Finite Group Databasebeta

← C3×#80204 #11884047

Subgroups — C3×#80204 #11884047

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×C3×#918C211yesmaximal, characteristic, complemented
4C3×#5630C211yesmaximal, characteristic
5C32×#451C211yesmaximal, characteristic, complemented
6C3×#5190C211yesmaximal, characteristic, complemented
7C3×#5187C211yesmaximal, characteristic, complemented
8C3×#5185C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#4818C211yesmaximal, characteristic, complemented
11C3×#4817C211yesmaximal, characteristic, complemented
12C3×#4812C211yesmaximal, characteristic, complemented
13C3×#4806C211yesmaximal, characteristic, complemented
14C3×#4731C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#80204C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×C32×Q16C2211yescharacteristic, complemented
24C32×C22⋊Q8C2211yescharacteristic
25C3×#947C2211yescharacteristic
26C3×#946—21no—
27C3×#946C2211yescharacteristic, complemented
28C3×Q8×Dic3C2211yescharacteristic, complemented
29C3×#944—21no—
30C3×#944C2211yescharacteristic, complemented
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#215—24no—
33C2×C3×#215C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic
35C2×C3×#215C2211yescharacteristic
36C2×C3×#215C2211yescharacteristic
37C3×C4×#67—21no—
38C3×C4×#67C2211yescharacteristic
39C3×#924—21no—
40C3×#924C2211yescharacteristic
41C22×C3×C3⋊C8C2211yescharacteristic
42C3×#918—24no—
43C2×C3×#204C2211yescharacteristic
44C2×C3×#204C2211yescharacteristic
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
46C3×#895—21no—
47C3×#895C2211yescharacteristic
48C3×#894—21no—
49C3×#893C2211yescharacteristic
50C3×#882—21no—
51C3×D3×C22⋊C4—21no—
52C32×#103C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×C22⋊C8C2211yescharacteristic
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic
57C3×#821C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×Dic3⋊C8C2211yescharacteristic, complemented
61C3×#810C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—31no—
67Q8×#67C2×C311yescharacteristic, complemented
68C22×#215C2×C311yescharacteristic, complemented
69C2×#918C2×C311yescharacteristic, complemented
70#5630C2×C311yescharacteristic
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—31no—
74C3×#464—31no—
75C3×#461—31no—
76C3×#452—31no—
77C3×#451—21no—
78C3×#451D311yescharacteristic, complemented
79C3×#451C2×C311yescharacteristic, complemented
80C3×#450—31no—
81C3×#448—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5190C2×C311yescharacteristic, complemented
85#5187C2×C311yescharacteristic, complemented
86#5185C2×C311yescharacteristic, complemented
87#5051C2×C311yescharacteristic, complemented
88#4818C2×C311yescharacteristic, complemented
89#4817C2×C311yescharacteristic, complemented
90#4812C2×C311yescharacteristic, complemented
91#4806C2×C311yescharacteristic, complemented
92#4731C2×C311yescharacteristic, complemented
93#4730C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8—21no—
96C2×C32×Q8—22no—
97C2×C32×Q8—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67D411yescharacteristic
104C3×#239—22no—
105C3×#239—41no—
106C3×D3×Q8—22no—
107C3×D3×Q8—41no—
108C2×C3×D12—22no—
109C2×C3×D12—21no—
110C2×C3×D12—21no—
111C2×C3×D12—21no—
112C2×C3×D12—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6—21no—
120C2×C3×Dic6C2311yescharacteristic
121C32×Q16—22no—
122C32×Q16—41no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4—21no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×#216—22no—
131C3×#215—22no—
132C3×#215—22no—
133C3×#215—22no—
134C3×#215D414yescomplemented
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)⋊C4D411yescharacteristic
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4D411yescharacteristic
148C3×C4×Dic3—21no—
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×#204—22no—
154C3×#204—41no—
155C3×ΓL(1,𝔽25)—22no—
156#3266—31noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—21no—
159C22×C3×Q8—31no—
160C22×C3×Q8C2×D311yescharacteristic
161C22×C3×Q8C22×C311yescharacteristic
162C22×C3×D4—31no—
163C2×#239C22×C311yescharacteristic
164C2×D3×Q8C22×C311yescharacteristic, complemented
165C22×D12C22×C311yescharacteristic
166C3×#137—64no—
167C2×C3×Q16—21no—
168C2×C3×Q16—21no—
169C2×C3×Q16—31no—
170C2×C3×Q16C2×D311yescharacteristic, complemented
171C2×C3×Q16C2×D311yescharacteristic, complemented
172C2×C3×Q16C22×C311yescharacteristic, complemented
173C2×C3×Q16C22×C311yescharacteristic, complemented
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16—31no—
178C2×C3×SD16—31no—
179C2×C3×SD16—31no—
180C2×C3×SD16—64no—
181C2×C3×M16—31no—
182C22×C3×C8—31no—
183C3×C4⋊Q8—31no—
184C3×C4⋊Q8—61no—
185C3×#124—31no—
186C3×#123—61no—
187C3×C22⋊Q8—21no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—61no—
191C3×C22⋊Q8—61no—
192C3×C22⋊Q8C2×D311yescharacteristic
193C3×C22⋊Q8C22×C311yescharacteristic
194C3×#121—31no—
195C3×#121—61no—
196C3×#120—61no—
197C3×C4×Q8—31no—
198C3×C4×D4—31no—
199C3×C4×D4—31no—
200C3×C4×D4—61no—
201C2×C3×C22⋊C4—61no—
202#947C22×C311yescharacteristic
203#946—21no—
204#946C22×C311yescharacteristic, complemented
205Q8×Dic3C22×C311yescharacteristic, complemented
206#944—21no—
207#944C22×C311yescharacteristic, complemented
208C2×#216C22×C311yescharacteristic, complemented
209C2×#215—24no—
210C2×#215C22×C311yescharacteristic
211C2×#215C22×C311yescharacteristic
212C2×#215C22×C311yescharacteristic
213C2×#215C22×C311yescharacteristic
214C4×#67—21no—
215C4×#67C22×C311yescharacteristic
216#924—21no—
217#924C22×C311yescharacteristic
218C22×C3⋊C8C22×C311yescharacteristic
219#918—24no—
220C2×#204C22×C311yescharacteristic
221C2×#204C22×C311yescharacteristic
222C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
223#895—21no—
224#895C22×C311yescharacteristic
225#894—21no—
226#893C22×C311yescharacteristic
227#882—21no—
228D3×C22⋊C4—21no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—21no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103C2×D311yescharacteristic, complemented
236C3×#103C2×D311yescharacteristic, complemented
237C3×#103C22×C311yescharacteristic, complemented
238C3×#103C22×C311yescharacteristic, complemented
239C3×#102—31no—
240C3×#102—31no—
241C3×C22⋊C8—21no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8C2×D311yescharacteristic
244C3×C22⋊C8C22×C311yescharacteristic
245C3×#97—31no—
246#835C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic
248#821C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250#815C22×C311yescharacteristic, complemented
251Dic3⋊C8C22×C311yescharacteristic, complemented
252#810C22×C311yescharacteristic, complemented
253#807C22×C311yescharacteristic, complemented
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×Q8—42no—
267C32×Q8C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277C3×#67—22no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×D12—42no—
288C3×D12—81no—
289C3×D12C2×D412yes—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×C4×D3—81no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—42no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—31no—
303C22×SD16—31no—
304D4×Q8—31no—
305#546—31no—
306#497—31no—
307#468—31no—
308#467—31no—
309#464—31no—
310#461—31no—
311#452—31no—
312#451C3×D311yescharacteristic, complemented
313#450—31no—
314#448—31no—
315#440—31no—
316#435—31no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—21no—
323C2×C3×Q8—22no—
324C2×C3×Q8—22no—
325C2×C3×Q8—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8—41no—
330C2×C3×Q8—42no—
331C2×C3×Q8—41no—
332C2×C3×Q8—41no—
333C2×C3×Q8—42no—
334C2×C3×Q8—61no—
335C2×C3×Q8—62no—
336C2×C3×Q8—121no—
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×Q8C22×D311yescharacteristic
339C2×C3×Q8C22×D311yescharacteristic
340C2×C3×Q8C23×C311yescharacteristic
341C2×C3×Q8C23×C311yescharacteristic
342C2×C3×Q8C23×C311yescharacteristic
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—31no—
346C2×C3×D4—62no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—121no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—41no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4—61no—
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C23×C311yescharacteristic
361C2×#67C3×D411yescharacteristic
362#239—22no—
363#239—41no—
364D3×Q8—22no—
365D3×Q8—41no—
366C2×D12—22no—
367C2×D12—21no—
368C2×D12—21no—
369C2×D12—21no—
370C2×D12—41no—
371C2×D12C23×C311yescharacteristic
372C2×D12C23×C311yescharacteristic
373C2×C4×D3—21no—
374C2×C4×D3—21no—
375C2×C4×D3—21no—
376C2×C4×D3C23×C311yescharacteristic
377C2×Dic6—21no—
378C2×Dic6C23×C311yescharacteristic
379C3×Q16—22no—
380C3×Q16—22no—
381C3×Q16—42no—
382C3×Q16—41no—
383C3×Q16—41no—
384C3×Q16—42no—
385C3×Q16—62no—
386C3×SD16—34no—
387C3×SD16—62no—
388C3×SD16—62no—
389C3×SD16—62no—
390C3×SD16—62no—
391C3×SD16—121no—
392C3×M16—62no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—62no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C23×C311yescharacteristic
401C2×C3×C8C23×C311yescharacteristic
402C3×C4⋊C4—21no—
403C3×C4⋊C4—21no—
404C3×C4⋊C4—21no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—41no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4—61no—
412C3×C4⋊C4—61no—
413C3×C4⋊C4C22×D311yescharacteristic
414C3×C4⋊C4C23×C311yescharacteristic
415C3×C22⋊C4—21no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—31no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—41no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C42—31no—
427C3×C42—61no—
428#217—21no—
429#217C3×D411yescharacteristic
430#216—22no—
431#215—22no—
432#215—22no—
433#215—22no—
434#215C3×D414yescomplemented
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4—21no—
440(C2×D3)⋊C4C3×D411yescharacteristic
441C4⋊Dic3—21no—
442C4⋊Dic3C23×C311yescharacteristic
443Dic3⋊C4—21no—
444Dic3⋊C4—21no—
445Dic3⋊C4—21no—
446Dic3⋊C4—21no—
447Dic3⋊C4C3×D411yescharacteristic
448C4×Dic3—21no—
449C4×Dic3C23×C311yescharacteristic
450C2×C3⋊C8—22no—
451C2×C3⋊C8C23×C311yescharacteristic
452C2×C3⋊C8C23×C311yescharacteristic
453#204—22no—
454#204—41no—
455ΓL(1,𝔽25)—22no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32#13712yescomplemented
459C22×C32C22×D411yescharacteristic
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—84no—
470C32×C4—22no—
471C32×C4—21no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C22×Q8—31no—
484C22×Q8C2×C3×D311yescharacteristic
485C22×D4—31no—
486#137—64no—
487C2×Q16—31no—
488C2×Q16C2×C3×D311yescharacteristic, complemented
489C2×Q16C2×C3×D311yescharacteristic, complemented
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—31no—
496C2×SD16—64no—
497C2×M16—31no—
498C22×C8—31no—
499C4⋊Q8—31no—
500C4⋊Q8—61no—
501#124—31no—
502#123—61no—
503C22⋊Q8—31no—
504C22⋊Q8—31no—
505C22⋊Q8—61no—
506C22⋊Q8—61no—
507C22⋊Q8C2×C3×D311yescharacteristic
508#121—31no—
509#121—61no—
510#120—61no—
511C4×Q8—31no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—61no—
515C2×C22⋊C4—61no—
516#107—31no—
517C4⋊C8—31no—
518#103—31no—
519#103—31no—
520#103C2×C3×D311yescharacteristic, complemented
521#103C2×C3×D311yescharacteristic, complemented
522#102—31no—
523#102—31no—
524C22⋊C8—31no—
525C22⋊C8C2×C3×D311yescharacteristic
526#97—31no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C23×C3—241no—
534C23×C3D3×D411yescharacteristic
535C23×C3C2×C3×D411yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—81no—
541C22×D3C2×C3×D411yescharacteristic
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—22no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—22no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×Q8—41no—
557C3×Q8—41no—
558C3×Q8—42no—
559C3×Q8—42no—
560C3×Q8—44no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×Q8—122no—
564C3×Q8D3×D412yes—
565C3×Q8C2×C3×D412yes—
566C3×D4—32no—
567C3×D4—62no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—241no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
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—31no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—42no—
598C2×C3×C4—42no—
599C2×C3×C4—44no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—122no—
605C2×C3×C4—122no—
606C2×C3×C4—241no—
607C2×C3×C4D3×D411yescharacteristic
608C2×C3×C4C2×C3×D411yescharacteristic
609C2×C3×C4C23×D311yescharacteristic
610C2×C3×C4C24×C311yescharacteristic
611#67—22no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3C2×C3×D411yescharacteristic
615C2×Dic3C2×C3×D411yescharacteristic
616C2×Dic3C2×C3×D411yescharacteristic
617D12—21no—
618D12—21no—
619D12—21no—
620D12—42no—
621D12—42no—
622D12—81no—
623D12C2×C3×D412yes—
624C4×D3—21no—
625C4×D3—21no—
626C4×D3—42no—
627C4×D3—42no—
628C4×D3—81no—
629Dic6—21no—
630Dic6—21no—
631Dic6—42no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—32no—
637C3×C8—41no—
638C3×C8—41no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8C2×C3×D412yes—
642C2×C32—22no—
643C2×C32D4211yescharacteristic
644C2×C32C2×#13711yescharacteristic
645C2×C32#57711yescharacteristic
646C3×D3—41no—
647C3×D3—42no—
648C3×D3—81no—
649C24—61no—
650#41—62no—
651#41—121no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—31no—
655C2×Q8—41no—
656C2×Q8—61no—
657C2×Q8—62no—
658C2×Q8—121no—
659C2×Q8C22×C3×D311yescharacteristic
660C2×Q8C22×C3×D311yescharacteristic
661C2×Q8C22×C3×D311yescharacteristic
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—61no—
669C2×D4—121no—
670C22×C4—21no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4C22×C3×D311yescharacteristic
676Q16—22no—
677Q16—41no—
678Q16—62no—
679SD16—34no—
680SD16—62no—
681SD16—62no—
682SD16—62no—
683SD16—62no—
684SD16—121no—
685M16—62no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—62no—
689C2×C8C22×C3×D311yescharacteristic
690C2×C8C22×C3×D311yescharacteristic
691C4⋊C4—21no—
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4C22×C3×D311yescharacteristic
700C22⋊C4—21no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C42—31no—
710C42—61no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—22no—
716C22×C3—21no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—62no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—244no—
729C22×C3#91812yescomplemented
730C22×C3C3×#13712yescomplemented
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C22×C3×D411yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—22no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—84no—
743C3×C4—21no—
744C3×C4—22no—
745C3×C4—22no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—41no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—81no—
762C3×C4—81no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4C2×D3×D411yescharacteristic
766C3×C4#100411yescharacteristic
767C3×C4C22×C3×D411yescharacteristic
768C3×C4C3×H(5,𝔽2)11yescharacteristic
769Dic3—21no—
770Dic3—21no—
771Dic3—21no—
772Dic3—41no—
773Dic3—41no—
774C32#326611yescharacteristic, complemented, Sylow
775C23—31no—
776C23—61no—
777C23—61no—
778C23—122no—
779C23—122no—
780C23—241no—
781C23C3×D3×D411yescharacteristic
782Q8—21no—
783Q8—21no—
784Q8—21no—
785Q8—21no—
786Q8—21no—
787Q8—42no—
788Q8—61no—
789Q8—61no—
790Q8—122no—
791Q8C3×D3×D412yes—
792D4—32no—
793D4—62no—
794D4—61no—
795D4—61no—
796D4—61no—
797D4—122no—
798D4—122no—
799D4—241no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—42no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—241no—
817C2×C4C3×D3×D411yescharacteristic
818C2×C4C23×C3×D311yescharacteristic
819C8—21no—
820C8—21no—
821C8—32no—
822C8—61no—
823C2×C3—22no—
824C2×C3—22no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—42no—
829C2×C3—121no—
830C2×C3—122no—
831C2×C3—241no—
832C2×C3#559011yescharacteristic
833C2×C3C2×#91811yescharacteristic
834C2×C3#577811yescharacteristic
835C2×C3C3×D4211yescharacteristic
836C2×C3C2×C3×#13711yescharacteristic
837C2×C3C3×#57711yescharacteristic
838D3—41no—
839D3—42no—
840D3—81no—
841C22—21no—
842C22—21no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—62no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—244no—
853C22C3×#91812yescomplemented
854C22C2×C3×D3×D411yescharacteristic
855C4—21no—
856C4—22no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—61no—
861C4—61no—
862C4—61no—
863C4—121no—
864C4—121no—
865C4C2×C3×D3×D411yescharacteristic
866C4C3×#100411yescharacteristic
867C3—21no—
868C3#8020411yescharacteristic, direct product factor
869C3C3×#326611yescharacteristic, complemented
870C2—22no—
871C2—121no—
872C2—122no—
873C2—241no—
874C2C3×#559011yescharacteristic
875C2C2×C3×#91811yescharacteristic
876C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC3×#5630C2
hypercenterC3×#451D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
1. C3×Q8×#67C2semidirect
2. C22×C3×#215C2semidirect
3. C2×C3×#918C2semidirect
5. C32×#451C2semidirect
6. C3×#5190C2semidirect
7. C3×#5187C2semidirect
8. C3×#5185C2semidirect
9. C3×#5051C2semidirect
10. C3×#4818C2semidirect
11. C3×#4817C2semidirect
12. C3×#4812C2semidirect
13. C3×#4806C2semidirect
14. C3×#4731C2semidirect
15. C3×#4730C2semidirect
17. #80204C3direct (N × H)
20. C2×C3×D3×Q8C22semidirect
22. C2×C32×Q16C22semidirect
23. C2×C32×Q16C22semidirect
27. C3×#946C22semidirect
28. C3×Q8×Dic3C22semidirect
30. C3×#944C22semidirect
31. C2×C3×#216C22semidirect
45. C2×C3×ΓL(1,𝔽25)C22semidirect
52. C32×#103C22semidirect
53. C32×#103C22semidirect
55. C3×#835C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
61. C3×#810C22semidirect
62. C3×#807C22semidirect
67. Q8×#67C2×C3semidirect
68. C22×#215C2×C3semidirect
69. C2×#918C2×C3semidirect
78. C3×#451D3semidirect
79. C3×#451C2×C3semidirect
84. #5190C2×C3semidirect
85. #5187C2×C3semidirect
86. #5185C2×C3semidirect
87. #5051C2×C3semidirect
88. #4818C2×C3semidirect
89. #4817C2×C3semidirect
90. #4812C2×C3semidirect
91. #4806C2×C3semidirect
92. #4731C2×C3semidirect
93. #4730C2×C3semidirect
134. C3×#215D4semidirect
164. C2×D3×Q8C22×C3semidirect
170. C2×C3×Q16C2×D3semidirect
171. C2×C3×Q16C2×D3semidirect
172. C2×C3×Q16C22×C3semidirect
173. C2×C3×Q16C22×C3semidirect
204. #946C22×C3semidirect
205. Q8×Dic3C22×C3semidirect
207. #944C22×C3semidirect
208. C2×#216C22×C3semidirect
222. C2×ΓL(1,𝔽25)C22×C3semidirect
235. C3×#103C2×D3semidirect
236. C3×#103C2×D3semidirect
237. C3×#103C22×C3semidirect
238. C3×#103C22×C3semidirect
246. #835C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. #815C22×C3semidirect
251. Dic3⋊C8C22×C3semidirect
252. #810C22×C3semidirect
253. #807C22×C3semidirect
312. #451C3×D3semidirect
434. #215C3×D4semidirect
458. C22×C32#137semidirect
488. C2×Q16C2×C3×D3semidirect
489. C2×Q16C2×C3×D3semidirect
520. #103C2×C3×D3semidirect
521. #103C2×C3×D3semidirect
729. C22×C3#918semidirect
730. C22×C3C3×#137semidirect
774. C32#3266semidirect
853. C22C3×#918semidirect
868. C3#80204direct (N × H)
869. C3C3×#3266semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
C22×C3×#2152
C2×C3×#9182
C3×#56302
C32×#4512
C3×#51902
C3×#51872
C3×#51852
C3×#50512
C3×#48182
C3×#48172
C3×#48122
C3×#48062
C3×#47312
C3×#47302
C3×#32663
#802043