Finite Group Databasebeta

← #13147907

Subgroups — #13147907

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
1C2×#88655C211yesmaximal, characteristic, complemented
2C2×#88649C211yesmaximal, characteristic, complemented
3C4×C4⋊#272C211yesmaximal, characteristic, complemented
4#64084⋊C3C211yesmaximal, characteristic, complemented
5C4×C4⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
6#11721163C212yesmaximal, complemented
7#11721160C212yesmaximal, complemented
8#11721159C211yesmaximal, characteristic, complemented
9#11721140C212yesmaximal, complemented
10#11721131C212yesmaximal, complemented
11#11721094C211yesmaximal, characteristic, complemented
12#10594007—31nomaximal
13#10594003—31nomaximal
14C22×((C3⋊D3)⋊C3)⋊C2C2212yes—
15C2×C4⋊#272C2211yescharacteristic
16C2×C4×#272C2211yescharacteristic
17C2×C4×#272C2211yescharacteristic, complemented
18C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
19C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3C2212yescomplemented
21C2×#634⋊C3C2211yescharacteristic, complemented
22C2×#6200C2212yescomplemented
23C2×#6200C2212yescomplemented
24C2×#6198C2212yes—
25C2×((C3⋊D3)⋊C3)⋊C4C2212yescomplemented
26#88655—24no—
27#88649—24no—
28C42×H(3,𝔽3)C2211yescharacteristic, complemented
29#88542C2211yescharacteristic
30#88542C2211yescharacteristic, complemented
31C4⋊#1084C2211yescharacteristic, complemented
32#3752⋊C3C2212yescomplemented
33#3752⋊C3C2212yescomplemented
34#3752⋊C3C2212yescomplemented
35C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
36#88451C2212yes—
37#88450C2212yescomplemented
38#88448C2212yescomplemented
39C2×D3×D12—31no—
40C2×D3×D12—31no—
41C2×#3799—31no—
42C2×#3795—31no—
43#64084D311yescharacteristic, complemented
44C4×C4⋊(C3⋊D3)D311yescharacteristic, complemented
45C3×#875—31no—
46C3×C4×D12—31no—
47C3×C4×D12—31no—
48C3×C4×D12—31no—
49C3×C4×D12—61no—
50#63922—32no—
51#63922—32no—
52#63921—32no—
53D3×(C2×D3)⋊C4—32no—
54#63912—32no—
55#63909—31no—
56#63908—31no—
57#63906—32no—
58#63890—32no—
59#63857—31no—
60#63856—31no—
61#63854—32no—
62C22×#272C2311yescharacteristic
63C22×#272C2311yescharacteristic
64C22×(C3⋊D3)⋊C3C2312yes—
65C22×(C3⋊D3)⋊C3C2312yes—
66C2×((C3⋊D3)⋊C3)⋊C2—24no—
67C2×((C3⋊D3)⋊C3)⋊C2—24no—
68C2×((C3⋊D3)⋊C3)⋊C2—42no—
69C2×C4×H(3,𝔽3)C2311yescharacteristic
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×C4×H(3,𝔽3)C2311yescharacteristic
72C2×#1084C2311yescharacteristic
73C2×#1084C2311yescharacteristic
74C4⋊#272—22no—
75C4×#272—22no—
76C4×#272—22no—
77C2×(C3⋊Dic3)⋊C3C2312yes—
78C2×(C3⋊Dic3)⋊C3C2312yes—
79C4⋊((C3⋊D3)⋊C3)—22no—
80C4⋊((C3⋊D3)⋊C3)D414yescomplemented
81C4×(C3⋊D3)⋊C3—42no—
82#634⋊C3—22no—
83#6200—24no—
84#6200—42no—
85#6198—24no—
86((C3⋊D3)⋊C3)⋊C4—24no—
87#5676—91no—
88#5554—91no—
89#5550—91no—
90C22×D32—32no—
91C22×D32—32no—
92C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
93C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
94C2×C4×C3⋊D3C2×D312yescomplemented
95C2×#634C2×D311yescharacteristic, complemented
96C2×C3×D12—31no—
97C2×C3×D12—31no—
98C2×C3×D12—31no—
99C2×C3×D12—31no—
100C2×C3×D12—61no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—31no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—61no—
107C2×C3×C4×D3—61no—
108C2×C3×Dic6—31no—
109C2×#626—32no—
110C2×#626—32no—
111C2×#626—32no—
112C2×#626—32no—
113C2×#625—32no—
114C2×#625—32no—
115C2×#624—32no—
116C2×D3×Dic3—32no—
117D3×D12—64no—
118D3×D12—64no—
119#3799—64no—
120#3795—64no—
121C32×C42—21no—
122C32×C42C2×D311yescharacteristic, complemented
123C32×C42C2×D311yescharacteristic, complemented
124#3752C2×D312yescomplemented
125#3752C2×D312yescomplemented
126#3752C2×D312yescomplemented
127C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
128C3×(C2×D3)⋊C4—32no—
129C3×(C2×D3)⋊C4—32no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—32no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—61no—
136C3×(C2×D3)⋊C4—61no—
137C3×C4⋊Dic3—31no—
138C3×C4⋊Dic3—31no—
139C3×C4⋊Dic3—31no—
140C3×C4⋊Dic3—61no—
141#3724—32no—
142Dic3⋊Dic3—32no—
143#3722—32no—
144(C2×D3)⋊Dic3—32no—
145(C2×D3)⋊Dic3—32no—
146(C2×D3)⋊Dic3—32no—
147C22×H(3,𝔽3)C2411yescharacteristic
148C2×#272—21no—
149C2×#272—21no—
150C2×#272—21no—
151C2×#272—21no—
152C2×#272—21no—
153C2×#272#4112yescomplemented
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)⋊C3C2×D414yes—
160((C3⋊D3)⋊C3)⋊C2—48no—
161C4×H(3,𝔽3)—21no—
162C4×H(3,𝔽3)—21no—
163C4×H(3,𝔽3)C2×D412yes—
164#1084—21no—
165#1084—21no—
166(C3⋊Dic3)⋊C3—22no—
167(C3⋊Dic3)⋊C3—22no—
168C2×#239—91no—
169C2×#237—91no—
170C2×D3×D4—91no—
171C2×D3×D4—91no—
172C2×#235—91no—
173C22×D12—91no—
174C3×#124—91no—
175C3×C4×D4—91no—
176C3×C4×D4—91no—
177#946—91no—
178#938—91no—
179#937—92no—
180#930—91no—
181#930—92no—
182C2×(C2×D3)⋊C4—92no—
183#924—91no—
184#897—91no—
185#895—91no—
186#894—92no—
187#886—92no—
188#884—92no—
189#884—92no—
190#883—92no—
191#882—92no—
192#882—92no—
193D3×C22⋊C4—92no—
194D3×C22⋊C4—92no—
195#875—31no—
196#875—91no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—61no—
201C4×D12—91no—
202C22×C3⋊D3C22×D312yes—
203C22×C3⋊D3C22×D312yes—
204C22×C3×D3—31no—
205C22×C3×D3—31no—
206C22×C3×D3—32no—
207C22×C3×D3—32no—
208C22×C3×D3—31no—
209C22×C3×D3—31no—
210C22×C3×D3—61no—
211C22×C3×D3—61no—
212C2×D32—64no—
213C2×D32—64no—
214C2×D32—64no—
215C2×D32—64no—
216C2×D32—122no—
217C2×D32—122no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C22×D311yescharacteristic
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)—22no—
230C4⋊(C3⋊D3)D1214yescomplemented
231C4×C3⋊D3—42no—
232#634—22no—
233C2×C3×Dic3—32no—
234C2×C3×Dic3—32no—
235C2×C3×Dic3—31no—
236C2×C3×Dic3—31no—
237C2×C3×Dic3—31no—
238C2×C3×Dic3—31no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C3×D12—34no—
242C3×D12—62no—
243C3×D12—62no—
244C3×D12—64no—
245C3×D12—62no—
246C3×C4×D3—62no—
247C3×C4×D3—62no—
248C3×C4×D3—62no—
249C3×C4×D3—62no—
250C3×C4×D3—122no—
251C3×C4×D3—122no—
252C3×C4×D3—122no—
253C3×Dic6—62no—
254#626—64no—
255#626—64no—
256#626—64no—
257#626—122no—
258#625—64no—
259#625—122no—
260#624—64no—
261D3×Dic3—64no—
262#546—271noSylow
263C2×H(3,𝔽3)C22×D411yescharacteristic
264C2×H(3,𝔽3)C2×#4111yescharacteristic
265C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
266#272—22no—
267#272—41no—
268(C3⋊D3)⋊C3—24no—
269(C3⋊D3)⋊C3—42no—
270C23×D3—92no—
271C23×D3—92no—
272C23×D3—92no—
273C2×C3×Q8—91no—
274C2×C3×D4—91no—
275C2×C3×D4—91no—
276C2×C3×D4—91no—
277C22×C3×C4—92no—
278C22×C3×C4—91no—
279C22×C3×C4—91no—
280C2×#67—92no—
281C2×#67—92no—
282C2×#67—92no—
283C2×#67—92no—
284C2×#67—92no—
285C2×#67—92no—
286C22×Dic3—92no—
287#239—184no—
288#237—184no—
289D3×D4—184no—
290D3×D4—184no—
291#235—184no—
292C2×D12—31no—
293C2×D12—31no—
294C2×D12—31no—
295C2×D12—31no—
296C2×D12—61no—
297C2×D12—91no—
298C2×D12—91no—
299C2×D12—92no—
300C2×D12—92no—
301C2×D12—92no—
302C2×D12—184no—
303C2×C4×D3—31no—
304C2×C4×D3—31no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—32no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
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—91no—
317C3×C22⋊C4—92no—
318C3×C22⋊C4—92no—
319C3×C22⋊C4—92no—
320C3×C22⋊C4—91no—
321C3×C22⋊C4—91no—
322C3×C42—31no—
323C3×C42—31no—
324C3×C42—61no—
325C3×C42D3211yescharacteristic
326#217—92no—
327#217—92no—
328(C2×D3)⋊C4—31no—
329(C2×D3)⋊C4—31no—
330(C2×D3)⋊C4—31no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—32no—
333(C2×D3)⋊C4—32no—
334(C2×D3)⋊C4—32no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
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—
342(C2×D3)⋊C4—92no—
343(C2×D3)⋊C4—92no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—61no—
348C4⋊Dic3—91no—
349C4⋊Dic3—92no—
350Dic3⋊C4—92no—
351Dic3⋊C4—92no—
352C22×C32—21no—
353C22×C32C23×D311yescharacteristic
354C22×C32C23×D311yescharacteristic
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3C2×D1214yes—
361C2×C3×D3—34no—
362C2×C3×D3—32no—
363C2×C3×D3—32no—
364C2×C3×D3—62no—
365C2×C3×D3—61no—
366C2×C3×D3—61no—
367C2×C3×D3—61no—
368C2×C3×D3—62no—
369C2×C3×D3—62no—
370C2×C3×D3—61no—
371C2×C3×D3—62no—
372C2×C3×D3—62no—
373C2×C3×D3—61no—
374C2×C3×D3—61no—
375C2×C3×D3—62no—
376C2×C3×D3—61no—
377C2×C3×D3—62no—
378C2×C3×D3—61no—
379C2×C3×D3—61no—
380C2×C3×D3—61no—
381C2×C3×D3—121no—
382C2×C3×D3—121no—
383C2×C3×D3—121no—
384C2×C3×D3—121no—
385D32—128no—
386D32—128no—
387C32×C4—22no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—22no—
393C32×C4—41no—
394C32×C4C2×D1212yes—
395C32×C4D3×D412yes—
396C3⋊Dic3—22no—
397C3⋊Dic3—22no—
398C3×Dic3—62no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C3×Dic3—61no—
402C3×Dic3—61no—
403C3×Dic3—62no—
404C3×Dic3—121no—
405C3×Dic3—121no—
406C2×#41—271no—
407C22×D4—271no—
408#124—91no—
409#123—272no—
410C22⋊Q8—271no—
411#121—272no—
412#121—271no—
413#120—272no—
414C4×D4—91no—
415C4×D4—91no—
416C2×C22⋊C4—272no—
417H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
418C23×C3—92no—
419C23×C3—92no—
420C23×C3—91no—
421C23×C3—91no—
422C22×D3—31no—
423C22×D3—31no—
424C22×D3—32no—
425C22×D3—31no—
426C22×D3—31no—
427C22×D3—32no—
428C22×D3—61no—
429C22×D3—61no—
430C22×D3—92no—
431C22×D3—92no—
432C22×D3—184no—
433C22×D3—184no—
434C22×D3—184no—
435C22×D3—184no—
436C22×D3—184no—
437C22×D3—184no—
438C22×D3—362no—
439C22×D3—362no—
440C22×D3—362no—
441C3×Q8—182no—
442C3×D4—94no—
443C3×D4—182no—
444C3×D4—182no—
445C2×C3×C4—31no—
446C2×C3×C4—31no—
447C2×C3×C4—31no—
448C2×C3×C4—31no—
449C2×C3×C4—31no—
450C2×C3×C4—31no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—92no—
455C2×C3×C4—92no—
456C2×C3×C4—91no—
457C2×C3×C4—91no—
458C2×C3×C4—182no—
459C2×C3×C4—182no—
460C2×C3×C4—362no—
461C2×C3×C4C2×D3211yescharacteristic
462C2×C3×C4C2×D3211yescharacteristic
463C2×C3×C4C2×D3211yescharacteristic
464#67—184no—
465#67—184no—
466#67—184no—
467#67—184no—
468#67—362no—
469#67—362no—
470C2×Dic3—31no—
471C2×Dic3—31no—
472C2×Dic3—31no—
473C2×Dic3—31no—
474C2×Dic3—32no—
475C2×Dic3—32no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—92no—
479C2×Dic3—92no—
480C2×Dic3—184no—
481D12—34no—
482D12—62no—
483D12—62no—
484D12—64no—
485D12—62no—
486D12—94no—
487D12—182no—
488D12—184no—
489D12—184no—
490D12—362no—
491C4×D3—62no—
492C4×D3—62no—
493C4×D3—62no—
494C4×D3—62no—
495C4×D3—122no—
496C4×D3—122no—
497C4×D3—122no—
498C4×D3—184no—
499C4×D3—184no—
500C4×D3—362no—
501Dic6—62no—
502Dic6—182no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32C22×D1211yescharacteristic
507C2×C32C2×D3×D411yescharacteristic
508C2×C32#100411yescharacteristic
509C2×C32D3×#4111yescharacteristic
510C2×C32D3×#4111yescharacteristic
511C2×C32#100911yescharacteristic
512C3⋊D3—24no—
513C3⋊D3—42no—
514C3×D3—64no—
515C3×D3—62no—
516C3×D3—62no—
517C3×D3—122no—
518C3×D3—122no—
519C3×D3—121no—
520C3×D3—122no—
521C3×D3—121no—
522C24—272no—
523#41—544no—
524C2×Q8—91no—
525C2×D4—91no—
526C2×D4—91no—
527C2×D4—91no—
528C2×D4—272no—
529C2×D4—272no—
530C2×D4—272no—
531C2×D4—544no—
532C22×C4—91no—
533C22×C4—91no—
534C22×C4—92no—
535C22×C4—272no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—272no—
539C22⋊C4—91no—
540C22⋊C4—92no—
541C22⋊C4—92no—
542C22⋊C4—91no—
543C22⋊C4—92no—
544C22⋊C4—272no—
545C22⋊C4—272no—
546C42((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
547C22×C3—31no—
548C22×C3—31no—
549C22×C3—61no—
550C22×C3—94no—
551C22×C3—92no—
552C22×C3—182no—
553C22×C3—182no—
554C22×C3—182no—
555C22×C3—182no—
556C22×C3—182no—
557C22×C3—181no—
558C22×C3—181no—
559C22×C3—181no—
560C22×C3—181no—
561C22×C3—181no—
562C22×C3C22×D3211yescharacteristic
563C2×D3—32no—
564C2×D3—32no—
565C2×D3—34no—
566C2×D3—62no—
567C2×D3—61no—
568C2×D3—61no—
569C2×D3—61no—
570C2×D3—61no—
571C2×D3—62no—
572C2×D3—62no—
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—61no—
576C2×D3—61no—
577C2×D3—61no—
578C2×D3—61no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—94no—
584C2×D3—121no—
585C2×D3—121no—
586C2×D3—121no—
587C2×D3—121no—
588C2×D3—182no—
589C2×D3—182no—
590C2×D3—182no—
591C2×D3—182no—
592C2×D3—182no—
593C2×D3—368no—
594C2×D3—368no—
595C2×D3—368no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—32no—
599C3×C4—32no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—62no—
605C3×C4—62no—
606C3×C4—121no—
607C3×C4—182no—
608C3×C4—182no—
609C3×C4—181no—
610C3×C4—181no—
611C3×C4D3×D1212yes—
612Dic3—61no—
613Dic3—61no—
614Dic3—61no—
615Dic3—61no—
616Dic3—62no—
617Dic3—62no—
618Dic3—121no—
619Dic3—121no—
620Dic3—182no—
621Dic3—182no—
622C32—21no—
623C32#555411yescharacteristic, complemented
624C32#567611yescharacteristic, complemented
625C23—91no—
626C23—92no—
627C23—92no—
628C23—91no—
629C23—544no—
630C23—544no—
631C23—1082no—
632Q8—182no—
633D4—94no—
634D4—182no—
635D4—182no—
636D4—544no—
637D4—544no—
638D4—1082no—
639C2×C4—92no—
640C2×C4—92no—
641C2×C4—91no—
642C2×C4—91no—
643C2×C4—182no—
644C2×C4—182no—
645C2×C4—362no—
646C2×C4—544no—
647C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
648C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
649C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
650C2×C3—31no—
651C2×C3—31no—
652C2×C3—31no—
653C2×C3—31no—
654C2×C3—31no—
655C2×C3—31no—
656C2×C3—61no—
657C2×C3—61no—
658C2×C3—61no—
659C2×C3—184no—
660C2×C3—182no—
661C2×C3—362no—
662C2×C3—361no—
663C2×C3C2×D3×D1211yescharacteristic
664C2×C3#6430611yescharacteristic
665C2×C3#6430711yescharacteristic
666D3—62no—
667D3—62no—
668D3—64no—
669D3—122no—
670D3—121no—
671D3—121no—
672D3—122no—
673D3—122no—
674D3—184no—
675D3—362no—
676C22—94no—
677C22—92no—
678C22—181no—
679C22—182no—
680C22—182no—
681C22—181no—
682C22—181no—
683C22—182no—
684C22—181no—
685C22—182no—
686C22—181no—
687C22—182no—
688C22—1088no—
689C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
690C4—21no—
691C4—21no—
692C4—181no—
693C4—181no—
694C4—182no—
695C4—182no—
696C4#8865412yes—
697C3—31no—
698C3—31no—
699C3—61no—
700C3#1059400511yescharacteristic
701C2—182no—
702C2—184no—
703C2—362no—
704C2—361no—
705C2C2×#8865411yescharacteristic
706C2#1172249111yescharacteristic
707C2#1172249211yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC42×H(3,𝔽3)C22
hypercenterC42((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#546
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×#88655C2semidirect
2. C2×#88649C2semidirect
3. C4×C4⋊#272C2semidirect
4. #64084⋊C3C2semidirect
5. C4×C4⋊((C3⋊D3)⋊C3)C2semidirect
6. #11721163C2semidirect
7. #11721160C2semidirect
8. #11721159C2semidirect
9. #11721140C2semidirect
10. #11721131C2semidirect
11. #11721094C2semidirect
17. C2×C4×#272C22semidirect
20. C2×C4×(C3⋊D3)⋊C3C22semidirect
21. C2×#634⋊C3C22semidirect
22. C2×#6200C22semidirect
23. C2×#6200C22semidirect
25. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
28. C42×H(3,𝔽3)C22semidirect
30. #88542C22semidirect
31. C4⋊#1084C22semidirect
32. #3752⋊C3C22semidirect
33. #3752⋊C3C22semidirect
34. #3752⋊C3C22semidirect
35. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
37. #88450C22semidirect
38. #88448C22semidirect
43. #64084D3semidirect
44. C4×C4⋊(C3⋊D3)D3semidirect
80. C4⋊((C3⋊D3)⋊C3)D4semidirect
94. C2×C4×C3⋊D3C2×D3semidirect
95. C2×#634C2×D3semidirect
122. C32×C42C2×D3semidirect
123. C32×C42C2×D3semidirect
124. #3752C2×D3semidirect
125. #3752C2×D3semidirect
126. #3752C2×D3semidirect
127. C4⋊(C3⋊Dic3)C2×D3semidirect
153. C2×#272#41semidirect
230. C4⋊(C3⋊D3)D12semidirect
417. H(3,𝔽3)#546semidirect
546. C42((C3⋊D3)⋊C3)⋊C2semidirect
623. C32#5554semidirect
624. C32#5676semidirect

Maximal subgroups

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

subgroupindex
C2×#886552
C2×#886492
C4×C4⋊#2722
#64084⋊C32
C4×C4⋊((C3⋊D3)⋊C3)2
#117211632
#117211602
#117211592
#117211402
#117211312
#117210942
#105940073
#105940033