Finite Group Databasebeta

← C3×#80042 #11864653

Subgroups — C3×#80042 #11864653

Order 1152.

1503 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×C3×#916C211yesmaximal, characteristic, complemented
3C2×C3×#915C211yesmaximal, characteristic, complemented
4C3×#5608C211yesmaximal, characteristic, complemented
5C32×#448C211yesmaximal, characteristic, complemented
6C3×#5228C211yesmaximal, characteristic, complemented
7C3×#5172C211yesmaximal, characteristic, complemented
8C3×#5170C211yesmaximal, characteristic, complemented
9C3×#5037C211yesmaximal, characteristic, complemented
10C3×#4809C211yesmaximal, characteristic, complemented
11C3×#4808C211yesmaximal, characteristic, complemented
12C3×#4803C211yesmaximal, characteristic, complemented
13C3×D3×#103C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic, complemented
16C3×#3013—31nomaximal
17#80042C311yesmaximal, 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×#237C2211yescharacteristic
28C2×C3×#235—21no—
29C2×C3×#235—21no—
30C2×C3×#235C2211yescharacteristic
31C2×C3×#235C2211yescharacteristic
32C2×C32×SD16C2211yescharacteristic
33C2×C32×SD16C2211yescharacteristic
34C32×#121C2211yescharacteristic
35C2×C3×#216C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic
37C3×#939—21no—
38C3×#938—21no—
39C3×#938C2211yescharacteristic
40C2×C3×#214C2211yescharacteristic
41C2×C3×#213C2211yescharacteristic
42C3×#924C2211yescharacteristic
43C3×#916—24no—
44C3×#915—24no—
45C2×C3×Dic12C2211yescharacteristic
46C2×C3×#204C2211yescharacteristic
47C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
48C2×C3×D3×C8C2211yescharacteristic
49C3×#897C2211yescharacteristic
50C3×D3×C4⋊C4C2211yescharacteristic
51C3×#884—21no—
52C3×#878—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, complemented
67C2×C3×#137—31no—
68C2×C3×#135—31no—
69C3×#537—31no—
70C2×#916C2×C311yescharacteristic, complemented
71C2×#915C2×C311yescharacteristic, complemented
72#5608C2×C311yescharacteristic, complemented
73C3×#452—31no—
74C3×#452—31no—
75C3×#451—31no—
76C3×#451—31no—
77C3×#449—31no—
78C3×#449—31no—
79C3×#448—21no—
80C3×#448—31no—
81C3×#448D311yescharacteristic, complemented
82C3×#448C2×C311yescharacteristic, complemented
83C3×#417—31no—
84C2×C3×#103—31no—
85C3×#408—31no—
86#5228C2×C311yescharacteristic, complemented
87#5172C2×C311yescharacteristic, complemented
88#5170C2×C311yescharacteristic, complemented
89#5037C2×C311yescharacteristic, complemented
90#4809C2×C311yescharacteristic, complemented
91#4808C2×C311yescharacteristic, complemented
92#4803C2×C311yescharacteristic, complemented
93D3×#103C2×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×D4—21no—
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4—21no—
104C22×C32×C4C2311yescharacteristic
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C2×C3×#67D411yescharacteristic
110C22×C3×Dic3—21no—
111C3×#239—28no—
112C3×#239—22no—
113C3×#239—22no—
114C3×#239—22no—
115C3×#239D414yescomplemented
116C3×D3×Q8—28no—
117C3×D3×Q8—22no—
118C3×D3×Q8—22no—
119C3×D3×Q8—22no—
120C3×D3×Q8D414yescomplemented
121C3×#237—22no—
122C3×#237—22no—
123C3×#235—28no—
124C3×#235—28no—
125C3×#235—22no—
126C3×#235—22no—
127C3×#235—22no—
128C3×#235—22no—
129C2×C3×D12—21no—
130C2×C3×D12—21no—
131C2×C3×D12D411yescharacteristic
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3—21no—
137C2×C3×C4×D3—21no—
138C2×C3×C4×D3—21no—
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×Dic6—21no—
142C2×C3×Dic6—21no—
143C2×C3×Dic6D411yescharacteristic
144C2×C3×Dic6C2311yescharacteristic
145C2×C3×Dic6C2311yescharacteristic
146C32×SD16—22no—
147C32×SD16—22no—
148C2×C32×C8C2311yescharacteristic
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151C32×C22⋊C4—21no—
152C3×#217—21no—
153C3×#217—21no—
154C3×#216—22no—
155C3×#216—22no—
156C3×#214—22no—
157C3×#213—22no—
158C3×(C2×D3)⋊C4—21no—
159C3×C4⋊Dic3—21no—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4—21no—
162C3×Dic3⋊C4—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#3013—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—31no—
177C2×C3×#41—61no—
178C2×C3×#41—61no—
179C2×C3×#41—61no—
180C22×C3×Q8—21no—
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×#237C22×C311yescharacteristic
195C2×#235—21no—
196C2×#235—21no—
197C2×#235C22×C311yescharacteristic
198C2×#235C22×C311yescharacteristic
199C3×#137—64no—
200C3×#135—64no—
201C2×C3×Q16—31no—
202C2×C3×Q16—31no—
203C2×C3×Q16—31no—
204C2×C3×SD16—21no—
205C2×C3×SD16—21no—
206C2×C3×SD16—31no—
207C2×C3×SD16—31no—
208C2×C3×SD16C2×D311yescharacteristic
209C2×C3×SD16C2×D311yescharacteristic
210C2×C3×SD16C22×C311yescharacteristic
211C2×C3×SD16C22×C311yescharacteristic
212C2×C3×D8—31no—
213C2×C3×M16—31no—
214C22×C3×C8—31no—
215C3×C22⋊Q8—31no—
216C3×C22⋊Q8—31no—
217C3×C22⋊Q8—61no—
218C3×#121—21no—
219C3×#121—31no—
220C3×#121—61no—
221C3×#121—61no—
222C3×#121—61no—
223C3×#121C2×D311yescharacteristic
224C3×#121C22×C311yescharacteristic
225C2×C3×C4⋊C4—31no—
226C2×#216C22×C311yescharacteristic
227C2×#216C22×C311yescharacteristic
228#939—21no—
229#938—21no—
230#938C22×C311yescharacteristic
231C2×#214C22×C311yescharacteristic
232C2×#213C22×C311yescharacteristic
233#924C22×C311yescharacteristic
234#916—24no—
235#915—24no—
236C2×Dic12C22×C311yescharacteristic
237C2×#204C22×C311yescharacteristic
238C2×ΓL(1,𝔽25)C22×C311yescharacteristic
239C2×D3×C8C22×C311yescharacteristic
240#897C22×C311yescharacteristic
241D3×C4⋊C4C22×C311yescharacteristic
242#884—21no—
243#878—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×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3C2×D411yescharacteristic
275C22×C3×D3C2×D411yescharacteristic
276C32×Q8—24no—
277C32×Q8—21no—
278C32×Q8—21no—
279C32×Q8C2×D412yes—
280C32×Q8C2×D412yes—
281C32×D4—21no—
282C32×D4—21no—
283C32×D4—81no—
284C2×C32×C4—24no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4C2×D411yescharacteristic
291C2×C32×C4C2411yescharacteristic
292C3×#67—24no—
293C3×#67—22no—
294C3×#67—22no—
295C3×#67—42no—
296C3×#67—81no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—42no—
301C2×C3×Dic3C2×D411yescharacteristic
302C2×C3×Dic3C2×D411yescharacteristic
303C3×D12—24no—
304C3×D12—24no—
305C3×D12—22no—
306C3×D12—21no—
307C3×D12C2×D412yes—
308C3×C4×D3—24no—
309C3×C4×D3—24no—
310C3×C4×D3—24no—
311C3×C4×D3—24no—
312C3×C4×D3—21no—
313C3×C4×D3—21no—
314C3×C4×D3—24no—
315C3×C4×D3—81no—
316C3×C4×D3C2×D412yes—
317C3×C4×D3C2×D412yes—
318C3×Dic6—24no—
319C3×Dic6—21no—
320C3×Dic6—24no—
321C3×Dic6—22no—
322C3×Dic6—21no—
323C3×Dic6—21no—
324C3×Dic6C2×D412yes—
325C32×C8—21no—
326C32×C8—21no—
327C3×C3⋊C8—21no—
328C3×C3⋊C8—21no—
329C2×2−1+4—31no—
330C2×#137—31no—
331C2×#135—31no—
332#537—31no—
333#452—31no—
334#452—31no—
335#451—31no—
336#451—31no—
337#449—31no—
338#449—31no—
339#448—31no—
340#448C3×D311yescharacteristic, complemented
341#417—31no—
342C2×#103—31no—
343#408—31no—
344C3×#41—34no—
345C3×#41—62no—
346C3×#41—62no—
347C3×#41—62no—
348C3×#41—62no—
349C3×#41—68no—
350C3×#41—68no—
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—62no—
355C3×#41—68no—
356C3×#41—62no—
357C2×C3×Q8—22no—
358C2×C3×Q8—22no—
359C2×C3×Q8—22no—
360C2×C3×Q8—22no—
361C2×C3×Q8—21no—
362C2×C3×Q8—21no—
363C2×C3×Q8—21no—
364C2×C3×Q8—21no—
365C2×C3×Q8—31no—
366C2×C3×Q8—34no—
367C2×C3×Q8—31no—
368C2×C3×Q8—31no—
369C2×C3×Q8—41no—
370C2×C3×Q8—42no—
371C2×C3×Q8—42no—
372C2×C3×Q8—61no—
373C2×C3×Q8—61no—
374C2×C3×Q8—62no—
375C2×C3×Q8—62no—
376C2×C3×Q8—68no—
377C2×C3×Q8—62no—
378C2×C3×Q8C22×D311yescharacteristic
379C2×C3×Q8C22×D311yescharacteristic
380C2×C3×Q8C23×C311yescharacteristic
381C2×C3×Q8C23×C311yescharacteristic
382C2×C3×D4—21no—
383C2×C3×D4—21no—
384C2×C3×D4—21no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—31no—
388C2×C3×D4—31no—
389C2×C3×D4—41no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—61no—
393C2×C3×D4—61no—
394C2×C3×D4—61no—
395C2×C3×D4C22×D311yescharacteristic
396C2×C3×D4C23×C311yescharacteristic
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—41no—
403C22×C3×C4—61no—
404C22×C3×C4—61no—
405C22×C3×C4—61no—
406C22×C3×C4—61no—
407C22×C3×C4—61no—
408C22×C3×C4—61no—
409C22×C3×C4—61no—
410C22×C3×C4C22×D311yescharacteristic
411C22×C3×C4C23×C311yescharacteristic
412C2×#67—21no—
413C2×#67—21no—
414C2×#67—21no—
415C2×#67C3×D411yescharacteristic
416C2×#67C3×D411yescharacteristic
417C22×Dic3—21no—
418#239—28no—
419#239—22no—
420#239—22no—
421#239—22no—
422#239C3×D414yescomplemented
423D3×Q8—28no—
424D3×Q8—22no—
425D3×Q8—22no—
426D3×Q8—22no—
427D3×Q8C3×D414yescomplemented
428#237—22no—
429#237—22no—
430#235—28no—
431#235—28no—
432#235—22no—
433#235—22no—
434#235—22no—
435#235—22no—
436C2×D12—21no—
437C2×D12—21no—
438C2×D12C3×D411yescharacteristic
439C2×D12C23×C311yescharacteristic
440C2×C4×D3—21no—
441C2×C4×D3—21no—
442C2×C4×D3—21no—
443C2×C4×D3—21no—
444C2×C4×D3—21no—
445C2×C4×D3—21no—
446C2×C4×D3C23×C311yescharacteristic
447C2×C4×D3C23×C311yescharacteristic
448C2×Dic6—21no—
449C2×Dic6—21no—
450C2×Dic6C3×D411yescharacteristic
451C2×Dic6C23×C311yescharacteristic
452C2×Dic6C23×C311yescharacteristic
453C3×Q16—62no—
454C3×Q16—62no—
455C3×Q16—62no—
456C3×SD16—22no—
457C3×SD16—22no—
458C3×SD16—22no—
459C3×SD16—22no—
460C3×SD16—42no—
461C3×SD16—42no—
462C3×SD16—62no—
463C3×SD16—62no—
464C3×D8—62no—
465C3×M16—62no—
466C2×C3×C8—21no—
467C2×C3×C8—21no—
468C2×C3×C8—31no—
469C2×C3×C8—31no—
470C2×C3×C8—62no—
471C2×C3×C8C22×D311yescharacteristic
472C2×C3×C8C22×D311yescharacteristic
473C2×C3×C8C23×C311yescharacteristic
474C2×C3×C8C23×C311yescharacteristic
475C3×C4⋊C4—21no—
476C3×C4⋊C4—31no—
477C3×C4⋊C4—61no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4—61no—
480C3×C4⋊C4C22×D311yescharacteristic
481C3×C4⋊C4C23×C311yescharacteristic
482C3×C22⋊C4—21no—
483C3×C22⋊C4—21no—
484C3×C22⋊C4—41no—
485C3×C22⋊C4—61no—
486C3×C22⋊C4—61no—
487C3×C22⋊C4—61no—
488#217—21no—
489#217—21no—
490#216—22no—
491#216—22no—
492#214—22no—
493#213—22no—
494(C2×D3)⋊C4—21no—
495C4⋊Dic3—21no—
496C4⋊Dic3C23×C311yescharacteristic
497Dic3⋊C4—21no—
498Dic3⋊C4—21no—
499C2×C3⋊C8C23×C311yescharacteristic
500C2×C3⋊C8C23×C311yescharacteristic
501Dic12—22no—
502#204—22no—
503ΓL(1,𝔽25)—22no—
504D3×C8—22no—
505C22×C32—21no—
506C22×C32—21no—
507C22×C32—21no—
508C22×C32—41no—
509C22×C32—41no—
510C22×C32—41no—
511C22×C32C22×D411yescharacteristic
512C2×C3×D3—21no—
513C2×C3×D3—21no—
514C2×C3×D3—21no—
515C2×C3×D3—22no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—41no—
519C2×C3×D3—41no—
520C2×C3×D3#12012yes—
521C32×C4—22no—
522C32×C4—22no—
523C32×C4—21no—
524C32×C4—41no—
525C32×C4C22×D411yescharacteristic
526C32×C4C22×D411yescharacteristic
527C3×Dic3—21no—
528C3×Dic3—22no—
529C3×Dic3—41no—
530C3×Dic3—41no—
531C3×Dic3#12012yes—
5322−1+4—64no—
5332−1+4—64no—
534C2×#41—31no—
535C2×#41—31no—
536C2×#41—31no—
537C2×#41—31no—
538C2×#41—31no—
539C2×#41—61no—
540C2×#41—61no—
541C2×#41—61no—
542C22×Q8—31no—
543C22×Q8—31no—
544C22×Q8—61no—
545C22×Q8C2×C3×D311yescharacteristic
546#137—64no—
547#135—64no—
548C2×Q16—31no—
549C2×Q16—31no—
550C2×Q16—31no—
551C2×SD16—31no—
552C2×SD16—31no—
553C2×SD16C2×C3×D311yescharacteristic
554C2×SD16C2×C3×D311yescharacteristic
555C2×D8—31no—
556C2×M16—31no—
557C22×C8—31no—
558C22⋊Q8—31no—
559C22⋊Q8—31no—
560C22⋊Q8—61no—
561#121—31no—
562#121—61no—
563#121—61no—
564#121—61no—
565#121C2×C3×D311yescharacteristic
566C2×C4⋊C4—31no—
567#103—31no—
568#103—31no—
569#103—31no—
570#103—31no—
571#103C2×C3×D311yescharacteristic
572#103C2×C3×D311yescharacteristic
573#102—31no—
574#102—31no—
575C22⋊C8—31no—
576C22⋊C8—31no—
577C22⋊C8—31no—
578C22⋊C8C2×C3×D311yescharacteristic
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—31no—
583C23×C3—31no—
584C23×C3—41no—
585C23×C3—61no—
586C23×C3D3×D411yescharacteristic
587C23×C3C2×C3×D411yescharacteristic
588C22×D3—21no—
589C22×D3C2×C3×D411yescharacteristic
590C22×D3C2×C3×D411yescharacteristic
591C3×Q8—24no—
592C3×Q8—24no—
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—21no—
596C3×Q8—21no—
597C3×Q8—22no—
598C3×Q8—22no—
599C3×Q8—32no—
600C3×Q8—41no—
601C3×Q8—41no—
602C3×Q8—44no—
603C3×Q8—64no—
604C3×Q8—62no—
605C3×Q8—64no—
606C3×Q8—61no—
607C3×Q8—61no—
608C3×Q8—61no—
609C3×Q8D3×D412yes—
610C3×Q8D3×D412yes—
611C3×Q8C2×C3×D412yes—
612C3×Q8C2×C3×D412yes—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—32no—
618C3×D4—41no—
619C3×D4—41no—
620C3×D4—62no—
621C3×D4—64no—
622C3×D4—64no—
623C3×D4—62no—
624C3×D4—62no—
625C3×D4—64no—
626C3×D4—61no—
627C3×D4—81no—
628C3×D4—81no—
629C3×D4—82no—
630C3×D4—122no—
631C3×D4—241no—
632C2×C3×C4—24no—
633C2×C3×C4—24no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—31no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—31no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—44no—
655C2×C3×C4—41no—
656C2×C3×C4—64no—
657C2×C3×C4—64no—
658C2×C3×C4—64no—
659C2×C3×C4—64no—
660C2×C3×C4—64no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—122no—
667C2×C3×C4—241no—
668C2×C3×C4D3×D411yescharacteristic
669C2×C3×C4C2×C3×D411yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C24×C311yescharacteristic
672#67—24no—
673#67—22no—
674#67—22no—
675#67—42no—
676#67—81no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—42no—
681C2×Dic3C2×C3×D411yescharacteristic
682C2×Dic3C2×C3×D411yescharacteristic
683D12—24no—
684D12—24no—
685D12—22no—
686D12—21no—
687D12C2×C3×D412yes—
688C4×D3—24no—
689C4×D3—24no—
690C4×D3—24no—
691C4×D3—24no—
692C4×D3—21no—
693C4×D3—21no—
694C4×D3—24no—
695C4×D3—81no—
696C4×D3C2×C3×D412yes—
697C4×D3C2×C3×D412yes—
698Dic6—24no—
699Dic6—21no—
700Dic6—24no—
701Dic6—22no—
702Dic6—21no—
703Dic6—21no—
704Dic6C2×C3×D412yes—
705C3×C8—21no—
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—21no—
709C3×C8—41no—
710C3×C8—41no—
711C3×C8—61no—
712C3×C8—61no—
713C3⋊C8—21no—
714C3⋊C8—21no—
715C2×C32—41no—
716C2×C32—81no—
717C2×C32C2×#12011yescharacteristic
718C2×C32#57711yescharacteristic
719C2×C32#57811yescharacteristic
720C3×D3—22no—
721C3×D3—41no—
722C3×D3—42no—
723#41—34no—
724#41—62no—
725#41—62no—
726#41—62no—
727#41—62no—
728#41—68no—
729#41—68no—
730#41—62no—
731#41—62no—
732#41—62no—
733#41—62no—
734#41—68no—
735#41—62no—
736C2×Q8—22no—
737C2×Q8—22no—
738C2×Q8—21no—
739C2×Q8—31no—
740C2×Q8—34no—
741C2×Q8—31no—
742C2×Q8—31no—
743C2×Q8—61no—
744C2×Q8—61no—
745C2×Q8—62no—
746C2×Q8—62no—
747C2×Q8—68no—
748C2×Q8—62no—
749C2×Q8C22×C3×D311yescharacteristic
750C2×Q8C22×C3×D311yescharacteristic
751C2×D4—21no—
752C2×D4—31no—
753C2×D4—31no—
754C2×D4—31no—
755C2×D4—31no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—61no—
761C2×D4C22×C3×D311yescharacteristic
762C22×C4—21no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4C22×C3×D311yescharacteristic
773Q16—62no—
774Q16—62no—
775Q16—62no—
776SD16—22no—
777SD16—22no—
778SD16—62no—
779SD16—62no—
780D8—62no—
781M16—62no—
782C2×C8—31no—
783C2×C8—31no—
784C2×C8—62no—
785C2×C8C22×C3×D311yescharacteristic
786C2×C8C22×C3×D311yescharacteristic
787C4⋊C4—31no—
788C4⋊C4—61no—
789C4⋊C4—61no—
790C4⋊C4—61no—
791C4⋊C4C22×C3×D311yescharacteristic
792C22⋊C4—21no—
793C22⋊C4—61no—
794C22⋊C4—61no—
795C22⋊C4—61no—
796C22×C3—22no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—32no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—62no—
818C22×C3—61no—
819C22×C3—81no—
820C22×C3—81no—
821C22×C3—81no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3C2×D3×D411yescharacteristic
825C22×C3C22×C3×D411yescharacteristic
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—21no—
830C2×D3—21no—
831C2×D3—22no—
832C2×D3—41no—
833C2×D3—41no—
834C2×D3C3×#12012yes—
835C3×C4—22no—
836C3×C4—22no—
837C3×C4—21no—
838C3×C4—22no—
839C3×C4—22no—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—32no—
844C3×C4—41no—
845C3×C4—42no—
846C3×C4—42no—
847C3×C4—41no—
848C3×C4—41no—
849C3×C4—61no—
850C3×C4—62no—
851C3×C4—81no—
852C3×C4—121no—
853C3×C4—121no—
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C2×D3×D411yescharacteristic
856C3×C4C22×C3×D411yescharacteristic
857C3×C4C22×C3×D411yescharacteristic
858Dic3—21no—
859Dic3—22no—
860Dic3—41no—
861Dic3—41no—
862Dic3C3×#12012yes—
863C32#301311yescharacteristic, complemented, Sylow
864C23—21no—
865C23—31no—
866C23—31no—
867C23—61no—
868C23C3×D3×D411yescharacteristic
869Q8—24no—
870Q8—21no—
871Q8—21no—
872Q8—32no—
873Q8—64no—
874Q8—62no—
875Q8—64no—
876Q8—61no—
877Q8—61no—
878Q8—61no—
879Q8C3×D3×D412yes—
880Q8C3×D3×D412yes—
881D4—21no—
882D4—21no—
883D4—32no—
884D4—62no—
885D4—64no—
886D4—64no—
887D4—62no—
888D4—62no—
889D4—64no—
890D4—61no—
891D4—81no—
892D4—122no—
893D4—241no—
894C2×C4—24no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—31no—
901C2×C4—32no—
902C2×C4—32no—
903C2×C4—31no—
904C2×C4—64no—
905C2×C4—64no—
906C2×C4—64no—
907C2×C4—64no—
908C2×C4—64no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—61no—
914C2×C4—122no—
915C2×C4—241no—
916C2×C4C3×D3×D411yescharacteristic
917C2×C4C23×C3×D311yescharacteristic
918C8—21no—
919C8—21no—
920C8—61no—
921C8—61no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
925C2×C3—42no—
926C2×C3—41no—
927C2×C3—41no—
928C2×C3—62no—
929C2×C3—81no—
930C2×C3—81no—
931C2×C3—121no—
932C2×C3—122no—
933C2×C3—161no—
934C2×C3D3×#12011yescharacteristic
935C2×C3#576211yescharacteristic
936C2×C3#577911yescharacteristic
937C2×C3C2×C3×#12011yescharacteristic
938C2×C3C3×#57711yescharacteristic
939C2×C3C3×#57811yescharacteristic
940D3—22no—
941D3—41no—
942D3—42no—
943C22—21no—
944C22—21no—
945C22—21no—
946C22—32no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—61no—
951C22—61no—
952C22—61no—
953C22—61no—
954C22—62no—
955C22—61no—
956C22—121no—
957C22—121no—
958C22C2×C3×D3×D411yescharacteristic
959C4—22no—
960C4—22no—
961C4—21no—
962C4—32no—
963C4—41no—
964C4—61no—
965C4—62no—
966C4—121no—
967C4—121no—
968C4C2×C3×D3×D411yescharacteristic
969C4C2×C3×D3×D411yescharacteristic
970C3—21no—
971C3#8004211yescharacteristic, direct product factor
972C3C3×#301311yescharacteristic, complemented
973C2—41no—
974C2—62no—
975C2—81no—
976C2—121no—
977C2—122no—
978C2C3×D3×#12011yescharacteristic
979C2C3×#576211yescharacteristic
980C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#448C2
socleC22×C32C22×D4
hypercenterC3×#448D3
hypocenterC3C3×#3013
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#448

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×C3×#916C2semidirect
3. C2×C3×#915C2semidirect
4. C3×#5608C2semidirect
5. C32×#448C2semidirect
6. C3×#5228C2semidirect
7. C3×#5172C2semidirect
8. C3×#5170C2semidirect
9. C3×#5037C2semidirect
10. C3×#4809C2semidirect
11. C3×#4808C2semidirect
12. C3×#4803C2semidirect
13. C3×D3×#103C2semidirect
14. C3×#4733C2semidirect
15. C3×#4727C2semidirect
17. #80042C3direct (N × H)
66. C2×#1007C2×C3semidirect
70. C2×#916C2×C3semidirect
71. C2×#915C2×C3semidirect
72. #5608C2×C3semidirect
81. C3×#448D3semidirect
82. C3×#448C2×C3semidirect
86. #5228C2×C3semidirect
87. #5172C2×C3semidirect
88. #5170C2×C3semidirect
89. #5037C2×C3semidirect
90. #4809C2×C3semidirect
91. #4808C2×C3semidirect
92. #4803C2×C3semidirect
93. D3×#103C2×C3semidirect
94. #4733C2×C3semidirect
95. #4727C2×C3semidirect
115. C3×#239D4semidirect
120. C3×D3×Q8D4semidirect
340. #448C3×D3semidirect
422. #239C3×D4semidirect
427. D3×Q8C3×D4semidirect
863. C32#3013semidirect
971. C3#80042direct (N × H)
972. C3C3×#3013semidirect

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×#9162
C2×C3×#9152
C3×#56082
C32×#4482
C3×#52282
C3×#51722
C3×#51702
C3×#50372
C3×#48092
C3×#48082
C3×#48032
C3×D3×#1032
C3×#47332
C3×#47272
C3×#30133
#800423