Finite Group Databasebeta

← C3×#82097 #11804963

Subgroups — C3×#82097 #11804963

Order 1152.

1921 conjugacy classes of subgroups.

The subgroup lattice has 741 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C22⋊C4C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C3×#5247C211yesmaximal, characteristic
5C3×#5212C211yesmaximal, characteristic, complemented
6C3×#5211C211yesmaximal, characteristic, complemented
7C3×C4×#217C211yesmaximal, characteristic, complemented
8C3×#4951C212yesmaximal, complemented
9C3×#4951C212yesmaximal, complemented
10C3×#4950C212yesmaximal, complemented
11C3×Dic3×C22⋊C4C212yesmaximal, complemented
12C3×#2342—31nomaximal
13#82097C311yesmaximal, characteristic, direct product factor
14C25×C32C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C2×C32×C22⋊C4C418yescomplemented
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C3×#217—24no—
24C2×C3×#217C2212yes—
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2212yes—
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2212yes—
30C2×C3×#217C2211yescharacteristic
31C3×#926—24no—
32C2×C3×C4⋊Dic3C2212yescomplemented
33C2×C3×C4⋊Dic3C2212yescomplemented
34C2×C3×C4×Dic3C2212yescomplemented
35C2×C3×C4×Dic3C2212yescomplemented
36C3×C3⋊#95C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39C3×C3⋊#95C2212yescomplemented
40C2×C3×#117—31no—
41C22×C3×C22⋊C4—21no—
42C22×C3×C22⋊C4—31no—
43C22×C3×C22⋊C4D311yescharacteristic
44C22×C3×C22⋊C4C2×C311yescharacteristic
45C22×#217C2×C311yescharacteristic
46C2×#926C2×C311yescharacteristic, complemented
47C3×#388—32no—
48C3×#388—32no—
49C3×#385—32no—
50C3×#381—31no—
51C3×#380—31no—
52C3×#379—31no—
53C3×C4×C22⋊C4—31no—
54C3×C4×C22⋊C4—32no—
55#5247C2×C311yescharacteristic
56#5212C2×C311yescharacteristic, complemented
57#5211C2×C311yescharacteristic, complemented
58C4×#217C2×C311yescharacteristic, complemented
59#4951C2×C312yescomplemented
60#4951C2×C312yescomplemented
61#4950C2×C312yescomplemented
62Dic3×C22⋊C4C2×C312yescomplemented
63C24×C32—22no—
64C24×C32—24no—
65C24×C32—22no—
66C24×C32—42no—
67C24×C32C2×C414yes—
68C24×C32C2311yescharacteristic
69C24×C32C2311yescharacteristic
70C24×C32C2311yescharacteristic
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4—42no—
74C22×C32×C4C2×C414yescomplemented
75C22×C32×C4C2×C414yescomplemented
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C3×Dic3—24no—
81C22×C3×Dic3—24no—
82C22×C3×Dic3—42no—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C32×C22⋊C4C2×C414yes—
88C32×C22⋊C4C2×C414yes—
89C32×C22⋊C4C2×C414yescomplemented
90C32×C22⋊C4C2×C414yescomplemented
91C3×#217—22no—
92C3×#217—22no—
93C3×#217—24no—
94C3×#217—22no—
95C3×#217—24no—
96C3×#217—42no—
97C3×#217D414yes—
98C3×C4⋊Dic3—24no—
99C3×C4⋊Dic3—42no—
100C3×C4×Dic3—24no—
101C3×C4×Dic3—42no—
102#2342—31noSylow
103C25×C3—21no—
104C25×C3C2×D311yescharacteristic
105C25×C3C22×C311yescharacteristic
106C23×C3×C4—21no—
107C23×C3×C4—21no—
108C23×C3×C4—32no—
109C23×C3×C4C2×D311yescharacteristic
110C23×C3×C4C2×D311yescharacteristic
111C23×C3×C4C22×C311yescharacteristic
112C23×C3×C4C22×C311yescharacteristic
113C23×Dic3C22×C312yes—
114C3×#117—64no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C22⋊C4—28no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C22⋊C4—32no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4—64no—
130C2×C3×C22⋊C4Dic318yescomplemented
131C2×C3×C22⋊C4C3×C418yescomplemented
132C2×C3×C22⋊C4C2×D311yescharacteristic
133C2×C3×C22⋊C4C2×D311yescharacteristic
134C2×C3×C22⋊C4C2×D311yescharacteristic
135C2×C3×C22⋊C4C2×D311yescharacteristic
136C2×C3×C22⋊C4C22×C311yescharacteristic
137C2×C3×C22⋊C4C22×C311yescharacteristic
138C2×C3×C22⋊C4C22×C311yescharacteristic
139C2×C3×C22⋊C4C22×C311yescharacteristic
140C2×C3×C42—32no—
141C2×C3×C42—32no—
142C2×#217—24no—
143C2×#217C22×C312yes—
144C2×#217C22×C312yes—
145C2×#217C22×C311yescharacteristic
146C2×#217C22×C311yescharacteristic
147C2×#217C22×C311yescharacteristic
148C2×#217C22×C312yes—
149C2×#217C22×C311yescharacteristic
150#926—24no—
151C2×C4⋊Dic3C22×C312yescomplemented
152C2×C4⋊Dic3C22×C312yescomplemented
153C2×C4×Dic3C22×C312yescomplemented
154C2×C4×Dic3C22×C312yescomplemented
155C3×#95—32no—
156C3×#95—32no—
157C3×#95—32no—
158C3×#95—32no—
159C3⋊#95C22×C312yescomplemented
160C3⋊#95C22×C312yescomplemented
161C3⋊#95C22×C312yescomplemented
162C3⋊#95C22×C312yescomplemented
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—28no—
166C23×C32—22no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—22no—
170C23×C32—28no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—22no—
174C23×C32—44no—
175C23×C32—48no—
176C23×C32—48no—
177C23×C32C22×C412yes—
178C23×C32C22×C412yes—
179C23×C32C22×C412yes—
180C23×C32C2×D412yes—
181C23×C32#4114yes—
182C23×C32#4112yes—
183C23×C32C2411yescharacteristic
184C2×C32×C4—28no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—44no—
192C2×C32×C4C22×C412yes—
193C2×C32×C4C22×C412yes—
194C2×C32×C4C22×C412yes—
195C2×C32×C4C22×C412yes—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
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×Dic3—22no—
207C2×C3×Dic3—48no—
208C2×C3×Dic3C2×D414yes—
209C2×#117—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4C3×D311yescharacteristic
212#388—32no—
213#388—32no—
214#385—32no—
215#381—31no—
216#380—31no—
217#379—31no—
218C4×C22⋊C4—31no—
219C4×C22⋊C4—32no—
220C24×C3—28no—
221C24×C3—24no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—24no—
226C24×C3—22no—
227C24×C3—24no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—42no—
232C24×C3—42no—
233C24×C3—42no—
234C24×C3—42no—
235C24×C3—44no—
236C24×C3C2×Dic314yes—
237C24×C3C2×C3×C414yes—
238C24×C3C22×D311yescharacteristic
239C24×C3C22×D311yescharacteristic
240C24×C3C22×D311yescharacteristic
241C24×C3C23×C311yescharacteristic
242C24×C3C23×C311yescharacteristic
243C24×C3C23×C311yescharacteristic
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—32no—
255C22×C3×C4—32no—
256C22×C3×C4—32no—
257C22×C3×C4—32no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4—42no—
262C22×C3×C4—44no—
263C22×C3×C4—64no—
264C22×C3×C4—64no—
265C22×C3×C4—122no—
266C22×C3×C4C2×Dic314yescomplemented
267C22×C3×C4C2×Dic314yescomplemented
268C22×C3×C4C2×C3×C414yescomplemented
269C22×C3×C4C2×C3×C414yescomplemented
270C22×C3×C4C22×D311yescharacteristic
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C23×C311yescharacteristic
275C22×C3×C4C23×C311yescharacteristic
276C22×C3×C4C23×C311yescharacteristic
277C22×C3×C4C23×C311yescharacteristic
278C22×Dic3—24no—
279C22×Dic3—24no—
280C22×Dic3—42no—
281C22×Dic3C23×C312yes—
282C22×Dic3C23×C312yes—
283C22×Dic3C23×C312yes—
284C22×Dic3C23×C312yes—
285C3×C4⋊C4—64no—
286C3×C4⋊C4—122no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—24no—
289C3×C22⋊C4—24no—
290C3×C22⋊C4—24no—
291C3×C22⋊C4—34no—
292C3×C22⋊C4—64no—
293C3×C22⋊C4—64no—
294C3×C22⋊C4—62no—
295C3×C22⋊C4—62no—
296C3×C22⋊C4—62no—
297C3×C22⋊C4—122no—
298C3×C22⋊C4C2×Dic314yes—
299C3×C22⋊C4C2×Dic314yes—
300C3×C22⋊C4C2×Dic314yescomplemented
301C3×C22⋊C4C2×Dic314yescomplemented
302C3×C22⋊C4C2×C3×C414yes—
303C3×C22⋊C4C2×C3×C414yes—
304C3×C22⋊C4C2×C3×C414yescomplemented
305C3×C22⋊C4C2×C3×C414yescomplemented
306C3×C42—64no—
307C3×C42—122no—
308#217—22no—
309#217—22no—
310#217—24no—
311#217—22no—
312#217—24no—
313#217—42no—
314#217C3×D414yes—
315C4⋊Dic3—24no—
316C4⋊Dic3—42no—
317C4×Dic3—24no—
318C4×Dic3—42no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—24no—
327C22×C32—24no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—416no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32#11714yescomplemented
334C22×C32C4×D414yes—
335C22×C32C23×C411yescharacteristic
336C22×C32C22×D411yescharacteristic
337C22×C32C2×#4112yes—
338C22×C32C2×#4111yescharacteristic
339C22×C32H(5,𝔽2)12yes—
340C32×C4—22no—
341C32×C4—22no—
342C32×C4—22no—
343C32×C4—22no—
344C3×Dic3—24no—
345C3×Dic3—42no—
346C3×Dic3—42no—
347C3×Dic3—42no—
348C25C2×C3×D311yescharacteristic
349C23×C4—32no—
350C23×C4C2×C3×D311yescharacteristic
351C23×C4C2×C3×D311yescharacteristic
352#117—64no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4—32no—
355C2×C22⋊C4—31no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—31no—
359C2×C22⋊C4—31no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—64no—
363C2×C22⋊C4C3×Dic318yescomplemented
364C2×C22⋊C4C2×C3×D311yescharacteristic
365C2×C22⋊C4C2×C3×D311yescharacteristic
366C2×C22⋊C4C2×C3×D311yescharacteristic
367C2×C22⋊C4C2×C3×D311yescharacteristic
368C2×C42—32no—
369C2×C42—32no—
370#95—32no—
371#95—32no—
372#95—32no—
373#95—32no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—21no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—216no—
387C23×C3—24no—
388C23×C3—28no—
389C23×C3—28no—
390C23×C3—28no—
391C23×C3—28no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—22no—
396C23×C3—21no—
397C23×C3—22no—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—24no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—42no—
410C23×C3—48no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—42no—
414C23×C3—44no—
415C23×C3—44no—
416C23×C3—48no—
417C23×C3—48no—
418C23×C3—48no—
419C23×C3—48no—
420C23×C3—48no—
421C23×C3—416no—
422C23×C3—416no—
423C23×C3#23514yes—
424C23×C3D3×D412yes—
425C23×C3#23712yes—
426C23×C3C22×Dic312yes—
427C23×C3C22×Dic312yes—
428C23×C3C22×Dic312yes—
429C23×C3C22×C3×C412yes—
430C23×C3C22×C3×C412yes—
431C23×C3C22×C3×C412yes—
432C23×C3C2×C3×D412yes—
433C23×C3C3×#4114yes—
434C23×C3C3×#4112yes—
435C23×C3C23×D311yescharacteristic
436C23×C3C24×C311yescharacteristic
437C2×C3×C4—28no—
438C2×C3×C4—28no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—34no—
456C2×C3×C4—48no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465C2×C3×C4—48no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—128no—
478C2×C3×C4C22×Dic312yes—
479C2×C3×C4C22×Dic312yes—
480C2×C3×C4C22×Dic312yes—
481C2×C3×C4C22×Dic312yes—
482C2×C3×C4C22×C3×C412yes—
483C2×C3×C4C22×C3×C412yes—
484C2×C3×C4C22×C3×C412yes—
485C2×C3×C4C22×C3×C412yes—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—48no—
498C2×Dic3C2×C3×D414yes—
499C2×C32—24no—
500C2×C32—24no—
501C2×C32—42no—
502C2×C32C2×#11711yescharacteristic
503C2×C32C2×C4×D411yescharacteristic
504C2×C32#51811yescharacteristic
505C2×C32#54612yes—
506C2×C32#55112yes—
507C24—24no—
508C24—22no—
509C24—22no—
510C24—42no—
511C24C2×C3×Dic314yes—
512C24C22×C3×D311yescharacteristic
513C24C22×C3×D311yescharacteristic
514C24C22×C3×D311yescharacteristic
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—42no—
522C22×C4—64no—
523C22×C4—64no—
524C22×C4—122no—
525C22×C4C2×C3×Dic314yescomplemented
526C22×C4C2×C3×Dic314yescomplemented
527C22×C4C22×C3×D311yescharacteristic
528C22×C4C22×C3×D311yescharacteristic
529C22×C4C22×C3×D311yescharacteristic
530C22×C4C22×C3×D311yescharacteristic
531C4⋊C4—64no—
532C4⋊C4—122no—
533C22⋊C4—34no—
534C22⋊C4—64no—
535C22⋊C4—64no—
536C22⋊C4—62no—
537C22⋊C4—62no—
538C22⋊C4—62no—
539C22⋊C4—122no—
540C22⋊C4C2×C3×Dic314yes—
541C22⋊C4C2×C3×Dic314yes—
542C22⋊C4C2×C3×Dic314yescomplemented
543C22⋊C4C2×C3×Dic314yescomplemented
544C42—64no—
545C42—122no—
546C22×C3—24no—
547C22×C3—24no—
548C22×C3—28no—
549C22×C3—28no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—24no—
553C22×C3—24no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—24no—
563C22×C3—24no—
564C22×C3—24no—
565C22×C3—24no—
566C22×C3—24no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—22no—
579C22×C3—21no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—416no—
587C22×C3—416no—
588C22×C3—432no—
589C22×C3—44no—
590C22×C3—44no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3#92614yescomplemented
596C22×C3D4×Dic314yes—
597C22×C3C3×#11714yescomplemented
598C22×C3C3×C4×D414yes—
599C22×C3C2×#23512yes—
600C22×C3C2×D3×D411yescharacteristic
601C22×C3C2×#23711yescharacteristic
602C22×C3#100412yes—
603C22×C3C23×Dic311yescharacteristic
604C22×C3C23×C3×C411yescharacteristic
605C22×C3C22×C3×D411yescharacteristic
606C22×C3C2×C3×#4112yes—
607C22×C3C2×C3×#4111yescharacteristic
608C22×C3C3×H(5,𝔽2)12yes—
609C3×C4—22no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—64no—
622C3×C4—122no—
623C3×C4—122no—
624C3×C4—122no—
625Dic3—24no—
626Dic3—42no—
627Dic3—42no—
628Dic3—42no—
629C32#234211yescharacteristic, complemented, Sylow
630C23—22no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—22no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—22no—
641C23—44no—
642C23—48no—
643C23—48no—
644C23C3×#23514yes—
645C23C3×D3×D412yes—
646C23C3×#23712yes—
647C23C22×C3×Dic312yes—
648C23C22×C3×Dic312yes—
649C23C22×C3×Dic312yes—
650C23C23×C3×D311yescharacteristic
651C2×C4—28no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—34no—
659C2×C4—44no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—128no—
672C2×C4C22×C3×Dic312yes—
673C2×C4C22×C3×Dic312yes—
674C2×C4C22×C3×Dic312yes—
675C2×C4C22×C3×Dic312yes—
676C2×C3—28no—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—24no—
680C2×C3—24no—
681C2×C3—22no—
682C2×C3—22no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—44no—
687C2×C3—44no—
688C2×C3—42no—
689C2×C3—42no—
690C2×C3#549012yes—
691C2×C3#549512yes—
692C2×C3C2×#92611yescharacteristic
693C2×C3C2×D4×Dic311yescharacteristic
694C2×C3#579811yescharacteristic
695C2×C3C2×C3×#11711yescharacteristic
696C2×C3C2×C3×C4×D411yescharacteristic
697C2×C3C3×#51811yescharacteristic
698C2×C3C3×#54612yes—
699C2×C3C3×#55112yes—
700C22—24no—
701C22—24no—
702C22—24no—
703C22—24no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—416no—
712C22—42no—
713C22—42no—
714C22C3×#92614yescomplemented
715C22C3×D4×Dic314yes—
716C22C2×C3×#23512yes—
717C22C2×C3×D3×D411yescharacteristic
718C22C2×C3×#23711yescharacteristic
719C22C3×#100412yes—
720C22C23×C3×Dic311yescharacteristic
721C4—22no—
722C4—22no—
723C4—22no—
724C4—22no—
725C4—64no—
726C4—122no—
727C4—122no—
728C4—122no—
729C3—21no—
730C3#8209711yescharacteristic, direct product factor
731C3C3×#234211yescharacteristic, complemented
732C2—24no—
733C2—24no—
734C2—42no—
735C2C3×#549012yes—
736C2C3×#549512yes—
737C2C2×C3×#92611yescharacteristic
738C2C2×C3×D4×Dic311yescharacteristic
739C2C3×#579811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC23×C32C24
prime radicalC25×C32C22
cosocleC23×C3C24×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C3×#2342
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#926C2semidirect
5. C3×#5212C2semidirect
6. C3×#5211C2semidirect
7. C3×C4×#217C2semidirect
8. C3×#4951C2semidirect
9. C3×#4951C2semidirect
10. C3×#4950C2semidirect
11. C3×Dic3×C22⋊C4C2semidirect
13. #82097C3direct (N × H)
18. C2×C32×C22⋊C4C4semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C2×C3×C4×Dic3C22semidirect
36. C3×C3⋊#95C22semidirect
37. C3×C3⋊#95C22semidirect
38. C3×C3⋊#95C22semidirect
39. C3×C3⋊#95C22semidirect
46. C2×#926C2×C3semidirect
56. #5212C2×C3semidirect
57. #5211C2×C3semidirect
58. C4×#217C2×C3semidirect
59. #4951C2×C3semidirect
60. #4951C2×C3semidirect
61. #4950C2×C3semidirect
62. Dic3×C22⋊C4C2×C3semidirect
74. C22×C32×C4C2×C4semidirect
75. C22×C32×C4C2×C4semidirect
89. C32×C22⋊C4C2×C4semidirect
90. C32×C22⋊C4C2×C4semidirect
130. C2×C3×C22⋊C4Dic3semidirect
131. C2×C3×C22⋊C4C3×C4semidirect
151. C2×C4⋊Dic3C22×C3semidirect
152. C2×C4⋊Dic3C22×C3semidirect
153. C2×C4×Dic3C22×C3semidirect
154. C2×C4×Dic3C22×C3semidirect
159. C3⋊#95C22×C3semidirect
160. C3⋊#95C22×C3semidirect
161. C3⋊#95C22×C3semidirect
162. C3⋊#95C22×C3semidirect
266. C22×C3×C4C2×Dic3semidirect
267. C22×C3×C4C2×Dic3semidirect
268. C22×C3×C4C2×C3×C4semidirect
269. C22×C3×C4C2×C3×C4semidirect
300. C3×C22⋊C4C2×Dic3semidirect
301. C3×C22⋊C4C2×Dic3semidirect
304. C3×C22⋊C4C2×C3×C4semidirect
305. C3×C22⋊C4C2×C3×C4semidirect
333. C22×C32#117semidirect
363. C2×C22⋊C4C3×Dic3semidirect
525. C22×C4C2×C3×Dic3semidirect
526. C22×C4C2×C3×Dic3semidirect
542. C22⋊C4C2×C3×Dic3semidirect
543. C22⋊C4C2×C3×Dic3semidirect
595. C22×C3#926semidirect
597. C22×C3C3×#117semidirect
629. C32#2342semidirect
714. C22C3×#926semidirect
730. C3#82097direct (N × H)
731. C3C3×#2342semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊C42
C22×C3×#2172
C2×C3×#9262
C3×#52472
C3×#52122
C3×#52112
C3×C4×#2172
C3×#49512
C3×#49502
C3×Dic3×C22⋊C42
C3×#23423
#820973