Finite Group Databasebeta

← C3×#82236 #11803555

Subgroups — C3×#82236 #11803555

Order 1152.

1501 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5C3×#4990C212yesmaximal, complemented
6C3×#4989C212yesmaximal, complemented
7C3×#4957C212yesmaximal, complemented
8C3×#4956C212yesmaximal, complemented
9C3×#4939C211yesmaximal, characteristic, complemented
10C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
11C3×#4928C211yesmaximal, characteristic, complemented
12C3×#2324—31nomaximal
13#82236C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C32×#117—24no—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C3×#217C2212yes—
26C3×#930C418yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2212yes—
35C2×C3×C4×Dic3C2212yes—
36C3×C4×D12—24no—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×#121—31no—
41C2×C3×C4×D4—31no—
42C2×C3×#117—21no—
43C2×C3×#117D311yescharacteristic, complemented
44C2×C3×#117C2×C311yescharacteristic, complemented
45C2×#930C2×C311yescharacteristic
46C2×C4×D12C2×C311yescharacteristic, complemented
47C3×#390—32no—
48C3×#390—31no—
49C3×#389—31no—
50C3×#388—32no—
51C3×#386—32no—
52C3×#385—32no—
53C3×#380—31no—
54C3×C4×C4⋊C4—31no—
55#5212C2×C311yescharacteristic, complemented
56#4990C2×C312yescomplemented
57#4989C2×C312yescomplemented
58#4957C2×C312yescomplemented
59#4956C2×C312yescomplemented
60#4939C2×C311yescharacteristic, complemented
61C4×C4⋊Dic3C2×C311yescharacteristic, complemented
62#4928C2×C311yescharacteristic, complemented
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yescomplemented
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—42no—
75C2×C3×#67—42no—
76C2×C3×#67C2×C418yescomplemented
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×C3×D12—22no—
81C2×C3×D12—22no—
82C2×C3×D12C2×C414yes—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3—42no—
85C2×C3×C4×D3—42no—
86C32×C4⋊C4—22no—
87C32×C4⋊C4—22no—
88C32×C22⋊C4—22no—
89C32×C22⋊C4—22no—
90C32×C42—22no—
91C32×C42D414yescomplemented
92C3×#217—42no—
93C3×(C2×D3)⋊C4—24no—
94C3×(C2×D3)⋊C4—42no—
95C3×(C2×D3)⋊C4—42no—
96C3×(C2×D3)⋊C4C2×C418yescomplemented
97C3×C4⋊Dic3—22no—
98C3×C4⋊Dic3—22no—
99C3×C4⋊Dic3C2×C414yescomplemented
100C3×Dic3⋊C4—42no—
101C3×C4×Dic3—42no—
102#2324—31noSylow
103C22×C3×D4—32no—
104C22×C3×D4—31no—
105C23×C3×C4—21no—
106C23×C3×C4—32no—
107C23×C3×C4C2×D311yescharacteristic
108C23×C3×C4C22×C311yescharacteristic
109C22×#67C22×C312yes—
110C22×D12C22×C311yescharacteristic
111C22×C4×D3C22×C312yes—
112C3×#121—38no—
113C3×C4×D4—64no—
114C3×#117—28no—
115C3×#117—24no—
116C3×#117—24no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4C2×D311yescharacteristic
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C4⋊C4C22×C311yescharacteristic
126C2×C3×C4⋊C4C22×C311yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4C2×D311yescharacteristic
135C2×C3×C22⋊C4C2×D311yescharacteristic
136C2×C3×C22⋊C4C22×C311yescharacteristic
137C2×C3×C22⋊C4C22×C311yescharacteristic
138C2×C3×C42—21no—
139C2×C3×C42—21no—
140C2×C3×C42—32no—
141C2×C3×C42C2×D311yescharacteristic
142C2×C3×C42C2×D311yescharacteristic
143C2×C3×C42C22×C311yescharacteristic
144C2×C3×C42C22×C311yescharacteristic
145C2×#217C22×C312yes—
146#930C3×C418yescomplemented
147C2×(C2×D3)⋊C4C22×C312yes—
148C2×(C2×D3)⋊C4C22×C312yes—
149C2×(C2×D3)⋊C4C22×C312yes—
150C2×(C2×D3)⋊C4C22×C312yes—
151C2×C4⋊Dic3C22×C311yescharacteristic
152C2×C4⋊Dic3C22×C311yescharacteristic
153C2×C4⋊Dic3C22×C311yescharacteristic
154C2×Dic3⋊C4C22×C312yes—
155C2×C4×Dic3C22×C312yes—
156C4×D12—24no—
157C3×#95—32no—
158C3×#95—32no—
159C3×#95—32no—
160C3⋊#95C22×C312yes—
161C3⋊#95C22×C312yes—
162C3⋊#95C22×C312yes—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32C22×C412yes—
170C23×C32C2411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3C22×C414yes—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—28no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C22×C412yes—
193C2×C32×C4C2×D412yes—
194C2×C32×C4C2×D412yes—
195C2×C32×C4C2×D412yes—
196C2×C32×C4#4112yes—
197C3×#67—48no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3C22×C414yes—
207C3×D12—28no—
208C3×C4×D3—48no—
209C2×#121—31no—
210C2×C4×D4—31no—
211C2×#117C3×D311yescharacteristic, complemented
212#390—32no—
213#390—31no—
214#389—31no—
215#388—32no—
216#386—32no—
217#385—32no—
218#380—31no—
219C4×C4⋊C4—31no—
220C24×C3—21no—
221C24×C3—32no—
222C24×C3C22×D311yescharacteristic
223C24×C3C23×C311yescharacteristic
224C23×D3C23×C312yes—
225C2×C3×D4—38no—
226C2×C3×D4—34no—
227C2×C3×D4—62no—
228C2×C3×D4—62no—
229C2×C3×D4—122no—
230C2×C3×D4—122no—
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—24no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—32no—
247C22×C3×C4—64no—
248C22×C3×C4—122no—
249C22×C3×C4—122no—
250C22×C3×C4C4×D314yescomplemented
251C22×C3×C4C2×C3×C414yescomplemented
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C23×C311yescharacteristic
259C22×C3×C4C23×C311yescharacteristic
260C22×C3×C4C23×C311yescharacteristic
261C22×C3×C4C23×C311yescharacteristic
262C22×C3×C4C23×C311yescharacteristic
263C22×C3×C4C23×C311yescharacteristic
264C2×#67—42no—
265C2×#67—42no—
266C2×#67C2×C3×C418yescomplemented
267C22×Dic3C23×C312yes—
268C22×Dic3C23×C312yes—
269C22×Dic3C23×C312yes—
270C2×D12—22no—
271C2×D12—22no—
272C2×D12C2×C3×C414yes—
273C2×C4×D3—24no—
274C2×C4×D3—42no—
275C2×C4×D3—42no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—22no—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—34no—
283C3×C4⋊C4—62no—
284C3×C4⋊C4—62no—
285C3×C4⋊C4—122no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—22no—
290C3×C22⋊C4—22no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—38no—
293C3×C22⋊C4—64no—
294C3×C22⋊C4—122no—
295C3×C22⋊C4—122no—
296C3×C22⋊C4—122no—
297C3×C42—24no—
298C3×C42—22no—
299C3×C42—22no—
300C3×C42—24no—
301C3×C42—122no—
302C3×C42#6714yescomplemented
303C3×C42C3×D414yescomplemented
304#217—42no—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4C2×C3×C418yescomplemented
309C4⋊Dic3—22no—
310C4⋊Dic3—22no—
311C4⋊Dic3C2×C3×C414yescomplemented
312Dic3⋊C4—42no—
313C4×Dic3—42no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—41no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32C23×C411yescharacteristic
322C22×C32C22×D411yescharacteristic
323C22×C32C2×#4111yescharacteristic
324C22×C32H(5,𝔽2)11yescharacteristic
325C22×C32H(5,𝔽2)11yescharacteristic
326C22×C32H(5,𝔽2)11yescharacteristic
327C22×C322−1+411yescharacteristic
328C2×C3×D3—24no—
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—42no—
332C2×C3×D3—42no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C32×C4—22no—
336C32×C4—22no—
337C32×C4—22no—
338C32×C4—41no—
339C32×C4—41no—
340C32×C4C4×D414yes—
341C3×Dic3—24no—
342C3×Dic3—42no—
343C3×Dic3—42no—
344C22×D4—32no—
345C22×D4—31no—
346C23×C4—32no—
347C23×C4C2×C3×D311yescharacteristic
348#121—38no—
349C4×D4—64no—
350#117—24no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4C2×C3×D311yescharacteristic
356C2×C4⋊C4C2×C3×D311yescharacteristic
357C2×C22⋊C4—32no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—32no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4C2×C3×D311yescharacteristic
363C2×C22⋊C4C2×C3×D311yescharacteristic
364C2×C42—32no—
365C2×C42C2×C3×D311yescharacteristic
366C2×C42C2×C3×D311yescharacteristic
367#95—32no—
368#95—32no—
369#95—32no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—34no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3C2×C4×D312yes—
398C23×C3C22×C3×C412yes—
399C23×C3C23×D311yescharacteristic
400C23×C3C24×C311yescharacteristic
401C22×D3—22no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—22no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3C22×C3×C414yes—
408C3×D4—68no—
409C3×D4—128no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—216no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—28no—
426C2×C3×C4—28no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—34no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4—62no—
462C2×C3×C4—62no—
463C2×C3×C4—62no—
464C2×C3×C4—128no—
465C2×C3×C4C2×C4×D312yes—
466C2×C3×C4C2×C4×D312yes—
467C2×C3×C4#23512yes—
468C2×C3×C4C2×#6712yes—
469C2×C3×C4C2×#6712yes—
470C2×C3×C4C2×#6712yes—
471C2×C3×C4C22×C3×C412yes—
472C2×C3×C4C22×C3×C412yes—
473C2×C3×C4C2×C3×D412yes—
474C2×C3×C4C2×C3×D412yes—
475C2×C3×C4C2×C3×D412yes—
476C2×C3×C4C3×#4112yes—
477#67—48no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3C22×C3×C414yes—
487D12—28no—
488C4×D3—48no—
489C2×C32—42no—
490C2×C32C2×C4×D411yescharacteristic
491C2×C32#51811yescharacteristic
492C2×C32#52011yescharacteristic
493C2×C32#53511yescharacteristic
494C2×C32#53711yescharacteristic
495C2×C32#54011yescharacteristic
496C2×C32#54211yescharacteristic
497C3×D3—44no—
498C24—32no—
499C24C22×C3×D311yescharacteristic
500C2×D4—38no—
501C2×D4—34no—
502C2×D4—62no—
503C2×D4—62no—
504C2×D4—122no—
505C2×D4—122no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—32no—
509C22×C4—32no—
510C22×C4—32no—
511C22×C4—64no—
512C22×C4—122no—
513C22×C4—122no—
514C22×C4C3×C4×D314yescomplemented
515C22×C4C22×C3×D311yescharacteristic
516C22×C4C22×C3×D311yescharacteristic
517C22×C4C22×C3×D311yescharacteristic
518C22×C4C22×C3×D311yescharacteristic
519C22×C4C22×C3×D311yescharacteristic
520C22×C4C22×C3×D311yescharacteristic
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—34no—
524C4⋊C4—62no—
525C4⋊C4—62no—
526C4⋊C4—122no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—38no—
530C22⋊C4—64no—
531C22⋊C4—122no—
532C22⋊C4—122no—
533C22⋊C4—122no—
534C42—22no—
535C42—122no—
536C42C3×#6714yescomplemented
537C22×C3—24no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—64no—
566C22×C3—64no—
567C22×C3—64no—
568C22×C3—122no—
569C22×C3—122no—
570C22×C3—122no—
571C22×C3—122no—
572C22×C3C22×C4×D311yescharacteristic
573C22×C3C2×#23511yescharacteristic
574C22×C3#100911yescharacteristic
575C22×C3#100911yescharacteristic
576C22×C3#100911yescharacteristic
577C22×C3#101011yescharacteristic
578C22×C3C22×#6711yescharacteristic
579C22×C3C23×C3×C411yescharacteristic
580C22×C3C22×C3×D411yescharacteristic
581C22×C3C2×C3×#4111yescharacteristic
582C22×C3C3×H(5,𝔽2)11yescharacteristic
583C22×C3C3×H(5,𝔽2)11yescharacteristic
584C22×C3C3×H(5,𝔽2)11yescharacteristic
585C22×C3C3×2−1+411yescharacteristic
586C2×D3—24no—
587C2×D3—24no—
588C2×D3—24no—
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—42no—
593C3×C4—24no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—22no—
600C3×C4—24no—
601C3×C4—42no—
602C3×C4—42no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—64no—
610C3×C4—122no—
611C3×C4—122no—
612C3×C4C4×#6714yes—
613C3×C4C3×C4×D414yes—
614Dic3—24no—
615Dic3—42no—
616Dic3—42no—
617C32#232411yescharacteristic, complemented, Sylow
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—34no—
625C23—62no—
626C23—62no—
627C23—62no—
628C23—62no—
629C23—62no—
630C23—62no—
631C23C2×C3×C4×D312yes—
632C23C23×C3×D311yescharacteristic
633D4—68no—
634D4—128no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—28no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—34no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—62no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—128no—
658C2×C4C2×C3×C4×D312yes—
659C2×C4C2×C3×C4×D312yes—
660C2×C4C3×#23512yes—
661C2×C4C2×C3×#6712yes—
662C2×C4C2×C3×#6712yes—
663C2×C4C2×C3×#6712yes—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—44no—
672C2×C3—42no—
673C2×C3—42no—
674C2×C3—124no—
675C2×C3#552111yescharacteristic
676C2×C3#552311yescharacteristic
677C2×C3#553411yescharacteristic
678C2×C3#553511yescharacteristic
679C2×C3C2×C4×#6711yescharacteristic
680C2×C3#583011yescharacteristic
681C2×C3#583311yescharacteristic
682C2×C3C2×C3×C4×D411yescharacteristic
683C2×C3C3×#51811yescharacteristic
684C2×C3C3×#52011yescharacteristic
685C2×C3C3×#53511yescharacteristic
686C2×C3C3×#53711yescharacteristic
687C2×C3C3×#54011yescharacteristic
688C2×C3C3×#54211yescharacteristic
689D3—44no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—64no—
698C22—64no—
699C22—64no—
700C22—122no—
701C22—122no—
702C22—122no—
703C22—122no—
704C22C22×C3×C4×D311yescharacteristic
705C22C2×C3×#23511yescharacteristic
706C22C3×#100911yescharacteristic
707C22C3×#100911yescharacteristic
708C22C3×#100911yescharacteristic
709C22C3×#101011yescharacteristic
710C22C22×C3×#6711yescharacteristic
711C4—22no—
712C4—22no—
713C4—22no—
714C4—41no—
715C4—41no—
716C4—64no—
717C4—122no—
718C4—122no—
719C4C3×C4×#6714yes—
720C3—21no—
721C3#8223611yescharacteristic, direct product factor
722C3C3×#232411yescharacteristic, complemented
723C2—42no—
724C2—124no—
725C2C3×#552111yescharacteristic
726C2C3×#552311yescharacteristic
727C2C3×#553411yescharacteristic
728C2C3×#553511yescharacteristic
729C2C2×C3×C4×#6711yescharacteristic
730C2C3×#583011yescharacteristic
731C2C3×#583311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#117C2
socleC23×C32C24
prime radicalC2×C3×#930C2
cosocleC23×C3C24×C3
hypercenterC2×C3×#117D3
hypocenterC3C3×#2324
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C32×#117C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C3×#5212C2semidirect
5. C3×#4990C2semidirect
6. C3×#4989C2semidirect
7. C3×#4957C2semidirect
8. C3×#4956C2semidirect
9. C3×#4939C2semidirect
10. C3×C4×C4⋊Dic3C2semidirect
11. C3×#4928C2semidirect
13. #82236C3direct (N × H)
26. C3×#930C4semidirect
43. C2×C3×#117D3semidirect
44. C2×C3×#117C2×C3semidirect
46. C2×C4×D12C2×C3semidirect
55. #5212C2×C3semidirect
56. #4990C2×C3semidirect
57. #4989C2×C3semidirect
58. #4957C2×C3semidirect
59. #4956C2×C3semidirect
60. #4939C2×C3semidirect
61. C4×C4⋊Dic3C2×C3semidirect
62. #4928C2×C3semidirect
67. C22×C32×C4C2×C4semidirect
76. C2×C3×#67C2×C4semidirect
91. C32×C42D4semidirect
96. C3×(C2×D3)⋊C4C2×C4semidirect
99. C3×C4⋊Dic3C2×C4semidirect
146. #930C3×C4semidirect
211. C2×#117C3×D3semidirect
250. C22×C3×C4C4×D3semidirect
251. C22×C3×C4C2×C3×C4semidirect
266. C2×#67C2×C3×C4semidirect
302. C3×C42#67semidirect
303. C3×C42C3×D4semidirect
308. (C2×D3)⋊C4C2×C3×C4semidirect
311. C4⋊Dic3C2×C3×C4semidirect
514. C22×C4C3×C4×D3semidirect
536. C42C3×#67semidirect
617. C32#2324semidirect
721. C3#82236direct (N × H)
722. C3C3×#2324semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C2×C3×#9302
C2×C3×C4×D122
C3×#52122
C3×#49902
C3×#49892
C3×#49572
C3×#49562
C3×#49392
C3×C4×C4⋊Dic32
C3×#49282
C3×#23243
#822363