Finite Group Databasebeta

← C3×#80185 #11864473

Subgroups — C3×#80185 #11864473

Order 1152.

1474 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2C2×C3×#918C211yesmaximal, characteristic, complemented
3C2×C3×D3×Q16C211yesmaximal, characteristic, complemented
4C3×#5628C211yesmaximal, characteristic, complemented
5C32×#451C211yesmaximal, characteristic, complemented
6C3×#5228C211yesmaximal, characteristic, complemented
7C3×#5187C211yesmaximal, characteristic, complemented
8C3×#5186C211yesmaximal, characteristic, complemented
9C3×#5047C211yesmaximal, characteristic, complemented
10C3×#4809C211yesmaximal, characteristic, complemented
11C3×#4808C211yesmaximal, characteristic, complemented
12C3×#4804C211yesmaximal, characteristic, complemented
13C3×#4802C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic, complemented
16C3×#3011—31nomaximal
17#80185C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C3×#1007—24no—
20C3×#1007—24no—
21C2×C3×#239—21no—
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2211yescharacteristic
24C2×C3×D3×Q8—21no—
25C2×C3×D3×Q8C2211yescharacteristic
26C2×C3×D3×Q8C2211yescharacteristic
27C2×C3×D3×Q8C2211yescharacteristic
28C2×C3×#235—21no—
29C2×C3×#235—21no—
30C2×C3×#235C2211yescharacteristic
31C2×C3×#235C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic
33C2×C32×Q16C2211yescharacteristic
34C32×C22⋊Q8C2211yescharacteristic
35C3×#946C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic
37C2×C3×#216C2211yescharacteristic
38C2×C3×#216C2211yescharacteristic
39C2×C3×#215C2211yescharacteristic
40C3×#924C2211yescharacteristic
41C3×#918—24no—
42C3×D3×Q16—24no—
43C2×C3×Dic12C2211yescharacteristic
44C2×C3×#204C2211yescharacteristic
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
46C2×C3×D3×C8C2211yescharacteristic
47C3×#897C2211yescharacteristic
48C3×#894—21no—
49C3×#892C2211yescharacteristic
50C3×#888—21no—
51C3×#885—21no—
52C3×#883—21no—
53C32×#103C2211yescharacteristic
54C32×#103C2211yescharacteristic
55C32×C22⋊C8C2211yescharacteristic
56C3×#835C2211yescharacteristic
57C3×#835C2211yescharacteristic
58C3×#830C2211yescharacteristic
59C3×#821C2211yescharacteristic
60C3×(C2×D3)⋊C8C2211yescharacteristic
61C3×(C2×D3)⋊C8C2211yescharacteristic
62C3×#816C2211yescharacteristic
63C3×#810C2211yescharacteristic
64C3×#809C2211yescharacteristic
65C2×C3×2−1+4—31no—
66C2×#1007C2×C311yescharacteristic
67C2×C3×#137—31no—
68C22×C3×Q16—31no—
69C3×#536—31no—
70C2×#918C2×C311yescharacteristic, complemented
71C2×D3×Q16C2×C311yescharacteristic, complemented
72#5628C2×C311yescharacteristic, complemented
73C3×#452—31no—
74C3×#452—31no—
75C3×#452—31no—
76C3×#452—31no—
77C3×#451—21no—
78C3×#451—31no—
79C3×#451—31no—
80C3×#451—31no—
81C3×#451D311yescharacteristic, complemented
82C3×#451C2×C311yescharacteristic, complemented
83C3×#419—31no—
84C3×#416—31no—
85C3×#408—31no—
86#5228C2×C311yescharacteristic, complemented
87#5187C2×C311yescharacteristic, complemented
88#5186C2×C311yescharacteristic, complemented
89#5047C2×C311yescharacteristic, complemented
90#4809C2×C311yescharacteristic, complemented
91#4808C2×C311yescharacteristic, complemented
92#4804C2×C311yescharacteristic, complemented
93#4802C2×C311yescharacteristic, complemented
94#4733C2×C311yescharacteristic, complemented
95#4727C2×C311yescharacteristic, complemented
96C2×C32×Q8—22no—
97C2×C32×Q8—22no—
98C2×C32×Q8—21no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×Q8C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C22×C32×C4—21no—
103C22×C32×C4C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C2×C3×#67D411yescharacteristic
107C3×#239—28no—
108C3×#239—22no—
109C3×#239—22no—
110C3×#239—22no—
111C3×#239D414yes—
112C3×D3×Q8—28no—
113C3×D3×Q8—22no—
114C3×D3×Q8—22no—
115C3×D3×Q8—22no—
116C3×D3×Q8—22no—
117C3×D3×Q8—22no—
118C3×D3×Q8D414yes—
119C3×#235—28no—
120C3×#235—28no—
121C3×#235—22no—
122C3×#235—22no—
123C3×#235—22no—
124C3×#235—22no—
125C2×C3×D12—21no—
126C2×C3×D12—21no—
127C2×C3×D12D411yescharacteristic
128C2×C3×D12C2311yescharacteristic
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—21no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×Dic6—21no—
138C2×C3×Dic6—21no—
139C2×C3×Dic6—21no—
140C2×C3×Dic6D411yescharacteristic
141C2×C3×Dic6C2311yescharacteristic
142C2×C3×Dic6C2311yescharacteristic
143C32×Q16—22no—
144C32×Q16—22no—
145C2×C32×C8C2311yescharacteristic
146C2×C32×C8C2311yescharacteristic
147C32×C4⋊C4—21no—
148C32×C4⋊C4C2311yescharacteristic
149C32×C22⋊C4—21no—
150C3×#217—21no—
151C3×#216—22no—
152C3×#216—22no—
153C3×#216—22no—
154C3×#215—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×(C2×D3)⋊C4—21no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3—21no—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×Dic3⋊C4—21no—
161C3×Dic3⋊C4—21no—
162C3×C4×Dic3—21no—
163C2×C3×C3⋊C8C2311yescharacteristic
164C2×C3×C3⋊C8C2311yescharacteristic
165C3×Dic12—22no—
166C3×#204—22no—
167C3×ΓL(1,𝔽25)—22no—
168C3×D3×C8—22no—
169#3011—31noSylow
170C3×2−1+4—64no—
171C3×2−1+4—64no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C2×C3×#41—61no—
178C2×C3×#41—61no—
179C22×C3×Q8—21no—
180C22×C3×Q8—31no—
181C22×C3×Q8—31no—
182C22×C3×Q8—31no—
183C22×C3×Q8—61no—
184C22×C3×Q8C2×D311yescharacteristic
185C22×C3×Q8C22×C311yescharacteristic
186#1007—24no—
187#1007—24no—
188C2×#239—21no—
189C2×#239C22×C311yescharacteristic
190C2×#239C22×C311yescharacteristic
191C2×D3×Q8—21no—
192C2×D3×Q8C22×C311yescharacteristic
193C2×D3×Q8C22×C311yescharacteristic
194C2×D3×Q8C22×C311yescharacteristic
195C2×#235—21no—
196C2×#235—21no—
197C2×#235C22×C311yescharacteristic
198C2×#235C22×C311yescharacteristic
199C3×#137—64no—
200C2×C3×Q16—21no—
201C2×C3×Q16—21no—
202C2×C3×Q16—31no—
203C2×C3×Q16—31no—
204C2×C3×Q16—31no—
205C2×C3×Q16—31no—
206C2×C3×Q16—64no—
207C2×C3×Q16C2×D311yescharacteristic
208C2×C3×Q16C2×D311yescharacteristic
209C2×C3×Q16C22×C311yescharacteristic
210C2×C3×Q16C22×C311yescharacteristic
211C2×C3×SD16—31no—
212C2×C3×SD16—31no—
213C2×C3×M16—31no—
214C22×C3×C8—31no—
215C3×C4⋊Q8—61no—
216C3×#124—61no—
217C3×#123—61no—
218C3×#123—61no—
219C3×C22⋊Q8—21no—
220C3×C22⋊Q8—31no—
221C3×C22⋊Q8—31no—
222C3×C22⋊Q8—31no—
223C3×C22⋊Q8C2×D311yescharacteristic
224C3×C22⋊Q8C22×C311yescharacteristic
225C3×#117—31no—
226#946C22×C311yescharacteristic
227C2×#216C22×C311yescharacteristic
228C2×#216C22×C311yescharacteristic
229C2×#216C22×C311yescharacteristic
230C2×#215C22×C311yescharacteristic
231#924C22×C311yescharacteristic
232#918—24no—
233D3×Q16—24no—
234C2×Dic12C22×C311yescharacteristic
235C2×#204C22×C311yescharacteristic
236C2×ΓL(1,𝔽25)C22×C311yescharacteristic
237C2×D3×C8C22×C311yescharacteristic
238#897C22×C311yescharacteristic
239#894—21no—
240#892C22×C311yescharacteristic
241#888—21no—
242#885—21no—
243#883—21no—
244C3×#103—21no—
245C3×#103—21no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103—31no—
249C3×#103—31no—
250C3×#103C2×D311yescharacteristic
251C3×#103C2×D311yescharacteristic
252C3×#103C22×C311yescharacteristic
253C3×#103C22×C311yescharacteristic
254C3×#102—31no—
255C3×#102—31no—
256C3×C22⋊C8—21no—
257C3×C22⋊C8—31no—
258C3×C22⋊C8—31no—
259C3×C22⋊C8—31no—
260C3×C22⋊C8C2×D311yescharacteristic
261C3×C22⋊C8C22×C311yescharacteristic
262#835C22×C311yescharacteristic
263#835C22×C311yescharacteristic
264#830C22×C311yescharacteristic
265#821C22×C311yescharacteristic
266(C2×D3)⋊C8C22×C311yescharacteristic
267(C2×D3)⋊C8C22×C311yescharacteristic
268#816C22×C311yescharacteristic
269#810C22×C311yescharacteristic
270#809C22×C311yescharacteristic
271C23×C32C2×D411yescharacteristic
272C22×C3×D3—21no—
273C22×C3×D3C2×D411yescharacteristic
274C22×C3×D3C2×D411yescharacteristic
275C32×Q8—24no—
276C32×Q8—21no—
277C32×Q8—21no—
278C32×Q8—21no—
279C32×Q8—21no—
280C32×Q8C2×D412yes—
281C32×Q8C2×D412yes—
282C2×C32×C4—24no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2×D411yescharacteristic
290C2×C32×C4C2411yescharacteristic
291C3×#67—24no—
292C3×#67—22no—
293C3×#67—22no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3C2×D411yescharacteristic
298C2×C3×Dic3C2×D411yescharacteristic
299C3×D12—24no—
300C3×D12—24no—
301C3×D12—22no—
302C3×D12—21no—
303C3×D12C2×D412yes—
304C3×C4×D3—24no—
305C3×C4×D3—24no—
306C3×C4×D3—24no—
307C3×C4×D3—24no—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310C3×C4×D3—24no—
311C3×C4×D3—42no—
312C3×C4×D3C2×D412yes—
313C3×C4×D3C2×D412yes—
314C3×Dic6—24no—
315C3×Dic6—21no—
316C3×Dic6—24no—
317C3×Dic6—22no—
318C3×Dic6—21no—
319C3×Dic6—21no—
320C3×Dic6—42no—
321C3×Dic6C2×D412yes—
322C32×C8—21no—
323C32×C8—21no—
324C3×C3⋊C8—21no—
325C3×C3⋊C8—21no—
326C2×2−1+4—31no—
327C2×#137—31no—
328C22×Q16—31no—
329#536—31no—
330#452—31no—
331#452—31no—
332#452—31no—
333#452—31no—
334#451—31no—
335#451—31no—
336#451—31no—
337#451C3×D311yescharacteristic, complemented
338#419—31no—
339#416—31no—
340#408—31no—
341C3×#41—34no—
342C3×#41—62no—
343C3×#41—62no—
344C3×#41—62no—
345C3×#41—62no—
346C3×#41—68no—
347C3×#41—68no—
348C3×#41—62no—
349C3×#41—62no—
350C3×#41—68no—
351C3×#41—62no—
352C2×C3×Q8—22no—
353C2×C3×Q8—22no—
354C2×C3×Q8—22no—
355C2×C3×Q8—22no—
356C2×C3×Q8—21no—
357C2×C3×Q8—21no—
358C2×C3×Q8—21no—
359C2×C3×Q8—21no—
360C2×C3×Q8—21no—
361C2×C3×Q8—31no—
362C2×C3×Q8—34no—
363C2×C3×Q8—31no—
364C2×C3×Q8—31no—
365C2×C3×Q8—41no—
366C2×C3×Q8—42no—
367C2×C3×Q8—42no—
368C2×C3×Q8—61no—
369C2×C3×Q8—61no—
370C2×C3×Q8—61no—
371C2×C3×Q8—62no—
372C2×C3×Q8—62no—
373C2×C3×Q8—62no—
374C2×C3×Q8—62no—
375C2×C3×Q8—68no—
376C2×C3×Q8—62no—
377C2×C3×Q8C22×D311yescharacteristic
378C2×C3×Q8C22×D311yescharacteristic
379C2×C3×Q8C22×D311yescharacteristic
380C2×C3×Q8C23×C311yescharacteristic
381C2×C3×Q8C23×C311yescharacteristic
382C2×C3×Q8C23×C311yescharacteristic
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—61no—
388C2×C3×D4—61no—
389C2×C3×D4—61no—
390C22×C3×C4—21no—
391C22×C3×C4—21no—
392C22×C3×C4—21no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—41no—
396C22×C3×C4—61no—
397C22×C3×C4—61no—
398C22×C3×C4—61no—
399C22×C3×C4—61no—
400C22×C3×C4—61no—
401C22×C3×C4—61no—
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C23×C311yescharacteristic
404C2×#67—21no—
405C2×#67C3×D411yescharacteristic
406C2×#67C3×D411yescharacteristic
407#239—28no—
408#239—22no—
409#239—22no—
410#239—22no—
411#239C3×D414yes—
412D3×Q8—28no—
413D3×Q8—22no—
414D3×Q8—22no—
415D3×Q8—22no—
416D3×Q8—22no—
417D3×Q8—22no—
418D3×Q8C3×D414yes—
419#235—28no—
420#235—28no—
421#235—22no—
422#235—22no—
423#235—22no—
424#235—22no—
425C2×D12—21no—
426C2×D12—21no—
427C2×D12C3×D411yescharacteristic
428C2×D12C23×C311yescharacteristic
429C2×C4×D3—21no—
430C2×C4×D3—21no—
431C2×C4×D3—21no—
432C2×C4×D3—21no—
433C2×C4×D3—21no—
434C2×C4×D3—21no—
435C2×C4×D3C23×C311yescharacteristic
436C2×C4×D3C23×C311yescharacteristic
437C2×Dic6—21no—
438C2×Dic6—21no—
439C2×Dic6—21no—
440C2×Dic6C3×D411yescharacteristic
441C2×Dic6C23×C311yescharacteristic
442C2×Dic6C23×C311yescharacteristic
443C3×Q16—22no—
444C3×Q16—22no—
445C3×Q16—22no—
446C3×Q16—22no—
447C3×Q16—42no—
448C3×Q16—42no—
449C3×Q16—62no—
450C3×Q16—62no—
451C3×Q16—62no—
452C3×Q16—62no—
453C3×SD16—62no—
454C3×SD16—62no—
455C3×M16—62no—
456C2×C3×C8—21no—
457C2×C3×C8—21no—
458C2×C3×C8—31no—
459C2×C3×C8—31no—
460C2×C3×C8—62no—
461C2×C3×C8C22×D311yescharacteristic
462C2×C3×C8C22×D311yescharacteristic
463C2×C3×C8C23×C311yescharacteristic
464C2×C3×C8C23×C311yescharacteristic
465C3×C4⋊C4—21no—
466C3×C4⋊C4—21no—
467C3×C4⋊C4—21no—
468C3×C4⋊C4—31no—
469C3×C4⋊C4—41no—
470C3×C4⋊C4—61no—
471C3×C4⋊C4—61no—
472C3×C4⋊C4—61no—
473C3×C4⋊C4C22×D311yescharacteristic
474C3×C4⋊C4C23×C311yescharacteristic
475C3×C22⋊C4—21no—
476C3×C22⋊C4—21no—
477C3×C22⋊C4—41no—
478C3×C22⋊C4—61no—
479C3×C22⋊C4—61no—
480C3×C22⋊C4—61no—
481C3×C22⋊C4—61no—
482C3×C42—61no—
483#217—21no—
484#216—22no—
485#216—22no—
486#216—22no—
487#215—22no—
488(C2×D3)⋊C4—21no—
489(C2×D3)⋊C4—21no—
490(C2×D3)⋊C4—21no—
491C4⋊Dic3—21no—
492C4⋊Dic3C23×C311yescharacteristic
493Dic3⋊C4—21no—
494Dic3⋊C4—21no—
495C4×Dic3—21no—
496C2×C3⋊C8C23×C311yescharacteristic
497C2×C3⋊C8C23×C311yescharacteristic
498Dic12—22no—
499#204—22no—
500ΓL(1,𝔽25)—22no—
501D3×C8—22no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32C22×D411yescharacteristic
506C2×C3×D3—21no—
507C2×C3×D3—21no—
508C2×C3×D3—21no—
509C2×C3×D3—22no—
510C2×C3×D3—21no—
511C2×C3×D3—21no—
512C2×C3×D3—41no—
513C2×C3×D3—41no—
514C2×C3×D3#12012yes—
515C32×C4—22no—
516C32×C4—22no—
517C32×C4—21no—
518C32×C4—41no—
519C32×C4—41no—
520C32×C4C22×D411yescharacteristic
521C32×C4C22×D411yescharacteristic
522C3×Dic3—21no—
523C3×Dic3—22no—
524C3×Dic3—41no—
525C3×Dic3—41no—
526C3×Dic3#12012yes—
5272−1+4—64no—
5282−1+4—64no—
529C2×#41—31no—
530C2×#41—31no—
531C2×#41—31no—
532C2×#41—31no—
533C2×#41—61no—
534C2×#41—61no—
535C2×#41—61no—
536C22×Q8—31no—
537C22×Q8—31no—
538C22×Q8—31no—
539C22×Q8—61no—
540C22×Q8C2×C3×D311yescharacteristic
541#137—64no—
542C2×Q16—31no—
543C2×Q16—31no—
544C2×Q16—31no—
545C2×Q16—31no—
546C2×Q16—64no—
547C2×Q16C2×C3×D311yescharacteristic
548C2×Q16C2×C3×D311yescharacteristic
549C2×SD16—31no—
550C2×SD16—31no—
551C2×M16—31no—
552C22×C8—31no—
553C4⋊Q8—61no—
554#124—61no—
555#123—61no—
556#123—61no—
557C22⋊Q8—31no—
558C22⋊Q8—31no—
559C22⋊Q8—31no—
560C22⋊Q8C2×C3×D311yescharacteristic
561#117—31no—
562#103—31no—
563#103—31no—
564#103—31no—
565#103—31no—
566#103C2×C3×D311yescharacteristic
567#103C2×C3×D311yescharacteristic
568#102—31no—
569#102—31no—
570C22⋊C8—31no—
571C22⋊C8—31no—
572C22⋊C8—31no—
573C22⋊C8C2×C3×D311yescharacteristic
574C23×C3—21no—
575C23×C3—31no—
576C23×C3—31no—
577C23×C3—61no—
578C23×C3D3×D411yescharacteristic
579C23×C3C2×C3×D411yescharacteristic
580C22×D3—21no—
581C22×D3C2×C3×D411yescharacteristic
582C22×D3C2×C3×D411yescharacteristic
583C3×Q8—24no—
584C3×Q8—24no—
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—21no—
588C3×Q8—21no—
589C3×Q8—21no—
590C3×Q8—21no—
591C3×Q8—21no—
592C3×Q8—21no—
593C3×Q8—22no—
594C3×Q8—22no—
595C3×Q8—32no—
596C3×Q8—41no—
597C3×Q8—41no—
598C3×Q8—41no—
599C3×Q8—41no—
600C3×Q8—44no—
601C3×Q8—64no—
602C3×Q8—62no—
603C3×Q8—64no—
604C3×Q8—61no—
605C3×Q8—61no—
606C3×Q8—61no—
607C3×Q8—122no—
608C3×Q8D3×D412yes—
609C3×Q8D3×D412yes—
610C3×Q8C2×C3×D412yes—
611C3×Q8C2×C3×D412yes—
612C3×D4—32no—
613C3×D4—62no—
614C3×D4—64no—
615C3×D4—64no—
616C3×D4—62no—
617C3×D4—62no—
618C3×D4—64no—
619C3×D4—61no—
620C2×C3×C4—24no—
621C2×C3×C4—24no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—31no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—31no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—44no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—64no—
648C2×C3×C4—64no—
649C2×C3×C4—64no—
650C2×C3×C4—64no—
651C2×C3×C4—64no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—122no—
658C2×C3×C4D3×D411yescharacteristic
659C2×C3×C4C2×C3×D411yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C24×C311yescharacteristic
662#67—24no—
663#67—22no—
664#67—22no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3C2×C3×D411yescharacteristic
669C2×Dic3C2×C3×D411yescharacteristic
670D12—24no—
671D12—24no—
672D12—22no—
673D12—21no—
674D12C2×C3×D412yes—
675C4×D3—24no—
676C4×D3—24no—
677C4×D3—24no—
678C4×D3—24no—
679C4×D3—21no—
680C4×D3—21no—
681C4×D3—24no—
682C4×D3—42no—
683C4×D3C2×C3×D412yes—
684C4×D3C2×C3×D412yes—
685Dic6—24no—
686Dic6—21no—
687Dic6—24no—
688Dic6—22no—
689Dic6—21no—
690Dic6—21no—
691Dic6—42no—
692Dic6C2×C3×D412yes—
693C3×C8—21no—
694C3×C8—21no—
695C3×C8—21no—
696C3×C8—21no—
697C3×C8—41no—
698C3×C8—41no—
699C3×C8—61no—
700C3×C8—61no—
701C3⋊C8—21no—
702C3⋊C8—21no—
703C2×C32—41no—
704C2×C32C2×#12011yescharacteristic
705C2×C32#57811yescharacteristic
706C2×C32#57811yescharacteristic
707C3×D3—22no—
708C3×D3—41no—
709C3×D3—42no—
710#41—34no—
711#41—62no—
712#41—62no—
713#41—62no—
714#41—62no—
715#41—68no—
716#41—68no—
717#41—62no—
718#41—62no—
719#41—68no—
720#41—62no—
721C2×Q8—22no—
722C2×Q8—22no—
723C2×Q8—21no—
724C2×Q8—31no—
725C2×Q8—34no—
726C2×Q8—31no—
727C2×Q8—31no—
728C2×Q8—61no—
729C2×Q8—61no—
730C2×Q8—61no—
731C2×Q8—62no—
732C2×Q8—62no—
733C2×Q8—62no—
734C2×Q8—62no—
735C2×Q8—68no—
736C2×Q8—62no—
737C2×Q8C22×C3×D311yescharacteristic
738C2×Q8C22×C3×D311yescharacteristic
739C2×Q8C22×C3×D311yescharacteristic
740C2×D4—31no—
741C2×D4—31no—
742C2×D4—31no—
743C2×D4—31no—
744C2×D4—61no—
745C2×D4—61no—
746C2×D4—61no—
747C22×C4—21no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4C22×C3×D311yescharacteristic
757Q16—22no—
758Q16—22no—
759Q16—62no—
760Q16—62no—
761Q16—62no—
762Q16—62no—
763SD16—62no—
764SD16—62no—
765M16—62no—
766C2×C8—31no—
767C2×C8—31no—
768C2×C8—62no—
769C2×C8C22×C3×D311yescharacteristic
770C2×C8C22×C3×D311yescharacteristic
771C4⋊C4—21no—
772C4⋊C4—31no—
773C4⋊C4—61no—
774C4⋊C4—61no—
775C4⋊C4—61no—
776C4⋊C4C22×C3×D311yescharacteristic
777C22⋊C4—21no—
778C22⋊C4—61no—
779C22⋊C4—61no—
780C22⋊C4—61no—
781C22⋊C4—61no—
782C42—61no—
783C22×C3—22no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—32no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—61no—
795C22×C3—61no—
796C22×C3—61no—
797C22×C3—61no—
798C22×C3—62no—
799C22×C3—61no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3C2×D3×D411yescharacteristic
803C22×C3C22×C3×D411yescharacteristic
804C2×D3—21no—
805C2×D3—21no—
806C2×D3—21no—
807C2×D3—21no—
808C2×D3—21no—
809C2×D3—22no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3C3×#12012yes—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—21no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—32no—
822C3×C4—41no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—61no—
830C3×C4—62no—
831C3×C4—81no—
832C3×C4—81no—
833C3×C4—121no—
834C3×C4—121no—
835C3×C4C2×D3×D411yescharacteristic
836C3×C4C2×D3×D411yescharacteristic
837C3×C4C22×C3×D411yescharacteristic
838C3×C4C22×C3×D411yescharacteristic
839Dic3—21no—
840Dic3—22no—
841Dic3—41no—
842Dic3—41no—
843Dic3C3×#12012yes—
844C32#301111yescharacteristic, complemented, Sylow
845C23—31no—
846C23—31no—
847C23—61no—
848C23C3×D3×D411yescharacteristic
849Q8—24no—
850Q8—21no—
851Q8—21no—
852Q8—21no—
853Q8—21no—
854Q8—32no—
855Q8—64no—
856Q8—62no—
857Q8—64no—
858Q8—61no—
859Q8—61no—
860Q8—61no—
861Q8—122no—
862Q8C3×D3×D412yes—
863Q8C3×D3×D412yes—
864D4—32no—
865D4—62no—
866D4—64no—
867D4—64no—
868D4—62no—
869D4—62no—
870D4—64no—
871D4—61no—
872C2×C4—24no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—31no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—31no—
883C2×C4—64no—
884C2×C4—64no—
885C2×C4—64no—
886C2×C4—64no—
887C2×C4—64no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—122no—
894C2×C4C3×D3×D411yescharacteristic
895C2×C4C23×C3×D311yescharacteristic
896C8—21no—
897C8—21no—
898C8—61no—
899C8—61no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—42no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—62no—
907C2×C3—121no—
908C2×C3—122no—
909C2×C3D3×#12011yescharacteristic
910C2×C3#576611yescharacteristic
911C2×C3#577911yescharacteristic
912C2×C3C2×C3×#12011yescharacteristic
913C2×C3C3×#57811yescharacteristic
914C2×C3C3×#57811yescharacteristic
915D3—22no—
916D3—41no—
917D3—42no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—32no—
922C22—61no—
923C22—61no—
924C22—61no—
925C22—61no—
926C22—62no—
927C22—61no—
928C22—121no—
929C22—121no—
930C22C2×C3×D3×D411yescharacteristic
931C4—22no—
932C4—22no—
933C4—21no—
934C4—32no—
935C4—41no—
936C4—41no—
937C4—61no—
938C4—62no—
939C4—121no—
940C4—121no—
941C4C2×C3×D3×D411yescharacteristic
942C4C2×C3×D3×D411yescharacteristic
943C3—21no—
944C3#8018511yescharacteristic, direct product factor
945C3C3×#301111yescharacteristic, complemented
946C2—41no—
947C2—62no—
948C2—121no—
949C2—122no—
950C2C3×D3×#12011yescharacteristic
951C2C3×#576611yescharacteristic
952C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC2×C3×#1007C2
hypercenterC3×#451D3
hypocenterC3C3×#3011
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
2. C2×C3×#918C2semidirect
3. C2×C3×D3×Q16C2semidirect
4. C3×#5628C2semidirect
5. C32×#451C2semidirect
6. C3×#5228C2semidirect
7. C3×#5187C2semidirect
8. C3×#5186C2semidirect
9. C3×#5047C2semidirect
10. C3×#4809C2semidirect
11. C3×#4808C2semidirect
12. C3×#4804C2semidirect
13. C3×#4802C2semidirect
14. C3×#4733C2semidirect
15. C3×#4727C2semidirect
17. #80185C3direct (N × H)
70. C2×#918C2×C3semidirect
71. C2×D3×Q16C2×C3semidirect
72. #5628C2×C3semidirect
81. C3×#451D3semidirect
82. C3×#451C2×C3semidirect
86. #5228C2×C3semidirect
87. #5187C2×C3semidirect
88. #5186C2×C3semidirect
89. #5047C2×C3semidirect
90. #4809C2×C3semidirect
91. #4808C2×C3semidirect
92. #4804C2×C3semidirect
93. #4802C2×C3semidirect
94. #4733C2×C3semidirect
95. #4727C2×C3semidirect
337. #451C3×D3semidirect
844. C32#3011semidirect
944. C3#80185direct (N × H)
945. C3C3×#3011semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×C3×#9182
C2×C3×D3×Q162
C3×#56282
C32×#4512
C3×#52282
C3×#51872
C3×#51862
C3×#50472
C3×#48092
C3×#48082
C3×#48042
C3×#48022
C3×#47332
C3×#47272
C3×#30113
#801853