Finite Group Databasebeta

← C3×#80168 #11885785

Subgroups — C3×#80168 #11885785

Order 1152.

1146 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×C3×#916C211yesmaximal, characteristic, complemented
4C3×#5630C211yesmaximal, characteristic, complemented
5C32×#450C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7C3×#5168C211yesmaximal, characteristic, complemented
8C3×#5165C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#4787C211yesmaximal, characteristic, complemented
11C3×#4781C211yesmaximal, characteristic, complemented
12C3×#4775C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4731C211yesmaximal, characteristic, complemented
15C3×#67⋊C8C211yesmaximal, characteristic, complemented
16C3×#3280—31nomaximal
17#80168C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23C2×C32×SD16C2211yescharacteristic, complemented
24C32×C22⋊Q8C2211yescharacteristic
25C3×#953—21no—
26C2×C3×#217—21no—
27C3×#947C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C3×#939—21no—
30C3×#938C2211yescharacteristic, complemented
31C3×#936C2211yescharacteristic, complemented
32C3×#935—21no—
33C3×D4×Dic3C2211yescharacteristic, complemented
34C2×C3×#213—24no—
35C2×C3×#213C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C2×C3×#213C2211yescharacteristic
38C2×C3×#213C2211yescharacteristic
39C3×C4×#67C2211yescharacteristic
40C3×#924C2211yescharacteristic
41C22×C3×C3⋊C8C2211yescharacteristic
42C3×#916—24no—
43C2×C3×#204C2211yescharacteristic, complemented
44C2×C3×#204C2211yescharacteristic, complemented
45C2×C3×D3×C8C2211yescharacteristic, complemented
46C3×#895—21no—
47C3×#895C2211yescharacteristic, complemented
48C3×#894—21no—
49C3×#893C2211yescharacteristic, complemented
50C3×#882—21no—
51C3×D3×C22⋊C4—21no—
52C32×#102C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C32×C22⋊C8C2211yescharacteristic
55C3×#835C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60C3×C8×Dic3C2211yescharacteristic, complemented
61C3×#810C2211yescharacteristic, complemented
62C3×#807C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64C22×C3×D8—31no—
65C3×#546—31no—
66C3×#546—31no—
67#5806C2×C311yescharacteristic, complemented
68C22×#213C2×C311yescharacteristic, complemented
69C2×#916C2×C311yescharacteristic, complemented
70#5630C2×C311yescharacteristic, complemented
71C3×#495—31no—
72C3×#467—31no—
73C3×#466—31no—
74C3×#463—31no—
75C3×#463—31no—
76C3×#450—21no—
77C3×#450—31no—
78C3×#450D311yescharacteristic, complemented
79C3×#450C2×C311yescharacteristic, complemented
80C3×#449—31no—
81C3×#449—31no—
82C3×C4×D8—31no—
83C3×C8×D4—31no—
84#5172C2×C311yescharacteristic, complemented
85#5168C2×C311yescharacteristic, complemented
86#5165C2×C311yescharacteristic, complemented
87#5051C2×C311yescharacteristic, complemented
88#4787C2×C311yescharacteristic, complemented
89#4781C2×C311yescharacteristic, complemented
90#4775C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic, complemented
92#4731C2×C311yescharacteristic, complemented
93#67⋊C8C2×C311yescharacteristic, complemented
94C24×C32—21no—
95C23×C3×D3—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4—22no—
98C2×C32×D4—21no—
99C2×C32×D4—41no—
100C2×C32×D4C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C3×#239—22no—
109C3×#239—41no—
110C3×#237—22no—
111C3×#237—41no—
112C2×C3×D12—22no—
113C2×C3×D12—21no—
114C2×C3×D12—21no—
115C2×C3×D12—21no—
116C2×C3×D12—41no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123C32×SD16—22no—
124C32×SD16—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4—21no—
128C32×C4⋊C4C2311yescharacteristic
129C32×C22⋊C4—21no—
130C3×#217—21no—
131C3×#217—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×#217—21no—
135C3×#217D411yescharacteristic
136C3×#216—22no—
137C3×#213—22no—
138C3×#213—22no—
139C3×#213—22no—
140C3×#213D414yescomplemented
141C3×(C2×D3)⋊C4—21no—
142C3×(C2×D3)⋊C4—21no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4D411yescharacteristic
146C3×C4⋊Dic3C2311yescharacteristic
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4D411yescharacteristic
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8—22no—
151C2×C3×C3⋊C8C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×#204—22no—
154C3×#204—41no—
155C3×D3×C8—22no—
156#3280—31noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—21no—
160C22×C3×D4—31no—
161C22×C3×D4C2×D311yescharacteristic
162C22×C3×D4C22×C311yescharacteristic
163C2×#239C22×C311yescharacteristic, complemented
164C2×#237C22×C311yescharacteristic, complemented
165C22×D12C22×C311yescharacteristic
166C3×#135—64no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—21no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16C2×D311yescharacteristic, complemented
173C2×C3×SD16C2×D311yescharacteristic, complemented
174C2×C3×SD16C22×C311yescharacteristic, complemented
175C2×C3×SD16C22×C311yescharacteristic, complemented
176C2×C3×D8—31no—
177C2×C3×D8—31no—
178C2×C3×D8—31no—
179C2×C3×D8—31no—
180C2×C3×D8—64no—
181C22×C3×C8—31no—
182C22×C3×C8—31no—
183C3×#124—31no—
184C3×#124—31no—
185C3×#123—61no—
186C3×#123—61no—
187C3×C22⋊Q8—21no—
188C3×C22⋊Q8—31no—
189C3×C22⋊Q8C2×D311yescharacteristic
190C3×C22⋊Q8C22×C311yescharacteristic
191C3×#121—31no—
192C3×#121—31no—
193C3×#121—61no—
194C3×#121—61no—
195C3×#120—61no—
196C3×#120—61no—
197C3×C4×D4—31no—
198C3×C4×D4—31no—
199C3×C4×D4—31no—
200C2×C3×C22⋊C4—61no—
201C2×C3×C22⋊C4—61no—
202#953—21no—
203C2×#217—21no—
204#947C22×C311yescharacteristic, complemented
205C2×#216C22×C311yescharacteristic, complemented
206#939—21no—
207#938C22×C311yescharacteristic, complemented
208#936C22×C311yescharacteristic, complemented
209#935—21no—
210D4×Dic3C22×C311yescharacteristic, complemented
211C2×#213—24no—
212C2×#213C22×C311yescharacteristic
213C2×#213C22×C311yescharacteristic
214C2×#213C22×C311yescharacteristic
215C2×#213C22×C311yescharacteristic
216C4×#67C22×C311yescharacteristic
217#924C22×C311yescharacteristic
218C22×C3⋊C8C22×C311yescharacteristic
219#916—24no—
220C2×#204C22×C311yescharacteristic, complemented
221C2×#204C22×C311yescharacteristic, complemented
222C2×D3×C8C22×C311yescharacteristic, complemented
223#895—21no—
224#895C22×C311yescharacteristic, complemented
225#894—21no—
226#893C22×C311yescharacteristic, complemented
227#882—21no—
228D3×C22⋊C4—21no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#102—21no—
234C3×#102—21no—
235C3×#102—31no—
236C3×#102—31no—
237C3×#102C2×D311yescharacteristic, complemented
238C3×#102C2×D311yescharacteristic, complemented
239C3×#102C22×C311yescharacteristic, complemented
240C3×#102C22×C311yescharacteristic, complemented
241C3×C22⋊C8—21no—
242C3×C22⋊C8—31no—
243C3×C22⋊C8C2×D311yescharacteristic
244C3×C22⋊C8C22×C311yescharacteristic
245C3×C4×C8—31no—
246#835C22×C311yescharacteristic, complemented
247#821C22×C311yescharacteristic, complemented
248#821C22×C311yescharacteristic, complemented
249(C2×D3)⋊C8C22×C311yescharacteristic, complemented
250Dic3⋊C8C22×C311yescharacteristic, complemented
251C8×Dic3C22×C311yescharacteristic, complemented
252#810C22×C311yescharacteristic, complemented
253#807C22×C311yescharacteristic, complemented
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—42no—
257C23×C32—42no—
258C23×C32—81no—
259C23×C32C2×D411yescharacteristic
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—42no—
263C22×C3×D3—42no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C32×Q8—21no—
267C32×Q8—21no—
268C32×D4—21no—
269C32×D4—21no—
270C32×D4—21no—
271C32×D4—42no—
272C32×D4C2×D412yes—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279C3×#67—22no—
280C3×#67—42no—
281C3×#67—81no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3—81no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×D12—21no—
292C3×D12—42no—
293C3×D12—42no—
294C3×D12—81no—
295C3×D12C2×D412yes—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298C3×C4×D3—42no—
299C3×C4×D3—81no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302C32×C8—21no—
303C32×C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#135—31no—
307C22×D8—31no—
308#546—31no—
309#546—31no—
310#495—31no—
311#467—31no—
312#466—31no—
313#463—31no—
314#463—31no—
315#450—31no—
316#450C3×D311yescharacteristic, complemented
317#449—31no—
318#449—31no—
319C4×D8—31no—
320C8×D4—31no—
321C24×C3—21no—
322C24×C3—21no—
323C24×C3—41no—
324C24×C3—61no—
325C23×D3—21no—
326C3×#41—62no—
327C3×#41—62no—
328C3×#41—121no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×Q8C23×C311yescharacteristic
334C2×C3×D4—22no—
335C2×C3×D4—22no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—21no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—41no—
344C2×C3×D4—42no—
345C2×C3×D4—41no—
346C2×C3×D4—41no—
347C2×C3×D4—42no—
348C2×C3×D4—62no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—61no—
352C2×C3×D4—61no—
353C2×C3×D4—61no—
354C2×C3×D4—121no—
355C2×C3×D4C22×D311yescharacteristic
356C2×C3×D4C22×D311yescharacteristic
357C2×C3×D4C23×C311yescharacteristic
358C2×C3×D4C23×C311yescharacteristic
359C22×C3×C4—21no—
360C22×C3×C4—31no—
361C22×C3×C4—61no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C22×C3×C4—61no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C23×C311yescharacteristic
367C2×#67—21no—
368C2×#67—21no—
369C2×#67C3×D411yescharacteristic
370C22×Dic3—21no—
371C22×Dic3—21no—
372#239—22no—
373#239—41no—
374#237—22no—
375#237—41no—
376C2×D12—22no—
377C2×D12—21no—
378C2×D12—21no—
379C2×D12—21no—
380C2×D12—41no—
381C2×D12C23×C311yescharacteristic
382C2×D12C23×C311yescharacteristic
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—42no—
391C3×SD16—41no—
392C3×SD16—41no—
393C3×SD16—42no—
394C3×SD16—62no—
395C3×SD16—121no—
396C3×D8—34no—
397C3×D8—62no—
398C3×D8—62no—
399C3×D8—62no—
400C2×C3×C8—21no—
401C2×C3×C8—21no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8—62no—
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—31no—
414C3×C4⋊C4—31no—
415C3×C4⋊C4—41no—
416C3×C4⋊C4—61no—
417C3×C4⋊C4C22×D311yescharacteristic
418C3×C4⋊C4C23×C311yescharacteristic
419C3×C22⋊C4—21no—
420C3×C22⋊C4—21no—
421C3×C22⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—41no—
424C3×C22⋊C4—61no—
425C3×C22⋊C4—61no—
426C3×C22⋊C4—61no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C22⋊C4—61no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C42—31no—
434#217—21no—
435#217—21no—
436#217—21no—
437#217—21no—
438#217—21no—
439#217C3×D411yescharacteristic
440#216—22no—
441#213—22no—
442#213—22no—
443#213—22no—
444#213C3×D414yescomplemented
445(C2×D3)⋊C4—21no—
446(C2×D3)⋊C4—21no—
447(C2×D3)⋊C4—21no—
448(C2×D3)⋊C4—21no—
449(C2×D3)⋊C4C3×D411yescharacteristic
450C4⋊Dic3C23×C311yescharacteristic
451Dic3⋊C4—21no—
452Dic3⋊C4C3×D411yescharacteristic
453C4×Dic3C23×C311yescharacteristic
454C2×C3⋊C8—22no—
455C2×C3⋊C8C23×C311yescharacteristic
456C2×C3⋊C8C23×C311yescharacteristic
457#204—22no—
458#204—41no—
459D3×C8—22no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—84no—
469C22×C32#13512yescomplemented
470C22×C32C22×D411yescharacteristic
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—84no—
481C32×C4—21no—
482C32×C4—41no—
483C32×C4—41no—
484C32×C4C22×D411yescharacteristic
485C32×C4H(5,𝔽2)11yescharacteristic
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—31no—
493C22×D4—31no—
494C22×D4C2×C3×D311yescharacteristic
495#135—64no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16C2×C3×D311yescharacteristic, complemented
500C2×SD16C2×C3×D311yescharacteristic, complemented
501C2×D8—31no—
502C2×D8—31no—
503C2×D8—31no—
504C2×D8—31no—
505C2×D8—64no—
506C22×C8—31no—
507C22×C8—31no—
508#124—31no—
509#124—31no—
510#123—61no—
511#123—61no—
512C22⋊Q8—31no—
513C22⋊Q8C2×C3×D311yescharacteristic
514#121—31no—
515#121—31no—
516#121—61no—
517#121—61no—
518#120—61no—
519#120—61no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—31no—
523C2×C22⋊C4—61no—
524C2×C22⋊C4—61no—
525#107—31no—
526C4⋊C8—31no—
527#103—31no—
528#103—31no—
529#102—31no—
530#102—31no—
531#102C2×C3×D311yescharacteristic, complemented
532#102C2×C3×D311yescharacteristic, complemented
533C22⋊C8—31no—
534C22⋊C8C2×C3×D311yescharacteristic
535C4×C8—31no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—42no—
545C23×C3—42no—
546C23×C3—44no—
547C23×C3—42no—
548C23×C3—42no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—82no—
552C23×C3—81no—
553C23×C3—81no—
554C23×C3—82no—
555C23×C3—122no—
556C23×C3—122no—
557C23×C3—241no—
558C23×C3D3×D411yescharacteristic
559C23×C3C2×C3×D411yescharacteristic
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—42no—
563C22×D3—42no—
564C22×D3—81no—
565C22×D3C2×C3×D411yescharacteristic
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—61no—
574C3×D4—22no—
575C3×D4—21no—
576C3×D4—21no—
577C3×D4—21no—
578C3×D4—21no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—22no—
582C3×D4—32no—
583C3×D4—41no—
584C3×D4—41no—
585C3×D4—42no—
586C3×D4—42no—
587C3×D4—44no—
588C3×D4—62no—
589C3×D4—61no—
590C3×D4—61no—
591C3×D4—61no—
592C3×D4—122no—
593C3×D4—122no—
594C3×D4—122no—
595C3×D4—241no—
596C3×D4—241no—
597C3×D4D3×D412yes—
598C3×D4C2×C3×D412yes—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—31no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—122no—
621C2×C3×C4—122no—
622C2×C3×C4—241no—
623C2×C3×C4—241no—
624C2×C3×C4D3×D411yescharacteristic
625C2×C3×C4C2×C3×D411yescharacteristic
626C2×C3×C4C23×D311yescharacteristic
627C2×C3×C4C24×C311yescharacteristic
628#67—22no—
629#67—42no—
630#67—81no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—42no—
634C2×Dic3—81no—
635C2×Dic3C2×C3×D411yescharacteristic
636C2×Dic3C2×C3×D411yescharacteristic
637C2×Dic3C2×C3×D411yescharacteristic
638D12—21no—
639D12—21no—
640D12—21no—
641D12—42no—
642D12—42no—
643D12—81no—
644D12C2×C3×D412yes—
645C4×D3—21no—
646C4×D3—21no—
647C4×D3—42no—
648C4×D3—81no—
649Dic6—21no—
650Dic6—21no—
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—32no—
656C3×C8—41no—
657C3×C8—41no—
658C3×C8—61no—
659C3⋊C8—21no—
660C3⋊C8C2×C3×D412yes—
661C2×C32—22no—
662C2×C32—42no—
663C2×C32—81no—
664C2×C32D4211yescharacteristic
665C2×C32C2×#13511yescharacteristic
666C2×C32#57611yescharacteristic
667C3×D3—41no—
668C3×D3—42no—
669C3×D3—81no—
670C24—21no—
671C24—61no—
672#41—62no—
673#41—62no—
674#41—121no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8C22×C3×D311yescharacteristic
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—41no—
684C2×D4—62no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—121no—
691C2×D4C22×C3×D311yescharacteristic
692C2×D4C22×C3×D311yescharacteristic
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4C22×C3×D311yescharacteristic
699Q16—62no—
700SD16—22no—
701SD16—41no—
702SD16—62no—
703SD16—121no—
704D8—34no—
705D8—62no—
706D8—62no—
707D8—62no—
708C2×C8—31no—
709C2×C8—31no—
710C2×C8—62no—
711C2×C8—62no—
712C2×C8C22×C3×D311yescharacteristic
713C2×C8C22×C3×D311yescharacteristic
714C4⋊C4—21no—
715C4⋊C4—31no—
716C4⋊C4—31no—
717C4⋊C4—61no—
718C4⋊C4C22×C3×D311yescharacteristic
719C22⋊C4—21no—
720C22⋊C4—31no—
721C22⋊C4—31no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—61no—
731C42—31no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—21no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—61no—
755C22×C3—61no—
756C22×C3—61no—
757C22×C3—62no—
758C22×C3—81no—
759C22×C3—81no—
760C22×C3—81no—
761C22×C3—81no—
762C22×C3—84no—
763C22×C3—84no—
764C22×C3—88no—
765C22×C3—121no—
766C22×C3—121no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—244no—
771C22×C3#91612yescomplemented
772C22×C3C3×#13512yescomplemented
773C22×C3C2×D3×D411yescharacteristic
774C22×C3C22×C3×D411yescharacteristic
775C2×D3—21no—
776C2×D3—21no—
777C2×D3—21no—
778C2×D3—22no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—84no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—81no—
798C3×C4—81no—
799C3×C4—121no—
800C3×C4—121no—
801C3×C4C2×D3×D411yescharacteristic
802C3×C4#100411yescharacteristic
803C3×C4C22×C3×D411yescharacteristic
804C3×C4C3×H(5,𝔽2)11yescharacteristic
805Dic3—21no—
806Dic3—21no—
807Dic3—21no—
808Dic3—41no—
809Dic3—41no—
810C32#328011yescharacteristic, complemented, Sylow
811C23—21no—
812C23—21no—
813C23—31no—
814C23—42no—
815C23—42no—
816C23—61no—
817C23—61no—
818C23—81no—
819C23—122no—
820C23—122no—
821C23—241no—
822C23C3×D3×D411yescharacteristic
823Q8—21no—
824Q8—21no—
825Q8—61no—
826Q8—61no—
827D4—21no—
828D4—21no—
829D4—21no—
830D4—32no—
831D4—42no—
832D4—62no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—122no—
837D4—122no—
838D4—122no—
839D4—241no—
840D4—241no—
841D4C3×D3×D412yes—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—122no—
854C2×C4—122no—
855C2×C4—241no—
856C2×C4—241no—
857C2×C4C3×D3×D411yescharacteristic
858C2×C4C23×C3×D311yescharacteristic
859C8—21no—
860C8—21no—
861C8—32no—
862C8—61no—
863C2×C3—22no—
864C2×C3—22no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—42no—
869C2×C3—42no—
870C2×C3—42no—
871C2×C3—82no—
872C2×C3—82no—
873C2×C3—81no—
874C2×C3—81no—
875C2×C3—121no—
876C2×C3—122no—
877C2×C3—241no—
878C2×C3#559011yescharacteristic
879C2×C3C2×#91611yescharacteristic
880C2×C3#577411yescharacteristic
881C2×C3C3×D4211yescharacteristic
882C2×C3C2×C3×#13511yescharacteristic
883C2×C3C3×#57611yescharacteristic
884D3—41no—
885D3—42no—
886D3—81no—
887C22—21no—
888C22—21no—
889C22—22no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—61no—
896C22—61no—
897C22—61no—
898C22—62no—
899C22—84no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—244no—
906C22C3×#91612yescomplemented
907C22C2×C3×D3×D411yescharacteristic
908C4—21no—
909C4—41no—
910C4—41no—
911C4—61no—
912C4—61no—
913C4—61no—
914C4—121no—
915C4—121no—
916C4C2×C3×D3×D411yescharacteristic
917C4C3×#100411yescharacteristic
918C3—21no—
919C3#8016811yescharacteristic, direct product factor
920C3C3×#328011yescharacteristic, complemented
921C2—22no—
922C2—42no—
923C2—81no—
924C2—121no—
925C2—122no—
926C2—241no—
927C2C3×#559011yescharacteristic
928C2C2×C3×#91611yescharacteristic
929C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
hypercenterC3×#450D3
hypocenterC3C3×#3280
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C3×#5806C2semidirect
2. C22×C3×#213C2semidirect
3. C2×C3×#916C2semidirect
4. C3×#5630C2semidirect
5. C32×#450C2semidirect
6. C3×#5172C2semidirect
7. C3×#5168C2semidirect
8. C3×#5165C2semidirect
9. C3×#5051C2semidirect
10. C3×#4787C2semidirect
11. C3×#4781C2semidirect
12. C3×#4775C2semidirect
13. C3×#4756C2semidirect
14. C3×#4731C2semidirect
15. C3×#67⋊C8C2semidirect
17. #80168C3direct (N × H)
19. C2×C3×#239C22semidirect
20. C2×C3×#237C22semidirect
22. C2×C32×SD16C22semidirect
23. C2×C32×SD16C22semidirect
27. C3×#947C22semidirect
28. C2×C3×#216C22semidirect
30. C3×#938C22semidirect
31. C3×#936C22semidirect
33. C3×D4×Dic3C22semidirect
43. C2×C3×#204C22semidirect
44. C2×C3×#204C22semidirect
45. C2×C3×D3×C8C22semidirect
47. C3×#895C22semidirect
49. C3×#893C22semidirect
52. C32×#102C22semidirect
53. C32×#102C22semidirect
55. C3×#835C22semidirect
56. C3×#821C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. C3×C8×Dic3C22semidirect
61. C3×#810C22semidirect
62. C3×#807C22semidirect
67. #5806C2×C3semidirect
68. C22×#213C2×C3semidirect
69. C2×#916C2×C3semidirect
70. #5630C2×C3semidirect
78. C3×#450D3semidirect
79. C3×#450C2×C3semidirect
84. #5172C2×C3semidirect
85. #5168C2×C3semidirect
86. #5165C2×C3semidirect
87. #5051C2×C3semidirect
88. #4787C2×C3semidirect
89. #4781C2×C3semidirect
90. #4775C2×C3semidirect
91. #4756C2×C3semidirect
92. #4731C2×C3semidirect
93. #67⋊C8C2×C3semidirect
140. C3×#213D4semidirect
163. C2×#239C22×C3semidirect
164. C2×#237C22×C3semidirect
172. C2×C3×SD16C2×D3semidirect
173. C2×C3×SD16C2×D3semidirect
174. C2×C3×SD16C22×C3semidirect
175. C2×C3×SD16C22×C3semidirect
204. #947C22×C3semidirect
205. C2×#216C22×C3semidirect
207. #938C22×C3semidirect
208. #936C22×C3semidirect
210. D4×Dic3C22×C3semidirect
220. C2×#204C22×C3semidirect
221. C2×#204C22×C3semidirect
222. C2×D3×C8C22×C3semidirect
224. #895C22×C3semidirect
226. #893C22×C3semidirect
237. C3×#102C2×D3semidirect
238. C3×#102C2×D3semidirect
239. C3×#102C22×C3semidirect
240. C3×#102C22×C3semidirect
246. #835C22×C3semidirect
247. #821C22×C3semidirect
248. #821C22×C3semidirect
249. (C2×D3)⋊C8C22×C3semidirect
250. Dic3⋊C8C22×C3semidirect
251. C8×Dic3C22×C3semidirect
252. #810C22×C3semidirect
253. #807C22×C3semidirect
316. #450C3×D3semidirect
444. #213C3×D4semidirect
469. C22×C32#135semidirect
499. C2×SD16C2×C3×D3semidirect
500. C2×SD16C2×C3×D3semidirect
531. #102C2×C3×D3semidirect
532. #102C2×C3×D3semidirect
771. C22×C3#916semidirect
772. C22×C3C3×#135semidirect
810. C32#3280semidirect
906. C22C3×#916semidirect
919. C3#80168direct (N × H)
920. C3C3×#3280semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C22×C3×#2132
C2×C3×#9162
C3×#56302
C32×#4502
C3×#51722
C3×#51682
C3×#51652
C3×#50512
C3×#47872
C3×#47812
C3×#47752
C3×#47562
C3×#47312
C3×#67⋊C82
C3×#32803
#801683