Finite Group Databasebeta

← #123×(C3⋊D3)⋊C3 #13153043

Subgroups — #123×(C3⋊D3)⋊C3 #13153043

Order 1728.

1275 conjugacy classes of subgroups.

The subgroup lattice has 675 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
2C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
4#64144⋊C3C211yesmaximal, characteristic, complemented
5#64138⋊C3C211yesmaximal, characteristic, complemented
6#64103⋊C3C212yesmaximal, complemented
7C4⋊C4×(C3⋊D3)⋊C3C212yesmaximal, complemented
8#64095⋊C3C211yesmaximal, characteristic, complemented
9#64092⋊C3C212yesmaximal, complemented
10C22⋊C4×(C3⋊D3)⋊C3C212yesmaximal, complemented
11C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
12C3⋊D3×#123C311yesmaximal, characteristic, complemented
13C3×D3×#123—31nomaximal
14C23×(C3⋊D3)⋊C3C2211yescharacteristic
15C23×(C3⋊D3)⋊C3C2211yescharacteristic
16C2×D4×H(3,𝔽3)C2211yescharacteristic
17C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
18C2×#638⋊C3C2211yescharacteristic
19C2×#638⋊C3C2211yescharacteristic
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
21D4×(C3⋊D3)⋊C3—24no—
22C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3—24no—
24C2×C4×(C3⋊D3)⋊C3C2212yes—
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×C4×(C3⋊D3)⋊C3C2212yes—
27C2×C4×(C3⋊D3)⋊C3C2212yescomplemented
28C4⋊C4×H(3,𝔽3)C2212yescomplemented
29C22⋊C4×H(3,𝔽3)C2212yescomplemented
30C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
31#3757⋊C3C2211yescharacteristic, complemented
32#3757⋊C3C2212yescomplemented
33#3752⋊C3C2212yescomplemented
34#3752⋊C3C2212yescomplemented
35#3752⋊C3C2212yescomplemented
36C4⋊((C3⋊Dic3)⋊C3)C2212yescomplemented
37#3750⋊C3C2212yescomplemented
38#3750⋊C3C2212yescomplemented
39C2×D4×C3⋊D3C2×C311yescharacteristic
40C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
41C2×C3×D3×D4—31no—
42C22×C3×C4×D3—31no—
43C32×#123—21no—
44C32×#123D311yescharacteristic, complemented
45C32×#123C2×C311yescharacteristic, complemented
46#64144C2×C311yescharacteristic, complemented
47#64138C2×C311yescharacteristic, complemented
48#64103C2×C312yescomplemented
49C4⋊C4×C3⋊D3C2×C312yescomplemented
50#64095C2×C311yescharacteristic, complemented
51#64092C2×C312yescomplemented
52C22⋊C4×C3⋊D3C2×C312yescomplemented
53C22⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
54C3×#935—31no—
55C3×#929—31no—
56C3×#894—32no—
57C3×D3×C4⋊C4—32no—
58C3×#886—31no—
59C3×#883—32no—
60C3×D3×C22⋊C4—31no—
61C3×D3×C22⋊C4—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C23×H(3,𝔽3)C2311yescharacteristic
64C22×(C3⋊D3)⋊C3—24no—
65C22×(C3⋊D3)⋊C3—22no—
66C22×(C3⋊D3)⋊C3—24no—
67C22×(C3⋊D3)⋊C3D414yes—
68C22×(C3⋊D3)⋊C3C2311yescharacteristic
69C22×(C3⋊D3)⋊C3C2311yescharacteristic
70C22×(C3⋊D3)⋊C3C2311yescharacteristic
71D4×H(3,𝔽3)—22no—
72C2×C4×H(3,𝔽3)—22no—
73C2×C4×H(3,𝔽3)C2312yes—
74C2×C4×H(3,𝔽3)C2311yescharacteristic
75C2×C4×H(3,𝔽3)C2312yes—
76#638⋊C3—22no—
77#638⋊C3—22no—
78C2×(C3⋊Dic3)⋊C3—22no—
79C2×(C3⋊Dic3)⋊C3C2312yes—
80C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
81C2×(C3⋊Dic3)⋊C3C2312yes—
82C4⋊((C3⋊D3)⋊C3)—22no—
83C4×(C3⋊D3)⋊C3—24no—
84C4×(C3⋊D3)⋊C3—24no—
85C4×(C3⋊D3)⋊C3—22no—
86C4×(C3⋊D3)⋊C3—24no—
87C2×C3×#123—91no—
88D3×#123—31no—
89D3×#123—91no—
90C23×C3⋊D3C22×C311yescharacteristic
91C23×C3⋊D3C22×C311yescharacteristic
92C23×C3×D3—31no—
93C23×C3×D3—31no—
94C2×C32×D4—21no—
95C2×C32×D4C2×D311yescharacteristic
96C2×C32×D4C22×C311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2×D311yescharacteristic, complemented
99C22×C32×C4C22×C311yescharacteristic, complemented
100C2×#638C22×C311yescharacteristic
101C2×#638C22×C311yescharacteristic
102C22×C3⋊Dic3C22×C311yescharacteristic, complemented
103D4×C3⋊D3—24no—
104C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
105C2×C4×C3⋊D3—24no—
106C2×C4×C3⋊D3C22×C312yes—
107C2×C4×C3⋊D3C22×C312yes—
108C2×C4×C3⋊D3C22×C311yescharacteristic
109C2×C4×C3⋊D3C22×C312yescomplemented
110C2×C3×#67—31no—
111C2×C3×#67—31no—
112C22×C3×Dic3—31no—
113C3×D3×D4—64no—
114C2×C3×D12—31no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—31no—
119C2×C3×C4×D3—64no—
120C32×C4⋊C4—22no—
121C32×C4⋊C4C2×D312yescomplemented
122C32×C4⋊C4C22×C312yescomplemented
123C32×C22⋊C4—21no—
124C32×C22⋊C4—22no—
125C32×C22⋊C4C2×D312yescomplemented
126C32×C22⋊C4C2×D311yescharacteristic, complemented
127C32×C22⋊C4C22×C312yescomplemented
128C32×C22⋊C4C22×C311yescharacteristic, complemented
129#3757C22×C312yescomplemented
130#3757C22×C311yescharacteristic, complemented
131#3752C22×C312yescomplemented
132#3752C22×C312yescomplemented
133#3752C22×C312yescomplemented
134C4⋊(C3⋊Dic3)C22×C312yescomplemented
135#3750C22×C312yescomplemented
136#3750C22×C312yescomplemented
137C3×#217—32no—
138C3×#217—31no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×C4⋊Dic3—32no—
143C3×Dic3⋊C4—32no—
144C3×Dic3⋊C4—32no—
145C22×H(3,𝔽3)—22no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)—22no—
148C22×H(3,𝔽3)C2×D412yes—
149C22×H(3,𝔽3)C2411yescharacteristic
150C2×(C3⋊D3)⋊C3—22no—
151C2×(C3⋊D3)⋊C3—28no—
152C2×(C3⋊D3)⋊C3—21no—
153C2×(C3⋊D3)⋊C3—22no—
154C2×(C3⋊D3)⋊C3—44no—
155C2×(C3⋊D3)⋊C3C2×D412yes—
156C2×(C3⋊D3)⋊C3C2×D412yes—
157C2×(C3⋊D3)⋊C3#4114yes—
158C4×H(3,𝔽3)—22no—
159C4×H(3,𝔽3)—21no—
160C4×H(3,𝔽3)—22no—
161(C3⋊Dic3)⋊C3—22no—
162(C3⋊Dic3)⋊C3—21no—
163(C3⋊Dic3)⋊C3—22no—
164C22×C3×D4—91no—
165C23×C3×C4—91no—
166C2×D3×D4—31no—
167C2×D3×D4—91no—
168C22×C4×D3—31no—
169C22×C4×D3—91no—
170C3×#123—31no—
171C3×#123—31no—
172C3×#123—61no—
173C3×#123—92no—
174C3×#123—91no—
175C3×#123—92no—
176C3×#123—91no—
177C3×#123—91no—
178C3×#123C3×D311yescharacteristic
179C2×C3×C4⋊C4—92no—
180C2×C3×C22⋊C4—91no—
181C2×C3×C22⋊C4—92no—
182#935—31no—
183#935—91no—
184#929—31no—
185#929—91no—
186#894—32no—
187#894—92no—
188D3×C4⋊C4—32no—
189D3×C4⋊C4—92no—
190#886—31no—
191#886—91no—
192#883—32no—
193#883—92no—
194D3×C22⋊C4—31no—
195D3×C22⋊C4—32no—
196D3×C22⋊C4—91no—
197D3×C22⋊C4—92no—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32C22×D311yescharacteristic
201C23×C32C22×D311yescharacteristic
202C23×C32C23×C311yescharacteristic
203C23×C32C23×C311yescharacteristic
204C22×C3⋊D3—24no—
205C22×C3⋊D3—22no—
206C22×C3⋊D3—24no—
207C22×C3⋊D3C3×D414yes—
208C22×C3⋊D3C23×C311yescharacteristic
209C22×C3⋊D3C23×C311yescharacteristic
210C22×C3⋊D3C23×C311yescharacteristic
211C22×C3×D3—31no—
212C22×C3×D3—34no—
213C22×C3×D3—31no—
214C22×C3×D3—31no—
215C22×C3×D3—64no—
216C22×C3×D3—64no—
217C22×C3×D3—62no—
218C32×D4—22no—
219C32×D4—22no—
220C32×D4—42no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4—22no—
224C2×C32×C4—22no—
225C2×C32×C4—21no—
226C2×C32×C4—42no—
227C2×C32×C4C22×D311yescharacteristic
228C2×C32×C4C22×D312yes—
229C2×C32×C4C22×D312yes—
230C2×C32×C4C23×C311yescharacteristic
231C2×C32×C4C23×C312yes—
232C2×C32×C4C23×C312yes—
233#638—22no—
234#638—22no—
235C2×C3⋊Dic3—22no—
236C2×C3⋊Dic3C23×C311yescharacteristic
237C2×C3⋊Dic3C23×C312yes—
238C2×C3⋊Dic3C23×C312yes—
239C4⋊(C3⋊D3)—22no—
240C4×C3⋊D3—24no—
241C4×C3⋊D3—24no—
242C4×C3⋊D3—22no—
243C4×C3⋊D3—24no—
244C3×#67—62no—
245C3×#67—62no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—32no—
248C2×C3×Dic3—32no—
249C2×C3×Dic3—62no—
250C3×D12—62no—
251C3×C4×D3—64no—
252C3×C4×D3—64no—
253C3×C4×D3—64no—
254C3×C4×D3—62no—
255C2×#123—91noSylow
256C2×H(3,𝔽3)—22no—
257C2×H(3,𝔽3)—41no—
258C2×H(3,𝔽3)C22×D411yescharacteristic
259C2×H(3,𝔽3)C2×#4112yes—
260(C3⋊D3)⋊C3—22no—
261(C3⋊D3)⋊C3—41no—
262(C3⋊D3)⋊C3#12314yesdirect product factor
263C24×C3—91no—
264C24×C3—91no—
265C23×D3—31no—
266C23×D3—31no—
267C23×D3—91no—
268C23×D3—91no—
269C2×C3×D4—31no—
270C2×C3×D4—31no—
271C2×C3×D4—61no—
272C2×C3×D4—91no—
273C2×C3×D4—91no—
274C2×C3×D4—91no—
275C2×C3×D4—184no—
276C2×C3×D4C2×C3×D311yescharacteristic
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—61no—
280C22×C3×C4—92no—
281C22×C3×C4—92no—
282C22×C3×C4—91no—
283C22×C3×C4—92no—
284C22×C3×C4—91no—
285C22×C3×C4—184no—
286C22×C3×C4C2×C3×D311yescharacteristic
287C2×#67—31no—
288C2×#67—31no—
289C2×#67—91no—
290C2×#67—91no—
291C22×Dic3—31no—
292C22×Dic3—91no—
293D3×D4—64no—
294D3×D4—184no—
295C2×D12—31no—
296C2×D12—91no—
297C2×C4×D3—32no—
298C2×C4×D3—32no—
299C2×C4×D3—32no—
300C2×C4×D3—31no—
301C2×C4×D3—64no—
302C2×C4×D3—92no—
303C2×C4×D3—92no—
304C2×C4×D3—92no—
305C2×C4×D3—91no—
306C2×C4×D3—184no—
307C3×C4⋊C4—32no—
308C3×C4⋊C4—32no—
309C3×C4⋊C4—62no—
310C3×C4⋊C4—92no—
311C3×C4⋊C4—92no—
312C3×C4⋊C4—92no—
313C3×C4⋊C4C2×C3×D312yes—
314C3×C22⋊C4—32no—
315C3×C22⋊C4—31no—
316C3×C22⋊C4—31no—
317C3×C22⋊C4—32no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—62no—
320C3×C22⋊C4—92no—
321C3×C22⋊C4—92no—
322C3×C22⋊C4—92no—
323C3×C22⋊C4—91no—
324C3×C22⋊C4—92no—
325C3×C22⋊C4C2×C3×D312yes—
326C3×C22⋊C4C2×C3×D311yescharacteristic
327#217—32no—
328#217—31no—
329#217—92no—
330#217—91no—
331(C2×D3)⋊C4—32no—
332(C2×D3)⋊C4—32no—
333(C2×D3)⋊C4—32no—
334(C2×D3)⋊C4—92no—
335(C2×D3)⋊C4—92no—
336(C2×D3)⋊C4—92no—
337C4⋊Dic3—32no—
338C4⋊Dic3—92no—
339Dic3⋊C4—32no—
340Dic3⋊C4—32no—
341Dic3⋊C4—92no—
342Dic3⋊C4—92no—
343C22×C32—22no—
344C22×C32—22no—
345C22×C32—21no—
346C22×C32—22no—
347C22×C32—21no—
348C22×C32—22no—
349C22×C32—21no—
350C22×C32—22no—
351C22×C32—42no—
352C22×C32—41no—
353C22×C32—42no—
354C22×C32D3×D412yes—
355C22×C32C2×C3×D412yes—
356C22×C32C23×D311yescharacteristic
357C22×C32C24×C311yescharacteristic
358C2×C3⋊D3—22no—
359C2×C3⋊D3—28no—
360C2×C3⋊D3—21no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—44no—
363C2×C3⋊D3C2×C3×D412yes—
364C2×C3⋊D3C2×C3×D412yes—
365C2×C3⋊D3C3×#4114yes—
366C2×C3×D3—32no—
367C2×C3×D3—34no—
368C2×C3×D3—32no—
369C2×C3×D3—68no—
370C2×C3×D3—62no—
371C2×C3×D3—61no—
372C2×C3×D3—62no—
373C2×C3×D3—124no—
374C32×C4—22no—
375C32×C4—21no—
376C32×C4—22no—
377C32×C4—22no—
378C32×C4—21no—
379C32×C4—22no—
380C32×C4—42no—
381C32×C4—42no—
382C32×C4—41no—
383C3⋊Dic3—22no—
384C3⋊Dic3—21no—
385C3⋊Dic3—22no—
386C3×Dic3—62no—
387C3×Dic3—61no—
388C3×Dic3—62no—
389C22×D4—91no—
390C23×C4—91no—
391#123—91no—
392#123—91no—
393#123—92no—
394#123—92no—
395#123—91no—
396#123(C3⋊D3)⋊C311yescharacteristic, direct product factor
397C2×C4⋊C4—92no—
398C2×C22⋊C4—91no—
399C2×C22⋊C4—92no—
400H(3,𝔽3)C2×#12311yescharacteristic, complemented, Sylow
401C23×C3—31no—
402C23×C3—31no—
403C23×C3—31no—
404C23×C3—31no—
405C23×C3—61no—
406C23×C3—61no—
407C23×C3—91no—
408C23×C3—91no—
409C23×C3—94no—
410C23×C3—91no—
411C23×C3—184no—
412C23×C3—182no—
413C23×C3—184no—
414C23×C3C22×C3×D311yescharacteristic
415C23×C3C22×C3×D311yescharacteristic
416C22×D3—31no—
417C22×D3—31no—
418C22×D3—34no—
419C22×D3—31no—
420C22×D3—64no—
421C22×D3—62no—
422C22×D3—64no—
423C22×D3—91no—
424C22×D3—94no—
425C22×D3—91no—
426C22×D3—91no—
427C22×D3—184no—
428C22×D3—182no—
429C22×D3—184no—
430C3×D4—22no—
431C3×D4—62no—
432C3×D4—62no—
433C3×D4—122no—
434C3×D4—182no—
435C3×D4—182no—
436C3×D4—182no—
437C2×C3×C4—22no—
438C2×C3×C4—32no—
439C2×C3×C4—32no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—61no—
449C2×C3×C4—92no—
450C2×C3×C4—92no—
451C2×C3×C4—91no—
452C2×C3×C4—122no—
453C2×C3×C4—184no—
454C2×C3×C4—184no—
455C2×C3×C4—184no—
456C2×C3×C4—182no—
457C2×C3×C4—182no—
458C2×C3×C4C22×C3×D311yescharacteristic
459C2×C3×C4C22×C3×D312yes—
460C2×C3×C4C22×C3×D312yes—
461#67—62no—
462#67—62no—
463#67—182no—
464#67—182no—
465C2×Dic3—31no—
466C2×Dic3—32no—
467C2×Dic3—32no—
468C2×Dic3—62no—
469C2×Dic3—91no—
470C2×Dic3—92no—
471C2×Dic3—92no—
472C2×Dic3—182no—
473D12—62no—
474D12—182no—
475C4×D3—64no—
476C4×D3—64no—
477C4×D3—64no—
478C4×D3—62no—
479C4×D3—184no—
480C4×D3—184no—
481C4×D3—184no—
482C4×D3—182no—
483C2×C32—22no—
484C2×C32—22no—
485C2×C32—21no—
486C2×C32—22no—
487C2×C32—42no—
488C2×C32—41no—
489C2×C32—41no—
490C2×C32—81no—
491C2×C32C2×D3×D411yescharacteristic
492C2×C32D3×#4112yes—
493C2×C32C22×C3×D411yescharacteristic
494C2×C32C2×C3×#4112yes—
495C3⋊D3—22no—
496C3⋊D3—41no—
497C3⋊D3C3×#12314yescomplemented
498C3×D3—34no—
499C3×D3—62no—
500C3×D3—121no—
501C24—91no—
502C24—91no—
503C2×D4—91no—
504C2×D4—91no—
505C2×D4—91no—
506C2×D4—184no—
507C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
508C22×C4—91no—
509C22×C4—92no—
510C22×C4—92no—
511C22×C4—91no—
512C22×C4—92no—
513C22×C4—184no—
514C22×C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
515C4⋊C4—92no—
516C4⋊C4—92no—
517C4⋊C4—92no—
518C4⋊C4C2×(C3⋊D3)⋊C312yescomplemented
519C22⋊C4—91no—
520C22⋊C4—92no—
521C22⋊C4—92no—
522C22⋊C4—92no—
523C22⋊C4—92no—
524C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic, complemented
525C22⋊C4C2×(C3⋊D3)⋊C312yescomplemented
526C22×C3—22no—
527C22×C3—21no—
528C22×C3—22no—
529C22×C3—31no—
530C22×C3—31no—
531C22×C3—32no—
532C22×C3—32no—
533C22×C3—62no—
534C22×C3—62no—
535C22×C3—61no—
536C22×C3—61no—
537C22×C3—62no—
538C22×C3—62no—
539C22×C3—61no—
540C22×C3—62no—
541C22×C3—92no—
542C22×C3—94no—
543C22×C3—92no—
544C22×C3—122no—
545C22×C3—121no—
546C22×C3—122no—
547C22×C3—182no—
548C22×C3—181no—
549C22×C3—182no—
550C22×C3—188no—
551C22×C3—364no—
552C22×C3C3×D3×D412yes—
553C22×C3C23×C3×D311yescharacteristic
554C2×D3—32no—
555C2×D3—34no—
556C2×D3—32no—
557C2×D3—68no—
558C2×D3—62no—
559C2×D3—61no—
560C2×D3—62no—
561C2×D3—92no—
562C2×D3—94no—
563C2×D3—92no—
564C2×D3—124no—
565C2×D3—188no—
566C2×D3—182no—
567C2×D3—181no—
568C2×D3—182no—
569C2×D3—364no—
570C3×C4—22no—
571C3×C4—21no—
572C3×C4—22no—
573C3×C4—62no—
574C3×C4—61no—
575C3×C4—62no—
576C3×C4—62no—
577C3×C4—61no—
578C3×C4—62no—
579C3×C4—122no—
580C3×C4—121no—
581C3×C4—122no—
582C3×C4—182no—
583C3×C4—181no—
584C3×C4—182no—
585Dic3—62no—
586Dic3—61no—
587Dic3—62no—
588Dic3—182no—
589Dic3—181no—
590Dic3—182no—
591C32—21no—
592C32D3×#12311yescharacteristic, complemented
593C32C2×C3×#12311yescharacteristic, complemented
594C23—91no—
595C23—91no—
596C23—94no—
597C23—91no—
598C23—184no—
599C23—182no—
600C23—184no—
601C23C22×(C3⋊D3)⋊C311yescharacteristic
602C23C22×(C3⋊D3)⋊C311yescharacteristic
603D4—22no—
604D4—182no—
605D4—182no—
606D4—182no—
607C2×C4—22no—
608C2×C4—92no—
609C2×C4—92no—
610C2×C4—91no—
611C2×C4—184no—
612C2×C4—184no—
613C2×C4—182no—
614C2×C4—184no—
615C2×C4—182no—
616C2×C4C22×(C3⋊D3)⋊C312yes—
617C2×C4C22×(C3⋊D3)⋊C312yes—
618C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
619C2×C3—22no—
620C2×C3—31no—
621C2×C3—31no—
622C2×C3—32no—
623C2×C3—32no—
624C2×C3—41no—
625C2×C3—62no—
626C2×C3—62no—
627C2×C3—61no—
628C2×C3—62no—
629C2×C3—94no—
630C2×C3—122no—
631C2×C3—121no—
632C2×C3—121no—
633C2×C3—182no—
634C2×C3—241no—
635C2×C3—361no—
636C2×C3C2×C3×D3×D411yescharacteristic
637C2×C3C3×D3×#4112yes—
638D3—34no—
639D3—62no—
640D3—94no—
641D3—121no—
642D3—182no—
643D3—361no—
644C22—22no—
645C22—21no—
646C22—22no—
647C22—92no—
648C22—94no—
649C22—92no—
650C22—188no—
651C22—182no—
652C22—181no—
653C22—182no—
654C22—364no—
655C22D4×(C3⋊D3)⋊C312yes—
656C22C23×(C3⋊D3)⋊C311yescharacteristic
657C4—22no—
658C4—21no—
659C4—22no—
660C4—182no—
661C4—181no—
662C4—182no—
663C3—31no—
664C3—31no—
665C3—61no—
666C3C3×D3×#12311yescharacteristic
667C2—22no—
668C2—41no—
669C2—94no—
670C2—182no—
671C2—361no—
672C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
673C2#41×(C3⋊D3)⋊C312yes—
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
prime radicalC2×D4×(C3⋊D3)⋊C3C2
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C2×C3×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C22×C4×(C3⋊D3)⋊C3C2semidirect
3. H(3,𝔽3)×#123C2semidirect
4. #64144⋊C3C2semidirect
5. #64138⋊C3C2semidirect
6. #64103⋊C3C2semidirect
7. C4⋊C4×(C3⋊D3)⋊C3C2semidirect
8. #64095⋊C3C2semidirect
9. #64092⋊C3C2semidirect
10. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
11. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
12. C3⋊D3×#123C3semidirect
17. C22×C4×H(3,𝔽3)C22semidirect
20. C22×(C3⋊Dic3)⋊C3C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. C4⋊C4×H(3,𝔽3)C22semidirect
29. C22⋊C4×H(3,𝔽3)C22semidirect
30. C22⋊C4×H(3,𝔽3)C22semidirect
31. #3757⋊C3C22semidirect
32. #3757⋊C3C22semidirect
33. #3752⋊C3C22semidirect
34. #3752⋊C3C22semidirect
35. #3752⋊C3C22semidirect
36. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
37. #3750⋊C3C22semidirect
38. #3750⋊C3C22semidirect
40. C22×C4×C3⋊D3C2×C3semidirect
44. C32×#123D3semidirect
45. C32×#123C2×C3semidirect
46. #64144C2×C3semidirect
47. #64138C2×C3semidirect
48. #64103C2×C3semidirect
49. C4⋊C4×C3⋊D3C2×C3semidirect
50. #64095C2×C3semidirect
51. #64092C2×C3semidirect
52. C22⋊C4×C3⋊D3C2×C3semidirect
53. C22⋊C4×C3⋊D3C2×C3semidirect
98. C22×C32×C4C2×D3semidirect
99. C22×C32×C4C22×C3semidirect
102. C22×C3⋊Dic3C22×C3semidirect
109. C2×C4×C3⋊D3C22×C3semidirect
121. C32×C4⋊C4C2×D3semidirect
122. C32×C4⋊C4C22×C3semidirect
125. C32×C22⋊C4C2×D3semidirect
126. C32×C22⋊C4C2×D3semidirect
127. C32×C22⋊C4C22×C3semidirect
128. C32×C22⋊C4C22×C3semidirect
129. #3757C22×C3semidirect
130. #3757C22×C3semidirect
131. #3752C22×C3semidirect
132. #3752C22×C3semidirect
133. #3752C22×C3semidirect
134. C4⋊(C3⋊Dic3)C22×C3semidirect
135. #3750C22×C3semidirect
136. #3750C22×C3semidirect
262. (C3⋊D3)⋊C3#123direct (N × H)
396. #123(C3⋊D3)⋊C3direct (N × H)
400. H(3,𝔽3)C2×#123semidirect
497. C3⋊D3C3×#123semidirect
514. C22×C4C2×(C3⋊D3)⋊C3semidirect
518. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
524. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
525. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
592. C32D3×#123semidirect
593. C32C2×C3×#123semidirect

Maximal subgroups

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

subgroupindex
C2×D4×(C3⋊D3)⋊C32
C22×C4×(C3⋊D3)⋊C32
H(3,𝔽3)×#1232
#64144⋊C32
#64138⋊C32
#64103⋊C32
C4⋊C4×(C3⋊D3)⋊C32
#64095⋊C32
#64092⋊C32
C22⋊C4×(C3⋊D3)⋊C32
C3⋊D3×#1233
C3×D3×#1233