Finite Group Databasebeta

← #10596249⋊C3 #13153517

Subgroups — #10596249⋊C3 #13153517

Order 1728.

963 conjugacy classes of subgroups.

The subgroup lattice has 687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11722638C211yesmaximal, characteristic, complemented
2#11722627C211yesmaximal, characteristic, complemented
3H(3,𝔽3)×#137C211yesmaximal, characteristic, complemented
4#64159⋊C3C211yesmaximal, characteristic, complemented
5C2×#3755⋊C3C211yesmaximal, characteristic, complemented
6#64128⋊C3C212yesmaximal, complemented
7#64127⋊C3C212yesmaximal, complemented
8#64123⋊C3C212yesmaximal, complemented
9SD16×(C3⋊D3)⋊C3C212yesmaximal, complemented
10#64117⋊C3C211yesmaximal, characteristic, complemented
11#64116⋊C3C211yesmaximal, characteristic, complemented
12#10596249C311yesmaximal, characteristic, complemented
13C3×#5778—31nomaximal
14#41×H(3,𝔽3)C2211yescharacteristic
15C2×Q8×H(3,𝔽3)C2211yescharacteristic, complemented
16#88722—21no—
17#88722C2212yes—
18#88722C2212yescomplemented
19Q8×(C3⋊D3)⋊C3—21no—
20Q8×(C3⋊D3)⋊C3C2212yescomplemented
21D4×(C3⋊D3)⋊C3—22no—
22D4×(C3⋊D3)⋊C3C2212yes—
23#3828⋊C3—22no—
24#3828⋊C3—21no—
25#3828⋊C3C2211yescharacteristic
26#3828⋊C3C2211yescharacteristic, complemented
27C2×C4⋊((C3⋊D3)⋊C3)—21no—
28C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
29Q16×H(3,𝔽3)C2212yescomplemented
30SD16×H(3,𝔽3)C2212yescomplemented
31M16×H(3,𝔽3)C2211yescharacteristic, complemented
32#3755⋊C3C2212yescomplemented
33#3755⋊C3C2212yescomplemented
34#3755⋊C3C2211yescharacteristic, complemented
35#3756⋊C3C2211yescharacteristic, complemented
36#3753⋊C3C2211yescharacteristic, complemented
37#3754⋊C3C2211yescharacteristic, complemented
38C2×(C3⋊(C3⋊C8))⋊C3C2211yescharacteristic, complemented
39#3745⋊C3C2212yescomplemented
40#3744⋊C3C2212yescomplemented
41#3743⋊C3C2212yescomplemented
42C8×(C3⋊D3)⋊C3C2212yescomplemented
43#64366C2×C311yescharacteristic, complemented
44#64364C2×C311yescharacteristic, complemented
45C3×#1009—31no—
46C3×#1007—31no—
47C32×#137—21no—
48C32×#137D311yescharacteristic, complemented
49C32×#137C2×C311yescharacteristic, complemented
50#64159C2×C311yescharacteristic, complemented
51C2×#3755C2×C311yescharacteristic, complemented
52#64128C2×C312yescomplemented
53#64127C2×C312yescomplemented
54#64123C2×C312yescomplemented
55SD16×C3⋊D3C2×C312yescomplemented
56#64117C2×C311yescharacteristic, complemented
57#64116C2×C311yescharacteristic, complemented
58C3×#950—31no—
59C2×C3×#215—31no—
60C3×#919—32no—
61C3×#918—32no—
62C3×#914—32no—
63C3×D3×SD16—32no—
64C3×#908—31no—
65C3×#907—31no—
66C22×(C3⋊D3)⋊C3—21no—
67C22×(C3⋊D3)⋊C3—22no—
68Q8×H(3,𝔽3)—21no—
69Q8×H(3,𝔽3)C2312yes—
70Q8×H(3,𝔽3)C2311yescharacteristic
71D4×H(3,𝔽3)—21no—
72D4×H(3,𝔽3)C2311yescharacteristic
73C2×C4×H(3,𝔽3)—21no—
74C2×C4×H(3,𝔽3)—21no—
75C2×C4×H(3,𝔽3)C2311yescharacteristic
76#638⋊C3—21no—
77#638⋊C3—22no—
78#638⋊C3D412yes—
79C4⋊((C3⋊D3)⋊C3)—22no—
80C4⋊((C3⋊D3)⋊C3)—22no—
81C4⋊((C3⋊D3)⋊C3)—21no—
82C4⋊((C3⋊D3)⋊C3)D411yescharacteristic
83C4⋊((C3⋊D3)⋊C3)C2312yes—
84C4⋊((C3⋊D3)⋊C3)C2311yescharacteristic
85C4×(C3⋊D3)⋊C3—22no—
86C4×(C3⋊D3)⋊C3—21no—
87C4×(C3⋊D3)⋊C3—22no—
88C4×(C3⋊D3)⋊C3—22no—
89C4×(C3⋊D3)⋊C3C2312yes—
90#634⋊C3—22no—
91#634⋊C3D411yescharacteristic
92#634⋊C3C2311yescharacteristic
93C8×H(3,𝔽3)C2312yes—
94(C3⋊(C3⋊C8))⋊C3C2311yescharacteristic
95(C3⋊(C3⋊C8))⋊C3C2311yescharacteristic
96C3×#577—91no—
97#5778—31no—
98#5778—91no—
99C32×#41—21no—
100C32×#41C2×D311yescharacteristic
101C32×#41C22×C311yescharacteristic
102C2×C32×Q8—21no—
103C2×C32×Q8C2×D311yescharacteristic, complemented
104C2×C32×Q8C22×C311yescharacteristic, complemented
105#3832—21no—
106#3832C22×C312yes—
107#3832C22×C312yescomplemented
108Q8×C3⋊D3—21no—
109Q8×C3⋊D3C22×C312yescomplemented
110D4×C3⋊D3—22no—
111D4×C3⋊D3C22×C312yes—
112#3828—22no—
113#3828—21no—
114#3828C22×C311yescharacteristic
115#3828C22×C311yescharacteristic, complemented
116C2×C4⋊(C3⋊D3)—21no—
117C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
118C3×#239—32no—
119C3×#239—32no—
120C3×#239—61no—
121C3×D3×Q8—32no—
122C3×D3×Q8—61no—
123C3×D3×D4—32no—
124C3×D3×D4—62no—
125C3×#235—31no—
126C3×#235—31no—
127C3×#235—61no—
128C3×#235—62no—
129C2×C3×D12—31no—
130C2×C3×D12—61no—
131C32×Q16—22no—
132C32×Q16C2×D312yescomplemented
133C32×Q16C22×C312yescomplemented
134C32×SD16—22no—
135C32×SD16C2×D312yescomplemented
136C32×SD16C22×C312yescomplemented
137C32×M16—21no—
138C32×M16C2×D311yescharacteristic, complemented
139C32×M16C22×C311yescharacteristic, complemented
140#3756C22×C311yescharacteristic, complemented
141#3755C22×C312yescomplemented
142#3755C22×C312yescomplemented
143#3755C22×C311yescharacteristic, complemented
144#3754C22×C311yescharacteristic, complemented
145#3753C22×C311yescharacteristic, complemented
146C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
147#3745C22×C312yescomplemented
148#3744C22×C312yescomplemented
149#3743C22×C312yescomplemented
150C8×C3⋊D3C22×C312yescomplemented
151C3×#216—31no—
152C3×#215—32no—
153C3×#215—32no—
154C3×#215—31no—
155C3×#214—31no—
156C3×#213—31no—
157C2×C3×C3⋊C8—31no—
158C3×D24—32no—
159C3×#204—32no—
160C3×ΓL(1,𝔽25)—32no—
161C3×D3×C8—32no—
162C22×H(3,𝔽3)—21no—
163C22×H(3,𝔽3)C2×D411yescharacteristic
164C2×(C3⋊D3)⋊C3—21no—
165C2×(C3⋊D3)⋊C3—22no—
166C2×(C3⋊D3)⋊C3—82no—
167C2×(C3⋊D3)⋊C3—81no—
168C2×(C3⋊D3)⋊C3C2×D412yes—
169C4×H(3,𝔽3)—22no—
170C4×H(3,𝔽3)—21no—
171C4×H(3,𝔽3)C2×D411yescharacteristic
172C4×H(3,𝔽3)C2411yescharacteristic
173(C3⋊Dic3)⋊C3—21no—
174(C3⋊Dic3)⋊C3C2×D412yes—
175C3×2−1+4—91no—
176C3×H(5,𝔽2)—91no—
177#1009—31no—
178#1009—91no—
179#1007—31no—
180#1007—91no—
181C3×#137—31no—
182C3×#137—31no—
183C3×#137—61no—
184C3×#137—92no—
185C3×#137C3×D311yescharacteristic
186C3×AGL(1,ℤ/8)—91no—
187C3×AGL(1,ℤ/8)—92no—
188C3×#135—92no—
189C3×#135—91no—
190C2×C3×SD16—92no—
191C2×C3×SD16—91no—
192C3×#131—91no—
193#950—31no—
194#950—91no—
195C2×#215—31no—
196C2×#215—91no—
197#919—32no—
198#919—92no—
199#918—32no—
200#918—92no—
201#914—32no—
202#914—92no—
203D3×SD16—32no—
204D3×SD16—92no—
205#908—31no—
206#908—91no—
207#907—31no—
208#907—91no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—22no—
211C22×C3×D3—62no—
212C22×C3×D3—61no—
213C32×Q8—21no—
214C32×Q8—21no—
215C32×Q8—22no—
216C32×Q8—21no—
217C32×Q8—41no—
218C32×Q8C22×D312yes—
219C32×Q8C22×D311yescharacteristic
220C32×Q8C23×C312yes—
221C32×Q8C23×C311yescharacteristic
222C32×D4—21no—
223C32×D4—21no—
224C32×D4—21no—
225C32×D4—41no—
226C32×D4C22×D311yescharacteristic
227C32×D4C23×C311yescharacteristic
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—41no—
234C2×C32×C4—41no—
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C23×C311yescharacteristic
237#638—21no—
238#638—22no—
239#638C3×D412yes—
240C4⋊(C3⋊D3)—22no—
241C4⋊(C3⋊D3)—22no—
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)C3×D411yescharacteristic
244C4⋊(C3⋊D3)C23×C312yes—
245C4⋊(C3⋊D3)C23×C311yescharacteristic
246C4×C3⋊D3—22no—
247C4×C3⋊D3—21no—
248C4×C3⋊D3—22no—
249C4×C3⋊D3—22no—
250C4×C3⋊D3C23×C312yes—
251#634—22no—
252#634C3×D411yescharacteristic
253#634C23×C311yescharacteristic
254C3×#67—32no—
255C3×#67—62no—
256C3×#67—61no—
257C3×D12—31no—
258C3×D12—32no—
259C3×D12—31no—
260C3×D12—62no—
261C3×D12—62no—
262C3×D12—61no—
263C3×C4×D3—32no—
264C3×C4×D3—62no—
265C3×C4×D3—62no—
266C3×C4×D3—62no—
267C3×C4×D3—61no—
268C3×Dic6—31no—
269C3×Dic6—31no—
270C3×Dic6—62no—
271C32×C8—22no—
272C32×C8C22×D312yes—
273C32×C8C23×C312yes—
274C3⋊(C3⋊C8)C23×C311yescharacteristic
275C3⋊(C3⋊C8)C23×C311yescharacteristic
276C3×C3⋊C8—31no—
277C3×C3⋊C8—31no—
278#577—91noSylow
279C2×H(3,𝔽3)—21no—
280C2×H(3,𝔽3)—41no—
281C2×H(3,𝔽3)C22×D411yescharacteristic
282(C3⋊D3)⋊C3—22no—
283(C3⋊D3)⋊C3—41no—
284(C3⋊D3)⋊C3—42no—
285C3×#41—31no—
286C3×#41—31no—
287C3×#41—61no—
288C3×#41—91no—
289C3×#41—91no—
290C3×#41—92no—
291C3×#41—92no—
292C3×#41—182no—
293C3×#41—181no—
294C3×#41—181no—
295C3×#41C2×C3×D311yescharacteristic
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8—92no—
300C2×C3×Q8—181no—
301C2×C3×Q8C2×C3×D311yescharacteristic
302C2×C3×D4—91no—
303C2×C3×D4—92no—
304C2×C3×D4—181no—
305C2×C3×D4—182no—
306#239—32no—
307#239—32no—
308#239—61no—
309#239—92no—
310#239—92no—
311#239—181no—
312D3×Q8—32no—
313D3×Q8—61no—
314D3×Q8—92no—
315D3×Q8—181no—
316D3×D4—32no—
317D3×D4—62no—
318D3×D4—92no—
319D3×D4—182no—
320#235—31no—
321#235—31no—
322#235—61no—
323#235—62no—
324#235—91no—
325#235—91no—
326#235—181no—
327#235—182no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—91no—
331C2×D12—181no—
332C3×Q16—32no—
333C3×Q16—32no—
334C3×Q16—62no—
335C3×Q16—91no—
336C3×Q16C2×C3×D312yes—
337C3×SD16—32no—
338C3×SD16—32no—
339C3×SD16—62no—
340C3×SD16—92no—
341C3×SD16—91no—
342C3×SD16—92no—
343C3×SD16—92no—
344C3×SD16—91no—
345C3×SD16C2×C3×D312yes—
346C3×D8—92no—
347C3×D8—91no—
348C3×M16—31no—
349C3×M16—31no—
350C3×M16—61no—
351C3×M16—92no—
352C3×M16C2×C3×D311yescharacteristic
353C2×C3×C8—92no—
354C2×C3×C8—91no—
355#216—31no—
356#216—91no—
357#215—32no—
358#215—32no—
359#215—31no—
360#215—92no—
361#215—92no—
362#215—91no—
363#214—31no—
364#214—91no—
365#213—31no—
366#213—91no—
367C2×C3⋊C8—31no—
368C2×C3⋊C8—91no—
369D24—32no—
370D24—92no—
371#204—32no—
372#204—92no—
373ΓL(1,𝔽25)—32no—
374ΓL(1,𝔽25)—92no—
375D3×C8—32no—
376D3×C8—92no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—41no—
381C22×C32D3×D411yescharacteristic
382C22×C32C2×C3×D411yescharacteristic
383C2×C3⋊D3—21no—
384C2×C3⋊D3—22no—
385C2×C3⋊D3—82no—
386C2×C3⋊D3—81no—
387C2×C3⋊D3C2×C3×D412yes—
388C2×C3×D3—32no—
389C2×C3×D3—61no—
390C2×C3×D3—62no—
391C2×C3×D3—242no—
392C2×C3×D3—241no—
393C32×C4—22no—
394C32×C4—21no—
395C32×C4—22no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—42no—
401C32×C4D3×D411yescharacteristic
402C32×C4C2×C3×D411yescharacteristic
403C32×C4C23×D311yescharacteristic
404C32×C4C24×C311yescharacteristic
405C3⋊Dic3—21no—
406C3⋊Dic3C2×C3×D412yes—
407C3×Dic3—32no—
408C3×Dic3—61no—
4092−1+4—91no—
410H(5,𝔽2)—91no—
411#137—92no—
412#137(C3⋊D3)⋊C311yescharacteristic, complemented
413AGL(1,ℤ/8)—92no—
414AGL(1,ℤ/8)—91no—
415#135—91no—
416#135—92no—
417C2×SD16—91no—
418C2×SD16—92no—
419#131—91no—
420H(3,𝔽3)#57711yescharacteristic, complemented, Sylow
421C23×C3—181no—
422C23×C3—182no—
423C22×D3—62no—
424C22×D3—61no—
425C22×D3—182no—
426C22×D3—181no—
427C3×Q8—21no—
428C3×Q8—32no—
429C3×Q8—31no—
430C3×Q8—32no—
431C3×Q8—31no—
432C3×Q8—61no—
433C3×Q8—61no—
434C3×Q8—62no—
435C3×Q8—61no—
436C3×Q8—91no—
437C3×Q8—91no—
438C3×Q8—121no—
439C3×Q8—182no—
440C3×Q8C22×C3×D312yes—
441C3×Q8C22×C3×D311yescharacteristic
442C3×D4—21no—
443C3×D4—31no—
444C3×D4—31no—
445C3×D4—61no—
446C3×D4—61no—
447C3×D4—61no—
448C3×D4—91no—
449C3×D4—91no—
450C3×D4—92no—
451C3×D4—92no—
452C3×D4—121no—
453C3×D4—181no—
454C3×D4—182no—
455C3×D4—182no—
456C3×D4—182no—
457C3×D4—181no—
458C3×D4C22×C3×D311yescharacteristic
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—92no—
469C2×C3×C4—121no—
470C2×C3×C4—121no—
471C2×C3×C4—181no—
472C2×C3×C4—182no—
473C2×C3×C4—182no—
474C2×C3×C4—182no—
475C2×C3×C4C22×C3×D311yescharacteristic
476#67—32no—
477#67—62no—
478#67—61no—
479#67—92no—
480#67—182no—
481#67—181no—
482D12—32no—
483D12—31no—
484D12—31no—
485D12—62no—
486D12—62no—
487D12—61no—
488D12—91no—
489D12—92no—
490D12—91no—
491D12—181no—
492D12—182no—
493D12—182no—
494C4×D3—32no—
495C4×D3—62no—
496C4×D3—62no—
497C4×D3—62no—
498C4×D3—61no—
499C4×D3—92no—
500C4×D3—182no—
501C4×D3—182no—
502C4×D3—181no—
503C4×D3—182no—
504Dic6—31no—
505Dic6—31no—
506Dic6—62no—
507Dic6—91no—
508Dic6—91no—
509Dic6—182no—
510C3×C8—32no—
511C3×C8—32no—
512C3×C8—62no—
513C3×C8—91no—
514C3×C8—91no—
515C3×C8C22×C3×D312yes—
516C3⋊C8—31no—
517C3⋊C8—31no—
518C3⋊C8—91no—
519C3⋊C8—91no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—41no—
524C2×C32—41no—
525C2×C32—41no—
526C2×C32—81no—
527C2×C32C2×D3×D411yescharacteristic
528C2×C32C22×C3×D411yescharacteristic
529C3⋊D3—22no—
530C3⋊D3—41no—
531C3⋊D3—42no—
532C3×D3—62no—
533C3×D3—121no—
534C3×D3—122no—
535#41—91no—
536#41—92no—
537#41—92no—
538#41—91no—
539#41—182no—
540#41—181no—
541#41—181no—
542#41C2×(C3⋊D3)⋊C311yescharacteristic
543C2×Q8—92no—
544C2×Q8—181no—
545C2×Q8C2×(C3⋊D3)⋊C311yescharacteristic, complemented
546C2×D4—92no—
547C2×D4—91no—
548C2×D4—181no—
549C2×D4—182no—
550Q16—91no—
551Q16C2×(C3⋊D3)⋊C312yescomplemented
552SD16—92no—
553SD16—92no—
554SD16—91no—
555SD16—91no—
556SD16—92no—
557SD16C2×(C3⋊D3)⋊C312yescomplemented
558D8—91no—
559D8—92no—
560M16—92no—
561M16C2×(C3⋊D3)⋊C311yescharacteristic, complemented
562C2×C8—91no—
563C2×C8—92no—
564C22×C3—21no—
565C22×C3—31no—
566C22×C3—31no—
567C22×C3—61no—
568C22×C3—61no—
569C22×C3—61no—
570C22×C3—92no—
571C22×C3—121no—
572C22×C3—181no—
573C22×C3—182no—
574C22×C3—721no—
575C22×C3—722no—
576C22×C3C3×D3×D411yescharacteristic
577C2×D3—32no—
578C2×D3—61no—
579C2×D3—62no—
580C2×D3—92no—
581C2×D3—181no—
582C2×D3—182no—
583C2×D3—242no—
584C2×D3—241no—
585C2×D3—722no—
586C2×D3—721no—
587C3×C4—22no—
588C3×C4—21no—
589C3×C4—31no—
590C3×C4—31no—
591C3×C4—31no—
592C3×C4—31no—
593C3×C4—62no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—62no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4—92no—
600C3×C4—121no—
601C3×C4—122no—
602C3×C4—181no—
603C3×C4C3×D3×D411yescharacteristic
604C3×C4C23×C3×D311yescharacteristic
605Dic3—32no—
606Dic3—61no—
607Dic3—92no—
608Dic3—181no—
609C32—21no—
610C32#577811yescharacteristic, complemented
611C32C3×#57711yescharacteristic, complemented
612C23—182no—
613C23—181no—
614Q8—21no—
615Q8—91no—
616Q8—91no—
617Q8—182no—
618Q8C22×(C3⋊D3)⋊C312yes—
619Q8C22×(C3⋊D3)⋊C311yescharacteristic
620D4—21no—
621D4—92no—
622D4—91no—
623D4—92no—
624D4—91no—
625D4—182no—
626D4—182no—
627D4—182no—
628D4—181no—
629D4—181no—
630D4C22×(C3⋊D3)⋊C311yescharacteristic
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—92no—
634C2×C4—182no—
635C2×C4—182no—
636C2×C4—182no—
637C2×C4—181no—
638C2×C4C22×(C3⋊D3)⋊C311yescharacteristic
639C8—91no—
640C8—91no—
641C8C22×(C3⋊D3)⋊C312yes—
642C2×C3—21no—
643C2×C3—31no—
644C2×C3—31no—
645C2×C3—41no—
646C2×C3—61no—
647C2×C3—61no—
648C2×C3—61no—
649C2×C3—121no—
650C2×C3—121no—
651C2×C3—121no—
652C2×C3—182no—
653C2×C3—241no—
654C2×C3—362no—
655C2×C3—361no—
656C2×C3C2×C3×D3×D411yescharacteristic
657D3—62no—
658D3—122no—
659D3—121no—
660D3—182no—
661D3—362no—
662D3—361no—
663C22—21no—
664C22—92no—
665C22—181no—
666C22—182no—
667C22—721no—
668C22—722no—
669C22D4×(C3⋊D3)⋊C311yescharacteristic
670C4—21no—
671C4—22no—
672C4—92no—
673C4—181no—
674C4D4×(C3⋊D3)⋊C311yescharacteristic
675C4C23×(C3⋊D3)⋊C311yescharacteristic
676C3—31no—
677C3—31no—
678C3—61no—
679C3C3×#577811yescharacteristic
680C2—21no—
681C2—41no—
682C2—182no—
683C2—362no—
684C2—361no—
685C2C2×D4×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC2C2×D4×(C3⋊D3)⋊C3
commutator, cosocleC32×C4C24×C3
FrattiniC3×C4C23×C3×D3
FittingH(3,𝔽3)×#137C2
socleC2×C3C2×C3×D3×D4
hypercenter#137(C3⋊D3)⋊C3
hypocenterC32C3×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #11722638C2semidirect
2. #11722627C2semidirect
3. H(3,𝔽3)×#137C2semidirect
4. #64159⋊C3C2semidirect
5. C2×#3755⋊C3C2semidirect
6. #64128⋊C3C2semidirect
7. #64127⋊C3C2semidirect
8. #64123⋊C3C2semidirect
9. SD16×(C3⋊D3)⋊C3C2semidirect
10. #64117⋊C3C2semidirect
11. #64116⋊C3C2semidirect
12. #10596249C3semidirect
15. C2×Q8×H(3,𝔽3)C22semidirect
18. #88722C22semidirect
20. Q8×(C3⋊D3)⋊C3C22semidirect
26. #3828⋊C3C22semidirect
29. Q16×H(3,𝔽3)C22semidirect
30. SD16×H(3,𝔽3)C22semidirect
31. M16×H(3,𝔽3)C22semidirect
32. #3755⋊C3C22semidirect
33. #3755⋊C3C22semidirect
34. #3755⋊C3C22semidirect
35. #3756⋊C3C22semidirect
36. #3753⋊C3C22semidirect
37. #3754⋊C3C22semidirect
38. C2×(C3⋊(C3⋊C8))⋊C3C22semidirect
39. #3745⋊C3C22semidirect
40. #3744⋊C3C22semidirect
41. #3743⋊C3C22semidirect
42. C8×(C3⋊D3)⋊C3C22semidirect
43. #64366C2×C3semidirect
44. #64364C2×C3semidirect
48. C32×#137D3semidirect
49. C32×#137C2×C3semidirect
50. #64159C2×C3semidirect
51. C2×#3755C2×C3semidirect
52. #64128C2×C3semidirect
53. #64127C2×C3semidirect
54. #64123C2×C3semidirect
55. SD16×C3⋊D3C2×C3semidirect
56. #64117C2×C3semidirect
57. #64116C2×C3semidirect
103. C2×C32×Q8C2×D3semidirect
104. C2×C32×Q8C22×C3semidirect
107. #3832C22×C3semidirect
109. Q8×C3⋊D3C22×C3semidirect
115. #3828C22×C3semidirect
132. C32×Q16C2×D3semidirect
133. C32×Q16C22×C3semidirect
135. C32×SD16C2×D3semidirect
136. C32×SD16C22×C3semidirect
138. C32×M16C2×D3semidirect
139. C32×M16C22×C3semidirect
140. #3756C22×C3semidirect
141. #3755C22×C3semidirect
142. #3755C22×C3semidirect
143. #3755C22×C3semidirect
144. #3754C22×C3semidirect
145. #3753C22×C3semidirect
146. C2×C3⋊(C3⋊C8)C22×C3semidirect
147. #3745C22×C3semidirect
148. #3744C22×C3semidirect
149. #3743C22×C3semidirect
150. C8×C3⋊D3C22×C3semidirect
412. #137(C3⋊D3)⋊C3semidirect
420. H(3,𝔽3)#577semidirect
545. C2×Q8C2×(C3⋊D3)⋊C3semidirect
551. Q16C2×(C3⋊D3)⋊C3semidirect
557. SD16C2×(C3⋊D3)⋊C3semidirect
561. M16C2×(C3⋊D3)⋊C3semidirect
610. C32#5778semidirect
611. C32C3×#577semidirect

Maximal subgroups

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

subgroupindex
#117226382
#117226272
H(3,𝔽3)×#1372
#64159⋊C32
C2×#3755⋊C32
#64128⋊C32
#64127⋊C32
#64123⋊C32
SD16×(C3⋊D3)⋊C32
#64117⋊C32
#64116⋊C32
#105962493
C3×#57783