Finite Group Databasebeta

← C4×D3×#215 #11859882

Subgroups — C4×D3×#215 #11859882

Order 1152.

1165 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic
3C4×D3×D12C211yesmaximal, characteristic
4C4×#3755C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic, complemented
6Dic3×#215C211yesmaximal, characteristic, complemented
7D3×#835C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9D3×#809C211yesmaximal, characteristic
10D3×#808C211yesmaximal, characteristic, complemented
11#10590458C211yesmaximal, characteristic, complemented
12#10590453C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
16C2×C4×#215—31nomaximal
17C4×D3×SD16—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C4×D32—21no—
21C32×C4×Q8C2211yescharacteristic, complemented
22C2×#3755C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×D3×C4⋊C4—21no—
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#887—21no—
29C3×#887C2211yescharacteristic, complemented
30C3×C4×D12C2211yescharacteristic
31C3×C42×D3—21no—
32C3×C42×D3C2211yescharacteristic
33C3×C4×Dic6—21no—
34C3×C4×Dic6C2211yescharacteristic, complemented
35D3×#215C418yesdirect product factor
36D3×(C2×D3)⋊C4—21no—
37C4×#626—21no—
38#63894C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41#63880—21no—
42C2×#3717C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63635C2211yescharacteristic, complemented
49C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63562C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C2×C3×C4×Q8—31no—
63C22×#215—31no—
64C2×D3×SD16—31no—
65C4×D3×Q8D311yescharacteristic, complemented
66C4×D3×D4—31no—
67C2×C4×D12—31no—
68C3×C4×SD16—31no—
69C2×#835—31no—
70Dic3×SD16—31no—
71C4×#215—31no—
72C4×#215—31no—
73C4×#215—31no—
74C4×#215—31no—
75C4×#215—31no—
76C4×#215—31no—
77C4×#215—31no—
78C4×#215—31no—
79C4×#215—61no—
80C4×#215D311yescharacteristic, direct product factor
81C4×#214—31no—
82C2×#809—31no—
83C2×#808—31no—
84C2×C4×C3⋊C8—31no—
85D3×#106—31no—
86#4852—31no—
87D3×#103—31no—
88#4788—31no—
89D3×#102—31no—
90#4758—31no—
91C4×#204—31no—
92C4×D3×C8—31no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8C2×C414yescomplemented
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×#626—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12C2×C414yes—
114C4×D32—44no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C42—21no—
118C32×C42C2311yescharacteristic
119#3755C2×C414yescomplemented
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C3×#215C2×C414yescomplemented
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3D411yescharacteristic
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140Dic3⋊Dic3—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143#3717C2×C414yescomplemented
144#3715C2×C414yescomplemented
145D3×C3⋊C8—22no—
146D3×C3⋊C8C2×C414yescomplemented
147C2×C4×SD16—91noSylow
148C22×C3×Q8—31no—
149C2×D3×Q8C2×D311yescharacteristic
150C2×D3×D4—31no—
151C22×D12—31no—
152C22×C4×D3—61no—
153C22×C4×D3—61no—
154C2×C3×SD16—31no—
155C3×C4×Q8—21no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—61no—
160C3×C4×Q8—61no—
161C3×C4×Q8C2×D311yescharacteristic, complemented
162C3×C4×Q8C2×D311yescharacteristic, complemented
163C3×C4×D4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—61no—
166C2×C3×C42—31no—
167C2×C3×C42—61no—
168Q8×Dic3C2×D311yescharacteristic, complemented
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—38no—
173C2×#215—31no—
174C2×#215—61no—
175C2×#215C2×D311yescharacteristic
176D4×Dic3—31no—
177C2×#214—31no—
178C4×#67—61no—
179C2×(C2×D3)⋊C4—61no—
180C2×C4⋊Dic3—31no—
181C22×C3⋊C8—31no—
182C22×C3⋊C8—31no—
183D3×SD16—38no—
184C2×#204—31no—
185C2×D3×C8—31no—
186C2×D3×C8—31no—
187#893—31no—
188D3×C4⋊C4—21no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4C2×D311yescharacteristic
191#887—21no—
192#887C2×D311yescharacteristic, complemented
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195C4×D12—31no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200C4×D12—61no—
201C4×D12—61no—
202C4×D12C2×D311yescharacteristic
203C42×D3—21no—
204C42×D3C2×D311yescharacteristic
205C4×Dic6—21no—
206C4×Dic6C2×D311yescharacteristic, complemented
207C3×#106—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×C4×C8—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—61no—
216#835C2×D311yescharacteristic, complemented
217#832—31no—
218#821—31no—
219#817—31no—
220#816—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223#810—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#809C2×D311yescharacteristic
230#808—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#808—61no—
236#808C2×D311yescharacteristic, complemented
237C4×C3⋊C8—31no—
238C4×C3⋊C8—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8—61no—
242C4×C3⋊C8C2×D311yescharacteristic, complemented
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—24no—
247C2×D32—42no—
248C2×D32—42no—
249C32×Q8—21no—
250C32×Q8C22×C412yescomplemented
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)C22×C412yes—
259C4×C3⋊D3—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12C22×C412yes—
268C3×C4×D3—24no—
269C3×C4×D3—22no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×C4×D3SD1614yescomplemented
273C3×C4×D3C22×C412yes—
274C3×C4×D3#4112yes—
275C3×Dic6—21no—
276C3×Dic6—24no—
277C3×Dic6C22×C412yescomplemented
278#626—24no—
279#624—42no—
280D3×Dic3—42no—
281D3×Dic3—42no—
282C3⋊(C3⋊C8)—21no—
283C3⋊(C3⋊C8)C22×C412yescomplemented
284C3×C3⋊C8—21no—
285C3×C3⋊C8C22×C412yescomplemented
286C22×SD16—91no—
287C2×C4×Q8—31no—
288C2×C4×D4—91no—
289C4×SD16—31no—
290C4×SD16—91no—
291C4×SD16—91no—
292C4×SD16—91no—
293C4×SD16—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296C4×SD16—91no—
297C2×#106—91no—
298C2×#103—91no—
299C2×#102—91no—
300C2×C4×C8—91no—
301C23×D3—61no—
302C23×D3—61no—
303C2×C3×Q8—21no—
304C2×C3×Q8—34no—
305C2×C3×Q8—31no—
306C2×C3×Q8—61no—
307C2×C3×Q8—62no—
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×D4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C2×#67—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320D3×Q8—22no—
321D3×Q8C4×D314yescomplemented
322D3×D4—34no—
323D3×D4—62no—
324C2×D12—31no—
325C2×D12—31no—
326C2×D12—34no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—121no—
341C2×C4×D3—124no—
342C2×C4×D3—124no—
343C2×C4×D3#6711yescharacteristic
344C2×C4×D3#6711yescharacteristic
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6—21no—
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—34no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—41no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364C3×C42—21no—
365C3×C42—21no—
366C3×C42—21no—
367C3×C42—31no—
368C3×C42—31no—
369C3×C42—31no—
370C3×C42—41no—
371C3×C42—61no—
372C3×C42—61no—
373C3×C42—61no—
374C3×C42C22×D311yescharacteristic
375C3×C42C22×D311yescharacteristic
376#217—61no—
377#215—34no—
378#215—34no—
379#215—34no—
380#215—34no—
381#215—64no—
382#215C4×D314yesdirect product factor
383#214—34no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—121no—
391C4⋊Dic3—21no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—61no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3#6711yescharacteristic
406C4×Dic3#6711yescharacteristic
407C4×Dic3C22×D311yescharacteristic
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—34no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8—62no—
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418#204—34no—
419D3×C8—34no—
420D3×C8—62no—
421C22×C32C22×D411yescharacteristic
422C2×C3⋊D3—22no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3×D3—22no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3C4×D412yes—
429C2×C3×D3C2×SD1612yes—
430C2×C3×D3#13512yes—
431D32—48no—
432C32×C4—22no—
433C32×C4—21no—
434C32×C4—41no—
435C32×C4C2×SD1612yescomplemented
436C32×C4C23×C411yescharacteristic
437C32×C4C2×#4111yescharacteristic
438C3⋊Dic3—41no—
439C3×Dic3—22no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3C4×D412yes—
444C3×Dic3C2×SD1612yescomplemented
445C22×Q8—31no—
446C22×D4—91no—
447C23×C4—181no—
448C2×SD16—31no—
449C2×SD16—91no—
450C2×SD16—98no—
451C2×SD16—91no—
452C2×SD16—91no—
453C22×C8—91no—
454C22×C8—91no—
455C4×Q8—31no—
456C4×Q8—31no—
457C4×Q8—31no—
458C4×Q8—61no—
459C4×Q8—61no—
460C4×Q8D3211yescharacteristic, complemented
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—181no—
466C4×D4—181no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—61no—
469C2×C4⋊C4—91no—
470C2×C22⋊C4—181no—
471C2×C42—31no—
472C2×C42—61no—
473#106—31no—
474#106—91no—
475#106—91no—
476#106—91no—
477#103—31no—
478#103—91no—
479#103—91no—
480#103—91no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485C4×C8—31no—
486C4×C8—91no—
487C4×C8—91no—
488C4×C8—91no—
489C23×C3—31no—
490C23×C3—61no—
491C22×D3—21no—
492C22×D3—64no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—64no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3C2×#6711yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—22no—
505C3×Q8—32no—
506C3×Q8—41no—
507C3×Q8—64no—
508C3×Q8—61no—
509C3×Q8C2×C4×D312yescomplemented
510C3×Q8C2×C4×D312yescomplemented
511C3×D4—32no—
512C3×D4—61no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—34no—
523C2×C3×C4—32no—
524C2×C3×C4—32no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—62no—
529C2×C3×C4—64no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—64no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—122no—
549C2×Dic3—122no—
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552C2×Dic3C2×#6711yescharacteristic
553D12—21no—
554D12—32no—
555D12—32no—
556D12—62no—
557D12—64no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12C2×C4×D312yes—
562C4×D3—24no—
563C4×D3—22no—
564C4×D3—42no—
565C4×D3—42no—
566C4×D3—122no—
567C4×D3—122no—
568C4×D3—122no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—122no—
572C4×D3—242no—
573C4×D3#21514yesdirect product factor
574C4×D3C2×C4×D312yes—
575C4×D3#23512yes—
576Dic6—21no—
577Dic6—24no—
578Dic6C2×C4×D312yescomplemented
579C3×C8—32no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—32no—
583C3⋊C8—32no—
584C3⋊C8—62no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—121no—
588C3⋊C8C2×C4×D312yescomplemented
589C2×C32C2×C4×D411yescharacteristic
590C2×C32C22×SD1611yescharacteristic
591C2×C32C2×#13511yescharacteristic
592C3⋊D3—42no—
593C3×D3—42no—
594C3×D3C4×SD1614yescomplemented
595C24—181no—
596C2×Q8—34no—
597C2×Q8—31no—
598C2×Q8—61no—
599C2×Q8—62no—
600C2×Q8C2×D3211yescharacteristic
601C2×D4—31no—
602C2×D4—94no—
603C2×D4—91no—
604C2×D4—182no—
605C2×D4—181no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615C22×C4—181no—
616C22×C4—364no—
617SD16—34no—
618SD16—94no—
619SD16—94no—
620SD16—94no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—94no—
624C2×C8—91no—
625C2×C8—91no—
626C2×C8—182no—
627C4⋊C4—21no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—21no—
642C42—31no—
643C42—31no—
644C42—31no—
645C42—61no—
646C42—61no—
647C42—61no—
648C42C2×D3211yescharacteristic
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—32no—
652C22×C3—32no—
653C22×C3—62no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C22×#6711yescharacteristic
658C2×D3—22no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—122no—
664C2×D3—128no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—128no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3C4×#6712yes—
673C2×D3C2×#21512yes—
674C2×D3#95012yes—
675C3×C4—21no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—22no—
682C3×C4—32no—
683C3×C4—32no—
684C3×C4—41no—
685C3×C4—42no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—62no—
690C3×C4—81no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4D3×SD1612yescomplemented
694C3×C4C2×#21512yescomplemented
695C3×C4C22×C4×D311yescharacteristic
696C3×C4C22×C4×D311yescharacteristic
697C3×C4C2×#23511yescharacteristic
698C3×C4D3×#4111yescharacteristic
699Dic3—22no—
700Dic3—21no—
701Dic3—41no—
702Dic3—41no—
703Dic3—121no—
704Dic3—121no—
705Dic3—241no—
706Dic3C4×#6712yes—
707Dic3C2×#21512yescomplemented
708C32C2×C4×SD1611yescharacteristic, complemented, Sylow
709C23—31no—
710C23—61no—
711C23—184no—
712C23—181no—
713C23—362no—
714C23—362no—
715Q8—21no—
716Q8—32no—
717Q8—64no—
718Q8—61no—
719Q8C4×D3212yescomplemented
720D4—32no—
721D4—61no—
722D4—92no—
723D4—184no—
724D4—181no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—34no—
732C2×C4—31no—
733C2×C4—62no—
734C2×C4—64no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—181no—
741C2×C4—362no—
742C2×C4—362no—
743C2×C4—362no—
744C2×C4—362no—
745C2×C4D3×#6711yescharacteristic
746C2×C4D3×#6711yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—32no—
749C8—61no—
750C8—92no—
751C8—181no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—34no—
756C2×C3—122no—
757C2×C3C4×D3×D411yescharacteristic
758C2×C3C2×D3×SD1611yescharacteristic
759C2×C3D3×#13511yescharacteristic
760C2×C3C2×C4×#6711yescharacteristic
761C2×C3C22×#21511yescharacteristic
762C2×C3C2×#95011yescharacteristic
763D3—42no—
764D3—122no—
765D3—122no—
766D3—242no—
767D3C4×#21514yesdirect product factor
768C22—32no—
769C22—32no—
770C22—32no—
771C22—62no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—368no—
776C22—361no—
777C22—361no—
778C22C2×D3×#6711yescharacteristic
779C4—21no—
780C4—22no—
781C4—32no—
782C4—32no—
783C4—41no—
784C4—61no—
785C4—62no—
786C4—121no—
787C4—121no—
788C4—361no—
789C4D3×#21512yesdirect product factor
790C4C2×C4×D3211yescharacteristic
791C4D3×#23511yescharacteristic
792C3—21no—
793C3C4×D3×SD1611yescharacteristic, complemented
794C3C2×C4×#21511yescharacteristic, complemented
795C2—34no—
796C2—122no—
797C2—362no—
798C2C4×D3×#6711yescharacteristic
799C2C2×D3×#21511yescharacteristic
800C2D3×#95011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32C2×C4×SD16
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
1. C3×C4×D3×Q8C2semidirect
4. C4×#3755C2semidirect
5. C3×C4×#215C2semidirect
6. Dic3×#215C2semidirect
7. D3×#835C2semidirect
8. #10591536C2semidirect
10. D3×#808C2semidirect
11. #10590458C2semidirect
12. #10590453C2semidirect
13. C4×#3717C2semidirect
14. C4×#3715C2semidirect
15. C4×D3×C3⋊C8C2semidirect
21. C32×C4×Q8C22semidirect
24. C3×Q8×Dic3C22semidirect
29. C3×#887C22semidirect
34. C3×C4×Dic6C22semidirect
35. D3×#215C4direct (N × H)
46. #63662C22semidirect
48. #63635C22semidirect
49. C4×C3⋊(C3⋊C8)C22semidirect
50. C3×#835C22semidirect
52. C3×#808C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63566C22semidirect
57. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
61. Dic3×C3⋊C8C22semidirect
65. C4×D3×Q8D3semidirect
80. C4×#215D3direct (N × H)
98. C3×D3×Q8C2×C4semidirect
119. #3755C2×C4semidirect
124. C3×#215C2×C4semidirect
143. #3717C2×C4semidirect
144. #3715C2×C4semidirect
146. D3×C3⋊C8C2×C4semidirect
161. C3×C4×Q8C2×D3semidirect
162. C3×C4×Q8C2×D3semidirect
168. Q8×Dic3C2×D3semidirect
192. #887C2×D3semidirect
206. C4×Dic6C2×D3semidirect
216. #835C2×D3semidirect
236. #808C2×D3semidirect
242. C4×C3⋊C8C2×D3semidirect
250. C32×Q8C22×C4semidirect
272. C3×C4×D3SD16semidirect
277. C3×Dic6C22×C4semidirect
283. C3⋊(C3⋊C8)C22×C4semidirect
285. C3×C3⋊C8C22×C4semidirect
321. D3×Q8C4×D3semidirect
382. #215C4×D3direct (N × H)
435. C32×C4C2×SD16semidirect
444. C3×Dic3C2×SD16semidirect
460. C4×Q8D32semidirect
509. C3×Q8C2×C4×D3semidirect
510. C3×Q8C2×C4×D3semidirect
573. C4×D3#215direct (N × H)
578. Dic6C2×C4×D3semidirect
588. C3⋊C8C2×C4×D3semidirect
594. C3×D3C4×SD16semidirect
693. C3×C4D3×SD16semidirect
694. C3×C4C2×#215semidirect
707. Dic3C2×#215semidirect
708. C32C2×C4×SD16semidirect
719. Q8C4×D32semidirect
767. D3C4×#215direct (N × H)
789. C4D3×#215direct (N × H)
793. C3C4×D3×SD16semidirect
794. C3C2×C4×#215semidirect

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×#2152
C4×D3×D122
C4×#37552
C3×C4×#2152
Dic3×#2152
D3×#8352
#105915362
D3×#8092
D3×#8082
#105904582
#105904532
C4×#37172
C4×#37152
C4×D3×C3⋊C82
C2×C4×#2153
C4×D3×SD163