Finite Group Databasebeta

← C3×#80771 #11884059

Subgroups — C3×#80771 #11884059

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#918C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C3×#5632C211yesmaximal, characteristic, complemented
4C3×#5630C211yesmaximal, characteristic
5C32×#467C211yesmaximal, characteristic, complemented
6C3×#5190C211yesmaximal, characteristic, complemented
7C3×#5111C211yesmaximal, characteristic, complemented
8C3×#5050C211yesmaximal, characteristic, complemented
9C3×#5046C211yesmaximal, characteristic, complemented
10C3×#4889C211yesmaximal, characteristic, complemented
11C3×#4886C211yesmaximal, characteristic, complemented
12C3×#4818C211yesmaximal, characteristic, complemented
13C3×#4808C211yesmaximal, characteristic, complemented
14C3×#4806C211yesmaximal, characteristic, complemented
15C3×#4798C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#80771C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C2×C32×Q16C2211yescharacteristic, complemented
23C22×C32×C8C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C32×C22⋊Q8C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C3×#944C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×#67C2211yescharacteristic
33C3×#918—24no—
34C2×C3×#204—24no—
35C2×C3×#204C2211yescharacteristic
36C2×C3×#204C2211yescharacteristic
37C2×C3×#204C2211yescharacteristic
38C2×C3×#204C2211yescharacteristic
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
40C3×#897C2211yescharacteristic, complemented
41C3×#896—21no—
42C3×#895—21no—
43C3×#895C2211yescharacteristic
44C3×#894—21no—
45C3×#893C2211yescharacteristic
46C3×#888—21no—
47C3×#887C2211yescharacteristic, complemented
48C3×#882—21no—
49C3×#67⋊C4—21no—
50C3×D3×C22⋊C4—21no—
51C3×#878—21no—
52C32×#107C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#103C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic
62C3×#809C2211yescharacteristic
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—31no—
67C2×#918C2×C311yescharacteristic, complemented
68C22×#204C2×C311yescharacteristic, complemented
69#5632C2×C311yescharacteristic, complemented
70#5630C2×C311yescharacteristic
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—21no—
74C3×#467D311yescharacteristic, complemented
75C3×#467C2×C311yescharacteristic, complemented
76C3×#464—31no—
77C3×#461—31no—
78C3×#452—31no—
79C3×#451—31no—
80C3×#450—31no—
81C3×#448—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5190C2×C311yescharacteristic, complemented
85#5111C2×C311yescharacteristic, complemented
86#5050C2×C311yescharacteristic, complemented
87#5046C2×C311yescharacteristic, complemented
88#4889C2×C311yescharacteristic, complemented
89#4886C2×C311yescharacteristic, complemented
90#4818C2×C311yescharacteristic, complemented
91#4808C2×C311yescharacteristic, complemented
92#4806C2×C311yescharacteristic, complemented
93#4798C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C3×#239—22no—
101C3×#239—41no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—22no—
116C2×C3×Dic6—21no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6—41no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×Q16—22no—
122C2×C32×C8—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4—21no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C3×#217D411yescharacteristic
132C3×#216—22no—
133C3×#216—41no—
134C3×#215—22no—
135C3×#215—41no—
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×(C2×D3)⋊C4D411yescharacteristic
142C3×C4⋊Dic3—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4D411yescharacteristic
147C3×C4×Dic3—21no—
148C3×C4×Dic3C2311yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C3×#204—22no—
152C3×#204—22no—
153C3×#204—22no—
154C3×#204D414yescomplemented
155C3×ΓL(1,𝔽25)—22no—
156#3266—31noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C2×#239C22×C311yescharacteristic
162C2×D3×Q8C22×C311yescharacteristic, complemented
163C22×D12C22×C311yescharacteristic
164C22×Dic6C22×C311yescharacteristic
165C3×#137—64no—
166C2×C3×Q16—21no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×Q16C2×D311yescharacteristic, complemented
170C2×C3×Q16C22×C311yescharacteristic, complemented
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16—64no—
178C2×C3×M16—31no—
179C22×C3×C8—21no—
180C22×C3×C8C2×D311yescharacteristic
181C22×C3×C8C22×C311yescharacteristic
182C3×C4⋊Q8—31no—
183C3×C4⋊Q8—61no—
184C3×#124—31no—
185C3×#123—61no—
186C3×C22⋊Q8—21no—
187C3×C22⋊Q8—21no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—61no—
190C3×C22⋊Q8—61no—
191C3×C22⋊Q8C2×D311yescharacteristic
192C3×C22⋊Q8C2×D311yescharacteristic
193C3×C22⋊Q8C22×C311yescharacteristic
194C3×C22⋊Q8C22×C311yescharacteristic
195C3×#121—31no—
196C3×#121—61no—
197C3×#120—61no—
198C3×C4×Q8—31no—
199C3×C4×D4—31no—
200C3×C4×D4—31no—
201C3×C4×D4—61no—
202C2×C3×C22⋊C4—61no—
203#947C22×C311yescharacteristic
204#944C22×C311yescharacteristic, complemented
205C2×#216C22×C311yescharacteristic, complemented
206C2×#216C22×C311yescharacteristic, complemented
207C2×#215C22×C311yescharacteristic
208C2×#215C22×C311yescharacteristic
209C4×#67C22×C311yescharacteristic
210#918—24no—
211C2×#204—24no—
212C2×#204C22×C311yescharacteristic
213C2×#204C22×C311yescharacteristic
214C2×#204C22×C311yescharacteristic
215C2×#204C22×C311yescharacteristic
216C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
217#897C22×C311yescharacteristic, complemented
218#896—21no—
219#895—21no—
220#895C22×C311yescharacteristic
221#894—21no—
222#893C22×C311yescharacteristic
223#888—21no—
224#887C22×C311yescharacteristic, complemented
225#882—21no—
226#67⋊C4—21no—
227D3×C22⋊C4—21no—
228#878—21no—
229C3×#107—21no—
230C3×#107C2×D311yescharacteristic, complemented
231C3×#107C22×C311yescharacteristic, complemented
232C3×C4⋊C8—31no—
233C3×#103—21no—
234C3×#103—21no—
235C3×#103—31no—
236C3×#103—31no—
237C3×#103C2×D311yescharacteristic, complemented
238C3×#103C2×D311yescharacteristic, complemented
239C3×#103C22×C311yescharacteristic, complemented
240C3×#103C22×C311yescharacteristic, complemented
241C3×#102—31no—
242C3×#102—31no—
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—31no—
246#830C22×C311yescharacteristic
247(C2×D3)⋊C8C22×C311yescharacteristic, complemented
248#815C22×C311yescharacteristic, complemented
249Dic3⋊C8C22×C311yescharacteristic, complemented
250#810C22×C311yescharacteristic, complemented
251#810C22×C311yescharacteristic, complemented
252#809C22×C311yescharacteristic
253#809C22×C311yescharacteristic
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—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2411yescharacteristic
273C3×#67—22no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×D12—42no—
285C3×D12—81no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×C4×D3—42no—
291C3×C4×D3—81no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yes—
298C32×C8—21no—
299C32×C8C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—31no—
303C22×SD16—31no—
304D4×Q8—31no—
305#546—31no—
306#497—31no—
307#468—31no—
308#467C3×D311yescharacteristic, complemented
309#464—31no—
310#461—31no—
311#452—31no—
312#451—31no—
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—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—61no—
326C2×C3×Q8—62no—
327C2×C3×Q8—61no—
328C2×C3×Q8—62no—
329C2×C3×Q8—121no—
330C2×C3×Q8—121no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C23×C311yescharacteristic
334C2×C3×Q8C23×C311yescharacteristic
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—121no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C23×C311yescharacteristic
351C2×#67C3×D411yescharacteristic
352C22×Dic3—21no—
353#239—22no—
354#239—41no—
355D3×Q8—22no—
356D3×Q8—41no—
357C2×D12—22no—
358C2×D12—21no—
359C2×D12—21no—
360C2×D12—21no—
361C2×D12—41no—
362C2×D12C23×C311yescharacteristic
363C2×D12C23×C311yescharacteristic
364C2×C4×D3—21no—
365C2×C4×D3—21no—
366C2×C4×D3—21no—
367C2×C4×D3C23×C311yescharacteristic
368C2×Dic6—22no—
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6—41no—
372C2×Dic6C23×C311yescharacteristic
373C2×Dic6C23×C311yescharacteristic
374C3×Q16—22no—
375C3×Q16—22no—
376C3×Q16—42no—
377C3×Q16—62no—
378C3×Q16—121no—
379C3×SD16—34no—
380C3×SD16—62no—
381C3×SD16—62no—
382C3×SD16—62no—
383C3×SD16—62no—
384C3×SD16—121no—
385C3×M16—62no—
386C2×C3×C8—22no—
387C2×C3×C8—22no—
388C2×C3×C8—21no—
389C2×C3×C8—21no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C2×C3×C8—42no—
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C23×C311yescharacteristic
396C2×C3×C8C23×C311yescharacteristic
397C3×C4⋊C4—21no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—21no—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—41no—
405C3×C4⋊C4—41no—
406C3×C4⋊C4—61no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4C22×D311yescharacteristic
411C3×C4⋊C4C22×D311yescharacteristic
412C3×C4⋊C4C23×C311yescharacteristic
413C3×C4⋊C4C23×C311yescharacteristic
414C3×C22⋊C4—21no—
415C3×C22⋊C4—21no—
416C3×C22⋊C4—21no—
417C3×C22⋊C4—21no—
418C3×C22⋊C4—31no—
419C3×C22⋊C4—31no—
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×C42—31no—
428C3×C42—61no—
429#217C3×D411yescharacteristic
430#216—22no—
431#216—41no—
432#215—22no—
433#215—41no—
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—
439(C2×D3)⋊C4C3×D411yescharacteristic
440C4⋊Dic3—21no—
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444Dic3⋊C4C3×D411yescharacteristic
445C4×Dic3—21no—
446C4×Dic3C23×C311yescharacteristic
447C2×C3⋊C8C23×C311yescharacteristic
448C2×C3⋊C8C23×C311yescharacteristic
449#204—22no—
450#204—22no—
451#204—22no—
452#204C3×D414yescomplemented
453ΓL(1,𝔽25)—22no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32#13712yescomplemented
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—84no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3×Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—31no—
482C22×Q8—31no—
483C22×D4—31no—
484#137—64no—
485C2×Q16—31no—
486C2×Q16—31no—
487C2×Q16C2×C3×D311yescharacteristic, complemented
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—64no—
495C2×M16—31no—
496C22×C8C2×C3×D311yescharacteristic
497C4⋊Q8—31no—
498C4⋊Q8—61no—
499#124—31no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—61no—
503C22⋊Q8—61no—
504C22⋊Q8C2×C3×D311yescharacteristic
505C22⋊Q8C2×C3×D311yescharacteristic
506#121—31no—
507#121—61no—
508#120—61no—
509C4×Q8—31no—
510C4×D4—31no—
511C4×D4—31no—
512C4×D4—61no—
513C2×C22⋊C4—61no—
514#107C2×C3×D311yescharacteristic, complemented
515C4⋊C8—31no—
516#103—31no—
517#103—31no—
518#103C2×C3×D311yescharacteristic, complemented
519#103C2×C3×D311yescharacteristic, complemented
520#102—31no—
521#102—31no—
522C22⋊C8—31no—
523C22⋊C8—31no—
524#97—31no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—122no—
530C23×C3—122no—
531C23×C3—241no—
532C23×C3D3×D411yescharacteristic
533C23×C3C2×C3×D411yescharacteristic
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—81no—
539C22×D3C2×C3×D411yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—32no—
549C3×Q8—41no—
550C3×Q8—41no—
551C3×Q8—41no—
552C3×Q8—41no—
553C3×Q8—61no—
554C3×Q8—61no—
555C3×Q8—61no—
556C3×Q8—122no—
557C3×Q8—122no—
558C3×D4—32no—
559C3×D4—62no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4—241no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
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—31no—
581C2×C3×C4—31no—
582C2×C3×C4—31no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4—122no—
595C2×C3×C4—122no—
596C2×C3×C4—241no—
597C2×C3×C4D3×D411yescharacteristic
598C2×C3×C4C2×C3×D411yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C24×C311yescharacteristic
601#67—22no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—42no—
605C2×Dic3C2×C3×D411yescharacteristic
606C2×Dic3C2×C3×D411yescharacteristic
607C2×Dic3C2×C3×D411yescharacteristic
608D12—21no—
609D12—21no—
610D12—21no—
611D12—42no—
612D12—42no—
613D12—81no—
614D12C2×C3×D412yes—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—42no—
618C4×D3—42no—
619C4×D3—81no—
620Dic6—21no—
621Dic6—21no—
622Dic6—21no—
623Dic6—42no—
624Dic6—42no—
625Dic6C2×C3×D412yes—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—22no—
629C3×C8—41no—
630C3×C8—61no—
631C3×C8—61no—
632C3×C8D3×D412yes—
633C3×C8C2×C3×D412yes—
634C3⋊C8—21no—
635C3⋊C8—21no—
636C2×C32—22no—
637C2×C32D4211yescharacteristic
638C2×C32C2×#13711yescharacteristic
639C2×C32#57711yescharacteristic
640C3×D3—41no—
641C3×D3—42no—
642C3×D3—81no—
643C24—61no—
644#41—62no—
645#41—121no—
646C2×Q8—31no—
647C2×Q8—31no—
648C2×Q8—61no—
649C2×Q8—62no—
650C2×Q8—61no—
651C2×Q8—62no—
652C2×Q8—121no—
653C2×Q8—121no—
654C2×Q8C22×C3×D311yescharacteristic
655C2×Q8C22×C3×D311yescharacteristic
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—121no—
664C22×C4—31no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—61no—
668C22×C4—61no—
669C22×C4C22×C3×D311yescharacteristic
670Q16—22no—
671Q16—62no—
672Q16—121no—
673SD16—34no—
674SD16—62no—
675SD16—62no—
676SD16—62no—
677SD16—62no—
678SD16—121no—
679M16—62no—
680C2×C8—22no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8C22×C3×D311yescharacteristic
684C2×C8C22×C3×D311yescharacteristic
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—31no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4C22×C3×D311yescharacteristic
693C4⋊C4C22×C3×D311yescharacteristic
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—31no—
697C22⋊C4—31no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C42—31no—
704C42—61no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—22no—
710C22×C3—21no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3#91812yescomplemented
724C22×C3C3×#13712yescomplemented
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C22×C3×D411yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—22no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—84no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—61no—
751C3×C4—61no—
752C3×C4—61no—
753C3×C4—62no—
754C3×C4—81no—
755C3×C4—81no—
756C3×C4—81no—
757C3×C4—81no—
758C3×C4—121no—
759C3×C4C2×D3×D411yescharacteristic
760C3×C4#100911yescharacteristic
761C3×C4C22×C3×D411yescharacteristic
762C3×C4C3×H(5,𝔽2)11yescharacteristic
763Dic3—21no—
764Dic3—21no—
765Dic3—22no—
766Dic3—21no—
767Dic3—41no—
768C32#326611yescharacteristic, complemented, Sylow
769C23—31no—
770C23—61no—
771C23—61no—
772C23—122no—
773C23—122no—
774C23—241no—
775C23C3×D3×D411yescharacteristic
776Q8—21no—
777Q8—21no—
778Q8—21no—
779Q8—21no—
780Q8—32no—
781Q8—61no—
782Q8—61no—
783Q8—61no—
784Q8—122no—
785Q8—122no—
786D4—32no—
787D4—62no—
788D4—61no—
789D4—61no—
790D4—61no—
791D4—122no—
792D4—122no—
793D4—241no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—31no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—122no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—241no—
811C2×C4C3×D3×D411yescharacteristic
812C2×C4C23×C3×D311yescharacteristic
813C8—21no—
814C8—61no—
815C8—61no—
816C8C3×D3×D412yes—
817C2×C3—22no—
818C2×C3—22no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—42no—
823C2×C3—121no—
824C2×C3—122no—
825C2×C3—241no—
826C2×C3#560911yescharacteristic
827C2×C3C2×#91811yescharacteristic
828C2×C3#577011yescharacteristic
829C2×C3C3×D4211yescharacteristic
830C2×C3C2×C3×#13711yescharacteristic
831C2×C3C3×#57711yescharacteristic
832D3—41no—
833D3—42no—
834D3—81no—
835C22—21no—
836C22—21no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—62no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—244no—
847C22C3×#91812yescomplemented
848C22C2×C3×D3×D411yescharacteristic
849C4—21no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—61no—
855C4—61no—
856C4—61no—
857C4—62no—
858C4—121no—
859C4C2×C3×D3×D411yescharacteristic
860C4C3×#100911yescharacteristic
861C3—21no—
862C3#8077111yescharacteristic, direct product factor
863C3C3×#326611yescharacteristic, complemented
864C2—22no—
865C2—121no—
866C2—122no—
867C2—241no—
868C2C3×#560911yescharacteristic
869C2C2×C3×#91811yescharacteristic
870C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#467C2
socleC22×C32C22×D4
prime radicalC3×#5630C2
hypercenterC3×#467D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#467

Complements

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

NH ≅ G/Ntype
1. C2×C3×#918C2semidirect
2. C22×C3×#204C2semidirect
3. C3×#5632C2semidirect
5. C32×#467C2semidirect
6. C3×#5190C2semidirect
7. C3×#5111C2semidirect
8. C3×#5050C2semidirect
9. C3×#5046C2semidirect
10. C3×#4889C2semidirect
11. C3×#4886C2semidirect
12. C3×#4818C2semidirect
13. C3×#4808C2semidirect
14. C3×#4806C2semidirect
15. C3×#4798C2semidirect
17. #80771C3direct (N × H)
19. C2×C3×D3×Q8C22semidirect
22. C2×C32×Q16C22semidirect
27. C3×#944C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#216C22semidirect
39. C2×C3×ΓL(1,𝔽25)C22semidirect
40. C3×#897C22semidirect
47. C3×#887C22semidirect
52. C32×#107C22semidirect
53. C32×#103C22semidirect
54. C32×#103C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#810C22semidirect
67. C2×#918C2×C3semidirect
68. C22×#204C2×C3semidirect
69. #5632C2×C3semidirect
74. C3×#467D3semidirect
75. C3×#467C2×C3semidirect
84. #5190C2×C3semidirect
85. #5111C2×C3semidirect
86. #5050C2×C3semidirect
87. #5046C2×C3semidirect
88. #4889C2×C3semidirect
89. #4886C2×C3semidirect
90. #4818C2×C3semidirect
91. #4808C2×C3semidirect
92. #4806C2×C3semidirect
93. #4798C2×C3semidirect
154. C3×#204D4semidirect
162. C2×D3×Q8C22×C3semidirect
169. C2×C3×Q16C2×D3semidirect
170. C2×C3×Q16C22×C3semidirect
204. #944C22×C3semidirect
205. C2×#216C22×C3semidirect
206. C2×#216C22×C3semidirect
216. C2×ΓL(1,𝔽25)C22×C3semidirect
217. #897C22×C3semidirect
224. #887C22×C3semidirect
230. C3×#107C2×D3semidirect
231. C3×#107C22×C3semidirect
237. C3×#103C2×D3semidirect
238. C3×#103C2×D3semidirect
239. C3×#103C22×C3semidirect
240. C3×#103C22×C3semidirect
247. (C2×D3)⋊C8C22×C3semidirect
248. #815C22×C3semidirect
249. Dic3⋊C8C22×C3semidirect
250. #810C22×C3semidirect
251. #810C22×C3semidirect
308. #467C3×D3semidirect
452. #204C3×D4semidirect
456. C22×C32#137semidirect
487. C2×Q16C2×C3×D3semidirect
514. #107C2×C3×D3semidirect
518. #103C2×C3×D3semidirect
519. #103C2×C3×D3semidirect
723. C22×C3#918semidirect
724. C22×C3C3×#137semidirect
768. C32#3266semidirect
847. C22C3×#918semidirect
862. C3#80771direct (N × H)
863. C3C3×#3266semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9182
C22×C3×#2042
C3×#56322
C3×#56302
C32×#4672
C3×#51902
C3×#51112
C3×#50502
C3×#50462
C3×#48892
C3×#48862
C3×#48182
C3×#48082
C3×#48062
C3×#47982
C3×#32663
#807713