Finite Group Databasebeta

← C3×#10594812 #13174646

Subgroups — C3×#10594812 #13174646

Order 1728.

1118 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64133C211yesmaximal, characteristic
2C32×#924C211yesmaximal, characteristic
3C2×C32×Dic3⋊C4C211yesmaximal, characteristic
4C3×#63964C212yesmaximal
5C3×#63955C212yesmaximal
6C3×#63846C212yesmaximal, complemented
7C3×#63845C212yesmaximal, complemented
8C3×#63840C212yesmaximal, complemented
9C3×#63839C212yesmaximal, complemented
10C3×#5623—31nomaximal
11C3×#5500—31nomaximal
12#10594812C311yesmaximal, characteristic, direct product factor
13C22×C33×C4C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic
18C2×C3×#627C2212yes—
19C3×#3757C2212yes—
20C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C3×#3750C2212yes—
22C32×#217C2212yes—
23C32×C4⋊Dic3C2211yescharacteristic
24C32×Dic3⋊C4C2212yes—
25C32×Dic3⋊C4C2212yes—
26C32×Dic3⋊C4C2212yes—
27C3×#3724C2212yes—
28C3×Dic3⋊Dic3C2212yes—
29C3×Dic3⋊Dic3C2212yes—
30C3×Dic3⋊Dic3C2212yes—
31C3×Dic3⋊Dic3C2212yes—
32C3×Dic32C2212yes—
33C3×Dic32C2212yes—
34C32×C22⋊Q8—31no—
35C2×C32×C4⋊C4—31no—
36#64133C2×C311yescharacteristic
37C3×#944—32no—
38C3×#926—32no—
39C3×#924—21no—
40C3×#924—31no—
41C3×#924—31no—
42C3×#924—32no—
43C3×#924—61no—
44C3×#924D311yescharacteristic
45C3×#924C2×C311yescharacteristic
46C2×C3×Dic3⋊C4—21no—
47C2×C3×Dic3⋊C4D311yescharacteristic
48C2×C3×Dic3⋊C4C2×C311yescharacteristic
49C3×#890—32no—
50C3×#890—32no—
51C3×#889—32no—
52C3×#889—32no—
53C3×#888—32no—
54C3×#888—32no—
55C3×#888—32no—
56C3×#878—32no—
57C3×#877—32no—
58#63964C2×C312yes—
59#63955C2×C312yes—
60#63846C2×C312yescomplemented
61#63845C2×C312yescomplemented
62#63840C2×C312yescomplemented
63#63839C2×C312yescomplemented
64C23×C33C2311yescharacteristic
65C2×C33×C4—41no—
66C2×C33×C4C2311yescharacteristic
67C2×C33×C4C2311yescharacteristic
68C2×C3×C3⋊Dic3C2312yes—
69C2×C3×C3⋊Dic3C2312yes—
70C3×#634—41no—
71C2×C32×Dic3—41no—
72C2×C32×Dic3Q814yescomplemented
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2312yes—
77C32×Dic6—41no—
78C3×#627—42no—
79C3×#544—91no—
80#5623—31no—
81#5500—31no—
82C2×C32×Q8—31no—
83C22×C32×C4—21no—
84C22×C32×C4—21no—
85C22×C32×C4—21no—
86C22×C32×C4—31no—
87C22×C32×C4—31no—
88C22×C32×C4—41no—
89C22×C32×C4C2×D311yescharacteristic
90C22×C32×C4C2×D311yescharacteristic
91C22×C32×C4C22×C311yescharacteristic
92C2×#634C22×C311yescharacteristic
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3C2×D311yescharacteristic
96C22×C3×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C22×C311yescharacteristic
98C22×C3×Dic3C22×C311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6—31no—
101C2×C3×Dic6—31no—
102C2×C3×Dic6—32no—
103C2×C3×Dic6—32no—
104C2×C3×Dic6—61no—
105C2×C3×Dic6C2×D311yescharacteristic
106C2×C3×Dic6C22×C311yescharacteristic
107C2×#627C22×C312yes—
108C32×C4⋊C4—32no—
109C32×C4⋊C4—32no—
110C32×C4⋊C4—32no—
111C32×C4⋊C4—31no—
112C32×C22⋊C4—32no—
113#3757C22×C312yes—
114C4⋊(C3⋊Dic3)C22×C311yescharacteristic
115#3750C22×C312yes—
116C3×#217—22no—
117C3×#217—32no—
118C3×#217—32no—
119C3×#217—62no—
120C3×#217C2×D312yes—
121C3×#217C22×C312yes—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3—31no—
124C3×C4⋊Dic3—31no—
125C3×C4⋊Dic3—32no—
126C3×C4⋊Dic3—32no—
127C3×C4⋊Dic3—32no—
128C3×C4⋊Dic3—32no—
129C3×C4⋊Dic3—61no—
130C3×C4⋊Dic3C2×D311yescharacteristic
131C3×C4⋊Dic3C22×C311yescharacteristic
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—32no—
136C3×Dic3⋊C4—32no—
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—32no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—62no—
144C3×Dic3⋊C4C2×D312yes—
145C3×Dic3⋊C4C2×D312yes—
146C3×Dic3⋊C4C2×D312yes—
147C3×Dic3⋊C4C22×C312yes—
148C3×Dic3⋊C4C22×C312yes—
149C3×Dic3⋊C4C22×C312yes—
150C3×C4×Dic3—32no—
151C3×C4×Dic3—32no—
152C3×C4×Dic3—32no—
153C3×C4×Dic3—32no—
154#3724C22×C312yes—
155Dic3⋊Dic3C22×C312yes—
156Dic3⋊Dic3C22×C312yes—
157Dic3⋊Dic3C22×C312yes—
158Dic3⋊Dic3C22×C312yes—
159Dic32C22×C312yes—
160Dic32C22×C312yes—
161C22×C33—21no—
162C22×C33—21no—
163C22×C33C2×Q812yes—
164C22×C33C2411yescharacteristic
165C33×C4—21no—
166C33×C4—21no—
167C3×C3⋊Dic3—22no—
168C3×C3⋊Dic3—22no—
169C32×Dic3—22no—
170C32×Dic3—22no—
171C32×Dic3—22no—
172C32×Dic3C2×Q814yes—
173C3×C4⋊Q8—92no—
174C3×C4⋊Q8—92no—
175C3×#125—92no—
176C3×#125—92no—
177C3×C22⋊Q8—31no—
178C3×C22⋊Q8—31no—
179C3×C22⋊Q8—61no—
180C3×C22⋊Q8—92no—
181C3×C22⋊Q8—91no—
182C3×#117—92no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—61no—
186#944—32no—
187#926—32no—
188#924—31no—
189#924—31no—
190#924—32no—
191#924—61no—
192#924C3×D311yescharacteristic
193C2×Dic3⋊C4C3×D311yescharacteristic
194#890—32no—
195#890—32no—
196#889—32no—
197#889—32no—
198#888—32no—
199#888—32no—
200#888—32no—
201#878—32no—
202#877—32no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—41no—
207C23×C32C22×D311yescharacteristic
208C23×C32C22×D311yescharacteristic
209C23×C32C23×C311yescharacteristic
210C32×Q8—121no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—34no—
218C2×C32×C4—32no—
219C2×C32×C4—32no—
220C2×C32×C4—32no—
221C2×C32×C4—32no—
222C2×C32×C4—41no—
223C2×C32×C4—41no—
224C2×C32×C4—41no—
225C2×C32×C4—41no—
226C2×C32×C4—41no—
227C2×C32×C4—42no—
228C2×C32×C4—42no—
229C2×C32×C4—42no—
230C2×C32×C4—44no—
231C2×C32×C4—121no—
232C2×C32×C4C22×D311yescharacteristic
233C2×C32×C4C22×D311yescharacteristic
234C2×C32×C4C22×D311yescharacteristic
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C23×C311yescharacteristic
237C2×C32×C4C23×C311yescharacteristic
238C2×C3⋊Dic3C23×C312yes—
239C2×C3⋊Dic3C23×C312yes—
240#634—41no—
241C2×C3×Dic3—24no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—22no—
246C2×C3×Dic3—32no—
247C2×C3×Dic3—32no—
248C2×C3×Dic3—32no—
249C2×C3×Dic3—32no—
250C2×C3×Dic3—41no—
251C2×C3×Dic3—41no—
252C2×C3×Dic3—42no—
253C2×C3×Dic3—62no—
254C2×C3×Dic3—62no—
255C2×C3×Dic3Dic614yescomplemented
256C2×C3×Dic3C3×Q814yescomplemented
257C2×C3×Dic3C22×D312yes—
258C2×C3×Dic3C22×D312yes—
259C2×C3×Dic3C22×D312yes—
260C2×C3×Dic3C22×D312yes—
261C2×C3×Dic3C23×C312yes—
262C2×C3×Dic3C23×C312yes—
263C2×C3×Dic3C23×C312yes—
264C2×C3×Dic3C23×C312yes—
265C3×Dic6—41no—
266C3×Dic6—41no—
267C3×Dic6—42no—
268C3×Dic6—122no—
269C3×Dic6—122no—
270C3×Dic6—121no—
271C3×Dic6—121no—
272C3×Dic6—122no—
273#627—42no—
274#544—91noSylow
275C2×C33—22no—
276C2×C33C22×Q811yescharacteristic
277C2×C33H(5,𝔽2)11yescharacteristic
278C2×C332−1+411yescharacteristic
279C2×C3×Q8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8—92no—
283C2×C3×Q8—91no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—41no—
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C22×C3×C4D3211yescharacteristic
295C22×C3×C4C2×C3×D311yescharacteristic
296C22×C3×C4C2×C3×D311yescharacteristic
297C22×Dic3C2×C3×D311yescharacteristic
298C22×Dic3C2×C3×D311yescharacteristic
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—32no—
302C2×Dic6—32no—
303C2×Dic6—61no—
304C2×Dic6C2×C3×D311yescharacteristic
305C3×C4⋊C4—32no—
306C3×C4⋊C4—32no—
307C3×C4⋊C4—32no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—32no—
310C3×C4⋊C4—32no—
311C3×C4⋊C4—32no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—62no—
314C3×C4⋊C4—62no—
315C3×C4⋊C4—62no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—92no—
318C3×C4⋊C4—92no—
319C3×C4⋊C4—92no—
320C3×C4⋊C4—92no—
321C3×C4⋊C4—92no—
322C3×C4⋊C4—92no—
323C3×C4⋊C4—91no—
324C3×C22⋊C4—32no—
325C3×C22⋊C4—32no—
326C3×C22⋊C4—62no—
327C3×C22⋊C4—92no—
328C3×C42—92no—
329C3×C42—92no—
330#217—32no—
331#217—32no—
332#217—62no—
333#217C2×C3×D312yes—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—32no—
337C4⋊Dic3—32no—
338C4⋊Dic3—32no—
339C4⋊Dic3—32no—
340C4⋊Dic3—61no—
341C4⋊Dic3C2×C3×D311yescharacteristic
342Dic3⋊C4—32no—
343Dic3⋊C4—32no—
344Dic3⋊C4—32no—
345Dic3⋊C4—32no—
346Dic3⋊C4—32no—
347Dic3⋊C4—32no—
348Dic3⋊C4—32no—
349Dic3⋊C4—32no—
350Dic3⋊C4—62no—
351Dic3⋊C4C2×C3×D312yes—
352Dic3⋊C4C2×C3×D312yes—
353Dic3⋊C4C2×C3×D312yes—
354C4×Dic3—32no—
355C4×Dic3—32no—
356C4×Dic3—32no—
357C4×Dic3—32no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—42no—
373C22×C32—41no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32—42no—
379C22×C32—42no—
380C22×C32C2×Dic612yes—
381C22×C32D3×Q812yes—
382C22×C32C2×C3×Q812yes—
383C22×C32C23×D311yescharacteristic
384C22×C32C23×D311yescharacteristic
385C22×C32C24×C311yescharacteristic
386C32×C4—21no—
387C32×C4—21no—
388C32×C4—22no—
389C32×C4—22no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—34no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4—42no—
400C32×C4—42no—
401C32×C4—62no—
402C32×C4—62no—
403C32×C4—62no—
404C3⋊Dic3—22no—
405C3⋊Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—22no—
409C3×Dic3—22no—
410C3×Dic3—22no—
411C3×Dic3—22no—
412C3×Dic3—24no—
413C3×Dic3—42no—
414C3×Dic3—42no—
415C3×Dic3—42no—
416C3×Dic3—62no—
417C3×Dic3—62no—
418C3×Dic3—62no—
419C3×Dic3—62no—
420C3×Dic3—122no—
421C3×Dic3—122no—
422C3×Dic3C2×Dic614yes—
423C3×Dic3C2×C3×Q814yes—
424C4⋊Q8—92no—
425C4⋊Q8—92no—
426#125—92no—
427#125—92no—
428C22⋊Q8—31no—
429C22⋊Q8—92no—
430C22⋊Q8—91no—
431#117—92no—
432C2×C4⋊C4—31no—
433C33#54411yescharacteristic, complemented, Sylow
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—41no—
438C23×C3C2×D3211yescharacteristic
439C23×C3C22×C3×D311yescharacteristic
440C23×C3C22×C3×D311yescharacteristic
441C3×Q8—121no—
442C3×Q8—121no—
443C3×Q8—122no—
444C3×Q8—361no—
445C3×Q8—362no—
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—32no—
453C2×C3×C4—32no—
454C2×C3×C4—34no—
455C2×C3×C4—34no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—32no—
461C2×C3×C4—32no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—44no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—62no—
472C2×C3×C4—64no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—62no—
476C2×C3×C4—92no—
477C2×C3×C4—92no—
478C2×C3×C4—121no—
479C2×C3×C4—121no—
480C2×C3×C4—122no—
481C2×C3×C4C2×D3211yescharacteristic
482C2×C3×C4C2×D3211yescharacteristic
483C2×C3×C4C22×C3×D311yescharacteristic
484C2×C3×C4C22×C3×D311yescharacteristic
485C2×C3×C4C22×C3×D311yescharacteristic
486C2×C3×C4C22×C3×D311yescharacteristic
487C2×Dic3—32no—
488C2×Dic3—32no—
489C2×Dic3—32no—
490C2×Dic3—32no—
491C2×Dic3—41no—
492C2×Dic3—62no—
493C2×Dic3—62no—
494C2×Dic3C3×Dic614yescomplemented
495C2×Dic3C22×C3×D312yes—
496C2×Dic3C22×C3×D312yes—
497C2×Dic3C22×C3×D312yes—
498C2×Dic3C22×C3×D312yes—
499Dic6—41no—
500Dic6—122no—
501Dic6—122no—
502Dic6—121no—
503Dic6—121no—
504Dic6—122no—
505C2×C32—22no—
506C2×C32—24no—
507C2×C32—22no—
508C2×C32—22no—
509C2×C32—21no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—41no—
519C2×C32—41no—
520C2×C32—41no—
521C2×C32—42no—
522C2×C32—42no—
523C2×C32—44no—
524C2×C32C22×Dic611yescharacteristic
525C2×C32#100411yescharacteristic
526C2×C32#100411yescharacteristic
527C2×C32C2×D3×Q811yescharacteristic
528C2×C32#100711yescharacteristic
529C2×C32#101011yescharacteristic
530C2×C32C22×C3×Q811yescharacteristic
531C2×C32C3×H(5,𝔽2)11yescharacteristic
532C2×C32C3×2−1+411yescharacteristic
533C2×Q8—31no—
534C2×Q8—92no—
535C2×Q8—91no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4C3×D3211yescharacteristic
539C4⋊C4—32no—
540C4⋊C4—32no—
541C4⋊C4—31no—
542C4⋊C4—32no—
543C4⋊C4—92no—
544C4⋊C4—92no—
545C4⋊C4—92no—
546C4⋊C4—92no—
547C4⋊C4—92no—
548C4⋊C4—91no—
549C4⋊C4—92no—
550C22⋊C4—32no—
551C22⋊C4—92no—
552C42—92no—
553C42—92no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—41no—
575C22×C3—42no—
576C22×C3D3×Dic612yes—
577C22×C3C2×C3×Dic612yes—
578C22×C3C3×D3×Q812yes—
579C22×C3C22×D3211yescharacteristic
580C22×C3C23×C3×D311yescharacteristic
581C22×C3C23×C3×D311yescharacteristic
582C3×C4—22no—
583C3×C4—22no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—34no—
591C3×C4—34no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—64no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4—62no—
604C3×C4—62no—
605C3×C4—122no—
606C3×C4—122no—
607C3×C4—122no—
608C3×C4—182no—
609C3×C4—182no—
610Dic3—22no—
611Dic3—22no—
612Dic3—22no—
613Dic3—62no—
614Dic3—62no—
615Dic3—62no—
616Dic3—62no—
617Dic3—122no—
618Dic3—122no—
619Dic3C2×C3×Dic614yes—
620C32—21no—
621C32—21no—
622C32—21no—
623C32—41no—
624C32#550011yescharacteristic, complemented
625C32#562311yescharacteristic, complemented
626C32C3×#54411yescharacteristic, complemented
627C23C2×C3×D3211yescharacteristic
628Q8—121no—
629Q8—361no—
630Q8—362no—
631C2×C4—32no—
632C2×C4—34no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—32no—
636C2×C4—41no—
637C2×C4—92no—
638C2×C4—92no—
639C2×C4—121no—
640C2×C4C2×C3×D3211yescharacteristic
641C2×C4C2×C3×D3211yescharacteristic
642C2×C3—24no—
643C2×C3—22no—
644C2×C3—22no—
645C2×C3—22no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—42no—
656C2×C3—42no—
657C2×C3—44no—
658C2×C3—41no—
659C2×C3—41no—
660C2×C3—41no—
661C2×C3C2×D3×Dic611yescharacteristic
662C2×C3#6429711yescharacteristic
663C2×C3#6433011yescharacteristic
664C2×C3C22×C3×Dic611yescharacteristic
665C2×C3C3×#100411yescharacteristic
666C2×C3C3×#100411yescharacteristic
667C2×C3C2×C3×D3×Q811yescharacteristic
668C2×C3C3×#100711yescharacteristic
669C2×C3C3×#101011yescharacteristic
670C22—21no—
671C22—21no—
672C22C3×D3×Dic612yes—
673C22C22×C3×D3211yescharacteristic
674C4—21no—
675C4—21no—
676C4—34no—
677C4—62no—
678C4—62no—
679C4—62no—
680C4—182no—
681C4—182no—
682C3—21no—
683C3—21no—
684C3—21no—
685C3—41no—
686C3#1059481211yescharacteristic, direct product factor
687C3C3×#550011yescharacteristic, complemented
688C3C3×#562311yescharacteristic, complemented
689C2—22no—
690C2C2×C3×D3×Dic611yescharacteristic
691C2C3×#6429711yescharacteristic
692C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
6. C3×#63846C2semidirect
7. C3×#63845C2semidirect
8. C3×#63840C2semidirect
9. C3×#63839C2semidirect
12. #10594812C3direct (N × H)
60. #63846C2×C3semidirect
61. #63845C2×C3semidirect
62. #63840C2×C3semidirect
63. #63839C2×C3semidirect
72. C2×C32×Dic3Q8semidirect
255. C2×C3×Dic3Dic6semidirect
256. C2×C3×Dic3C3×Q8semidirect
433. C33#544semidirect
494. C2×Dic3C3×Dic6semidirect
624. C32#5500semidirect
625. C32#5623semidirect
626. C32C3×#544semidirect
686. C3#10594812direct (N × H)
687. C3C3×#5500semidirect
688. C3C3×#5623semidirect

Maximal subgroups

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

subgroupindex
C3×#641332
C32×#9242
C2×C32×Dic3⋊C42
C3×#639642
C3×#639552
C3×#638462
C3×#638452
C3×#638402
C3×#638392
C3×#56233
C3×#55003
#105948123