Finite Group Databasebeta

← C4×D3×#216 #11859938

Subgroups — C4×D3×#216 #11859938

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×Q8C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic
3C4×D3×Dic6C211yesmaximal, characteristic
4C4×#3756C211yesmaximal, characteristic, complemented
5C3×C4×#216C211yesmaximal, characteristic, complemented
6Dic3×#216C211yesmaximal, characteristic, complemented
7D3×#835C211yesmaximal, characteristic
8#10591537C211yesmaximal, characteristic, complemented
9D3×#810C211yesmaximal, characteristic
10D3×#807C211yesmaximal, characteristic
11#10590481C211yesmaximal, characteristic, complemented
12#10590476C211yesmaximal, characteristic, complemented
13C4×#3719C211yesmaximal, characteristic, complemented
14C4×#3718C211yesmaximal, characteristic, complemented
15C4×D3×C3⋊C8C211yesmaximal, characteristic
16C2×C4×#216—31nomaximal
17C4×D3×Q16—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×D3×C4⋊C4—21no—
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887—21no—
28C3×#887C2211yescharacteristic
29C3×C42×D3—21no—
30C3×C42×D3C2211yescharacteristic
31C3×C4×Dic6—21no—
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34D3×#216C418yesdirect product factor
35C4×#627—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37D3×Dic3⋊C4—21no—
38C4×D3×Dic3—21no—
39#63844C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41#63837—21no—
42C2×#3719C2211yescharacteristic
43C2×#3718C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63637C2211yescharacteristic
48#63634C2211yescharacteristic
49C4×C3⋊(C3⋊C8)C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#807C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63576C2211yescharacteristic
55#63575C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×C3×C4×Q8—31no—
63C22×#216—31no—
64C2×D3×Q16—31no—
65C4×D3×Q8—31no—
66C4×D3×Q8D311yescharacteristic
67C2×C4×Dic6—31no—
68C3×C4×Q16—31no—
69C2×#835—31no—
70Dic3×Q16—31no—
71C4×#216—31no—
72C4×#216—31no—
73C4×#216—31no—
74C4×#216—31no—
75C4×#216—31no—
76C4×#216—31no—
77C4×#216—31no—
78C4×#216—31no—
79C4×#216—31no—
80C4×#216—61no—
81C4×#216D311yescharacteristic, direct product factor
82C2×#810—31no—
83C2×#807—31no—
84C2×C4×C3⋊C8—31no—
85D3×#107—31no—
86#4873—31no—
87D3×#103—31no—
88D3×#103—31no—
89#4790—31no—
90#4790—31no—
91C4×Dic12—31no—
92C4×D3×C8—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8C2×C414yes—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3D411yescharacteristic
100C2×C3×C4×D3D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6C2×C414yes—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114#3756C2×C414yescomplemented
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#216C2×C414yescomplemented
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3D411yescharacteristic
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3719C2×C414yescomplemented
143#3718C2×C414yescomplemented
144D3×C3⋊C8—22no—
145D3×C3⋊C8C2×C414yes—
146C2×C4×Q16—91noSylow
147C22×C3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C22×Dic6—31no—
151C2×C3×Q16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—61no—
158C3×C4×Q8—61no—
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×Q8C2×D311yescharacteristic
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—61no—
163C2×C3×C42—31no—
164C2×C3×C42—61no—
165Q8×Dic3—31no—
166Q8×Dic3C2×D311yescharacteristic
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—38no—
172C2×#216—31no—
173C2×#216—61no—
174C2×#216C2×D311yescharacteristic
175C2×C4⋊Dic3—31no—
176C2×Dic3⋊C4—61no—
177C2×C4×Dic3—61no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180D3×Q16—38no—
181C2×Dic12—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184D3×C4⋊C4—21no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—61no—
187D3×C4⋊C4C2×D311yescharacteristic
188#887—21no—
189#887—31no—
190#887—61no—
191#887C2×D311yescharacteristic
192C42×D3—21no—
193C42×D3—61no—
194C42×D3C2×D311yescharacteristic
195C4×Dic6—21no—
196C4×Dic6—31no—
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C4×Dic6—61no—
202C4×Dic6—61no—
203C4×Dic6—61no—
204C4×Dic6C2×D311yescharacteristic
205C4×Dic6C2×D311yescharacteristic
206C3×#107—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—61no—
216#835C2×D311yescharacteristic
217#818—31no—
218#816—31no—
219#816—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—61no—
228#810C2×D311yescharacteristic
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic
236C4×C3⋊C8—31no—
237C4×C3⋊C8—31no—
238C4×C3⋊C8—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—61no—
241C4×C3⋊C8C2×D311yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C32×Q8—21no—
244C32×Q8C22×C412yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252#634—21no—
253#634C22×C412yes—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—24no—
262C3×C4×D3—22no—
263C3×C4×D3—42no—
264C3×C4×D3Q1614yescomplemented
265C3×C4×D3C22×C412yes—
266C3×C4×D3#4112yes—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—24no—
270C3×Dic6C22×C412yes—
271C3×Dic6C22×C412yes—
272#627—24no—
273D3×Dic3—24no—
274D3×Dic3—42no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)C22×C412yes—
277C3×C3⋊C8—21no—
278C3×C3⋊C8C22×C412yes—
279C22×Q16—91no—
280C2×C4×Q8—31no—
281C2×C4×Q8—91no—
282C4×Q16—31no—
283C4×Q16—91no—
284C4×Q16—91no—
285C4×Q16—91no—
286C4×Q16—91no—
287C4×Q16—91no—
288C4×Q16—91no—
289C4×Q16—91no—
290C2×#107—91no—
291C2×#103—91no—
292C2×#103—91no—
293C2×C4×C8—91no—
294C2×C3×Q8—21no—
295C2×C3×Q8—34no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309D3×Q8—22no—
310D3×Q8—34no—
311D3×Q8—62no—
312D3×Q8C4×D314yes—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3#6711yescharacteristic
318C2×C4×D3#6711yescharacteristic
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—21no—
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—34no—
324C2×Dic6—61no—
325C2×Dic6—62no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C3×Q16—34no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—41no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42—31no—
352C3×C42—41no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359#216—34no—
360#216—34no—
361#216—34no—
362#216—34no—
363#216—34no—
364#216—64no—
365#216C4×D314yesdirect product factor
366C4⋊Dic3—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
396C4×Dic3#6711yescharacteristic
397C4×Dic3#6711yescharacteristic
398C4×Dic3C22×D311yescharacteristic
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—34no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—62no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409Dic12—34no—
410D3×C8—34no—
411D3×C8—62no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3C4×D412yes—
414C2×C3×D3C2×Q1612yes—
415C2×C3×D3#13512yes—
416C32×C4—22no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4C2×Q1612yescomplemented
420C32×C4C23×C411yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—22no—
423C3⋊Dic3—41no—
424C3×Dic3—22no—
425C3×Dic3—22no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3C4×D412yes—
430C3×Dic3C2×Q1612yescomplemented
431C22×Q8—31no—
432C22×Q8—91no—
433C2×Q16—31no—
434C2×Q16—91no—
435C2×Q16—98no—
436C2×Q16—91no—
437C2×Q16—91no—
438C22×C8—91no—
439C22×C8—91no—
440C4×Q8—31no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—61no—
445C4×Q8—61no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×Q8D3211yescharacteristic
452C2×C4⋊C4—31no—
453C2×C4⋊C4—61no—
454C2×C4⋊C4—91no—
455C2×C4⋊C4—181no—
456C2×C42—31no—
457C2×C42—61no—
458C2×C42—181no—
459#107—31no—
460#107—91no—
461#107—91no—
462#107—91no—
463#103—31no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471C4×C8—31no—
472C4×C8—91no—
473C4×C8—91no—
474C4×C8—91no—
475C23×C3—31no—
476C22×D3C2×#6711yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—32no—
481C3×Q8—32no—
482C3×Q8—41no—
483C3×Q8—64no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8C2×C4×D312yes—
487C3×Q8C2×C4×D312yes—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—34no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—62no—
504C2×C3×C4—64no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—64no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—122no—
528C2×Dic3C2×#6711yescharacteristic
529C2×Dic3C2×#6711yescharacteristic
530C2×Dic3C2×#6711yescharacteristic
531C4×D3—24no—
532C4×D3—22no—
533C4×D3—42no—
534C4×D3—64no—
535C4×D3—122no—
536C4×D3#21614yesdirect product factor
537C4×D3C2×C4×D312yes—
538C4×D3#23512yes—
539Dic6—21no—
540Dic6—21no—
541Dic6—24no—
542Dic6—32no—
543Dic6—32no—
544Dic6—62no—
545Dic6—64no—
546Dic6—61no—
547Dic6—61no—
548Dic6—64no—
549Dic6—121no—
550Dic6C2×C4×D312yes—
551Dic6C2×C4×D312yes—
552C3×C8—32no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—32no—
556C3⋊C8—32no—
557C3⋊C8—62no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—121no—
561C3⋊C8C2×C4×D312yes—
562C2×C32C2×C4×D411yescharacteristic
563C2×C32C22×Q1611yescharacteristic
564C2×C32C2×#13511yescharacteristic
565C3×D3C4×Q1614yescomplemented
566C2×Q8—34no—
567C2×Q8—31no—
568C2×Q8—31no—
569C2×Q8—61no—
570C2×Q8—62no—
571C2×Q8—94no—
572C2×Q8—91no—
573C2×Q8—181no—
574C2×Q8—182no—
575C2×Q8C2×D3211yescharacteristic
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—181no—
582C22×C4—181no—
583Q16—34no—
584Q16—94no—
585Q16—94no—
586Q16—94no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—94no—
590C2×C8—91no—
591C2×C8—91no—
592C2×C8—182no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4C2×D3211yescharacteristic
607C42—21no—
608C42—31no—
609C42—31no—
610C42—31no—
611C42—61no—
612C42—61no—
613C42—61no—
614C42—61no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—32no—
622C22×C3—32no—
623C22×C3C2×D3×D411yescharacteristic
624C22×C3C22×#6711yescharacteristic
625C2×D3C4×#6712yes—
626C2×D3C2×#21612yes—
627C2×D3#95012yes—
628C3×C4—21no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—22no—
635C3×C4—32no—
636C3×C4—32no—
637C3×C4—41no—
638C3×C4—42no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—61no—
642C3×C4—62no—
643C3×C4—62no—
644C3×C4—81no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4D3×Q1612yescomplemented
648C3×C4C2×#21612yescomplemented
649C3×C4C22×C4×D311yescharacteristic
650C3×C4C22×C4×D311yescharacteristic
651C3×C4C2×#23511yescharacteristic
652C3×C4D3×#4111yescharacteristic
653Dic3—22no—
654Dic3—22no—
655Dic3—21no—
656Dic3—41no—
657Dic3—41no—
658Dic3—62no—
659Dic3—62no—
660Dic3—122no—
661Dic3—121no—
662Dic3—121no—
663Dic3—241no—
664Dic3C4×#6712yes—
665Dic3C2×#21612yescomplemented
666C32C2×C4×Q1611yescharacteristic, complemented, Sylow
667C23—31no—
668Q8—21no—
669Q8—32no—
670Q8—32no—
671Q8—64no—
672Q8—61no—
673Q8—61no—
674Q8—92no—
675Q8—184no—
676Q8—181no—
677Q8C4×D3212yes—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—32no—
683C2×C4—32no—
684C2×C4—34no—
685C2×C4—31no—
686C2×C4—62no—
687C2×C4—64no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—122no—
693C2×C4—184no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—362no—
697C2×C4D3×#6711yescharacteristic
698C2×C4D3×#6711yescharacteristic
699C2×C4C22×D3211yescharacteristic
700C8—32no—
701C8—61no—
702C8—92no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—34no—
708C2×C3C4×D3×D411yescharacteristic
709C2×C3C2×D3×Q1611yescharacteristic
710C2×C3D3×#13511yescharacteristic
711C2×C3C2×C4×#6711yescharacteristic
712C2×C3C22×#21611yescharacteristic
713C2×C3C2×#95011yescharacteristic
714D3C4×#21614yesdirect product factor
715C22—32no—
716C22—32no—
717C22—32no—
718C22C2×D3×#6711yescharacteristic
719C4—21no—
720C4—22no—
721C4—32no—
722C4—32no—
723C4—41no—
724C4—61no—
725C4—62no—
726C4—62no—
727C4—121no—
728C4—121no—
729C4—182no—
730C4—361no—
731C4D3×#21612yesdirect product factor
732C4C2×C4×D3211yescharacteristic
733C4D3×#23511yescharacteristic
734C3—21no—
735C3C4×D3×Q1611yescharacteristic, complemented
736C3C2×C4×#21611yescharacteristic, complemented
737C2—34no—
738C2C4×D3×#6711yescharacteristic
739C2C2×D3×#21611yescharacteristic
740C2D3×#95011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32C2×C4×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. C4×#3756C2semidirect
5. C3×C4×#216C2semidirect
6. Dic3×#216C2semidirect
8. #10591537C2semidirect
11. #10590481C2semidirect
12. #10590476C2semidirect
13. C4×#3719C2semidirect
14. C4×#3718C2semidirect
34. D3×#216C4direct (N × H)
81. C4×#216D3direct (N × H)
114. #3756C2×C4semidirect
120. C3×#216C2×C4semidirect
142. #3719C2×C4semidirect
143. #3718C2×C4semidirect
264. C3×C4×D3Q16semidirect
365. #216C4×D3direct (N × H)
419. C32×C4C2×Q16semidirect
430. C3×Dic3C2×Q16semidirect
536. C4×D3#216direct (N × H)
565. C3×D3C4×Q16semidirect
647. C3×C4D3×Q16semidirect
648. C3×C4C2×#216semidirect
665. Dic3C2×#216semidirect
666. C32C2×C4×Q16semidirect
714. D3C4×#216direct (N × H)
731. C4D3×#216direct (N × H)
735. C3C4×D3×Q16semidirect
736. C3C2×C4×#216semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
C2×D3×#2162
C4×D3×Dic62
C4×#37562
C3×C4×#2162
Dic3×#2162
D3×#8352
#105915372
D3×#8102
D3×#8072
#105904812
#105904762
C4×#37192
C4×#37182
C4×D3×C3⋊C82
C2×C4×#2163
C4×D3×Q163