Finite Group Databasebeta

← C3×#79794 #11883919

Subgroups — C3×#79794 #11883919

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic, complemented
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3C3×#5576C211yesmaximal, characteristic, complemented
4C3×D4×D12C211yesmaximal, characteristic, complemented
5C32×#440C211yesmaximal, characteristic, complemented
6C3×#5027C211yesmaximal, characteristic, complemented
7C3×#5016C211yesmaximal, characteristic, complemented
8C3×#4886C211yesmaximal, characteristic, complemented
9C3×#4883C211yesmaximal, characteristic, complemented
10C3×#4810C211yesmaximal, characteristic, complemented
11C3×#4806C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic, complemented
13C3×#4773C211yesmaximal, characteristic, complemented
14C3×#4712C211yesmaximal, characteristic, complemented
15C3×#4706C211yesmaximal, characteristic, complemented
16C3×#3265—31nomaximal
17#79794C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C22×C3×D12—21no—
23C2×C32×SD16C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic, complemented
25C32×C4×D4C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C2×C3×#214C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#930—21no—
31C3×#914—24no—
32C3×D3×SD16—24no—
33C2×C3×D24C2211yescharacteristic, complemented
34C2×C3×D24C2211yescharacteristic, complemented
35C2×C3×#204C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic, complemented
39C3×#897—21no—
40C3×#897C2211yescharacteristic, complemented
41C3×#895—21no—
42C3×#895C2211yescharacteristic
43C3×#895C2211yescharacteristic
44C3×#895C2211yescharacteristic, complemented
45C3×#882—21no—
46C3×#882—21no—
47C3×#875—21no—
48C3×#875C2211yescharacteristic, complemented
49C3×#874C2211yescharacteristic
50C3×C4×D12—21no—
51C3×C4×D12C2211yescharacteristic
52C32×#107C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic
55C32×#97C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59C3×#809C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic, complemented
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×SD16—31no—
65C3×#548—31no—
66C3×D42—31no—
67C2×#914C2×C311yescharacteristic, complemented
68C2×D3×SD16C2×C311yescharacteristic, complemented
69#5576C2×C311yescharacteristic, complemented
70D4×D12C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#468—31no—
73C3×#466—31no—
74C3×#463—31no—
75C3×#460—31no—
76C3×#450—31no—
77C3×#449—31no—
78C3×#448—31no—
79C3×#447—31no—
80C3×#440—21no—
81C3×#440D311yescharacteristic, complemented
82C3×#440C2×C311yescharacteristic, complemented
83C3×#435—31no—
84#5027C2×C311yescharacteristic, complemented
85#5016C2×C311yescharacteristic, complemented
86#4886C2×C311yescharacteristic, complemented
87#4883C2×C311yescharacteristic, complemented
88#4810C2×C311yescharacteristic, complemented
89#4806C2×C311yescharacteristic, complemented
90#4776C2×C311yescharacteristic, complemented
91#4773C2×C311yescharacteristic, complemented
92#4712C2×C311yescharacteristic, complemented
93#4706C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×#239—22no—
102C3×#239—41no—
103C3×D3×Q8—22no—
104C3×D3×Q8—41no—
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C3×D3×D4—41no—
108C3×D3×D4—41no—
109C2×C3×D12—21no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12—44no—
116C2×C3×D12D411yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6—21no—
125C2×C3×Dic6C2311yescharacteristic
126C32×SD16D414yescomplemented
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129C32×C4⋊C4—21no—
130C32×C4⋊C4C2311yescharacteristic
131C32×C4⋊C4C2311yescharacteristic
132C32×C22⋊C4—21no—
133C32×C42—21no—
134C32×C42C2311yescharacteristic
135C3×#215—22no—
136C3×#215—22no—
137C3×#214—22no—
138C3×#213—22no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4D411yescharacteristic
146C3×(C2×D3)⋊C4D411yescharacteristic
147C3×C4⋊Dic3—21no—
148C3×C4⋊Dic3D411yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C3×D24—22no—
152C3×D24—41no—
153C3×#204—22no—
154C3×#204—41no—
155C3×ΓL(1,𝔽25)—22no—
156C3×D3×C8—22no—
157#3265—31noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C22×C3×D4—61no—
163C2×#239C22×C311yescharacteristic, complemented
164C2×D3×Q8C22×C311yescharacteristic, complemented
165C2×D3×D4C22×C311yescharacteristic
166C2×D3×D4C22×C311yescharacteristic
167C22×D12—21no—
168C3×AGL(1,ℤ/8)—64no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—64no—
176C2×C3×SD16C2×D311yescharacteristic
177C2×C3×SD16C22×C311yescharacteristic
178C2×C3×D8—31no—
179C2×C3×D8—31no—
180C2×C3×D8—31no—
181C2×C3×M16—31no—
182C22×C3×C8—31no—
183C3×#127—31no—
184C3×#124—31no—
185C3×#124—61no—
186C3×C22⋊Q8—31no—
187C3×C22⋊Q8—61no—
188C3×#121—31no—
189C3×#121—31no—
190C3×#121—31no—
191C3×#121—61no—
192C3×#121—61no—
193C3×#120—61no—
194C3×#120—61no—
195C3×C4×Q8—21no—
196C3×C4×Q8C2×D311yescharacteristic, complemented
197C3×C4×Q8C22×C311yescharacteristic, complemented
198C3×C4×D4—21no—
199C3×C4×D4—31no—
200C3×C4×D4—61no—
201C3×C4×D4C2×D311yescharacteristic
202C3×C4×D4C22×C311yescharacteristic
203C2×#215C22×C311yescharacteristic, complemented
204C2×#215C22×C311yescharacteristic, complemented
205C2×#214C22×C311yescharacteristic
206C2×#213C22×C311yescharacteristic
207#930—21no—
208#914—24no—
209D3×SD16—24no—
210C2×D24C22×C311yescharacteristic, complemented
211C2×D24C22×C311yescharacteristic, complemented
212C2×#204C22×C311yescharacteristic, complemented
213C2×#204C22×C311yescharacteristic, complemented
214C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
215C2×D3×C8C22×C311yescharacteristic, complemented
216#897—21no—
217#897C22×C311yescharacteristic, complemented
218#895—21no—
219#895C22×C311yescharacteristic
220#895C22×C311yescharacteristic
221#895C22×C311yescharacteristic, complemented
222#882—21no—
223#882—21no—
224#875—21no—
225#875C22×C311yescharacteristic, complemented
226#874C22×C311yescharacteristic
227C4×D12—21no—
228C4×D12C22×C311yescharacteristic
229C3×#107—21no—
230C3×#107C2×D311yescharacteristic, complemented
231C3×#107C22×C311yescharacteristic, complemented
232C3×C4⋊C8—31no—
233C3×#103—21no—
234C3×#103—31no—
235C3×#103C2×D311yescharacteristic, complemented
236C3×#103C22×C311yescharacteristic, complemented
237C3×#102—21no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102C2×D311yescharacteristic
242C3×#102C22×C311yescharacteristic
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—21no—
246C3×#97C2×D311yescharacteristic, complemented
247C3×#97C22×C311yescharacteristic, complemented
248(C2×D3)⋊C8C22×C311yescharacteristic, complemented
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250#810C22×C311yescharacteristic, complemented
251#809C22×C311yescharacteristic, complemented
252#809C22×C311yescharacteristic, complemented
253#809C22×C311yescharacteristic, complemented
254C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
255C23×C32—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—81no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C32×Q8—21no—
268C32×Q8C2×D412yescomplemented
269C32×D4—21no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—22no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12—42no—
292C3×D12—42no—
293C3×D12—42no—
294C3×D12—42no—
295C3×D12—81no—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298C3×C4×D3—21no—
299C3×C4×D3—21no—
300C3×C4×D3—42no—
301C3×C4×D3—42no—
302C3×Dic6—21no—
303C3×Dic6—21no—
304C3×Dic6—42no—
305C32×C8—21no—
306C32×C8C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—31no—
310C22×SD16—31no—
311#548—31no—
312D42—31no—
313#496—31no—
314#468—31no—
315#466—31no—
316#463—31no—
317#460—31no—
318#450—31no—
319#449—31no—
320#448—31no—
321#447—31no—
322#440C3×D311yescharacteristic, complemented
323#435—31no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8—61no—
333C2×C3×Q8—62no—
334C2×C3×Q8—121no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C23×C311yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—62no—
349C2×C3×D4—62no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—124no—
353C2×C3×D4—121no—
354C2×C3×D4—121no—
355C2×C3×D4C22×D311yescharacteristic
356C2×C3×D4C23×C311yescharacteristic
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—41no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C2×#67—21no—
365C2×#67—21no—
366#239—22no—
367#239—41no—
368D3×Q8—22no—
369D3×Q8—41no—
370D3×D4—22no—
371D3×D4—22no—
372D3×D4—41no—
373D3×D4—41no—
374C2×D12—21no—
375C2×D12—21no—
376C2×D12—21no—
377C2×D12—21no—
378C2×D12—21no—
379C2×D12—21no—
380C2×D12—44no—
381C2×D12C3×D411yescharacteristic
382C2×D12C23×C311yescharacteristic
383C2×D12C23×C311yescharacteristic
384C2×D12C23×C311yescharacteristic
385C2×C4×D3—21no—
386C2×C4×D3—21no—
387C2×C4×D3C23×C311yescharacteristic
388C2×C4×D3C23×C311yescharacteristic
389C2×Dic6—21no—
390C2×Dic6C23×C311yescharacteristic
391C3×SD16—24no—
392C3×SD16—62no—
393C3×SD16—62no—
394C3×SD16—62no—
395C3×SD16—62no—
396C3×SD16—121no—
397C3×SD16D1214yescomplemented
398C3×SD16C3×D414yescomplemented
399C3×D8—62no—
400C3×D8—62no—
401C3×D8—121no—
402C3×M16—62no—
403C2×C3×C8—21no—
404C2×C3×C8—21no—
405C2×C3×C8—31no—
406C2×C3×C8—31no—
407C2×C3×C8—62no—
408C2×C3×C8C22×D311yescharacteristic
409C2×C3×C8C22×D311yescharacteristic
410C2×C3×C8C23×C311yescharacteristic
411C2×C3×C8C23×C311yescharacteristic
412C3×C4⋊C4—21no—
413C3×C4⋊C4—21no—
414C3×C4⋊C4—21no—
415C3×C4⋊C4—21no—
416C3×C4⋊C4—31no—
417C3×C4⋊C4—41no—
418C3×C4⋊C4—61no—
419C3×C4⋊C4C22×D311yescharacteristic
420C3×C4⋊C4C22×D311yescharacteristic
421C3×C4⋊C4C23×C311yescharacteristic
422C3×C4⋊C4C23×C311yescharacteristic
423C3×C22⋊C4—21no—
424C3×C22⋊C4—21no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—41no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C22⋊C4—61no—
434C3×C42—21no—
435C3×C42—21no—
436C3×C42—21no—
437C3×C42—41no—
438C3×C42C22×D311yescharacteristic
439C3×C42C23×C311yescharacteristic
440#215—22no—
441#215—22no—
442#214—22no—
443#213—22no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—21no—
449(C2×D3)⋊C4—21no—
450(C2×D3)⋊C4C3×D411yescharacteristic
451(C2×D3)⋊C4C3×D411yescharacteristic
452C4⋊Dic3—21no—
453C4⋊Dic3C3×D411yescharacteristic
454C2×C3⋊C8C23×C311yescharacteristic
455C2×C3⋊C8C23×C311yescharacteristic
456D24—22no—
457D24—41no—
458#204—22no—
459#204—41no—
460ΓL(1,𝔽25)—22no—
461D3×C8—22no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32C22×D411yescharacteristic
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—84no—
481C2×C3×D3—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483C32×C4—22no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—41no—
487C32×C4—41no—
488C32×C4C22×D411yescharacteristic
489C32×C4H(5,𝔽2)11yescharacteristic
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C2×#41—31no—
494C22×Q8—31no—
495C22×D4—31no—
496C22×D4—31no—
497C22×D4—61no—
498AGL(1,ℤ/8)—64no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—31no—
504C2×SD16—64no—
505C2×SD16C2×C3×D311yescharacteristic
506C2×D8—31no—
507C2×D8—31no—
508C2×D8—31no—
509C2×M16—31no—
510C22×C8—31no—
511#127—31no—
512#124—31no—
513#124—61no—
514C22⋊Q8—31no—
515C22⋊Q8—61no—
516#121—31no—
517#121—31no—
518#121—31no—
519#121—61no—
520#121—61no—
521#120—61no—
522#120—61no—
523C4×Q8C2×C3×D311yescharacteristic, complemented
524C4×D4—31no—
525C4×D4—61no—
526C4×D4C2×C3×D311yescharacteristic
527#107C2×C3×D311yescharacteristic, complemented
528C4⋊C8—31no—
529#103—31no—
530#103C2×C3×D311yescharacteristic, complemented
531#102—31no—
532#102—31no—
533#102—31no—
534#102C2×C3×D311yescharacteristic
535C22⋊C8—31no—
536C22⋊C8—31no—
537#97C2×C3×D311yescharacteristic, complemented
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—241no—
551C23×C3—241no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—42no—
559C22×D3—81no—
560C22×D3—81no—
561C22×D3C2×C3×D411yescharacteristic
562C22×D3C2×C3×D411yescharacteristic
563C3×Q8—21no—
564C3×Q8—21no—
565C3×Q8—22no—
566C3×Q8—41no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—122no—
570C3×Q8C2×D1212yescomplemented
571C3×Q8C2×C3×D412yescomplemented
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—22no—
575C3×D4—41no—
576C3×D4—62no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—122no—
584C3×D4—122no—
585C3×D4—122no—
586C3×D4—122no—
587C3×D4—122no—
588C3×D4—122no—
589C3×D4—122no—
590C3×D4—241no—
591C3×D4C2×D1212yes—
592C3×D4C2×C3×D412yes—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—42no—
608C2×C3×C4—42no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—82no—
615C2×C3×C4—122no—
616C2×C3×C4—122no—
617C2×C3×C4D3×D411yescharacteristic
618C2×C3×C4D3×D411yescharacteristic
619C2×C3×C4C2×C3×D411yescharacteristic
620C2×C3×C4C2×C3×D411yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C24×C311yescharacteristic
623#67—42no—
624#67—42no—
625C2×Dic3—21no—
626C2×Dic3C2×C3×D411yescharacteristic
627C2×Dic3C2×C3×D411yescharacteristic
628D12—22no—
629D12—21no—
630D12—21no—
631D12—21no—
632D12—21no—
633D12—21no—
634D12—21no—
635D12—42no—
636D12—42no—
637D12—42no—
638D12—42no—
639D12—42no—
640D12—81no—
641C4×D3—21no—
642C4×D3—21no—
643C4×D3—21no—
644C4×D3—21no—
645C4×D3—42no—
646C4×D3—42no—
647Dic6—21no—
648Dic6—21no—
649Dic6—42no—
650C3×C8—21no—
651C3×C8—21no—
652C3×C8—22no—
653C3×C8—41no—
654C3×C8—61no—
655C3×C8—61no—
656C3×C8C2×D1212yescomplemented
657C3×C8C2×C3×D412yescomplemented
658C3⋊C8—21no—
659C3⋊C8—21no—
660C2×C32—42no—
661C2×C32D4211yescharacteristic
662C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
663C2×C32#57711yescharacteristic
664C3×D3—22no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C3×D3—81no—
669C24—61no—
670C24—61no—
671#41—62no—
672#41—121no—
673C2×Q8—31no—
674C2×Q8—61no—
675C2×Q8—62no—
676C2×Q8—121no—
677C2×Q8C22×C3×D311yescharacteristic
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—62no—
689C2×D4—62no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—124no—
693C2×D4—121no—
694C2×D4—121no—
695C2×D4C22×C3×D311yescharacteristic
696C22×C4—21no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—61no—
700C22×C4—61no—
701SD16—62no—
702SD16—62no—
703SD16—62no—
704SD16—62no—
705SD16—121no—
706SD16C3×D1214yescomplemented
707D8—62no—
708D8—62no—
709D8—121no—
710M16—62no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—62no—
714C2×C8C22×C3×D311yescharacteristic
715C2×C8C22×C3×D311yescharacteristic
716C4⋊C4—21no—
717C4⋊C4—31no—
718C4⋊C4—61no—
719C4⋊C4C22×C3×D311yescharacteristic
720C4⋊C4C22×C3×D311yescharacteristic
721C22⋊C4—21no—
722C22⋊C4—31no—
723C22⋊C4—31no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C42—21no—
731C42C22×C3×D311yescharacteristic
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—21no—
735C22×C3—32no—
736C22×C3—42no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3—244no—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C22×C3×D411yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—84no—
776C2×D3—84no—
777C2×D3C3×AGL(1,ℤ/8)12yescomplemented
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—42no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—81no—
796C3×C4—81no—
797C3×C4—121no—
798C3×C4C22×D1211yescharacteristic
799C3×C4#100911yescharacteristic
800C3×C4C22×C3×D411yescharacteristic
801C3×C4C3×H(5,𝔽2)11yescharacteristic
802Dic3—21no—
803Dic3—21no—
804Dic3—41no—
805C32#326511yescharacteristic, complemented, Sylow
806C23—21no—
807C23—31no—
808C23—31no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—122no—
813C23—122no—
814C23—122no—
815C23—122no—
816C23—241no—
817C23—241no—
818Q8—21no—
819Q8—61no—
820Q8—61no—
821Q8—122no—
822Q8C2×C3×D1212yescomplemented
823D4—21no—
824D4—62no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—61no—
831D4—122no—
832D4—122no—
833D4—122no—
834D4—122no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—241no—
839D4C2×C3×D1212yes—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—42no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—122no—
852C2×C4—122no—
853C2×C4C3×D3×D411yescharacteristic
854C2×C4C3×D3×D411yescharacteristic
855C2×C4C23×C3×D311yescharacteristic
856C8—21no—
857C8—61no—
858C8—61no—
859C8C2×C3×D1212yescomplemented
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—42no—
864C2×C3—42no—
865C2×C3—62no—
866C2×C3—82no—
867C2×C3—121no—
868C2×C3—241no—
869C2×C3—241no—
870C2×C3—241no—
871C2×C3D4×D1211yescharacteristic
872C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
873C2×C3#577811yescharacteristic
874C2×C3C3×D4211yescharacteristic
875C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
876C2×C3C3×#57711yescharacteristic
877D3—22no—
878D3—41no—
879D3—81no—
880D3—81no—
881D3—81no—
882C22—22no—
883C22—32no—
884C22—41no—
885C22—41no—
886C22—61no—
887C22—61no—
888C22—61no—
889C22—61no—
890C22—61no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—244no—
901C22—244no—
902C22C2×C3×D3×D411yescharacteristic
903C4—21no—
904C4—21no—
905C4—22no—
906C4—41no—
907C4—41no—
908C4—61no—
909C4—61no—
910C4—121no—
911C4C22×C3×D1211yescharacteristic
912C4C3×#100911yescharacteristic
913C3—21no—
914C3#7979411yescharacteristic, direct product factor
915C3C3×#326511yescharacteristic, complemented
916C2—42no—
917C2—62no—
918C2—121no—
919C2—241no—
920C2—241no—
921C2—241no—
922C2C3×D4×D1211yescharacteristic
923C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
924C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
hypercenterC3×#440D3
hypocenterC3C3×#3265
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. C2×C3×D3×SD16C2semidirect
3. C3×#5576C2semidirect
4. C3×D4×D12C2semidirect
5. C32×#440C2semidirect
6. C3×#5027C2semidirect
7. C3×#5016C2semidirect
8. C3×#4886C2semidirect
9. C3×#4883C2semidirect
10. C3×#4810C2semidirect
11. C3×#4806C2semidirect
12. C3×#4776C2semidirect
13. C3×#4773C2semidirect
14. C3×#4712C2semidirect
15. C3×#4706C2semidirect
17. #79794C3direct (N × H)
18. C2×C3×#239C22semidirect
19. C2×C3×D3×Q8C22semidirect
24. C32×C4×Q8C22semidirect
26. C2×C3×#215C22semidirect
27. C2×C3×#215C22semidirect
33. C2×C3×D24C22semidirect
34. C2×C3×D24C22semidirect
35. C2×C3×#204C22semidirect
36. C2×C3×#204C22semidirect
37. C2×C3×ΓL(1,𝔽25)C22semidirect
38. C2×C3×D3×C8C22semidirect
40. C3×#897C22semidirect
44. C3×#895C22semidirect
48. C3×#875C22semidirect
52. C32×#107C22semidirect
53. C32×#103C22semidirect
55. C32×#97C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#810C22semidirect
59. C3×#809C22semidirect
60. C3×#809C22semidirect
61. C3×#809C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#914C2×C3semidirect
68. C2×D3×SD16C2×C3semidirect
69. #5576C2×C3semidirect
70. D4×D12C2×C3semidirect
81. C3×#440D3semidirect
82. C3×#440C2×C3semidirect
84. #5027C2×C3semidirect
85. #5016C2×C3semidirect
86. #4886C2×C3semidirect
87. #4883C2×C3semidirect
88. #4810C2×C3semidirect
89. #4806C2×C3semidirect
90. #4776C2×C3semidirect
91. #4773C2×C3semidirect
92. #4712C2×C3semidirect
93. #4706C2×C3semidirect
126. C32×SD16D4semidirect
163. C2×#239C22×C3semidirect
164. C2×D3×Q8C22×C3semidirect
196. C3×C4×Q8C2×D3semidirect
197. C3×C4×Q8C22×C3semidirect
203. C2×#215C22×C3semidirect
204. C2×#215C22×C3semidirect
210. C2×D24C22×C3semidirect
211. C2×D24C22×C3semidirect
212. C2×#204C22×C3semidirect
213. C2×#204C22×C3semidirect
214. C2×ΓL(1,𝔽25)C22×C3semidirect
215. C2×D3×C8C22×C3semidirect
217. #897C22×C3semidirect
221. #895C22×C3semidirect
225. #875C22×C3semidirect
230. C3×#107C2×D3semidirect
231. C3×#107C22×C3semidirect
235. C3×#103C2×D3semidirect
236. C3×#103C22×C3semidirect
246. C3×#97C2×D3semidirect
247. C3×#97C22×C3semidirect
248. (C2×D3)⋊C8C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. #810C22×C3semidirect
251. #809C22×C3semidirect
252. #809C22×C3semidirect
253. #809C22×C3semidirect
254. C4⋊(C3⋊C8)C22×C3semidirect
268. C32×Q8C2×D4semidirect
306. C32×C8C2×D4semidirect
322. #440C3×D3semidirect
397. C3×SD16D12semidirect
398. C3×SD16C3×D4semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
523. C4×Q8C2×C3×D3semidirect
527. #107C2×C3×D3semidirect
530. #103C2×C3×D3semidirect
537. #97C2×C3×D3semidirect
570. C3×Q8C2×D12semidirect
571. C3×Q8C2×C3×D4semidirect
656. C3×C8C2×D12semidirect
657. C3×C8C2×C3×D4semidirect
706. SD16C3×D12semidirect
777. C2×D3C3×AGL(1,ℤ/8)semidirect
805. C32#3265semidirect
822. Q8C2×C3×D12semidirect
859. C8C2×C3×D12semidirect
914. C3#79794direct (N × H)
915. C3C3×#3265semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
C2×C3×D3×SD162
C3×#55762
C3×D4×D122
C32×#4402
C3×#50272
C3×#50162
C3×#48862
C3×#48832
C3×#48102
C3×#48062
C3×#47762
C3×#47732
C3×#47122
C3×#47062
C3×#32653
#797943