Finite Group Databasebeta

← C3×#80656 #11866814

Subgroups — C3×#80656 #11866814

Order 1152.

1102 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2C22×C3×D3×C8C211yesmaximal, characteristic, complemented
3C3×#5627C211yesmaximal, characteristic, complemented
4C3×#5606C211yesmaximal, characteristic, complemented
5C32×#465C211yesmaximal, characteristic, complemented
6C3×#5171C211yesmaximal, characteristic, complemented
7C3×#5114C211yesmaximal, characteristic, complemented
8C3×#5051C211yesmaximal, characteristic, complemented
9C3×#5038C211yesmaximal, characteristic, complemented
10C3×#4864C211yesmaximal, characteristic, complemented
11C3×#4860C211yesmaximal, characteristic, complemented
12C3×#4813C211yesmaximal, characteristic, complemented
13C3×#4804C211yesmaximal, characteristic, complemented
14C3×#4775C211yesmaximal, characteristic, complemented
15C3×#4772C211yesmaximal, characteristic, complemented
16C3×#3050—31nomaximal
17#80656C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic, complemented
22C22×C32×C8C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C32×#121C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic, complemented
27C3×#938C2211yescharacteristic
28C3×#937—21no—
29C3×D4×Dic3—21no—
30C2×C3×#213C2211yescharacteristic, complemented
31C3×#930C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34C3×#916—24no—
35C2×C3×#204C2211yescharacteristic, complemented
36C2×C3×D3×C8—24no—
37C2×C3×D3×C8C2211yescharacteristic
38C2×C3×D3×C8C2211yescharacteristic
39C2×C3×D3×C8C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic
41C3×#897C2211yescharacteristic
42C3×#895C2211yescharacteristic
43C3×#894—21no—
44C3×#893—21no—
45C3×#892C2211yescharacteristic
46C3×#892C2211yescharacteristic
47C3×#883—21no—
48C3×#882—21no—
49C3×#67⋊C4—21no—
50C3×#67⋊C4—21no—
51C32×#106C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#817C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61C3×#807C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64C23×C3×C8—31no—
65C3×#525—31no—
66C3×#525—31no—
67C2×#916C2×C311yescharacteristic, complemented
68C22×D3×C8C2×C311yescharacteristic, complemented
69#5627C2×C311yescharacteristic, complemented
70#5606C2×C311yescharacteristic, complemented
71C3×#467—31no—
72C3×#467—31no—
73C3×#466—31no—
74C3×#466—31no—
75C3×#465—21no—
76C3×#465—31no—
77C3×#465—31no—
78C3×#465—31no—
79C3×#465D311yescharacteristic, complemented
80C3×#465C2×C311yescharacteristic, complemented
81C3×#427—31no—
82C3×#416—31no—
83C3×#416—31no—
84#5171C2×C311yescharacteristic, complemented
85#5114C2×C311yescharacteristic, complemented
86#5051C2×C311yescharacteristic, complemented
87#5038C2×C311yescharacteristic, complemented
88#4864C2×C311yescharacteristic, complemented
89#4860C2×C311yescharacteristic, complemented
90#4813C2×C311yescharacteristic, complemented
91#4804C2×C311yescharacteristic, complemented
92#4775C2×C311yescharacteristic, complemented
93#4772C2×C311yescharacteristic, complemented
94C23×C3×D3D411yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3D411yescharacteristic
104C3×#239—22no—
105C3×#239—22no—
106C3×#237—22no—
107C3×#237—22no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3D411yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C32×SD16—22no—
120C2×C32×C8—22no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127C32×C22⋊C4—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#216—22no—
131C3×#213—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×C4⋊Dic3C2311yescharacteristic
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×C4×Dic3—21no—
144C3×C4×Dic3—21no—
145C2×C3×C3⋊C8—22no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C3×#204—22no—
149C3×D3×C8—22no—
150C3×D3×C8—22no—
151C3×D3×C8—22no—
152C3×D3×C8D414yescomplemented
153#3050—31noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C23×C3×C4—31no—
157C2×#239C22×C311yescharacteristic
158C2×#237C22×C311yescharacteristic
159C22×C4×D3C22×C311yescharacteristic
160C3×#135—64no—
161C2×C3×Q16—31no—
162C2×C3×SD16—21no—
163C2×C3×SD16—31no—
164C2×C3×SD16C2×D311yescharacteristic, complemented
165C2×C3×SD16C22×C311yescharacteristic, complemented
166C2×C3×D8—31no—
167C22×C3×C8—21no—
168C22×C3×C8—31no—
169C22×C3×C8—31no—
170C22×C3×C8—31no—
171C22×C3×C8—31no—
172C22×C3×C8—31no—
173C22×C3×C8—64no—
174C22×C3×C8C2×D311yescharacteristic
175C22×C3×C8C22×C311yescharacteristic
176C3×#123—61no—
177C3×#123—61no—
178C3×C22⋊Q8—21no—
179C3×C22⋊Q8—31no—
180C3×C22⋊Q8—31no—
181C3×C22⋊Q8—31no—
182C3×C22⋊Q8C2×D311yescharacteristic
183C3×C22⋊Q8C22×C311yescharacteristic
184C3×#121—21no—
185C3×#121—31no—
186C3×#121—31no—
187C3×#121—31no—
188C3×#121C2×D311yescharacteristic
189C3×#121C22×C311yescharacteristic
190C3×#120—61no—
191C3×#120—61no—
192C3×C4×D4—61no—
193C3×C4×D4—61no—
194C3×C4×D4—61no—
195C3×C4×D4—61no—
196C3×#117—31no—
197C3×#117—31no—
198#946C22×C311yescharacteristic
199C2×#216C22×C311yescharacteristic, complemented
200#938C22×C311yescharacteristic
201#937—21no—
202D4×Dic3—21no—
203C2×#213C22×C311yescharacteristic, complemented
204#930C22×C311yescharacteristic
205#924C22×C311yescharacteristic
206C22×C3⋊C8C22×C311yescharacteristic
207#916—24no—
208C2×#204C22×C311yescharacteristic, complemented
209C2×D3×C8—24no—
210C2×D3×C8C22×C311yescharacteristic
211C2×D3×C8C22×C311yescharacteristic
212C2×D3×C8C22×C311yescharacteristic
213C2×D3×C8C22×C311yescharacteristic
214#897C22×C311yescharacteristic
215#895C22×C311yescharacteristic
216#894—21no—
217#893—21no—
218#892C22×C311yescharacteristic
219#892C22×C311yescharacteristic
220#883—21no—
221#882—21no—
222#67⋊C4—21no—
223#67⋊C4—21no—
224C3×#107—31no—
225C3×#107—31no—
226C3×#106—21no—
227C3×#106—31no—
228C3×#106C2×D311yescharacteristic, complemented
229C3×#106C22×C311yescharacteristic, complemented
230C3×#103—21no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103C2×D311yescharacteristic, complemented
235C3×#103C22×C311yescharacteristic, complemented
236C3×#102—21no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102C2×D311yescharacteristic, complemented
241C3×#102C22×C311yescharacteristic, complemented
242#835C22×C311yescharacteristic, complemented
243#832C22×C311yescharacteristic, complemented
244#821C22×C311yescharacteristic, complemented
245#817C22×C311yescharacteristic, complemented
246#816C22×C311yescharacteristic, complemented
247#810C22×C311yescharacteristic, complemented
248#809C22×C311yescharacteristic, complemented
249#807C22×C311yescharacteristic, complemented
250#807C22×C311yescharacteristic, complemented
251C23×C32—21no—
252C23×C32C2×D411yescharacteristic
253C22×C3×D3—22no—
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C32×Q8—21no—
260C32×Q8—21no—
261C32×D4—21no—
262C32×D4—21no—
263C32×D4—42no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C3×#67—42no—
272C3×#67—42no—
273C3×#67—42no—
274C2×C3×Dic3—22no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×D12—42no—
285C3×C4×D3—22no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—22no—
289C3×C4×D3—42no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C32×C8—21no—
295C32×C8C2×D412yes—
296C3×C3⋊C8—21no—
297C3×C3⋊C8C2×D412yes—
298C2×#135—31no—
299C23×C8—31no—
300#525—31no—
301#525—31no—
302#467—31no—
303#467—31no—
304#466—31no—
305#466—31no—
306#465—31no—
307#465—31no—
308#465—31no—
309#465C3×D311yescharacteristic, complemented
310#427—31no—
311#416—31no—
312#416—31no—
313C24×C3—31no—
314C23×D3C3×D411yescharacteristic
315C3×#41—62no—
316C3×#41—62no—
317C3×#41—62no—
318C3×#41—62no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C23×C311yescharacteristic
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—41no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C23×C311yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—62no—
342C22×C3×C4—62no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C23×C311yescharacteristic
347C2×#67—21no—
348C2×#67—21no—
349C2×#67—21no—
350C22×Dic3—21no—
351C22×Dic3C3×D411yescharacteristic
352#239—22no—
353#239—22no—
354#237—22no—
355#237—22no—
356C2×D12—21no—
357C2×D12—21no—
358C2×D12C23×C311yescharacteristic
359C2×C4×D3—22no—
360C2×C4×D3—22no—
361C2×C4×D3—21no—
362C2×C4×D3C3×D411yescharacteristic
363C2×C4×D3C3×D411yescharacteristic
364C2×C4×D3C23×C311yescharacteristic
365C2×C4×D3C23×C311yescharacteristic
366C2×Dic6C23×C311yescharacteristic
367C3×Q16—62no—
368C3×SD16—22no—
369C3×SD16—22no—
370C3×SD16—42no—
371C3×SD16—62no—
372C3×D8—62no—
373C2×C3×C8—22no—
374C2×C3×C8—22no—
375C2×C3×C8—21no—
376C2×C3×C8—21no—
377C2×C3×C8—31no—
378C2×C3×C8—34no—
379C2×C3×C8—31no—
380C2×C3×C8—42no—
381C2×C3×C8—62no—
382C2×C3×C8—62no—
383C2×C3×C8—62no—
384C2×C3×C8—62no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C23×C311yescharacteristic
388C2×C3×C8C23×C311yescharacteristic
389C3×C4⋊C4—21no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—31no—
395C3×C4⋊C4—41no—
396C3×C4⋊C4—61no—
397C3×C4⋊C4—61no—
398C3×C4⋊C4—61no—
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C4⋊C4C22×D311yescharacteristic
401C3×C4⋊C4C23×C311yescharacteristic
402C3×C4⋊C4C23×C311yescharacteristic
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—21no—
407C3×C22⋊C4—41no—
408C3×C22⋊C4—41no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C22⋊C4—61no—
417C3×C42—61no—
418C3×C42—61no—
419#217—21no—
420#217—21no—
421#216—22no—
422#213—22no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
429C4⋊Dic3—21no—
430C4⋊Dic3C23×C311yescharacteristic
431C4⋊Dic3C23×C311yescharacteristic
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434C4×Dic3—21no—
435C4×Dic3—21no—
436C2×C3⋊C8—22no—
437C2×C3⋊C8C23×C311yescharacteristic
438C2×C3⋊C8C23×C311yescharacteristic
439#204—22no—
440D3×C8—22no—
441D3×C8—22no—
442D3×C8—22no—
443D3×C8C3×D414yescomplemented
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32#13512yescomplemented
450C22×C32C22×D411yescharacteristic
451C2×C3×D3—28no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3#12112yes—
460C2×C3×D3#13512yescomplemented
461C32×C4—21no—
462C32×C4—41no—
463C32×C4—41no—
464C32×C4—41no—
465C32×C4C22×D411yescharacteristic
466C32×C4C2×#4111yescharacteristic
467C3×Dic3—21no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C3×Dic3#12112yes—
472C2×#41—31no—
473C2×#41—31no—
474C23×C4—31no—
475#135—64no—
476C2×Q16—31no—
477C2×SD16—31no—
478C2×SD16C2×C3×D311yescharacteristic, complemented
479C2×D8—31no—
480C22×C8—31no—
481C22×C8—31no—
482C22×C8—31no—
483C22×C8—31no—
484C22×C8—31no—
485C22×C8—64no—
486C22×C8C2×C3×D311yescharacteristic
487#123—61no—
488#123—61no—
489C22⋊Q8—31no—
490C22⋊Q8—31no—
491C22⋊Q8—31no—
492C22⋊Q8C2×C3×D311yescharacteristic
493#121—31no—
494#121—31no—
495#121—31no—
496#121C2×C3×D311yescharacteristic
497#120—61no—
498#120—61no—
499C4×D4—61no—
500C4×D4—61no—
501C4×D4—61no—
502C4×D4—61no—
503#117—31no—
504#117—31no—
505#107—31no—
506#107—31no—
507#106—31no—
508#106C2×C3×D311yescharacteristic, complemented
509#103—31no—
510#103—31no—
511#103—31no—
512#103C2×C3×D311yescharacteristic, complemented
513#102—31no—
514#102—31no—
515#102—31no—
516#102C2×C3×D311yescharacteristic, complemented
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—31no—
521C23×C3—31no—
522C23×C3—41no—
523C23×C3—62no—
524C23×C3—62no—
525C23×C3—62no—
526C23×C3—61no—
527C23×C3D3×D411yescharacteristic
528C23×C3C2×C3×D411yescharacteristic
529C22×D3—22no—
530C22×D3—22no—
531C22×D3—22no—
532C22×D3—21no—
533C22×D3C2×C3×D411yescharacteristic
534C22×D3C2×C3×D411yescharacteristic
535C3×Q8—21no—
536C3×Q8—21no—
537C3×Q8—21no—
538C3×Q8—21no—
539C3×Q8—41no—
540C3×Q8—41no—
541C3×Q8—61no—
542C3×Q8—61no—
543C3×D4—21no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—41no—
548C3×D4—41no—
549C3×D4—42no—
550C3×D4—42no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—82no—
554C3×D4—122no—
555C3×D4—122no—
556C3×D4—122no—
557C3×D4—122no—
558C3×D4—122no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—31no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—62no—
581C2×C3×C4—62no—
582C2×C3×C4—62no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—122no—
589C2×C3×C4—122no—
590C2×C3×C4D3×D411yescharacteristic
591C2×C3×C4C2×C3×D411yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C24×C311yescharacteristic
594#67—42no—
595#67—42no—
596#67—42no—
597C2×Dic3—22no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—42no—
602C2×Dic3C2×C3×D411yescharacteristic
603C2×Dic3C2×C3×D411yescharacteristic
604D12—21no—
605D12—21no—
606D12—42no—
607D12—42no—
608C4×D3—22no—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—22no—
612C4×D3—42no—
613C4×D3C2×C3×D412yes—
614C4×D3C3×#4112yes—
615Dic6—21no—
616Dic6—21no—
617C3×C8—21no—
618C3×C8—21no—
619C3×C8—22no—
620C3×C8—32no—
621C3×C8—41no—
622C3×C8—61no—
623C3×C8D3×D412yes—
624C3×C8C2×C3×D412yes—
625C3⋊C8—21no—
626C3⋊C8C2×C3×D412yes—
627C2×C32—22no—
628C2×C32—81no—
629C2×C32C2×#12111yescharacteristic
630C2×C32C2×#13511yescharacteristic
631C2×C32C2×#13511yescharacteristic
632C3×D3—22no—
633C3×D3—22no—
634C3×D3—81no—
635C24—31no—
636#41—62no—
637#41—62no—
638#41—62no—
639#41—62no—
640C2×Q8—31no—
641C2×Q8C22×C3×D311yescharacteristic
642C2×D4—21no—
643C2×D4—31no—
644C2×D4—61no—
645C2×D4—61no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—61no—
649C2×D4C22×C3×D311yescharacteristic
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4C22×C3×D311yescharacteristic
660Q16—62no—
661SD16—22no—
662SD16—62no—
663D8—62no—
664C2×C8—22no—
665C2×C8—31no—
666C2×C8—34no—
667C2×C8—31no—
668C2×C8—62no—
669C2×C8—62no—
670C2×C8—62no—
671C2×C8—62no—
672C2×C8C22×C3×D311yescharacteristic
673C2×C8C22×C3×D311yescharacteristic
674C4⋊C4—21no—
675C4⋊C4—31no—
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—61no—
679C4⋊C4—61no—
680C4⋊C4C22×C3×D311yescharacteristic
681C4⋊C4C22×C3×D311yescharacteristic
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—61no—
688C22⋊C4—61no—
689C22⋊C4—61no—
690C22⋊C4—61no—
691C22⋊C4—61no—
692C42—61no—
693C42—61no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—32no—
701C22×C3—32no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—68no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3#91612yescomplemented
722C22×C3C3×#13512yescomplemented
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C22×C3×D411yescharacteristic
725C2×D3—28no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3C3×#12112yes—
734C2×D3C3×#13512yescomplemented
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—32no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—41no—
745C3×C4—41no—
746C3×C4—41no—
747C3×C4—61no—
748C3×C4—81no—
749C3×C4—81no—
750C3×C4—81no—
751C3×C4—121no—
752C3×C4—121no—
753C3×C4—121no—
754C3×C4C2×D3×D411yescharacteristic
755C3×C4D3×#4111yescharacteristic
756C3×C4C22×C3×D411yescharacteristic
757C3×C4C2×C3×#4111yescharacteristic
758Dic3—21no—
759Dic3—41no—
760Dic3—41no—
761Dic3—41no—
762Dic3C3×#12112yes—
763C32#305011yescharacteristic, complemented, Sylow
764C23—21no—
765C23—31no—
766C23—31no—
767C23—62no—
768C23—62no—
769C23—62no—
770C23—61no—
771C23C3×D3×D411yescharacteristic
772Q8—21no—
773Q8—21no—
774Q8—61no—
775Q8—61no—
776D4—21no—
777D4—21no—
778D4—42no—
779D4—61no—
780D4—61no—
781D4—122no—
782D4—122no—
783D4—122no—
784D4—122no—
785D4—122no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—31no—
792C2×C4—32no—
793C2×C4—32no—
794C2×C4—31no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—122no—
804C2×C4—122no—
805C2×C4C3×D3×D411yescharacteristic
806C2×C4C23×C3×D311yescharacteristic
807C8—21no—
808C8—32no—
809C8—61no—
810C8C3×D3×D412yes—
811C2×C3—22no—
812C2×C3—22no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—42no—
817C2×C3—62no—
818C2×C3—62no—
819C2×C3—81no—
820C2×C3—81no—
821C2×C3—161no—
822C2×C3—241no—
823C2×C3D3×#12111yescharacteristic
824C2×C3C2×#91611yescharacteristic
825C2×C3D3×#13511yescharacteristic
826C2×C3C2×C3×#12111yescharacteristic
827C2×C3C2×C3×#13511yescharacteristic
828C2×C3C2×C3×#13511yescharacteristic
829D3—22no—
830D3—22no—
831D3—81no—
832C22—21no—
833C22—21no—
834C22—32no—
835C22—32no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—68no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22C3×#91612yescomplemented
848C22C2×C3×D3×D411yescharacteristic
849C4—21no—
850C4—32no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—61no—
855C4—121no—
856C4—121no—
857C4—121no—
858C4C2×C3×D3×D411yescharacteristic
859C4C3×D3×#4111yescharacteristic
860C3—21no—
861C3#8065611yescharacteristic, direct product factor
862C3C3×#305011yescharacteristic, complemented
863C2—22no—
864C2—62no—
865C2—62no—
866C2—81no—
867C2—241no—
868C2C3×D3×#12111yescharacteristic
869C2C2×C3×#91611yescharacteristic
870C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
hypercenterC3×#465D3
hypocenterC3C3×#3050
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#465

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. C22×C3×D3×C8C2semidirect
3. C3×#5627C2semidirect
4. C3×#5606C2semidirect
5. C32×#465C2semidirect
6. C3×#5171C2semidirect
7. C3×#5114C2semidirect
8. C3×#5051C2semidirect
9. C3×#5038C2semidirect
10. C3×#4864C2semidirect
11. C3×#4860C2semidirect
12. C3×#4813C2semidirect
13. C3×#4804C2semidirect
14. C3×#4775C2semidirect
15. C3×#4772C2semidirect
17. #80656C3direct (N × H)
21. C2×C32×SD16C22semidirect
26. C2×C3×#216C22semidirect
30. C2×C3×#213C22semidirect
35. C2×C3×#204C22semidirect
51. C32×#106C22semidirect
52. C32×#103C22semidirect
53. C32×#102C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×#817C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. C3×#807C22semidirect
62. C3×#807C22semidirect
67. C2×#916C2×C3semidirect
68. C22×D3×C8C2×C3semidirect
69. #5627C2×C3semidirect
70. #5606C2×C3semidirect
79. C3×#465D3semidirect
80. C3×#465C2×C3semidirect
84. #5171C2×C3semidirect
85. #5114C2×C3semidirect
86. #5051C2×C3semidirect
87. #5038C2×C3semidirect
88. #4864C2×C3semidirect
89. #4860C2×C3semidirect
90. #4813C2×C3semidirect
91. #4804C2×C3semidirect
92. #4775C2×C3semidirect
93. #4772C2×C3semidirect
152. C3×D3×C8D4semidirect
164. C2×C3×SD16C2×D3semidirect
165. C2×C3×SD16C22×C3semidirect
199. C2×#216C22×C3semidirect
203. C2×#213C22×C3semidirect
208. C2×#204C22×C3semidirect
228. C3×#106C2×D3semidirect
229. C3×#106C22×C3semidirect
234. C3×#103C2×D3semidirect
235. C3×#103C22×C3semidirect
240. C3×#102C2×D3semidirect
241. C3×#102C22×C3semidirect
242. #835C22×C3semidirect
243. #832C22×C3semidirect
244. #821C22×C3semidirect
245. #817C22×C3semidirect
246. #816C22×C3semidirect
247. #810C22×C3semidirect
248. #809C22×C3semidirect
249. #807C22×C3semidirect
250. #807C22×C3semidirect
309. #465C3×D3semidirect
443. D3×C8C3×D4semidirect
449. C22×C32#135semidirect
460. C2×C3×D3#135semidirect
478. C2×SD16C2×C3×D3semidirect
508. #106C2×C3×D3semidirect
512. #103C2×C3×D3semidirect
516. #102C2×C3×D3semidirect
721. C22×C3#916semidirect
722. C22×C3C3×#135semidirect
734. C2×D3C3×#135semidirect
763. C32#3050semidirect
847. C22C3×#916semidirect
861. C3#80656direct (N × H)
862. C3C3×#3050semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
C22×C3×D3×C82
C3×#56272
C3×#56062
C32×#4652
C3×#51712
C3×#51142
C3×#50512
C3×#50382
C3×#48642
C3×#48602
C3×#48132
C3×#48042
C3×#47752
C3×#47722
C3×#30503
#806563