Finite Group Databasebeta

← C2×C3×#10593663 #72269031

Subgroups — C2×C3×#10593663 #72269031

Order 3456.

2042 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#994C211yesmaximal, characteristic, complemented
2C2×C3×#64267C211yesmaximal, characteristic, complemented
3C3×#10593663C214yesmaximal, direct product factor
4C2×C3×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic, complemented
5C2×#10593663C311yesmaximal, characteristic, direct product factor
6C2×C3×#5429—33nomaximal
7C2×C3×#5241—31nomaximal
8C32×#994—21no—
9C32×#994C2212yescomplemented
10C2×C32×#41⋊C3—21no—
11C2×C32×#41⋊C3C2211yescharacteristic
12C3×#64267—21no—
13C3×#64267C2212yescomplemented
14C2×C3×C3⋊GL(2,𝔽3)—21no—
15C2×C3×#3755—41nomaximal
16C3×C3⋊GU(2,𝔽3)C2212yescomplemented
17C2×C32×H(5,𝔽2)D311yescharacteristic, complemented
18C2×C3×#994—21no—
19C2×C3×#994—23no—
20C2×C3×#994D313yescomplemented
21C2×C3×#994C2×C311yescharacteristic, complemented
22C2×#64267C2×C311yescharacteristic, complemented
23C2×C3×#986—33no—
24C2×C3×#949—31no—
25C2×C3×#949—31no—
26C2×C3×#940—31no—
27#10593663C2×C314yesdirect product factor
28C2×C3⋊GU(2,𝔽3)C2×C311yescharacteristic, complemented
29C3×#5429—312no—
30C2×C3×GU(2,𝔽3)—33no—
31C3×#5241—34no—
32C3×#5241—34no—
33C2×C3×#837—31no—
34C2×C3×#837—31no—
35C2×C3×#833—31no—
36C2×C33×Q8—41no—
37C2×C3×C4⋊(C3⋊D3)—41no—
38C32×#41⋊C3—22no—
39C32×#41⋊C3D411yescharacteristic, complemented
40C32×#41⋊C3C2311yescharacteristic
41C2×C32×SL(2,𝔽3)D411yescharacteristic, complemented
42C3×C3⋊GL(2,𝔽3)—22no—
43C3×#3755—44no—
44C2×C3×C3⋊(C3⋊C8)—41no—
45C2×#5429—33no—
46C2×C3×#453—91no—
47C2×#5241—31no—
48C32×H(5,𝔽2)—21no—
49C32×H(5,𝔽2)—32no—
50C32×H(5,𝔽2)—61no—
51C32×H(5,𝔽2)C2×D312yescomplemented
52C2×C32×#41—21no—
53C2×C32×#41—31no—
54C2×C32×#41C2×D311yescharacteristic
55C22×C32×D4—31no—
56C22×C32×D4—61no—
57C22×C3×#67—62no—
58C22×C3×D12—31no—
59C3×#994—22no—
60C3×#994—26no—
61C3×#994—22no—
62C3×#994—23no—
63C3×#994—21no—
64C3×#994—26no—
65C3×#994C2×D316yescomplemented
66C3×#994C22×C312yescomplemented
67C2×C3×#41⋊C3—22no—
68C2×C3×#41⋊C3—26no—
69C2×C3×#41⋊C3—21no—
70C2×C3×#41⋊C3—23no—
71C2×C3×#41⋊C3—21no—
72C2×C3×#41⋊C3—23no—
73C2×C3×#41⋊C3C2×D313yes—
74C2×C3×#41⋊C3C22×C311yescharacteristic
75#64267—21no—
76#64267C22×C312yescomplemented
77C2×C3⋊GL(2,𝔽3)—21no—
78C3×#986—36no—
79C3×#986—63no—
80C2×C3×GL(2,𝔽3)—63no—
81C2×#3755—41no—
82C3×#949—32no—
83C3×#949—34no—
84C3×#949—32no—
85C3×#949—61no—
86C3×#949—62no—
87C3×#949—61no—
88C2×C3×#215—61no—
89C2×C3×#215—61no—
90C2×C3×#215—123no—
91C3×#940—34no—
92C3×#940—62no—
93C2×C3×#213—61no—
94C2×C3×#213—61no—
95C2×C3×C4×Dic3—31no—
96C2×C3×#208—31no—
97C2×C3×#208—31no—
98C3⋊GU(2,𝔽3)C22×C312yescomplemented
99C3×GU(2,𝔽3)—36no—
100C3×#837—32no—
101C3×#837—34no—
102C3×#837—32no—
103C3×#833—34no—
104C22×C3×C3⋊D3—81no—
105C33×Q8—42no—
106C33×Q8—81no—
107C2×C33×C4—41no—
108C2×C33×C4—81no—
109C3×C4⋊(C3⋊D3)—42no—
110C3×C4⋊(C3⋊D3)—81no—
111C32×SL(2,𝔽3)C2×D411yescharacteristic, complemented
112C3×C3⋊(C3⋊C8)—42no—
113C2×C3×H(5,𝔽2)—21no—
114C2×C3×H(5,𝔽2)C3×D311yescharacteristic, complemented
115C2×C3×H(5,𝔽2)C3⋊D311yescharacteristic, complemented
116C2×#994—23no—
117C2×#994C3×D313yescomplemented
118C2×#986—33no—
119C2×C3×AGL(1,ℤ/8)—91no—
120C2×C3×AGL(1,ℤ/8)—91no—
121C2×C3×#127—91no—
122C2×#949—31no—
123C2×#949—31no—
124C2×#940—31no—
125#5429—312no—
126C2×GU(2,𝔽3)—33no—
127C3×#453—94no—
128C3×#453—94no—
129C2×C3×#104—91no—
130C2×C3×#104—91no—
131C2×C3×#100—91no—
132#5241—34no—
133#5241—34no—
134C2×#837—31no—
135C2×#837—31no—
136C2×#833—31no—
137C24×C32—32no—
138C23×C3×D3—61no—
139C32×#41—22no—
140C32×#41—31no—
141C32×#41—31no—
142C32×#41—32no—
143C32×#41—32no—
144C32×#41—61no—
145C32×#41—61no—
146C32×#41—62no—
147C32×#41#6711yescharacteristic
148C32×#41C22×D311yescharacteristic
149C2×C32×Q8—41no—
150C2×C32×Q8—43no—
151C2×C32×Q8—83no—
152C2×C32×Q8—81no—
153C2×C32×Q8#6711yescharacteristic
154C2×C32×Q8S411yescharacteristic
155C2×C32×D4—31no—
156C2×C32×D4—32no—
157C2×C32×D4—32no—
158C2×C32×D4—31no—
159C2×C32×D4—61no—
160C2×C32×D4—61no—
161C2×C32×D4—61no—
162C2×C32×D4—61no—
163C2×C32×D4—62no—
164C2×C32×D4—62no—
165C2×C32×D4—64no—
166C22×C32×C4—31no—
167C22×C32×C4—61no—
168C2×C4⋊(C3⋊D3)—41no—
169C2×C3×#67—68no—
170C2×C3×#67—128no—
171C22×C3×Dic3—61no—
172C2×C3×D12—32no—
173C2×C3×D12—61no—
174C2×C3×D12—61no—
175C2×C3×D12—61no—
176C2×C3×D12—61no—
177C2×C3×D12—61no—
178C2×C3×D12—123no—
179C3×#41⋊C3—24no—
180C3×#41⋊C3—212no—
181C3×#41⋊C3—21no—
182C3×#41⋊C3—21no—
183C3×#41⋊C3—23no—
184C3×#41⋊C3—23no—
185C3×#41⋊C3—26no—
186C3×#41⋊C3—22no—
187C3×#41⋊C3#6713yescomplemented
188C3×#41⋊C3C3×D411yescharacteristic, complemented
189C3×#41⋊C3C22×D313yes—
190C3×#41⋊C3C23×C311yescharacteristic
191C2×C3×SL(2,𝔽3)—21no—
192C2×C3×SL(2,𝔽3)—23no—
193C2×C3×SL(2,𝔽3)#6713yescomplemented
194C2×C3×SL(2,𝔽3)C3×D411yescharacteristic, complemented
195C3⋊GL(2,𝔽3)—22no—
196C3×GL(2,𝔽3)—66no—
197#3755—44no—
198C2×C3⋊(C3⋊C8)—41no—
199C3×#215—62no—
200C3×#215—62no—
201C3×#215—64no—
202C3×#215—1212no—
203C3×#213—62no—
204C3×#213—62no—
205C3×#213—64no—
206C3×C4×Dic3—32no—
207C3×C4×Dic3—61no—
208C3×#208—32no—
209C3×#208—32no—
210C3×#208—61no—
211C3×#208—61no—
212C2×C3×C3⋊C8—61no—
213C2×C3×C3⋊C8—61no—
214C2×C3×C3⋊C8—123no—
215C2×#453—91noSylow
216C22×C33—41no—
217C2×C3×C3⋊D3—82no—
218C2×C3×C3⋊D3—162no—
219C33×C4—41no—
220C33×C4—41no—
221C33×C4—82no—
222C3×H(5,𝔽2)—22no—
223C3×H(5,𝔽2)—21no—
224C3×H(5,𝔽2)—21no—
225C3×H(5,𝔽2)—22no—
226C3×H(5,𝔽2)—32no—
227C3×H(5,𝔽2)—32no—
228C3×H(5,𝔽2)—62no—
229C3×H(5,𝔽2)—61no—
230C3×H(5,𝔽2)—61no—
231C3×H(5,𝔽2)—62no—
232C3×H(5,𝔽2)C2×C3×D312yescomplemented
233C3×H(5,𝔽2)C2×C3⋊D312yescomplemented
234C2×C3×#41—22no—
235C2×C3×#41—21no—
236C2×C3×#41—21no—
237C2×C3×#41—21no—
238C2×C3×#41—31no—
239C2×C3×#41—31no—
240C2×C3×#41—61no—
241C2×C3×#41C2×C3×D311yescharacteristic
242C2×C3×#41C2×C3⋊D311yescharacteristic
243C22×C3×D4—31no—
244C22×C3×D4—31no—
245C22×C3×D4—61no—
246C22×C3×D4—61no—
247C22×C3×D4—61no—
248C22×C3×D4—62no—
249C22×C3×D4—91no—
250C22×C3×D4—182no—
251C22×#67—62no—
252C22×D12—31no—
253#994—26no—
254#994—23no—
255#994—26no—
256#994C2×C3×D316yescomplemented
257C2×#41⋊C3—26no—
258C2×#41⋊C3—23no—
259C2×#41⋊C3—23no—
260C2×#41⋊C3C2×C3×D313yes—
261#986—36no—
262#986—63no—
263C2×GL(2,𝔽3)—63no—
264C3×AGL(1,ℤ/8)—92no—
265C3×AGL(1,ℤ/8)—94no—
266C3×AGL(1,ℤ/8)—92no—
267C3×AGL(1,ℤ/8)—181no—
268C3×AGL(1,ℤ/8)—182no—
269C3×AGL(1,ℤ/8)—181no—
270C2×C3×SD16—181no—
271C2×C3×SD16—181no—
272C2×C3×D8—181no—
273C2×C3×D8—181no—
274C2×C3×M16—91no—
275C2×C3×M16—91no—
276C3×#127—94no—
277C3×#127—182no—
278C2×C3×C42—91no—
279#949—32no—
280#949—34no—
281#949—32no—
282#949—61no—
283#949—62no—
284#949—61no—
285C2×#215—61no—
286C2×#215—61no—
287C2×#215—123no—
288#940—34no—
289#940—62no—
290C2×#213—61no—
291C2×#213—61no—
292C2×C4×Dic3—31no—
293C2×#208—31no—
294C2×#208—31no—
295GU(2,𝔽3)—36no—
296C3×#104—92no—
297C3×#104—94no—
298C3×#104—92no—
299C3×#100—94no—
300#837—32no—
301#837—34no—
302#837—32no—
303#833—34no—
304C23×C32—31no—
305C23×C32—34no—
306C23×C32—62no—
307C23×C32—61no—
308C23×C32—124no—
309C22×C3⋊D3—81no—
310C22×C3×D3—62no—
311C22×C3×D3—121no—
312C22×C3×D3—124no—
313C22×C3×D3—121no—
314C22×C3×D3—243no—
315C32×Q8—21no—
316C32×Q8—31no—
317C32×Q8—42no—
318C32×Q8—46no—
319C32×Q8—86no—
320C32×Q8—81no—
321C32×Q8—83no—
322C32×Q8—86no—
323C32×Q8—82no—
324C32×Q8—82no—
325C32×Q8C2×#6711yescharacteristic
326C32×Q8C2×S412yes—
327C32×D4—31no—
328C32×D4—31no—
329C32×D4—32no—
330C32×D4—62no—
331C32×D4—62no—
332C32×D4—61no—
333C32×D4—62no—
334C32×D4—62no—
335C32×D4—61no—
336C2×C32×C4—21no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—41no—
343C2×C32×C4—43no—
344C2×C32×C4—62no—
345C2×C32×C4—62no—
346C2×C32×C4—83no—
347C2×C32×C4—81no—
348C2×C32×C4—83no—
349C2×C32×C4—86no—
350C2×C32×C4—82no—
351C2×C32×C4—81no—
352C2×C32×C4C2×S411yescharacteristic
353C4⋊(C3⋊D3)—42no—
354C4⋊(C3⋊D3)—81no—
355C3×#67—1216no—
356C2×C3×Dic3—62no—
357C2×C3×Dic3—64no—
358C3×D12—62no—
359C3×D12—62no—
360C3×D12—126no—
361C3×D12—121no—
362C3×D12—121no—
363C3×D12—243no—
364C3×SL(2,𝔽3)—21no—
365C3×SL(2,𝔽3)—23no—
366C3×SL(2,𝔽3)C2×#6713yescomplemented
367C3×SL(2,𝔽3)C2×C3×D411yescharacteristic, complemented
368C3⋊(C3⋊C8)—42no—
369C3×C3⋊C8—62no—
370C3×C3⋊C8—62no—
371C3×C3⋊C8—126no—
372C2×H(5,𝔽2)C3×C3⋊D311yescharacteristic, complemented
373C2×AGL(1,ℤ/8)—91no—
374C2×AGL(1,ℤ/8)—91no—
375C2×#127—91no—
376#453—94no—
377#453—94no—
378C2×#104—91no—
379C2×#104—91no—
380C2×#100—91no—
381C2×C33—41no—
382C2×C33—42no—
383C3×C3⋊D3—162no—
384C24×C3—32no—
385C24×C3—32no—
386C24×C3—62no—
387C24×C3—181no—
388C23×D3—61no—
389C3×#41—24no—
390C3×#41—22no—
391C3×#41—22no—
392C3×#41—21no—
393C3×#41—21no—
394C3×#41—31no—
395C3×#41—31no—
396C3×#41—31no—
397C3×#41—31no—
398C3×#41—32no—
399C3×#41—32no—
400C3×#41—32no—
401C3×#41—32no—
402C3×#41—62no—
403C3×#41—62no—
404C3×#41—61no—
405C3×#41—61no—
406C3×#41—61no—
407C3×#41—61no—
408C3×#41—61no—
409C3×#41—61no—
410C3×#41—62no—
411C3×#41—62no—
412C3×#41—62no—
413C3×#41—62no—
414C3×#41—64no—
415C3×#41C3×#6711yescharacteristic
416C3×#41#63811yescharacteristic
417C3×#41C22×C3×D311yescharacteristic
418C3×#41C22×C3⋊D311yescharacteristic
419C2×C3×Q8—21no—
420C2×C3×Q8—21no—
421C2×C3×Q8—43no—
422C2×C3×Q8—83no—
423C2×C3×Q8C3×#6711yescharacteristic
424C2×C3×Q8#63811yescharacteristic
425C2×C3×Q8C3×S411yescharacteristic
426C2×C3×Q8C3⋊S411yescharacteristic
427C2×C3×D4—31no—
428C2×C3×D4—31no—
429C2×C3×D4—32no—
430C2×C3×D4—32no—
431C2×C3×D4—32no—
432C2×C3×D4—32no—
433C2×C3×D4—31no—
434C2×C3×D4—31no—
435C2×C3×D4—61no—
436C2×C3×D4—61no—
437C2×C3×D4—62no—
438C2×C3×D4—62no—
439C2×C3×D4—61no—
440C2×C3×D4—61no—
441C2×C3×D4—62no—
442C2×C3×D4—61no—
443C2×C3×D4—61no—
444C2×C3×D4—61no—
445C2×C3×D4—61no—
446C2×C3×D4—61no—
447C2×C3×D4—61no—
448C2×C3×D4—62no—
449C2×C3×D4—62no—
450C2×C3×D4—62no—
451C2×C3×D4—62no—
452C2×C3×D4—64no—
453C2×C3×D4—64no—
454C2×C3×D4—62no—
455C2×C3×D4—62no—
456C2×C3×D4—68no—
457C2×C3×D4—62no—
458C2×C3×D4—64no—
459C2×C3×D4—64no—
460C2×C3×D4—92no—
461C2×C3×D4—181no—
462C2×C3×D4—181no—
463C2×C3×D4—181no—
464C2×C3×D4—181no—
465C2×C3×D4—188no—
466C2×C3×D4—181no—
467C2×C3×D4—368no—
468C22×C3×C4—31no—
469C22×C3×C4—31no—
470C22×C3×C4—61no—
471C22×C3×C4—61no—
472C22×C3×C4—61no—
473C22×C3×C4—62no—
474C22×C3×C4—181no—
475C2×#67—68no—
476C2×#67—128no—
477C22×Dic3—61no—
478C2×D12—32no—
479C2×D12—61no—
480C2×D12—61no—
481C2×D12—61no—
482C2×D12—61no—
483C2×D12—61no—
484C2×D12—123no—
485#41⋊C3—212no—
486#41⋊C3—26no—
487#41⋊C3—23no—
488#41⋊C3—23no—
489#41⋊C3C3×#6713yescomplemented
490#41⋊C3C22×C3×D313yes—
491C2×SL(2,𝔽3)—23no—
492C2×SL(2,𝔽3)C3×#6713yescomplemented
493GL(2,𝔽3)—66no—
494C3×SD16—182no—
495C3×SD16—184no—
496C3×SD16—182no—
497C3×D8—182no—
498C3×D8—182no—
499C3×D8—184no—
500C3×M16—92no—
501C3×M16—92no—
502C3×M16—181no—
503C3×M16—181no—
504C2×C3×C8—181no—
505C2×C3×C8—181no—
506C3×C42—92no—
507C3×C42—181no—
508#215—62no—
509#215—64no—
510#215—62no—
511#215—1212no—
512#213—62no—
513#213—62no—
514#213—64no—
515C4×Dic3—32no—
516C4×Dic3—61no—
517#208—32no—
518#208—32no—
519#208—61no—
520#208—61no—
521C2×C3⋊C8—61no—
522C2×C3⋊C8—61no—
523C2×C3⋊C8—123no—
524C22×C32—31no—
525C22×C32—31no—
526C22×C32—41no—
527C22×C32—43no—
528C22×C32—62no—
529C22×C32—62no—
530C22×C32—83no—
531C22×C32—81no—
532C22×C32—122no—
533C22×C32—124no—
534C22×C32—242no—
535C22×C32GL(2,ℤ/4)11yescharacteristic
536C2×C3⋊D3—82no—
537C2×C3⋊D3—162no—
538C2×C3×D3—124no—
539C2×C3×D3—122no—
540C2×C3×D3—246no—
541C2×C3×D3—242no—
542C2×C3×D3—242no—
543C2×C3×D3—486no—
544C32×C4—22no—
545C32×C4—31no—
546C32×C4—31no—
547C32×C4—41no—
548C32×C4—41no—
549C32×C4—43no—
550C32×C4—43no—
551C32×C4—83no—
552C32×C4—83no—
553C32×C4—82no—
554C32×C4—86no—
555C32×C4—812no—
556C32×C4—84no—
557C32×C4—81no—
558C32×C4—81no—
559C32×C4GL(2,ℤ/4)11yescharacteristic
560C32×C4C22×S411yescharacteristic
561C3×Dic3—64no—
562H(5,𝔽2)—21no—
563H(5,𝔽2)—32no—
564H(5,𝔽2)—61no—
565H(5,𝔽2)C2×C3×C3⋊D312yescomplemented
566C2×#41—21no—
567C2×#41—31no—
568C2×#41C2×C3×C3⋊D311yescharacteristic
569C22×D4—31no—
570C22×D4—61no—
571C22×D4—91no—
572C22×D4—182no—
573AGL(1,ℤ/8)—92no—
574AGL(1,ℤ/8)—94no—
575AGL(1,ℤ/8)—92no—
576AGL(1,ℤ/8)—181no—
577AGL(1,ℤ/8)—182no—
578AGL(1,ℤ/8)—181no—
579C2×SD16—181no—
580C2×SD16—181no—
581C2×D8—181no—
582C2×D8—181no—
583C2×M16—91no—
584C2×M16—91no—
585#127—94no—
586#127—182no—
587C2×C42—91no—
588#104—92no—
589#104—94no—
590#104—92no—
591#100—94no—
592C33—41noSylow
593C23×C3—31no—
594C23×C3—31no—
595C23×C3—34no—
596C23×C3—34no—
597C23×C3—61no—
598C23×C3—64no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3—62no—
602C23×C3—64no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—124no—
606C23×C3—124no—
607C23×C3—182no—
608C23×C3—244no—
609C23×C3—361no—
610C23×C3—364no—
611C23×C3—361no—
612C22×D3—62no—
613C22×D3—121no—
614C22×D3—124no—
615C22×D3—121no—
616C22×D3—243no—
617C3×Q8—22no—
618C3×Q8—21no—
619C3×Q8—21no—
620C3×Q8—22no—
621C3×Q8—21no—
622C3×Q8—31no—
623C3×Q8—31no—
624C3×Q8—46no—
625C3×Q8—61no—
626C3×Q8—83no—
627C3×Q8—86no—
628C3×Q8—86no—
629C3×Q8C2×C3×#6711yescharacteristic
630C3×Q8C2×#63811yescharacteristic
631C3×Q8C2×C3×S412yes—
632C3×Q8C2×C3⋊S412yes—
633C3×D4—31no—
634C3×D4—31no—
635C3×D4—31no—
636C3×D4—31no—
637C3×D4—32no—
638C3×D4—32no—
639C3×D4—62no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—62no—
643C3×D4—62no—
644C3×D4—62no—
645C3×D4—62no—
646C3×D4—64no—
647C3×D4—64no—
648C3×D4—62no—
649C3×D4—61no—
650C3×D4—61no—
651C3×D4—62no—
652C3×D4—62no—
653C3×D4—62no—
654C3×D4—62no—
655C3×D4—64no—
656C3×D4—62no—
657C3×D4—64no—
658C3×D4—61no—
659C3×D4—61no—
660C3×D4—182no—
661C3×D4—182no—
662C3×D4—361no—
663C3×D4—3616no—
664C3×D4—361no—
665C2×C3×C4—22no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—43no—
680C2×C3×C4—61no—
681C2×C3×C4—61no—
682C2×C3×C4—61no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4—62no—
688C2×C3×C4—62no—
689C2×C3×C4—64no—
690C2×C3×C4—64no—
691C2×C3×C4—83no—
692C2×C3×C4—86no—
693C2×C3×C4—83no—
694C2×C3×C4—182no—
695C2×C3×C4—184no—
696C2×C3×C4C2×C3×S411yescharacteristic
697C2×C3×C4C2×C3⋊S411yescharacteristic
698#67—1216no—
699C2×Dic3—62no—
700C2×Dic3—64no—
701D12—62no—
702D12—62no—
703D12—126no—
704D12—121no—
705D12—121no—
706D12—243no—
707SL(2,𝔽3)—23no—
708SL(2,𝔽3)C2×C3×#6713yescomplemented
709C3×C8—182no—
710C3×C8—182no—
711C3⋊C8—62no—
712C3⋊C8—62no—
713C3⋊C8—126no—
714C2×C32—42no—
715C2×C32—41no—
716C2×C32—46no—
717C2×C32—43no—
718C2×C32—61no—
719C2×C32—61no—
720C2×C32—83no—
721C2×C32—86no—
722C2×C32—82no—
723C2×C32—81no—
724C2×C32—122no—
725C2×C32#542912yescomplemented
726C2×C32C2×GL(2,ℤ/4)11yescharacteristic
727C3⋊D3—162no—
728C3×D3—242no—
729C3×D3—486no—
730C24—32no—
731C24—181no—
732#41—22no—
733#41—31no—
734#41—31no—
735#41—32no—
736#41—32no—
737#41—61no—
738#41—61no—
739#41—62no—
740#41C3×#63811yescharacteristic
741#41C22×C3×C3⋊D311yescharacteristic
742C2×Q8C3×#63811yescharacteristic
743C2×Q8C3×C3⋊S411yescharacteristic
744C2×D4—31no—
745C2×D4—32no—
746C2×D4—32no—
747C2×D4—31no—
748C2×D4—61no—
749C2×D4—61no—
750C2×D4—61no—
751C2×D4—61no—
752C2×D4—62no—
753C2×D4—62no—
754C2×D4—64no—
755C2×D4—92no—
756C2×D4—181no—
757C2×D4—181no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—188no—
761C2×D4—181no—
762C2×D4—368no—
763C22×C4—31no—
764C22×C4—61no—
765C22×C4—181no—
766SD16—182no—
767SD16—184no—
768SD16—182no—
769D8—182no—
770D8—182no—
771D8—184no—
772M16—92no—
773M16—92no—
774M16—181no—
775M16—181no—
776C2×C8—181no—
777C2×C8—181no—
778C42—92no—
779C42—181no—
780C22×C3—21no—
781C22×C3—31no—
782C22×C3—31no—
783C22×C3—31no—
784C22×C3—31no—
785C22×C3—43no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—64no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—83no—
794C22×C3—122no—
795C22×C3—124no—
796C22×C3—124no—
797C22×C3—124no—
798C22×C3—122no—
799C22×C3—122no—
800C22×C3—244no—
801C22×C3—242no—
802C22×C3—242no—
803C22×C3—244no—
804C22×C3—364no—
805C22×C3—362no—
806C22×C3—722no—
807C22×C3—722no—
808C22×C3C3×GL(2,ℤ/4)11yescharacteristic
809C22×C3#6426911yescharacteristic
810C2×D3—124no—
811C2×D3—122no—
812C2×D3—246no—
813C2×D3—242no—
814C2×D3—242no—
815C2×D3—486no—
816C3×C4—24no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—31no—
822C3×C4—31no—
823C3×C4—31no—
824C3×C4—31no—
825C3×C4—43no—
826C3×C4—43no—
827C3×C4—61no—
828C3×C4—61no—
829C3×C4—86no—
830C3×C4—812no—
831C3×C4—83no—
832C3×C4—83no—
833C3×C4—184no—
834C3×C4C3×GL(2,ℤ/4)11yescharacteristic
835C3×C4#6426911yescharacteristic
836C3×C4C22×C3×S411yescharacteristic
837C3×C4C22×C3⋊S411yescharacteristic
838Dic3—64no—
839C32—41no—
840C32—43no—
841C32—83no—
842C32—81no—
843C32C2×#542911yescharacteristic, complemented
844C23—31no—
845C23—34no—
846C23—62no—
847C23—61no—
848C23—124no—
849C23—182no—
850C23—361no—
851C23—364no—
852C23—361no—
853Q8—21no—
854Q8—31no—
855Q8C2×C3×#63811yescharacteristic
856Q8C2×C3×C3⋊S412yes—
857D4—31no—
858D4—31no—
859D4—32no—
860D4—62no—
861D4—62no—
862D4—61no—
863D4—62no—
864D4—62no—
865D4—61no—
866D4—182no—
867D4—182no—
868D4—361no—
869D4—3616no—
870D4—361no—
871C2×C4—21no—
872C2×C4—31no—
873C2×C4—31no—
874C2×C4—31no—
875C2×C4—31no—
876C2×C4—31no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—182no—
880C2×C4—184no—
881C2×C4C2×C3×C3⋊S411yescharacteristic
882C8—182no—
883C8—182no—
884C2×C3—22no—
885C2×C3—21no—
886C2×C3—46no—
887C2×C3—43no—
888C2×C3—61no—
889C2×C3—61no—
890C2×C3—61no—
891C2×C3—61no—
892C2×C3—86no—
893C2×C3—83no—
894C2×C3—121no—
895C2×C3—121no—
896C2×C3—124no—
897C2×C3—122no—
898C2×C3—122no—
899C2×C3—722no—
900C2×C3C3×#542912yescomplemented
901C2×C3#1059366312yesdirect product factor
902C2×C3C2×C3×GL(2,ℤ/4)11yescharacteristic
903C2×C3C2×#6426911yescharacteristic
904D3—242no—
905D3—486no—
906C22—31no—
907C22—31no—
908C22—62no—
909C22—62no—
910C22—124no—
911C22—122no—
912C22—242no—
913C22—364no—
914C22—362no—
915C22—722no—
916C22—722no—
917C22C3×#6426911yescharacteristic
918C4—22no—
919C4—31no—
920C4—31no—
921C4—184no—
922C4C3×#6426911yescharacteristic
923C4C22×C3×C3⋊S411yescharacteristic
924C3—21no—
925C3—43no—
926C3—83no—
927C3C2×C3×#542911yescharacteristic, complemented
928C3C2×#1059366311yescharacteristic, direct product factor
929C2—61no—
930C2—61no—
931C2—122no—
932C2—722no—
933C2C3×#1059366312yesdirect product factor
934C2C2×C3×#6426911yescharacteristic
subgroupG/H
centerC22×C3#64269
commutator, cosocleC3×#41⋊C3C23×C3
FrattiniC4C22×C3×C3⋊S4
FittingC2×C32×H(5,𝔽2)D3
socleC22×C32GL(2,ℤ/4)
hypercenterC2×C3×Q8C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×C3×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×#994C2semidirect
2. C2×C3×#64267C2semidirect
3. C3×#10593663C2direct (N × H)
4. C2×C3×C3⋊GU(2,𝔽3)C2semidirect
5. C2×#10593663C3direct (N × H)
9. C32×#994C22semidirect
13. C3×#64267C22semidirect
16. C3×C3⋊GU(2,𝔽3)C22semidirect
17. C2×C32×H(5,𝔽2)D3semidirect
20. C2×C3×#994D3semidirect
21. C2×C3×#994C2×C3semidirect
22. C2×#64267C2×C3semidirect
27. #10593663C2×C3direct (N × H)
28. C2×C3⋊GU(2,𝔽3)C2×C3semidirect
39. C32×#41⋊C3D4semidirect
41. C2×C32×SL(2,𝔽3)D4semidirect
51. C32×H(5,𝔽2)C2×D3semidirect
65. C3×#994C2×D3semidirect
66. C3×#994C22×C3semidirect
76. #64267C22×C3semidirect
98. C3⋊GU(2,𝔽3)C22×C3semidirect
111. C32×SL(2,𝔽3)C2×D4semidirect
114. C2×C3×H(5,𝔽2)C3×D3semidirect
115. C2×C3×H(5,𝔽2)C3⋊D3semidirect
117. C2×#994C3×D3semidirect
187. C3×#41⋊C3#67semidirect
188. C3×#41⋊C3C3×D4semidirect
193. C2×C3×SL(2,𝔽3)#67semidirect
194. C2×C3×SL(2,𝔽3)C3×D4semidirect
232. C3×H(5,𝔽2)C2×C3×D3semidirect
233. C3×H(5,𝔽2)C2×C3⋊D3semidirect
256. #994C2×C3×D3semidirect
366. C3×SL(2,𝔽3)C2×#67semidirect
367. C3×SL(2,𝔽3)C2×C3×D4semidirect
372. C2×H(5,𝔽2)C3×C3⋊D3semidirect
489. #41⋊C3C3×#67semidirect
492. C2×SL(2,𝔽3)C3×#67semidirect
565. H(5,𝔽2)C2×C3×C3⋊D3semidirect
708. SL(2,𝔽3)C2×C3×#67semidirect
725. C2×C32#5429semidirect
843. C32C2×#5429semidirect
900. C2×C3C3×#5429semidirect
901. C2×C3#10593663direct (N × H)
927. C3C2×C3×#5429semidirect
928. C3C2×#10593663direct (N × H)
933. C2C3×#10593663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#9942
C2×C3×#642672
C3×#105936632
C2×C3×C3⋊GU(2,𝔽3)2
C2×#105936633
C2×C3×#54293
C2×C3×#52413
C2×C3×#37554