Finite Group Databasebeta

← C3×#10589742 #13152896

Subgroups — C3×#10589742 #13152896

Order 1728.

722 conjugacy classes of subgroups.

The subgroup lattice has 688 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×#63506C211yesmaximal, characteristic, complemented
4C3×#63491C211yesmaximal, characteristic, complemented
5C3×C4×#611C211yesmaximal, characteristic, complemented
6C3×#63460C211yesmaximal, characteristic, complemented
7C3×#63458C211yesmaximal, characteristic, complemented
8C3×#63458C211yesmaximal, characteristic, complemented
9C3×#63456C211yesmaximal, characteristic, complemented
10C3×#63454C211yesmaximal, characteristic, complemented
11C3×#63449C211yesmaximal, characteristic, complemented
12C3×#63447C211yesmaximal, characteristic, complemented
13C3×#63447C211yesmaximal, characteristic, complemented
14C3×#63446C211yesmaximal, characteristic
15C3×#63441C211yesmaximal, characteristic, complemented
16C3×#5640—31nomaximal
17#10589742C311yesmaximal, characteristic, direct product factor
18C2×C3×Q8×C9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic
20C2×C3×#611C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
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×#3676C2211yescharacteristic
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×C4⋊Dic9C2211yescharacteristic
43C3×Dic9⋊C4C2211yescharacteristic
44C3×Dic9⋊C4C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×C4×Dic9C2211yescharacteristic
50C3×C4×Dic9C2211yescharacteristic
51C3×C4×Dic9C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×C22⋊Q8D311yescharacteristic
54C3×#947—31no—
55C3×#944—31no—
56C3×#929—31no—
57C3×C4×#67—31no—
58C3×#898—31no—
59C3×#896—31no—
60C3×#896—31no—
61C3×#894—31no—
62C3×#892—31no—
63C3×#887—31no—
64C3×#885—31no—
65C3×#885—31no—
66C3×#884—31no—
67C3×#879—31no—
68C9×C22⋊Q8—21no—
69C9×C22⋊Q8C2×C311yescharacteristic, complemented
70#63509C2×C311yescharacteristic, complemented
71#63506C2×C311yescharacteristic, complemented
72#63491C2×C311yescharacteristic, complemented
73C4×#611C2×C311yescharacteristic, complemented
74#63460C2×C311yescharacteristic, complemented
75#63458C2×C311yescharacteristic, complemented
76#63458C2×C311yescharacteristic, complemented
77#63456C2×C311yescharacteristic, complemented
78#63454C2×C311yescharacteristic, complemented
79#63449C2×C311yescharacteristic, complemented
80#63447C2×C311yescharacteristic, complemented
81#63447C2×C311yescharacteristic, complemented
82#63446C2×C311yescharacteristic
83#63441C2×C311yescharacteristic, complemented
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C3×Q8×C9—41no—
88C2×C3×C4×C9—41no—
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C3×#611—22no—
96C3×#611—41no—
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C3×D36—41no—
104C3×C4×D9—22no—
105C3×C4×D9—41no—
106C3×Dic18—22no—
107C3×Dic18—41no—
108C3×#542—91no—
109#5640—31no—
110C2×C32×Q8C2×D311yescharacteristic
111C22×C32×C4C2×D311yescharacteristic
112C2×C3×#67—31no—
113C2×C3×#67—31no—
114C2×C3×D12—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—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
124C3×#217—31no—
125C3×#217—31no—
126C3×(C2×D3)⋊C4—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×C4⋊Dic3—31no—
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137C3×Dic3⋊C4—31no—
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4—31no—
141C3×C4×Dic3—31no—
142C3×C4×Dic3—31no—
143C3×C4×Dic3—31no—
144C3×C4×Dic3—31no—
145C2×Q8×C9—21no—
146C2×Q8×C9C22×C311yescharacteristic
147C22×C4×C9—21no—
148C22×C4×C9C22×C311yescharacteristic
149C2×#611C22×C311yescharacteristic
150C2×#611C22×C311yescharacteristic
151C2×D36C22×C311yescharacteristic
152C2×C4×D9C22×C311yescharacteristic
153C2×C4×D9C22×C311yescharacteristic
154C2×Dic18C22×C311yescharacteristic
155C2×Dic18C22×C311yescharacteristic
156C9×C4⋊C4—21no—
157C9×C4⋊C4—21no—
158C9×C4⋊C4—21no—
159C9×C4⋊C4C22×C311yescharacteristic
160C9×C4⋊C4C22×C311yescharacteristic
161C9×C4⋊C4C22×C311yescharacteristic
162C9×C22⋊C4—21no—
163C9×C22⋊C4—21no—
164C9×C22⋊C4C22×C311yescharacteristic
165C9×C22⋊C4C22×C311yescharacteristic
166#3676C22×C311yescharacteristic
167#3676C22×C311yescharacteristic
168(C2×D9)⋊C4C22×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
176C4⋊Dic9C22×C311yescharacteristic
177Dic9⋊C4C22×C311yescharacteristic
178Dic9⋊C4C22×C311yescharacteristic
179Dic9⋊C4C22×C311yescharacteristic
180Dic9⋊C4C22×C311yescharacteristic
181Dic9⋊C4C22×C311yescharacteristic
182Dic9⋊C4C22×C311yescharacteristic
183C4×Dic9C22×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—91no—
211C3×#126—91no—
212C3×#124—91no—
213C3×#124—91no—
214C3×#124—91no—
215C3×#123—91no—
216C3×#123—91no—
217C3×C22⋊Q8—21no—
218C3×C22⋊Q8—91no—
219C3×C22⋊Q8—91no—
220C3×C22⋊Q8D911yescharacteristic, complemented
221C3×C22⋊Q8C3×D311yescharacteristic
222C3×#121—91no—
223C3×C4×Q8—91no—
224C3×C4×D4—91no—
225C3×#117—91no—
226#947—31no—
227#944—31no—
228#929—31no—
229C4×#67—31no—
230#898—31no—
231#896—31no—
232#896—31no—
233#894—31no—
234#892—31no—
235#887—31no—
236#885—31no—
237#885—31no—
238#884—31no—
239#879—31no—
240C23×C32C22×D311yescharacteristic
241C22×C3×D3—31no—
242C22×C3×D3—31no—
243C32×Q8—41no—
244C2×C32×C4—41no—
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C3×#67—62no—
252C3×#67—121no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3—31no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—31no—
258C2×C3×Dic3—31no—
259C3×D12—121no—
260C3×C4×D3—62no—
261C3×C4×D3—121no—
262C3×Dic6—62no—
263C3×Dic6—121no—
264C23×C9—21no—
265C23×C9C23×C311yescharacteristic
266C22×D9C23×C311yescharacteristic
267C22×D9C23×C311yescharacteristic
268Q8×C9—41no—
269Q8×C9—42no—
270C2×C4×C9—21no—
271C2×C4×C9—21no—
272C2×C4×C9—21no—
273C2×C4×C9—21no—
274C2×C4×C9—21no—
275C2×C4×C9—21no—
276C2×C4×C9—41no—
277C2×C4×C9—42no—
278C2×C4×C9C23×C311yescharacteristic
279C2×C4×C9C23×C311yescharacteristic
280C2×C4×C9C23×C311yescharacteristic
281C2×C4×C9C23×C311yescharacteristic
282C2×C4×C9C23×C311yescharacteristic
283C2×C4×C9C23×C311yescharacteristic
284#611—22no—
285#611—41no—
286C2×Dic9C23×C311yescharacteristic
287C2×Dic9C23×C311yescharacteristic
288C2×Dic9C23×C311yescharacteristic
289C2×Dic9C23×C311yescharacteristic
290C2×Dic9C23×C311yescharacteristic
291C2×Dic9C23×C311yescharacteristic
292D36—41no—
293C4×D9—22no—
294C4×D9—41no—
295Dic18—22no—
296Dic18—41no—
297#542—91noSylow
298C2×C3×C9—41no—
299C2×C3×C9C2×#4111yescharacteristic
300C2×C3×C9H(5,𝔽2)11yescharacteristic
301C2×C3×C92−1+411yescharacteristic
302C3×D9—41no—
303C3×D9—41no—
304C2×C3×Q8—21no—
305C2×C3×Q8—91no—
306C2×C3×Q8—91no—
307C2×C3×Q8C2×D911yescharacteristic
308C2×C3×Q8C2×C3×D311yescharacteristic
309C2×C3×D4—91no—
310C2×C3×D4—91no—
311C2×C3×D4—91no—
312C22×C3×C4—21no—
313C22×C3×C4—91no—
314C22×C3×C4—91no—
315C22×C3×C4C2×D911yescharacteristic
316C22×C3×C4C2×C3×D311yescharacteristic
317C2×#67—31no—
318C2×#67—31no—
319C2×D12—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×Dic6—31no—
323C2×Dic6—31no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4C2×D911yescharacteristic
335C3×C4⋊C4C2×D911yescharacteristic
336C3×C4⋊C4C2×D911yescharacteristic
337C3×C4⋊C4C2×C3×D311yescharacteristic
338C3×C4⋊C4C2×C3×D311yescharacteristic
339C3×C4⋊C4C2×C3×D311yescharacteristic
340C3×C22⋊C4—21no—
341C3×C22⋊C4—21no—
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⋊C4—91no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4C2×D911yescharacteristic
353C3×C22⋊C4C2×D911yescharacteristic
354C3×C22⋊C4C2×C3×D311yescharacteristic
355C3×C22⋊C4C2×C3×D311yescharacteristic
356C3×C42—91no—
357C3×C42—91no—
358C3×C42—91no—
359C3×C42—91no—
360#217—31no—
361#217—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—
369(C2×D3)⋊C4—31no—
370C4⋊Dic3—31no—
371Dic3⋊C4—31no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32C23×D311yescharacteristic
385C2×C3×D3—61no—
386C2×C3×D3—61no—
387C2×C3×D3—61no—
388C2×C3×D3—61no—
389C2×C3×D3—61no—
390C2×C3×D3—61no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C3×Dic3—32no—
398C3×Dic3—61no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C3×Dic3—61no—
402C3×Dic3—61no—
403C22×C9—22no—
404C22×C9—21no—
405C22×C9—21no—
406C22×C9—21no—
407C22×C9—21no—
408C22×C9—41no—
409C22×C9—41no—
410C22×C9C24×C311yescharacteristic
411C2×D9—21no—
412C2×D9—21no—
413C2×D9—21no—
414C2×D9—21no—
415C2×D9—21no—
416C2×D9—21no—
417C4×C9—22no—
418C4×C9—21no—
419C4×C9—21no—
420C4×C9—21no—
421C4×C9—21no—
422C4×C9—21no—
423C4×C9—21no—
424C4×C9—41no—
425C4×C9—41no—
426C4×C9—41no—
427C4×C9—41no—
428C4×C9—41no—
429Dic9—21no—
430Dic9—21no—
431Dic9—21no—
432Dic9—21no—
433Dic9—21no—
434Dic9C3×#4112yes—
435C4⋊Q8—91no—
436#126—91no—
437#126—91no—
438#124—91no—
439#124—91no—
440#124—91no—
441#123—91no—
442#123—91no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C22⋊Q8C3×D911yescharacteristic, complemented
446#121—91no—
447C4×Q8—91no—
448C4×D4—91no—
449#117—91no—
450C3×C9#54211yescharacteristic, complemented, Sylow
451C23×C3—21no—
452C23×C3—91no—
453C23×C3—91no—
454C23×C3C22×D911yescharacteristic
455C23×C3C22×C3×D311yescharacteristic
456C22×D3—31no—
457C22×D3—31no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×Q8—42no—
461C3×Q8—182no—
462C3×Q8—361no—
463C3×D4—182no—
464C3×D4—361no—
465C3×D4—361no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—42no—
475C2×C3×C4—91no—
476C2×C3×C4—91no—
477C2×C3×C4—91no—
478C2×C3×C4—91no—
479C2×C3×C4—91no—
480C2×C3×C4—91no—
481C2×C3×C4—182no—
482C2×C3×C4—361no—
483C2×C3×C4C22×D911yescharacteristic
484C2×C3×C4C22×D911yescharacteristic
485C2×C3×C4C22×D911yescharacteristic
486C2×C3×C4C22×D911yescharacteristic
487C2×C3×C4C22×D911yescharacteristic
488C2×C3×C4C22×D911yescharacteristic
489C2×C3×C4C22×C3×D311yescharacteristic
490C2×C3×C4C22×C3×D311yescharacteristic
491C2×C3×C4C22×C3×D311yescharacteristic
492C2×C3×C4C22×C3×D311yescharacteristic
493C2×C3×C4C22×C3×D311yescharacteristic
494C2×C3×C4C22×C3×D311yescharacteristic
495#67—62no—
496#67—121no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503D12—121no—
504C4×D3—62no—
505C4×D3—121no—
506Dic6—62no—
507Dic6—121no—
508C2×C32—41no—
509C2×C32#100411yescharacteristic
510C2×C32#100711yescharacteristic
511C2×C32D3×#4111yescharacteristic
512C3×D3—121no—
513C3×D3—121no—
514C2×C9—21no—
515C2×C9—21no—
516C2×C9—21no—
517C2×C9—42no—
518C2×C9—41no—
519C2×C9C2×C3×#4111yescharacteristic
520C2×C9C3×H(5,𝔽2)11yescharacteristic
521C2×C9C3×2−1+411yescharacteristic
522D9—41no—
523D9—41no—
524C2×Q8—91no—
525C2×Q8—91no—
526C2×Q8C2×C3×D911yescharacteristic
527C2×D4—91no—
528C2×D4—91no—
529C2×D4—91no—
530C22×C4—91no—
531C22×C4—91no—
532C22×C4C2×C3×D911yescharacteristic
533C4⋊C4—91no—
534C4⋊C4—91no—
535C4⋊C4—91no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4C2×C3×D911yescharacteristic
541C4⋊C4C2×C3×D911yescharacteristic
542C4⋊C4C2×C3×D911yescharacteristic
543C22⋊C4—91no—
544C22⋊C4—91no—
545C22⋊C4—91no—
546C22⋊C4—91no—
547C22⋊C4—91no—
548C22⋊C4—91no—
549C22⋊C4—91no—
550C22⋊C4—91no—
551C22⋊C4—91no—
552C22⋊C4—91no—
553C22⋊C4C2×C3×D911yescharacteristic
554C22⋊C4C2×C3×D911yescharacteristic
555C42—91no—
556C42—91no—
557C42—91no—
558C42—91no—
559C22×C3—22no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—181no—
570C22×C3—181no—
571C22×C3—181no—
572C22×C3—181no—
573C22×C3—181no—
574C22×C3—181no—
575C22×C3C23×D911yescharacteristic
576C22×C3C23×C3×D311yescharacteristic
577C2×D3—61no—
578C2×D3—61no—
579C2×D3—61no—
580C2×D3—61no—
581C2×D3—61no—
582C2×D3—61no—
583C3×C4—22no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601C3×C4—92no—
602C3×C4—181no—
603C3×C4—181no—
604C3×C4—181no—
605C3×C4—181no—
606C3×C4—181no—
607Dic3—32no—
608Dic3—61no—
609Dic3—61no—
610Dic3—61no—
611Dic3—61no—
612Dic3—61no—
613C32#564011yescharacteristic
614C9—21no—
615C9C3×#54211yescharacteristic, complemented
616C23—91no—
617C23—91no—
618C23C22×C3×D911yescharacteristic
619Q8—41no—
620Q8—182no—
621Q8—361no—
622D4—182no—
623D4—361no—
624D4—361no—
625C2×C4—41no—
626C2×C4—91no—
627C2×C4—91no—
628C2×C4—91no—
629C2×C4—91no—
630C2×C4—91no—
631C2×C4—91no—
632C2×C4—182no—
633C2×C4—361no—
634C2×C4C22×C3×D911yescharacteristic
635C2×C4C22×C3×D911yescharacteristic
636C2×C4C22×C3×D911yescharacteristic
637C2×C4C22×C3×D911yescharacteristic
638C2×C4C22×C3×D911yescharacteristic
639C2×C4C22×C3×D911yescharacteristic
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—42no—
644C2×C3—41no—
645C2×C3—41no—
646C2×C3—361no—
647C2×C3—361no—
648C2×C3#6371011yescharacteristic
649C2×C3#6371311yescharacteristic
650C2×C3#41×D911yescharacteristic
651C2×C3C3×#100411yescharacteristic
652C2×C3C3×#100711yescharacteristic
653C2×C3C3×D3×#4111yescharacteristic
654D3—121no—
655D3—121no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—181no—
660C22—181no—
661C22—181no—
662C22—181no—
663C22—181no—
664C22—181no—
665C22C23×C3×D911yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—21no—
671C4—21no—
672C4—92no—
673C4—181no—
674C4—181no—
675C4—181no—
676C4—181no—
677C4—181no—
678C3—21no—
679C3#1058974211yescharacteristic, direct product factor
680C3C3×#564011yescharacteristic
681C2—41no—
682C2—361no—
683C2—361no—
684C2C3×#6371011yescharacteristic
685C2C3×#6371311yescharacteristic
686C2C3×#41×D911yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×C22⋊Q8C2
socleC22×C32C23×D3
prime radicalC3×#63446C2
hypercenterC3×C22⋊Q8D9
hypocenterC9C3×#542
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×#63506C2semidirect
4. C3×#63491C2semidirect
5. C3×C4×#611C2semidirect
6. C3×#63460C2semidirect
7. C3×#63458C2semidirect
8. C3×#63458C2semidirect
9. C3×#63456C2semidirect
10. C3×#63454C2semidirect
11. C3×#63449C2semidirect
12. C3×#63447C2semidirect
13. C3×#63447C2semidirect
15. C3×#63441C2semidirect
17. #10589742C3direct (N × H)
69. C9×C22⋊Q8C2×C3semidirect
70. #63509C2×C3semidirect
71. #63506C2×C3semidirect
72. #63491C2×C3semidirect
73. C4×#611C2×C3semidirect
74. #63460C2×C3semidirect
75. #63458C2×C3semidirect
76. #63458C2×C3semidirect
77. #63456C2×C3semidirect
78. #63454C2×C3semidirect
79. #63449C2×C3semidirect
80. #63447C2×C3semidirect
81. #63447C2×C3semidirect
83. #63441C2×C3semidirect
220. C3×C22⋊Q8D9semidirect
445. C22⋊Q8C3×D9semidirect
450. C3×C9#542semidirect
615. C9C3×#542semidirect
679. C3#10589742direct (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×#635062
C3×#634912
C3×C4×#6112
C3×#634602
C3×#634582
C3×#634562
C3×#634542
C3×#634492
C3×#634472
C3×#634462
C3×#634412
C3×#56403
#105897423