Finite Group Databasebeta

← #13150684

Subgroups — #13150684

Order 1728.

1263 conjugacy classes of subgroups.

The subgroup lattice has 709 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×#88649C211yesmaximal, characteristic, complemented
3C4×#6235C211yesmaximal, characteristic, complemented
4#64133⋊C3C211yesmaximal, characteristic, complemented
5#11721321C212yesmaximal, complemented
6#11721310C212yesmaximal, complemented
7#11721159C211yesmaximal, characteristic, complemented
8#11721136C211yesmaximal, characteristic, complemented
9#11721127C212yesmaximal, complemented
10#11721125C212yesmaximal, complemented
11#11721113C211yesmaximal, characteristic, complemented
12#10595018—31nomaximal
13#10594886—31nomaximal
14C23×(C3⋊D3)⋊C3C2212yes—
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#6235C2211yescharacteristic
17C2×C4×#272C2211yescharacteristic, complemented
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×#634⋊C3C2211yescharacteristic, complemented
23C2×#6200C2212yescomplemented
24C2×#6200C2212yescomplemented
25C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
26C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
27#88649—24no—
28#88552C2211yescharacteristic
29#88542C2211yescharacteristic, complemented
30#88540C2211yescharacteristic, complemented
31C4×#1084C2211yescharacteristic, complemented
32#3757⋊C3C2212yes—
33C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
34#3750⋊C3C2212yescomplemented
35#88450C2212yescomplemented
36#88450C2212yescomplemented
37#88450C2212yescomplemented
38#88450C2212yescomplemented
39C22×C4⋊(C3⋊D3)D311yescharacteristic, complemented
40C22×C3×D12—31no—
41C2×#3799—31no—
42C2×#3795—31no—
43#64133D311yescharacteristic, complemented
44C3×C4×#67—31no—
45C3×C4×#67—31no—
46C3×C4×#67—61no—
47C3×#924—31no—
48#63981—32no—
49#63976—32no—
50#63974—32no—
51D3×#217—32no—
52#63910—32no—
53#63909—31no—
54#63908—31no—
55#63897—32no—
56#63894—31no—
57Dic3×D12—31no—
58#63885—32no—
59#63884—32no—
60#63864—31no—
61#63860—31no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×#272C2311yescharacteristic
64C22×(C3⋊D3)⋊C3—24no—
65C22×(C3⋊D3)⋊C3—24no—
66C22×(C3⋊D3)⋊C3—42no—
67C22×(C3⋊D3)⋊C3C2312yes—
68C22×(C3⋊D3)⋊C3C2312yes—
69C2×C4×H(3,𝔽3)—22no—
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72#6235—22no—
73C2×#1084C2311yescharacteristic
74C2×#1084C2311yescharacteristic
75C2×#1084C2311yescharacteristic
76C4×#272—22no—
77C2×(C3⋊Dic3)⋊C3C2312yes—
78C2×(C3⋊Dic3)⋊C3C2312yes—
79C4⋊((C3⋊D3)⋊C3)—24no—
80C4⋊((C3⋊D3)⋊C3)—22no—
81C4⋊((C3⋊D3)⋊C3)D414yescomplemented
82#634⋊C3—22no—
83#6200—24no—
84#6200—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×C4⋊(C3⋊D3)—24no—
96C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
97C2×C4⋊(C3⋊D3)C2×D312yes—
98C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
99C2×#634C2×D311yescharacteristic, complemented
100C2×C3×#67—31no—
101C2×C3×#67—31no—
102C2×C3×#67—61no—
103C2×C3×D12—31no—
104C2×C3×D12—31no—
105C2×C3×D12—32no—
106C2×C3×D12—64no—
107C2×C3×C4×D3—31no—
108C2×C3×C4×D3—31no—
109C2×C3×C4×D3—61no—
110C2×C3×Dic6—31no—
111C2×#626—32no—
112C2×#626—32no—
113C2×#625—32no—
114C2×#625—32no—
115C2×#624—32no—
116C2×#624—32no—
117C2×D3×Dic3—32no—
118C2×D3×Dic3—32no—
119#3799—64no—
120#3795—64no—
121#3757C2×D312yes—
122C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
123#3750C2×D312yescomplemented
124C3×#217—32no—
125C3×#217—31no—
126C3×#217—31no—
127C3×#217—61no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—61no—
131C3×C4⋊Dic3—31no—
132C3×Dic3⋊C4—32no—
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—61no—
136C3×C4×Dic3—31no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—61no—
139#3722—32no—
140#3722—32no—
141#3722—32no—
142#3722—32no—
143(C2×D3)⋊Dic3—32no—
144(C2×D3)⋊Dic3—32no—
145(C2×D3)⋊Dic3—32no—
146(C2×D3)⋊Dic3—32no—
147C22×H(3,𝔽3)—21no—
148C22×H(3,𝔽3)—21no—
149C22×H(3,𝔽3)#4112yescomplemented
150C22×H(3,𝔽3)C2411yescharacteristic
151C2×#272—21no—
152C2×#272—21no—
153C2×#272—21no—
154C2×(C3⋊D3)⋊C3—22no—
155C2×(C3⋊D3)⋊C3—22no—
156C2×(C3⋊D3)⋊C3—22no—
157C2×(C3⋊D3)⋊C3—22no—
158C2×(C3⋊D3)⋊C3—22no—
159C2×(C3⋊D3)⋊C3—48no—
160C2×(C3⋊D3)⋊C3C2×D414yes—
161C4×H(3,𝔽3)—21no—
162C4×H(3,𝔽3)C2×D412yes—
163#1084—21no—
164#1084—21no—
165#1084—21no—
166(C3⋊Dic3)⋊C3—22no—
167(C3⋊Dic3)⋊C3—22no—
168C22×C3×D4—91no—
169C2×#239—91no—
170C2×#237—91no—
171C2×#235—91no—
172C22×D12—31no—
173C22×D12—91no—
174C3×C22⋊Q8—91no—
175C3×C4×D4—91no—
176#953—92no—
177C2×#217—92no—
178#947—91no—
179#939—92no—
180#938—91no—
181#937—92no—
182#936—91no—
183#935—92no—
184D4×Dic3—91no—
185#930—91no—
186C4×#67—31no—
187C4×#67—31no—
188C4×#67—61no—
189#924—31no—
190#924—91no—
191#895—92no—
192#895—91no—
193#894—92no—
194#894—92no—
195#893—91no—
196#884—92no—
197#882—92no—
198D3×C22⋊C4—92no—
199D3×C22⋊C4—92no—
200#875—91no—
201C4×D12—91no—
202C23×C32—21no—
203C23×C32C22×D311yescharacteristic
204C23×C32C22×D311yescharacteristic
205C22×C3⋊D3—24no—
206C22×C3⋊D3—24no—
207C22×C3⋊D3—42no—
208C22×C3⋊D3C22×D312yes—
209C22×C3⋊D3C22×D312yes—
210C22×C3×D3—32no—
211C22×C3×D3—32no—
212C22×C3×D3—31no—
213C22×C3×D3—31no—
214C22×C3×D3—61no—
215C22×C3×D3—64no—
216C22×C3×D3—64no—
217C22×C3×D3—122no—
218C2×C32×C4—22no—
219C2×C32×C4—22no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—42no—
223C2×C32×C4C22×D311yescharacteristic
224C2×C32×C4C22×D311yescharacteristic
225C2×C32×C4C22×D311yescharacteristic
226C2×C32×C4C22×D311yescharacteristic
227C2×C3⋊Dic3C22×D312yes—
228C2×C3⋊Dic3C22×D312yes—
229C4⋊(C3⋊D3)—24no—
230C4⋊(C3⋊D3)—22no—
231C4⋊(C3⋊D3)#6714yescomplemented
232#634—22no—
233C3×#67—64no—
234C3×#67—62no—
235C3×#67—62no—
236C2×C3×Dic3—32no—
237C2×C3×Dic3—32no—
238C2×C3×Dic3—31no—
239C2×C3×Dic3—31no—
240C2×C3×Dic3—31no—
241C2×C3×Dic3—31no—
242C2×C3×Dic3—31no—
243C2×C3×Dic3—31no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—61no—
246C2×C3×Dic3—61no—
247C3×D12—34no—
248C3×D12—64no—
249C3×D12—62no—
250C3×C4×D3—62no—
251C3×C4×D3—62no—
252C3×C4×D3—122no—
253C3×Dic6—62no—
254#626—64no—
255#626—122no—
256#625—64no—
257#625—122no—
258#624—64no—
259#624—122no—
260D3×Dic3—64no—
261D3×Dic3—122no—
262#546—271noSylow
263C2×H(3,𝔽3)—22no—
264C2×H(3,𝔽3)C22×D411yescharacteristic
265C2×H(3,𝔽3)C2×#4111yescharacteristic
266C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
267#272—41no—
268(C3⋊D3)⋊C3—24no—
269(C3⋊D3)⋊C3—42no—
270C24×C3—92no—
271C23×D3—32no—
272C23×D3—92no—
273C2×C3×Q8—91no—
274C2×C3×D4—91no—
275C2×C3×D4—92no—
276C2×C3×D4—91no—
277C2×C3×D4—91no—
278C2×C3×D4—184no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—61no—
282C22×C3×C4—91no—
283C22×C3×C4D3211yescharacteristic
284C2×#67—31no—
285C2×#67—31no—
286C2×#67—61no—
287C2×#67—92no—
288C2×#67—92no—
289C2×#67—92no—
290C2×#67—92no—
291C22×Dic3—92no—
292C22×Dic3—92no—
293#239—184no—
294#237—184no—
295#235—184no—
296C2×D12—31no—
297C2×D12—31no—
298C2×D12—32no—
299C2×D12—64no—
300C2×D12—91no—
301C2×D12—92no—
302C2×D12—91no—
303C2×D12—92no—
304C2×D12—92no—
305C2×D12—184no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—61no—
309C2×C4×D3—92no—
310C2×C4×D3—92no—
311C2×C4×D3—92no—
312C2×C4×D3—92no—
313C2×Dic6—31no—
314C2×Dic6—91no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4—92no—
317C3×C4⋊C4—91no—
318C3×C22⋊C4—92no—
319C3×C22⋊C4—91no—
320C3×C22⋊C4—91no—
321C3×C42—91no—
322#217—31no—
323#217—31no—
324#217—32no—
325#217—61no—
326#217—92no—
327#217—92no—
328#217—92no—
329#217—92no—
330#217—92no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—92no—
335(C2×D3)⋊C4—92no—
336(C2×D3)⋊C4—92no—
337(C2×D3)⋊C4—92no—
338(C2×D3)⋊C4—92no—
339(C2×D3)⋊C4—92no—
340(C2×D3)⋊C4—92no—
341(C2×D3)⋊C4—92no—
342C4⋊Dic3—31no—
343C4⋊Dic3—91no—
344Dic3⋊C4—31no—
345Dic3⋊C4—31no—
346Dic3⋊C4—32no—
347Dic3⋊C4—61no—
348Dic3⋊C4—92no—
349C4×Dic3—31no—
350C4×Dic3—31no—
351C4×Dic3—61no—
352C22×C32—21no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—22no—
358C22×C32—41no—
359C22×C32—41no—
360C22×C32#23712yescomplemented
361C22×C32#23912yescomplemented
362C22×C32C23×D311yescharacteristic
363C22×C32C23×D311yescharacteristic
364C2×C3⋊D3—22no—
365C2×C3⋊D3—22no—
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—22no—
369C2×C3⋊D3—48no—
370C2×C3⋊D3C2×#6714yes—
371C2×C3×D3—34no—
372C2×C3×D3—62no—
373C2×C3×D3—62no—
374C2×C3×D3—62no—
375C2×C3×D3—62no—
376C2×C3×D3—61no—
377C2×C3×D3—61no—
378C2×C3×D3—61no—
379C2×C3×D3—62no—
380C2×C3×D3—61no—
381C2×C3×D3—62no—
382C2×C3×D3—61no—
383C2×C3×D3—61no—
384C2×C3×D3—121no—
385C2×C3×D3—121no—
386C2×C3×D3—128no—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4—22no—
390C32×C4—41no—
391C32×C4D3×D412yes—
392C32×C4C2×#6712yes—
393C3⋊Dic3—22no—
394C3⋊Dic3—22no—
395C3×Dic3—62no—
396C3×Dic3—61no—
397C3×Dic3—61no—
398C3×Dic3—62no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C3×Dic3—61no—
402C3×Dic3—62no—
403C3×Dic3—61no—
404C3×Dic3—121no—
405C3×Dic3—121no—
406C2×#41—271no—
407C22×D4—91no—
408#124—271no—
409#123—272no—
410C22⋊Q8—91no—
411#121—272no—
412#121—271no—
413#120—272no—
414C4×D4—91no—
415C4×D4—271no—
416C2×C22⋊C4—272no—
417H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
418C23×C3—31no—
419C23×C3—31no—
420C23×C3—61no—
421C23×C3—92no—
422C23×C3—92no—
423C23×C3—91no—
424C23×C3—184no—
425C23×C3—184no—
426C23×C3—362no—
427C23×C3C2×D3211yescharacteristic
428C22×D3—32no—
429C22×D3—31no—
430C22×D3—31no—
431C22×D3—32no—
432C22×D3—61no—
433C22×D3—64no—
434C22×D3—64no—
435C22×D3—92no—
436C22×D3—92no—
437C22×D3—122no—
438C22×D3—184no—
439C22×D3—184no—
440C22×D3—362no—
441C3×Q8—182no—
442C3×D4—94no—
443C3×D4—182no—
444C3×D4—184no—
445C3×D4—182no—
446C2×C3×C4—22no—
447C2×C3×C4—31no—
448C2×C3×C4—31no—
449C2×C3×C4—31no—
450C2×C3×C4—31no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—92no—
456C2×C3×C4—92no—
457C2×C3×C4—91no—
458C2×C3×C4—91no—
459C2×C3×C4—91no—
460C2×C3×C4—122no—
461C2×C3×C4—182no—
462C2×C3×C4C2×D3211yescharacteristic
463C2×C3×C4C2×D3211yescharacteristic
464#67—62no—
465#67—62no—
466#67—64no—
467#67—184no—
468#67—184no—
469#67—362no—
470#67—362no—
471C2×Dic3—31no—
472C2×Dic3—31no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—32no—
478C2×Dic3—32no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—92no—
483C2×Dic3—92no—
484C2×Dic3—184no—
485C2×Dic3—362no—
486D12—34no—
487D12—64no—
488D12—62no—
489D12—94no—
490D12—182no—
491D12—184no—
492D12—184no—
493D12—362no—
494C4×D3—62no—
495C4×D3—62no—
496C4×D3—122no—
497C4×D3—184no—
498C4×D3—184no—
499C4×D3—362no—
500C4×D3—362no—
501Dic6—62no—
502Dic6—182no—
503C2×C32—22no—
504C2×C32—22no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—42no—
509C2×C32C2×D3×D411yescharacteristic
510C2×C32C2×#23711yescharacteristic
511C2×C32#100411yescharacteristic
512C2×C32C2×#23911yescharacteristic
513C2×C32#100911yescharacteristic
514C2×C32C22×#6711yescharacteristic
515C3⋊D3—24no—
516C3⋊D3—42no—
517C3×D3—64no—
518C3×D3—122no—
519C3×D3—121no—
520C3×D3—122no—
521C3×D3—121no—
522C24—92no—
523#41—544no—
524C2×Q8—91no—
525C2×D4—91no—
526C2×D4—91no—
527C2×D4—92no—
528C2×D4—91no—
529C2×D4—184no—
530C2×D4—272no—
531C2×D4—272no—
532C22×C4—91no—
533C22×C4—272no—
534C22×C4—272no—
535C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—92no—
539C22⋊C4—91no—
540C22⋊C4—92no—
541C22⋊C4—91no—
542C22⋊C4—272no—
543C22⋊C4—272no—
544C22⋊C4—272no—
545C22⋊C4—272no—
546C42—91no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—31no—
550C22×C3—31no—
551C22×C3—32no—
552C22×C3—32no—
553C22×C3—61no—
554C22×C3—61no—
555C22×C3—61no—
556C22×C3—61no—
557C22×C3—61no—
558C22×C3—62no—
559C22×C3—94no—
560C22×C3—121no—
561C22×C3—121no—
562C22×C3—182no—
563C22×C3—182no—
564C22×C3—182no—
565C22×C3—182no—
566C22×C3—182no—
567C22×C3—181no—
568C22×C3—181no—
569C22×C3—181no—
570C22×C3—368no—
571C22×C3#379612yes—
572C22×C3C22×D3211yescharacteristic
573C2×D3—34no—
574C2×D3—62no—
575C2×D3—62no—
576C2×D3—61no—
577C2×D3—61no—
578C2×D3—61no—
579C2×D3—61no—
580C2×D3—61no—
581C2×D3—61no—
582C2×D3—62no—
583C2×D3—62no—
584C2×D3—62no—
585C2×D3—62no—
586C2×D3—94no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—128no—
590C2×D3—182no—
591C2×D3—182no—
592C2×D3—182no—
593C2×D3—182no—
594C2×D3—182no—
595C2×D3—368no—
596C3×C4—21no—
597C3×C4—32no—
598C3×C4—32no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—62no—
602C3×C4—121no—
603C3×C4—182no—
604C3×C4—182no—
605C3×C4—181no—
606C3×C4—181no—
607C3×C4—181no—
608C3×C4D3×#6712yes—
609Dic3—61no—
610Dic3—61no—
611Dic3—61no—
612Dic3—61no—
613Dic3—61no—
614Dic3—61no—
615Dic3—62no—
616Dic3—62no—
617Dic3—62no—
618Dic3—121no—
619Dic3—121no—
620Dic3—182no—
621Dic3—182no—
622C32—21no—
623C32#563011yescharacteristic, complemented
624C32#580611yescharacteristic, complemented
625C23—92no—
626C23—91no—
627C23—92no—
628C23—184no—
629C23—184no—
630C23—362no—
631C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
632Q8—182no—
633D4—94no—
634D4—184no—
635D4—182no—
636D4—182no—
637D4—544no—
638D4—1082no—
639C2×C4—22no—
640C2×C4—91no—
641C2×C4—91no—
642C2×C4—92no—
643C2×C4—91no—
644C2×C4—92no—
645C2×C4—182no—
646C2×C4—544no—
647C2×C4—1082no—
648C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
649C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
650C2×C3—22no—
651C2×C3—31no—
652C2×C3—31no—
653C2×C3—31no—
654C2×C3—31no—
655C2×C3—31no—
656C2×C3—31no—
657C2×C3—62no—
658C2×C3—62no—
659C2×C3—61no—
660C2×C3—61no—
661C2×C3—61no—
662C2×C3—122no—
663C2×C3—184no—
664C2×C3—362no—
665C2×C3—361no—
666C2×C3C2×#379611yescharacteristic
667C2×C3#6430711yescharacteristic
668C2×C3C2×D3×#6711yescharacteristic
669D3—64no—
670D3—121no—
671D3—121no—
672D3—122no—
673D3—122no—
674D3—184no—
675D3—362no—
676C22—21no—
677C22—21no—
678C22—94no—
679C22—182no—
680C22—182no—
681C22—181no—
682C22—182no—
683C22—181no—
684C22—182no—
685C22—181no—
686C22—182no—
687C22—368no—
688C22#8864912yescomplemented
689C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
690C4—21no—
691C4—181no—
692C4—182no—
693C4—181no—
694C4—181no—
695C4—182no—
696C4#8867612yes—
697C3—31no—
698C3—31no—
699C3—61no—
700C3#1059488911yescharacteristic
701C2—22no—
702C2—184no—
703C2—362no—
704C2—361no—
705C2C2×#8864911yescharacteristic
706C2#1172249211yescharacteristic
707C2C2×#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×#88649C2semidirect
3. C4×#6235C2semidirect
4. #64133⋊C3C2semidirect
5. #11721321C2semidirect
6. #11721310C2semidirect
7. #11721159C2semidirect
8. #11721136C2semidirect
9. #11721127C2semidirect
10. #11721125C2semidirect
11. #11721113C2semidirect
17. C2×C4×#272C22semidirect
22. C2×#634⋊C3C22semidirect
23. C2×#6200C22semidirect
24. C2×#6200C22semidirect
25. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
26. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
29. #88542C22semidirect
30. #88540C22semidirect
31. C4×#1084C22semidirect
33. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
34. #3750⋊C3C22semidirect
35. #88450C22semidirect
36. #88450C22semidirect
37. #88450C22semidirect
38. #88450C22semidirect
39. C22×C4⋊(C3⋊D3)D3semidirect
43. #64133D3semidirect
81. C4⋊((C3⋊D3)⋊C3)D4semidirect
99. C2×#634C2×D3semidirect
122. C4⋊(C3⋊Dic3)C2×D3semidirect
123. #3750C2×D3semidirect
149. C22×H(3,𝔽3)#41semidirect
231. C4⋊(C3⋊D3)#67semidirect
360. C22×C32#237semidirect
361. C22×C32#239semidirect
417. H(3,𝔽3)#546semidirect
623. C32#5630semidirect
624. C32#5806semidirect
688. C22#88649semidirect

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×#886492
C4×#62352
#64133⋊C32
#117213212
#117213102
#117211592
#117211362
#117211272
#117211252
#117211132
#105950183
#105948863