Finite Group Databasebeta

← C3×#80715 #11867117

Subgroups — C3×#80715 #11867117

Order 1152.

1163 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#911C211yesmaximal, characteristic, complemented
2C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C3×#5606C211yesmaximal, characteristic, complemented
4C3×D3×#121C211yesmaximal, characteristic, complemented
5C32×#466C211yesmaximal, characteristic, complemented
6C3×#5159C211yesmaximal, characteristic, complemented
7C3×#5114C211yesmaximal, characteristic, complemented
8C3×#5041C211yesmaximal, characteristic, complemented
9C3×#5038C211yesmaximal, characteristic, complemented
10C3×#4886C211yesmaximal, characteristic, complemented
11C3×#4881C211yesmaximal, characteristic, complemented
12C3×#4782C211yesmaximal, characteristic, complemented
13C3×#4780C211yesmaximal, characteristic, complemented
14C3×#4771C211yesmaximal, characteristic, complemented
15C3×#4770C211yesmaximal, characteristic, complemented
16C3×#3055—31nomaximal
17#80715C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic, complemented
23C22×C32×C8C2211yescharacteristic, complemented
24C32×#121C2211yescharacteristic
25C32×#121C2211yescharacteristic, complemented
26C3×#939—21no—
27C3×#938C2211yescharacteristic
28C3×#938C2211yescharacteristic, complemented
29C3×#937—21no—
30C3×D4×Dic3—21no—
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33C3×#930C2211yescharacteristic
34C3×#924C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36C3×#911—24no—
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)—24no—
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
40C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
41C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
42C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
43C3×#897C2211yescharacteristic, complemented
44C3×#895C2211yescharacteristic
45C3×#892C2211yescharacteristic
46C3×D3×C4⋊C4C2211yescharacteristic
47C3×#884—21no—
48C3×#883—21no—
49C3×#67⋊C4—21no—
50C3×D3×C22⋊C4—21no—
51C32×#107C2211yescharacteristic, complemented
52C32×#102C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#817C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, 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×#911C2×C311yescharacteristic, complemented
68C22×ΓL(1,𝔽25)C2×C311yescharacteristic, complemented
69#5606C2×C311yescharacteristic, complemented
70D3×#121C2×C311yescharacteristic, complemented
71C3×#469—31no—
72C3×#469—31no—
73C3×#468—31no—
74C3×#468—31no—
75C3×#466—21no—
76C3×#466—31no—
77C3×#466D311yescharacteristic, complemented
78C3×#466C2×C311yescharacteristic, complemented
79C3×#465—31no—
80C3×#465—31no—
81C3×#428—31no—
82C3×#418—31no—
83C3×#417—31no—
84#5159C2×C311yescharacteristic, complemented
85#5114C2×C311yescharacteristic, complemented
86#5041C2×C311yescharacteristic, complemented
87#5038C2×C311yescharacteristic, complemented
88#4886C2×C311yescharacteristic, complemented
89#4881C2×C311yescharacteristic, complemented
90#4782C2×C311yescharacteristic, complemented
91#4780C2×C311yescharacteristic, complemented
92#4771C2×C311yescharacteristic, complemented
93#4770C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3D411yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3D411yescharacteristic
108C3×#237—22no—
109C3×#237—22no—
110C3×D3×D4—22no—
111C3×D3×D4—22no—
112C3×D3×D4—44no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3D411yescharacteristic
119C2×C3×C4×D3D411yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123C32×D8—22no—
124C2×C32×C8—22no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#214—22no—
135C3×#213—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3—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×#204—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×#237C22×C311yescharacteristic
160C2×D3×D4—21no—
161C2×D3×D4C22×C311yescharacteristic
162C22×C4×D3C22×C311yescharacteristic
163C3×AGL(1,ℤ/8)—64no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—21no—
167C2×C3×D8—31no—
168C2×C3×D8C2×D311yescharacteristic, complemented
169C2×C3×D8C22×C311yescharacteristic, complemented
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—31no—
181C3×C22⋊Q8—31no—
182C3×#121—21no—
183C3×#121—21no—
184C3×#121—31no—
185C3×#121—31no—
186C3×#121—31no—
187C3×#121—31no—
188C3×#121—61no—
189C3×#121—61no—
190C3×#121C2×D311yescharacteristic
191C3×#121C2×D311yescharacteristic, complemented
192C3×#121C22×C311yescharacteristic
193C3×#121C22×C311yescharacteristic, complemented
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#939—21no—
201#938C22×C311yescharacteristic
202#938C22×C311yescharacteristic, complemented
203#937—21no—
204D4×Dic3—21no—
205C2×#214C22×C311yescharacteristic, complemented
206C2×#213C22×C311yescharacteristic, complemented
207#930C22×C311yescharacteristic
208#924C22×C311yescharacteristic, complemented
209C22×C3⋊C8C22×C311yescharacteristic, complemented
210#911—24no—
211C2×#204C22×C311yescharacteristic, complemented
212C2×ΓL(1,𝔽25)—24no—
213C2×ΓL(1,𝔽25)C22×C311yescharacteristic
214C2×ΓL(1,𝔽25)C22×C311yescharacteristic
215C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
216C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
217#897C22×C311yescharacteristic, complemented
218#895C22×C311yescharacteristic
219#892C22×C311yescharacteristic
220D3×C4⋊C4C22×C311yescharacteristic
221#884—21no—
222#883—21no—
223#67⋊C4—21no—
224D3×C22⋊C4—21no—
225C3×#107—21no—
226C3×#107—31no—
227C3×#107C2×D311yescharacteristic, complemented
228C3×#107C22×C311yescharacteristic, complemented
229C3×#106—31no—
230C3×#106—31no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#102—21no—
234C3×#102—21no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102C2×D311yescharacteristic, complemented
240C3×#102C2×D311yescharacteristic, complemented
241C3×#102C22×C311yescharacteristic, complemented
242C3×#102C22×C311yescharacteristic, complemented
243#832C22×C311yescharacteristic, complemented
244#832C22×C311yescharacteristic, complemented
245#821C22×C311yescharacteristic, complemented
246#817C22×C311yescharacteristic, complemented
247#816C22×C311yescharacteristic, complemented
248#810C22×C311yescharacteristic, complemented
249#809C22×C311yescharacteristic, complemented
250#808C22×C311yescharacteristic, complemented
251#807C22×C311yescharacteristic, complemented
252C23×C32—21no—
253C23×C32—21no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—22no—
256C22×C3×D3—22no—
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×D4—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—21no—
268C32×D4—42no—
269C32×D4—42no—
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—
280C3×#67—42no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×C4×D3—22no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—22no—
295C3×C4×D3—42no—
296C3×C4×D3C2×D412yes—
297C3×C4×D3#4112yes—
298C3×Dic6—21no—
299C3×Dic6—21no—
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#466C3×D311yescharacteristic, complemented
314#465—31no—
315#465—31no—
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—31no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—41no—
334C2×C3×D4—41no—
335C2×C3×D4—61no—
336C2×C3×D4—62no—
337C2×C3×D4—62no—
338C2×C3×D4—61no—
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×D4C22×D311yescharacteristic
346C2×C3×D4C23×C311yescharacteristic
347C2×C3×D4C23×C311yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—62no—
355C22×C3×C4—62no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C23×C311yescharacteristic
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—21no—
365C22×Dic3—21no—
366C22×Dic3C3×D411yescharacteristic
367#237—22no—
368#237—22no—
369D3×D4—22no—
370D3×D4—22no—
371D3×D4—44no—
372C2×D12—21no—
373C2×D12C23×C311yescharacteristic
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—21no—
377C2×C4×D3C3×D411yescharacteristic
378C2×C4×D3C3×D411yescharacteristic
379C2×C4×D3C23×C311yescharacteristic
380C2×C4×D3C23×C311yescharacteristic
381C2×Dic6C23×C311yescharacteristic
382C3×SD16—62no—
383C3×SD16—62no—
384C3×D8—22no—
385C3×D8—22no—
386C3×D8—42no—
387C3×D8—62no—
388C3×M16—34no—
389C3×M16—62no—
390C3×M16—62no—
391C3×M16—62no—
392C2×C3×C8—22no—
393C2×C3×C8—22no—
394C2×C3×C8—21no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8—42no—
399C2×C3×C8—62no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C23×C311yescharacteristic
403C2×C3×C8C23×C311yescharacteristic
404C3×C4⋊C4—21no—
405C3×C4⋊C4—21no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4C22×D311yescharacteristic
412C3×C4⋊C4C22×D311yescharacteristic
413C3×C4⋊C4C23×C311yescharacteristic
414C3×C4⋊C4C23×C311yescharacteristic
415C3×C22⋊C4—21no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—41no—
421C3×C22⋊C4—61no—
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×C42—61no—
429#217—21no—
430#217—21no—
431#217—21no—
432#214—22no—
433#213—22no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438C4⋊Dic3—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
447#204—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×C32—41no—
458C22×C32—41no—
459C22×C32—41no—
460C22×C32AGL(1,ℤ/8)12yescomplemented
461C22×C32C22×D411yescharacteristic
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—44no—
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×C4C22×D411yescharacteristic
477C32×C4C2×#4111yescharacteristic
478C3×Dic3—21no—
479C3×Dic3—41no—
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×SD16—31no—
490C2×D8—31no—
491C2×D8C2×C3×D311yescharacteristic, complemented
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⋊Q8—31no—
502#121—31no—
503#121—31no—
504#121—31no—
505#121—31no—
506#121—61no—
507#121—61no—
508#121C2×C3×D311yescharacteristic
509#121C2×C3×D311yescharacteristic, complemented
510#120—61no—
511C4×D4—61no—
512C4×D4—61no—
513#117—31no—
514C2×C4⋊C4—31no—
515C2×C22⋊C4—61no—
516#107—31no—
517#107C2×C3×D311yescharacteristic, complemented
518#106—31no—
519#106—31no—
520#103—31no—
521#103—31no—
522#102—31no—
523#102—31no—
524#102—31no—
525#102—31no—
526#102C2×C3×D311yescharacteristic, complemented
527#102C2×C3×D311yescharacteristic, complemented
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—31no—
534C23×C3—31no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—62no—
538C23×C3—62no—
539C23×C3—61no—
540C23×C3—121no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—122no—
544C23×C3D3×D411yescharacteristic
545C23×C3C2×C3×D411yescharacteristic
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—21no—
549C22×D3—41no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3C2×C3×D411yescharacteristic
554C22×D3C2×C3×D411yescharacteristic
555C3×Q8—61no—
556C3×Q8—61no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—41no—
569C3×D4—42no—
570C3×D4—42no—
571C3×D4—42no—
572C3×D4—42no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—82no—
576C3×D4—82no—
577C3×D4—122no—
578C3×D4—122no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—122no—
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—21no—
593C2×C3×C4—31no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—31no—
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—61no—
609C2×C3×C4—122no—
610C2×C3×C4—122no—
611C2×C3×C4D3×D411yescharacteristic
612C2×C3×C4C2×C3×D411yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C24×C311yescharacteristic
615#67—42no—
616#67—42no—
617#67—42no—
618#67—42no—
619#67—42no—
620C2×Dic3—22no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—42no—
625C2×Dic3C2×C3×D411yescharacteristic
626C2×Dic3C2×C3×D411yescharacteristic
627D12—21no—
628D12—21no—
629D12—42no—
630C4×D3—22no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—22no—
634C4×D3—42no—
635C4×D3C2×C3×D412yes—
636C4×D3C3×#4112yes—
637Dic6—21no—
638Dic6—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—22no—
642C3×C8—32no—
643C3×C8—41no—
644C3×C8—61no—
645C3×C8D3×D412yescomplemented
646C3×C8C2×C3×D412yescomplemented
647C3⋊C8—21no—
648C3⋊C8C2×C3×D412yescomplemented
649C2×C32—22no—
650C2×C32—81no—
651C2×C32—81no—
652C2×C32C2×#12111yescharacteristic
653C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
654C2×C32#57511yescharacteristic
655C3×D3—22no—
656C3×D3—41no—
657C3×D3—81no—
658C24—31no—
659C24—61no—
660#41—62no—
661#41—62no—
662C2×Q8—31no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—31no—
666C2×D4—61no—
667C2×D4—62no—
668C2×D4—62no—
669C2×D4—61no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—124no—
675C2×D4C22×C3×D311yescharacteristic
676C2×D4C22×C3×D311yescharacteristic
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4C22×C3×D311yescharacteristic
687SD16—62no—
688SD16—62no—
689D8—22no—
690D8—62no—
691M16—34no—
692M16—62no—
693M16—62no—
694M16—62no—
695C2×C8—22no—
696C2×C8—31no—
697C2×C8—31no—
698C2×C8—62no—
699C2×C8C22×C3×D311yescharacteristic
700C2×C8C22×C3×D311yescharacteristic
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—61no—
704C4⋊C4—61no—
705C4⋊C4—61no—
706C4⋊C4C22×C3×D311yescharacteristic
707C4⋊C4C22×C3×D311yescharacteristic
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—61no—
711C22⋊C4—61no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C42—61no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—32no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—124no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—244no—
755C22×C3#91112yescomplemented
756C22×C3C3×AGL(1,ℤ/8)12yescomplemented
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C22×C3×D411yescharacteristic
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—44no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—84no—
769C2×D3C3×#12112yes—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—32no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—61no—
781C3×C4—81no—
782C3×C4—81no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4—121no—
786C3×C4C2×D3×D411yescharacteristic
787C3×C4D3×#4111yescharacteristic
788C3×C4C22×C3×D411yescharacteristic
789C3×C4C2×C3×#4111yescharacteristic
790Dic3—21no—
791Dic3—41no—
792Dic3—41no—
793Dic3—41no—
794Dic3C3×#12112yes—
795C32#305511yescharacteristic, complemented, Sylow
796C23—21no—
797C23—21no—
798C23—31no—
799C23—31no—
800C23—62no—
801C23—62no—
802C23—61no—
803C23—121no—
804C23—122no—
805C23—122no—
806C23—122no—
807C23C3×D3×D411yescharacteristic
808Q8—61no—
809Q8—61no—
810D4—21no—
811D4—21no—
812D4—21no—
813D4—21no—
814D4—42no—
815D4—42no—
816D4—61no—
817D4—61no—
818D4—122no—
819D4—122no—
820D4—122no—
821D4—122no—
822D4—122no—
823D4—122no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—31no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—31no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—122no—
841C2×C4—122no—
842C2×C4C3×D3×D411yescharacteristic
843C2×C4C23×C3×D311yescharacteristic
844C8—21no—
845C8—32no—
846C8—61no—
847C8C3×D3×D412yescomplemented
848C2×C3—22no—
849C2×C3—22no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—42no—
854C2×C3—62no—
855C2×C3—81no—
856C2×C3—81no—
857C2×C3—81no—
858C2×C3—81no—
859C2×C3—121no—
860C2×C3—161no—
861C2×C3—161no—
862C2×C3—241no—
863C2×C3D3×#12111yescharacteristic
864C2×C3C2×#91111yescharacteristic
865C2×C3#576811yescharacteristic
866C2×C3C2×C3×#12111yescharacteristic
867C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
868C2×C3C3×#57511yescharacteristic
869D3—22no—
870D3—41no—
871D3—81no—
872C22—21no—
873C22—21no—
874C22—32no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—61no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—61no—
886C22—124no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—244no—
891C22C3×#91112yescomplemented
892C22C2×C3×D3×D411yescharacteristic
893C4—21no—
894C4—32no—
895C4—41no—
896C4—41no—
897C4—61no—
898C4—121no—
899C4—121no—
900C4—121no—
901C4C2×C3×D3×D411yescharacteristic
902C4C3×D3×#4111yescharacteristic
903C3—21no—
904C3#8071511yescharacteristic, direct product factor
905C3C3×#305511yescharacteristic, complemented
906C2—22no—
907C2—62no—
908C2—81no—
909C2—81no—
910C2—121no—
911C2—241no—
912C2C3×D3×#12111yescharacteristic
913C2C2×C3×#91111yescharacteristic
914C2C3×#576811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#466C2
socleC22×C32C22×D4
hypercenterC3×#466D3
hypocenterC3C3×#3055
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#466

Complements

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

NH ≅ G/Ntype
1. C2×C3×#911C2semidirect
2. C22×C3×ΓL(1,𝔽25)C2semidirect
3. C3×#5606C2semidirect
4. C3×D3×#121C2semidirect
5. C32×#466C2semidirect
6. C3×#5159C2semidirect
7. C3×#5114C2semidirect
8. C3×#5041C2semidirect
9. C3×#5038C2semidirect
10. C3×#4886C2semidirect
11. C3×#4881C2semidirect
12. C3×#4782C2semidirect
13. C3×#4780C2semidirect
14. C3×#4771C2semidirect
15. C3×#4770C2semidirect
17. #80715C3direct (N × H)
22. C2×C32×D8C22semidirect
23. C22×C32×C8C22semidirect
25. C32×#121C22semidirect
28. C3×#938C22semidirect
31. C2×C3×#214C22semidirect
32. C2×C3×#213C22semidirect
34. C3×#924C22semidirect
35. C22×C3×C3⋊C8C22semidirect
37. C2×C3×#204C22semidirect
41. C2×C3×ΓL(1,𝔽25)C22semidirect
42. C2×C3×ΓL(1,𝔽25)C22semidirect
43. C3×#897C22semidirect
51. C32×#107C22semidirect
52. C32×#102C22semidirect
53. C32×#102C22semidirect
54. C3×#832C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×#817C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. C3×#808C22semidirect
62. C3×#807C22semidirect
67. C2×#911C2×C3semidirect
68. C22×ΓL(1,𝔽25)C2×C3semidirect
69. #5606C2×C3semidirect
70. D3×#121C2×C3semidirect
77. C3×#466D3semidirect
78. C3×#466C2×C3semidirect
84. #5159C2×C3semidirect
85. #5114C2×C3semidirect
86. #5041C2×C3semidirect
87. #5038C2×C3semidirect
88. #4886C2×C3semidirect
89. #4881C2×C3semidirect
90. #4782C2×C3semidirect
91. #4780C2×C3semidirect
92. #4771C2×C3semidirect
93. #4770C2×C3semidirect
153. C3×ΓL(1,𝔽25)D4semidirect
168. C2×C3×D8C2×D3semidirect
169. C2×C3×D8C22×C3semidirect
177. C22×C3×C8C2×D3semidirect
178. C22×C3×C8C22×C3semidirect
191. C3×#121C2×D3semidirect
193. C3×#121C22×C3semidirect
202. #938C22×C3semidirect
205. C2×#214C22×C3semidirect
206. C2×#213C22×C3semidirect
208. #924C22×C3semidirect
209. C22×C3⋊C8C22×C3semidirect
211. C2×#204C22×C3semidirect
215. C2×ΓL(1,𝔽25)C22×C3semidirect
216. C2×ΓL(1,𝔽25)C22×C3semidirect
217. #897C22×C3semidirect
227. C3×#107C2×D3semidirect
228. C3×#107C22×C3semidirect
239. C3×#102C2×D3semidirect
240. C3×#102C2×D3semidirect
241. C3×#102C22×C3semidirect
242. C3×#102C22×C3semidirect
243. #832C22×C3semidirect
244. #832C22×C3semidirect
245. #821C22×C3semidirect
246. #817C22×C3semidirect
247. #816C22×C3semidirect
248. #810C22×C3semidirect
249. #809C22×C3semidirect
250. #808C22×C3semidirect
251. #807C22×C3semidirect
301. C32×C8C2×D4semidirect
303. C3×C3⋊C8C2×D4semidirect
313. #466C3×D3semidirect
451. ΓL(1,𝔽25)C3×D4semidirect
460. C22×C32AGL(1,ℤ/8)semidirect
491. C2×D8C2×C3×D3semidirect
498. C22×C8C2×C3×D3semidirect
509. #121C2×C3×D3semidirect
517. #107C2×C3×D3semidirect
526. #102C2×C3×D3semidirect
527. #102C2×C3×D3semidirect
645. C3×C8D3×D4semidirect
646. C3×C8C2×C3×D4semidirect
648. C3⋊C8C2×C3×D4semidirect
755. C22×C3#911semidirect
756. C22×C3C3×AGL(1,ℤ/8)semidirect
795. C32#3055semidirect
847. C8C3×D3×D4semidirect
891. C22C3×#911semidirect
904. C3#80715direct (N × H)
905. C3C3×#3055semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9112
C22×C3×ΓL(1,𝔽25)2
C3×#56062
C3×D3×#1212
C32×#4662
C3×#51592
C3×#51142
C3×#50412
C3×#50382
C3×#48862
C3×#48812
C3×#47822
C3×#47802
C3×#47712
C3×#47702
C3×#30553
#807153