Finite Group Databasebeta

← #13150834

Subgroups — #13150834

Order 1728.

1249 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
2C2×#88652C211yesmaximal, characteristic, complemented
3#11721830C211yesmaximal, characteristic, complemented
4#64133⋊C3C211yesmaximal, characteristic, complemented
5#11721321C212yesmaximal, complemented
6#11721293C212yesmaximal, complemented
7#11721156C211yesmaximal, characteristic, complemented
8#11721154C212yesmaximal, complemented
9#11721106C211yesmaximal, characteristic, complemented
10#11721100C212yesmaximal, complemented
11#11721081C211yesmaximal, characteristic, complemented
12#10594922—31nomaximal
13#10594892—31nomaximal
14C23×(C3⋊D3)⋊C3C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#6235C2212yes—
17C2×C4⋊#272C2211yescharacteristic, complemented
18C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
19C2×C4×(C3⋊D3)⋊C3—24no—
20C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×#634⋊C3C2211yescharacteristic, complemented
25C2×#6200C2212yes—
26C2×#6200C2212yes—
27C2×#6199C2212yescomplemented
28#88652—24no—
29#88542C2212yescomplemented
30C4⋊#1084C2211yescharacteristic, complemented
31#3757⋊C3C2212yes—
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
33#3750⋊C3C2212yescomplemented
34#88451C2212yescomplemented
35#88450C2212yes—
36#88450C2212yes—
37#88449C2212yescomplemented
38#88447C2212yescomplemented
39C22×C4×C3⋊D3D311yescharacteristic, complemented
40C22×C3×C4×D3—31no—
41C2×#3796—31no—
42C2×#3795—31no—
43#64133D311yescharacteristic, complemented
44C3×#930—31no—
45C3×#930—31no—
46C3×#930—61no—
47C3×#924—31no—
48#63981—32no—
49#63976—32no—
50#67⋊Dic3—32no—
51Dic3×#67—32no—
52#63916—31no—
53#63908—31no—
54#63905—32no—
55#63881—32no—
56#63879—32no—
57#63871—31no—
58#63857—31no—
59#63853—32no—
60#63849—31no—
61#63841—31no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×#272C2312yes—
64C22×(C3⋊D3)⋊C3—22no—
65C22×(C3⋊D3)⋊C3—22no—
66C22×(C3⋊D3)⋊C3—22no—
67C22×(C3⋊D3)⋊C3C2311yescharacteristic
68C22×(C3⋊D3)⋊C3C2311yescharacteristic
69C2×C4×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72#6235—24no—
73C2×#1084C2312yes—
74C4⋊#272—22no—
75C2×(C3⋊Dic3)⋊C3—22no—
76C2×(C3⋊Dic3)⋊C3C2312yes—
77C2×(C3⋊Dic3)⋊C3C2312yes—
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
80C4×(C3⋊D3)⋊C3—22no—
81C4×(C3⋊D3)⋊C3—22no—
82C4×(C3⋊D3)⋊C3—22no—
83C4×(C3⋊D3)⋊C3D414yescomplemented
84#634⋊C3—22no—
85#6200—24no—
86#6200—24no—
87#6199—24no—
88#5791—91no—
89#5627—91no—
90#5606—91no—
91C23×C3⋊D3C2×D311yescharacteristic
92C23×C3×D3—31no—
93C22×C32×C4—21no—
94C22×C32×C4C2×D311yescharacteristic
95C22×C32×C4C2×D311yescharacteristic
96C22×C3⋊Dic3C2×D311yescharacteristic
97C2×C4×C3⋊D3—24no—
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×C4×C3⋊D3C2×D311yescharacteristic
100C2×C4×C3⋊D3C2×D311yescharacteristic
101C2×C4×C3⋊D3C2×D311yescharacteristic
102C2×#634C2×D311yescharacteristic, complemented
103C2×C3×#67—32no—
104C2×C3×#67—32no—
105C2×C3×#67—62no—
106C22×C3×Dic3—31no—
107C2×C3×D12—31no—
108C2×C3×D12—31no—
109C2×C3×D12—61no—
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—64no—
115C2×C3×Dic6—31no—
116C2×#626—32no—
117C2×#626—32no—
118C2×#625—32no—
119C2×#625—32no—
120C2×D3×Dic3—32no—
121C2×D3×Dic3—32no—
122#3796—64no—
123#3795—64no—
124#3757C2×D312yes—
125C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
126#3750C2×D312yescomplemented
127C3×#217—32no—
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—62no—
131C3×C4⋊Dic3—31no—
132C3×C4⋊Dic3—31no—
133C3×C4⋊Dic3—31no—
134C3×C4⋊Dic3—61no—
135C3×Dic3⋊C4—32no—
136Dic3⋊Dic3—32no—
137Dic3⋊Dic3—32no—
138#3722—32no—
139#3722—32no—
140(C2×D3)⋊Dic3—32no—
141(C2×D3)⋊Dic3—32no—
142(C2×D3)⋊Dic3—32no—
143(C2×D3)⋊Dic3—32no—
144Dic32—32no—
145Dic32—32no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)—21no—
148C22×H(3,𝔽3)#4112yescomplemented
149C22×H(3,𝔽3)C2411yescharacteristic
150C2×#272—22no—
151C2×#272—22no—
152C2×#272—22no—
153C2×(C3⋊D3)⋊C3—28no—
154C2×(C3⋊D3)⋊C3—21no—
155C2×(C3⋊D3)⋊C3—21no—
156C2×(C3⋊D3)⋊C3—21no—
157C2×(C3⋊D3)⋊C3—21no—
158C2×(C3⋊D3)⋊C3C2×D412yes—
159C2×(C3⋊D3)⋊C3#4112yescomplemented
160C4×H(3,𝔽3)—21no—
161C4×H(3,𝔽3)C2×D412yes—
162#1084—22no—
163(C3⋊Dic3)⋊C3—22no—
164(C3⋊Dic3)⋊C3—21no—
165(C3⋊Dic3)⋊C3—22no—
166(C3⋊Dic3)⋊C3C2×D412yes—
167C23×C3×C4—91no—
168C2×#239—91no—
169C2×#237—91no—
170C2×#235—91no—
171C22×C4×D3—31no—
172C22×C4×D3—91no—
173C3×C22⋊Q8—91no—
174C3×#121—91no—
175#953—92no—
176#946—91no—
177#938—91no—
178#937—92no—
179D4×Dic3—92no—
180#930—31no—
181#930—31no—
182#930—61no—
183#930—91no—
184#929—92no—
185C4×#67—92no—
186C4×#67—92no—
187#926—91no—
188#924—31no—
189#924—91no—
190#924—91no—
191#897—91no—
192#895—91no—
193#894—92no—
194#893—92no—
195#892—91no—
196#892—91no—
197#883—92no—
198#882—92no—
199#67⋊C4—92no—
200#67⋊C4—92no—
201C23×C32—21no—
202C23×C32C22×D311yescharacteristic
203C23×C32C22×D311yescharacteristic
204C22×C3⋊D3—22no—
205C22×C3⋊D3—22no—
206C22×C3⋊D3—22no—
207C22×C3⋊D3C22×D311yescharacteristic
208C22×C3⋊D3C22×D311yescharacteristic
209C22×C3×D3—31no—
210C22×C3×D3—31no—
211C22×C3×D3—32no—
212C22×C3×D3—32no—
213C22×C3×D3—62no—
214C22×C3×D3—62no—
215C22×C3×D3—62no—
216C22×C3×D3—62no—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—42no—
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C22×D311yescharacteristic
224C2×C32×C4C22×D311yescharacteristic
225C2×C32×C4C22×D311yescharacteristic
226C2×C3⋊Dic3—22no—
227C2×C3⋊Dic3C22×D312yes—
228C2×C3⋊Dic3C22×D311yescharacteristic
229C2×C3⋊Dic3C22×D312yes—
230C2×C3⋊Dic3C22×D311yescharacteristic
231C4×C3⋊D3—22no—
232C4×C3⋊D3—22no—
233C4×C3⋊D3—22no—
234C4×C3⋊D3#6714yescomplemented
235#634—22no—
236C3×#67—64no—
237C3×#67—64no—
238C3×#67—124no—
239C2×C3×Dic3—31no—
240C2×C3×Dic3—32no—
241C2×C3×Dic3—31no—
242C2×C3×Dic3—32no—
243C2×C3×Dic3—32no—
244C2×C3×Dic3—32no—
245C2×C3×Dic3—62no—
246C2×C3×Dic3—62no—
247C3×D12—62no—
248C3×D12—62no—
249C3×D12—122no—
250C3×C4×D3—34no—
251C3×C4×D3—62no—
252C3×C4×D3—62no—
253C3×C4×D3—62no—
254C3×Dic6—62no—
255#626—64no—
256#626—64no—
257#625—64no—
258#625—64no—
259D3×Dic3—64no—
260D3×Dic3—64no—
261#525—271noSylow
262C2×H(3,𝔽3)—22no—
263C2×H(3,𝔽3)C22×D411yescharacteristic
264C2×H(3,𝔽3)C2×#4111yescharacteristic
265C2×H(3,𝔽3)C2×#4111yescharacteristic
266#272—42no—
267(C3⋊D3)⋊C3—22no—
268(C3⋊D3)⋊C3—22no—
269C24×C3—91no—
270C23×D3—31no—
271C23×D3—91no—
272C2×C3×Q8—91no—
273C2×C3×D4—92no—
274C2×C3×D4—91no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—61no—
278C22×C3×C4—91no—
279C22×C3×C4—91no—
280C22×C3×C4—91no—
281C22×C3×C4—91no—
282C22×C3×C4—91no—
283C22×C3×C4—184no—
284C22×C3×C4D3211yescharacteristic
285C2×#67—32no—
286C2×#67—32no—
287C2×#67—62no—
288C2×#67—92no—
289C2×#67—92no—
290C2×#67—92no—
291C2×#67—92no—
292C22×Dic3—31no—
293C22×Dic3—91no—
294C22×Dic3—92no—
295#239—184no—
296#237—184no—
297#235—184no—
298C2×D12—31no—
299C2×D12—31no—
300C2×D12—61no—
301C2×D12—92no—
302C2×D12—92no—
303C2×C4×D3—31no—
304C2×C4×D3—31no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—64no—
308C2×C4×D3—91no—
309C2×C4×D3—91no—
310C2×C4×D3—91no—
311C2×C4×D3—91no—
312C2×C4×D3—92no—
313C2×C4×D3—92no—
314C2×C4×D3—184no—
315C2×Dic6—31no—
316C2×Dic6—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4—92no—
319C3×C4⋊C4—91no—
320C3×C22⋊C4—92no—
321C3×C22⋊C4—92no—
322#217—32no—
323#217—92no—
324#217—92no—
325#217—92no—
326#217—92no—
327(C2×D3)⋊C4—32no—
328(C2×D3)⋊C4—32no—
329(C2×D3)⋊C4—62no—
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—
335(C2×D3)⋊C4—92no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—61no—
340C4⋊Dic3—91no—
341C4⋊Dic3—92no—
342Dic3⋊C4—32no—
343Dic3⋊C4—92no—
344Dic3⋊C4—92no—
345Dic3⋊C4—92no—
346C4×Dic3—92no—
347C4×Dic3—92no—
348C4×Dic3—92no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—21no—
354C22×C32—22no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32#23512yescomplemented
358C22×C32#23912yescomplemented
359C22×C32C23×D311yescharacteristic
360C22×C32C23×D311yescharacteristic
361C2×C3⋊D3—28no—
362C2×C3⋊D3—21no—
363C2×C3⋊D3—21no—
364C2×C3⋊D3—21no—
365C2×C3⋊D3—21no—
366C2×C3⋊D3#23512yescomplemented
367C2×C3⋊D3C2×#6712yes—
368C2×C3×D3—32no—
369C2×C3×D3—32no—
370C2×C3×D3—68no—
371C2×C3×D3—61no—
372C2×C3×D3—61no—
373C2×C3×D3—61no—
374C2×C3×D3—61no—
375C2×C3×D3—62no—
376C2×C3×D3—62no—
377C2×C3×D3—62no—
378C2×C3×D3—62no—
379C2×C3×D3—62no—
380C2×C3×D3—62no—
381C2×C3×D3—122no—
382C2×C3×D3—122no—
383C2×C3×D3—122no—
384C32×C4—21no—
385C32×C4—21no—
386C32×C4—22no—
387C32×C4—41no—
388C32×C4D3×D412yes—
389C32×C4C2×#6712yes—
390C3⋊Dic3—22no—
391C3⋊Dic3—22no—
392C3⋊Dic3—21no—
393C3⋊Dic3C2×#6712yes—
394C3×Dic3—32no—
395C3×Dic3—62no—
396C3×Dic3—62no—
397C3×Dic3—61no—
398C3×Dic3—62no—
399C3×Dic3—62no—
400C3×Dic3—122no—
401C2×#41—271no—
402C23×C4—91no—
403#123—272no—
404C22⋊Q8—91no—
405C22⋊Q8—271no—
406#121—91no—
407#121—271no—
408#120—272no—
409C4×D4—272no—
410C4×D4—272no—
411#117—271no—
412H(3,𝔽3)#52511yescharacteristic, complemented, Sylow
413C23×C3—31no—
414C23×C3—31no—
415C23×C3—61no—
416C23×C3—91no—
417C23×C3—91no—
418C23×C3—92no—
419C23×C3—182no—
420C23×C3—182no—
421C23×C3—182no—
422C23×C3C2×D3211yescharacteristic
423C22×D3—31no—
424C22×D3—31no—
425C22×D3—32no—
426C22×D3—32no—
427C22×D3—62no—
428C22×D3—62no—
429C22×D3—62no—
430C22×D3—62no—
431C22×D3—91no—
432C22×D3—91no—
433C22×D3—182no—
434C22×D3—182no—
435C22×D3—182no—
436C3×Q8—182no—
437C3×D4—184no—
438C3×D4—182no—
439C2×C3×C4—22no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—94no—
449C2×C3×C4—91no—
450C2×C3×C4—92no—
451C2×C3×C4—91no—
452C2×C3×C4—92no—
453C2×C3×C4—92no—
454C2×C3×C4—122no—
455C2×C3×C4—182no—
456C2×C3×C4—182no—
457C2×C3×C4—182no—
458C2×C3×C4—182no—
459C2×C3×C4C2×D3211yescharacteristic
460C2×C3×C4C2×D3211yescharacteristic
461#67—64no—
462#67—64no—
463#67—124no—
464#67—184no—
465#67—184no—
466#67—184no—
467#67—184no—
468C2×Dic3—31no—
469C2×Dic3—32no—
470C2×Dic3—32no—
471C2×Dic3—32no—
472C2×Dic3—32no—
473C2×Dic3—31no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—91no—
477C2×Dic3—92no—
478C2×Dic3—91no—
479C2×Dic3—92no—
480C2×Dic3—182no—
481C2×Dic3—184no—
482D12—62no—
483D12—62no—
484D12—122no—
485D12—184no—
486D12—184no—
487C4×D3—34no—
488C4×D3—62no—
489C4×D3—62no—
490C4×D3—62no—
491C4×D3—94no—
492C4×D3—182no—
493C4×D3—182no—
494C4×D3—182no—
495C4×D3—184no—
496C4×D3—184no—
497Dic6—62no—
498Dic6—182no—
499C2×C32—22no—
500C2×C32—22no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—42no—
505C2×C32C2×#23511yescharacteristic
506C2×C32C2×#23511yescharacteristic
507C2×C32C2×D3×D411yescharacteristic
508C2×C32C2×#23911yescharacteristic
509C2×C32D3×#4111yescharacteristic
510C2×C32C22×#6711yescharacteristic
511C3⋊D3—22no—
512C3⋊D3—22no—
513C3×D3—62no—
514C3×D3—62no—
515C3×D3—122no—
516C3×D3—122no—
517C3×D3—242no—
518C24—91no—
519#41—544no—
520C2×Q8—91no—
521C2×D4—92no—
522C2×D4—91no—
523C2×D4—272no—
524C2×D4—272no—
525C22×C4—91no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4—91no—
530C22×C4—184no—
531C22×C4—272no—
532C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
533C4⋊C4—91no—
534C4⋊C4—91no—
535C4⋊C4—92no—
536C4⋊C4—272no—
537C22⋊C4—92no—
538C22⋊C4—92no—
539C22⋊C4—272no—
540C22⋊C4—272no—
541C22⋊C4—272no—
542C42—272no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—31no—
546C22×C3—31no—
547C22×C3—32no—
548C22×C3—32no—
549C22×C3—61no—
550C22×C3—61no—
551C22×C3—61no—
552C22×C3—61no—
553C22×C3—61no—
554C22×C3—62no—
555C22×C3—92no—
556C22×C3—92no—
557C22×C3—121no—
558C22×C3—121no—
559C22×C3—181no—
560C22×C3—181no—
561C22×C3—181no—
562C22×C3—181no—
563C22×C3—188no—
564C22×C3—182no—
565C22×C3—182no—
566C22×C3—182no—
567C22×C3#379912yes—
568C22×C3C22×D3211yescharacteristic
569C2×D3—32no—
570C2×D3—32no—
571C2×D3—68no—
572C2×D3—61no—
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—61no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—92no—
583C2×D3—92no—
584C2×D3—122no—
585C2×D3—122no—
586C2×D3—122no—
587C2×D3—181no—
588C2×D3—181no—
589C2×D3—181no—
590C2×D3—181no—
591C2×D3—188no—
592C3×C4—21no—
593C3×C4—32no—
594C3×C4—32no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—62no—
598C3×C4—92no—
599C3×C4—121no—
600C3×C4—182no—
601C3×C4—182no—
602C3×C4—181no—
603C3×C4—182no—
604C3×C4D3×#6712yes—
605Dic3—32no—
606Dic3—62no—
607Dic3—62no—
608Dic3—62no—
609Dic3—62no—
610Dic3—61no—
611Dic3—92no—
612Dic3—122no—
613Dic3—182no—
614Dic3—181no—
615Dic3—182no—
616C32—21no—
617C32#562711yescharacteristic, complemented
618C32#579111yescharacteristic, complemented
619C23—91no—
620C23—91no—
621C23—92no—
622C23—182no—
623C23—182no—
624C23—182no—
625C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
626Q8—182no—
627D4—184no—
628D4—182no—
629D4—544no—
630D4—544no—
631C2×C4—22no—
632C2×C4—91no—
633C2×C4—94no—
634C2×C4—92no—
635C2×C4—92no—
636C2×C4—92no—
637C2×C4—91no—
638C2×C4—182no—
639C2×C4—182no—
640C2×C4—182no—
641C2×C4—182no—
642C2×C4—544no—
643C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
644C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
645C2×C3—22no—
646C2×C3—31no—
647C2×C3—31no—
648C2×C3—31no—
649C2×C3—31no—
650C2×C3—31no—
651C2×C3—31no—
652C2×C3—62no—
653C2×C3—62no—
654C2×C3—61no—
655C2×C3—61no—
656C2×C3—61no—
657C2×C3—122no—
658C2×C3—182no—
659C2×C3—182no—
660C2×C3—362no—
661C2×C3C2×#379911yescharacteristic
662C2×C3D3×#23511yescharacteristic
663C2×C3C2×D3×#6711yescharacteristic
664D3—62no—
665D3—62no—
666D3—122no—
667D3—122no—
668D3—182no—
669D3—182no—
670D3—242no—
671C22—21no—
672C22—21no—
673C22—92no—
674C22—92no—
675C22—188no—
676C22—181no—
677C22—181no—
678C22—181no—
679C22—181no—
680C22—182no—
681C22—182no—
682C22—182no—
683C22#8865212yescomplemented
684C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
685C4—21no—
686C4—92no—
687C4—181no—
688C4—182no—
689C4—182no—
690C4—182no—
691C4#8867612yes—
692C3—31no—
693C3—31no—
694C3—61no—
695C3#1059500511yescharacteristic
696C2—22no—
697C2—182no—
698C2—182no—
699C2—362no—
700C2C2×#8865211yescharacteristic
701C2#1172249011yescharacteristic
702C2C2×#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)#525
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)⋊C3C2semidirect
2. C2×#88652C2semidirect
3. #11721830C2semidirect
4. #64133⋊C3C2semidirect
5. #11721321C2semidirect
6. #11721293C2semidirect
7. #11721156C2semidirect
8. #11721154C2semidirect
9. #11721106C2semidirect
10. #11721100C2semidirect
11. #11721081C2semidirect
17. C2×C4⋊#272C22semidirect
24. C2×#634⋊C3C22semidirect
27. C2×#6199C22semidirect
29. #88542C22semidirect
30. C4⋊#1084C22semidirect
32. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
33. #3750⋊C3C22semidirect
34. #88451C22semidirect
37. #88449C22semidirect
38. #88447C22semidirect
39. C22×C4×C3⋊D3D3semidirect
43. #64133D3semidirect
83. C4×(C3⋊D3)⋊C3D4semidirect
102. C2×#634C2×D3semidirect
125. C4⋊(C3⋊Dic3)C2×D3semidirect
126. #3750C2×D3semidirect
148. C22×H(3,𝔽3)#41semidirect
159. C2×(C3⋊D3)⋊C3#41semidirect
234. C4×C3⋊D3#67semidirect
357. C22×C32#235semidirect
358. C22×C32#239semidirect
366. C2×C3⋊D3#235semidirect
412. H(3,𝔽3)#525semidirect
617. C32#5627semidirect
618. C32#5791semidirect
683. C22#88652semidirect

Maximal subgroups

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

subgroupindex
C22×C4×(C3⋊D3)⋊C32
C2×#886522
#117218302
#64133⋊C32
#117213212
#117212932
#117211562
#117211542
#117211062
#117211002
#117210812
#105949223
#105948923