Finite Group Databasebeta

← C3×#10589695 #13152757

Subgroups — C3×#10589695 #13152757

Order 1728.

880 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#120C211yesmaximal, characteristic, complemented
2C3×#63515C211yesmaximal, characteristic, complemented
3C2×C3×#3676C211yesmaximal, characteristic, complemented
4C3×#63501C211yesmaximal, characteristic, complemented
5C3×#63501C211yesmaximal, characteristic, complemented
6C3×#63500C211yesmaximal, characteristic, complemented
7C3×#63498C211yesmaximal, characteristic, complemented
8C3×#63497C211yesmaximal, characteristic, complemented
9C3×D4×Dic9C211yesmaximal, characteristic, complemented
10C3×#63447C211yesmaximal, characteristic, complemented
11C3×#63445C211yesmaximal, characteristic, complemented
12C3×#611⋊C4C211yesmaximal, characteristic, complemented
13C3×#63441C211yesmaximal, characteristic, complemented
14C3×#63441C211yesmaximal, characteristic, complemented
15C3×#63440C211yesmaximal, characteristic, complemented
16C3×#5593—31nomaximal
17#10589695C311yesmaximal, characteristic, direct product factor
18C24×C3×C9C2211yescharacteristic
19C2×C3×D4×C9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C2×C3×D4×C9C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic, complemented
26C22×C3×Dic9C2211yescharacteristic
27C22×C3×Dic9C2211yescharacteristic
28C22×C3×Dic9C2211yescharacteristic, complemented
29C2×C3×C4×D9C2211yescharacteristic, complemented
30C2×C3×Dic18C2211yescharacteristic, complemented
31C3×C9×C22⋊C4C2211yescharacteristic
32C3×C9×C22⋊C4C2211yescharacteristic
33C3×C9×C22⋊C4C2211yescharacteristic
34C3×#3676C2211yescharacteristic
35C3×#3676C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C3×#3676C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41C3×#3676C2211yescharacteristic, complemented
42C3×#3676C2211yescharacteristic, 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×Dic9⋊C4C2211yescharacteristic, complemented
51C3×C4×Dic9C2211yescharacteristic, complemented
52C3×C4×Dic9C2211yescharacteristic, complemented
53C32×#120D311yescharacteristic
54C3×#953—31no—
55C2×C3×#217—31no—
56C3×#939—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#936—31no—
60C3×#935—31no—
61C3×D4×Dic3—31no—
62C3×#885—31no—
63C3×#883—31no—
64C3×#67⋊C4—31no—
65C3×#879—31no—
66C3×#879—31no—
67C3×#878—31no—
68C9×#120—21no—
69C9×#120C2×C311yescharacteristic, complemented
70#63515C2×C311yescharacteristic, complemented
71C2×#3676C2×C311yescharacteristic, complemented
72#63501C2×C311yescharacteristic, complemented
73#63501C2×C311yescharacteristic, complemented
74#63500C2×C311yescharacteristic, complemented
75#63498C2×C311yescharacteristic, complemented
76#63497C2×C311yescharacteristic, complemented
77D4×Dic9C2×C311yescharacteristic, complemented
78#63447C2×C311yescharacteristic, complemented
79#63445C2×C311yescharacteristic, complemented
80#611⋊C4C2×C311yescharacteristic, complemented
81#63441C2×C311yescharacteristic, complemented
82#63441C2×C311yescharacteristic, complemented
83#63440C2×C311yescharacteristic, complemented
84C23×C3×C9—22no—
85C23×C3×C9—41no—
86C23×C3×C9—41no—
87C23×C3×C9C2311yescharacteristic
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C23×C3×C9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92C3×D4×C9—22no—
93C3×D4×C9—41no—
94C3×D4×C9—41no—
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98C3×#611—22no—
99C3×#611—41no—
100C3×#611—41no—
101C3×#611—41no—
102C2×C3×Dic9—41no—
103C2×C3×Dic9—41no—
104C2×C3×Dic9—41no—
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C3×C4×D9—41no—
113C3×Dic18—41no—
114C3×#538—91no—
115#5593—31no—
116C24×C32C2×D311yescharacteristic
117C2×C32×D4C2×D311yescharacteristic
118C2×C32×D4C2×D311yescharacteristic
119C2×C32×D4C2×D311yescharacteristic
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C22×C3×Dic3—31no—
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×Dic6—31no—
129C24×C9—21no—
130C24×C9C22×C311yescharacteristic
131C32×C22⋊C4C2×D311yescharacteristic
132C32×C22⋊C4C2×D311yescharacteristic
133C32×C22⋊C4C2×D311yescharacteristic
134C3×#217—31no—
135C3×#217—31no—
136C3×#217—31no—
137C3×#217—31no—
138C3×#217—31no—
139C3×#217—31no—
140C3×#217—31no—
141C3×#217—31no—
142C3×#217—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—
152C3×C4×Dic3—31no—
153C2×D4×C9—21no—
154C2×D4×C9—21no—
155C2×D4×C9—21no—
156C2×D4×C9C22×C311yescharacteristic
157C2×D4×C9C22×C311yescharacteristic
158C2×D4×C9C22×C311yescharacteristic
159C2×#611C22×C311yescharacteristic
160C2×#611C22×C311yescharacteristic
161C2×#611C22×C311yescharacteristic
162C2×#611C22×C311yescharacteristic, complemented
163C22×Dic9C22×C311yescharacteristic
164C22×Dic9C22×C311yescharacteristic
165C22×Dic9C22×C311yescharacteristic, complemented
166C2×C4×D9C22×C311yescharacteristic, complemented
167C2×Dic18C22×C311yescharacteristic, complemented
168C9×C22⋊C4—21no—
169C9×C22⋊C4—21no—
170C9×C22⋊C4—21no—
171C9×C22⋊C4C22×C311yescharacteristic
172C9×C22⋊C4C22×C311yescharacteristic
173C9×C22⋊C4C22×C311yescharacteristic
174#3676C22×C311yescharacteristic
175#3676C22×C311yescharacteristic
176#3676C22×C311yescharacteristic
177#3676C22×C311yescharacteristic
178#3676C22×C311yescharacteristic
179#3676C22×C311yescharacteristic
180#3676C22×C311yescharacteristic
181#3676C22×C311yescharacteristic, complemented
182#3676C22×C311yescharacteristic, complemented
183(C2×D9)⋊C4C22×C311yescharacteristic, complemented
184(C2×D9)⋊C4C22×C311yescharacteristic, complemented
185C4⋊Dic9C22×C311yescharacteristic, complemented
186C4⋊Dic9C22×C311yescharacteristic, complemented
187Dic9⋊C4C22×C311yescharacteristic, complemented
188Dic9⋊C4C22×C311yescharacteristic, complemented
189Dic9⋊C4C22×C311yescharacteristic, complemented
190Dic9⋊C4C22×C311yescharacteristic, complemented
191C4×Dic9C22×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×C9—21no—
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9—21no—
203C22×C3×C9—21no—
204C22×C3×C9—44no—
205C22×C3×C9#4112yes—
206C22×C3×C9C2411yescharacteristic
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3×C4×C9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×Dic9—21no—
216C3×Dic9—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#126—91no—
221C3×#126—91no—
222C3×#124—91no—
223C3×#124—91no—
224C3×#123—91no—
225C3×#123—91no—
226C3×C22⋊Q8—91no—
227C3×#121—91no—
228C3×#121—91no—
229C3×#121—91no—
230C3×#120—21no—
231C3×#120—91no—
232C3×#120D911yescharacteristic, complemented
233C3×#120C3×D311yescharacteristic
234C3×C4×D4—91no—
235C3×C4×D4—91no—
236C2×C3×C22⋊C4—91no—
237#953—31no—
238C2×#217—31no—
239#939—31no—
240#939—31no—
241#938—31no—
242#936—31no—
243#935—31no—
244D4×Dic3—31no—
245#885—31no—
246#883—31no—
247#67⋊C4—31no—
248#879—31no—
249#879—31no—
250#878—31no—
251C23×C32—22no—
252C23×C32—41no—
253C23×C32—41no—
254C23×C32C22×D311yescharacteristic
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C23×C32C22×D311yescharacteristic
258C22×C3×D3—31no—
259C32×D4—22no—
260C32×D4—41no—
261C32×D4—41no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C3×#67—62no—
266C3×#67—121no—
267C3×#67—121no—
268C3×#67—121no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—31no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—121no—
277C2×C3×Dic3—121no—
278C2×C3×Dic3—121no—
279C3×C4×D3—121no—
280C3×Dic6—121no—
281C23×C9—22no—
282C23×C9—21no—
283C23×C9—21no—
284C23×C9—21no—
285C23×C9—21no—
286C23×C9—42no—
287C23×C9—41no—
288C23×C9—41no—
289C23×C9—42no—
290C23×C9—42no—
291C23×C9C23×C311yescharacteristic
292C23×C9C23×C311yescharacteristic
293C23×C9C23×C311yescharacteristic
294C23×C9C23×C311yescharacteristic
295C22×D9C23×C311yescharacteristic
296D4×C9—22no—
297D4×C9—42no—
298D4×C9—41no—
299D4×C9—41no—
300D4×C9—42no—
301D4×C9—42no—
302C2×C4×C9—21no—
303C2×C4×C9—21no—
304C2×C4×C9—21no—
305C2×C4×C9C23×C311yescharacteristic
306C2×C4×C9C23×C311yescharacteristic
307C2×C4×C9C23×C311yescharacteristic
308#611—22no—
309#611—41no—
310#611—41no—
311#611—41no—
312C2×Dic9—41no—
313C2×Dic9—41no—
314C2×Dic9—41no—
315C2×Dic9C23×C311yescharacteristic
316C2×Dic9C23×C311yescharacteristic
317C2×Dic9C23×C311yescharacteristic
318C2×Dic9C23×C311yescharacteristic
319C2×Dic9C23×C311yescharacteristic
320C2×Dic9C23×C311yescharacteristic
321C2×Dic9C23×C311yescharacteristic
322C4×D9—41no—
323Dic18—41no—
324#538—91noSylow
325C2×C3×C9—22no—
326C2×C3×C9—41no—
327C2×C3×C9—41no—
328C2×C3×C9—41no—
329C2×C3×C9C2×#4111yescharacteristic
330C2×C3×C9H(5,𝔽2)11yescharacteristic
331C2×C3×C9H(5,𝔽2)11yescharacteristic
332C3×D9—41no—
333C24×C3—21no—
334C24×C3C2×D911yescharacteristic
335C24×C3C2×C3×D311yescharacteristic
336C2×C3×Q8—91no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—91no—
341C2×C3×D4—91no—
342C2×C3×D4—91no—
343C2×C3×D4—91no—
344C2×C3×D4C2×D911yescharacteristic
345C2×C3×D4C2×D911yescharacteristic
346C2×C3×D4C2×D911yescharacteristic
347C2×C3×D4C2×C3×D311yescharacteristic
348C2×C3×D4C2×C3×D311yescharacteristic
349C2×C3×D4C2×C3×D311yescharacteristic
350C22×C3×C4—91no—
351C22×C3×C4—91no—
352C22×C3×C4—91no—
353C22×C3×C4—91no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—31no—
357C2×#67—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C2×C4×D3—31no—
362C2×Dic6—31no—
363C3×C4⋊C4—91no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4—91no—
368C3×C4⋊C4—91no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4C2×D911yescharacteristic
384C3×C22⋊C4C2×D911yescharacteristic
385C3×C22⋊C4C2×D911yescharacteristic
386C3×C22⋊C4C2×C3×D311yescharacteristic
387C3×C22⋊C4C2×C3×D311yescharacteristic
388C3×C22⋊C4C2×C3×D311yescharacteristic
389C3×C42—91no—
390C3×C42—91no—
391#217—31no—
392#217—31no—
393#217—31no—
394#217—31no—
395#217—31no—
396#217—31no—
397#217—31no—
398#217—31no—
399#217—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—31no—
406Dic3⋊C4—31no—
407Dic3⋊C4—31no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—44no—
422C22×C32#23712yes—
423C22×C32C23×D311yescharacteristic
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—21no—
430C3×Dic3—61no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C3×Dic3—61no—
434C3×Dic3—61no—
435C3×Dic3—61no—
436C3×Dic3—61no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—22no—
440C22×C9—22no—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—21no—
446C22×C9—21no—
447C22×C9—21no—
448C22×C9—21no—
449C22×C9—21no—
450C22×C9—21no—
451C22×C9—22no—
452C22×C9—41no—
453C22×C9—41no—
454C22×C9—41no—
455C22×C9—41no—
456C22×C9—41no—
457C22×C9—41no—
458C22×C9—41no—
459C22×C9—41no—
460C22×C9—41no—
461C22×C9—44no—
462C22×C9—48no—
463C22×C9C3×#4112yes—
464C22×C9C24×C311yescharacteristic
465C2×D9—21no—
466C2×D9—21no—
467C2×D9—21no—
468C4×C9—21no—
469C4×C9—21no—
470C4×C9—21no—
471C4×C9—41no—
472C4×C9—41no—
473C4×C9—41no—
474Dic9—21no—
475Dic9—21no—
476Dic9—21no—
477Dic9—21no—
478Dic9—21no—
479Dic9—21no—
480Dic9—21no—
481#126—91no—
482#126—91no—
483#124—91no—
484#124—91no—
485#123—91no—
486#123—91no—
487C22⋊Q8—91no—
488#121—91no—
489#121—91no—
490#121—91no—
491#120—91no—
492#120C3×D911yescharacteristic, complemented
493C4×D4—91no—
494C4×D4—91no—
495C2×C22⋊C4—91no—
496C3×C9#53811yescharacteristic, complemented, Sylow
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—42no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—41no—
508C23×C3—42no—
509C23×C3—42no—
510C23×C3—91no—
511C23×C3C22×D911yescharacteristic
512C23×C3C22×D911yescharacteristic
513C23×C3C22×D911yescharacteristic
514C23×C3C22×D911yescharacteristic
515C23×C3C22×C3×D311yescharacteristic
516C23×C3C22×C3×D311yescharacteristic
517C23×C3C22×C3×D311yescharacteristic
518C23×C3C22×C3×D311yescharacteristic
519C22×D3—31no—
520C3×Q8—361no—
521C3×D4—22no—
522C3×D4—22no—
523C3×D4—42no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—42no—
529C3×D4—42no—
530C3×D4—182no—
531C3×D4—361no—
532C3×D4—361no—
533C3×D4—361no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—91no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—91no—
542C2×C3×C4—91no—
543C2×C3×C4—91no—
544C2×C3×C4—361no—
545C2×C3×C4—361no—
546C2×C3×C4—361no—
547C2×C3×C4—361no—
548C2×C3×C4C22×D911yescharacteristic
549C2×C3×C4C22×D911yescharacteristic
550C2×C3×C4C22×D911yescharacteristic
551C2×C3×C4C22×C3×D311yescharacteristic
552C2×C3×C4C22×C3×D311yescharacteristic
553C2×C3×C4C22×C3×D311yescharacteristic
554#67—62no—
555#67—121no—
556#67—121no—
557#67—121no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C4×D3—121no—
569Dic6—121no—
570C2×C32—22no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32—41no—
574C2×C32C2×#23711yescharacteristic
575C2×C32#100411yescharacteristic
576C2×C32#100411yescharacteristic
577C3×D3—121no—
578C2×C9—22no—
579C2×C9—21no—
580C2×C9—21no—
581C2×C9—21no—
582C2×C9—42no—
583C2×C9—42no—
584C2×C9—42no—
585C2×C9—41no—
586C2×C9—41no—
587C2×C9—41no—
588C2×C9—81no—
589C2×C9C2×C3×#4111yescharacteristic
590C2×C9C3×H(5,𝔽2)11yescharacteristic
591C2×C9C3×H(5,𝔽2)11yescharacteristic
592D9—41no—
593C24C2×C3×D911yescharacteristic
594C2×Q8—91no—
595C2×D4—91no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—91no—
599C2×D4C2×C3×D911yescharacteristic
600C2×D4C2×C3×D911yescharacteristic
601C2×D4C2×C3×D911yescharacteristic
602C22×C4—91no—
603C22×C4—91no—
604C22×C4—91no—
605C22×C4—91no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C22⋊C4—91no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4C2×C3×D911yescharacteristic
624C22⋊C4C2×C3×D911yescharacteristic
625C22⋊C4C2×C3×D911yescharacteristic
626C42—91no—
627C42—91no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—48no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3—181no—
669C22×C3#369912yes—
670C22×C3C23×D911yescharacteristic
671C22×C3C3×#23712yes—
672C22×C3C23×C3×D311yescharacteristic
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—181no—
686C3×C4—181no—
687C3×C4—181no—
688C3×C4—181no—
689C3×C4—181no—
690C3×C4—181no—
691C3×C4—181no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699C32#559311yescharacteristic
700C9—21no—
701C9C3×#53811yescharacteristic, complemented
702C23—22no—
703C23—41no—
704C23—41no—
705C23—91no—
706C23C22×C3×D911yescharacteristic
707C23C22×C3×D911yescharacteristic
708C23C22×C3×D911yescharacteristic
709C23C22×C3×D911yescharacteristic
710Q8—361no—
711D4—22no—
712D4—41no—
713D4—41no—
714D4—182no—
715D4—361no—
716D4—361no—
717D4—361no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—361no—
726C2×C4—361no—
727C2×C4—361no—
728C2×C4—361no—
729C2×C4C22×C3×D911yescharacteristic
730C2×C4C22×C3×D911yescharacteristic
731C2×C4C22×C3×D911yescharacteristic
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—41no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—41no—
745C2×C3—41no—
746C2×C3—81no—
747C2×C3—361no—
748C2×C3C2×#369911yescharacteristic
749C2×C3#6371011yescharacteristic
750C2×C3#6371011yescharacteristic
751C2×C3C2×C3×#23711yescharacteristic
752C2×C3C3×#100411yescharacteristic
753C2×C3C3×#100411yescharacteristic
754D3—121no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—44no—
767C22—181no—
768C22—181no—
769C22—181no—
770C22C3×#369912yes—
771C22C23×C3×D911yescharacteristic
772C4—21no—
773C4—21no—
774C4—21no—
775C4—181no—
776C4—181no—
777C4—181no—
778C4—181no—
779C4—181no—
780C4—181no—
781C4—181no—
782C3—21no—
783C3#1058969511yescharacteristic, direct product factor
784C3C3×#559311yescharacteristic
785C2—22no—
786C2—41no—
787C2—41no—
788C2—41no—
789C2—361no—
790C2C2×C3×#369911yescharacteristic
791C2C3×#6371011yescharacteristic
792C2C3×#6371011yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#120C2
socleC22×C32C23×D3
hypercenterC3×#120D9
hypocenterC9C3×#538
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#120

Complements

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

NH ≅ G/Ntype
1. C3×C9×#120C2semidirect
2. C3×#63515C2semidirect
3. C2×C3×#3676C2semidirect
4. C3×#63501C2semidirect
5. C3×#63501C2semidirect
6. C3×#63500C2semidirect
7. C3×#63498C2semidirect
8. C3×#63497C2semidirect
9. C3×D4×Dic9C2semidirect
10. C3×#63447C2semidirect
11. C3×#63445C2semidirect
12. C3×#611⋊C4C2semidirect
13. C3×#63441C2semidirect
14. C3×#63441C2semidirect
15. C3×#63440C2semidirect
17. #10589695C3direct (N × H)
25. C2×C3×#611C22semidirect
28. C22×C3×Dic9C22semidirect
29. C2×C3×C4×D9C22semidirect
30. C2×C3×Dic18C22semidirect
41. C3×#3676C22semidirect
42. C3×#3676C22semidirect
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×Dic9⋊C4C22semidirect
51. C3×C4×Dic9C22semidirect
52. C3×C4×Dic9C22semidirect
69. C9×#120C2×C3semidirect
70. #63515C2×C3semidirect
71. C2×#3676C2×C3semidirect
72. #63501C2×C3semidirect
73. #63501C2×C3semidirect
74. #63500C2×C3semidirect
75. #63498C2×C3semidirect
76. #63497C2×C3semidirect
77. D4×Dic9C2×C3semidirect
78. #63447C2×C3semidirect
79. #63445C2×C3semidirect
80. #611⋊C4C2×C3semidirect
81. #63441C2×C3semidirect
82. #63441C2×C3semidirect
83. #63440C2×C3semidirect
162. C2×#611C22×C3semidirect
165. C22×Dic9C22×C3semidirect
166. C2×C4×D9C22×C3semidirect
167. C2×Dic18C22×C3semidirect
181. #3676C22×C3semidirect
182. #3676C22×C3semidirect
183. (C2×D9)⋊C4C22×C3semidirect
184. (C2×D9)⋊C4C22×C3semidirect
185. C4⋊Dic9C22×C3semidirect
186. C4⋊Dic9C22×C3semidirect
187. Dic9⋊C4C22×C3semidirect
188. Dic9⋊C4C22×C3semidirect
189. Dic9⋊C4C22×C3semidirect
190. Dic9⋊C4C22×C3semidirect
191. C4×Dic9C22×C3semidirect
192. C4×Dic9C22×C3semidirect
232. C3×#120D9semidirect
492. #120C3×D9semidirect
496. C3×C9#538semidirect
701. C9C3×#538semidirect
783. C3#10589695direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C9×#1202
C3×#635152
C2×C3×#36762
C3×#635012
C3×#635002
C3×#634982
C3×#634972
C3×D4×Dic92
C3×#634472
C3×#634452
C3×#611⋊C42
C3×#634412
C3×#634402
C3×#55933
#105896953