Finite Group Databasebeta

← C3×#80537 #11866240

Subgroups — C3×#80537 #11866240

Order 1152.

1050 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic
3C3×#5675C211yesmaximal, characteristic, complemented
4C3×#5545C211yesmaximal, characteristic, complemented
5C32×#463C211yesmaximal, characteristic, complemented
6C3×#5162C211yesmaximal, characteristic, complemented
7C3×#5153C211yesmaximal, characteristic, complemented
8C3×#5057C211yesmaximal, characteristic, complemented
9C3×#5019C211yesmaximal, characteristic, complemented
10C3×#4841C211yesmaximal, characteristic, complemented
11C3×#4839C211yesmaximal, characteristic, complemented
12C3×#4818C211yesmaximal, characteristic, complemented
13C3×#4802C211yesmaximal, characteristic, complemented
14C3×#4787C211yesmaximal, characteristic, complemented
15C3×#4772C211yesmaximal, characteristic, complemented
16C3×#3042—31nomaximal
17#80537C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C2×C32×D8C2211yescharacteristic
23C32×#124C2211yescharacteristic, complemented
24C32×C4×D4C2211yescharacteristic
25C3×#944C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C3×#936C2211yescharacteristic, complemented
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×C4×#67—21no—
33C2×C3×(C2×D3)⋊C4—21no—
34C3×D3×SD16—24no—
35C3×#911—24no—
36C2×C3×#204C2211yescharacteristic
37C2×C3×#204C2211yescharacteristic
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
39C2×C3×D3×C8C2211yescharacteristic
40C3×#893C2211yescharacteristic
41C3×#892C2211yescharacteristic
42C3×#883—21no—
43C3×#883—21no—
44C3×#67⋊C4—21no—
45C3×D3×C22⋊C4—21no—
46C3×#878—21no—
47C3×#878—21no—
48C3×C4×D12C2211yescharacteristic
49C3×#872C2211yescharacteristic
50C3×#869C2211yescharacteristic, complemented
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61C3×#810C2211yescharacteristic, complemented
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C22×C3×SD16—31no—
65C3×#536—31no—
66C3×#518—31no—
67C2×D3×SD16C2×C311yescharacteristic, complemented
68C2×#911C2×C311yescharacteristic
69#5675C2×C311yescharacteristic, complemented
70#5545C2×C311yescharacteristic, complemented
71C3×#463—21no—
72C3×#463—31no—
73C3×#463—31no—
74C3×#463—31no—
75C3×#463D311yescharacteristic, complemented
76C3×#463C2×C311yescharacteristic, complemented
77C3×#461—31no—
78C3×#461—31no—
79C3×#461—31no—
80C3×#461—31no—
81C3×#424—31no—
82C3×#419—31no—
83C3×#416—31no—
84#5162C2×C311yescharacteristic, complemented
85#5153C2×C311yescharacteristic, complemented
86#5057C2×C311yescharacteristic, complemented
87#5019C2×C311yescharacteristic, complemented
88#4841C2×C311yescharacteristic, complemented
89#4839C2×C311yescharacteristic, complemented
90#4818C2×C311yescharacteristic, complemented
91#4802C2×C311yescharacteristic, complemented
92#4787C2×C311yescharacteristic, complemented
93#4772C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×D3×Q8—22no—
104C3×D3×Q8—22no—
105C3×#237—22no—
106C3×#237—22no—
107C3×D3×D4—22no—
108C3×D3×D4D414yes—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6—21no—
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C32×SD16—22no—
118C32×D8—22no—
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C22⋊C4—21no—
124C32×C22⋊C4—21no—
125C32×C42C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#217—21no—
129C3×#215—22no—
130C3×#214—22no—
131C3×#214—22no—
132C3×#213—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×Dic3⋊C4D411yescharacteristic
145C3×C4×Dic3—21no—
146C3×C4×Dic3C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C3×#204—22no—
150C3×#204—22no—
151C3×ΓL(1,𝔽25)—22no—
152C3×D3×C8—22no—
153#3042—31noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C22×C3×D4—31no—
157C2×D3×Q8C22×C311yescharacteristic
158C2×#237C22×C311yescharacteristic
159C2×D3×D4C22×C311yescharacteristic
160C3×AGL(1,ℤ/8)—64no—
161C2×C3×SD16—21no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—64no—
168C2×C3×SD16C2×D311yescharacteristic
169C2×C3×SD16C22×C311yescharacteristic
170C2×C3×D8—21no—
171C2×C3×D8—31no—
172C2×C3×D8C2×D311yescharacteristic
173C2×C3×D8C22×C311yescharacteristic
174C2×C3×M16—31no—
175C22×C3×C8—31no—
176C3×C4⋊Q8—31no—
177C3×C4⋊Q8—31no—
178C3×#124—21no—
179C3×#124—31no—
180C3×#124C2×D311yescharacteristic, complemented
181C3×#124C22×C311yescharacteristic, complemented
182C3×#123—61no—
183C3×#123—61no—
184C3×C22⋊Q8—61no—
185C3×C22⋊Q8—61no—
186C3×C4×D4—21no—
187C3×C4×D4—31no—
188C3×C4×D4—31no—
189C3×C4×D4—31no—
190C3×C4×D4—61no—
191C3×C4×D4—61no—
192C3×C4×D4C2×D311yescharacteristic
193C3×C4×D4C22×C311yescharacteristic
194C3×#117—31no—
195C3×#117—31no—
196C2×C3×C22⋊C4—61no—
197C2×C3×C22⋊C4—61no—
198#944C22×C311yescharacteristic, complemented
199C2×#215C22×C311yescharacteristic
200#936C22×C311yescharacteristic, complemented
201D4×Dic3C22×C311yescharacteristic
202C2×#214C22×C311yescharacteristic
203C2×#214C22×C311yescharacteristic
204C2×#213C22×C311yescharacteristic
205C4×#67—21no—
206C2×(C2×D3)⋊C4—21no—
207D3×SD16—24no—
208#911—24no—
209C2×#204C22×C311yescharacteristic
210C2×#204C22×C311yescharacteristic
211C2×ΓL(1,𝔽25)C22×C311yescharacteristic
212C2×D3×C8C22×C311yescharacteristic
213#893C22×C311yescharacteristic
214#892C22×C311yescharacteristic
215#883—21no—
216#883—21no—
217#67⋊C4—21no—
218D3×C22⋊C4—21no—
219#878—21no—
220#878—21no—
221C4×D12C22×C311yescharacteristic
222#872C22×C311yescharacteristic
223#869C22×C311yescharacteristic, complemented
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic, complemented
229C3×C4⋊C8C22×C311yescharacteristic, complemented
230C3×#103—21no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103—31no—
236C3×#103C2×D311yescharacteristic, complemented
237C3×#103C22×C311yescharacteristic, complemented
238C3×#102—21no—
239C3×#102—31no—
240C3×#102C2×D311yescharacteristic, complemented
241C3×#102C22×C311yescharacteristic, complemented
242#835C22×C311yescharacteristic, complemented
243#832C22×C311yescharacteristic, complemented
244#816C22×C311yescharacteristic, complemented
245#816C22×C311yescharacteristic, complemented
246Dic3⋊C8C22×C311yescharacteristic, complemented
247Dic3⋊C8C22×C311yescharacteristic, complemented
248#810C22×C311yescharacteristic, complemented
249#810C22×C311yescharacteristic, complemented
250C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
251C23×C32—21no—
252C23×C32—21no—
253C22×C3×D3—21no—
254C22×C3×D3—24no—
255C22×C3×D3—81no—
256C22×C3×D3—81no—
257C22×C3×D3C2×D411yescharacteristic
258C32×Q8—21no—
259C32×Q8—21no—
260C32×D4—21no—
261C32×D4—21no—
262C32×D4—21no—
263C32×D4C2×D412yes—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—81no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C3×#67—24no—
271C3×#67—42no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—42no—
276C2×C3×Dic3—81no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12C2×D412yes—
282C3×C4×D3—42no—
283C3×C4×D3—81no—
284C3×C4×D3—81no—
285C3×C4×D3C2×D412yes—
286C3×C4×D3#4112yes—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292C32×C8—21no—
293C32×C8—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×AGL(1,ℤ/8)—31no—
297C22×SD16—31no—
298#536—31no—
299#518—31no—
300#463—31no—
301#463—31no—
302#463—31no—
303#463C3×D311yescharacteristic, complemented
304#461—31no—
305#461—31no—
306#461—31no—
307#461—31no—
308#424—31no—
309#419—31no—
310#416—31no—
311C24×C3—61no—
312C23×D3—21no—
313C3×#41—62no—
314C3×#41—62no—
315C2×C3×Q8—21no—
316C2×C3×Q8—31no—
317C2×C3×Q8—31no—
318C2×C3×Q8—61no—
319C2×C3×Q8—62no—
320C2×C3×Q8—62no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C23×C311yescharacteristic
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—34no—
326C2×C3×D4—31no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C23×C311yescharacteristic
333C2×C3×D4C23×C311yescharacteristic
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—41no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C22×C3×C4—61no—
343C2×#67—21no—
344C2×#67—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347D3×Q8—22no—
348D3×Q8—22no—
349#237—22no—
350#237—22no—
351D3×D4—22no—
352D3×D4C3×D414yes—
353C2×D12C23×C311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—21no—
357C2×C4×D3C23×C311yescharacteristic
358C2×Dic6—21no—
359C2×Dic6C23×C311yescharacteristic
360C2×Dic6C23×C311yescharacteristic
361C3×SD16—22no—
362C3×SD16—22no—
363C3×SD16—42no—
364C3×SD16—62no—
365C3×SD16—62no—
366C3×SD16—62no—
367C3×SD16—62no—
368C3×SD16—62no—
369C3×D8—22no—
370C3×D8—22no—
371C3×D8—42no—
372C3×D8—62no—
373C3×M16—62no—
374C2×C3×C8—21no—
375C2×C3×C8—21no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C2×C3×C8—62no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C2×C3×C8C23×C311yescharacteristic
382C2×C3×C8C23×C311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C4⋊C4C23×C311yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—31no—
401C3×C22⋊C4—41no—
402C3×C22⋊C4—41no—
403C3×C22⋊C4—41no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—21no—
411C3×C42—31no—
412C3×C42—61no—
413C3×C42C22×D311yescharacteristic
414C3×C42C23×C311yescharacteristic
415#217—21no—
416#217—21no—
417#217—21no—
418#215—22no—
419#214—22no—
420#214—22no—
421#213—22no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4C3×D411yescharacteristic
426(C2×D3)⋊C4C3×D411yescharacteristic
427C4⋊Dic3—21no—
428C4⋊Dic3—21no—
429C4⋊Dic3C23×C311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—21no—
432Dic3⋊C4C3×D411yescharacteristic
433Dic3⋊C4C3×D411yescharacteristic
434C4×Dic3—21no—
435C4×Dic3C23×C311yescharacteristic
436C2×C3⋊C8C23×C311yescharacteristic
437C2×C3⋊C8C23×C311yescharacteristic
438#204—22no—
439#204—22no—
440ΓL(1,𝔽25)—22no—
441D3×C8—22no—
442C22×C32—22no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32C22×D411yescharacteristic
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—22no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—84no—
455C2×C3×D3#12112yes—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—41no—
459C32×C4—41no—
460C32×C4C22×D411yescharacteristic
461C32×C4C2×#4111yescharacteristic
462C3×Dic3—21no—
463C3×Dic3—21no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—31no—
469C22×Q8—31no—
470C22×D4—31no—
471AGL(1,ℤ/8)—64no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—31no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—64no—
478C2×SD16C2×C3×D311yescharacteristic
479C2×D8—31no—
480C2×D8C2×C3×D311yescharacteristic
481C2×M16—31no—
482C22×C8—31no—
483C4⋊Q8—31no—
484C4⋊Q8—31no—
485#124—31no—
486#124C2×C3×D311yescharacteristic, complemented
487#123—61no—
488#123—61no—
489C22⋊Q8—61no—
490C22⋊Q8—61no—
491C4×D4—31no—
492C4×D4—31no—
493C4×D4—31no—
494C4×D4—61no—
495C4×D4—61no—
496C4×D4C2×C3×D311yescharacteristic
497#117—31no—
498#117—31no—
499C2×C22⋊C4—61no—
500C2×C22⋊C4—61no—
501C4⋊C8—31no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8C2×C3×D311yescharacteristic, complemented
505#103—31no—
506#103—31no—
507#103—31no—
508#103—31no—
509#103—31no—
510#103C2×C3×D311yescharacteristic, complemented
511#102—31no—
512#102C2×C3×D311yescharacteristic, complemented
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—31no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—64no—
521C23×C3—61no—
522C23×C3—241no—
523C23×C3—241no—
524C22×D3—21no—
525C22×D3—24no—
526C22×D3—81no—
527C22×D3—81no—
528C22×D3C2×C3×D411yescharacteristic
529C3×Q8—21no—
530C3×Q8—21no—
531C3×Q8—21no—
532C3×Q8—21no—
533C3×Q8—41no—
534C3×Q8—41no—
535C3×Q8—61no—
536C3×Q8—61no—
537C3×Q8—61no—
538C3×Q8—61no—
539C3×Q8—122no—
540C3×D4—21no—
541C3×D4—21no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—22no—
547C3×D4—32no—
548C3×D4—41no—
549C3×D4—41no—
550C3×D4—41no—
551C3×D4—64no—
552C3×D4—61no—
553C3×D4—122no—
554C3×D4D3×D412yes—
555C3×D4C2×C3×D412yes—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—81no—
574C2×C3×C4—81no—
575C2×C3×C4—82no—
576C2×C3×C4—122no—
577C2×C3×C4—122no—
578C2×C3×C4—241no—
579C2×C3×C4—241no—
580C2×C3×C4—241no—
581C2×C3×C4D3×D411yescharacteristic
582C2×C3×C4D3×D411yescharacteristic
583C2×C3×C4C2×C3×D411yescharacteristic
584C2×C3×C4C2×C3×D411yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C24×C311yescharacteristic
587#67—24no—
588#67—42no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—42no—
593C2×Dic3—81no—
594C2×Dic3C2×C3×D411yescharacteristic
595C2×Dic3C2×C3×D411yescharacteristic
596C2×Dic3C2×C3×D411yescharacteristic
597D12—21no—
598D12C2×C3×D412yes—
599C4×D3—42no—
600C4×D3—81no—
601C4×D3—81no—
602C4×D3C2×C3×D412yes—
603C4×D3C3×#4112yes—
604Dic6—21no—
605Dic6—21no—
606Dic6—21no—
607Dic6—21no—
608Dic6—42no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—41no—
614C3×C8—41no—
615C3×C8—61no—
616C3×C8—61no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C2×C32—42no—
620C2×C32—81no—
621C2×C32C2×#12111yescharacteristic
622C2×C32#57711yescharacteristic
623C2×C32#57711yescharacteristic
624C3×D3—22no—
625C3×D3—42no—
626C24—61no—
627#41—62no—
628#41—62no—
629C2×Q8—31no—
630C2×Q8—31no—
631C2×Q8—61no—
632C2×Q8—62no—
633C2×Q8—62no—
634C2×Q8C22×C3×D311yescharacteristic
635C2×D4—34no—
636C2×D4—31no—
637C2×D4—62no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4C22×C3×D311yescharacteristic
641C2×D4C22×C3×D311yescharacteristic
642C22×C4—21no—
643C22×C4—31no—
644C22×C4—61no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649SD16—22no—
650SD16—62no—
651SD16—62no—
652SD16—62no—
653SD16—62no—
654SD16—62no—
655D8—22no—
656D8—62no—
657M16—62no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—62no—
661C2×C8C22×C3×D311yescharacteristic
662C2×C8C22×C3×D311yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—31no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4C22×C3×D311yescharacteristic
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C22⋊C4—61no—
680C22⋊C4—61no—
681C22⋊C4—61no—
682C42—31no—
683C42—61no—
684C42C22×C3×D311yescharacteristic
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—21no—
688C22×C3—32no—
689C22×C3—42no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—62no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—244no—
711C22×C3C2×D3×D411yescharacteristic
712C22×C3C22×C3×D411yescharacteristic
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—22no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—84no—
719C2×D3C3×#12112yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—32no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—81no—
736C3×C4—81no—
737C3×C4—121no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4C2×D3×D411yescharacteristic
741C3×C4D3×#4111yescharacteristic
742C3×C4C22×C3×D411yescharacteristic
743C3×C4C2×C3×#4111yescharacteristic
744Dic3—21no—
745Dic3—21no—
746Dic3—41no—
747Dic3—41no—
748Dic3—41no—
749Dic3C3×#12112yes—
750C32#304211yescharacteristic, complemented, Sylow
751C23—21no—
752C23—21no—
753C23—31no—
754C23—64no—
755C23—61no—
756C23—241no—
757C23—241no—
758Q8—21no—
759Q8—21no—
760Q8—61no—
761Q8—61no—
762Q8—61no—
763Q8—61no—
764Q8—122no—
765D4—21no—
766D4—21no—
767D4—21no—
768D4—32no—
769D4—64no—
770D4—61no—
771D4—122no—
772D4C3×D3×D412yes—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—31no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—81no—
784C2×C4—122no—
785C2×C4—122no—
786C2×C4—241no—
787C2×C4—241no—
788C2×C4—241no—
789C2×C4C3×D3×D411yescharacteristic
790C2×C4C3×D3×D411yescharacteristic
791C2×C4C23×C3×D311yescharacteristic
792C8—21no—
793C8—21no—
794C8—61no—
795C8—61no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—42no—
800C2×C3—42no—
801C2×C3—62no—
802C2×C3—82no—
803C2×C3—81no—
804C2×C3—81no—
805C2×C3—122no—
806C2×C3—161no—
807C2×C3D3×#12111yescharacteristic
808C2×C3#577011yescharacteristic
809C2×C3#577511yescharacteristic
810C2×C3C2×C3×#12111yescharacteristic
811C2×C3C3×#57711yescharacteristic
812C2×C3C3×#57711yescharacteristic
813D3—22no—
814D3—42no—
815C22—22no—
816C22—32no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—61no—
823C22—61no—
824C22—62no—
825C22—121no—
826C22—121no—
827C22—244no—
828C22C2×C3×D3×D411yescharacteristic
829C4—21no—
830C4—21no—
831C4—32no—
832C4—41no—
833C4—41no—
834C4—61no—
835C4—61no—
836C4—121no—
837C4—121no—
838C4—121no—
839C4C2×C3×D3×D411yescharacteristic
840C4C3×D3×#4111yescharacteristic
841C3—21no—
842C3#8053711yescharacteristic, direct product factor
843C3C3×#304211yescharacteristic, complemented
844C2—42no—
845C2—62no—
846C2—81no—
847C2—122no—
848C2C3×D3×#12111yescharacteristic
849C2C3×#577011yescharacteristic
850C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
prime radicalC2×C3×#911C2
hypercenterC3×#463D3
hypocenterC3C3×#3042
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×SD16C2semidirect
3. C3×#5675C2semidirect
4. C3×#5545C2semidirect
5. C32×#463C2semidirect
6. C3×#5162C2semidirect
7. C3×#5153C2semidirect
8. C3×#5057C2semidirect
9. C3×#5019C2semidirect
10. C3×#4841C2semidirect
11. C3×#4839C2semidirect
12. C3×#4818C2semidirect
13. C3×#4802C2semidirect
14. C3×#4787C2semidirect
15. C3×#4772C2semidirect
17. #80537C3direct (N × H)
23. C32×#124C22semidirect
25. C3×#944C22semidirect
27. C3×#936C22semidirect
50. C3×#869C22semidirect
51. C32×C4⋊C8C22semidirect
52. C32×#103C22semidirect
53. C32×#102C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#816C22semidirect
57. C3×#816C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. C3×#810C22semidirect
61. C3×#810C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×D3×SD16C2×C3semidirect
69. #5675C2×C3semidirect
70. #5545C2×C3semidirect
75. C3×#463D3semidirect
76. C3×#463C2×C3semidirect
84. #5162C2×C3semidirect
85. #5153C2×C3semidirect
86. #5057C2×C3semidirect
87. #5019C2×C3semidirect
88. #4841C2×C3semidirect
89. #4839C2×C3semidirect
90. #4818C2×C3semidirect
91. #4802C2×C3semidirect
92. #4787C2×C3semidirect
93. #4772C2×C3semidirect
180. C3×#124C2×D3semidirect
181. C3×#124C22×C3semidirect
198. #944C22×C3semidirect
200. #936C22×C3semidirect
223. #869C22×C3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C22×C3semidirect
236. C3×#103C2×D3semidirect
237. C3×#103C22×C3semidirect
240. C3×#102C2×D3semidirect
241. C3×#102C22×C3semidirect
242. #835C22×C3semidirect
243. #832C22×C3semidirect
244. #816C22×C3semidirect
245. #816C22×C3semidirect
246. Dic3⋊C8C22×C3semidirect
247. Dic3⋊C8C22×C3semidirect
248. #810C22×C3semidirect
249. #810C22×C3semidirect
250. C4⋊(C3⋊C8)C22×C3semidirect
303. #463C3×D3semidirect
486. #124C2×C3×D3semidirect
504. C4⋊C8C2×C3×D3semidirect
510. #103C2×C3×D3semidirect
512. #102C2×C3×D3semidirect
750. C32#3042semidirect
842. C3#80537direct (N × H)
843. C3C3×#3042semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
C2×C3×#9112
C3×#56752
C3×#55452
C32×#4632
C3×#51622
C3×#51532
C3×#50572
C3×#50192
C3×#48412
C3×#48392
C3×#48182
C3×#48022
C3×#47872
C3×#47722
C3×#30423
#805373