Finite Group Databasebeta

← C2×C3×#5132 #11857628

Subgroups — C2×C3×#5132 #11857628

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 699 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C22×C32×M16C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C2×C3×#824C212yesmaximal, complemented
5C3×#5132C218yesmaximal, direct product factor
6C2×C3×#823C212yesmaximal, complemented
7C2×C3×#413—31nomaximal
8C2×#5132C311yesmaximal, characteristic, direct product factor
9C23×C32×C4C2211yescharacteristic
10C22×C3×#67C412yes—
11C2×C3×#235—21no—
12C2×C3×#235—21no—
13C2×C3×#235—22no—
14C2×C3×#235—21no—
15C2×C3×#235—21no—
16C2×C3×#235—22no—
17C2×C3×#235C414yes—
18C2×C3×#235C2214yes—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C412yes—
21C22×C3×Dic6C2211yescharacteristic
22C2×C32×M16—21no—
23C2×C32×M16—22no—
24C2×C32×M16C2212yes—
25C2×C32×M16C2214yescomplemented
26C22×C32×C8—21no—
27C2×C3×#208—21no—
28C2×C3×#208—22no—
29C2×C3×#208C2212yes—
30C2×C3×#208C2214yescomplemented
31C22×C3×C3⋊C8—21no—
32C3×#824C2218yescomplemented
33C3×#823C2218yescomplemented
34C22×C3×#41—31no—
35C22×#235C2×C311yescharacteristic
36C22×C3×M16—21no—
37C22×C3×M16—31no—
38C22×C3×M16D311yescharacteristic, complemented
39C22×C3×M16C2×C311yescharacteristic, complemented
40C22×#208C2×C311yescharacteristic, complemented
41C3×#413—38no—
42C2×C3×#101—32no—
43C2×C3×#100—32no—
44C2×#824C2×C312yescomplemented
45#5132C2×C318yesdirect product factor
46C2×#823C2×C312yescomplemented
47C24×C32C2×C411yescharacteristic
48C23×C3×D3C2×C412yes—
49C22×C32×C4C2×C411yescharacteristic
50C22×C32×C4C2×C412yes—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D412yes—
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D411yescharacteristic
56C22×C32×C4D412yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2312yes—
59C2×C3×#67—22no—
60C2×C3×#67—22no—
61C2×C3×#67—24no—
62C2×C3×#67C2×C418yes—
63C22×C3×Dic3C2×C412yes—
64C3×#235—24no—
65C3×#235—24no—
66C3×#235—24no—
67C3×#235—24no—
68C3×#235—24no—
69C3×#235—24no—
70C3×#235—24no—
71C3×#235—24no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2×C412yes—
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3C2×C418yes—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—21no—
84C2×C3×Dic6—21no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6C2×C412yes—
87C2×C3×Dic6C2312yes—
88C32×M16—22no—
89C32×M16—24no—
90C32×M16C2314yes—
91C2×C32×C8—22no—
92C2×C32×C8—24no—
93C3×#208—22no—
94C3×#208—24no—
95C3×#208C2314yes—
96C2×C3×C3⋊C8—22no—
97C2×C3×C3⋊C8—24no—
98C2×#413—31noSylow
99C2×C3×#41—34no—
100C2×C3×#41—34no—
101C2×C3×#41—61no—
102C2×C3×#41—62no—
103C2×C3×#41—61no—
104C2×C3×#41—61no—
105C2×C3×#41—62no—
106C2×C3×#41—61no—
107C22×C3×Q8—31no—
108C22×C3×D4—32no—
109C22×C3×D4—31no—
110C23×C3×C4—21no—
111C23×C3×C4—32no—
112C23×C3×C4C2×D311yescharacteristic
113C23×C3×C4C22×C311yescharacteristic
114C22×#67C3×C412yes—
115C2×#235—21no—
116C2×#235—21no—
117C2×#235—22no—
118C2×#235—21no—
119C2×#235—21no—
120C2×#235—22no—
121C2×#235C3×C414yes—
122C2×#235C22×C314yes—
123C22×D12C22×C311yescharacteristic
124C22×C4×D3C3×C412yes—
125C22×Dic6C22×C311yescharacteristic
126C2×C3×M16—22no—
127C2×C3×M16—24no—
128C2×C3×M16—21no—
129C2×C3×M16—22no—
130C2×C3×M16—21no—
131C2×C3×M16—22no—
132C2×C3×M16—22no—
133C2×C3×M16—24no—
134C2×C3×M16—32no—
135C2×C3×M16—34no—
136C2×C3×M16—61no—
137C2×C3×M16—62no—
138C2×C3×M16C2×D312yes—
139C2×C3×M16C2×D314yescomplemented
140C2×C3×M16C22×C312yes—
141C2×C3×M16C22×C314yescomplemented
142C22×C3×C8—22no—
143C22×C3×C8—21no—
144C22×C3×C8—21no—
145C22×C3×C8—61no—
146C2×#208—21no—
147C2×#208—22no—
148C2×#208C22×C312yes—
149C2×#208C22×C314yescomplemented
150C22×C3⋊C8—21no—
151C3×#101—38no—
152C3×#100—38no—
153#824C22×C318yescomplemented
154#823C22×C318yescomplemented
155C23×C32—42no—
156C23×C32C22⋊C411yescharacteristic
157C23×C32C22⋊C411yescharacteristic
158C23×C32C22⋊C412yes—
159C23×C32C22×C411yescharacteristic
160C23×C32C22×C412yes—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—44no—
164C22×C3×D3C22×C414yes—
165C2×C32×C4C22⋊C412yes—
166C2×C32×C4C22⋊C411yescharacteristic
167C2×C32×C4C22⋊C412yes—
168C2×C32×C4C22⋊C412yes—
169C2×C32×C4C22⋊C412yes—
170C2×C32×C4C22⋊C412yes—
171C2×C32×C4C22⋊C411yescharacteristic
172C2×C32×C4C22×C411yescharacteristic
173C2×C32×C4C22×C412yes—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2411yescharacteristic
183C3×#67—28no—
184C3×#67—28no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C22×C414yes—
188C3×D12—22no—
189C3×D12—22no—
190C3×D12—22no—
191C3×D12—22no—
192C3×C4×D3—28no—
193C3×C4×D3—28no—
194C3×Dic6—22no—
195C3×Dic6—22no—
196C3×Dic6—22no—
197C3×Dic6—22no—
198C32×C8—24no—
199C3×C3⋊C8—24no—
200C22×#41—31no—
201C22×M16—31no—
202C22×M16C3×D311yescharacteristic, complemented
203#413—38no—
204C2×#101—32no—
205C2×#100—32no—
206C24×C3—21no—
207C24×C3—32no—
208C24×C3C4×D311yescharacteristic
209C24×C3C2×C3×C411yescharacteristic
210C23×D3C2×C3×C412yes—
211C3×#41—64no—
212C3×#41—64no—
213C3×#41—64no—
214C3×#41—64no—
215C3×#41—64no—
216C3×#41—64no—
217C3×#41—64no—
218C3×#41—64no—
219C2×C3×Q8—32no—
220C2×C3×Q8—32no—
221C2×C3×Q8—61no—
222C2×C3×Q8—61no—
223C2×C3×Q8—61no—
224C2×C3×Q8—61no—
225C2×C3×D4—38no—
226C2×C3×D4—32no—
227C2×C3×D4—32no—
228C2×C3×D4—62no—
229C2×C3×D4—62no—
230C2×C3×D4—64no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C2×C3×D4—61no—
234C2×C3×D4—61no—
235C22×C3×C4—21no—
236C22×C3×C4—22no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—22no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—32no—
246C22×C3×C4—38no—
247C22×C3×C4—64no—
248C22×C3×C4—62no—
249C22×C3×C4—62no—
250C22×C3×C4C4×D312yes—
251C22×C3×C4C4×D311yescharacteristic
252C22×C3×C4D1211yescharacteristic
253C22×C3×C4D1212yes—
254C22×C3×C4D1211yescharacteristic
255C22×C3×C4#6711yescharacteristic
256C22×C3×C4#6712yes—
257C22×C3×C4#6711yescharacteristic
258C22×C3×C4C2×C3×C411yescharacteristic
259C22×C3×C4C2×C3×C412yes—
260C22×C3×C4C3×D411yescharacteristic
261C22×C3×C4C3×D411yescharacteristic
262C22×C3×C4C3×D412yes—
263C22×C3×C4C3×D411yescharacteristic
264C22×C3×C4C3×D411yescharacteristic
265C22×C3×C4C3×D412yes—
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D312yes—
268C22×C3×C4C23×C311yescharacteristic
269C22×C3×C4C23×C312yes—
270C2×#67—22no—
271C2×#67—22no—
272C2×#67—24no—
273C2×#67C2×C3×C418yes—
274C22×Dic3C2×C3×C412yes—
275#235—24no—
276#235—24no—
277#235—24no—
278#235—24no—
279#235—24no—
280#235—24no—
281#235—24no—
282#235—24no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12C2×C3×C412yes—
288C2×D12C23×C312yes—
289C2×C4×D3—24no—
290C2×C4×D3—22no—
291C2×C4×D3—22no—
292C2×C4×D3C2×C3×C418yes—
293C2×Dic6—21no—
294C2×Dic6—21no—
295C2×Dic6—21no—
296C2×Dic6—21no—
297C2×Dic6C2×C3×C412yes—
298C2×Dic6C23×C312yes—
299C3×M16—24no—
300C3×M16—28no—
301C3×M16—22no—
302C3×M16—24no—
303C3×M16—22no—
304C3×M16—24no—
305C3×M16—24no—
306C3×M16—34no—
307C3×M16—62no—
308C3×M16—64no—
309C3×M16C22×D314yes—
310C3×M16C23×C314yes—
311C2×C3×C8—24no—
312C2×C3×C8—28no—
313C2×C3×C8—22no—
314C2×C3×C8—24no—
315C2×C3×C8—22no—
316C2×C3×C8—24no—
317C2×C3×C8—62no—
318C2×C3×C8—64no—
319#208—22no—
320#208—24no—
321#208C23×C314yes—
322C2×C3⋊C8—22no—
323C2×C3⋊C8—24no—
324C22×C32—22no—
325C22×C32—22no—
326C22×C32—22no—
327C22×C32—42no—
328C22×C32—42no—
329C22×C32C2×C22⋊C411yescharacteristic
330C22×C32C2×C22⋊C412yes—
331C22×C32C2×C22⋊C412yes—
332C22×C32C2×C22⋊C411yescharacteristic
333C22×C32C23×C411yescharacteristic
334C2×C3×D3—24no—
335C2×C3×D3—44no—
336C2×C3×D3—44no—
337C2×C3×D3—44no—
338C32×C4C2×C22⋊C411yescharacteristic
339C32×C4C2×C22⋊C411yescharacteristic
340C32×C4C2×C22⋊C412yes—
341C32×C4C2×C22⋊C412yes—
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3×Dic3—24no—
345C2×#41—34no—
346C2×#41—34no—
347C2×#41—61no—
348C2×#41—61no—
349C2×#41—62no—
350C2×#41—61no—
351C2×#41—61no—
352C2×#41—62no—
353C22×Q8—31no—
354C22×D4—32no—
355C22×D4—31no—
356C23×C4—32no—
357C23×C4C2×C3×D311yescharacteristic
358C2×M16—21no—
359C2×M16—22no—
360C2×M16—32no—
361C2×M16—34no—
362C2×M16—61no—
363C2×M16—62no—
364C2×M16C2×C3×D312yes—
365C2×M16C2×C3×D314yescomplemented
366C22×C8—21no—
367C22×C8—61no—
368#101—38no—
369#100—38no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—22no—
373C23×C3—21no—
374C23×C3—22no—
375C23×C3—34no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—44no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—124no—
382C23×C3(C2×D3)⋊C411yescharacteristic
383C23×C3(C2×D3)⋊C411yescharacteristic
384C23×C3(C2×D3)⋊C412yes—
385C23×C3C3×C22⋊C411yescharacteristic
386C23×C3C3×C22⋊C411yescharacteristic
387C23×C3C3×C22⋊C412yes—
388C23×C3C2×C4×D311yescharacteristic
389C23×C3C2×C4×D312yes—
390C23×C3C22×C3×C411yescharacteristic
391C23×C3C22×C3×C412yes—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—44no—
395C22×D3C22×C3×C414yes—
396C3×Q8—62no—
397C3×Q8—62no—
398C3×Q8—62no—
399C3×Q8—62no—
400C3×D4—68no—
401C3×D4—68no—
402C3×D4—62no—
403C3×D4—62no—
404C3×D4—62no—
405C3×D4—62no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—22no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—34no—
425C2×C3×C4—62no—
426C2×C3×C4—62no—
427C2×C3×C4—68no—
428C2×C3×C4—68no—
429C2×C3×C4(C2×D3)⋊C411yescharacteristic
430C2×C3×C4(C2×D3)⋊C412yes—
431C2×C3×C4(C2×D3)⋊C412yes—
432C2×C3×C4(C2×D3)⋊C412yes—
433C2×C3×C4(C2×D3)⋊C412yes—
434C2×C3×C4(C2×D3)⋊C412yes—
435C2×C3×C4(C2×D3)⋊C411yescharacteristic
436C2×C3×C4C3×C22⋊C412yes—
437C2×C3×C4C3×C22⋊C411yescharacteristic
438C2×C3×C4C3×C22⋊C411yescharacteristic
439C2×C3×C4C3×C22⋊C412yes—
440C2×C3×C4C3×C22⋊C412yes—
441C2×C3×C4C3×C22⋊C412yes—
442C2×C3×C4C3×C22⋊C412yes—
443C2×C3×C4C2×C4×D312yes—
444C2×C3×C4C2×C4×D311yescharacteristic
445C2×C3×C4C2×D1211yescharacteristic
446C2×C3×C4C2×D1212yes—
447C2×C3×C4C2×D1211yescharacteristic
448C2×C3×C4C2×D1212yes—
449C2×C3×C4C2×#6711yescharacteristic
450C2×C3×C4C2×#6712yes—
451C2×C3×C4C2×#6711yescharacteristic
452C2×C3×C4C2×#6712yes—
453C2×C3×C4C22×C3×C411yescharacteristic
454C2×C3×C4C22×C3×C412yes—
455C2×C3×C4C2×C3×D411yescharacteristic
456C2×C3×C4C2×C3×D412yes—
457C2×C3×C4C2×C3×D411yescharacteristic
458C2×C3×C4C2×C3×D412yes—
459C2×C3×C4C2×C3×D411yescharacteristic
460C2×C3×C4C2×C3×D412yes—
461C2×C3×C4C2×C3×D411yescharacteristic
462C2×C3×C4C2×C3×D412yes—
463C2×C3×C4C23×D311yescharacteristic
464C2×C3×C4C24×C311yescharacteristic
465#67—28no—
466#67—28no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3C22×C3×C414yes—
470D12—22no—
471D12—22no—
472D12—22no—
473D12—22no—
474C4×D3—28no—
475C4×D3—28no—
476Dic6—22no—
477Dic6—22no—
478Dic6—22no—
479Dic6—22no—
480C3×C8—28no—
481C3×C8—24no—
482C3×C8—24no—
483C3×C8—64no—
484C3⋊C8—24no—
485C2×C32—22no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—22no—
489C2×C32#41312yescomplemented
490C2×C32C22×C22⋊C411yescharacteristic
491C3×D3—44no—
492C24—32no—
493C24C3×C4×D311yescharacteristic
494#41—64no—
495#41—64no—
496#41—64no—
497#41—64no—
498#41—64no—
499#41—64no—
500#41—64no—
501#41—64no—
502C2×Q8—32no—
503C2×Q8—32no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×D4—38no—
509C2×D4—32no—
510C2×D4—32no—
511C2×D4—62no—
512C2×D4—62no—
513C2×D4—64no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—61no—
518C22×C4—32no—
519C22×C4—38no—
520C22×C4—64no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4C3×C4×D311yescharacteristic
524C22×C4C3×C4×D312yes—
525C22×C4C3×D1211yescharacteristic
526C22×C4C3×D1211yescharacteristic
527C22×C4C3×D1212yes—
528C22×C4C3×#6711yescharacteristic
529C22×C4C3×#6711yescharacteristic
530C22×C4C3×#6712yes—
531C22×C4C22×C3×D311yescharacteristic
532C22×C4C22×C3×D312yes—
533M16—22no—
534M16—24no—
535M16—34no—
536M16—62no—
537M16—64no—
538M16C22×C3×D314yes—
539C2×C8—22no—
540C2×C8—24no—
541C2×C8—62no—
542C2×C8—64no—
543C22×C3—24no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—22no—
554C22×C3—21no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—44no—
562C22×C3—44no—
563C22×C3—64no—
564C22×C3—124no—
565C22×C3—124no—
566C22×C3—124no—
567C22×C3C2×(C2×D3)⋊C411yescharacteristic
568C22×C3C2×(C2×D3)⋊C412yes—
569C22×C3C2×(C2×D3)⋊C412yes—
570C22×C3C2×(C2×D3)⋊C411yescharacteristic
571C22×C3C2×C3×C22⋊C411yescharacteristic
572C22×C3C2×C3×C22⋊C412yes—
573C22×C3C2×C3×C22⋊C412yes—
574C22×C3C2×C3×C22⋊C411yescharacteristic
575C22×C3C22×C4×D311yescharacteristic
576C22×C3C23×C3×C411yescharacteristic
577C2×D3—24no—
578C2×D3—44no—
579C2×D3—44no—
580C2×D3—44no—
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—64no—
588C3×C4C2×(C2×D3)⋊C412yes—
589C3×C4C2×(C2×D3)⋊C412yes—
590C3×C4C2×(C2×D3)⋊C411yescharacteristic
591C3×C4C2×(C2×D3)⋊C411yescharacteristic
592C3×C4C2×C3×C22⋊C411yescharacteristic
593C3×C4C2×C3×C22⋊C411yescharacteristic
594C3×C4C2×C3×C22⋊C412yes—
595C3×C4C2×C3×C22⋊C412yes—
596C3×C4C22×D1211yescharacteristic
597C3×C4C22×#6711yescharacteristic
598C3×C4C22×C3×D411yescharacteristic
599C3×C4C22×C3×D411yescharacteristic
600Dic3—24no—
601C32C2×#41311yescharacteristic, complemented, Sylow
602C23—34no—
603C23—42no—
604C23—62no—
605C23—62no—
606C23—124no—
607C23C3×(C2×D3)⋊C411yescharacteristic
608C23C3×(C2×D3)⋊C411yescharacteristic
609C23C3×(C2×D3)⋊C412yes—
610C23C2×C3×C4×D311yescharacteristic
611C23C2×C3×C4×D312yes—
612Q8—62no—
613Q8—62no—
614Q8—62no—
615Q8—62no—
616D4—68no—
617D4—68no—
618D4—62no—
619D4—62no—
620D4—62no—
621D4—62no—
622C2×C4—34no—
623C2×C4—62no—
624C2×C4—62no—
625C2×C4—68no—
626C2×C4—68no—
627C2×C4C3×(C2×D3)⋊C412yes—
628C2×C4C3×(C2×D3)⋊C411yescharacteristic
629C2×C4C3×(C2×D3)⋊C411yescharacteristic
630C2×C4C3×(C2×D3)⋊C412yes—
631C2×C4C3×(C2×D3)⋊C412yes—
632C2×C4C3×(C2×D3)⋊C412yes—
633C2×C4C3×(C2×D3)⋊C412yes—
634C2×C4C2×C3×C4×D312yes—
635C2×C4C2×C3×C4×D311yescharacteristic
636C2×C4C2×C3×D1211yescharacteristic
637C2×C4C2×C3×D1212yes—
638C2×C4C2×C3×D1211yescharacteristic
639C2×C4C2×C3×D1212yes—
640C2×C4C2×C3×#6711yescharacteristic
641C2×C4C2×C3×#6712yes—
642C2×C4C2×C3×#6711yescharacteristic
643C2×C4C2×C3×#6712yes—
644C2×C4C23×C3×D311yescharacteristic
645C8—24no—
646C8—64no—
647C2×C3—24no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—22no—
651C2×C3—22no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—22no—
655C2×C3—22no—
656C2×C3—21no—
657C2×C3—22no—
658C2×C3—41no—
659C2×C3—41no—
660C2×C3—42no—
661C2×C3—124no—
662C2×C3#513212yesdirect product factor
663C2×C3C3×#41312yescomplemented
664C2×C3C22×(C2×D3)⋊C411yescharacteristic
665C2×C3C22×C3×C22⋊C411yescharacteristic
666D3—44no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—42no—
671C22—42no—
672C22—64no—
673C22—124no—
674C22—124no—
675C22—124no—
676C22C2×C3×(C2×D3)⋊C411yescharacteristic
677C22C2×C3×(C2×D3)⋊C412yes—
678C22C2×C3×(C2×D3)⋊C412yes—
679C22C2×C3×(C2×D3)⋊C411yescharacteristic
680C22C22×C3×C4×D311yescharacteristic
681C4—64no—
682C4C2×C3×(C2×D3)⋊C412yes—
683C4C2×C3×(C2×D3)⋊C412yes—
684C4C2×C3×(C2×D3)⋊C411yescharacteristic
685C4C2×C3×(C2×D3)⋊C411yescharacteristic
686C4C22×C3×D1211yescharacteristic
687C4C22×C3×#6711yescharacteristic
688C3—21no—
689C3C2×#513211yescharacteristic, direct product factor
690C3C2×C3×#41311yescharacteristic, complemented
691C2—21no—
692C2—21no—
693C2—22no—
694C2—22no—
695C2—124no—
696C2C3×#513212yesdirect product factor
697C2C22×C3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C3×C4(C2×D3)⋊C4
commutatorC22×C3C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC22×C32×M16C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#235C2
cosocleC2×C3×C4C24×C3
hypercenterC22×C3×M16D3
hypocenterC3C2×C3×#413
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C22×C3×M16

Complements

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

NH ≅ G/Ntype
2. C22×C32×M16C2semidirect
3. C22×C3×#208C2semidirect
4. C2×C3×#824C2semidirect
5. C3×#5132C2direct (N × H)
6. C2×C3×#823C2semidirect
8. C2×#5132C3direct (N × H)
25. C2×C32×M16C22semidirect
30. C2×C3×#208C22semidirect
32. C3×#824C22semidirect
33. C3×#823C22semidirect
38. C22×C3×M16D3semidirect
39. C22×C3×M16C2×C3semidirect
40. C22×#208C2×C3semidirect
44. C2×#824C2×C3semidirect
45. #5132C2×C3direct (N × H)
46. C2×#823C2×C3semidirect
139. C2×C3×M16C2×D3semidirect
141. C2×C3×M16C22×C3semidirect
149. C2×#208C22×C3semidirect
153. #824C22×C3semidirect
154. #823C22×C3semidirect
202. C22×M16C3×D3semidirect
365. C2×M16C2×C3×D3semidirect
489. C2×C32#413semidirect
601. C32C2×#413semidirect
662. C2×C3#5132direct (N × H)
663. C2×C3C3×#413semidirect
689. C3C2×#5132direct (N × H)
690. C3C2×C3×#413semidirect
696. C2C3×#5132direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×C32×M162
C22×C3×#2082
C2×C3×#8242
C3×#51322
C2×C3×#8232
C2×C3×#4133
C2×#51323