Finite Group Databasebeta

← C2×C3×#70918 #72227375

Subgroups — C2×C3×#70918 #72227375

Order 2304.

1724 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#5147C211yesmaximal, characteristic
2C2×C3×#4717C211yesmaximal, characteristic, complemented
3C3×#70918C218yesmaximal, direct product factor
4C2×C3×#4487C211yesmaximal, characteristic, complemented
5C2×C3×#4563C211yesmaximal, characteristic, complemented
6C2×C3×#4488C211yesmaximal, characteristic, complemented
7C2×C3×#4466C211yesmaximal, characteristic, complemented
8C2×C32×#442C211yesmaximal, characteristic, complemented
9C2×#70918C311yesmaximal, characteristic, direct product factor
10C2×C3×AGL(1,ℤ/16)—31nomaximal
11C22×C32×D8C2211yescharacteristic
12C2×C32×C4×D4—21no—
13C2×C3×#904C2211yescharacteristic
14C2×C3×#901—21no—
15C32×#442—22no—
16C32×#442C2214yescomplemented
17C2×C32×#106C2211yescharacteristic
18C2×C32×#102—21no—
19C2×C32×#97C2211yescharacteristic
20C2×C3×#827C412yescomplemented
21C3×#5147C414yescomplemented
22C3×#5147C2214yes—
23C2×C3×#826C412yescomplemented
24C2×C3×#819C2211yescharacteristic
25C2×C3×#812C2211yescharacteristic
26C2×C3×#812C2211yescharacteristic
27C2×C3×#805—21no—
28C3×#4717—22no—
29C3×#4717C2214yescomplemented
30C3×#4563C2214yescomplemented
31C3×#4488C2214yescomplemented
32C3×#4487C2214yescomplemented
33C3×#4466C2214yescomplemented
34C2×C3×#509—31no—
35C2×C3×#444—31no—
36C2×C3×#442—21no—
37C2×C3×#442D311yescharacteristic, complemented
38C2×C3×#442C2×C311yescharacteristic, complemented
39C2×#5147C2×C311yescharacteristic
40C2×#4717C2×C311yescharacteristic, complemented
41C3×AGL(1,ℤ/16)—38no—
42C2×C3×#365—31no—
43C2×C3×#361—31no—
44C2×C3×#360—31no—
45C2×C3×#347—31no—
46C2×#4563C2×C311yescharacteristic, complemented
47#70918C2×C318yesdirect product factor
48C2×#4488C2×C311yescharacteristic, complemented
49C2×#4487C2×C311yescharacteristic, complemented
50C2×#4466C2×C311yescharacteristic, complemented
51C22×C32×D4—21no—
52C23×C32×C4—41no—
53C2×C3×#235—21no—
54C2×C32×D8—21no—
55C2×C32×D8—21no—
56C2×C32×D8—21no—
57C2×C32×D8C2×C412yes—
58C2×C32×D8C2×C412yes—
59C2×C32×D8C2312yes—
60C22×C32×C8D411yescharacteristic
61C22×C32×C8C2311yescharacteristic
62C32×C4×D4—24no—
63C32×C4×D4—42no—
64C2×C32×C4⋊C4—21no—
65C2×C32×C22⋊C4—41no—
66C2×C32×C42D411yescharacteristic
67C2×C3×#208—21no—
68C2×C3×Dic12C2×C411yescharacteristic, complemented
69C3×#904—21no—
70C3×#904—21no—
71C3×#904C2×C412yescomplemented
72C3×#904C2312yes—
73C2×C3×D24C2×C411yescharacteristic, complemented
74C2×C3×#204—21no—
75C3×#901—24no—
76C3×#901—42no—
77C2×C3×ΓL(1,𝔽25)—41no—
78C2×C3×D3×C8—41no—
79C32×#106—21no—
80C32×#106C2312yes—
81C32×#102—24no—
82C32×#97D412yes—
83C32×#97C2312yes—
84C3×#827C2×C418yescomplemented
85C3×#826C2×C418yescomplemented
86C3×#819—21no—
87C3×#819C2312yes—
88C3×#812—21no—
89C3×#812C2×C412yescomplemented
90C3×#812C2312yes—
91C3×#812C2312yes—
92C2×C3×C3⋊C16—21no—
93C2×C3×C3⋊C16C2×C412yescomplemented
94C3×#805—24no—
95C2×AGL(1,ℤ/16)—31noSylow
96C2×C3×#135—31no—
97C22×C3×D8—21no—
98C22×C3×D8C2×D311yescharacteristic
99C22×C3×D8C22×C311yescharacteristic
100C2×C3×#131—61no—
101C2×C3×C4×D4—22no—
102C2×C3×C4×D4—21no—
103C2×C3×C4×D4—21no—
104C2×#904C22×C311yescharacteristic
105C2×#901—21no—
106C3×#509—34no—
107C3×#509—34no—
108C2×C3×SD32—32no—
109C2×C3×D16—32no—
110C2×C3×M32—31no—
111C2×C3×M32—31no—
112C3×#444—34no—
113C3×#444—62no—
114C3×#442—24no—
115C3×#442—24no—
116C3×#442—22no—
117C3×#442—22no—
118C3×#442C2×D314yescomplemented
119C3×#442C22×C314yescomplemented
120C2×C3×#108—31no—
121C2×C3×#106—21no—
122C2×C3×#106C2×D311yescharacteristic
123C2×C3×#106C22×C311yescharacteristic
124C2×C3×#104—61no—
125C2×C3×#102—22no—
126C2×C3×#102—21no—
127C2×C3×#102—21no—
128C2×C3×#97—21no—
129C2×C3×#97C2×D311yescharacteristic
130C2×C3×#97C22×C311yescharacteristic
131C2×#827C3×C412yescomplemented
132#5147C3×C414yescomplemented
133#5147C22×C314yes—
134C2×#826C3×C412yescomplemented
135C2×#819C22×C311yescharacteristic
136C2×#812C22×C311yescharacteristic
137C2×#812C22×C311yescharacteristic
138C2×#805—21no—
139#4717—22no—
140#4717C22×C314yescomplemented
141C3×#365—34no—
142C3×#361—34no—
143C3×#360—34no—
144C3×#347—34no—
145#4563C22×C314yescomplemented
146#4488C22×C314yescomplemented
147#4487C22×C314yescomplemented
148#4466C22×C314yescomplemented
149C24×C32—41no—
150C2×C32×D4—22no—
151C2×C32×D4—22no—
152C2×C32×D4—22no—
153C2×C32×D4—41no—
154C2×C32×D4—41no—
155C2×C32×D4—41no—
156C22×C32×C4—21no—
157C22×C32×C4—44no—
158C22×C32×C4—41no—
159C22×C32×C4—84no—
160C22×C32×C4C2×D411yescharacteristic
161C2×C3×#67—41no—
162C3×#235—22no—
163C3×#235—22no—
164C3×#235—41no—
165C3×#235—41no—
166C2×C3×D12—21no—
167C2×C3×C4×D3—41no—
168C2×C3×Dic6—21no—
169C32×D8—22no—
170C32×D8—22no—
171C32×D8—22no—
172C32×D8C22×C414yes—
173C2×C32×C8—21no—
174C2×C32×C8—21no—
175C2×C32×C8C22×C411yescharacteristic
176C2×C32×C8C22×C411yescharacteristic
177C2×C32×C8C2×D412yes—
178C2×C32×C8C2×D411yescharacteristic
179C2×C32×C8#4111yescharacteristic
180C2×C32×C8#4111yescharacteristic
181C2×C32×C8C2411yescharacteristic
182C32×C4⋊C4—22no—
183C32×C4⋊C4—41no—
184C32×C22⋊C4—44no—
185C32×C42—21no—
186C32×C42C2×D412yes—
187C3×#208—22no—
188C3×#208—41no—
189C2×C3×C3⋊C8—41no—
190C3×Dic12—21no—
191C3×Dic12C22×C412yescomplemented
192C3×D24—21no—
193C3×D24C22×C412yescomplemented
194C3×#204—22no—
195C3×#204—22no—
196C3×ΓL(1,𝔽25)—44no—
197C3×D3×C8—44no—
198C3×C3⋊C16—22no—
199C3×C3⋊C16C22×C414yescomplemented
200C2×#509—31no—
201C2×#444—31no—
202C2×#442C3×D311yescharacteristic, complemented
203AGL(1,ℤ/16)—38no—
204C2×#365—31no—
205C2×#361—31no—
206C2×#360—31no—
207C2×#347—31no—
208C2×C3×#41—61no—
209C22×C3×D4—22no—
210C22×C3×D4—21no—
211C22×C3×D4—21no—
212C23×C3×C4—42no—
213C23×C3×C4—41no—
214C23×C3×C4—41no—
215C2×#235—21no—
216C3×#135—32no—
217C3×#135—32no—
218C3×#135—61no—
219C3×#135—61no—
220C2×C3×Q16—31no—
221C2×C3×SD16—61no—
222C2×C3×D8—22no—
223C2×C3×D8—22no—
224C2×C3×D8—22no—
225C2×C3×D8—21no—
226C2×C3×D8—21no—
227C2×C3×D8—21no—
228C2×C3×D8—21no—
229C2×C3×D8—21no—
230C2×C3×D8—21no—
231C2×C3×D8—22no—
232C2×C3×D8—22no—
233C2×C3×D8—22no—
234C2×C3×D8—31no—
235C2×C3×D8C4×D312yes—
236C2×C3×D8C4×D312yes—
237C2×C3×D8C2×C3×C412yes—
238C2×C3×D8C2×C3×C412yes—
239C2×C3×D8C22×D312yes—
240C2×C3×D8C23×C312yes—
241C3×#131—64no—
242C3×#131—122no—
243C2×C3×M16—61no—
244C2×C3×M16—121no—
245C22×C3×C8—21no—
246C22×C3×C8—21no—
247C22×C3×C8—121no—
248C22×C3×C8#6711yescharacteristic
249C22×C3×C8C3×D411yescharacteristic
250C22×C3×C8C22×D311yescharacteristic
251C22×C3×C8C23×C311yescharacteristic
252C3×C4×D4—28no—
253C3×C4×D4—24no—
254C3×C4×D4—24no—
255C3×C4×D4—44no—
256C3×C4×D4—42no—
257C3×C4×D4—42no—
258C2×C3×C4⋊C4—22no—
259C2×C3×C4⋊C4—21no—
260C2×C3×C4⋊C4—21no—
261C2×C3×C22⋊C4—42no—
262C2×C3×C22⋊C4—41no—
263C2×C3×C22⋊C4—41no—
264C2×C3×C42—21no—
265C2×C3×C42#6711yescharacteristic
266C2×C3×C42C3×D411yescharacteristic
267C2×#208—21no—
268C2×Dic12C2×C3×C411yescharacteristic, complemented
269#904—21no—
270#904—21no—
271#904C2×C3×C412yescomplemented
272#904C23×C312yes—
273C2×D24C2×C3×C411yescharacteristic, complemented
274C2×#204—21no—
275#901—24no—
276#901—42no—
277C2×ΓL(1,𝔽25)—41no—
278C2×D3×C8—41no—
279C3×SD32—38no—
280C3×D16—38no—
281C3×M32—32no—
282C3×M32—32no—
283C3×M32—32no—
284C3×M32—61no—
285C2×C3×C16—32no—
286C2×C3×C16—61no—
287C3×#108—32no—
288C3×#108—61no—
289C3×#106—22no—
290C3×#106—21no—
291C3×#106—21no—
292C3×#106—22no—
293C3×#106C22×D312yes—
294C3×#106C23×C312yes—
295C3×#104—64no—
296C3×#102—28no—
297C3×#102—24no—
298C3×#102—24no—
299C3×#97—22no—
300C3×#97—22no—
301C3×#97#6712yes—
302C3×#97C3×D412yes—
303C3×#97C22×D312yes—
304C3×#97C23×C312yes—
305#827C2×C3×C418yescomplemented
306#826C2×C3×C418yescomplemented
307#819—21no—
308#819C23×C312yes—
309#812—21no—
310#812C2×C3×C412yescomplemented
311#812C23×C312yes—
312#812C23×C312yes—
313C2×C3⋊C16—21no—
314C2×C3⋊C16C2×C3×C412yescomplemented
315#805—24no—
316C23×C32—42no—
317C23×C32—42no—
318C23×C32—42no—
319C23×C32—82no—
320C23×C32—82no—
321C23×C32AGL(1,ℤ/8)11yescharacteristic
322C22×C3×D3—41no—
323C32×D4—24no—
324C32×D4—42no—
325C32×D4—42no—
326C32×D4—42no—
327C2×C32×C4—22no—
328C2×C32×C4—42no—
329C2×C32×C4—42no—
330C2×C32×C4—88no—
331C2×C32×C4—82no—
332C2×C32×C4C4×D411yescharacteristic
333C2×C32×C4C4×D411yescharacteristic
334C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
335C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
336C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
337C2×C32×C4C22×D411yescharacteristic
338C3×#67—42no—
339C3×#67—42no—
340C2×C3×Dic3—41no—
341C3×D12—22no—
342C3×D12—41no—
343C3×C4×D3—42no—
344C3×C4×D3—42no—
345C3×Dic6—22no—
346C3×Dic6—41no—
347C32×C8—22no—
348C32×C8C4×D411yescharacteristic
349C32×C8C4×D411yescharacteristic
350C32×C8C23×C411yescharacteristic
351C32×C8C2×#4111yescharacteristic
352C3×C3⋊C8—42no—
353C2×#135—31no—
354C22×D8C2×C3×D311yescharacteristic
355C2×#131—61no—
356C2×C4×D4—21no—
357#509—34no—
358#509—34no—
359C2×SD32—32no—
360C2×D16—32no—
361C2×M32—31no—
362C2×M32—31no—
363#444—34no—
364#444—62no—
365#442—22no—
366#442C2×C3×D314yescomplemented
367C2×#108—31no—
368C2×#106C2×C3×D311yescharacteristic
369C2×#104—61no—
370C2×#102—21no—
371C2×#97C2×C3×D311yescharacteristic
372#365—34no—
373#361—34no—
374#360—34no—
375#347—34no—
376C24×C3—42no—
377C24×C3—41no—
378C24×C3—41no—
379C3×#41—62no—
380C3×#41—62no—
381C3×#41—121no—
382C3×#41—121no—
383C2×C3×Q8—61no—
384C2×C3×D4—24no—
385C2×C3×D4—24no—
386C2×C3×D4—24no—
387C2×C3×D4—22no—
388C2×C3×D4—22no—
389C2×C3×D4—22no—
390C2×C3×D4—22no—
391C2×C3×D4—22no—
392C2×C3×D4—22no—
393C2×C3×D4—42no—
394C2×C3×D4—42no—
395C2×C3×D4—42no—
396C2×C3×D4—41no—
397C2×C3×D4—41no—
398C2×C3×D4—41no—
399C2×C3×D4—41no—
400C2×C3×D4—41no—
401C2×C3×D4—41no—
402C2×C3×D4—61no—
403C2×C3×D4—121no—
404C22×C3×C4—22no—
405C22×C3×C4—21no—
406C22×C3×C4—21no—
407C22×C3×C4—21no—
408C22×C3×C4—48no—
409C22×C3×C4—44no—
410C22×C3×C4—44no—
411C22×C3×C4—42no—
412C22×C3×C4—41no—
413C22×C3×C4—41no—
414C22×C3×C4—88no—
415C22×C3×C4—84no—
416C22×C3×C4—84no—
417C22×C3×C4—121no—
418C22×C3×C4C2×#6711yescharacteristic
419C22×C3×C4C2×C3×D411yescharacteristic
420C2×#67—41no—
421#235—22no—
422#235—22no—
423#235—41no—
424#235—41no—
425C2×D12—21no—
426C2×C4×D3—41no—
427C2×Dic6—21no—
428C3×Q16—32no—
429C3×Q16—61no—
430C3×SD16—62no—
431C3×SD16—62no—
432C3×D8—24no—
433C3×D8—24no—
434C3×D8—24no—
435C3×D8—22no—
436C3×D8—22no—
437C3×D8—22no—
438C3×D8—22no—
439C3×D8—22no—
440C3×D8—22no—
441C3×D8—24no—
442C3×D8—32no—
443C3×D8—61no—
444C3×D8C2×C4×D314yes—
445C3×D8C22×C3×C414yes—
446C3×M16—62no—
447C3×M16—124no—
448C3×M16—121no—
449C2×C3×C8—21no—
450C2×C3×C8—21no—
451C2×C3×C8—21no—
452C2×C3×C8—21no—
453C2×C3×C8—21no—
454C2×C3×C8—21no—
455C2×C3×C8—21no—
456C2×C3×C8—21no—
457C2×C3×C8—21no—
458C2×C3×C8—21no—
459C2×C3×C8—22no—
460C2×C3×C8—41no—
461C2×C3×C8—41no—
462C2×C3×C8—124no—
463C2×C3×C8—121no—
464C2×C3×C8C2×C4×D311yescharacteristic
465C2×C3×C8C2×C4×D311yescharacteristic
466C2×C3×C8#23511yescharacteristic
467C2×C3×C8#23511yescharacteristic
468C2×C3×C8C2×#6712yes—
469C2×C3×C8C2×#6711yescharacteristic
470C2×C3×C8C22×C3×C411yescharacteristic
471C2×C3×C8C22×C3×C411yescharacteristic
472C2×C3×C8C2×C3×D412yes—
473C2×C3×C8C2×C3×D411yescharacteristic
474C2×C3×C8C3×#4111yescharacteristic
475C2×C3×C8C3×#4111yescharacteristic
476C2×C3×C8C23×D311yescharacteristic
477C2×C3×C8C24×C311yescharacteristic
478C3×C4⋊C4—24no—
479C3×C4⋊C4—22no—
480C3×C4⋊C4—22no—
481C3×C4⋊C4—42no—
482C3×C4⋊C4—41no—
483C3×C4⋊C4—41no—
484C3×C22⋊C4—48no—
485C3×C22⋊C4—44no—
486C3×C22⋊C4—44no—
487C3×C42—22no—
488C3×C42—21no—
489C3×C42—21no—
490C3×C42—22no—
491C3×C42C2×#6712yes—
492C3×C42C2×C3×D412yes—
493#208—22no—
494#208—41no—
495C2×C3⋊C8—41no—
496Dic12—21no—
497Dic12C22×C3×C412yescomplemented
498D24—21no—
499D24C22×C3×C412yescomplemented
500#204—22no—
501#204—22no—
502ΓL(1,𝔽25)—44no—
503D3×C8—44no—
504C3×C16—34no—
505C3×C16—62no—
506C3⋊C16—22no—
507C3⋊C16C22×C3×C414yescomplemented
508C22×C32—22no—
509C22×C32—44no—
510C22×C32—82no—
511C22×C32—82no—
512C22×C32—84no—
513C22×C32—84no—
514C22×C32#44211yescharacteristic
515C22×C32#44211yescharacteristic
516C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
517C2×C3×D3—42no—
518C2×C3×D3—82no—
519C32×C4—42no—
520C32×C4—82no—
521C32×C4#44211yescharacteristic
522C32×C4#44211yescharacteristic
523C32×C4C2×C4×D411yescharacteristic
524C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
525C3×Dic3—42no—
526C2×#41—61no—
527C22×D4—21no—
528C23×C4—41no—
529#135—32no—
530#135—32no—
531#135—61no—
532#135—61no—
533C2×Q16—31no—
534C2×SD16—61no—
535C2×D8—21no—
536C2×D8—21no—
537C2×D8—21no—
538C2×D8—31no—
539C2×D8C3×C4×D312yes—
540C2×D8C3×C4×D312yes—
541C2×D8C22×C3×D312yes—
542#131—64no—
543#131—122no—
544C2×M16—61no—
545C2×M16—121no—
546C22×C8—121no—
547C22×C8C3×#6711yescharacteristic
548C22×C8C22×C3×D311yescharacteristic
549C4×D4—24no—
550C4×D4—42no—
551C2×C4⋊C4—21no—
552C2×C22⋊C4—41no—
553C2×C42C3×#6711yescharacteristic
554SD32—38no—
555D16—38no—
556M32—32no—
557M32—32no—
558M32—32no—
559M32—61no—
560C2×C16—32no—
561C2×C16—61no—
562#108—32no—
563#108—61no—
564#106—21no—
565#106C22×C3×D312yes—
566#104—64no—
567#102—24no—
568#97C3×#6712yes—
569#97C22×C3×D312yes—
570C23×C3—21no—
571C23×C3—44no—
572C23×C3—44no—
573C23×C3—44no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—42no—
577C23×C3—42no—
578C23×C3—42no—
579C23×C3—42no—
580C23×C3—84no—
581C23×C3—82no—
582C23×C3—82no—
583C23×C3—84no—
584C23×C3—82no—
585C23×C3—82no—
586C23×C3—121no—
587C23×C3#93211yescharacteristic
588C23×C3C3×AGL(1,ℤ/8)11yescharacteristic
589C22×D3—41no—
590C3×Q8—62no—
591C3×Q8—121no—
592C3×D4—28no—
593C3×D4—24no—
594C3×D4—24no—
595C3×D4—44no—
596C3×D4—44no—
597C3×D4—44no—
598C3×D4—42no—
599C3×D4—42no—
600C3×D4—42no—
601C3×D4—42no—
602C3×D4—42no—
603C3×D4—42no—
604C3×D4—62no—
605C3×D4—122no—
606C3×D4—122no—
607C3×D4—121no—
608C2×C3×C4—24no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—44no—
618C2×C3×C4—42no—
619C2×C3×C4—42no—
620C2×C3×C4—44no—
621C2×C3×C4—42no—
622C2×C3×C4—42no—
623C2×C3×C4—816no—
624C2×C3×C4—88no—
625C2×C3×C4—88no—
626C2×C3×C4—84no—
627C2×C3×C4—82no—
628C2×C3×C4—82no—
629C2×C3×C4—121no—
630C2×C3×C4—122no—
631C2×C3×C4—122no—
632C2×C3×C4C4×#6711yescharacteristic
633C2×C3×C4C4×#6711yescharacteristic
634C2×C3×C4#93211yescharacteristic
635C2×C3×C4#94911yescharacteristic
636C2×C3×C4#94911yescharacteristic
637C2×C3×C4C3×C4×D411yescharacteristic
638C2×C3×C4C3×C4×D411yescharacteristic
639C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
640C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
641C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
642C2×C3×C4C22×#6711yescharacteristic
643C2×C3×C4C22×C3×D411yescharacteristic
644#67—42no—
645#67—42no—
646C2×Dic3—41no—
647D12—22no—
648D12—41no—
649C4×D3—42no—
650C4×D3—42no—
651Dic6—22no—
652Dic6—41no—
653C3×C8—22no—
654C3×C8—22no—
655C3×C8—21no—
656C3×C8—21no—
657C3×C8—21no—
658C3×C8—21no—
659C3×C8—42no—
660C3×C8—122no—
661C3×C8C4×#6711yescharacteristic
662C3×C8C4×#6711yescharacteristic
663C3×C8C3×C4×D411yescharacteristic
664C3×C8C3×C4×D411yescharacteristic
665C3×C8C22×C4×D311yescharacteristic
666C3×C8C2×#23511yescharacteristic
667C3×C8C23×C3×C411yescharacteristic
668C3×C8C2×C3×#4111yescharacteristic
669C3⋊C8—42no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—84no—
673C2×C32AGL(1,ℤ/16)12yescomplemented
674C2×C32C2×#44211yescharacteristic
675C3×D3—82no—
676C24—41no—
677#41—62no—
678#41—62no—
679#41—121no—
680#41—121no—
681C2×Q8—61no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—61no—
689C2×D4—121no—
690C22×C4—21no—
691C22×C4—44no—
692C22×C4—41no—
693C22×C4—84no—
694C22×C4—121no—
695C22×C4C2×C3×#6711yescharacteristic
696Q16—32no—
697Q16—61no—
698SD16—62no—
699SD16—62no—
700D8—22no—
701D8—22no—
702D8—22no—
703D8—32no—
704D8—61no—
705D8C2×C3×C4×D314yes—
706M16—62no—
707M16—124no—
708M16—121no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—124no—
712C2×C8—121no—
713C2×C8C2×C3×C4×D311yescharacteristic
714C2×C8C2×C3×C4×D311yescharacteristic
715C2×C8C3×#23511yescharacteristic
716C2×C8C3×#23511yescharacteristic
717C2×C8C2×C3×#6712yes—
718C2×C8C2×C3×#6711yescharacteristic
719C2×C8C23×C3×D311yescharacteristic
720C4⋊C4—22no—
721C4⋊C4—41no—
722C22⋊C4—44no—
723C42—21no—
724C42C2×C3×#6712yes—
725C16—34no—
726C16—62no—
727C22×C3—24no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—48no—
734C22×C3—44no—
735C22×C3—44no—
736C22×C3—84no—
737C22×C3—82no—
738C22×C3—82no—
739C22×C3—84no—
740C22×C3—88no—
741C22×C3—82no—
742C22×C3—84no—
743C22×C3—82no—
744C22×C3—84no—
745C22×C3—88no—
746C22×C3—84no—
747C22×C3—84no—
748C22×C3—122no—
749C22×C3—242no—
750C22×C3#501411yescharacteristic
751C22×C3#501411yescharacteristic
752C22×C3C3×#44211yescharacteristic
753C22×C3C3×#44211yescharacteristic
754C22×C3C2×#93211yescharacteristic
755C22×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
756C2×D3—42no—
757C2×D3—82no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—44no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4—84no—
766C3×C4—82no—
767C3×C4—82no—
768C3×C4—122no—
769C3×C4#501411yescharacteristic
770C3×C4#501411yescharacteristic
771C3×C4C3×#44211yescharacteristic
772C3×C4C3×#44211yescharacteristic
773C3×C4C2×C4×#6711yescharacteristic
774C3×C4C2×#94911yescharacteristic
775C3×C4C2×C3×C4×D411yescharacteristic
776C3×C4C2×C3×AGL(1,ℤ/8)11yescharacteristic
777Dic3—42no—
778C32C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
779C23—42no—
780C23—42no—
781C23—42no—
782C23—82no—
783C23—82no—
784C23—121no—
785C23C3×#93211yescharacteristic
786Q8—62no—
787Q8—121no—
788D4—24no—
789D4—42no—
790D4—42no—
791D4—42no—
792D4—62no—
793D4—122no—
794D4—122no—
795D4—121no—
796C2×C4—22no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—88no—
800C2×C4—82no—
801C2×C4—121no—
802C2×C4—122no—
803C2×C4—122no—
804C2×C4C3×C4×#6711yescharacteristic
805C2×C4C3×C4×#6711yescharacteristic
806C2×C4C3×#93211yescharacteristic
807C2×C4C3×#94911yescharacteristic
808C2×C4C3×#94911yescharacteristic
809C2×C4C22×C3×#6711yescharacteristic
810C8—22no—
811C8—122no—
812C8C3×C4×#6711yescharacteristic
813C8C3×C4×#6711yescharacteristic
814C8C22×C3×C4×D311yescharacteristic
815C8C2×C3×#23511yescharacteristic
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—22no—
824C2×C3—88no—
825C2×C3—84no—
826C2×C3—84no—
827C2×C3—242no—
828C2×C3#7091812yesdirect product factor
829C2×C3C3×AGL(1,ℤ/16)12yescomplemented
830C2×C3C2×#501411yescharacteristic
831C2×C3C2×C3×#44211yescharacteristic
832D3—82no—
833C22—22no—
834C22—44no—
835C22—82no—
836C22—82no—
837C22—84no—
838C22—84no—
839C22—122no—
840C22—242no—
841C22C3×#501411yescharacteristic
842C22C3×#501411yescharacteristic
843C22C2×C3×#93211yescharacteristic
844C4—42no—
845C4—82no—
846C4—122no—
847C4C3×#501411yescharacteristic
848C4C3×#501411yescharacteristic
849C4C2×C3×C4×#6711yescharacteristic
850C4C2×C3×#94911yescharacteristic
851C3—21no—
852C3C2×C3×AGL(1,ℤ/16)11yescharacteristic, complemented
853C3C2×#7091811yescharacteristic, direct product factor
854C2—21no—
855C2—21no—
856C2—84no—
857C2—242no—
858C2C3×#7091812yesdirect product factor
859C2C2×C3×#501411yescharacteristic
subgroupG/H
centerC22×C3#5014
commutatorC3×C8C23×C3×C4
FrattiniC2×C8C23×C3×D3
FittingC2×C32×#442C2
socleC22×C32#442
prime radicalC2×C3×#5147C2
cosocleC2×C3×C8C24×C3
hypercenterC2×C3×#442D3
hypocenterC3C2×C3×AGL(1,ℤ/16)
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#97 ◁ C2×C3×#442

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4717C2semidirect
3. C3×#70918C2direct (N × H)
4. C2×C3×#4487C2semidirect
5. C2×C3×#4563C2semidirect
6. C2×C3×#4488C2semidirect
7. C2×C3×#4466C2semidirect
8. C2×C32×#442C2semidirect
9. C2×#70918C3direct (N × H)
16. C32×#442C22semidirect
20. C2×C3×#827C4semidirect
21. C3×#5147C4semidirect
23. C2×C3×#826C4semidirect
29. C3×#4717C22semidirect
30. C3×#4563C22semidirect
31. C3×#4488C22semidirect
32. C3×#4487C22semidirect
33. C3×#4466C22semidirect
37. C2×C3×#442D3semidirect
38. C2×C3×#442C2×C3semidirect
40. C2×#4717C2×C3semidirect
46. C2×#4563C2×C3semidirect
47. #70918C2×C3direct (N × H)
48. C2×#4488C2×C3semidirect
49. C2×#4487C2×C3semidirect
50. C2×#4466C2×C3semidirect
68. C2×C3×Dic12C2×C4semidirect
71. C3×#904C2×C4semidirect
73. C2×C3×D24C2×C4semidirect
84. C3×#827C2×C4semidirect
85. C3×#826C2×C4semidirect
89. C3×#812C2×C4semidirect
93. C2×C3×C3⋊C16C2×C4semidirect
118. C3×#442C2×D3semidirect
119. C3×#442C22×C3semidirect
131. C2×#827C3×C4semidirect
132. #5147C3×C4semidirect
134. C2×#826C3×C4semidirect
140. #4717C22×C3semidirect
145. #4563C22×C3semidirect
146. #4488C22×C3semidirect
147. #4487C22×C3semidirect
148. #4466C22×C3semidirect
191. C3×Dic12C22×C4semidirect
193. C3×D24C22×C4semidirect
199. C3×C3⋊C16C22×C4semidirect
202. C2×#442C3×D3semidirect
268. C2×Dic12C2×C3×C4semidirect
271. #904C2×C3×C4semidirect
273. C2×D24C2×C3×C4semidirect
305. #827C2×C3×C4semidirect
306. #826C2×C3×C4semidirect
310. #812C2×C3×C4semidirect
314. C2×C3⋊C16C2×C3×C4semidirect
366. #442C2×C3×D3semidirect
497. Dic12C22×C3×C4semidirect
499. D24C22×C3×C4semidirect
507. C3⋊C16C22×C3×C4semidirect
673. C2×C32AGL(1,ℤ/16)semidirect
778. C32C2×AGL(1,ℤ/16)semidirect
828. C2×C3#70918direct (N × H)
829. C2×C3C3×AGL(1,ℤ/16)semidirect
852. C3C2×C3×AGL(1,ℤ/16)semidirect
853. C3C2×#70918direct (N × H)
858. C2C3×#70918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#51472
C2×C3×#47172
C3×#709182
C2×C3×#44872
C2×C3×#45632
C2×C3×#44882
C2×C3×#44662
C2×C32×#4422
C2×#709183
C2×C3×AGL(1,ℤ/16)3