Finite Group Databasebeta

← C3×#80836 #11884399

Subgroups — C3×#80836 #11884399

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#916C211yesmaximal, characteristic, complemented
2C2×C3×#908C211yesmaximal, characteristic, complemented
3C3×#5630C211yesmaximal, characteristic, complemented
4C3×#5599C211yesmaximal, characteristic, complemented
5C32×#468C211yesmaximal, characteristic, complemented
6C3×#5176C211yesmaximal, characteristic, complemented
7C3×#5127C211yesmaximal, characteristic, complemented
8C3×#5047C211yesmaximal, characteristic, complemented
9C3×#5036C211yesmaximal, characteristic, complemented
10C3×#4889C211yesmaximal, characteristic, complemented
11C3×#4883C211yesmaximal, characteristic, complemented
12C3×#4810C211yesmaximal, characteristic, complemented
13C3×#4798C211yesmaximal, characteristic, complemented
14C3×#4786C211yesmaximal, characteristic, complemented
15C3×#4781C211yesmaximal, characteristic, complemented
16C3×#3268—31nomaximal
17#80836C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C2×C32×M16C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C32×#121C2211yescharacteristic
26C3×#947C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic, complemented
29C3×#940—21no—
30C3×#940C2211yescharacteristic, complemented
31C3×#939—21no—
32C2×C3×#213C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×C4×#67C2211yescharacteristic
35C3×#916—24no—
36C3×#908—24no—
37C2×C3×D24C2211yescharacteristic
38C2×C3×D24C2211yescharacteristic
39C2×C3×#204C2211yescharacteristic
40C2×C3×#204C2211yescharacteristic
41C2×C3×D3×C8C2211yescharacteristic, complemented
42C3×#895—21no—
43C3×#895C2211yescharacteristic
44C3×#895C2211yescharacteristic, complemented
45C3×#894—21no—
46C3×#893C2211yescharacteristic
47C3×#887C2211yescharacteristic, complemented
48C3×#884—21no—
49C3×#882—21no—
50C3×#67⋊C4—21no—
51C3×D3×C22⋊C4—21no—
52C32×#107C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic
61C3×#809C2211yescharacteristic
62C3×#809C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×#135—31no—
65C3×#550—31no—
66C3×#546—31no—
67C2×#916C2×C311yescharacteristic, complemented
68C2×#908C2×C311yescharacteristic, complemented
69#5630C2×C311yescharacteristic, complemented
70#5599C2×C311yescharacteristic, complemented
71C3×#496—31no—
72C3×#468—21no—
73C3×#468D311yescharacteristic, complemented
74C3×#468C2×C311yescharacteristic, complemented
75C3×#466—31no—
76C3×#464—31no—
77C3×#459—31no—
78C3×#452—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×#447—31no—
82C3×#440—31no—
83C3×#435—31no—
84#5176C2×C311yescharacteristic, complemented
85#5127C2×C311yescharacteristic, complemented
86#5047C2×C311yescharacteristic, complemented
87#5036C2×C311yescharacteristic, complemented
88#4889C2×C311yescharacteristic, complemented
89#4883C2×C311yescharacteristic, complemented
90#4810C2×C311yescharacteristic, complemented
91#4798C2×C311yescharacteristic, complemented
92#4786C2×C311yescharacteristic, complemented
93#4781C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
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—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C3×#239—22no—
106C3×#239—41no—
107C3×#237—22no—
108C3×#237—41no—
109C3×#235—22no—
110C3×#235—41no—
111C2×C3×D12—22no—
112C2×C3×D12—21no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12—21no—
116C2×C3×D12—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—21no—
122C2×C3×C4×D3—21no—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×Dic6C2311yescharacteristic
125C32×SD16—22no—
126C32×M16—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129C32×C4⋊C4—21no—
130C32×C4⋊C4C2311yescharacteristic
131C32×C4⋊C4C2311yescharacteristic
132C32×C22⋊C4—21no—
133C32×C22⋊C4—21no—
134C3×#217D411yescharacteristic
135C3×#216—22no—
136C3×#215—41no—
137C3×#213—22no—
138C3×#213—41no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4D411yescharacteristic
145C3×Dic3⋊C4—21no—
146C3×Dic3⋊C4D411yescharacteristic
147C3×C4×Dic3—21no—
148C3×C4×Dic3C2311yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C3×D24—22no—
152C3×D24—22no—
153C3×#204—22no—
154C3×#204D414yescomplemented
155C3×D3×C8—22no—
156#3268—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C22×C3×D4—31no—
161C2×#239C22×C311yescharacteristic
162C2×#237C22×C311yescharacteristic, complemented
163C2×#235C22×C311yescharacteristic
164C22×D12C22×C311yescharacteristic
165C3×AGL(1,ℤ/8)—64no—
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16C2×D311yescharacteristic, complemented
173C2×C3×SD16C22×C311yescharacteristic, complemented
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C2×C3×D8—31no—
178C2×C3×M16—21no—
179C2×C3×M16C2×D311yescharacteristic
180C2×C3×M16C22×C311yescharacteristic
181C22×C3×C8—31no—
182C3×#127—31no—
183C3×#127—61no—
184C3×#124—31no—
185C3×#123—61no—
186C3×C22⋊Q8—21no—
187C3×C22⋊Q8C2×D311yescharacteristic
188C3×C22⋊Q8C22×C311yescharacteristic
189C3×#121—21no—
190C3×#121—31no—
191C3×#121—31no—
192C3×#121—61no—
193C3×#121—61no—
194C3×#121—61no—
195C3×#121C2×D311yescharacteristic
196C3×#121C22×C311yescharacteristic
197C3×#120—61no—
198C3×C4×Q8—31no—
199C3×C4×D4—31no—
200C3×C4×D4—31no—
201C3×C4×D4—61no—
202C2×C3×C22⋊C4—61no—
203#947C22×C311yescharacteristic
204C2×#216C22×C311yescharacteristic, complemented
205C2×#215C22×C311yescharacteristic, complemented
206#940—21no—
207#940C22×C311yescharacteristic, complemented
208#939—21no—
209C2×#213C22×C311yescharacteristic
210C2×#213C22×C311yescharacteristic
211C4×#67C22×C311yescharacteristic
212#916—24no—
213#908—24no—
214C2×D24C22×C311yescharacteristic
215C2×D24C22×C311yescharacteristic
216C2×#204C22×C311yescharacteristic
217C2×#204C22×C311yescharacteristic
218C2×D3×C8C22×C311yescharacteristic, complemented
219#895—21no—
220#895C22×C311yescharacteristic
221#895C22×C311yescharacteristic, complemented
222#894—21no—
223#893C22×C311yescharacteristic
224#887C22×C311yescharacteristic, complemented
225#884—21no—
226#882—21no—
227#67⋊C4—21no—
228D3×C22⋊C4—21no—
229C3×#107—21no—
230C3×#107C2×D311yescharacteristic, complemented
231C3×#107C22×C311yescharacteristic, complemented
232C3×C4⋊C8—31no—
233C3×#103—21no—
234C3×#103—31no—
235C3×#103C2×D311yescharacteristic, complemented
236C3×#103C22×C311yescharacteristic, complemented
237C3×#102—21no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102C2×D311yescharacteristic, complemented
242C3×#102C22×C311yescharacteristic, complemented
243C3×C22⋊C8—31no—
244C3×C22⋊C8—31no—
245C3×#97—31no—
246#830C22×C311yescharacteristic
247(C2×D3)⋊C8C22×C311yescharacteristic, complemented
248#815C22×C311yescharacteristic, complemented
249Dic3⋊C8C22×C311yescharacteristic, complemented
250#810C22×C311yescharacteristic, complemented
251#809C22×C311yescharacteristic
252#809C22×C311yescharacteristic
253#809C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C32×D4—81no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275C3×#67—41no—
276C3×#67—42no—
277C3×#67—42no—
278C3×#67—42no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—42no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12—42no—
292C3×D12—81no—
293C3×D12—81no—
294C3×D12C2×D412yes—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—42no—
298C3×C4×D3—42no—
299C3×C4×D3—81no—
300C3×Dic6—21no—
301C3×Dic6C2×D412yes—
302C32×C8—21no—
303C32×C8C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—31no—
307C2×#135—31no—
308#550—31no—
309#546—31no—
310#496—31no—
311#468C3×D311yescharacteristic, complemented
312#466—31no—
313#464—31no—
314#459—31no—
315#452—31no—
316#449—31no—
317#449—31no—
318#447—31no—
319#440—31no—
320#435—31no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—121no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—21no—
330C2×C3×Q8—31no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C23×C311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—31no—
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—41no—
341C2×C3×D4—62no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—61no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—121no—
351C2×C3×D4C22×D311yescharacteristic
352C2×C3×D4C23×C311yescharacteristic
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—61no—
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×#67—21no—
364C2×#67—21no—
365C2×#67C3×D411yescharacteristic
366C22×Dic3—21no—
367#239—22no—
368#239—41no—
369#237—22no—
370#237—41no—
371#235—22no—
372#235—41no—
373C2×D12—22no—
374C2×D12—21no—
375C2×D12—21no—
376C2×D12—21no—
377C2×D12—21no—
378C2×D12—41no—
379C2×D12C23×C311yescharacteristic
380C2×D12C23×C311yescharacteristic
381C2×D12C23×C311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—21no—
384C2×C4×D3—21no—
385C2×C4×D3C23×C311yescharacteristic
386C2×Dic6C23×C311yescharacteristic
387C3×Q16—62no—
388C3×SD16—22no—
389C3×SD16—22no—
390C3×SD16—34no—
391C3×SD16—42no—
392C3×SD16—62no—
393C3×SD16—121no—
394C3×D8—62no—
395C3×D8—62no—
396C3×D8—62no—
397C3×D8—121no—
398C3×M16—22no—
399C3×M16—22no—
400C3×M16—42no—
401C2×C3×C8—21no—
402C2×C3×C8—21no—
403C2×C3×C8—31no—
404C2×C3×C8—31no—
405C2×C3×C8—62no—
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C2×C3×C8C23×C311yescharacteristic
409C2×C3×C8C23×C311yescharacteristic
410C3×C4⋊C4—21no—
411C3×C4⋊C4—21no—
412C3×C4⋊C4—21no—
413C3×C4⋊C4—21no—
414C3×C4⋊C4—31no—
415C3×C4⋊C4—41no—
416C3×C4⋊C4—61no—
417C3×C4⋊C4C22×D311yescharacteristic
418C3×C4⋊C4C22×D311yescharacteristic
419C3×C4⋊C4C23×C311yescharacteristic
420C3×C4⋊C4C23×C311yescharacteristic
421C3×C22⋊C4—21no—
422C3×C22⋊C4—21no—
423C3×C22⋊C4—21no—
424C3×C22⋊C4—21no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—41no—
428C3×C22⋊C4—41no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C22⋊C4—61no—
434C3×C42—31no—
435C3×C42—61no—
436#217C3×D411yescharacteristic
437#216—22no—
438#215—41no—
439#213—22no—
440#213—41no—
441(C2×D3)⋊C4—21no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4C3×D411yescharacteristic
447Dic3⋊C4—21no—
448Dic3⋊C4C3×D411yescharacteristic
449C4×Dic3—21no—
450C4×Dic3C23×C311yescharacteristic
451C2×C3⋊C8C23×C311yescharacteristic
452C2×C3⋊C8C23×C311yescharacteristic
453D24—22no—
454D24—22no—
455#204—22no—
456#204C3×D414yescomplemented
457D3×C8—22no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32C22×D411yescharacteristic
465C2×C3×D3—21no—
466C2×C3×D3—22no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—84no—
478C32×C4—21no—
479C32×C4—41no—
480C32×C4—41no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—31no—
491C22×D4—31no—
492AGL(1,ℤ/8)—64no—
493#135—64no—
494C2×Q16—31no—
495C2×SD16—31no—
496C2×SD16—31no—
497C2×SD16—31no—
498C2×SD16C2×C3×D311yescharacteristic, complemented
499C2×D8—31no—
500C2×D8—31no—
501C2×D8—31no—
502C2×D8—31no—
503C2×M16C2×C3×D311yescharacteristic
504C22×C8—31no—
505#127—31no—
506#127—61no—
507#124—31no—
508#123—61no—
509C22⋊Q8C2×C3×D311yescharacteristic
510#121—31no—
511#121—31no—
512#121—61no—
513#121—61no—
514#121—61no—
515#121C2×C3×D311yescharacteristic
516#120—61no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4—61no—
521C2×C22⋊C4—61no—
522#107C2×C3×D311yescharacteristic, complemented
523C4⋊C8—31no—
524#103—31no—
525#103C2×C3×D311yescharacteristic, complemented
526#102—31no—
527#102—31no—
528#102—31no—
529#102C2×C3×D311yescharacteristic, complemented
530C22⋊C8—31no—
531C22⋊C8—31no—
532#97—31no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—122no—
542C23×C3—122no—
543C23×C3—241no—
544C23×C3D3×D411yescharacteristic
545C23×C3C2×C3×D411yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—81no—
552C22×D3C2×C3×D411yescharacteristic
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—32no—
558C3×Q8—41no—
559C3×Q8—41no—
560C3×Q8—61no—
561C3×D4—21no—
562C3×D4—21no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—32no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—81no—
574C3×D4—81no—
575C3×D4—82no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4—121no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—241no—
583C3×D4—241no—
584C3×D4—241no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—122no—
609C2×C3×C4—122no—
610C2×C3×C4—122no—
611C2×C3×C4—241no—
612C2×C3×C4D3×D411yescharacteristic
613C2×C3×C4C2×C3×D411yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C24×C311yescharacteristic
616#67—41no—
617#67—42no—
618#67—42no—
619#67—42no—
620#67—81no—
621C2×Dic3—21no—
622C2×Dic3—42no—
623C2×Dic3C2×C3×D411yescharacteristic
624C2×Dic3C2×C3×D411yescharacteristic
625C2×Dic3C2×C3×D411yescharacteristic
626D12—21no—
627D12—21no—
628D12—21no—
629D12—21no—
630D12—21no—
631D12—42no—
632D12—42no—
633D12—81no—
634D12—81no—
635D12C2×C3×D412yes—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—42no—
639C4×D3—42no—
640C4×D3—81no—
641Dic6—21no—
642Dic6C2×C3×D412yes—
643C3×C8—21no—
644C3×C8—21no—
645C3×C8—22no—
646C3×C8—41no—
647C3×C8—61no—
648C3×C8—61no—
649C3×C8D3×D412yes—
650C3×C8C2×C3×D412yes—
651C3⋊C8—21no—
652C3⋊C8—21no—
653C2×C32—41no—
654C2×C32—81no—
655C2×C32D4211yescharacteristic
656C2×C32#57511yescharacteristic
657C2×C32#57611yescharacteristic
658C3×D3—41no—
659C3×D3—42no—
660C3×D3—81no—
661C3×D3—81no—
662C24—61no—
663#41—62no—
664#41—62no—
665#41—62no—
666#41—121no—
667#41—121no—
668#41—121no—
669C2×Q8—31no—
670C2×Q8C22×C3×D311yescharacteristic
671C2×D4—21no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—31no—
676C2×D4—62no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—121no—
686C2×D4C22×C3×D311yescharacteristic
687C22×C4—31no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4C22×C3×D311yescharacteristic
693Q16—62no—
694SD16—22no—
695SD16—34no—
696SD16—62no—
697SD16—121no—
698D8—62no—
699D8—62no—
700D8—62no—
701D8—121no—
702M16—22no—
703C2×C8—31no—
704C2×C8—31no—
705C2×C8—62no—
706C2×C8C22×C3×D311yescharacteristic
707C2×C8C22×C3×D311yescharacteristic
708C4⋊C4—21no—
709C4⋊C4—31no—
710C4⋊C4—61no—
711C4⋊C4C22×C3×D311yescharacteristic
712C4⋊C4C22×C3×D311yescharacteristic
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—31no—
716C22⋊C4—31no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C42—31no—
723C42—61no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—62no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—244no—
756C22×C3C2×D3×D411yescharacteristic
757C22×C3C22×C3×D411yescharacteristic
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—22no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—84no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—61no—
785C3×C4—62no—
786C3×C4—81no—
787C3×C4—81no—
788C3×C4—81no—
789C3×C4C2×D3×D411yescharacteristic
790C3×C4#100911yescharacteristic
791C3×C4C22×C3×D411yescharacteristic
792C3×C4C3×H(5,𝔽2)11yescharacteristic
793Dic3—21no—
794Dic3—21no—
795Dic3—22no—
796Dic3—21no—
797C32#326811yescharacteristic, complemented, Sylow
798C23—21no—
799C23—31no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—122no—
804C23—122no—
805C23—241no—
806C23C3×D3×D411yescharacteristic
807Q8—21no—
808Q8—21no—
809Q8—32no—
810Q8—61no—
811D4—21no—
812D4—21no—
813D4—32no—
814D4—61no—
815D4—61no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—81no—
820D4—122no—
821D4—122no—
822D4—121no—
823D4—122no—
824D4—122no—
825D4—122no—
826D4—241no—
827D4—241no—
828D4—241no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—31no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—122no—
841C2×C4—122no—
842C2×C4—122no—
843C2×C4—241no—
844C2×C4C3×D3×D411yescharacteristic
845C2×C4C23×C3×D311yescharacteristic
846C8—21no—
847C8—61no—
848C8—61no—
849C8C3×D3×D412yes—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—41no—
854C2×C3—41no—
855C2×C3—81no—
856C2×C3—81no—
857C2×C3—81no—
858C2×C3—121no—
859C2×C3—122no—
860C2×C3—161no—
861C2×C3—241no—
862C2×C3—241no—
863C2×C3#560911yescharacteristic
864C2×C3#577411yescharacteristic
865C2×C3#577711yescharacteristic
866C2×C3C3×D4211yescharacteristic
867C2×C3C3×#57511yescharacteristic
868C2×C3C3×#57611yescharacteristic
869D3—41no—
870D3—42no—
871D3—81no—
872D3—81no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—61no—
880C22—61no—
881C22—61no—
882C22—62no—
883C22—121no—
884C22—121no—
885C22—121no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—244no—
892C22C2×C3×D3×D411yescharacteristic
893C4—21no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—61no—
898C4—61no—
899C4—61no—
900C4—62no—
901C4C2×C3×D3×D411yescharacteristic
902C4C3×#100911yescharacteristic
903C3—21no—
904C3#8083611yescharacteristic, direct product factor
905C3C3×#326811yescharacteristic, complemented
906C2—41no—
907C2—81no—
908C2—121no—
909C2—122no—
910C2—241no—
911C2—241no—
912C2C3×#560911yescharacteristic
913C2C3×#577411yescharacteristic
914C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#468C2
socleC22×C32C22×D4
hypercenterC3×#468D3
hypocenterC3C3×#3268
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#468

Complements

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

NH ≅ G/Ntype
1. C2×C3×#916C2semidirect
2. C2×C3×#908C2semidirect
3. C3×#5630C2semidirect
4. C3×#5599C2semidirect
5. C32×#468C2semidirect
6. C3×#5176C2semidirect
7. C3×#5127C2semidirect
8. C3×#5047C2semidirect
9. C3×#5036C2semidirect
10. C3×#4889C2semidirect
11. C3×#4883C2semidirect
12. C3×#4810C2semidirect
13. C3×#4798C2semidirect
14. C3×#4786C2semidirect
15. C3×#4781C2semidirect
17. #80836C3direct (N × H)
19. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#215C22semidirect
30. C3×#940C22semidirect
41. C2×C3×D3×C8C22semidirect
44. C3×#895C22semidirect
47. C3×#887C22semidirect
52. C32×#107C22semidirect
53. C32×#103C22semidirect
54. C32×#102C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×#810C22semidirect
62. C3×#809C22semidirect
67. C2×#916C2×C3semidirect
68. C2×#908C2×C3semidirect
69. #5630C2×C3semidirect
70. #5599C2×C3semidirect
73. C3×#468D3semidirect
74. C3×#468C2×C3semidirect
84. #5176C2×C3semidirect
85. #5127C2×C3semidirect
86. #5047C2×C3semidirect
87. #5036C2×C3semidirect
88. #4889C2×C3semidirect
89. #4883C2×C3semidirect
90. #4810C2×C3semidirect
91. #4798C2×C3semidirect
92. #4786C2×C3semidirect
93. #4781C2×C3semidirect
154. C3×#204D4semidirect
162. C2×#237C22×C3semidirect
172. C2×C3×SD16C2×D3semidirect
173. C2×C3×SD16C22×C3semidirect
204. C2×#216C22×C3semidirect
205. C2×#215C22×C3semidirect
207. #940C22×C3semidirect
218. C2×D3×C8C22×C3semidirect
221. #895C22×C3semidirect
224. #887C22×C3semidirect
230. C3×#107C2×D3semidirect
231. C3×#107C22×C3semidirect
235. C3×#103C2×D3semidirect
236. C3×#103C22×C3semidirect
241. C3×#102C2×D3semidirect
242. C3×#102C22×C3semidirect
247. (C2×D3)⋊C8C22×C3semidirect
248. #815C22×C3semidirect
249. Dic3⋊C8C22×C3semidirect
250. #810C22×C3semidirect
253. #809C22×C3semidirect
311. #468C3×D3semidirect
456. #204C3×D4semidirect
498. C2×SD16C2×C3×D3semidirect
522. #107C2×C3×D3semidirect
525. #103C2×C3×D3semidirect
529. #102C2×C3×D3semidirect
797. C32#3268semidirect
904. C3#80836direct (N × H)
905. C3C3×#3268semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9162
C2×C3×#9082
C3×#56302
C3×#55992
C32×#4682
C3×#51762
C3×#51272
C3×#50472
C3×#50362
C3×#48892
C3×#48832
C3×#48102
C3×#47982
C3×#47862
C3×#47812
C3×#32683
#808363