Finite Group Databasebeta

← C3×D3×#451 #11863639

Subgroups — C3×D3×#451 #11863639

Order 1152.

1554 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic
2C2×C3×D3×Q16C212yesmaximal, complemented
3C3×D3×C22⋊Q8C211yesmaximal, characteristic
4C32×#451C211yesmaximal, characteristic, complemented
5C3×#5228C211yesmaximal, characteristic, complemented
6C3×#5186C212yesmaximal, complemented
7C3×#5050C211yesmaximal, characteristic, complemented
8C3×#4809C212yesmaximal, complemented
9C3×D3×#103C212yesmaximal, complemented
10C3×#4739C211yesmaximal, characteristic, complemented
11C3×D3×C22⋊C8C211yesmaximal, characteristic
12C2×C3×#451—31nomaximal
13D3×#451C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C2×C3×D3×Q8—28no—
16C2×C3×D3×Q8—21no—
17C2×C3×D3×Q8—21no—
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2212yes—
20C2×C3×D3×Q8C2212yes—
21C22×C3×C4×D3—21no—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6—21no—
24C22×C3×Dic6C2211yescharacteristic
25C2×C32×Q16C2212yescomplemented
26C32×C22⋊Q8C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C2×C3×#216C2212yescomplemented
29C2×C3×#216C2212yescomplemented
30C3×#924C2211yescharacteristic
31C3×D3×Q16—28no—
32C2×C3×Dic12C2212yescomplemented
33C2×C3×D3×C8C2212yes—
34C3×#897C2211yescharacteristic
35C3×#896—21no—
36C3×D3×C4⋊C4—21no—
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×D3×C22⋊C4—21no—
39C3×#878—21no—
40C32×#103C2212yescomplemented
41C32×C22⋊C8C2211yescharacteristic
42C3×#835C2212yescomplemented
43C3×#830C2211yescharacteristic
44C3×(C2×D3)⋊C8C2212yes—
45C3×#816C2212yescomplemented
46C3×#810C2212yescomplemented
47C23×C3×Q8—31no—
48C22×D3×Q8C2×C311yescharacteristic
49C22×C3×Q16—32no—
50C2×C3×C22⋊Q8—31no—
51C2×D3×Q16C2×C312yescomplemented
52D3×C22⋊Q8C2×C311yescharacteristic
53C3×#451—21no—
54C3×#451—31no—
55C3×#451—32no—
56C3×#451—31no—
57C3×#451—32no—
58C3×#451—31no—
59C3×#451D311yescharacteristic, direct product factor
60C3×#451C2×C311yescharacteristic, complemented
61C2×C3×#103—32no—
62C2×C3×C22⋊C8—31no—
63#5228C2×C311yescharacteristic, complemented
64#5186C2×C312yescomplemented
65#5050C2×C311yescharacteristic, complemented
66#4809C2×C312yescomplemented
67D3×#103C2×C312yescomplemented
68#4739C2×C311yescharacteristic, complemented
69D3×C22⋊C8C2×C311yescharacteristic
70C23×C3×D3D411yescharacteristic
71C2×C32×Q8—24no—
72C2×C32×Q8—21no—
73C2×C32×Q8C2311yescharacteristic
74C2×C32×Q8C2312yes—
75C22×C32×C4—21no—
76C22×C32×C4C2311yescharacteristic
77C22×C3×Dic3—21no—
78C22×C3×Dic3D411yescharacteristic
79C3×D3×Q8—28no—
80C3×D3×Q8—28no—
81C3×D3×Q8—24no—
82C3×D3×Q8—24no—
83C3×D3×Q8—24no—
84C3×D3×Q8—24no—
85C3×D3×Q8D418yes—
86C2×C3×C4×D3—28no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3—22no—
89C2×C3×C4×D3—24no—
90C2×C3×C4×D3—21no—
91C2×C3×C4×D3—21no—
92C2×C3×C4×D3D411yescharacteristic
93C2×C3×C4×D3D411yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6—28no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—22no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—24no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2312yes—
104C32×Q16—24no—
105C2×C32×C8C2312yes—
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C3×#217—21no—
110C3×#216—24no—
111C3×#216—24no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C2×C3×C3⋊C8C2312yes—
120C3×Dic12—24no—
121C3×D3×C8—24no—
122C2×#451—31noSylow
123C22×C3×Q8—21no—
124C22×C3×Q8—32no—
125C22×C3×Q8—31no—
126C22×C3×Q8—32no—
127C22×C3×Q8—31no—
128C22×C3×Q8—61no—
129C22×C3×Q8—61no—
130C22×C3×Q8—61no—
131C22×C3×Q8—68no—
132C22×C3×Q8C2×D311yescharacteristic
133C22×C3×Q8C22×C311yescharacteristic
134C23×C3×C4—31no—
135C23×C3×C4—61no—
136C2×D3×Q8—28no—
137C2×D3×Q8—21no—
138C2×D3×Q8—21no—
139C2×D3×Q8C22×C312yes—
140C2×D3×Q8C22×C311yescharacteristic
141C2×D3×Q8C22×C312yes—
142C22×C4×D3—21no—
143C22×C4×D3C22×C311yescharacteristic
144C22×Dic6—21no—
145C22×Dic6C22×C311yescharacteristic
146C2×C3×Q16—22no—
147C2×C3×Q16—32no—
148C2×C3×Q16—32no—
149C2×C3×Q16—32no—
150C2×C3×Q16—68no—
151C2×C3×Q16C2×D312yescomplemented
152C2×C3×Q16C22×C312yescomplemented
153C22×C3×C8—32no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C22⋊Q8C22×C311yescharacteristic
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—61no—
164C2×C3×C22⋊C4—61no—
165#946C22×C311yescharacteristic
166C2×#216C22×C312yescomplemented
167C2×#216C22×C312yescomplemented
168#924C22×C311yescharacteristic
169D3×Q16—28no—
170C2×Dic12C22×C312yescomplemented
171C2×D3×C8C22×C312yes—
172#897C22×C311yescharacteristic
173#896—21no—
174D3×C4⋊C4—21no—
175D3×C4⋊C4C22×C311yescharacteristic
176D3×C22⋊C4—21no—
177#878—21no—
178C3×#103—22no—
179C3×#103—32no—
180C3×#103—32no—
181C3×#103—32no—
182C3×#103C2×D312yescomplemented
183C3×#103C22×C312yescomplemented
184C3×C22⋊C8—21no—
185C3×C22⋊C8—31no—
186C3×C22⋊C8—32no—
187C3×C22⋊C8C2×D311yescharacteristic
188C3×C22⋊C8C22×C311yescharacteristic
189#835C22×C312yescomplemented
190#830C22×C311yescharacteristic
191(C2×D3)⋊C8C22×C312yes—
192#816C22×C312yescomplemented
193#810C22×C312yescomplemented
194C23×C32C2×D411yescharacteristic
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3Q1614yescomplemented
198C22×C3×D3C2×D411yescharacteristic
199C22×C3×D3C2×D411yescharacteristic
200C32×Q8—24no—
201C32×Q8—22no—
202C32×Q8—22no—
203C32×Q8C2×D414yes—
204C2×C32×C4—24no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4C2×D411yescharacteristic
210C2×C32×C4C2411yescharacteristic
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3C2×D411yescharacteristic
217C2×C3×Dic3C2×D411yescharacteristic
218C3×C4×D3—28no—
219C3×C4×D3—28no—
220C3×C4×D3—22no—
221C3×C4×D3—22no—
222C3×C4×D3—22no—
223C3×C4×D3—42no—
224C3×C4×D3—42no—
225C3×C4×D3C2×D414yes—
226C3×Dic6—28no—
227C3×Dic6—24no—
228C3×Dic6—22no—
229C3×Dic6—28no—
230C3×Dic6—22no—
231C3×Dic6—42no—
232C3×Dic6C2×D414yes—
233C32×C8—22no—
234C3×C3⋊C8—22no—
235C23×Q8—31no—
236C22×Q16—32no—
237C2×C22⋊Q8—31no—
238#451—31no—
239#451—32no—
240#451—31no—
241#451—32no—
242#451—31no—
243#451C3×D311yescharacteristic, direct product factor
244C2×#103—32no—
245C2×C22⋊C8—31no—
246C24×C3—31no—
247C23×D3C3×D411yescharacteristic
248C2×C3×Q8—24no—
249C2×C3×Q8—24no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—22no—
253C2×C3×Q8—21no—
254C2×C3×Q8—38no—
255C2×C3×Q8—32no—
256C2×C3×Q8—31no—
257C2×C3×Q8—41no—
258C2×C3×Q8—44no—
259C2×C3×Q8—62no—
260C2×C3×Q8—62no—
261C2×C3×Q8—61no—
262C2×C3×Q8—64no—
263C2×C3×Q8—68no—
264C2×C3×Q8—64no—
265C2×C3×Q8—64no—
266C2×C3×Q8—64no—
267C2×C3×Q8—68no—
268C2×C3×Q8—68no—
269C2×C3×Q8—64no—
270C2×C3×Q8—61no—
271C2×C3×Q8C22×D311yescharacteristic
272C2×C3×Q8C22×D312yes—
273C2×C3×Q8C23×C311yescharacteristic
274C2×C3×Q8C23×C312yes—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—41no—
284C22×C3×C4—64no—
285C22×C3×C4—62no—
286C22×C3×C4—62no—
287C22×C3×C4—68no—
288C22×C3×C4—61no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C23×C311yescharacteristic
293C22×Dic3—21no—
294C22×Dic3C3×D411yescharacteristic
295D3×Q8—28no—
296D3×Q8—28no—
297D3×Q8—24no—
298D3×Q8—24no—
299D3×Q8—24no—
300D3×Q8—24no—
301D3×Q8C3×D418yes—
302C2×C4×D3—28no—
303C2×C4×D3—22no—
304C2×C4×D3—22no—
305C2×C4×D3—24no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3C3×D411yescharacteristic
309C2×C4×D3C3×D411yescharacteristic
310C2×C4×D3C23×C311yescharacteristic
311C2×C4×D3C23×C311yescharacteristic
312C2×Dic6—28no—
313C2×Dic6—21no—
314C2×Dic6—22no—
315C2×Dic6—22no—
316C2×Dic6—24no—
317C2×Dic6—21no—
318C2×Dic6C23×C311yescharacteristic
319C2×Dic6C23×C312yes—
320C3×Q16—24no—
321C3×Q16—24no—
322C3×Q16—44no—
323C3×Q16—64no—
324C3×Q16—64no—
325C3×Q16—64no—
326C2×C3×C8—22no—
327C2×C3×C8—32no—
328C2×C3×C8—64no—
329C2×C3×C8C22×D312yes—
330C2×C3×C8C23×C312yes—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C23×C311yescharacteristic
342C3×C22⋊C4—21no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—41no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348#217—21no—
349#216—24no—
350#216—24no—
351(C2×D3)⋊C4—21no—
352(C2×D3)⋊C4—21no—
353C4⋊Dic3—21no—
354C4⋊Dic3C23×C311yescharacteristic
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358C2×C3⋊C8C23×C312yes—
359Dic12—24no—
360D3×C8—24no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32C2×Q1612yescomplemented
364C22×C32C22×D411yescharacteristic
365C2×C3×D3—21no—
366C2×C3×D3—21no—
367C2×C3×D3—28no—
368C2×C3×D3#12012yes—
369C2×C3×D3C2×Q1612yes—
370C2×C3×D3C2×Q1612yescomplemented
371C2×C3×D3#13712yes—
372C32×C4—24no—
373C32×C4—21no—
374C32×C4—41no—
375C32×C4—41no—
376C32×C4C22×D412yes—
377C3×Dic3—21no—
378C3×Dic3—24no—
379C3×Dic3—41no—
380C3×Dic3—41no—
381C3×Dic3#12012yes—
382C22×Q8—32no—
383C22×Q8—31no—
384C22×Q8—32no—
385C22×Q8—31no—
386C22×Q8—61no—
387C22×Q8—61no—
388C22×Q8—61no—
389C22×Q8—68no—
390C22×Q8C2×C3×D311yescharacteristic
391C23×C4—31no—
392C23×C4—61no—
393C2×Q16—32no—
394C2×Q16—32no—
395C2×Q16—32no—
396C2×Q16—68no—
397C2×Q16C2×C3×D312yescomplemented
398C22×C8—32no—
399C22⋊Q8—31no—
400C22⋊Q8—31no—
401C22⋊Q8—31no—
402C22⋊Q8—61no—
403C22⋊Q8—61no—
404C22⋊Q8C2×C3×D311yescharacteristic
405C2×C4⋊C4—31no—
406C2×C4⋊C4—61no—
407C2×C22⋊C4—61no—
408#103—32no—
409#103—32no—
410#103—32no—
411#103C2×C3×D312yescomplemented
412C22⋊C8—31no—
413C22⋊C8—32no—
414C22⋊C8C2×C3×D311yescharacteristic
415C23×C3—21no—
416C23×C3—31no—
417C23×C3—34no—
418C23×C3—31no—
419C23×C3—62no—
420C23×C3—62no—
421C23×C3D3×D411yescharacteristic
422C23×C3C2×C3×D411yescharacteristic
423C22×D3—22no—
424C22×D3—22no—
425C22×D3C3×Q1614yescomplemented
426C22×D3C2×C3×D411yescharacteristic
427C22×D3C2×C3×D411yescharacteristic
428C3×Q8—24no—
429C3×Q8—24no—
430C3×Q8—22no—
431C3×Q8—22no—
432C3×Q8—22no—
433C3×Q8—22no—
434C3×Q8—24no—
435C3×Q8—34no—
436C3×Q8—42no—
437C3×Q8—42no—
438C3×Q8—44no—
439C3×Q8—68no—
440C3×Q8—68no—
441C3×Q8—64no—
442C3×Q8—62no—
443C3×Q8—62no—
444C3×Q8—122no—
445C3×Q8D3×D414yes—
446C3×Q8C2×C3×D414yes—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—31no—
460C2×C3×C4—34no—
461C2×C3×C4—31no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—44no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—68no—
470C2×C3×C4—68no—
471C2×C3×C4—62no—
472C2×C3×C4—64no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—122no—
478C2×C3×C4—122no—
479C2×C3×C4D3×D411yescharacteristic
480C2×C3×C4C2×C3×D411yescharacteristic
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C24×C311yescharacteristic
483C2×Dic3—24no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3C2×C3×D411yescharacteristic
489C2×Dic3C2×C3×D411yescharacteristic
490C4×D3—28no—
491C4×D3—28no—
492C4×D3—22no—
493C4×D3—22no—
494C4×D3—22no—
495C4×D3—42no—
496C4×D3—42no—
497C4×D3C2×C3×D414yes—
498Dic6—28no—
499Dic6—24no—
500Dic6—22no—
501Dic6—28no—
502Dic6—22no—
503Dic6—42no—
504Dic6C2×C3×D414yes—
505C3×C8—22no—
506C3×C8—22no—
507C3×C8—42no—
508C3×C8—62no—
509C3⋊C8—22no—
510C2×C32—22no—
511C2×C32C2×#12011yescharacteristic
512C2×C32C22×Q1611yescharacteristic
513C2×C32C2×#13711yescharacteristic
514C3×D3—22no—
515C3×D3#45114yesdirect product factor
516C24—31no—
517C2×Q8—24no—
518C2×Q8—21no—
519C2×Q8—38no—
520C2×Q8—32no—
521C2×Q8—31no—
522C2×Q8—62no—
523C2×Q8—62no—
524C2×Q8—61no—
525C2×Q8—64no—
526C2×Q8—68no—
527C2×Q8—64no—
528C2×Q8—64no—
529C2×Q8—64no—
530C2×Q8—68no—
531C2×Q8—68no—
532C2×Q8—64no—
533C2×Q8—61no—
534C2×Q8C22×C3×D311yescharacteristic
535C2×Q8C22×C3×D312yes—
536C22×C4—21no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—64no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—68no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4C22×C3×D311yescharacteristic
550Q16—24no—
551Q16—64no—
552Q16—64no—
553Q16—64no—
554C2×C8—32no—
555C2×C8—64no—
556C2×C8C22×C3×D312yes—
557C4⋊C4—21no—
558C4⋊C4—31no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4C22×C3×D311yescharacteristic
564C22⋊C4—21no—
565C22⋊C4—61no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—22no—
573C22×C3—21no—
574C22×C3—32no—
575C22×C3—32no—
576C22×C3—32no—
577C22×C3—32no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—68no—
581C22×C3—61no—
582C22×C3—61no—
583C22×C3D3×Q1612yescomplemented
584C22×C3C2×C3×Q1612yescomplemented
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C22×C3×D411yescharacteristic
587C2×D3—21no—
588C2×D3—21no—
589C2×D3—28no—
590C2×D3C3×#12012yes—
591C2×D3C2×C3×Q1612yes—
592C2×D3C2×C3×Q1612yescomplemented
593C2×D3C3×#13712yes—
594C3×C4—24no—
595C3×C4—21no—
596C3×C4—24no—
597C3×C4—21no—
598C3×C4—22no—
599C3×C4—32no—
600C3×C4—41no—
601C3×C4—44no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—61no—
607C3×C4—64no—
608C3×C4—81no—
609C3×C4—81no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4C2×D3×D412yes—
613C3×C4C22×C3×D412yes—
614Dic3—21no—
615Dic3—24no—
616Dic3—41no—
617Dic3—41no—
618Dic3C3×#12012yes—
619C32C2×#45111yescharacteristic, complemented, Sylow
620C23—31no—
621C23—34no—
622C23—31no—
623C23—62no—
624C23—62no—
625C23C3×D3×D411yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—22no—
629Q8—34no—
630Q8—68no—
631Q8—68no—
632Q8—64no—
633Q8—62no—
634Q8—62no—
635Q8—122no—
636Q8C3×D3×D414yes—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—31no—
643C2×C4—34no—
644C2×C4—31no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—68no—
648C2×C4—68no—
649C2×C4—62no—
650C2×C4—64no—
651C2×C4—62no—
652C2×C4—62no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—122no—
656C2×C4—122no—
657C2×C4C3×D3×D411yescharacteristic
658C2×C4C23×C3×D311yescharacteristic
659C8—22no—
660C8—62no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—34no—
667C2×C3—42no—
668C2×C3—62no—
669C2×C3D3×#12011yescharacteristic
670C2×C3C2×D3×Q1611yescharacteristic
671C2×C3D3×#13711yescharacteristic
672C2×C3C2×C3×#12011yescharacteristic
673C2×C3C22×C3×Q1611yescharacteristic
674C2×C3C2×C3×#13711yescharacteristic
675D3—22no—
676D3C3×#45114yesdirect product factor
677C22—21no—
678C22—21no—
679C22—32no—
680C22—32no—
681C22—32no—
682C22—32no—
683C22—68no—
684C22—61no—
685C22—61no—
686C22C3×D3×Q1612yescomplemented
687C22C2×C3×D3×D411yescharacteristic
688C4—24no—
689C4—21no—
690C4—32no—
691C4—41no—
692C4—41no—
693C4—61no—
694C4—64no—
695C4—121no—
696C4—121no—
697C4C2×C3×D3×D412yes—
698C3—21no—
699C3D3×#45111yescharacteristic, direct product factor
700C3C2×C3×#45111yescharacteristic, complemented
701C2—22no—
702C2—34no—
703C2—62no—
704C2C3×D3×#12011yescharacteristic
705C2C2×C3×D3×Q1611yescharacteristic
706C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
hypercenterC3×#451D3
hypocenterC3C2×C3×#451
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Q16C2semidirect
4. C32×#451C2semidirect
5. C3×#5228C2semidirect
6. C3×#5186C2semidirect
7. C3×#5050C2semidirect
8. C3×#4809C2semidirect
9. C3×D3×#103C2semidirect
10. C3×#4739C2semidirect
13. D3×#451C3direct (N × H)
25. C2×C32×Q16C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#216C22semidirect
32. C2×C3×Dic12C22semidirect
40. C32×#103C22semidirect
42. C3×#835C22semidirect
45. C3×#816C22semidirect
46. C3×#810C22semidirect
51. C2×D3×Q16C2×C3semidirect
59. C3×#451D3direct (N × H)
60. C3×#451C2×C3semidirect
63. #5228C2×C3semidirect
64. #5186C2×C3semidirect
65. #5050C2×C3semidirect
66. #4809C2×C3semidirect
67. D3×#103C2×C3semidirect
68. #4739C2×C3semidirect
151. C2×C3×Q16C2×D3semidirect
152. C2×C3×Q16C22×C3semidirect
166. C2×#216C22×C3semidirect
167. C2×#216C22×C3semidirect
170. C2×Dic12C22×C3semidirect
182. C3×#103C2×D3semidirect
183. C3×#103C22×C3semidirect
189. #835C22×C3semidirect
192. #816C22×C3semidirect
193. #810C22×C3semidirect
197. C22×C3×D3Q16semidirect
243. #451C3×D3direct (N × H)
363. C22×C32C2×Q16semidirect
370. C2×C3×D3C2×Q16semidirect
397. C2×Q16C2×C3×D3semidirect
411. #103C2×C3×D3semidirect
425. C22×D3C3×Q16semidirect
515. C3×D3#451direct (N × H)
583. C22×C3D3×Q16semidirect
584. C22×C3C2×C3×Q16semidirect
592. C2×D3C2×C3×Q16semidirect
619. C32C2×#451semidirect
676. D3C3×#451direct (N × H)
686. C22C3×D3×Q16semidirect
699. C3D3×#451direct (N × H)
700. C3C2×C3×#451semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×C3×D3×Q162
C3×D3×C22⋊Q82
C32×#4512
C3×#52282
C3×#51862
C3×#50502
C3×#48092
C3×D3×#1032
C3×#47392
C3×D3×C22⋊C82
C2×C3×#4513
D3×#4513