Finite Group Databasebeta

← C3×#80241 #11884062

Subgroups — C3×#80241 #11884062

Order 1152.

1064 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
4C3×#5632C211yesmaximal, characteristic, complemented
5C32×#452C211yesmaximal, characteristic, complemented
6C3×#5190C211yesmaximal, characteristic, complemented
7C3×#5186C211yesmaximal, characteristic, complemented
8C3×#5162C211yesmaximal, characteristic, complemented
9C3×#5049C211yesmaximal, characteristic, complemented
10C3×#4813C211yesmaximal, characteristic, complemented
11C3×#4798C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic, complemented
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×#4738C211yesmaximal, characteristic, complemented
15C3×#4728C211yesmaximal, characteristic, complemented
16C3×#3266—31nomaximal
17#80241C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C2×C32×Q16C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic, complemented
25C3×#951—24no—
26C3×#947C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C3×#944C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#216C2211yescharacteristic, complemented
31C2×C3×#215C2211yescharacteristic
32C3×#939—21no—
33C3×#937—21no—
34C3×D4×Dic3C2211yescharacteristic
35C2×C3×#214C2211yescharacteristic
36C2×C3×#214C2211yescharacteristic
37C3×#930C2211yescharacteristic
38C3×#929—21no—
39C3×C4×#67C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4—21no—
41C2×C3×#208C2211yescharacteristic, complemented
42C3×D3×SD16—24no—
43C2×C3×#204C2211yescharacteristic
44C2×C3×#204C2211yescharacteristic
45C2×C3×D3×C8C2211yescharacteristic
46C3×#897C2211yescharacteristic
47C3×#896—21no—
48C3×#888—21no—
49C3×#887C2211yescharacteristic, complemented
50C3×#67⋊C4—21no—
51C3×#878—21no—
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic
54C32×C22⋊C8C2211yescharacteristic, complemented
55C3×#835C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#815C2211yescharacteristic, complemented
60C3×Dic3⋊C8C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic
62C3×#807C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65C3×D4×Q8—31no—
66C3×#546—31no—
67#5829C2×C311yescharacteristic
68C2×#951C2×C311yescharacteristic, complemented
69C2×D3×SD16C2×C311yescharacteristic, complemented
70#5632C2×C311yescharacteristic, complemented
71C3×#497—31no—
72C3×#468—31no—
73C3×#467—31no—
74C3×#464—31no—
75C3×#461—31no—
76C3×#452—21no—
77C3×#452D311yescharacteristic, complemented
78C3×#452C2×C311yescharacteristic, complemented
79C3×#451—31no—
80C3×#450—31no—
81C3×#448—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5190C2×C311yescharacteristic, complemented
85#5186C2×C311yescharacteristic, complemented
86#5162C2×C311yescharacteristic, complemented
87#5049C2×C311yescharacteristic, complemented
88#4813C2×C311yescharacteristic, complemented
89#4798C2×C311yescharacteristic, complemented
90#4776C2×C311yescharacteristic, complemented
91#4757C2×C311yescharacteristic, complemented
92#4738C2×C311yescharacteristic, complemented
93#4728C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C32×#41—22no—
96C32×#41—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4C2311yescharacteristic
101C22×C32×C4—21no—
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C3×D3×Q8—22no—
109C3×D3×Q8—41no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C2×C3×D12C2311yescharacteristic
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—41no—
122C32×SD16—22no—
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×#216—22no—
132C3×#215—22no—
133C3×#214—22no—
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)⋊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
150C3×#208—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×#204—22no—
154C3×#204—41no—
155C3×D3×C8—22no—
156#3266—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41C2×D311yescharacteristic
159C2×C3×#41C22×C311yescharacteristic
160C22×C3×Q8—31no—
161C22×C3×Q8—31no—
162C22×C3×D4—31no—
163C2×D3×Q8C22×C311yescharacteristic
164C2×D3×D4C22×C311yescharacteristic
165C22×Dic6C22×C311yescharacteristic, complemented
166C3×#137—64no—
167C2×C3×Q16—21no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C2×C3×Q16C2×D311yescharacteristic, complemented
171C2×C3×Q16C22×C311yescharacteristic, complemented
172C2×C3×SD16—21no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×SD16—31no—
178C2×C3×SD16—64no—
179C2×C3×SD16C2×D311yescharacteristic
180C2×C3×SD16C22×C311yescharacteristic
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, complemented
193C3×C22⋊Q8C22×C311yescharacteristic, complemented
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#951—24no—
203#947C22×C311yescharacteristic
204#946C22×C311yescharacteristic
205#944C22×C311yescharacteristic, complemented
206C2×#216C22×C311yescharacteristic, complemented
207C2×#216C22×C311yescharacteristic, complemented
208C2×#215C22×C311yescharacteristic
209#939—21no—
210#937—21no—
211D4×Dic3C22×C311yescharacteristic
212C2×#214C22×C311yescharacteristic
213C2×#214C22×C311yescharacteristic
214#930C22×C311yescharacteristic
215#929—21no—
216C4×#67C22×C311yescharacteristic
217C2×(C2×D3)⋊C4—21no—
218C2×#208C22×C311yescharacteristic, complemented
219D3×SD16—24no—
220C2×#204C22×C311yescharacteristic
221C2×#204C22×C311yescharacteristic
222C2×D3×C8C22×C311yescharacteristic
223#897C22×C311yescharacteristic
224#896—21no—
225#888—21no—
226#887C22×C311yescharacteristic, complemented
227#67⋊C4—21no—
228#878—21no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103C2×D311yescharacteristic, complemented
236C3×#103C22×C311yescharacteristic, complemented
237C3×#102—21no—
238C3×#102—31no—
239C3×#102C2×D311yescharacteristic
240C3×#102C22×C311yescharacteristic
241C3×C22⋊C8—21no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8C2×D311yescharacteristic, complemented
244C3×C22⋊C8C22×C311yescharacteristic, complemented
245C3×#97—31no—
246#835C22×C311yescharacteristic, complemented
247(C2×D3)⋊C8C22×C311yescharacteristic
248#816C22×C311yescharacteristic, complemented
249#816C22×C311yescharacteristic, complemented
250#815C22×C311yescharacteristic, complemented
251Dic3⋊C8C22×C311yescharacteristic, complemented
252#809C22×C311yescharacteristic
253#807C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
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×D4—21no—
266C32×D4—42no—
267C32×D4C2×D412yes—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—42no—
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2411yescharacteristic
276C3×#67—22no—
277C3×#67—42no—
278C3×#67—81no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3—81no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
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#461—31no—
311#452C3×D311yescharacteristic, complemented
312#451—31no—
313#450—31no—
314#448—31no—
315#440—31no—
316#435—31no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—22no—
320C3×#41—22no—
321C3×#41—42no—
322C3×#41—41no—
323C3×#41—41no—
324C3×#41—42no—
325C2×C3×Q8—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×Q8—61no—
330C2×C3×Q8—62no—
331C2×C3×Q8—61no—
332C2×C3×Q8—62no—
333C2×C3×Q8—121no—
334C2×C3×Q8—121no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×Q8C23×C311yescharacteristic
338C2×C3×Q8C23×C311yescharacteristic
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—31no—
343C2×C3×D4—31no—
344C2×C3×D4—41no—
345C2×C3×D4—61no—
346C2×C3×D4—62no—
347C2×C3×D4—61no—
348C2×C3×D4—121no—
349C2×C3×D4C22×D311yescharacteristic
350C2×C3×D4C23×C311yescharacteristic
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×#67—21no—
362C2×#67—21no—
363C2×#67C3×D411yescharacteristic
364C22×Dic3—21no—
365C22×Dic3—21no—
366D3×Q8—22no—
367D3×Q8—41no—
368D3×D4—22no—
369D3×D4—41no—
370C2×D12C23×C311yescharacteristic
371C2×C4×D3—21no—
372C2×C4×D3C23×C311yescharacteristic
373C2×Dic6—22no—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6—41no—
377C2×Dic6C23×C311yescharacteristic
378C2×Dic6C23×C311yescharacteristic
379C3×Q16—41no—
380C3×Q16—41no—
381C3×Q16—42no—
382C3×Q16—62no—
383C3×Q16—62no—
384C3×SD16—22no—
385C3×SD16—22no—
386C3×SD16—34no—
387C3×SD16—42no—
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#216—22no—
432#215—22no—
433#214—22no—
434#214C3×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
450#208—22no—
451C2×C3⋊C8C23×C311yescharacteristic
452C2×C3⋊C8C23×C311yescharacteristic
453#204—22no—
454#204—41no—
455D3×C8—22no—
456C22×C32—21no—
457C22×C32—22no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—41no—
461C22×C32—41no—
462C22×C32C22×D411yescharacteristic
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—84no—
469C2×C3×D3#13712yescomplemented
470C32×C4—21no—
471C32×C4—41no—
472C32×C4—41no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3×Dic3—22no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41C2×C3×D311yescharacteristic
483C22×Q8—31no—
484C22×Q8—31no—
485C22×D4—31no—
486#137—64no—
487C2×Q16—31no—
488C2×Q16—31no—
489C2×Q16C2×C3×D311yescharacteristic, complemented
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—31no—
494C2×SD16—31no—
495C2×SD16—64no—
496C2×SD16C2×C3×D311yescharacteristic
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, complemented
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#103—31no—
521#103C2×C3×D311yescharacteristic, complemented
522#102—31no—
523#102C2×C3×D311yescharacteristic
524C22⋊C8—31no—
525C22⋊C8C2×C3×D311yescharacteristic, complemented
526#97—31no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—41no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C23×C3—241no—
536C23×C3D3×D411yescharacteristic
537C23×C3C2×C3×D411yescharacteristic
538C22×D3—21no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—81no—
542C22×D3C2×C3×D411yescharacteristic
543C3×Q8—22no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—32no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—41no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×Q8—122no—
560C3×Q8—122no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—22no—
564C3×D4—41no—
565C3×D4—42no—
566C3×D4—42no—
567C3×D4—44no—
568C3×D4—62no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—122no—
572C3×D4—241no—
573C3×D4D3×D412yes—
574C3×D4C2×C3×D412yes—
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—31no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—44no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—122no—
604C2×C3×C4—122no—
605C2×C3×C4—241no—
606C2×C3×C4D3×D411yescharacteristic
607C2×C3×C4C2×C3×D411yescharacteristic
608C2×C3×C4C23×D311yescharacteristic
609C2×C3×C4C24×C311yescharacteristic
610#67—22no—
611#67—42no—
612#67—81no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—42no—
617C2×Dic3—81no—
618C2×Dic3C2×C3×D411yescharacteristic
619C2×Dic3C2×C3×D411yescharacteristic
620C2×Dic3C2×C3×D411yescharacteristic
621D12—21no—
622D12—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—42no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—42no—
630Dic6—42no—
631Dic6C2×C3×D412yes—
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—42no—
643C2×C32—41no—
644C2×C32D4211yescharacteristic
645C2×C32C2×#13711yescharacteristic
646C2×C32#57711yescharacteristic
647C3×D3—22no—
648C3×D3—81no—
649C24—61no—
650#41—22no—
651#41—41no—
652C2×Q8—31no—
653C2×Q8—31no—
654C2×Q8—61no—
655C2×Q8—62no—
656C2×Q8—61no—
657C2×Q8—62no—
658C2×Q8—121no—
659C2×Q8—121no—
660C2×Q8C22×C3×D311yescharacteristic
661C2×Q8C22×C3×D311yescharacteristic
662C2×D4—21no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—61no—
666C2×D4—62no—
667C2×D4—61no—
668C2×D4—121no—
669C2×D4C22×C3×D311yescharacteristic
670C22×C4—21no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4C22×C3×D311yescharacteristic
676Q16—41no—
677Q16—62no—
678Q16—62no—
679SD16—22no—
680SD16—34no—
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—21no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—22no—
719C22×C3—21no—
720C22×C3—32no—
721C22×C3—42no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—244no—
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C22×C3×D411yescharacteristic
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—84no—
745C2×D3C3×#13712yescomplemented
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—41no—
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—62no—
762C3×C4—81no—
763C3×C4—81no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4C2×D3×D411yescharacteristic
767C3×C4#100411yescharacteristic
768C3×C4C22×C3×D411yescharacteristic
769C3×C4C3×H(5,𝔽2)11yescharacteristic
770Dic3—21no—
771Dic3—21no—
772Dic3—22no—
773Dic3—21no—
774Dic3—41no—
775Dic3—41no—
776C32#326611yescharacteristic, complemented, Sylow
777C23—21no—
778C23—31no—
779C23—61no—
780C23—122no—
781C23—122no—
782C23—241no—
783C23C3×D3×D411yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—21no—
787Q8—21no—
788Q8—32no—
789Q8—61no—
790Q8—61no—
791Q8—61no—
792Q8—122no—
793Q8—122no—
794D4—21no—
795D4—42no—
796D4—62no—
797D4—61no—
798D4—61no—
799D4—122no—
800D4—241no—
801D4C3×D3×D412yes—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—31no—
810C2×C4—42no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—241no—
819C2×C4C3×D3×D411yescharacteristic
820C2×C4C23×C3×D311yescharacteristic
821C8—21no—
822C8—21no—
823C8—32no—
824C8—61no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—41no—
829C2×C3—42no—
830C2×C3—42no—
831C2×C3—41no—
832C2×C3—62no—
833C2×C3—81no—
834C2×C3—82no—
835C2×C3—241no—
836C2×C3#559011yescharacteristic
837C2×C3#577011yescharacteristic
838C2×C3D3×#13711yescharacteristic
839C2×C3C3×D4211yescharacteristic
840C2×C3C2×C3×#13711yescharacteristic
841C2×C3C3×#57711yescharacteristic
842D3—22no—
843D3—81no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—22no—
848C22—32no—
849C22—41no—
850C22—41no—
851C22—61no—
852C22—61no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—244no—
857C22C2×C3×D3×D411yescharacteristic
858C4—21no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—61no—
863C4—61no—
864C4—61no—
865C4—62no—
866C4—121no—
867C4—121no—
868C4C2×C3×D3×D411yescharacteristic
869C4C3×#100411yescharacteristic
870C3—21no—
871C3#8024111yescharacteristic, direct product factor
872C3C3×#326611yescharacteristic, complemented
873C2—41no—
874C2—42no—
875C2—62no—
876C2—241no—
877C2C3×#559011yescharacteristic
878C2C3×#577011yescharacteristic
879C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
prime radicalC3×#5829C2
hypercenterC3×#452D3
hypocenterC3C3×#3266
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×C3×D3×SD16C2semidirect
4. C3×#5632C2semidirect
5. C32×#452C2semidirect
6. C3×#5190C2semidirect
7. C3×#5186C2semidirect
8. C3×#5162C2semidirect
9. C3×#5049C2semidirect
10. C3×#4813C2semidirect
11. C3×#4798C2semidirect
12. C3×#4776C2semidirect
13. C3×#4757C2semidirect
14. C3×#4738C2semidirect
15. C3×#4728C2semidirect
17. #80241C3direct (N × H)
21. C22×C3×Dic6C22semidirect
22. C2×C32×Q16C22semidirect
24. C32×C22⋊Q8C22semidirect
28. C3×#944C22semidirect
29. C2×C3×#216C22semidirect
30. C2×C3×#216C22semidirect
41. C2×C3×#208C22semidirect
49. C3×#887C22semidirect
52. C32×#103C22semidirect
54. C32×C22⋊C8C22semidirect
55. C3×#835C22semidirect
57. C3×#816C22semidirect
58. C3×#816C22semidirect
59. C3×#815C22semidirect
60. C3×Dic3⋊C8C22semidirect
62. C3×#807C22semidirect
68. C2×#951C2×C3semidirect
69. C2×D3×SD16C2×C3semidirect
70. #5632C2×C3semidirect
77. C3×#452D3semidirect
78. C3×#452C2×C3semidirect
84. #5190C2×C3semidirect
85. #5186C2×C3semidirect
86. #5162C2×C3semidirect
87. #5049C2×C3semidirect
88. #4813C2×C3semidirect
89. #4798C2×C3semidirect
90. #4776C2×C3semidirect
91. #4757C2×C3semidirect
92. #4738C2×C3semidirect
93. #4728C2×C3semidirect
134. C3×#214D4semidirect
165. C22×Dic6C22×C3semidirect
170. C2×C3×Q16C2×D3semidirect
171. C2×C3×Q16C22×C3semidirect
192. C3×C22⋊Q8C2×D3semidirect
193. C3×C22⋊Q8C22×C3semidirect
205. #944C22×C3semidirect
206. C2×#216C22×C3semidirect
207. C2×#216C22×C3semidirect
218. C2×#208C22×C3semidirect
226. #887C22×C3semidirect
235. C3×#103C2×D3semidirect
236. C3×#103C22×C3semidirect
243. C3×C22⋊C8C2×D3semidirect
244. C3×C22⋊C8C22×C3semidirect
246. #835C22×C3semidirect
248. #816C22×C3semidirect
249. #816C22×C3semidirect
250. #815C22×C3semidirect
251. Dic3⋊C8C22×C3semidirect
253. #807C22×C3semidirect
311. #452C3×D3semidirect
434. #214C3×D4semidirect
469. C2×C3×D3#137semidirect
489. C2×Q16C2×C3×D3semidirect
507. C22⋊Q8C2×C3×D3semidirect
521. #103C2×C3×D3semidirect
525. C22⋊C8C2×C3×D3semidirect
745. C2×D3C3×#137semidirect
776. C32#3266semidirect
871. C3#80241direct (N × H)
872. C3C3×#3266semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
C2×C3×#9512
C2×C3×D3×SD162
C3×#56322
C32×#4522
C3×#51902
C3×#51862
C3×#51622
C3×#50492
C3×#48132
C3×#47982
C3×#47762
C3×#47572
C3×#47382
C3×#47282
C3×#32663
#802413