
534C42—91no—
535C22×C3—22no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—181no—
546C22×C3—181no—
547C22×C3—181no—
548C22×C3C23×D911yescharacteristic
549C22×C3C23×C3×D311yescharacteristic
550C2×D3—61no—
551C2×D3—61no—
552C2×D3—61no—
553C3×C4—22no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—41no—
567C3×C4—41no—
568C3×C4—41no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—181no—
572C3×C4—181no—
573C3×C4—181no—
574C3×C4—181no—
575C3×C4—181no—
576C3×C4—181no—
577C3×C4—181no—
578Dic3—61no—
579Dic3—61no—
580Dic3—61no—
581Dic3—61no—
582Dic3—61no—
583Dic3—61no—
584Dic3—61no—
585C32#564611yescharacteristic
586C9—21no—
587C9C3×#56311yescharacteristic, complemented
588C23—91no—
589C23C22×C3×D911yescharacteristic
590Q8—41no—
591Q8—361no—
592Q8—361no—
593D4—361no—
594C2×C4—41no—
595C2×C4—91no—
596C2×C4—91no—
597C2×C4—91no—
598C2×C4—91no—
599C2×C4—91no—
600C2×C4—91no—
601C2×C4—91no—
602C2×C4—361no—
603C2×C4C22×C3×D911yescharacteristic
604C2×C4C22×C3×D911yescharacteristic
605C2×C4C22×C3×D911yescharacteristic
606C2×C4C22×C3×D911yescharacteristic
607C2×C4C22×C3×D911yescharacteristic
608C2×C4C22×C3×D911yescharacteristic
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—42no—
613C2×C3—41no—
614C2×C3—41no—
615C2×C3—361no—
616C2×C3#6371011yescharacteristic
617C2×C3#6371311yescharacteristic
618C2×C3#6371611yescharacteristic
619C2×C3C3×#100411yescharacteristic
620C2×C3C3×#100711yescharacteristic
621C2×C3C3×#101011yescharacteristic
622D3—121no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—181no—
627C22—181no—
628C22—181no—
629C22C23×C3×D911yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—181no—
637C4—181no—
638C4—181no—
639C4—181no—
640C4—181no—
641C4—181no—
642C4—181no—
643C3—21no—
644C3#1058974811yescharacteristic, direct product factor
645C3C3×#564611yescharacteristic
646C2—41no—
647C2—361no—
648C2C3×#6371011yescharacteristic
649C2C3×#6371311yescharacteristic
650C2C3×#6371611yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×C22⋊Q8C2
socleC22×C32C23×D3
prime radicalC2×C3×#611C22
hypercenterC3×C22⋊Q8D9
hypocenterC9C3×#563
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×#63508C2semidirect
3. C3×#63506C2semidirect
5. C3×#63486C2semidirect
6. C3×#63460C2semidirect
7. C3×#63460C2semidirect
8. C3×#63458C2semidirect
9. C3×#63452C2semidirect
10. C3×#63451C2semidirect
11. C3×#63450C2semidirect
14. C3×#63441C2semidirect
15. C3×#63441C2semidirect
17. #10589748C3direct (N × H)
69. C9×C22⋊Q8C2×C3semidirect
70. #63508C2×C3semidirect
71. #63506C2×C3semidirect
73. #63486C2×C3semidirect
74. #63460C2×C3semidirect
75. #63460C2×C3semidirect
76. #63458C2×C3semidirect
77. #63452C2×C3semidirect
78. #63451C2×C3semidirect
79. #63450C2×C3semidirect
82. #63441C2×C3semidirect
83. #63441C2×C3semidirect
219. C3×C22⋊Q8D9semidirect
433. C22⋊Q8C3×D9semidirect
434. C3×C9#563semidirect
587. C9C3×#563semidirect
644. C3#10589748direct (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×#635082
C3×#635062
C3×#634912
C3×#634862
C3×#634602
C3×#634582
C3×#634522
C3×#634512
C3×#634502
C3×#634472
C3×#634452
C3×#634412
C3×#56463
#105897483