Finite Group Databasebeta

← #13151497

Subgroups — #13151497

Order 1728.

1333 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88744C211yesmaximal, characteristic, complemented
2C2×D4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4#11721322C212yesmaximal, complemented
5#11721321C212yesmaximal, complemented
6#11721307C212yesmaximal, complemented
7C2×#88450C212yesmaximal, complemented
8#11721159C211yesmaximal, characteristic, complemented
9C4×#6200C211yesmaximal, characteristic, complemented
10#11721110C211yesmaximal, characteristic, complemented
11#11721107C211yesmaximal, characteristic, complemented
12#10595254—31nomaximal
13#10595244—31nomaximal
14C23×(C3⋊D3)⋊C3C2212yes—
15C2×D4×H(3,𝔽3)C2211yescharacteristic
16C2×#6235C2212yescomplemented
17C22×#1084C2212yescomplemented
18#88744—24no—
19C2×C4×#272C2211yescharacteristic, complemented
20C2×#6229C2211yescharacteristic, complemented
21C2×#638⋊C3C2212yes—
22C22×(C3⋊Dic3)⋊C3C2212yescomplemented
23D4×(C3⋊D3)⋊C3—24no—
24C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
26C2×#6200C2211yescharacteristic
27C2×#6200C2212yescomplemented
28#3757⋊C3C2212yescomplemented
29C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
30C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
31#88451C2211yescharacteristic, complemented
32#88450C2211yescharacteristic
33#88450C2212yes—
34#88450C2212yescomplemented
35#88450C2212yescomplemented
36#88450C2212yescomplemented
37#88448C2211yescharacteristic, complemented
38#88448C2212yescomplemented
39C2×D4×C3⋊D3D311yescharacteristic, complemented
40C2×C3×#237—31no—
41C2×C3×#237—31no—
42C2×C3×#237—61no—
43C2×C3×D3×D4—31no—
44D4×C3⋊Dic3D311yescharacteristic, complemented
45C3×D4×Dic3—31no—
46#63981—32no—
47#63980—32no—
48#63978—32no—
49#63976—32no—
50#63966—32no—
51C2×#3722—32no—
52#63961—32no—
53C2×(C2×D3)⋊Dic3—32no—
54#63909—31no—
55#63908—31no—
56C4×#626—31no—
57C4×#625—31no—
58#63871—31no—
59#63864—31no—
60#63863—31no—
61#63856—31no—
62C23×H(3,𝔽3)C2312yes—
63C22×#272C2311yescharacteristic
64C22×(C3⋊D3)⋊C3—24no—
65C22×(C3⋊D3)⋊C3—24no—
66C22×(C3⋊D3)⋊C3—42no—
67C22×(C3⋊D3)⋊C3C2312yes—
68C22×(C3⋊D3)⋊C3C2311yescharacteristic
69D4×H(3,𝔽3)D414yescomplemented
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71#6235—24no—
72C2×#1084—24no—
73C2×#1084C2312yes—
74C2×#1084C2311yescharacteristic
75C4×#272—22no—
76#6229—22no—
77#638⋊C3—24no—
78C2×(C3⋊Dic3)⋊C3—42no—
79C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
80C2×(C3⋊Dic3)⋊C3C2312yes—
81C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
82C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
83C4⋊((C3⋊D3)⋊C3)—22no—
84C4×(C3⋊D3)⋊C3—22no—
85#6200—22no—
86#6200—42no—
87#5829—91no—
88#5806—91no—
89#5554—91no—
90C23×C3⋊D3C2×D312yes—
91C23×C3×D3—32no—
92C2×C32×D4—21no—
93C2×C32×D4C2×D311yescharacteristic
94C2×C32×D4C2×D311yescharacteristic
95C2×#638C2×D312yes—
96C22×C3⋊Dic3C2×D312yescomplemented
97D4×C3⋊D3—24no—
98C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
99C2×C4×C3⋊D3C2×D311yescharacteristic
100C2×C3×#67—32no—
101C2×C3×#67—32no—
102C2×C3×#67—32no—
103C2×C3×#67—62no—
104C22×C3×Dic3—32no—
105C22×C3×Dic3—32no—
106C22×C3×Dic3—32no—
107C22×C3×Dic3—62no—
108C3×#237—68no—
109C3×#237—64no—
110C3×#237—64no—
111C3×D3×D4—64no—
112C2×C3×D12—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—61no—
117C2×C3×Dic6—31no—
118C2×C3×Dic6—31no—
119C2×C3×Dic6—61no—
120C2×#626—31no—
121C2×#626—32no—
122C2×#625—31no—
123C2×#625—32no—
124#3757C2×D312yescomplemented
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
126C4×C3⋊Dic3C2×D311yescharacteristic, complemented
127C3×#217—32no—
128C3×C4⋊Dic3—31no—
129C3×C4×Dic3—31no—
130#3724—32no—
131#3724—31no—
132Dic3⋊Dic3—32no—
133Dic3⋊Dic3—31no—
134#3722—32no—
135#3722—32no—
136#3722—32no—
137#3722—31no—
138#3722—32no—
139(C2×D3)⋊Dic3—32no—
140(C2×D3)⋊Dic3—32no—
141(C2×D3)⋊Dic3—32no—
142(C2×D3)⋊Dic3—31no—
143(C2×D3)⋊Dic3—32no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146C22×H(3,𝔽3)—22no—
147C22×H(3,𝔽3)—22no—
148C22×H(3,𝔽3)C2×D414yes—
149C22×H(3,𝔽3)C2411yescharacteristic
150C2×#272—21no—
151C2×#272—21no—
152C2×#272—21no—
153C2×(C3⋊D3)⋊C3—21no—
154C2×(C3⋊D3)⋊C3—21no—
155C2×(C3⋊D3)⋊C3—22no—
156C2×(C3⋊D3)⋊C3—22no—
157C2×(C3⋊D3)⋊C3—22no—
158C2×(C3⋊D3)⋊C3—48no—
159C2×(C3⋊D3)⋊C3#4112yescomplemented
160C4×H(3,𝔽3)C2×D412yes—
161#1084—22no—
162#1084—21no—
163(C3⋊Dic3)⋊C3—21no—
164(C3⋊Dic3)⋊C3—21no—
165(C3⋊Dic3)⋊C3—22no—
166(C3⋊Dic3)⋊C3—21no—
167C2×C3×#41—91no—
168C22×C3×D4—91no—
169C2×#237—31no—
170C2×#237—31no—
171C2×#237—61no—
172C2×D3×D4—31no—
173C2×D3×D4—91no—
174C3×C4×D4—91no—
175#953—92no—
176C2×#217—92no—
177#947—91no—
178#946—91no—
179#939—92no—
180#939—92no—
181#938—91no—
182#937—92no—
183#936—91no—
184#935—92no—
185D4×Dic3—31no—
186D4×Dic3—91no—
187#930—91no—
188#930—92no—
189#929—92no—
190C4×#67—91no—
191C4×#67—91no—
192C2×(C2×D3)⋊C4—92no—
193C2×(C2×D3)⋊C4—92no—
194#924—91no—
195#897—91no—
196#895—91no—
197#886—92no—
198#882—92no—
199#875—91no—
200C4×D12—91no—
201C23×C32—22no—
202C23×C32C22×D312yes—
203C23×C32C22×D312yes—
204C22×C3⋊D3—24no—
205C22×C3⋊D3—24no—
206C22×C3⋊D3—42no—
207C22×C3⋊D3C22×D312yes—
208C22×C3⋊D3C22×D311yescharacteristic
209C22×C3×D3—31no—
210C22×C3×D3—32no—
211C22×C3×D3—31no—
212C22×C3×D3—31no—
213C22×C3×D3—61no—
214C22×C3×D3—64no—
215C22×C3×D3—64no—
216C22×C3×D3—122no—
217C32×D4—24no—
218C32×D4D1214yescomplemented
219C32×D4#6714yescomplemented
220C2×C32×C4—21no—
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C22×D311yescharacteristic
223#638—24no—
224C2×C3⋊Dic3—42no—
225C2×C3⋊Dic3C22×D311yescharacteristic
226C2×C3⋊Dic3C22×D311yescharacteristic
227C2×C3⋊Dic3C22×D312yes—
228C2×C3⋊Dic3C22×D311yescharacteristic
229C4⋊(C3⋊D3)—22no—
230C4×C3⋊D3—22no—
231C3×#67—68no—
232C3×#67—64no—
233C3×#67—64no—
234C3×#67—64no—
235C2×C3×Dic3—31no—
236C2×C3×Dic3—31no—
237C2×C3×Dic3—31no—
238C2×C3×Dic3—32no—
239C2×C3×Dic3—32no—
240C2×C3×Dic3—31no—
241C2×C3×Dic3—32no—
242C2×C3×Dic3—31no—
243C2×C3×Dic3—62no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—68no—
246C2×C3×Dic3—64no—
247C2×C3×Dic3—64no—
248C2×C3×Dic3—122no—
249C3×D12—62no—
250C3×C4×D3—64no—
251C3×C4×D3—62no—
252C3×C4×D3—62no—
253C3×C4×D3—62no—
254C3×Dic6—64no—
255C3×Dic6—62no—
256C3×Dic6—62no—
257#626—62no—
258#626—122no—
259#625—62no—
260#625—122no—
261#546—271noSylow
262C2×H(3,𝔽3)—24no—
263C2×H(3,𝔽3)C22×D411yescharacteristic
264C2×H(3,𝔽3)C2×#4111yescharacteristic
265C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
266#272—41no—
267(C3⋊D3)⋊C3—22no—
268(C3⋊D3)⋊C3—42no—
269C24×C3—92no—
270C23×D3—32no—
271C23×D3—92no—
272C3×#41—184no—
273C2×C3×Q8—91no—
274C2×C3×D4—31no—
275C2×C3×D4—31no—
276C2×C3×D4—61no—
277C2×C3×D4—91no—
278C2×C3×D4—92no—
279C2×C3×D4—92no—
280C2×C3×D4—184no—
281C2×C3×D4D3211yescharacteristic
282C22×C3×C4—91no—
283C22×C3×C4—92no—
284C22×C3×C4—92no—
285C22×C3×C4—91no—
286C2×#67—32no—
287C2×#67—32no—
288C2×#67—32no—
289C2×#67—62no—
290C2×#67—92no—
291C2×#67—91no—
292C2×#67—92no—
293C2×#67—91no—
294C2×#67—92no—
295C22×Dic3—32no—
296C22×Dic3—32no—
297C22×Dic3—32no—
298C22×Dic3—62no—
299C22×Dic3—92no—
300#237—64no—
301#237—64no—
302#237—68no—
303D3×D4—64no—
304D3×D4—184no—
305C2×D12—31no—
306C2×D12—91no—
307C2×D12—91no—
308C2×D12—92no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—61no—
313C2×C4×D3—91no—
314C2×Dic6—31no—
315C2×Dic6—31no—
316C2×Dic6—61no—
317C3×C4⋊C4—91no—
318C3×C22⋊C4—92no—
319C3×C42—91no—
320#217—32no—
321#217—92no—
322#217—91no—
323#217—92no—
324#217—91no—
325#217—92no—
326#217—92no—
327#217—92no—
328(C2×D3)⋊C4—91no—
329(C2×D3)⋊C4—92no—
330(C2×D3)⋊C4—92no—
331(C2×D3)⋊C4—92no—
332(C2×D3)⋊C4—92no—
333(C2×D3)⋊C4—91no—
334(C2×D3)⋊C4—92no—
335(C2×D3)⋊C4—92no—
336(C2×D3)⋊C4—92no—
337(C2×D3)⋊C4—92no—
338(C2×D3)⋊C4—91no—
339(C2×D3)⋊C4—91no—
340C4⋊Dic3—31no—
341C4⋊Dic3—91no—
342C4⋊Dic3—91no—
343C4⋊Dic3—92no—
344Dic3⋊C4—91no—
345Dic3⋊C4—92no—
346Dic3⋊C4—92no—
347Dic3⋊C4—91no—
348C4×Dic3—31no—
349C4×Dic3—91no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—21no—
355C22×C32—24no—
356C22×C32—42no—
357C22×C32—42no—
358C22×C32C2×D1214yes—
359C22×C32C2×#6714yes—
360C22×C32C23×D311yescharacteristic
361C22×C32C23×D311yescharacteristic
362C2×C3⋊D3—21no—
363C2×C3⋊D3—21no—
364C2×C3⋊D3—22no—
365C2×C3⋊D3—22no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—48no—
368C2×C3⋊D3#23712yescomplemented
369C2×C3×D3—32no—
370C2×C3×D3—61no—
371C2×C3×D3—61no—
372C2×C3×D3—62no—
373C2×C3×D3—62no—
374C2×C3×D3—61no—
375C2×C3×D3—61no—
376C2×C3×D3—62no—
377C2×C3×D3—61no—
378C2×C3×D3—61no—
379C2×C3×D3—62no—
380C2×C3×D3—61no—
381C2×C3×D3—61no—
382C2×C3×D3—121no—
383C2×C3×D3—121no—
384C2×C3×D3—128no—
385C32×C4—22no—
386C32×C4C2×D1212yes—
387C32×C4C2×#6712yes—
388C3⋊Dic3—22no—
389C3⋊Dic3—21no—
390C3⋊Dic3—21no—
391C3⋊Dic3—21no—
392C3×Dic3—64no—
393C3×Dic3—62no—
394C3×Dic3—61no—
395C3×Dic3—62no—
396C3×Dic3—61no—
397C3×Dic3—61no—
398C3×Dic3—62no—
399C3×Dic3—61no—
400C3×Dic3—62no—
401C3×Dic3—61no—
402C2×#41—91no—
403C22×D4—91no—
404#124—271no—
405#123—272no—
406C22⋊Q8—271no—
407#121—271no—
408#121—272no—
409#120—272no—
410C4×D4—91no—
411C4×D4—271no—
412C2×C22⋊C4—272no—
413H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
414C23×C3—32no—
415C23×C3—32no—
416C23×C3—62no—
417C23×C3—91no—
418C23×C3—92no—
419C23×C3—91no—
420C23×C3—184no—
421C23×C3—184no—
422C23×C3—362no—
423C23×C3C2×D3212yes—
424C22×D3—31no—
425C22×D3—31no—
426C22×D3—31no—
427C22×D3—32no—
428C22×D3—61no—
429C22×D3—64no—
430C22×D3—64no—
431C22×D3—91no—
432C22×D3—92no—
433C22×D3—122no—
434C22×D3—184no—
435C22×D3—184no—
436C22×D3—362no—
437C3×Q8—182no—
438C3×D4—34no—
439C3×D4—34no—
440C3×D4—64no—
441C3×D4—182no—
442C3×D4—184no—
443C3×D4—184no—
444C3×D4#62614yes—
445C2×C3×C4—31no—
446C2×C3×C4—31no—
447C2×C3×C4—61no—
448C2×C3×C4—91no—
449C2×C3×C4—91no—
450C2×C3×C4—92no—
451C2×C3×C4—91no—
452C2×C3×C4—91no—
453C2×C3×C4—92no—
454C2×C3×C4—182no—
455C2×C3×C4—184no—
456C2×C3×C4—182no—
457C2×C3×C4—362no—
458C2×C3×C4C2×D3211yescharacteristic
459#67—64no—
460#67—64no—
461#67—68no—
462#67—64no—
463#67—184no—
464#67—182no—
465#67—182no—
466#67—362no—
467#67—362no—
468C2×Dic3—32no—
469C2×Dic3—31no—
470C2×Dic3—32no—
471C2×Dic3—31no—
472C2×Dic3—31no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—32no—
476C2×Dic3—62no—
477C2×Dic3—61no—
478C2×Dic3—64no—
479C2×Dic3—64no—
480C2×Dic3—68no—
481C2×Dic3—91no—
482C2×Dic3—91no—
483C2×Dic3—92no—
484C2×Dic3—91no—
485C2×Dic3—122no—
486C2×Dic3—362no—
487D12—62no—
488D12—182no—
489D12—182no—
490D12—362no—
491C4×D3—62no—
492C4×D3—62no—
493C4×D3—64no—
494C4×D3—62no—
495C4×D3—182no—
496Dic6—62no—
497Dic6—62no—
498Dic6—64no—
499C2×C32—24no—
500C2×C32—24no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—44no—
505C2×C32C22×D1211yescharacteristic
506C2×C32C2×#23711yescharacteristic
507C2×C32#100411yescharacteristic
508C2×C32#100411yescharacteristic
509C2×C32D3×#4111yescharacteristic
510C2×C32C22×#6711yescharacteristic
511C3⋊D3—22no—
512C3⋊D3—42no—
513C3×D3—62no—
514C3×D3—122no—
515C3×D3—121no—
516C3×D3—122no—
517C3×D3—121no—
518C24—92no—
519#41—184no—
520C2×Q8—91no—
521C2×D4—92no—
522C2×D4—92no—
523C2×D4—91no—
524C2×D4—184no—
525C2×D4—271no—
526C2×D4—272no—
527C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic
528C22×C4—92no—
529C22×C4—92no—
530C22×C4—91no—
531C22×C4—91no—
532C4⋊C4—91no—
533C4⋊C4—271no—
534C4⋊C4—272no—
535C22⋊C4—92no—
536C22⋊C4—271no—
537C22⋊C4—272no—
538C22⋊C4—272no—
539C22⋊C4—272no—
540C22⋊C4—271no—
541C22⋊C4—272no—
542C42—91no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—31no—
546C22×C3—31no—
547C22×C3—34no—
548C22×C3—34no—
549C22×C3—62no—
550C22×C3—62no—
551C22×C3—62no—
552C22×C3—62no—
553C22×C3—61no—
554C22×C3—64no—
555C22×C3—92no—
556C22×C3—122no—
557C22×C3—122no—
558C22×C3—181no—
559C22×C3—181no—
560C22×C3—182no—
561C22×C3—182no—
562C22×C3—182no—
563C22×C3—181no—
564C22×C3—181no—
565C22×C3—181no—
566C22×C3—368no—
567C22×C3C2×#62614yes—
568C22×C3C22×D3211yescharacteristic
569C2×D3—32no—
570C2×D3—61no—
571C2×D3—61no—
572C2×D3—61no—
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—61no—
576C2×D3—61no—
577C2×D3—61no—
578C2×D3—62no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—92no—
583C2×D3—121no—
584C2×D3—121no—
585C2×D3—128no—
586C2×D3—181no—
587C2×D3—181no—
588C2×D3—182no—
589C2×D3—182no—
590C2×D3—182no—
591C2×D3—368no—
592C3×C4—32no—
593C3×C4—32no—
594C3×C4—62no—
595C3×C4—181no—
596C3×C4—182no—
597C3×C4—181no—
598C3×C4—181no—
599C3×C4—181no—
600C3×C4—182no—
601C3×C4C2×#62612yes—
602Dic3—62no—
603Dic3—62no—
604Dic3—61no—
605Dic3—61no—
606Dic3—64no—
607Dic3—62no—
608Dic3—61no—
609Dic3—61no—
610Dic3—62no—
611Dic3—61no—
612Dic3—181no—
613Dic3—181no—
614Dic3—182no—
615Dic3—181no—
616C32—21no—
617C32#555411yescharacteristic, complemented
618C32#580611yescharacteristic, complemented
619C23—91no—
620C23—92no—
621C23—91no—
622C23—184no—
623C23—184no—
624C23—362no—
625C23C2×((C3⋊D3)⋊C3)⋊C212yes—
626Q8—182no—
627D4—184no—
628D4—184no—
629D4—182no—
630D4—542no—
631D4—1082no—
632D4#620014yescomplemented
633C2×C4—91no—
634C2×C4—91no—
635C2×C4—92no—
636C2×C4—91no—
637C2×C4—92no—
638C2×C4—91no—
639C2×C4—184no—
640C2×C4—182no—
641C2×C4—182no—
642C2×C4—362no—
643C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
644C2×C3—24no—
645C2×C3—31no—
646C2×C3—31no—
647C2×C3—31no—
648C2×C3—31no—
649C2×C3—31no—
650C2×C3—31no—
651C2×C3—64no—
652C2×C3—64no—
653C2×C3—61no—
654C2×C3—61no—
655C2×C3—61no—
656C2×C3—124no—
657C2×C3—182no—
658C2×C3—362no—
659C2×C3—361no—
660C2×C3D3×#23711yescharacteristic
661C2×C3#6431311yescharacteristic
662C2×C3C22×#62611yescharacteristic
663D3—62no—
664D3—121no—
665D3—121no—
666D3—122no—
667D3—122no—
668D3—182no—
669D3—362no—
670C22—22no—
671C22—22no—
672C22—92no—
673C22—181no—
674C22—181no—
675C22—181no—
676C22—182no—
677C22—181no—
678C22—182no—
679C22—181no—
680C22—182no—
681C22—368no—
682C22C2×#620014yes—
683C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
684C4—181no—
685C4—181no—
686C4—182no—
687C4—181no—
688C4—181no—
689C4—182no—
690C4C2×#620012yes—
691C3—31no—
692C3—31no—
693C3—61no—
694C3#1059524611yescharacteristic
695C2—24no—
696C2—182no—
697C2—362no—
698C2—361no—
699C2#1172250411yescharacteristic
700C2#1172250611yescharacteristic
701C2C22×#620011yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC2×D4×H(3,𝔽3)C22
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#546
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#88744C2semidirect
2. C2×D4×(C3⋊D3)⋊C3C2semidirect
3. D4×(C3⋊Dic3)⋊C3C2semidirect
4. #11721322C2semidirect
5. #11721321C2semidirect
6. #11721307C2semidirect
7. C2×#88450C2semidirect
8. #11721159C2semidirect
9. C4×#6200C2semidirect
10. #11721110C2semidirect
11. #11721107C2semidirect
16. C2×#6235C22semidirect
17. C22×#1084C22semidirect
19. C2×C4×#272C22semidirect
20. C2×#6229C22semidirect
22. C22×(C3⋊Dic3)⋊C3C22semidirect
27. C2×#6200C22semidirect
28. #3757⋊C3C22semidirect
29. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
30. C4×(C3⋊Dic3)⋊C3C22semidirect
31. #88451C22semidirect
34. #88450C22semidirect
35. #88450C22semidirect
36. #88450C22semidirect
37. #88448C22semidirect
38. #88448C22semidirect
39. C2×D4×C3⋊D3D3semidirect
44. D4×C3⋊Dic3D3semidirect
69. D4×H(3,𝔽3)D4semidirect
96. C22×C3⋊Dic3C2×D3semidirect
124. #3757C2×D3semidirect
125. C4⋊(C3⋊Dic3)C2×D3semidirect
126. C4×C3⋊Dic3C2×D3semidirect
159. C2×(C3⋊D3)⋊C3#41semidirect
218. C32×D4D12semidirect
219. C32×D4#67semidirect
368. C2×C3⋊D3#237semidirect
413. H(3,𝔽3)#546semidirect
617. C32#5554semidirect
618. C32#5806semidirect
632. D4#6200semidirect

Maximal subgroups

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

subgroupindex
C2×#887442
C2×D4×(C3⋊D3)⋊C32
D4×(C3⋊Dic3)⋊C32
#117213222
#117213212
#117213072
C2×#884502
#117211592
C4×#62002
#117211102
#117211072
#105952543
#105952443