Finite Group Databasebeta

← #10596070⋊C3 #13152842

Subgroups — #10596070⋊C3 #13152842

Order 1728.

1186 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3830⋊C3C211yesmaximal, characteristic, complemented
2C2×#3828⋊C3C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#121C211yesmaximal, characteristic, complemented
4#64149⋊C3C211yesmaximal, characteristic, complemented
5#64149⋊C3C212yesmaximal, complemented
6#64148⋊C3C212yesmaximal, complemented
7C4×#638⋊C3C211yesmaximal, characteristic, complemented
8#64104⋊C3C211yesmaximal, characteristic, complemented
9#64096⋊C3C211yesmaximal, characteristic, complemented
10#64093⋊C3C212yesmaximal, complemented
11#64090⋊C3C212yesmaximal, complemented
12#10596070C311yesmaximal, characteristic, complemented
13C3×#5599—31nomaximal
14C2×D4×H(3,𝔽3)C2211yescharacteristic
15C2×D4×H(3,𝔽3)C2212yes—
16C22×C4×H(3,𝔽3)C2211yescharacteristic
17C2×#638⋊C3C2212yes—
18C2×#638⋊C3C2212yes—
19C2×#638⋊C3C2211yescharacteristic
20C2×#638⋊C3C2212yes—
21C2×#638⋊C3C2212yes—
22C22×(C3⋊Dic3)⋊C3C2212yes—
23#3830⋊C3—24no—
24#3828⋊C3—24no—
25C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
26C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
27C2×C4×(C3⋊D3)⋊C3C2212yes—
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
29C2×#634⋊C3C2211yescharacteristic
30C4⋊C4×H(3,𝔽3)C2211yescharacteristic
31C22⋊C4×H(3,𝔽3)C2212yes—
32#3757⋊C3C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic
34#3752⋊C3C2212yes—
35#3750⋊C3C2211yescharacteristic
36#3750⋊C3C2212yes—
37C4×(C3⋊Dic3)⋊C3C2211yescharacteristic
38C4×(C3⋊Dic3)⋊C3C2212yes—
39C2×#3830C2×C311yescharacteristic, complemented
40C2×#3828C2×C311yescharacteristic, complemented
41C2×C3×#237—31no—
42C2×C3×#235—31no—
43C32×#121—21no—
44C32×#121D311yescharacteristic, complemented
45C32×#121C2×C311yescharacteristic, complemented
46#64149C2×C312yescomplemented
47#64149C2×C311yescharacteristic, complemented
48#64148C2×C312yescomplemented
49C4×#638C2×C311yescharacteristic, complemented
50#64104C2×C311yescharacteristic, complemented
51#64096C2×C311yescharacteristic, complemented
52#64093C2×C312yescomplemented
53#64090C2×C312yescomplemented
54C3×#940—32no—
55C3×#940—31no—
56C3×#939—32no—
57C3×C4×#67—31no—
58C3×#895—31no—
59C3×#887—31no—
60C3×#884—32no—
61C3×#67⋊C4—32no—
62C23×H(3,𝔽3)C2312yes—
63C23×H(3,𝔽3)C2311yescharacteristic
64C22×(C3⋊D3)⋊C3C2312yes—
65C22×(C3⋊D3)⋊C3C2311yescharacteristic
66D4×H(3,𝔽3)—22no—
67D4×H(3,𝔽3)—42no—
68C2×C4×H(3,𝔽3)—22no—
69C2×C4×H(3,𝔽3)C2311yescharacteristic
70C2×C4×H(3,𝔽3)C2312yes—
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72#638⋊C3—24no—
73#638⋊C3—24no—
74#638⋊C3—22no—
75#638⋊C3—24no—
76#638⋊C3—42no—
77C2×(C3⋊Dic3)⋊C3—24no—
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
80C2×(C3⋊Dic3)⋊C3C2312yes—
81C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
82C4⋊((C3⋊D3)⋊C3)—22no—
83C4⋊((C3⋊D3)⋊C3)—42no—
84C4×(C3⋊D3)⋊C3—22no—
85C4×(C3⋊D3)⋊C3—24no—
86#634⋊C3D414yescomplemented
87C3×#550—91no—
88#5599—31no—
89#5599—91no—
90C2×C32×D4—21no—
91C2×C32×D4—22no—
92C2×C32×D4C2×D311yescharacteristic
93C2×C32×D4C2×D312yes—
94C2×C32×D4C22×C311yescharacteristic
95C2×C32×D4C22×C312yes—
96C22×C32×C4—21no—
97C22×C32×C4C2×D311yescharacteristic
98C22×C32×C4C22×C311yescharacteristic
99C2×#638C22×C312yes—
100C2×#638C22×C312yes—
101C2×#638C22×C312yes—
102C2×#638C22×C311yescharacteristic
103C2×#638C22×C312yes—
104C22×C3⋊Dic3C22×C312yes—
105#3830—24no—
106#3828—24no—
107C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
108C2×C4⋊(C3⋊D3)C22×C312yes—
109C2×C4×C3⋊D3C22×C312yes—
110C2×C4×C3⋊D3C22×C311yescharacteristic
111C2×#634C22×C311yescharacteristic
112C2×C3×#67—32no—
113C2×C3×#67—32no—
114C2×C3×#67—31no—
115C2×C3×#67—32no—
116C2×C3×#67—32no—
117C22×C3×Dic3—32no—
118C3×#237—64no—
119C3×#235—64no—
120C2×C3×D12—31no—
121C2×C3×D12—32no—
122C2×C3×C4×D3—32no—
123C2×C3×C4×D3—31no—
124C2×C3×Dic6—31no—
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2×D311yescharacteristic
127C32×C4⋊C4C22×C311yescharacteristic
128C32×C22⋊C4—22no—
129C32×C22⋊C4C2×D312yes—
130C32×C22⋊C4C22×C312yes—
131#3757C22×C311yescharacteristic
132#3752C22×C312yes—
133#3752C22×C311yescharacteristic
134#3750C22×C311yescharacteristic
135#3750C22×C312yes—
136C4×C3⋊Dic3C22×C312yes—
137C4×C3⋊Dic3C22×C311yescharacteristic
138C3×#217—31no—
139C3×(C2×D3)⋊C4—32no—
140C3×(C2×D3)⋊C4—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—32no—
143C3×C4×Dic3—32no—
144C3×C4×Dic3—31no—
145C22×H(3,𝔽3)—22no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)—21no—
148C22×H(3,𝔽3)—22no—
149C22×H(3,𝔽3)—21no—
150C22×H(3,𝔽3)—22no—
151C22×H(3,𝔽3)C2411yescharacteristic
152C2×(C3⋊D3)⋊C3—22no—
153C2×(C3⋊D3)⋊C3—21no—
154C2×(C3⋊D3)⋊C3—22no—
155C2×(C3⋊D3)⋊C3—21no—
156C2×(C3⋊D3)⋊C3—21no—
157C2×(C3⋊D3)⋊C3—22no—
158C4×H(3,𝔽3)—21no—
159C4×H(3,𝔽3)—22no—
160C4×H(3,𝔽3)C2×D412yes—
161(C3⋊Dic3)⋊C3—21no—
162(C3⋊Dic3)⋊C3—21no—
163(C3⋊Dic3)⋊C3C2×D414yes—
164(C3⋊Dic3)⋊C3#4112yescomplemented
165C2×C3×#41—91no—
166C2×C3×#41—91no—
167C2×#237—31no—
168C2×#237—91no—
169C2×#235—31no—
170C2×#235—91no—
171C3×#127—91no—
172C3×#127—92no—
173C3×#121—31no—
174C3×#121—31no—
175C3×#121—61no—
176C3×#121—92no—
177C3×#121—91no—
178C3×#121—92no—
179C3×#121C3×D311yescharacteristic
180C3×C4×Q8—91no—
181C3×C4×D4—92no—
182C3×C4×D4—91no—
183#940—32no—
184#940—31no—
185#940—92no—
186#940—91no—
187#939—32no—
188#939—92no—
189C4×#67—31no—
190C4×#67—91no—
191#895—31no—
192#895—91no—
193#887—31no—
194#887—91no—
195#884—32no—
196#884—92no—
197#67⋊C4—32no—
198#67⋊C4—92no—
199C23×C32—21no—
200C23×C32—22no—
201C23×C32C22×D311yescharacteristic
202C23×C32C22×D312yes—
203C23×C32C23×C311yescharacteristic
204C23×C32C23×C312yes—
205C22×C3⋊D3C23×C312yes—
206C22×C3⋊D3C23×C311yescharacteristic
207C22×C3×D3—32no—
208C22×C3×D3—31no—
209C32×D4—22no—
210C32×D4—22no—
211C32×D4—42no—
212C32×D4—42no—
213C32×D4—42no—
214C32×D4—44no—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—22no—
220C2×C32×C4—42no—
221C2×C32×C4C22×D312yes—
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C22×D311yescharacteristic
224C2×C32×C4C23×C312yes—
225C2×C32×C4C23×C311yescharacteristic
226C2×C32×C4C23×C311yescharacteristic
227#638—24no—
228#638—24no—
229#638—24no—
230#638—22no—
231#638—42no—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3C23×C311yescharacteristic
234C2×C3⋊Dic3C23×C311yescharacteristic
235C2×C3⋊Dic3C23×C312yes—
236C2×C3⋊Dic3C23×C311yescharacteristic
237C4⋊(C3⋊D3)—22no—
238C4⋊(C3⋊D3)—42no—
239C4×C3⋊D3—22no—
240C4×C3⋊D3—24no—
241#634C3×D414yescomplemented
242C3×#67—64no—
243C3×#67—64no—
244C3×#67—64no—
245C3×#67—62no—
246C3×#67—122no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3—32no—
249C2×C3×Dic3—31no—
250C2×C3×Dic3—31no—
251C2×C3×Dic3—64no—
252C3×D12—62no—
253C3×D12—122no—
254C3×C4×D3—64no—
255C3×C4×D3—62no—
256C3×Dic6—34no—
257#550—91noSylow
258C2×H(3,𝔽3)—41no—
259C2×H(3,𝔽3)—42no—
260C2×H(3,𝔽3)C22×D411yescharacteristic
261C2×H(3,𝔽3)C2×#4111yescharacteristic
262C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
263(C3⋊D3)⋊C3—42no—
264(C3⋊D3)⋊C3—41no—
265C3×#41—184no—
266C3×#41—184no—
267C2×C3×Q8—91no—
268C2×C3×D4—31no—
269C2×C3×D4—31no—
270C2×C3×D4—32no—
271C2×C3×D4—32no—
272C2×C3×D4—61no—
273C2×C3×D4—62no—
274C2×C3×D4—91no—
275C2×C3×D4—92no—
276C2×C3×D4—92no—
277C2×C3×D4—91no—
278C2×C3×D4—92no—
279C2×C3×D4—92no—
280C2×C3×D4—92no—
281C2×C3×D4C2×C3×D311yescharacteristic
282C2×C3×D4C2×C3×D312yes—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—61no—
286C22×C3×C4—91no—
287C22×C3×C4—92no—
288C22×C3×C4—92no—
289C22×C3×C4C2×C3×D311yescharacteristic
290C2×#67—32no—
291C2×#67—32no—
292C2×#67—31no—
293C2×#67—32no—
294C2×#67—32no—
295C2×#67—92no—
296C2×#67—92no—
297C2×#67—91no—
298C2×#67—92no—
299C2×#67—92no—
300C22×Dic3—32no—
301C22×Dic3—92no—
302#237—64no—
303#237—184no—
304#235—64no—
305#235—184no—
306C2×D12—31no—
307C2×D12—32no—
308C2×D12—91no—
309C2×D12—92no—
310C2×C4×D3—32no—
311C2×C4×D3—31no—
312C2×C4×D3—92no—
313C2×C4×D3—91no—
314C2×Dic6—31no—
315C2×Dic6—91no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—91no—
320C3×C4⋊C4—92no—
321C3×C4⋊C4C2×C3×D311yescharacteristic
322C3×C22⋊C4—32no—
323C3×C22⋊C4—32no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—92no—
326C3×C22⋊C4—91no—
327C3×C22⋊C4—91no—
328C3×C22⋊C4C2×C3×D312yes—
329C3×C42—91no—
330C3×C42—92no—
331#217—31no—
332#217—91no—
333(C2×D3)⋊C4—32no—
334(C2×D3)⋊C4—31no—
335(C2×D3)⋊C4—92no—
336(C2×D3)⋊C4—91no—
337Dic3⋊C4—31no—
338Dic3⋊C4—32no—
339Dic3⋊C4—91no—
340Dic3⋊C4—92no—
341C4×Dic3—32no—
342C4×Dic3—31no—
343C4×Dic3—92no—
344C4×Dic3—91no—
345C22×C32—22no—
346C22×C32—22no—
347C22×C32—21no—
348C22×C32—22no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—22no—
356C22×C32—22no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—41no—
360C22×C32—41no—
361C22×C32—42no—
362C22×C32—42no—
363C22×C32—42no—
364C22×C32C23×D311yescharacteristic
365C22×C32C24×C311yescharacteristic
366C2×C3⋊D3—22no—
367C2×C3⋊D3—21no—
368C2×C3⋊D3—22no—
369C2×C3⋊D3—21no—
370C2×C3⋊D3—21no—
371C2×C3⋊D3—22no—
372C2×C3×D3—62no—
373C2×C3×D3—61no—
374C2×C3×D3—61no—
375C2×C3×D3—62no—
376C2×C3×D3—62no—
377C2×C3×D3—61no—
378C32×C4—21no—
379C32×C4—22no—
380C32×C4—21no—
381C32×C4—22no—
382C32×C4—22no—
383C32×C4—41no—
384C32×C4—42no—
385C32×C4D3×D412yes—
386C32×C4C2×C3×D412yes—
387C3⋊Dic3—21no—
388C3⋊Dic3—21no—
389C3⋊Dic3C2×C3×D414yes—
390C3⋊Dic3C3×#4112yescomplemented
391C3×Dic3—34no—
392C3×Dic3—32no—
393C3×Dic3—61no—
394C3×Dic3—61no—
395C2×#41—91no—
396C2×#41—91no—
397#127—92no—
398#127—91no—
399#121—92no—
400#121—91no—
401#121—92no—
402#121(C3⋊D3)⋊C311yescharacteristic, complemented
403C4×Q8—91no—
404C4×D4—91no—
405C4×D4—92no—
406H(3,𝔽3)#55011yescharacteristic, complemented, Sylow
407C23×C3—32no—
408C23×C3—31no—
409C23×C3—31no—
410C23×C3—32no—
411C23×C3—61no—
412C23×C3—62no—
413C23×C3—92no—
414C23×C3—91no—
415C23×C3C22×C3×D311yescharacteristic
416C23×C3C22×C3×D312yes—
417C22×D3—32no—
418C22×D3—31no—
419C22×D3—92no—
420C22×D3—91no—
421C3×Q8—94no—
422C3×D4—22no—
423C3×D4—42no—
424C3×D4—62no—
425C3×D4—62no—
426C3×D4—122no—
427C3×D4—122no—
428C3×D4—122no—
429C3×D4—124no—
430C3×D4—182no—
431C3×D4—184no—
432C3×D4—182no—
433C3×D4—184no—
434C3×D4—184no—
435C3×D4—362no—
436C3×D4—362no—
437C2×C3×C4—22no—
438C2×C3×C4—31no—
439C2×C3×C4—31no—
440C2×C3×C4—32no—
441C2×C3×C4—31no—
442C2×C3×C4—32no—
443C2×C3×C4—31no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—62no—
449C2×C3×C4—91no—
450C2×C3×C4—92no—
451C2×C3×C4—91no—
452C2×C3×C4—91no—
453C2×C3×C4—122no—
454C2×C3×C4—182no—
455C2×C3×C4—184no—
456C2×C3×C4—184no—
457C2×C3×C4C22×C3×D312yes—
458C2×C3×C4C22×C3×D311yescharacteristic
459C2×C3×C4C22×C3×D311yescharacteristic
460#67—64no—
461#67—64no—
462#67—64no—
463#67—62no—
464#67—122no—
465#67—184no—
466#67—184no—
467#67—184no—
468#67—182no—
469#67—362no—
470C2×Dic3—31no—
471C2×Dic3—32no—
472C2×Dic3—31no—
473C2×Dic3—31no—
474C2×Dic3—64no—
475C2×Dic3—91no—
476C2×Dic3—92no—
477C2×Dic3—91no—
478C2×Dic3—91no—
479C2×Dic3—184no—
480D12—62no—
481D12—122no—
482D12—182no—
483D12—362no—
484C4×D3—64no—
485C4×D3—62no—
486C4×D3—184no—
487C4×D3—182no—
488Dic6—34no—
489Dic6—94no—
490C2×C32—21no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—42no—
494C2×C32—41no—
495C2×C32—42no—
496C2×C32—41no—
497C2×C32—42no—
498C2×C32—82no—
499C2×C32C2×D3×D411yescharacteristic
500C2×C32#100411yescharacteristic
501C2×C32D3×#4111yescharacteristic
502C2×C32C22×C3×D411yescharacteristic
503C2×C32C2×C3×#4111yescharacteristic
504C2×C32C3×H(5,𝔽2)11yescharacteristic
505C3⋊D3—42no—
506C3⋊D3—41no—
507C3×D3—122no—
508C3×D3—121no—
509#41—184no—
510#41—184no—
511C2×Q8—91no—
512C2×D4—91no—
513C2×D4—92no—
514C2×D4—92no—
515C2×D4—92no—
516C2×D4—92no—
517C2×D4—91no—
518C2×D4—92no—
519C2×D4C2×(C3⋊D3)⋊C311yescharacteristic
520C2×D4C2×(C3⋊D3)⋊C312yes—
521C22×C4—92no—
522C22×C4—92no—
523C22×C4—91no—
524C22×C4C2×(C3⋊D3)⋊C311yescharacteristic
525C4⋊C4—91no—
526C4⋊C4—92no—
527C4⋊C4C2×(C3⋊D3)⋊C311yescharacteristic
528C22⋊C4—91no—
529C22⋊C4—91no—
530C22⋊C4—92no—
531C22⋊C4C2×(C3⋊D3)⋊C312yes—
532C42—92no—
533C42—91no—
534C22×C3—22no—
535C22×C3—21no—
536C22×C3—22no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—22no—
540C22×C3—31no—
541C22×C3—31no—
542C22×C3—62no—
543C22×C3—61no—
544C22×C3—61no—
545C22×C3—62no—
546C22×C3—62no—
547C22×C3—61no—
548C22×C3—62no—
549C22×C3—61no—
550C22×C3—61no—
551C22×C3—62no—
552C22×C3—62no—
553C22×C3—61no—
554C22×C3—62no—
555C22×C3—61no—
556C22×C3—121no—
557C22×C3—121no—
558C22×C3—122no—
559C22×C3—122no—
560C22×C3—122no—
561C22×C3—181no—
562C22×C3—182no—
563C22×C3—182no—
564C22×C3—181no—
565C22×C3—181no—
566C22×C3—182no—
567C22×C3C23×C3×D311yescharacteristic
568C2×D3—62no—
569C2×D3—61no—
570C2×D3—61no—
571C2×D3—62no—
572C2×D3—62no—
573C2×D3—61no—
574C2×D3—182no—
575C2×D3—181no—
576C2×D3—181no—
577C2×D3—182no—
578C2×D3—182no—
579C2×D3—181no—
580C3×C4—21no—
581C3×C4—22no—
582C3×C4—32no—
583C3×C4—32no—
584C3×C4—61no—
585C3×C4—62no—
586C3×C4—61no—
587C3×C4—62no—
588C3×C4—62no—
589C3×C4—94no—
590C3×C4—92no—
591C3×C4—121no—
592C3×C4—122no—
593C3×C4—181no—
594C3×C4—181no—
595C3×C4C3×D3×D412yes—
596Dic3—34no—
597Dic3—32no—
598Dic3—61no—
599Dic3—61no—
600Dic3—94no—
601Dic3—92no—
602Dic3—181no—
603Dic3—181no—
604C32—21no—
605C32#559911yescharacteristic, complemented
606C32C3×#55011yescharacteristic, complemented
607C23—91no—
608C23—92no—
609C23C22×(C3⋊D3)⋊C311yescharacteristic
610C23C22×(C3⋊D3)⋊C312yes—
611Q8—94no—
612D4—22no—
613D4—42no—
614D4—184no—
615D4—184no—
616D4—182no—
617D4—184no—
618D4—182no—
619D4—362no—
620D4—362no—
621C2×C4—22no—
622C2×C4—91no—
623C2×C4—92no—
624C2×C4—91no—
625C2×C4—91no—
626C2×C4—184no—
627C2×C4—184no—
628C2×C4—182no—
629C2×C4C22×(C3⋊D3)⋊C312yes—
630C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
631C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
632C2×C3—31no—
633C2×C3—31no—
634C2×C3—31no—
635C2×C3—31no—
636C2×C3—31no—
637C2×C3—31no—
638C2×C3—41no—
639C2×C3—42no—
640C2×C3—61no—
641C2×C3—61no—
642C2×C3—61no—
643C2×C3—121no—
644C2×C3—121no—
645C2×C3—122no—
646C2×C3—122no—
647C2×C3—122no—
648C2×C3—242no—
649C2×C3—361no—
650C2×C3—362no—
651C2×C3C2×C3×D3×D411yescharacteristic
652C2×C3C3×#100411yescharacteristic
653C2×C3C3×D3×#4111yescharacteristic
654D3—122no—
655D3—121no—
656D3—362no—
657D3—361no—
658C22—21no—
659C22—22no—
660C22—21no—
661C22—22no—
662C22—21no—
663C22—22no—
664C22—182no—
665C22—181no—
666C22—181no—
667C22—182no—
668C22—181no—
669C22—182no—
670C22C23×(C3⋊D3)⋊C311yescharacteristic
671C4—21no—
672C4—22no—
673C4—94no—
674C4—92no—
675C4—181no—
676C4—181no—
677C4D4×(C3⋊D3)⋊C312yes—
678C3—31no—
679C3—31no—
680C3—61no—
681C3C3×#559911yescharacteristic
682C2—41no—
683C2—42no—
684C2—362no—
685C2—361no—
686C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
687C2#64361⋊C311yescharacteristic
688C2#41×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC22C23×(C3⋊D3)⋊C3
commutator, cosocleC22×C32C24×C3
Frattini, socleC22×C3C23×C3×D3
FittingH(3,𝔽3)×#121C2
hypercenter#121(C3⋊D3)⋊C3
hypocenterC32C3×#550
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#3830⋊C3C2semidirect
2. C2×#3828⋊C3C2semidirect
3. H(3,𝔽3)×#121C2semidirect
4. #64149⋊C3C2semidirect
5. #64149⋊C3C2semidirect
6. #64148⋊C3C2semidirect
7. C4×#638⋊C3C2semidirect
8. #64104⋊C3C2semidirect
9. #64096⋊C3C2semidirect
10. #64093⋊C3C2semidirect
11. #64090⋊C3C2semidirect
12. #10596070C3semidirect
39. C2×#3830C2×C3semidirect
40. C2×#3828C2×C3semidirect
44. C32×#121D3semidirect
45. C32×#121C2×C3semidirect
46. #64149C2×C3semidirect
47. #64149C2×C3semidirect
48. #64148C2×C3semidirect
49. C4×#638C2×C3semidirect
50. #64104C2×C3semidirect
51. #64096C2×C3semidirect
52. #64093C2×C3semidirect
53. #64090C2×C3semidirect
86. #634⋊C3D4semidirect
164. (C3⋊Dic3)⋊C3#41semidirect
241. #634C3×D4semidirect
390. C3⋊Dic3C3×#41semidirect
402. #121(C3⋊D3)⋊C3semidirect
406. H(3,𝔽3)#550semidirect
605. C32#5599semidirect
606. C32C3×#550semidirect

Maximal subgroups

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

subgroupindex
C2×#3830⋊C32
C2×#3828⋊C32
H(3,𝔽3)×#1212
#64149⋊C32
#64148⋊C32
C4×#638⋊C32
#64104⋊C32
#64096⋊C32
#64093⋊C32
#64090⋊C32
#105960703
C3×#55993