Finite Group Databasebeta

← #10596127⋊C3 #13153035

Subgroups — #10596127⋊C3 #13153035

Order 1728.

1233 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3830⋊C3C211yesmaximal, characteristic, complemented
2C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#123C211yesmaximal, characteristic, complemented
4#64146⋊C3C211yesmaximal, characteristic, complemented
5#64138⋊C3C211yesmaximal, characteristic, complemented
6#64105⋊C3C212yesmaximal, complemented
7#64102⋊C3C212yesmaximal, complemented
8#64093⋊C3C212yesmaximal, complemented
9#64091⋊C3C211yesmaximal, characteristic, complemented
10#64090⋊C3C212yesmaximal, complemented
11#64086⋊C3C211yesmaximal, characteristic, complemented
12#10596127C311yesmaximal, characteristic, complemented
13C3×#5656—31nomaximal
14C23×(C3⋊D3)⋊C3C2211yescharacteristic
15C2×D4×H(3,𝔽3)C2211yescharacteristic
16C22×C4×H(3,𝔽3)C2211yescharacteristic
17C2×#638⋊C3C2211yescharacteristic
18C2×#638⋊C3C2212yes—
19C2×#638⋊C3C2211yescharacteristic, complemented
20C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
22#3830⋊C3—24no—
23C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
24C2×C4×(C3⋊D3)⋊C3—24no—
25C2×C4×(C3⋊D3)⋊C3C2212yes—
26C2×C4×(C3⋊D3)⋊C3C2212yes—
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
28C2×#634⋊C3C2211yescharacteristic, complemented
29C4⋊C4×H(3,𝔽3)C2212yescomplemented
30C22⋊C4×H(3,𝔽3)C2211yescharacteristic
31C22⋊C4×H(3,𝔽3)C2212yescomplemented
32#3757⋊C3C2211yescharacteristic
33#3752⋊C3C2212yes—
34#3752⋊C3C2212yes—
35#3752⋊C3C2212yescomplemented
36#3750⋊C3C2212yescomplemented
37#3750⋊C3C2212yescomplemented
38C4×(C3⋊Dic3)⋊C3C2212yescomplemented
39C2×#3830C2×C311yescharacteristic, complemented
40C22×C4×C3⋊D3C2×C311yescharacteristic, complemented
41C2×C3×#237—31no—
42C22×C3×C4×D3—31no—
43C32×#123—21no—
44C32×#123D311yescharacteristic, complemented
45C32×#123C2×C311yescharacteristic, complemented
46#64146C2×C311yescharacteristic, complemented
47#64138C2×C311yescharacteristic, complemented
48#64105C2×C312yescomplemented
49#64102C2×C312yescomplemented
50#64093C2×C312yescomplemented
51#64091C2×C311yescharacteristic, complemented
52#64090C2×C312yescomplemented
53#64086C2×C311yescharacteristic, complemented
54C3×#937—31no—
55C3×#929—31no—
56C3×#896—32no—
57C3×#893—32no—
58C3×#884—32no—
59C3×#882—31no—
60C3×#67⋊C4—32no—
61C3×#877—31no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C23×H(3,𝔽3)C2311yescharacteristic
64C22×(C3⋊D3)⋊C3—22no—
65C22×(C3⋊D3)⋊C3—24no—
66C22×(C3⋊D3)⋊C3C2311yescharacteristic
67C22×(C3⋊D3)⋊C3C2312yes—
68D4×H(3,𝔽3)—22no—
69C2×C4×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×C4×H(3,𝔽3)C2312yes—
72C2×C4×H(3,𝔽3)C2312yes—
73#638⋊C3—22no—
74#638⋊C3—24no—
75#638⋊C3—22no—
76C2×(C3⋊Dic3)⋊C3—22no—
77C2×(C3⋊Dic3)⋊C3D414yescomplemented
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C2×(C3⋊Dic3)⋊C3C2312yes—
80C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
81C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
82C4⋊((C3⋊D3)⋊C3)—24no—
83C4×(C3⋊D3)⋊C3—24no—
84C4×(C3⋊D3)⋊C3—24no—
85C4×(C3⋊D3)⋊C3—22no—
86#634⋊C3—22no—
87C3×#525—91no—
88#5656—31no—
89#5656—91no—
90C23×C3⋊D3C22×C311yescharacteristic
91C23×C3×D3—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2×D311yescharacteristic
94C2×C32×D4C22×C311yescharacteristic
95C22×C32×C4—21no—
96C22×C32×C4C2×D311yescharacteristic
97C22×C32×C4C22×C311yescharacteristic
98C2×#638C22×C312yes—
99C2×#638C22×C311yescharacteristic
100C2×#638C22×C311yescharacteristic, complemented
101C22×C3⋊Dic3C22×C311yescharacteristic
102C22×C3⋊Dic3C22×C311yescharacteristic, complemented
103#3830—24no—
104C2×C4⋊(C3⋊D3)C22×C312yes—
105C2×C4×C3⋊D3—24no—
106C2×C4×C3⋊D3C22×C312yes—
107C2×C4×C3⋊D3C22×C312yes—
108C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
109C2×#634C22×C311yescharacteristic, complemented
110C2×C3×#67—32no—
111C2×C3×#67—31no—
112C2×C3×#67—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C3×#237—64no—
116C2×C3×D12—32no—
117C2×C3×C4×D3—32no—
118C2×C3×C4×D3—32no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—64no—
121C2×C3×Dic6—31no—
122C32×C4⋊C4—22no—
123C32×C4⋊C4C2×D312yescomplemented
124C32×C4⋊C4C22×C312yescomplemented
125C32×C22⋊C4—21no—
126C32×C22⋊C4—22no—
127C32×C22⋊C4C2×D311yescharacteristic
128C32×C22⋊C4C2×D312yescomplemented
129C32×C22⋊C4C22×C311yescharacteristic
130C32×C22⋊C4C22×C312yescomplemented
131#3757C22×C311yescharacteristic
132#3752C22×C312yes—
133#3752C22×C312yes—
134#3752C22×C312yescomplemented
135#3750C22×C312yescomplemented
136#3750C22×C312yescomplemented
137C4×C3⋊Dic3C22×C312yescomplemented
138C3×#217—31no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—32no—
141C3×(C2×D3)⋊C4—32no—
142C3×Dic3⋊C4—32no—
143C3×Dic3⋊C4—32no—
144C3×C4×Dic3—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—28no—
151C2×(C3⋊D3)⋊C3—22no—
152C2×(C3⋊D3)⋊C3—22no—
153C2×(C3⋊D3)⋊C3—21no—
154C2×(C3⋊D3)⋊C3—22no—
155C2×(C3⋊D3)⋊C3#4114yescomplemented
156C4×H(3,𝔽3)—21no—
157C4×H(3,𝔽3)—22no—
158C4×H(3,𝔽3)—22no—
159(C3⋊Dic3)⋊C3—21no—
160(C3⋊Dic3)⋊C3—22no—
161(C3⋊Dic3)⋊C3C2×D412yes—
162(C3⋊Dic3)⋊C3C2×D412yes—
163C2×C3×#41—91no—
164C23×C3×C4—91no—
165C2×#237—31no—
166C2×#237—91no—
167C22×C4×D3—31no—
168C22×C4×D3—91no—
169C3×#123—31no—
170C3×#123—31no—
171C3×#123—61no—
172C3×#123—91no—
173C3×#123C3×D311yescharacteristic
174C3×C22⋊Q8—92no—
175C3×#121—92no—
176C3×#120—91no—
177C3×#120—91no—
178C3×C4×D4—92no—
179C3×C4×D4—92no—
180C3×#117—91no—
181#937—31no—
182#937—91no—
183#929—31no—
184#929—91no—
185#896—32no—
186#896—92no—
187#893—32no—
188#893—92no—
189#884—32no—
190#884—92no—
191#882—31no—
192#882—91no—
193#67⋊C4—32no—
194#67⋊C4—92no—
195#877—31no—
196#877—91no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32C22×D311yescharacteristic
200C23×C32C22×D311yescharacteristic
201C23×C32C23×C311yescharacteristic
202C23×C32C23×C311yescharacteristic
203C22×C3⋊D3—22no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3C23×C311yescharacteristic
206C22×C3⋊D3C23×C312yes—
207C22×C3×D3—32no—
208C22×C3×D3—31no—
209C22×C3×D3—64no—
210C22×C3×D3—62no—
211C32×D4—22no—
212C32×D4—22no—
213C32×D4—42no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
217C2×C32×C4—22no—
218C2×C32×C4—21no—
219C2×C32×C4—42no—
220C2×C32×C4C22×D312yes—
221C2×C32×C4C22×D312yes—
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C23×C312yes—
224C2×C32×C4C23×C312yes—
225C2×C32×C4C23×C311yescharacteristic
226#638—22no—
227#638—24no—
228#638—22no—
229C2×C3⋊Dic3—22no—
230C2×C3⋊Dic3C3×D414yescomplemented
231C2×C3⋊Dic3C23×C312yes—
232C2×C3⋊Dic3C23×C311yescharacteristic
233C2×C3⋊Dic3C23×C311yescharacteristic
234C2×C3⋊Dic3C23×C311yescharacteristic
235C4⋊(C3⋊D3)—24no—
236C4×C3⋊D3—24no—
237C4×C3⋊D3—24no—
238C4×C3⋊D3—22no—
239#634—22no—
240C3×#67—62no—
241C3×#67—64no—
242C3×#67—62no—
243C2×C3×Dic3—34no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—32no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3—62no—
249C3×D12—64no—
250C3×C4×D3—64no—
251C3×C4×D3—64no—
252C3×C4×D3—62no—
253C3×Dic6—62no—
254#525—91noSylow
255C2×H(3,𝔽3)—22no—
256C2×H(3,𝔽3)—41no—
257C2×H(3,𝔽3)C22×D411yescharacteristic
258C2×H(3,𝔽3)C2×#4112yes—
259(C3⋊D3)⋊C3—24no—
260(C3⋊D3)⋊C3—41no—
261C24×C3—91no—
262C23×D3—31no—
263C23×D3—91no—
264C3×#41—184no—
265C2×C3×Q8—91no—
266C2×C3×D4—31no—
267C2×C3×D4—31no—
268C2×C3×D4—61no—
269C2×C3×D4—92no—
270C2×C3×D4—92no—
271C2×C3×D4—91no—
272C2×C3×D4—91no—
273C2×C3×D4C2×C3×D311yescharacteristic
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—61no—
277C22×C3×C4—92no—
278C22×C3×C4—91no—
279C22×C3×C4—92no—
280C22×C3×C4—91no—
281C22×C3×C4—91no—
282C22×C3×C4—184no—
283C22×C3×C4C2×C3×D311yescharacteristic
284C2×#67—32no—
285C2×#67—31no—
286C2×#67—31no—
287C2×#67—92no—
288C2×#67—91no—
289C2×#67—91no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—91no—
293C22×Dic3—91no—
294#237—64no—
295#237—184no—
296C2×D12—32no—
297C2×D12—92no—
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—91no—
305C2×C4×D3—184no—
306C2×Dic6—31no—
307C2×Dic6—91no—
308C3×C4⋊C4—32no—
309C3×C4⋊C4—32no—
310C3×C4⋊C4—62no—
311C3×C4⋊C4—92no—
312C3×C4⋊C4—92no—
313C3×C4⋊C4C2×C3×D312yes—
314C3×C22⋊C4—31no—
315C3×C22⋊C4—31no—
316C3×C22⋊C4—32no—
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⋊C4C2×C3×D311yescharacteristic
325C3×C22⋊C4C2×C3×D312yes—
326C3×C42—92no—
327#217—31no—
328#217—91no—
329(C2×D3)⋊C4—32no—
330(C2×D3)⋊C4—32no—
331(C2×D3)⋊C4—32no—
332(C2×D3)⋊C4—92no—
333(C2×D3)⋊C4—92no—
334(C2×D3)⋊C4—92no—
335Dic3⋊C4—32no—
336Dic3⋊C4—32no—
337Dic3⋊C4—92no—
338Dic3⋊C4—92no—
339C4×Dic3—32no—
340C4×Dic3—92no—
341C22×C32—22no—
342C22×C32—22no—
343C22×C32—21no—
344C22×C32—22no—
345C22×C32—21no—
346C22×C32—22no—
347C22×C32—21no—
348C22×C32—22no—
349C22×C32—42no—
350C22×C32—41no—
351C22×C32—42no—
352C22×C32D3×D412yes—
353C22×C32C2×C3×D412yes—
354C22×C32C23×D311yescharacteristic
355C22×C32C24×C311yescharacteristic
356C2×C3⋊D3—28no—
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—21no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3C3×#4114yescomplemented
362C2×C3×D3—34no—
363C2×C3×D3—68no—
364C2×C3×D3—62no—
365C2×C3×D3—62no—
366C2×C3×D3—61no—
367C2×C3×D3—62no—
368C32×C4—21no—
369C32×C4—22no—
370C32×C4—22no—
371C32×C4—21no—
372C32×C4—22no—
373C32×C4—22no—
374C32×C4—42no—
375C32×C4—42no—
376C32×C4—41no—
377C3⋊Dic3—21no—
378C3⋊Dic3—22no—
379C3⋊Dic3C2×C3×D412yes—
380C3⋊Dic3C2×C3×D412yes—
381C3×Dic3—32no—
382C3×Dic3—32no—
383C3×Dic3—61no—
384C3×Dic3—62no—
385C2×#41—91no—
386C23×C4—91no—
387#123—91no—
388#123(C3⋊D3)⋊C311yescharacteristic, complemented
389C22⋊Q8—92no—
390#121—92no—
391#120—91no—
392#120—91no—
393C4×D4—92no—
394C4×D4—92no—
395#117—91no—
396H(3,𝔽3)#52511yescharacteristic, complemented, Sylow
397C23×C3—31no—
398C23×C3—31no—
399C23×C3—31no—
400C23×C3—31no—
401C23×C3—61no—
402C23×C3—61no—
403C23×C3—92no—
404C23×C3—91no—
405C23×C3—182no—
406C23×C3—184no—
407C23×C3C22×C3×D311yescharacteristic
408C23×C3C22×C3×D311yescharacteristic
409C22×D3—32no—
410C22×D3—31no—
411C22×D3—64no—
412C22×D3—62no—
413C22×D3—92no—
414C22×D3—91no—
415C22×D3—184no—
416C22×D3—182no—
417C3×Q8—182no—
418C3×D4—22no—
419C3×D4—62no—
420C3×D4—62no—
421C3×D4—122no—
422C3×D4—184no—
423C3×D4—182no—
424C3×D4—182no—
425C3×D4—184no—
426C2×C3×C4—22no—
427C2×C3×C4—32no—
428C2×C3×C4—32no—
429C2×C3×C4—31no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—31no—
433C2×C3×C4—62no—
434C2×C3×C4—62no—
435C2×C3×C4—62no—
436C2×C3×C4—62no—
437C2×C3×C4—61no—
438C2×C3×C4—91no—
439C2×C3×C4—91no—
440C2×C3×C4—94no—
441C2×C3×C4—92no—
442C2×C3×C4—91no—
443C2×C3×C4—122no—
444C2×C3×C4—184no—
445C2×C3×C4—184no—
446C2×C3×C4—182no—
447C2×C3×C4—182no—
448C2×C3×C4C22×C3×D312yes—
449C2×C3×C4C22×C3×D312yes—
450C2×C3×C4C22×C3×D311yescharacteristic
451#67—62no—
452#67—64no—
453#67—62no—
454#67—182no—
455#67—184no—
456#67—182no—
457C2×Dic3—31no—
458C2×Dic3—31no—
459C2×Dic3—34no—
460C2×Dic3—32no—
461C2×Dic3—31no—
462C2×Dic3—62no—
463C2×Dic3—94no—
464C2×Dic3—91no—
465C2×Dic3—91no—
466C2×Dic3—92no—
467C2×Dic3—91no—
468C2×Dic3—182no—
469D12—64no—
470D12—184no—
471C4×D3—64no—
472C4×D3—64no—
473C4×D3—62no—
474C4×D3—184no—
475C4×D3—184no—
476C4×D3—182no—
477Dic6—62no—
478Dic6—182no—
479C2×C32—22no—
480C2×C32—22no—
481C2×C32—21no—
482C2×C32—22no—
483C2×C32—42no—
484C2×C32—41no—
485C2×C32—41no—
486C2×C32—81no—
487C2×C32C2×D3×D411yescharacteristic
488C2×C32D3×#4112yes—
489C2×C32C22×C3×D411yescharacteristic
490C2×C32C2×C3×#4112yes—
491C3⋊D3—24no—
492C3⋊D3—41no—
493C3×D3—64no—
494C3×D3—121no—
495C24—91no—
496#41—184no—
497C2×Q8—91no—
498C2×D4—92no—
499C2×D4—91no—
500C2×D4—91no—
501C2×D4—92no—
502C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
503C22×C4—91no—
504C22×C4—91no—
505C22×C4—92no—
506C22×C4—91no—
507C22×C4—92no—
508C22×C4—184no—
509C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
510C4⋊C4—92no—
511C4⋊C4—92no—
512C4⋊C4C2×(C3⋊D3)⋊C312yescomplemented
513C22⋊C4—91no—
514C22⋊C4—92no—
515C22⋊C4—92no—
516C22⋊C4—92no—
517C22⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
518C22⋊C4C2×(C3⋊D3)⋊C312yescomplemented
519C42—92no—
520C22×C3—22no—
521C22×C3—21no—
522C22×C3—22no—
523C22×C3—31no—
524C22×C3—31no—
525C22×C3—32no—
526C22×C3—32no—
527C22×C3—62no—
528C22×C3—62no—
529C22×C3—61no—
530C22×C3—62no—
531C22×C3—61no—
532C22×C3—62no—
533C22×C3—61no—
534C22×C3—62no—
535C22×C3—94no—
536C22×C3—122no—
537C22×C3—121no—
538C22×C3—122no—
539C22×C3—182no—
540C22×C3—182no—
541C22×C3—181no—
542C22×C3—182no—
543C22×C3—188no—
544C22×C3C3×D3×D412yes—
545C22×C3C23×C3×D311yescharacteristic
546C2×D3—34no—
547C2×D3—68no—
548C2×D3—62no—
549C2×D3—62no—
550C2×D3—61no—
551C2×D3—62no—
552C2×D3—94no—
553C2×D3—182no—
554C2×D3—182no—
555C2×D3—188no—
556C2×D3—181no—
557C2×D3—182no—
558C3×C4—21no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—61no—
562C3×C4—62no—
563C3×C4—62no—
564C3×C4—62no—
565C3×C4—61no—
566C3×C4—62no—
567C3×C4—92no—
568C3×C4—92no—
569C3×C4—122no—
570C3×C4—121no—
571C3×C4—122no—
572C3×C4—181no—
573C3×C4—182no—
574Dic3—32no—
575Dic3—32no—
576Dic3—61no—
577Dic3—62no—
578Dic3—92no—
579Dic3—92no—
580Dic3—181no—
581Dic3—182no—
582C32—21no—
583C32#565611yescharacteristic, complemented
584C32C3×#52511yescharacteristic, complemented
585C23—92no—
586C23—91no—
587C23—184no—
588C23—182no—
589C23C22×(C3⋊D3)⋊C311yescharacteristic
590C23C22×(C3⋊D3)⋊C311yescharacteristic
591Q8—182no—
592D4—22no—
593D4—184no—
594D4—182no—
595D4—184no—
596D4—182no—
597C2×C4—22no—
598C2×C4—91no—
599C2×C4—91no—
600C2×C4—94no—
601C2×C4—92no—
602C2×C4—91no—
603C2×C4—184no—
604C2×C4—184no—
605C2×C4—182no—
606C2×C4—182no—
607C2×C4C22×(C3⋊D3)⋊C312yes—
608C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
609C2×C4C22×(C3⋊D3)⋊C312yes—
610C2×C3—22no—
611C2×C3—31no—
612C2×C3—31no—
613C2×C3—32no—
614C2×C3—32no—
615C2×C3—41no—
616C2×C3—62no—
617C2×C3—62no—
618C2×C3—61no—
619C2×C3—62no—
620C2×C3—122no—
621C2×C3—121no—
622C2×C3—121no—
623C2×C3—184no—
624C2×C3—241no—
625C2×C3—361no—
626C2×C3C2×C3×D3×D411yescharacteristic
627C2×C3C3×D3×#4112yes—
628D3—64no—
629D3—121no—
630D3—184no—
631D3—361no—
632C22—22no—
633C22—21no—
634C22—22no—
635C22—94no—
636C22—188no—
637C22—182no—
638C22—182no—
639C22—181no—
640C22—182no—
641C22D4×(C3⋊D3)⋊C312yes—
642C22C23×(C3⋊D3)⋊C311yescharacteristic
643C4—22no—
644C4—21no—
645C4—22no—
646C4—92no—
647C4—92no—
648C4—181no—
649C4—182no—
650C3—31no—
651C3—31no—
652C3—61no—
653C3C3×#565611yescharacteristic
654C2—22no—
655C2—41no—
656C2—184no—
657C2—361no—
658C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
659C2#41×(C3⋊D3)⋊C312yes—
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#123C2
hypercenter#123(C3⋊D3)⋊C3
hypocenterC32C3×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#3830⋊C3C2semidirect
2. C22×C4×(C3⋊D3)⋊C3C2semidirect
3. H(3,𝔽3)×#123C2semidirect
4. #64146⋊C3C2semidirect
5. #64138⋊C3C2semidirect
6. #64105⋊C3C2semidirect
7. #64102⋊C3C2semidirect
8. #64093⋊C3C2semidirect
9. #64091⋊C3C2semidirect
10. #64090⋊C3C2semidirect
11. #64086⋊C3C2semidirect
12. #10596127C3semidirect
19. C2×#638⋊C3C22semidirect
21. C22×(C3⋊Dic3)⋊C3C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. C2×#634⋊C3C22semidirect
29. C4⋊C4×H(3,𝔽3)C22semidirect
31. C22⋊C4×H(3,𝔽3)C22semidirect
35. #3752⋊C3C22semidirect
36. #3750⋊C3C22semidirect
37. #3750⋊C3C22semidirect
38. C4×(C3⋊Dic3)⋊C3C22semidirect
39. C2×#3830C2×C3semidirect
40. C22×C4×C3⋊D3C2×C3semidirect
44. C32×#123D3semidirect
45. C32×#123C2×C3semidirect
46. #64146C2×C3semidirect
47. #64138C2×C3semidirect
48. #64105C2×C3semidirect
49. #64102C2×C3semidirect
50. #64093C2×C3semidirect
51. #64091C2×C3semidirect
52. #64090C2×C3semidirect
53. #64086C2×C3semidirect
77. C2×(C3⋊Dic3)⋊C3D4semidirect
100. C2×#638C22×C3semidirect
102. C22×C3⋊Dic3C22×C3semidirect
108. C2×C4×C3⋊D3C22×C3semidirect
109. C2×#634C22×C3semidirect
123. C32×C4⋊C4C2×D3semidirect
124. C32×C4⋊C4C22×C3semidirect
128. C32×C22⋊C4C2×D3semidirect
130. C32×C22⋊C4C22×C3semidirect
134. #3752C22×C3semidirect
135. #3750C22×C3semidirect
136. #3750C22×C3semidirect
137. C4×C3⋊Dic3C22×C3semidirect
155. C2×(C3⋊D3)⋊C3#41semidirect
230. C2×C3⋊Dic3C3×D4semidirect
361. C2×C3⋊D3C3×#41semidirect
388. #123(C3⋊D3)⋊C3semidirect
396. H(3,𝔽3)#525semidirect
512. C4⋊C4C2×(C3⋊D3)⋊C3semidirect
518. C22⋊C4C2×(C3⋊D3)⋊C3semidirect
583. C32#5656semidirect
584. C32C3×#525semidirect

Maximal subgroups

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

subgroupindex
C2×#3830⋊C32
C22×C4×(C3⋊D3)⋊C32
H(3,𝔽3)×#1232
#64146⋊C32
#64138⋊C32
#64105⋊C32
#64102⋊C32
#64093⋊C32
#64091⋊C32
#64090⋊C32
#64086⋊C32
#105961273
C3×#56563