Finite Group Databasebeta

← C3×#10591157 #13158334

Subgroups — C3×#10591157 #13158334

Order 1728.

770 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#638C211yesmaximal, characteristic
2C22×C32×C3⋊C8C211yesmaximal, characteristic, complemented
3C2×C3×#3712C211yesmaximal, characteristic, complemented
4C32×#830C211yesmaximal, characteristic, complemented
5C3×#63572C211yesmaximal, characteristic, complemented
6C3×#63557C211yesmaximal, characteristic, complemented
7C3×#63555C211yesmaximal, characteristic, complemented
8C3×#5111—31nomaximal
9C3×#4730—31nomaximal
10#10591157C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C2×C3×#638C411yescharacteristic
13C2×C3×C4×C3⋊D3C2211yescharacteristic
14C3×#3757C411yescharacteristic
15C3×#3752C411yescharacteristic
16C3×#3750C411yescharacteristic
17C3×C4×C3⋊Dic3C2211yescharacteristic
18C2×C32×C3⋊C8—22no—
19C2×C32×C3⋊C8C2211yescharacteristic
20C2×C32×C3⋊C8C2211yescharacteristic
21C2×C32×C3⋊C8C2211yescharacteristic
22C2×C32×C3⋊C8C2211yescharacteristic
23C3×#3712—22no—
24C22×C32×C8—31no—
25C4×#638C2×C311yescharacteristic
26C3×C4×#67—31no—
27C3×C4×#67—31no—
28C3×C4×#67—61no—
29C22×C3×C3⋊C8—21no—
30C22×C3×C3⋊C8D311yescharacteristic, complemented
31C22×C3×C3⋊C8C2×C311yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)—31no—
33C2×C3×ΓL(1,𝔽25)—31no—
34C2×#3712C2×C311yescharacteristic, complemented
35C32×C22⋊C8—31no—
36C3×#830—21no—
37C3×#830D311yescharacteristic, complemented
38C3×#830C2×C311yescharacteristic, complemented
39C3×(C2×D3)⋊C8—31no—
40C3×(C2×D3)⋊C8—31no—
41C3×#815—31no—
42C3×#815—31no—
43C3×Dic3⋊C8—31no—
44C3×Dic3⋊C8—31no—
45#63572C2×C311yescharacteristic, complemented
46#63557C2×C311yescharacteristic, complemented
47#63555C2×C311yescharacteristic, complemented
48C23×C33C2×C411yescharacteristic
49C22×C3×C3⋊D3C2×C411yescharacteristic
50C2×C33×C4—21no—
51C2×C33×C4—21no—
52C2×C33×C4C2×C411yescharacteristic
53C2×C33×C4C2311yescharacteristic
54C3×#638—22no—
55C2×C3×C3⋊Dic3C2×C411yescharacteristic
56C2×C3×C3⋊Dic3C2×C411yescharacteristic
57C2×C3×C3⋊Dic3C2×C411yescharacteristic
58C3×C4×C3⋊D3—21no—
59C3×C4×C3⋊D3—21no—
60C32×C3⋊C8—21no—
61C32×C3⋊C8—21no—
62C32×C3⋊C8—21no—
63C32×C3⋊C8D412yescomplemented
64C3×#435—91no—
65#5111—31no—
66#4730—31no—
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—41no—
71C22×C32×C4C2×D311yescharacteristic
72C22×C32×C4C2×D311yescharacteristic
73C22×C32×C4C22×C311yescharacteristic
74C2×#638C3×C411yescharacteristic
75C2×C4×C3⋊D3C22×C311yescharacteristic
76C2×C3×#67—31no—
77C2×C3×#67—31no—
78C2×C3×#67—61no—
79C2×C3×C4×D3—31no—
80C2×C3×C4×D3—31no—
81C2×C3×C4×D3—61no—
82C2×C32×C8—31no—
83C2×C32×C8—31no—
84C2×C32×C8—31no—
85C2×C32×C8—31no—
86C2×C32×C8—62no—
87#3757C3×C411yescharacteristic
88#3752C3×C411yescharacteristic
89#3750C3×C411yescharacteristic
90C4×C3⋊Dic3C22×C311yescharacteristic
91C3×#217—31no—
92C3×#217—31no—
93C3×#217—61no—
94C3×(C2×D3)⋊C4—31no—
95C3×(C2×D3)⋊C4—31no—
96C3×(C2×D3)⋊C4—61no—
97C3×Dic3⋊C4—31no—
98C3×Dic3⋊C4—31no—
99C3×Dic3⋊C4—61no—
100C3×C4×Dic3—31no—
101C3×C4×Dic3—31no—
102C3×C4×Dic3—61no—
103C2×C3×C3⋊C8—24no—
104C2×C3×C3⋊C8—21no—
105C2×C3×C3⋊C8—21no—
106C2×C3×C3⋊C8—22no—
107C2×C3×C3⋊C8—22no—
108C2×C3×C3⋊C8—21no—
109C2×C3×C3⋊C8—21no—
110C2×C3×C3⋊C8C2×D311yescharacteristic
111C2×C3×C3⋊C8C2×D311yescharacteristic
112C2×C3×C3⋊C8C2×D311yescharacteristic
113C2×C3×C3⋊C8C2×D311yescharacteristic
114C2×C3×C3⋊C8C22×C311yescharacteristic
115C2×C3×C3⋊C8C22×C311yescharacteristic
116C2×C3×C3⋊C8C22×C311yescharacteristic
117C2×C3×C3⋊C8C22×C311yescharacteristic
118C3×ΓL(1,𝔽25)—62no—
119C3×ΓL(1,𝔽25)—62no—
120#3712—22no—
121C22×C33—21no—
122C22×C33—21no—
123C22×C33M1612yescomplemented
124C22×C33C22×C411yescharacteristic
125C2×C3×C3⋊D3—21no—
126C2×C3×C3⋊D3—21no—
127C2×C3×C3⋊D3—21no—
128C33×C4—21no—
129C33×C4C2×D411yescharacteristic
130C33×C4#4111yescharacteristic
131C3×C3⋊Dic3—21no—
132C3×C3⋊Dic3—21no—
133C3×C3⋊Dic3—21no—
134C2×C3×M16—91no—
135C22×C3×C8—31no—
136C22×C3×C8—31no—
137C22×C3×C8—61no—
138C3×C4×D4—91no—
139C4×#67—31no—
140C4×#67—31no—
141C4×#67—61no—
142C22×C3⋊C8C3×D311yescharacteristic, complemented
143C2×ΓL(1,𝔽25)—31no—
144C2×ΓL(1,𝔽25)—31no—
145C3×C4⋊C8—91no—
146C3×C22⋊C8—31no—
147C3×C22⋊C8—31no—
148C3×C22⋊C8—61no—
149C3×C22⋊C8—91no—
150C3×#97—91no—
151#830C3×D311yescharacteristic, complemented
152(C2×D3)⋊C8—31no—
153(C2×D3)⋊C8—31no—
154#815—31no—
155#815—31no—
156Dic3⋊C8—31no—
157Dic3⋊C8—31no—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—41no—
162C23×C32C4×D311yescharacteristic
163C23×C32C4×D311yescharacteristic
164C23×C32C2×C3×C411yescharacteristic
165C22×C3⋊D3C2×C3×C411yescharacteristic
166C22×C3×D3—31no—
167C22×C3×D3—31no—
168C22×C3×D3—61no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—41no—
184C2×C32×C4—41no—
185C2×C32×C4—41no—
186C2×C32×C4—41no—
187C2×C32×C4—41no—
188C2×C32×C4—41no—
189C2×C32×C4—42no—
190C2×C32×C4—42no—
191C2×C32×C4C4×D311yescharacteristic
192C2×C32×C4C4×D311yescharacteristic
193C2×C32×C4C2×C3×C411yescharacteristic
194C2×C32×C4C22×D311yescharacteristic
195C2×C32×C4C22×D311yescharacteristic
196C2×C32×C4C23×C311yescharacteristic
197#638—22no—
198C2×C3⋊Dic3C2×C3×C411yescharacteristic
199C2×C3⋊Dic3C2×C3×C411yescharacteristic
200C2×C3⋊Dic3C2×C3×C411yescharacteristic
201C4×C3⋊D3—21no—
202C4×C3⋊D3—21no—
203C3×#67—64no—
204C3×#67—62no—
205C3×#67—62no—
206C2×C3×Dic3—31no—
207C2×C3×Dic3—31no—
208C2×C3×Dic3—31no—
209C2×C3×Dic3—31no—
210C2×C3×Dic3—31no—
211C2×C3×Dic3—31no—
212C2×C3×Dic3—61no—
213C2×C3×Dic3—61no—
214C2×C3×Dic3—61no—
215C3×C4×D3—61no—
216C3×C4×D3—61no—
217C3×C4×D3—61no—
218C3×C4×D3—61no—
219C3×C4×D3—121no—
220C3×C4×D3—121no—
221C32×C8—32no—
222C32×C8—61no—
223C32×C8—61no—
224C32×C8—61no—
225C3×C3⋊C8—22no—
226C3×C3⋊C8—21no—
227C3×C3⋊C8—21no—
228C3×C3⋊C8—21no—
229C3×C3⋊C8—21no—
230C3×C3⋊C8—21no—
231C3×C3⋊C8—21no—
232C3×C3⋊C8—22no—
233C3×C3⋊C8—41no—
234C3×C3⋊C8—41no—
235C3×C3⋊C8#6712yescomplemented
236C3×C3⋊C8C3×D412yescomplemented
237#435—91noSylow
238C2×C33—22no—
239C2×C33C4×D411yescharacteristic
240C2×C33C2×M1611yescharacteristic
241C2×C33#13111yescharacteristic
242C3×C3⋊D3—41no—
243C2×C3×D4—91no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—41no—
248C22×C3×C4—91no—
249C22×C3×C4D3211yescharacteristic
250C22×C3×C4C2×C3×D311yescharacteristic
251C22×C3×C4C2×C3×D311yescharacteristic
252C2×#67—31no—
253C2×#67—31no—
254C2×#67—61no—
255C2×C4×D3—31no—
256C2×C4×D3—31no—
257C2×C4×D3—61no—
258C3×M16—182no—
259C2×C3×C8—31no—
260C2×C3×C8—31no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—31no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—61no—
268C2×C3×C8—61no—
269C2×C3×C8—61no—
270C2×C3×C8—61no—
271C2×C3×C8—62no—
272C2×C3×C8—62no—
273C2×C3×C8—64no—
274C3×C4⋊C4—91no—
275C3×C22⋊C4—91no—
276C3×C22⋊C4—91no—
277C3×C42—91no—
278#217—31no—
279#217—31no—
280#217—61no—
281(C2×D3)⋊C4—31no—
282(C2×D3)⋊C4—31no—
283(C2×D3)⋊C4—61no—
284Dic3⋊C4—31no—
285Dic3⋊C4—31no—
286Dic3⋊C4—61no—
287C4×Dic3—31no—
288C4×Dic3—31no—
289C4×Dic3—61no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8C2×C3×D311yescharacteristic
292C2×C3⋊C8C2×C3×D311yescharacteristic
293C2×C3⋊C8C2×C3×D311yescharacteristic
294C2×C3⋊C8C2×C3×D311yescharacteristic
295ΓL(1,𝔽25)—62no—
296ΓL(1,𝔽25)—62no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—22no—
300C22×C32—22no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—22no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—42no—
312C22×C32—41no—
313C22×C32—41no—
314C22×C32—41no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32—42no—
318C22×C32—42no—
319C22×C32ΓL(1,𝔽25)12yescomplemented
320C22×C32ΓL(1,𝔽25)12yescomplemented
321C22×C32C3×M1612yescomplemented
322C22×C32C2×C4×D311yescharacteristic
323C22×C32C2×C4×D311yescharacteristic
324C22×C32C22×C3×C411yescharacteristic
325C2×C3⋊D3—21no—
326C2×C3⋊D3—21no—
327C2×C3⋊D3—21no—
328C2×C3×D3—62no—
329C2×C3×D3—61no—
330C2×C3×D3—61no—
331C2×C3×D3—61no—
332C2×C3×D3—61no—
333C2×C3×D3—61no—
334C2×C3×D3—61no—
335C2×C3×D3—121no—
336C2×C3×D3—121no—
337C32×C4—21no—
338C32×C4—22no—
339C32×C4—21no—
340C32×C4—21no—
341C32×C4—21no—
342C32×C4—21no—
343C32×C4—21no—
344C32×C4—21no—
345C32×C4—21no—
346C32×C4—21no—
347C32×C4—41no—
348C32×C4—41no—
349C32×C4—41no—
350C32×C4—41no—
351C32×C4—42no—
352C32×C4#23511yescharacteristic
353C32×C4D3×D411yescharacteristic
354C32×C4#23711yescharacteristic
355C32×C4C2×#6711yescharacteristic
356C32×C4C2×C3×D411yescharacteristic
357C32×C4C3×#4111yescharacteristic
358C3⋊Dic3—21no—
359C3⋊Dic3—21no—
360C3⋊Dic3—21no—
361C3×Dic3—62no—
362C3×Dic3—61no—
363C3×Dic3—61no—
364C3×Dic3—61no—
365C3×Dic3—61no—
366C3×Dic3—61no—
367C3×Dic3—61no—
368C3×Dic3—121no—
369C3×Dic3—121no—
370C2×M16—91no—
371C22×C8—31no—
372C4×D4—91no—
373C4⋊C8—91no—
374C22⋊C8—31no—
375C22⋊C8—91no—
376#97—91no—
377C33#43511yescharacteristic, complemented, Sylow
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—41no—
382C23×C3—91no—
383C23×C3#62411yescharacteristic
384C23×C3C3×C4×D311yescharacteristic
385C23×C3C3×C4×D311yescharacteristic
386C22×D3—31no—
387C22×D3—31no—
388C22×D3—61no—
389C3×D4—182no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—91no—
413C2×C3×C4—91no—
414C2×C3×C4—91no—
415C2×C3×C4—181no—
416C2×C3×C4—181no—
417C2×C3×C4#62411yescharacteristic
418C2×C3×C4C3×C4×D311yescharacteristic
419C2×C3×C4C3×C4×D311yescharacteristic
420C2×C3×C4C2×D3211yescharacteristic
421C2×C3×C4C22×C3×D311yescharacteristic
422C2×C3×C4C22×C3×D311yescharacteristic
423#67—64no—
424#67—62no—
425#67—62no—
426C2×Dic3—31no—
427C2×Dic3—31no—
428C2×Dic3—31no—
429C2×Dic3—31no—
430C2×Dic3—31no—
431C2×Dic3—31no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C4×D3—61no—
436C4×D3—61no—
437C4×D3—61no—
438C4×D3—61no—
439C4×D3—121no—
440C4×D3—121no—
441C3×C8—32no—
442C3×C8—32no—
443C3×C8—62no—
444C3×C8—62no—
445C3×C8—61no—
446C3×C8—61no—
447C3×C8—61no—
448C3×C8—61no—
449C3×C8—61no—
450C3×C8—61no—
451C3×C8—121no—
452C3×C8—121no—
453C3⋊C8—21no—
454C3⋊C8—21no—
455C3⋊C8—21no—
456C3⋊C8C3×#6712yescomplemented
457C2×C32—22no—
458C2×C32—24no—
459C2×C32—22no—
460C2×C32—22no—
461C2×C32—21no—
462C2×C32—21no—
463C2×C32—21no—
464C2×C32—21no—
465C2×C32—21no—
466C2×C32—21no—
467C2×C32—21no—
468C2×C32—21no—
469C2×C32—21no—
470C2×C32—41no—
471C2×C32—41no—
472C2×C32—41no—
473C2×C32—42no—
474C2×C32—42no—
475C2×C32—44no—
476C2×C32#67⋊C411yescharacteristic
477C2×C32C2×ΓL(1,𝔽25)11yescharacteristic
478C2×C32C2×ΓL(1,𝔽25)11yescharacteristic
479C2×C32#90111yescharacteristic
480C2×C32#90711yescharacteristic
481C2×C32C4×#6711yescharacteristic
482C2×C32C3×C4×D411yescharacteristic
483C2×C32C2×C3×M1611yescharacteristic
484C2×C32C3×#13111yescharacteristic
485C3⋊D3—41no—
486C3×D3—122no—
487C3×D3—121no—
488C3×D3—121no—
489C2×D4—91no—
490C22×C4—91no—
491C22×C4C3×D3211yescharacteristic
492M16—182no—
493C2×C8—31no—
494C2×C8—31no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—62no—
498C4⋊C4—91no—
499C22⋊C4—91no—
500C22⋊C4—91no—
501C42—91no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—41no—
523C22×C3—42no—
524C22×C3—181no—
525C22×C3—181no—
526C22×C3—181no—
527C22×C3#371212yescomplemented
528C22×C3C3×ΓL(1,𝔽25)12yescomplemented
529C22×C3C3×ΓL(1,𝔽25)12yescomplemented
530C22×C3C2×#62411yescharacteristic
531C22×C3C2×C3×C4×D311yescharacteristic
532C22×C3C2×C3×C4×D311yescharacteristic
533C2×D3—62no—
534C2×D3—61no—
535C2×D3—61no—
536C2×D3—61no—
537C2×D3—61no—
538C2×D3—61no—
539C2×D3—61no—
540C2×D3—121no—
541C2×D3—121no—
542C3×C4—22no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—41no—
553C3×C4—41no—
554C3×C4—42no—
555C3×C4—41no—
556C3×C4—41no—
557C3×C4—181no—
558C3×C4—181no—
559C3×C4—181no—
560C3×C4#380411yescharacteristic
561C3×C4D3×#6711yescharacteristic
562C3×C4C3×#23511yescharacteristic
563C3×C4C3×D3×D411yescharacteristic
564C3×C4C3×#23711yescharacteristic
565C3×C4C2×C3×#6711yescharacteristic
566Dic3—62no—
567Dic3—61no—
568Dic3—61no—
569Dic3—61no—
570Dic3—61no—
571Dic3—61no—
572Dic3—61no—
573Dic3—121no—
574Dic3—121no—
575C32—21no—
576C32—21no—
577C32—21no—
578C32—41no—
579C32#473011yescharacteristic, complemented
580C32#511111yescharacteristic, complemented
581C32C3×#43511yescharacteristic, complemented
582C23—91no—
583C23C3×#62411yescharacteristic
584D4—182no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—91no—
588C2×C4—91no—
589C2×C4—91no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4C3×#62411yescharacteristic
593C2×C4C2×C3×D3211yescharacteristic
594C8—32no—
595C8—61no—
596C8—61no—
597C8—61no—
598C2×C3—24no—
599C2×C3—22no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—42no—
612C2×C3—42no—
613C2×C3—44no—
614C2×C3—41no—
615C2×C3—41no—
616C2×C3—41no—
617C2×C3—361no—
618C2×C3#6381711yescharacteristic
619C2×C3C2×#371211yescharacteristic
620C2×C3#6395211yescharacteristic
621C2×C3C3×#67⋊C411yescharacteristic
622C2×C3C2×C3×ΓL(1,𝔽25)11yescharacteristic
623C2×C3C2×C3×ΓL(1,𝔽25)11yescharacteristic
624C2×C3C3×#90111yescharacteristic
625C2×C3C3×#90711yescharacteristic
626C2×C3C3×C4×#6711yescharacteristic
627D3—122no—
628D3—121no—
629D3—121no—
630C22—21no—
631C22—21no—
632C22—181no—
633C22—181no—
634C22—181no—
635C22C3×#371212yescomplemented
636C22C2×C3×#62411yescharacteristic
637C4—21no—
638C4—181no—
639C4—181no—
640C4—181no—
641C4C3×#380411yescharacteristic
642C4C3×D3×#6711yescharacteristic
643C3—21no—
644C3—21no—
645C3—21no—
646C3—41no—
647C3#1059115711yescharacteristic, direct product factor
648C3C3×#473011yescharacteristic, complemented
649C3C3×#511111yescharacteristic, complemented
650C2—22no—
651C2—361no—
652C2C3×#6381711yescharacteristic
653C2C2×C3×#371211yescharacteristic
654C2C3×#6395211yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC22×C33C22×C4
prime radicalC2×C3×#638C4
cosocleC2×C32×C4C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C22×C32×C3⋊C8C2semidirect
3. C2×C3×#3712C2semidirect
4. C32×#830C2semidirect
5. C3×#63572C2semidirect
6. C3×#63557C2semidirect
7. C3×#63555C2semidirect
10. #10591157C3direct (N × H)
30. C22×C3×C3⋊C8D3semidirect
31. C22×C3×C3⋊C8C2×C3semidirect
34. C2×#3712C2×C3semidirect
37. C3×#830D3semidirect
38. C3×#830C2×C3semidirect
45. #63572C2×C3semidirect
46. #63557C2×C3semidirect
47. #63555C2×C3semidirect
63. C32×C3⋊C8D4semidirect
123. C22×C33M16semidirect
142. C22×C3⋊C8C3×D3semidirect
151. #830C3×D3semidirect
235. C3×C3⋊C8#67semidirect
236. C3×C3⋊C8C3×D4semidirect
319. C22×C32ΓL(1,𝔽25)semidirect
320. C22×C32ΓL(1,𝔽25)semidirect
321. C22×C32C3×M16semidirect
377. C33#435semidirect
456. C3⋊C8C3×#67semidirect
527. C22×C3#3712semidirect
528. C22×C3C3×ΓL(1,𝔽25)semidirect
529. C22×C3C3×ΓL(1,𝔽25)semidirect
579. C32#4730semidirect
580. C32#5111semidirect
581. C32C3×#435semidirect
635. C22C3×#3712semidirect
647. C3#10591157direct (N × H)
648. C3C3×#4730semidirect
649. C3C3×#5111semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#6382
C22×C32×C3⋊C82
C2×C3×#37122
C32×#8302
C3×#635722
C3×#635572
C3×#635552
C3×#51113
C3×#47303
#105911573