Finite Group Databasebeta

← C3×#80444 #11884086

Subgroups — C3×#80444 #11884086

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic, complemented
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3C3×#5727C211yesmaximal, characteristic, complemented
4C3×#5554C211yesmaximal, characteristic
5C32×#461C211yesmaximal, characteristic, complemented
6C3×#5173C211yesmaximal, characteristic, complemented
7C3×#5169C211yesmaximal, characteristic, complemented
8C3×#5086C211yesmaximal, characteristic, complemented
9C3×#5018C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4813C211yesmaximal, characteristic, complemented
13C3×#4812C211yesmaximal, characteristic, complemented
14C3×#4809C211yesmaximal, characteristic, complemented
15C3×#4806C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#80444C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×C32×SD16C2211yescharacteristic
24C32×C4⋊Q8C2211yescharacteristic, complemented
25C32×C4×D4C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C3×#930—21no—
34C2×C3×(C2×D3)⋊C4—21no—
35C3×#915—24no—
36C3×D3×SD16—24no—
37C2×C3×Dic12C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
40C2×C3×D3×C8C2211yescharacteristic
41C3×#897C2211yescharacteristic
42C3×#896—21no—
43C3×#896—21no—
44C3×#895C2211yescharacteristic
45C3×#893—21no—
46C3×#888—21no—
47C3×#886—21no—
48C3×#882—21no—
49C3×#875C2211yescharacteristic
50C3×C4×D12C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic, complemented
52C32×C4⋊C8C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#103C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61C3×#807C2211yescharacteristic, complemented
62C3×#803C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—31no—
67C2×#915C2×C311yescharacteristic, complemented
68C2×D3×SD16C2×C311yescharacteristic, complemented
69#5727C2×C311yescharacteristic, complemented
70#5554C2×C311yescharacteristic
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—31no—
74C3×#464—31no—
75C3×#461—21no—
76C3×#461D311yescharacteristic, complemented
77C3×#461C2×C311yescharacteristic, complemented
78C3×#452—31no—
79C3×#451—31no—
80C3×#450—31no—
81C3×#448—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5173C2×C311yescharacteristic, complemented
85#5169C2×C311yescharacteristic, complemented
86#5086C2×C311yescharacteristic, complemented
87#5018C2×C311yescharacteristic, complemented
88#4845C2×C311yescharacteristic, complemented
89#4836C2×C311yescharacteristic, complemented
90#4813C2×C311yescharacteristic, complemented
91#4812C2×C311yescharacteristic, complemented
92#4809C2×C311yescharacteristic, complemented
93#4806C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—22no—
104C3×D3×Q8—41no—
105C3×D3×Q8—41no—
106C3×#237—22no—
107C3×#237—41no—
108C3×D3×D4—22no—
109C3×D3×D4—41no—
110C2×C3×D12—21no—
111C2×C3×D12D411yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6—21no—
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×SD16—22no—
122C32×SD16—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4—21no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C22⋊C4—21no—
129C32×C42C2311yescharacteristic
130C3×#216—22no—
131C3×#216—41no—
132C3×#215—22no—
133C3×#215—41no—
134C3×#214D414yescomplemented
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3D411yescharacteristic
145C3×C4⋊Dic3C2311yescharacteristic
146C3×Dic3⋊C4—21no—
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×Dic12—22no—
153C3×#204—22no—
154C3×ΓL(1,𝔽25)—22no—
155C3×D3×C8—22no—
156#3266—31noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C2×D3×Q8C22×C311yescharacteristic
162C2×D3×Q8C22×C311yescharacteristic, complemented
163C2×#237C22×C311yescharacteristic
164C2×D3×D4C22×C311yescharacteristic
165C3×#137—64no—
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C2×C3×SD16—21no—
170C2×C3×SD16—21no—
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×SD16C2×D311yescharacteristic
178C2×C3×SD16C22×C311yescharacteristic
179C2×C3×SD16C22×C311yescharacteristic
180C2×C3×M16—31no—
181C22×C3×C8—31no—
182C3×C4⋊Q8—21no—
183C3×C4⋊Q8—61no—
184C3×C4⋊Q8C2×D311yescharacteristic, complemented
185C3×C4⋊Q8C22×C311yescharacteristic, complemented
186C3×#124—31no—
187C3×#123—61no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8—31no—
190C3×C22⋊Q8—31no—
191C3×C22⋊Q8—61no—
192C3×C22⋊Q8—61no—
193C3×#121—31no—
194C3×#121—61no—
195C3×#120—61no—
196C3×C4×Q8—31no—
197C3×C4×D4—21no—
198C3×C4×D4—31no—
199C3×C4×D4—61no—
200C3×C4×D4C2×D311yescharacteristic
201C3×C4×D4C22×C311yescharacteristic
202C2×C3×C22⋊C4—61no—
203#946C22×C311yescharacteristic
204#946C22×C311yescharacteristic, complemented
205C2×#216C22×C311yescharacteristic, complemented
206C2×#216C22×C311yescharacteristic, complemented
207C2×#215C22×C311yescharacteristic
208C2×#215C22×C311yescharacteristic
209C2×#214C22×C311yescharacteristic
210#930—21no—
211C2×(C2×D3)⋊C4—21no—
212#915—24no—
213D3×SD16—24no—
214C2×Dic12C22×C311yescharacteristic, complemented
215C2×#204C22×C311yescharacteristic
216C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
217C2×D3×C8C22×C311yescharacteristic
218#897C22×C311yescharacteristic
219#896—21no—
220#896—21no—
221#895C22×C311yescharacteristic
222#893—21no—
223#888—21no—
224#886—21no—
225#882—21no—
226#875C22×C311yescharacteristic
227C4×D12C22×C311yescharacteristic
228C4×Dic6C22×C311yescharacteristic, complemented
229C3×#107—31no—
230C3×C4⋊C8—21no—
231C3×C4⋊C8C2×D311yescharacteristic, complemented
232C3×C4⋊C8C22×C311yescharacteristic, complemented
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#832C22×C311yescharacteristic
247#821C22×C311yescharacteristic
248(C2×D3)⋊C8C22×C311yescharacteristic
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250#816C22×C311yescharacteristic, complemented
251#810C22×C311yescharacteristic, complemented
252#807C22×C311yescharacteristic, complemented
253#803C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—81no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—22no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—81no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—42no—
296C3×Dic6—42no—
297C3×Dic6C2×D412yes—
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#461C3×D311yescharacteristic, complemented
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—61no—
327C2×C3×Q8—62no—
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—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—62no—
341C2×C3×D4—61no—
342C2×C3×D4—121no—
343C2×C3×D4C22×D311yescharacteristic
344C2×C3×D4C23×C311yescharacteristic
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—41no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C2×#67—21no—
354C2×#67—21no—
355C22×Dic3—21no—
356D3×Q8—22no—
357D3×Q8—22no—
358D3×Q8—41no—
359D3×Q8—41no—
360#237—22no—
361#237—41no—
362D3×D4—22no—
363D3×D4—41no—
364C2×D12—21no—
365C2×D12C3×D411yescharacteristic
366C2×D12C23×C311yescharacteristic
367C2×C4×D3—21no—
368C2×C4×D3—21no—
369C2×C4×D3C23×C311yescharacteristic
370C2×C4×D3C23×C311yescharacteristic
371C2×Dic6—21no—
372C2×Dic6—21no—
373C2×Dic6C23×C311yescharacteristic
374C2×Dic6C23×C311yescharacteristic
375C3×Q16—62no—
376C3×Q16—62no—
377C3×Q16—121no—
378C3×SD16—22no—
379C3×SD16—22no—
380C3×SD16—22no—
381C3×SD16—22no—
382C3×SD16—34no—
383C3×SD16—42no—
384C3×SD16—42no—
385C3×SD16—62no—
386C3×SD16—62no—
387C3×SD16—121no—
388C3×M16—62no—
389C2×C3×C8—21no—
390C2×C3×C8—21no—
391C2×C3×C8—31no—
392C2×C3×C8—31no—
393C2×C3×C8—62no—
394C2×C3×C8C22×D311yescharacteristic
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C23×C311yescharacteristic
397C2×C3×C8C23×C311yescharacteristic
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—31no—
405C3×C4⋊C4—41no—
406C3×C4⋊C4—41no—
407C3×C4⋊C4—61no—
408C3×C4⋊C4—61no—
409C3×C4⋊C4—61no—
410C3×C4⋊C4—61no—
411C3×C4⋊C4C22×D311yescharacteristic
412C3×C4⋊C4C23×C311yescharacteristic
413C3×C22⋊C4—21no—
414C3×C22⋊C4—21no—
415C3×C22⋊C4—31no—
416C3×C22⋊C4—31no—
417C3×C22⋊C4—41no—
418C3×C22⋊C4—61no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C22⋊C4—61no—
423C3×C22⋊C4—61no—
424C3×C42—21no—
425C3×C42—61no—
426C3×C42C22×D311yescharacteristic
427C3×C42C23×C311yescharacteristic
428#216—22no—
429#216—41no—
430#215—22no—
431#215—41no—
432#214C3×D414yescomplemented
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—21no—
439(C2×D3)⋊C4C3×D411yescharacteristic
440(C2×D3)⋊C4C3×D411yescharacteristic
441C4⋊Dic3—21no—
442C4⋊Dic3C3×D411yescharacteristic
443C4⋊Dic3C23×C311yescharacteristic
444Dic3⋊C4—21no—
445Dic3⋊C4—21no—
446Dic3⋊C4—21no—
447C4×Dic3—21no—
448C2×C3⋊C8C23×C311yescharacteristic
449C2×C3⋊C8C23×C311yescharacteristic
450Dic12—22no—
451#204—22no—
452ΓL(1,𝔽25)—22no—
453D3×C8—22no—
454C22×C32—22no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—84no—
467C2×C3×D3#13712yescomplemented
468C32×C4—21no—
469C32×C4—21no—
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—41no—
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×Q16—31no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—64no—
493C2×SD16C2×C3×D311yescharacteristic
494C2×SD16C2×C3×D311yescharacteristic
495C2×M16—31no—
496C22×C8—31no—
497C4⋊Q8—61no—
498C4⋊Q8C2×C3×D311yescharacteristic, complemented
499#124—31no—
500#123—61no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—31no—
504C22⋊Q8—61no—
505C22⋊Q8—61no—
506#121—31no—
507#121—61no—
508#120—61no—
509C4×Q8—31no—
510C4×D4—31no—
511C4×D4—61no—
512C4×D4C2×C3×D311yescharacteristic
513C2×C22⋊C4—61no—
514#107—31no—
515C4⋊C8C2×C3×D311yescharacteristic, complemented
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—21no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C23×C3—241no—
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—81no—
538C22×D3C2×C3×D411yescharacteristic
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—21no—
559C3×D4—21no—
560C3×D4—22no—
561C3×D4—41no—
562C3×D4—62no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—122no—
566C3×D4—122no—
567C3×D4—241no—
568C3×D4D3×D412yes—
569C3×D4C2×C3×D412yes—
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—31no—
580C2×C3×C4—31no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—81no—
592C2×C3×C4—81no—
593C2×C3×C4—82no—
594C2×C3×C4—122no—
595C2×C3×C4—122no—
596C2×C3×C4—122no—
597C2×C3×C4D3×D411yescharacteristic
598C2×C3×C4D3×D411yescharacteristic
599C2×C3×C4C2×C3×D411yescharacteristic
600C2×C3×C4C2×C3×D411yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C24×C311yescharacteristic
603#67—42no—
604#67—42no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—42no—
609C2×Dic3C2×C3×D411yescharacteristic
610C2×Dic3C2×C3×D411yescharacteristic
611D12—22no—
612D12—21no—
613D12—21no—
614D12—81no—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—21no—
619C4×D3—42no—
620C4×D3—42no—
621Dic6—21no—
622Dic6—21no—
623Dic6—21no—
624Dic6—42no—
625Dic6—42no—
626Dic6C2×C3×D412yes—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—21no—
630C3×C8—21no—
631C3×C8—32no—
632C3×C8—41no—
633C3×C8—41no—
634C3×C8—61no—
635C3⋊C8—21no—
636C3⋊C8C2×C3×D412yes—
637C2×C32—42no—
638C2×C32D4211yescharacteristic
639C2×C32C2×#13711yescharacteristic
640C2×C32#57711yescharacteristic
641C3×D3—22no—
642C3×D3—41no—
643C3×D3—81no—
644C24—61no—
645#41—62no—
646#41—121no—
647C2×Q8—31no—
648C2×Q8—31no—
649C2×Q8—61no—
650C2×Q8—61no—
651C2×Q8—62no—
652C2×Q8—62no—
653C2×Q8—121no—
654C2×Q8—121no—
655C2×Q8C22×C3×D311yescharacteristic
656C2×Q8C22×C3×D311yescharacteristic
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—62no—
662C2×D4—61no—
663C2×D4—121no—
664C2×D4C22×C3×D311yescharacteristic
665C22×C4—21no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—61no—
669C22×C4—61no—
670C22×C4—61no—
671Q16—62no—
672Q16—62no—
673Q16—121no—
674SD16—22no—
675SD16—22no—
676SD16—34no—
677SD16—62no—
678SD16—62no—
679SD16—121no—
680M16—62no—
681C2×C8—31no—
682C2×C8—31no—
683C2×C8—62no—
684C2×C8C22×C3×D311yescharacteristic
685C2×C8C22×C3×D311yescharacteristic
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—31no—
689C4⋊C4—31no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4C22×C3×D311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—31no—
697C22⋊C4—31no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C42—61no—
705C42C22×C3×D311yescharacteristic
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—32no—
710C22×C3—42no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—244no—
726C22×C3C2×D3×D411yescharacteristic
727C22×C3C22×C3×D411yescharacteristic
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—84no—
737C2×D3C3×#13712yescomplemented
738C3×C4—22no—
739C3×C4—21no—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—41no—
748C3×C4—41no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4—62no—
755C3×C4—81no—
756C3×C4—81no—
757C3×C4—81no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4C2×D3×D411yescharacteristic
761C3×C4#100911yescharacteristic
762C3×C4C22×C3×D411yescharacteristic
763C3×C4C3×H(5,𝔽2)11yescharacteristic
764Dic3—22no—
765Dic3—21no—
766Dic3—21no—
767Dic3—41no—
768Dic3—41no—
769C32#326611yescharacteristic, complemented, Sylow
770C23—21no—
771C23—31no—
772C23—31no—
773C23—61no—
774C23—122no—
775C23—122no—
776C23—241no—
777Q8—21no—
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—32no—
782Q8—61no—
783Q8—61no—
784Q8—61no—
785Q8—122no—
786Q8—122no—
787D4—21no—
788D4—62no—
789D4—61no—
790D4—61no—
791D4—122no—
792D4—122no—
793D4—241no—
794D4C3×D3×D412yes—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—81no—
808C2×C4—122no—
809C2×C4—122no—
810C2×C4—122no—
811C2×C4C3×D3×D411yescharacteristic
812C2×C4C3×D3×D411yescharacteristic
813C2×C4C23×C3×D311yescharacteristic
814C8—21no—
815C8—21no—
816C8—32no—
817C8—61no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—42no—
822C2×C3—42no—
823C2×C3—62no—
824C2×C3—82no—
825C2×C3—121no—
826C2×C3—241no—
827C2×C3#560911yescharacteristic
828C2×C3#576211yescharacteristic
829C2×C3D3×#13711yescharacteristic
830C2×C3C3×D4211yescharacteristic
831C2×C3C2×C3×#13711yescharacteristic
832C2×C3C3×#57711yescharacteristic
833D3—22no—
834D3—41no—
835D3—81no—
836C22—22no—
837C22—32no—
838C22—41no—
839C22—41no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—244no—
849C22C2×C3×D3×D411yescharacteristic
850C4—21no—
851C4—21no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—61no—
856C4—61no—
857C4—62no—
858C4—121no—
859C4—121no—
860C4C2×C3×D3×D411yescharacteristic
861C4C3×#100911yescharacteristic
862C3—21no—
863C3#8044411yescharacteristic, direct product factor
864C3C3×#326611yescharacteristic, complemented
865C2—42no—
866C2—62no—
867C2—121no—
868C2—241no—
869C2C3×#560911yescharacteristic
870C2C3×#576211yescharacteristic
871C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC3×#5554C2
hypercenterC3×#461D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C2×C3×#915C2semidirect
2. C2×C3×D3×SD16C2semidirect
3. C3×#5727C2semidirect
5. C32×#461C2semidirect
6. C3×#5173C2semidirect
7. C3×#5169C2semidirect
8. C3×#5086C2semidirect
9. C3×#5018C2semidirect
10. C3×#4845C2semidirect
11. C3×#4836C2semidirect
12. C3×#4813C2semidirect
13. C3×#4812C2semidirect
14. C3×#4809C2semidirect
15. C3×#4806C2semidirect
17. #80444C3direct (N × H)
19. C2×C3×D3×Q8C22semidirect
24. C32×C4⋊Q8C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#216C22semidirect
37. C2×C3×Dic12C22semidirect
39. C2×C3×ΓL(1,𝔽25)C22semidirect
51. C3×C4×Dic6C22semidirect
52. C32×C4⋊C8C22semidirect
53. C32×#103C22semidirect
54. C32×#103C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#816C22semidirect
60. C3×#810C22semidirect
61. C3×#807C22semidirect
62. C3×#803C22semidirect
67. C2×#915C2×C3semidirect
68. C2×D3×SD16C2×C3semidirect
69. #5727C2×C3semidirect
76. C3×#461D3semidirect
77. C3×#461C2×C3semidirect
84. #5173C2×C3semidirect
85. #5169C2×C3semidirect
86. #5086C2×C3semidirect
87. #5018C2×C3semidirect
88. #4845C2×C3semidirect
89. #4836C2×C3semidirect
90. #4813C2×C3semidirect
91. #4812C2×C3semidirect
92. #4809C2×C3semidirect
93. #4806C2×C3semidirect
134. C3×#214D4semidirect
162. C2×D3×Q8C22×C3semidirect
184. C3×C4⋊Q8C2×D3semidirect
185. C3×C4⋊Q8C22×C3semidirect
204. #946C22×C3semidirect
205. C2×#216C22×C3semidirect
206. C2×#216C22×C3semidirect
214. C2×Dic12C22×C3semidirect
216. C2×ΓL(1,𝔽25)C22×C3semidirect
228. C4×Dic6C22×C3semidirect
231. C3×C4⋊C8C2×D3semidirect
232. C3×C4⋊C8C22×C3semidirect
237. C3×#103C2×D3semidirect
238. C3×#103C2×D3semidirect
239. C3×#103C22×C3semidirect
240. C3×#103C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. #816C22×C3semidirect
251. #810C22×C3semidirect
252. #807C22×C3semidirect
253. #803C22×C3semidirect
310. #461C3×D3semidirect
432. #214C3×D4semidirect
467. C2×C3×D3#137semidirect
498. C4⋊Q8C2×C3×D3semidirect
515. C4⋊C8C2×C3×D3semidirect
518. #103C2×C3×D3semidirect
519. #103C2×C3×D3semidirect
737. C2×D3C3×#137semidirect
769. C32#3266semidirect
863. C3#80444direct (N × H)
864. C3C3×#3266semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
C2×C3×D3×SD162
C3×#57272
C3×#55542
C32×#4612
C3×#51732
C3×#51692
C3×#50862
C3×#50182
C3×#48452
C3×#48362
C3×#48132
C3×#48122
C3×#48092
C3×#48062
C3×#32663
#804443