Finite Group Databasebeta

← #13150681

Subgroups — #13150681

Order 1728.

1243 conjugacy classes of subgroups.

The subgroup lattice has 689 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
2C2×#88648C211yesmaximal, characteristic, complemented
3#11721824C211yesmaximal, characteristic, complemented
4C4×#638⋊C3C211yesmaximal, characteristic, complemented
5#11721316C212yesmaximal, complemented
6#11721310C212yesmaximal, complemented
7#11721141C211yesmaximal, characteristic, complemented
8#11721132C211yesmaximal, characteristic, complemented
9#11721126C212yesmaximal, complemented
10#11721125C212yesmaximal, complemented
11#11721110C211yesmaximal, characteristic, complemented
12#10595018—31nomaximal
13#10594889—31nomaximal
14C23×(C3⋊D3)⋊C3C2212yes—
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#6229C2211yescharacteristic, complemented
17C2×#638⋊C3C2211yescharacteristic
18C2×C4⋊((C3⋊D3)⋊C3)—24no—
19C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
20C2×C4⋊((C3⋊D3)⋊C3)C2212yes—
21C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
23C2×#6198C2212yescomplemented
24C2×#6198C2212yescomplemented
25C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
26C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
27#88648—24no—
28#88552C2212yes—
29C4⋊#1084C2211yescharacteristic, complemented
30#88540C2212yescomplemented
31#3757⋊C3C2211yescharacteristic
32#3752⋊C3C2211yescharacteristic, complemented
33#3750⋊C3C2211yescharacteristic, complemented
34C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
35#88450C2212yescomplemented
36#88450C2212yescomplemented
37#88450C2212yescomplemented
38#88450C2212yescomplemented
39C22×C4⋊(C3⋊D3)D311yescharacteristic, complemented
40C22×C3×D12—31no—
41C2×#3799—31no—
42C2×#3796—31no—
43C4×#638D311yescharacteristic, complemented
44C3×C4×#67—31no—
45C3×#924—31no—
46C3×#924—31no—
47C3×#924—61no—
48#63981—32no—
49#63977—32no—
50#63974—32no—
51D3×#217—32no—
52#63916—31no—
53#63910—32no—
54#63909—31no—
55#63898—31no—
56#63897—32no—
57#63894—31no—
58#63886—32no—
59#63884—32no—
60#63864—31no—
61#63863—31no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3—24no—
64C22×(C3⋊D3)⋊C3—24no—
65C22×(C3⋊D3)⋊C3—42no—
66C22×(C3⋊D3)⋊C3C2312yes—
67C22×(C3⋊D3)⋊C3C2311yescharacteristic
68C22×(C3⋊D3)⋊C3C2312yes—
69C2×C4×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72C2×#1084C2312yes—
73C2×#1084C2312yes—
74#6229—22no—
75#638⋊C3—22no—
76C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C4⋊((C3⋊D3)⋊C3)—24no—
80C4⋊((C3⋊D3)⋊C3)—22no—
81C4⋊((C3⋊D3)⋊C3)D414yescomplemented
82C4×(C3⋊D3)⋊C3—22no—
83#6198—24no—
84#6198—42no—
85((C3⋊D3)⋊C3)⋊C4—24no—
86((C3⋊D3)⋊C3)⋊C4—42no—
87#5806—91no—
88#5630—91no—
89#5550—91no—
90C23×C3⋊D3C2×D312yes—
91C23×C3×D3—32no—
92C22×C32×C4—21no—
93C22×C32×C4C2×D311yescharacteristic
94C22×C32×C4C2×D311yescharacteristic
95C2×#638C2×D311yescharacteristic
96C2×C4⋊(C3⋊D3)—24no—
97C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
98C2×C4⋊(C3⋊D3)C2×D312yes—
99C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
100C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
101C2×C3×#67—31no—
102C2×C3×D12—31no—
103C2×C3×D12—31no—
104C2×C3×D12—32no—
105C2×C3×D12—64no—
106C2×C3×C4×D3—31no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—61no—
110C2×#626—32no—
111C2×#626—32no—
112C2×#626—32no—
113C2×#626—32no—
114C2×#624—32no—
115C2×#624—32no—
116C2×D3×Dic3—32no—
117C2×D3×Dic3—32no—
118#3799—64no—
119#3796—64no—
120#3757C2×D311yescharacteristic
121#3752C2×D311yescharacteristic, complemented
122#3750C2×D311yescharacteristic, complemented
123C4×C3⋊Dic3C2×D311yescharacteristic, complemented
124C3×#217—32no—
125C3×#217—32no—
126C3×#217—31no—
127C3×#217—62no—
128C3×(C2×D3)⋊C4—31no—
129C3×C4⋊Dic3—31no—
130C3×C4⋊Dic3—31no—
131C3×C4⋊Dic3—61no—
132C3×Dic3⋊C4—32no—
133C3×Dic3⋊C4—32no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—62no—
136C3×C4×Dic3—31no—
137#3722—32no—
138#3722—32no—
139#3722—32no—
140#3722—32no—
141(C2×D3)⋊Dic3—32no—
142(C2×D3)⋊Dic3—32no—
143(C2×D3)⋊Dic3—32no—
144(C2×D3)⋊Dic3—32no—
145C22×H(3,𝔽3)—21no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)#4112yescomplemented
148C22×H(3,𝔽3)C2411yescharacteristic
149C2×(C3⋊D3)⋊C3—22no—
150C2×(C3⋊D3)⋊C3—22no—
151C2×(C3⋊D3)⋊C3—21no—
152C2×(C3⋊D3)⋊C3—22no—
153C2×(C3⋊D3)⋊C3—21no—
154C2×(C3⋊D3)⋊C3—22no—
155C2×(C3⋊D3)⋊C3—21no—
156C2×(C3⋊D3)⋊C3—22no—
157C2×(C3⋊D3)⋊C3—48no—
158C2×(C3⋊D3)⋊C3C2×D414yes—
159C4×H(3,𝔽3)—21no—
160C4×H(3,𝔽3)C2×D412yes—
161#1084—22no—
162#1084—22no—
163(C3⋊Dic3)⋊C3—21no—
164(C3⋊Dic3)⋊C3—21no—
165(C3⋊Dic3)⋊C3—21no—
166C22×C3×D4—91no—
167C2×#239—91no—
168C2×#237—91no—
169C2×#235—91no—
170C22×D12—31no—
171C22×D12—91no—
172C3×C22⋊Q8—91no—
173C3×C4×D4—91no—
174#953—92no—
175C2×#217—92no—
176#947—91no—
177#939—92no—
178#938—91no—
179#937—92no—
180#936—91no—
181#935—92no—
182D4×Dic3—91no—
183#930—91no—
184C4×#67—31no—
185C4×#67—91no—
186#924—31no—
187#924—31no—
188#924—61no—
189#895—92no—
190#895—91no—
191#894—92no—
192#894—92no—
193#893—91no—
194#884—92no—
195#882—92no—
196D3×C22⋊C4—92no—
197D3×C22⋊C4—92no—
198#875—91no—
199C4×D12—91no—
200C23×C32—21no—
201C23×C32C22×D311yescharacteristic
202C23×C32C22×D311yescharacteristic
203C22×C3⋊D3—24no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3—42no—
206C22×C3⋊D3C22×D312yes—
207C22×C3⋊D3C22×D311yescharacteristic
208C22×C3⋊D3C22×D312yes—
209C22×C3×D3—32no—
210C22×C3×D3—32no—
211C22×C3×D3—31no—
212C22×C3×D3—64no—
213C22×C3×D3—64no—
214C22×C3×D3—122no—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—42no—
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C22×D311yescharacteristic
224#638—22no—
225C2×C3⋊Dic3C22×D311yescharacteristic
226C2×C3⋊Dic3C22×D311yescharacteristic
227C2×C3⋊Dic3C22×D311yescharacteristic
228C4⋊(C3⋊D3)—24no—
229C4⋊(C3⋊D3)—22no—
230C4⋊(C3⋊D3)#6714yescomplemented
231C4×C3⋊D3—22no—
232C3×#67—62no—
233C2×C3×Dic3—31no—
234C2×C3×Dic3—31no—
235C2×C3×Dic3—31no—
236C2×C3×Dic3—32no—
237C2×C3×Dic3—32no—
238C2×C3×Dic3—32no—
239C2×C3×Dic3—32no—
240C2×C3×Dic3—62no—
241C2×C3×Dic3—62no—
242C3×D12—34no—
243C3×D12—64no—
244C3×D12—62no—
245C3×C4×D3—62no—
246C3×Dic6—62no—
247C3×Dic6—62no—
248C3×Dic6—122no—
249#626—64no—
250#626—64no—
251#626—122no—
252#626—122no—
253#624—64no—
254#624—122no—
255D3×Dic3—64no—
256D3×Dic3—122no—
257#546—271noSylow
258C2×H(3,𝔽3)—22no—
259C2×H(3,𝔽3)C22×D411yescharacteristic
260C2×H(3,𝔽3)C2×#4111yescharacteristic
261C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
262(C3⋊D3)⋊C3—24no—
263(C3⋊D3)⋊C3—41no—
264(C3⋊D3)⋊C3—42no—
265C24×C3—92no—
266C23×D3—32no—
267C23×D3—92no—
268C2×C3×Q8—91no—
269C2×C3×D4—91no—
270C2×C3×D4—92no—
271C2×C3×D4—91no—
272C2×C3×D4—91no—
273C2×C3×D4—184no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—61no—
277C22×C3×C4—91no—
278C22×C3×C4D3211yescharacteristic
279C2×#67—31no—
280C2×#67—91no—
281C2×#67—92no—
282C2×#67—92no—
283C2×#67—92no—
284C2×#67—92no—
285C22×Dic3—92no—
286C22×Dic3—92no—
287#239—184no—
288#237—184no—
289#235—184no—
290C2×D12—31no—
291C2×D12—32no—
292C2×D12—31no—
293C2×D12—64no—
294C2×D12—91no—
295C2×D12—91no—
296C2×D12—92no—
297C2×D12—92no—
298C2×D12—92no—
299C2×D12—184no—
300C2×C4×D3—31no—
301C2×C4×D3—91no—
302C2×C4×D3—92no—
303C2×C4×D3—92no—
304C2×C4×D3—92no—
305C2×C4×D3—92no—
306C2×Dic6—31no—
307C2×Dic6—31no—
308C2×Dic6—61no—
309C3×C4⋊C4—91no—
310C3×C4⋊C4—91no—
311C3×C4⋊C4—92no—
312C3×C22⋊C4—91no—
313C3×C22⋊C4—91no—
314C3×C22⋊C4—92no—
315C3×C42—91no—
316#217—32no—
317#217—32no—
318#217—31no—
319#217—62no—
320#217—91no—
321#217—92no—
322#217—92no—
323#217—92no—
324#217—92no—
325(C2×D3)⋊C4—31no—
326(C2×D3)⋊C4—91no—
327(C2×D3)⋊C4—92no—
328(C2×D3)⋊C4—92no—
329(C2×D3)⋊C4—92no—
330(C2×D3)⋊C4—92no—
331(C2×D3)⋊C4—92no—
332(C2×D3)⋊C4—92no—
333(C2×D3)⋊C4—92no—
334(C2×D3)⋊C4—92no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—61no—
338Dic3⋊C4—32no—
339Dic3⋊C4—32no—
340Dic3⋊C4—31no—
341Dic3⋊C4—62no—
342Dic3⋊C4—91no—
343C4×Dic3—31no—
344C4×Dic3—91no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—22no—
351C22×C32—41no—
352C22×C32—41no—
353C22×C32#23512yescomplemented
354C22×C32#23712yescomplemented
355C22×C32C23×D311yescharacteristic
356C22×C32C23×D311yescharacteristic
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—21no—
360C2×C3⋊D3—21no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—22no—
363C2×C3⋊D3—21no—
364C2×C3⋊D3—22no—
365C2×C3⋊D3—48no—
366C2×C3⋊D3C2×#6714yes—
367C2×C3×D3—34no—
368C2×C3×D3—62no—
369C2×C3×D3—62no—
370C2×C3×D3—62no—
371C2×C3×D3—62no—
372C2×C3×D3—61no—
373C2×C3×D3—61no—
374C2×C3×D3—62no—
375C2×C3×D3—61no—
376C2×C3×D3—128no—
377C32×C4—21no—
378C32×C4—21no—
379C32×C4—22no—
380C32×C4—41no—
381C32×C4D3×D412yes—
382C32×C4C2×#6712yes—
383C3⋊Dic3—21no—
384C3⋊Dic3—21no—
385C3⋊Dic3—21no—
386C3×Dic3—62no—
387C3×Dic3—61no—
388C3×Dic3—61no—
389C3×Dic3—62no—
390C3×Dic3—62no—
391C3×Dic3—61no—
392C3×Dic3—62no—
393C3×Dic3—122no—
394C3×Dic3—122no—
395C2×#41—271no—
396C22×D4—91no—
397#124—271no—
398#123—272no—
399C22⋊Q8—91no—
400#121—272no—
401#121—271no—
402#120—272no—
403C4×D4—91no—
404C4×D4—271no—
405C2×C22⋊C4—272no—
406H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
407C23×C3—31no—
408C23×C3—31no—
409C23×C3—61no—
410C23×C3—92no—
411C23×C3—92no—
412C23×C3—91no—
413C23×C3—184no—
414C23×C3—184no—
415C23×C3—362no—
416C23×C3C2×D3211yescharacteristic
417C22×D3—32no—
418C22×D3—31no—
419C22×D3—32no—
420C22×D3—64no—
421C22×D3—64no—
422C22×D3—92no—
423C22×D3—92no—
424C22×D3—91no—
425C22×D3—122no—
426C22×D3—184no—
427C22×D3—184no—
428C22×D3—362no—
429C3×Q8—182no—
430C3×D4—94no—
431C3×D4—182no—
432C3×D4—184no—
433C3×D4—182no—
434C2×C3×C4—22no—
435C2×C3×C4—31no—
436C2×C3×C4—31no—
437C2×C3×C4—31no—
438C2×C3×C4—31no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—91no—
444C2×C3×C4—91no—
445C2×C3×C4—91no—
446C2×C3×C4—92no—
447C2×C3×C4—92no—
448C2×C3×C4—122no—
449C2×C3×C4—182no—
450C2×C3×C4C2×D3211yescharacteristic
451C2×C3×C4C2×D3211yescharacteristic
452#67—62no—
453#67—182no—
454#67—184no—
455#67—184no—
456#67—362no—
457#67—362no—
458C2×Dic3—32no—
459C2×Dic3—32no—
460C2×Dic3—32no—
461C2×Dic3—32no—
462C2×Dic3—31no—
463C2×Dic3—31no—
464C2×Dic3—31no—
465C2×Dic3—62no—
466C2×Dic3—62no—
467C2×Dic3—91no—
468C2×Dic3—91no—
469C2×Dic3—91no—
470C2×Dic3—184no—
471C2×Dic3—362no—
472D12—34no—
473D12—64no—
474D12—62no—
475D12—94no—
476D12—182no—
477D12—184no—
478D12—184no—
479D12—362no—
480C4×D3—62no—
481C4×D3—182no—
482C4×D3—184no—
483C4×D3—184no—
484C4×D3—362no—
485C4×D3—362no—
486Dic6—62no—
487Dic6—62no—
488Dic6—122no—
489C2×C32—22no—
490C2×C32—22no—
491C2×C32—21no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—42no—
495C2×C32C2×#23511yescharacteristic
496C2×C32C2×D3×D411yescharacteristic
497C2×C32C2×#23711yescharacteristic
498C2×C32#100411yescharacteristic
499C2×C32#100911yescharacteristic
500C2×C32C22×#6711yescharacteristic
501C3⋊D3—24no—
502C3⋊D3—41no—
503C3⋊D3—42no—
504C3×D3—64no—
505C3×D3—122no—
506C3×D3—121no—
507C24—92no—
508#41—544no—
509C2×Q8—91no—
510C2×D4—91no—
511C2×D4—91no—
512C2×D4—92no—
513C2×D4—91no—
514C2×D4—184no—
515C2×D4—272no—
516C2×D4—272no—
517C22×C4—91no—
518C22×C4—272no—
519C22×C4—272no—
520C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
521C4⋊C4—91no—
522C4⋊C4—91no—
523C4⋊C4—92no—
524C22⋊C4—91no—
525C22⋊C4—92no—
526C22⋊C4—91no—
527C22⋊C4—272no—
528C22⋊C4—272no—
529C22⋊C4—272no—
530C22⋊C4—272no—
531C42—91no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—31no—
535C22×C3—31no—
536C22×C3—32no—
537C22×C3—32no—
538C22×C3—61no—
539C22×C3—61no—
540C22×C3—61no—
541C22×C3—61no—
542C22×C3—61no—
543C22×C3—62no—
544C22×C3—94no—
545C22×C3—121no—
546C22×C3—121no—
547C22×C3—182no—
548C22×C3—182no—
549C22×C3—181no—
550C22×C3—181no—
551C22×C3—182no—
552C22×C3—182no—
553C22×C3—181no—
554C22×C3—182no—
555C22×C3—368no—
556C22×C3#379512yes—
557C22×C3C22×D3211yescharacteristic
558C2×D3—34no—
559C2×D3—62no—
560C2×D3—62no—
561C2×D3—61no—
562C2×D3—62no—
563C2×D3—61no—
564C2×D3—62no—
565C2×D3—61no—
566C2×D3—62no—
567C2×D3—94no—
568C2×D3—128no—
569C2×D3—182no—
570C2×D3—182no—
571C2×D3—181no—
572C2×D3—182no—
573C2×D3—181no—
574C2×D3—181no—
575C2×D3—182no—
576C2×D3—182no—
577C2×D3—368no—
578C3×C4—21no—
579C3×C4—32no—
580C3×C4—32no—
581C3×C4—61no—
582C3×C4—61no—
583C3×C4—62no—
584C3×C4—121no—
585C3×C4—181no—
586C3×C4—181no—
587C3×C4—181no—
588C3×C4—182no—
589C3×C4—182no—
590C3×C4D3×#6712yes—
591Dic3—62no—
592Dic3—62no—
593Dic3—62no—
594Dic3—62no—
595Dic3—61no—
596Dic3—61no—
597Dic3—61no—
598Dic3—122no—
599Dic3—122no—
600Dic3—181no—
601Dic3—181no—
602Dic3—181no—
603C32—21no—
604C32#555011yescharacteristic, complemented
605C32#580611yescharacteristic, complemented
606C23—92no—
607C23—91no—
608C23—92no—
609C23—184no—
610C23—184no—
611C23—362no—
612C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
613Q8—182no—
614D4—94no—
615D4—184no—
616D4—182no—
617D4—182no—
618D4—544no—
619D4—1082no—
620C2×C4—22no—
621C2×C4—91no—
622C2×C4—91no—
623C2×C4—92no—
624C2×C4—91no—
625C2×C4—92no—
626C2×C4—182no—
627C2×C4—544no—
628C2×C4—1082no—
629C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
630C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
631C2×C3—22no—
632C2×C3—31no—
633C2×C3—31no—
634C2×C3—31no—
635C2×C3—31no—
636C2×C3—31no—
637C2×C3—31no—
638C2×C3—62no—
639C2×C3—62no—
640C2×C3—61no—
641C2×C3—61no—
642C2×C3—61no—
643C2×C3—122no—
644C2×C3—184no—
645C2×C3—362no—
646C2×C3—361no—
647C2×C3C2×#379511yescharacteristic
648C2×C3#6430711yescharacteristic
649C2×C3C2×D3×#6711yescharacteristic
650D3—64no—
651D3—122no—
652D3—121no—
653D3—184no—
654D3—362no—
655D3—361no—
656C22—21no—
657C22—21no—
658C22—94no—
659C22—182no—
660C22—182no—
661C22—181no—
662C22—182no—
663C22—181no—
664C22—182no—
665C22—181no—
666C22—182no—
667C22—368no—
668C22#8864812yescomplemented
669C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
670C4—21no—
671C4—181no—
672C4—182no—
673C4—181no—
674C4—181no—
675C4—182no—
676C4#8867612yes—
677C3—31no—
678C3—31no—
679C3—61no—
680C3#1059488611yescharacteristic
681C2—22no—
682C2—184no—
683C2—362no—
684C2—361no—
685C2C2×#8864811yescharacteristic
686C2#1172249211yescharacteristic
687C2C2×#8867611yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#546
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊((C3⋊D3)⋊C3)C2semidirect
2. C2×#88648C2semidirect
3. #11721824C2semidirect
4. C4×#638⋊C3C2semidirect
5. #11721316C2semidirect
6. #11721310C2semidirect
7. #11721141C2semidirect
8. #11721132C2semidirect
9. #11721126C2semidirect
10. #11721125C2semidirect
11. #11721110C2semidirect
16. C2×#6229C22semidirect
22. C2×C4×(C3⋊D3)⋊C3C22semidirect
23. C2×#6198C22semidirect
24. C2×#6198C22semidirect
25. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
26. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
29. C4⋊#1084C22semidirect
30. #88540C22semidirect
32. #3752⋊C3C22semidirect
33. #3750⋊C3C22semidirect
34. C4×(C3⋊Dic3)⋊C3C22semidirect
35. #88450C22semidirect
36. #88450C22semidirect
37. #88450C22semidirect
38. #88450C22semidirect
39. C22×C4⋊(C3⋊D3)D3semidirect
43. C4×#638D3semidirect
81. C4⋊((C3⋊D3)⋊C3)D4semidirect
100. C2×C4×C3⋊D3C2×D3semidirect
121. #3752C2×D3semidirect
122. #3750C2×D3semidirect
123. C4×C3⋊Dic3C2×D3semidirect
147. C22×H(3,𝔽3)#41semidirect
230. C4⋊(C3⋊D3)#67semidirect
353. C22×C32#235semidirect
354. C22×C32#237semidirect
406. H(3,𝔽3)#546semidirect
604. C32#5550semidirect
605. C32#5806semidirect
668. C22#88648semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊((C3⋊D3)⋊C3)2
C2×#886482
#117218242
C4×#638⋊C32
#117213162
#117213102
#117211412
#117211322
#117211262
#117211252
#117211102
#105950183
#105948893