Finite Group Databasebeta

← C3×#80657 #11867105

Subgroups — C3×#80657 #11867105

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C3×#5627C211yesmaximal, characteristic, complemented
4C3×D3×#121C211yesmaximal, characteristic, complemented
5C32×#465C211yesmaximal, characteristic, complemented
6C3×#5174C211yesmaximal, characteristic, complemented
7C3×#5115C211yesmaximal, characteristic, complemented
8C3×#5048C211yesmaximal, characteristic, complemented
9C3×#5038C211yesmaximal, characteristic, complemented
10C3×#4865C211yesmaximal, characteristic, complemented
11C3×#4861C211yesmaximal, characteristic, complemented
12C3×#4812C211yesmaximal, characteristic, complemented
13C3×#4803C211yesmaximal, characteristic, complemented
14C3×#4782C211yesmaximal, characteristic, complemented
15C3×#4770C211yesmaximal, characteristic, complemented
16C3×#3055—31nomaximal
17#80657C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C22×C32×C8C2211yescharacteristic, complemented
24C32×C22⋊Q8C2211yescharacteristic, complemented
25C32×#121C2211yescharacteristic
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic, complemented
31C3×#930C2211yescharacteristic
32C3×#930C2211yescharacteristic, complemented
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34C3×#914—24no—
35C2×C3×D24C2211yescharacteristic, complemented
36C2×C3×ΓL(1,𝔽25)—24no—
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
40C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
41C3×#895C2211yescharacteristic
42C3×#895C2211yescharacteristic, complemented
43C3×#894—21no—
44C3×#893—21no—
45C3×#892C2211yescharacteristic
46C3×D3×C4⋊C4C2211yescharacteristic
47C3×#884—21no—
48C3×#882—21no—
49C3×#67⋊C4—21no—
50C3×D3×C22⋊C4—21no—
51C32×#106C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×#818C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61C3×#808C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×M16—31no—
65C3×#525—31no—
66C2×C3×#121—31no—
67C2×#914C2×C311yescharacteristic, complemented
68C22×ΓL(1,𝔽25)C2×C311yescharacteristic, complemented
69#5627C2×C311yescharacteristic, complemented
70D3×#121C2×C311yescharacteristic, complemented
71C3×#469—31no—
72C3×#469—31no—
73C3×#468—31no—
74C3×#468—31no—
75C3×#466—31no—
76C3×#466—31no—
77C3×#465—21no—
78C3×#465—31no—
79C3×#465D311yescharacteristic, complemented
80C3×#465C2×C311yescharacteristic, complemented
81C3×#428—31no—
82C3×#418—31no—
83C3×#417—31no—
84#5174C2×C311yescharacteristic, complemented
85#5115C2×C311yescharacteristic, complemented
86#5048C2×C311yescharacteristic, complemented
87#5038C2×C311yescharacteristic, complemented
88#4865C2×C311yescharacteristic, complemented
89#4861C2×C311yescharacteristic, complemented
90#4812C2×C311yescharacteristic, complemented
91#4803C2×C311yescharacteristic, complemented
92#4782C2×C311yescharacteristic, complemented
93#4770C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3D411yescharacteristic
105C3×#239—22no—
106C3×#239—22no—
107C3×D3×D4—22no—
108C3×D3×D4—22no—
109C3×D3×D4—44no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3D411yescharacteristic
120C2×C3×C4×D3D411yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C32×SD16—22no—
124C2×C32×C8—22no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4—21no—
128C32×C4⋊C4C2311yescharacteristic
129C32×C4⋊C4C2311yescharacteristic
130C32×C22⋊C4—21no—
131C32×C22⋊C4—21no—
132C3×#217—21no—
133C3×#215—22no—
134C3×#213—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×C4⋊Dic3C2311yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×C4×Dic3—21no—
146C2×C3×C3⋊C8—22no—
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×D24—22no—
150C3×ΓL(1,𝔽25)—22no—
151C3×ΓL(1,𝔽25)—22no—
152C3×ΓL(1,𝔽25)—22no—
153C3×ΓL(1,𝔽25)D414yescomplemented
154#3055—31noSylow
155C2×C3×#41—31no—
156C22×C3×D4—31no—
157C22×C3×D4—61no—
158C23×C3×C4—31no—
159C2×#239C22×C311yescharacteristic
160C2×D3×D4—21no—
161C2×D3×D4C22×C311yescharacteristic
162C22×C4×D3C22×C311yescharacteristic
163C3×AGL(1,ℤ/8)—64no—
164C2×C3×SD16—21no—
165C2×C3×SD16—31no—
166C2×C3×SD16C2×D311yescharacteristic, complemented
167C2×C3×SD16C22×C311yescharacteristic, complemented
168C2×C3×D8—31no—
169C2×C3×D8—31no—
170C2×C3×M16—31no—
171C2×C3×M16—31no—
172C2×C3×M16—31no—
173C2×C3×M16—31no—
174C2×C3×M16—64no—
175C22×C3×C8—21no—
176C22×C3×C8—31no—
177C22×C3×C8C2×D311yescharacteristic, complemented
178C22×C3×C8C22×C311yescharacteristic, complemented
179C3×#123—61no—
180C3×C22⋊Q8—21no—
181C3×C22⋊Q8—31no—
182C3×C22⋊Q8C2×D311yescharacteristic, complemented
183C3×C22⋊Q8C22×C311yescharacteristic, complemented
184C3×#121—21no—
185C3×#121—31no—
186C3×#121—31no—
187C3×#121—31no—
188C3×#121—31no—
189C3×#121—31no—
190C3×#121—61no—
191C3×#121—61no—
192C3×#121C2×D311yescharacteristic
193C3×#121C22×C311yescharacteristic
194C3×#120—61no—
195C3×C4×D4—61no—
196C3×C4×D4—61no—
197C3×#117—31no—
198C2×C3×C4⋊C4—31no—
199C2×C3×C22⋊C4—61no—
200#946C22×C311yescharacteristic, complemented
201C2×#215C22×C311yescharacteristic, complemented
202#939—21no—
203#938C22×C311yescharacteristic
204C2×#213C22×C311yescharacteristic, complemented
205#930C22×C311yescharacteristic
206#930C22×C311yescharacteristic, complemented
207C22×C3⋊C8C22×C311yescharacteristic, complemented
208#914—24no—
209C2×D24C22×C311yescharacteristic, complemented
210C2×ΓL(1,𝔽25)—24no—
211C2×ΓL(1,𝔽25)C22×C311yescharacteristic
212C2×ΓL(1,𝔽25)C22×C311yescharacteristic
213C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
214C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
215#895C22×C311yescharacteristic
216#895C22×C311yescharacteristic, complemented
217#894—21no—
218#893—21no—
219#892C22×C311yescharacteristic
220D3×C4⋊C4C22×C311yescharacteristic
221#884—21no—
222#882—21no—
223#67⋊C4—21no—
224D3×C22⋊C4—21no—
225C3×#107—31no—
226C3×#107—31no—
227C3×#106—21no—
228C3×#106—31no—
229C3×#106C2×D311yescharacteristic, complemented
230C3×#106C22×C311yescharacteristic, complemented
231C3×#103—21no—
232C3×#103—31no—
233C3×#103C2×D311yescharacteristic, complemented
234C3×#103C22×C311yescharacteristic, complemented
235C3×#102—21no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102C2×D311yescharacteristic, complemented
242C3×#102C22×C311yescharacteristic, complemented
243#835C22×C311yescharacteristic, complemented
244#832C22×C311yescharacteristic, complemented
245#821C22×C311yescharacteristic, complemented
246#821C22×C311yescharacteristic, complemented
247#818C22×C311yescharacteristic, complemented
248#809C22×C311yescharacteristic, complemented
249#809C22×C311yescharacteristic, complemented
250#808C22×C311yescharacteristic, complemented
251#807C22×C311yescharacteristic, complemented
252C23×C32—21no—
253C23×C32C2×D411yescharacteristic
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—41no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3C2×D411yescharacteristic
263C22×C3×D3C2×D411yescharacteristic
264C32×Q8—21no—
265C32×Q8—21no—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4—42no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C3×#67—42no—
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×D12—42no—
291C3×D12—42no—
292C3×C4×D3—22no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—22no—
296C3×C4×D3—42no—
297C3×C4×D3—42no—
298C3×C4×D3C2×D412yes—
299C3×C4×D3#4112yes—
300C32×C8—21no—
301C32×C8C2×D412yescomplemented
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yescomplemented
304C2×AGL(1,ℤ/8)—31no—
305C22×M16—31no—
306#525—31no—
307C2×#121—31no—
308#469—31no—
309#469—31no—
310#468—31no—
311#468—31no—
312#466—31no—
313#466—31no—
314#465—31no—
315#465C3×D311yescharacteristic, complemented
316#428—31no—
317#418—31no—
318#417—31no—
319C24×C3—31no—
320C24×C3—61no—
321C23×D3—21no—
322C23×D3C3×D411yescharacteristic
323C3×#41—62no—
324C3×#41—62no—
325C2×C3×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C23×C311yescharacteristic
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—41no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—62no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—124no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C23×C311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—62no—
353C22×C3×C4—62no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C23×C311yescharacteristic
358C2×#67—21no—
359C2×#67—21no—
360C2×#67—21no—
361C2×#67—21no—
362C22×Dic3C3×D411yescharacteristic
363#239—22no—
364#239—22no—
365D3×D4—22no—
366D3×D4—22no—
367D3×D4—44no—
368C2×D12—21no—
369C2×D12—21no—
370C2×D12—21no—
371C2×D12C23×C311yescharacteristic
372C2×D12C23×C311yescharacteristic
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—21no—
376C2×C4×D3—21no—
377C2×C4×D3C3×D411yescharacteristic
378C2×C4×D3C3×D411yescharacteristic
379C2×C4×D3C23×C311yescharacteristic
380C2×C4×D3C23×C311yescharacteristic
381C3×SD16—22no—
382C3×SD16—22no—
383C3×SD16—42no—
384C3×SD16—62no—
385C3×D8—62no—
386C3×D8—62no—
387C3×M16—34no—
388C3×M16—62no—
389C3×M16—62no—
390C3×M16—62no—
391C2×C3×C8—22no—
392C2×C3×C8—22no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—42no—
398C2×C3×C8—62no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C23×C311yescharacteristic
402C2×C3×C8C23×C311yescharacteristic
403C3×C4⋊C4—21no—
404C3×C4⋊C4—21no—
405C3×C4⋊C4—21no—
406C3×C4⋊C4—21no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—31no—
409C3×C4⋊C4—41no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4C22×D311yescharacteristic
413C3×C4⋊C4C22×D311yescharacteristic
414C3×C4⋊C4C23×C311yescharacteristic
415C3×C4⋊C4C23×C311yescharacteristic
416C3×C22⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—21no—
420C3×C22⋊C4—41no—
421C3×C22⋊C4—41no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C42—61no—
430#217—21no—
431#215—22no—
432#213—22no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439C4⋊Dic3C23×C311yescharacteristic
440C4⋊Dic3C23×C311yescharacteristic
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443C4×Dic3—21no—
444C2×C3⋊C8—22no—
445C2×C3⋊C8C23×C311yescharacteristic
446C2×C3⋊C8C23×C311yescharacteristic
447D24—22no—
448ΓL(1,𝔽25)—22no—
449ΓL(1,𝔽25)—22no—
450ΓL(1,𝔽25)—22no—
451ΓL(1,𝔽25)C3×D414yescomplemented
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32AGL(1,ℤ/8)12yescomplemented
458C22×C32C22×D411yescharacteristic
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—44no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—84no—
472C2×C3×D3#12112yes—
473C32×C4—21no—
474C32×C4—41no—
475C32×C4—41no—
476C32×C4—41no—
477C32×C4C22×D411yescharacteristic
478C32×C4C2×#4111yescharacteristic
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3#12112yes—
483C2×#41—31no—
484C22×D4—31no—
485C22×D4—61no—
486C23×C4—31no—
487AGL(1,ℤ/8)—64no—
488C2×SD16—31no—
489C2×SD16C2×C3×D311yescharacteristic, complemented
490C2×D8—31no—
491C2×D8—31no—
492C2×M16—31no—
493C2×M16—31no—
494C2×M16—31no—
495C2×M16—31no—
496C2×M16—64no—
497C22×C8—31no—
498C22×C8C2×C3×D311yescharacteristic, complemented
499#123—61no—
500C22⋊Q8—31no—
501C22⋊Q8C2×C3×D311yescharacteristic, complemented
502#121—31no—
503#121—31no—
504#121—31no—
505#121—31no—
506#121—31no—
507#121—61no—
508#121—61no—
509#121C2×C3×D311yescharacteristic
510#120—61no—
511C4×D4—61no—
512C4×D4—61no—
513#117—31no—
514C2×C4⋊C4—31no—
515C2×C22⋊C4—61no—
516#107—31no—
517#107—31no—
518#106—31no—
519#106C2×C3×D311yescharacteristic, complemented
520#103—31no—
521#103C2×C3×D311yescharacteristic, complemented
522#102—31no—
523#102—31no—
524#102—31no—
525#102—31no—
526#102—31no—
527#102C2×C3×D311yescharacteristic, complemented
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—41no—
534C23×C3—62no—
535C23×C3—62no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—121no—
539C23×C3—122no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3D3×D411yescharacteristic
543C23×C3C2×C3×D411yescharacteristic
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—41no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3C2×C3×D411yescharacteristic
553C22×D3C2×C3×D411yescharacteristic
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—41no—
565C3×D4—41no—
566C3×D4—42no—
567C3×D4—42no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—82no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—122no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4—122no—
579C3×D4—122no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—31no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—31no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—62no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—122no—
609C2×C3×C4—122no—
610C2×C3×C4D3×D411yescharacteristic
611C2×C3×C4C2×C3×D411yescharacteristic
612C2×C3×C4C23×D311yescharacteristic
613C2×C3×C4C24×C311yescharacteristic
614#67—42no—
615#67—42no—
616#67—42no—
617#67—42no—
618C2×Dic3—22no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3C2×C3×D411yescharacteristic
622C2×Dic3C2×C3×D411yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—42no—
628D12—42no—
629D12—42no—
630C4×D3—22no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—22no—
634C4×D3—42no—
635C4×D3—42no—
636C4×D3C2×C3×D412yes—
637C4×D3C3×#4112yes—
638C3×C8—21no—
639C3×C8—21no—
640C3×C8—22no—
641C3×C8—32no—
642C3×C8—41no—
643C3×C8—61no—
644C3×C8D3×D412yescomplemented
645C3×C8C2×C3×D412yescomplemented
646C3⋊C8—21no—
647C3⋊C8C2×C3×D412yescomplemented
648C2×C32—22no—
649C2×C32—81no—
650C2×C32C2×#12111yescharacteristic
651C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
652C2×C32#57511yescharacteristic
653C3×D3—22no—
654C3×D3—41no—
655C3×D3—81no—
656C3×D3—81no—
657C24—31no—
658C24—61no—
659#41—62no—
660#41—62no—
661C2×Q8C22×C3×D311yescharacteristic
662C2×D4—21no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—62no—
669C2×D4—62no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—124no—
675C2×D4C22×C3×D311yescharacteristic
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4C22×C3×D311yescharacteristic
686SD16—22no—
687SD16—62no—
688D8—62no—
689D8—62no—
690M16—34no—
691M16—62no—
692M16—62no—
693M16—62no—
694C2×C8—22no—
695C2×C8—31no—
696C2×C8—31no—
697C2×C8—62no—
698C2×C8C22×C3×D311yescharacteristic
699C2×C8C22×C3×D311yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C4⋊C4C22×C3×D311yescharacteristic
706C4⋊C4C22×C3×D311yescharacteristic
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—61no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C42—61no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—32no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—124no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—244no—
748C22×C3#91412yescomplemented
749C22×C3C3×AGL(1,ℤ/8)12yescomplemented
750C22×C3C2×D3×D411yescharacteristic
751C22×C3C22×C3×D411yescharacteristic
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—44no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—84no—
765C2×D3C3×#12112yes—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—32no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—41no—
774C3×C4—41no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—61no—
779C3×C4—81no—
780C3×C4—81no—
781C3×C4—81no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4C2×D3×D411yescharacteristic
785C3×C4D3×#4111yescharacteristic
786C3×C4C22×C3×D411yescharacteristic
787C3×C4C2×C3×#4111yescharacteristic
788Dic3—21no—
789Dic3—41no—
790Dic3—41no—
791Dic3C3×#12112yes—
792C32#305511yescharacteristic, complemented, Sylow
793C23—21no—
794C23—31no—
795C23—31no—
796C23—62no—
797C23—62no—
798C23—61no—
799C23—61no—
800C23—121no—
801C23—122no—
802C23—122no—
803C23—122no—
804C23C3×D3×D411yescharacteristic
805Q8—21no—
806Q8—21no—
807D4—21no—
808D4—21no—
809D4—42no—
810D4—61no—
811D4—61no—
812D4—61no—
813D4—61no—
814D4—122no—
815D4—122no—
816D4—122no—
817D4—122no—
818D4—122no—
819D4—122no—
820D4—122no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—31no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—31no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—122no—
838C2×C4—122no—
839C2×C4C3×D3×D411yescharacteristic
840C2×C4C23×C3×D311yescharacteristic
841C8—21no—
842C8—32no—
843C8—61no—
844C8C3×D3×D412yescomplemented
845C2×C3—22no—
846C2×C3—22no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—42no—
851C2×C3—62no—
852C2×C3—81no—
853C2×C3—81no—
854C2×C3—121no—
855C2×C3—161no—
856C2×C3—241no—
857C2×C3—241no—
858C2×C3D3×#12111yescharacteristic
859C2×C3C2×#91411yescharacteristic
860C2×C3#576811yescharacteristic
861C2×C3C2×C3×#12111yescharacteristic
862C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
863C2×C3C3×#57511yescharacteristic
864D3—22no—
865D3—41no—
866D3—81no—
867D3—81no—
868C22—21no—
869C22—21no—
870C22—32no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—61no—
878C22—61no—
879C22—124no—
880C22—121no—
881C22—121no—
882C22—121no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—244no—
887C22C3×#91412yescomplemented
888C22C2×C3×D3×D411yescharacteristic
889C4—21no—
890C4—32no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—61no—
895C4—121no—
896C4—121no—
897C4C2×C3×D3×D411yescharacteristic
898C4C3×D3×#4111yescharacteristic
899C3—21no—
900C3#8065711yescharacteristic, direct product factor
901C3C3×#305511yescharacteristic, complemented
902C2—22no—
903C2—62no—
904C2—81no—
905C2—121no—
906C2—241no—
907C2—241no—
908C2C3×D3×#12111yescharacteristic
909C2C2×C3×#91411yescharacteristic
910C2C3×#576811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
hypercenterC3×#465D3
hypocenterC3C3×#3055
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#465

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. C22×C3×ΓL(1,𝔽25)C2semidirect
3. C3×#5627C2semidirect
4. C3×D3×#121C2semidirect
5. C32×#465C2semidirect
6. C3×#5174C2semidirect
7. C3×#5115C2semidirect
8. C3×#5048C2semidirect
9. C3×#5038C2semidirect
10. C3×#4865C2semidirect
11. C3×#4861C2semidirect
12. C3×#4812C2semidirect
13. C3×#4803C2semidirect
14. C3×#4782C2semidirect
15. C3×#4770C2semidirect
17. #80657C3direct (N × H)
22. C2×C32×SD16C22semidirect
23. C22×C32×C8C22semidirect
24. C32×C22⋊Q8C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#215C22semidirect
30. C2×C3×#213C22semidirect
32. C3×#930C22semidirect
33. C22×C3×C3⋊C8C22semidirect
35. C2×C3×D24C22semidirect
39. C2×C3×ΓL(1,𝔽25)C22semidirect
40. C2×C3×ΓL(1,𝔽25)C22semidirect
42. C3×#895C22semidirect
51. C32×#106C22semidirect
52. C32×#103C22semidirect
53. C32×#102C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×#821C22semidirect
58. C3×#818C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. C3×#808C22semidirect
62. C3×#807C22semidirect
67. C2×#914C2×C3semidirect
68. C22×ΓL(1,𝔽25)C2×C3semidirect
69. #5627C2×C3semidirect
70. D3×#121C2×C3semidirect
79. C3×#465D3semidirect
80. C3×#465C2×C3semidirect
84. #5174C2×C3semidirect
85. #5115C2×C3semidirect
86. #5048C2×C3semidirect
87. #5038C2×C3semidirect
88. #4865C2×C3semidirect
89. #4861C2×C3semidirect
90. #4812C2×C3semidirect
91. #4803C2×C3semidirect
92. #4782C2×C3semidirect
93. #4770C2×C3semidirect
153. C3×ΓL(1,𝔽25)D4semidirect
166. C2×C3×SD16C2×D3semidirect
167. C2×C3×SD16C22×C3semidirect
177. C22×C3×C8C2×D3semidirect
178. C22×C3×C8C22×C3semidirect
182. C3×C22⋊Q8C2×D3semidirect
183. C3×C22⋊Q8C22×C3semidirect
200. #946C22×C3semidirect
201. C2×#215C22×C3semidirect
204. C2×#213C22×C3semidirect
206. #930C22×C3semidirect
207. C22×C3⋊C8C22×C3semidirect
209. C2×D24C22×C3semidirect
213. C2×ΓL(1,𝔽25)C22×C3semidirect
214. C2×ΓL(1,𝔽25)C22×C3semidirect
216. #895C22×C3semidirect
229. C3×#106C2×D3semidirect
230. C3×#106C22×C3semidirect
233. C3×#103C2×D3semidirect
234. C3×#103C22×C3semidirect
241. C3×#102C2×D3semidirect
242. C3×#102C22×C3semidirect
243. #835C22×C3semidirect
244. #832C22×C3semidirect
245. #821C22×C3semidirect
246. #821C22×C3semidirect
247. #818C22×C3semidirect
248. #809C22×C3semidirect
249. #809C22×C3semidirect
250. #808C22×C3semidirect
251. #807C22×C3semidirect
301. C32×C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
315. #465C3×D3semidirect
451. ΓL(1,𝔽25)C3×D4semidirect
457. C22×C32AGL(1,ℤ/8)semidirect
489. C2×SD16C2×C3×D3semidirect
498. C22×C8C2×C3×D3semidirect
501. C22⋊Q8C2×C3×D3semidirect
519. #106C2×C3×D3semidirect
521. #103C2×C3×D3semidirect
527. #102C2×C3×D3semidirect
644. C3×C8D3×D4semidirect
645. C3×C8C2×C3×D4semidirect
647. C3⋊C8C2×C3×D4semidirect
748. C22×C3#914semidirect
749. C22×C3C3×AGL(1,ℤ/8)semidirect
792. C32#3055semidirect
844. C8C3×D3×D4semidirect
887. C22C3×#914semidirect
900. C3#80657direct (N × H)
901. C3C3×#3055semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
C22×C3×ΓL(1,𝔽25)2
C3×#56272
C3×D3×#1212
C32×#4652
C3×#51742
C3×#51152
C3×#50482
C3×#50382
C3×#48652
C3×#48612
C3×#48122
C3×#48032
C3×#47822
C3×#47702
C3×#30553
#806573