Finite Group Databasebeta

← C3×#79779 #11871321

Subgroups — C3×#79779 #11871321

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic
3C32×#440C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic
5C3×#5162C211yesmaximal, characteristic, complemented
6C3×#5026C211yesmaximal, characteristic, complemented
7C3×#5018C211yesmaximal, characteristic, complemented
8C3×#4890C211yesmaximal, characteristic, complemented
9C3×#4884C211yesmaximal, characteristic, complemented
10C3×#4818C211yesmaximal, characteristic, complemented
11C3×#4811C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic
13C3×#4759C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4705C211yesmaximal, characteristic, complemented
16C3×#3110—31nomaximal
17#79779C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#944C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C3×C4×#67—21no—
29C2×C3×#204C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#896—21no—
32C3×#893C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#889—21no—
35C3×#888C2211yescharacteristic, complemented
36C3×#67⋊C4—21no—
37C3×D3×C22⋊C4—21no—
38C3×C4×D12C2211yescharacteristic
39C3×#872—21no—
40C3×C42×D3C2211yescharacteristic
41C3×C4×Dic6—21no—
42C3×C4×Dic6C2211yescharacteristic, complemented
43C32×#107C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46C32×#97C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#807C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×#803C2211yescharacteristic, complemented
61C3×#533—31no—
62C2×C3×C4×D4—31no—
63#5578C2×C311yescharacteristic, complemented
64C4×D3×D4C2×C311yescharacteristic
65C3×#484—31no—
66C3×#484—31no—
67C3×#474—31no—
68C3×#474—31no—
69C3×#461—31no—
70C3×#461—31no—
71C3×#450—31no—
72C3×#450—31no—
73C3×#440—21no—
74C3×#440—31no—
75C3×#440—31no—
76C3×#440—31no—
77C3×#440D311yescharacteristic, complemented
78C3×#440C2×C311yescharacteristic, complemented
79C3×#432—31no—
80#5169C2×C311yescharacteristic
81#5162C2×C311yescharacteristic, complemented
82#5026C2×C311yescharacteristic, complemented
83#5018C2×C311yescharacteristic, complemented
84#4890C2×C311yescharacteristic, complemented
85#4884C2×C311yescharacteristic, complemented
86#4818C2×C311yescharacteristic, complemented
87#4811C2×C311yescharacteristic, complemented
88#4776C2×C311yescharacteristic
89#4759C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4705C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—44no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×SD16—22no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C42—21no—
118C32×C42C2311yescharacteristic
119C3×#217—21no—
120C3×#215—22no—
121C3×#214—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
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×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142#3110—31noSylow
143C22×C3×D4—31no—
144C23×C3×C4—61no—
145C2×D3×D4C22×C311yescharacteristic
146C22×C4×D3—21no—
147C2×C3×SD16—21no—
148C2×C3×SD16—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16C2×D311yescharacteristic
152C2×C3×SD16C22×C311yescharacteristic
153C3×C4⋊Q8—31no—
154C3×C4⋊Q8—31no—
155C3×#125—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C4×Q8—21no—
160C3×C4×Q8—31no—
161C3×C4×Q8—61no—
162C3×C4×Q8C2×D311yescharacteristic, complemented
163C3×C4×Q8C22×C311yescharacteristic, complemented
164C3×C4×D4—21no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—61no—
169C3×C4×D4—61no—
170C3×C4×D4C2×D311yescharacteristic
171C3×C4×D4C22×C311yescharacteristic
172C3×#117—61no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C22⋊C4—61no—
175C2×C3×C42—31no—
176#946C22×C311yescharacteristic
177#944C22×C311yescharacteristic, complemented
178C2×#215C22×C311yescharacteristic
179D4×Dic3C22×C311yescharacteristic
180C2×#214C22×C311yescharacteristic
181C4×#67—21no—
182C2×#204C22×C311yescharacteristic
183#897C22×C311yescharacteristic
184#896—21no—
185#893C22×C311yescharacteristic
186D3×C4⋊C4C22×C311yescharacteristic
187#889—21no—
188#888C22×C311yescharacteristic, complemented
189#67⋊C4—21no—
190D3×C22⋊C4—21no—
191C4×D12C22×C311yescharacteristic
192#872—21no—
193C42×D3C22×C311yescharacteristic
194C4×Dic6—21no—
195C4×Dic6C22×C311yescharacteristic, complemented
196C3×#107—21no—
197C3×#107—31no—
198C3×#107—31no—
199C3×#107—31no—
200C3×#107C2×D311yescharacteristic, complemented
201C3×#107C22×C311yescharacteristic, complemented
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic, complemented
209C3×#103C22×C311yescharacteristic, complemented
210C3×#102—21no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C22×C311yescharacteristic
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×#97—21no—
219C3×#97—31no—
220C3×#97C2×D311yescharacteristic, complemented
221C3×#97C22×C311yescharacteristic, complemented
222#835C22×C311yescharacteristic, complemented
223#832C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227#818C22×C311yescharacteristic, complemented
228#816C22×C311yescharacteristic, complemented
229Dic3⋊C8C22×C311yescharacteristic, complemented
230Dic3⋊C8C22×C311yescharacteristic, complemented
231#810C22×C311yescharacteristic, complemented
232#809C22×C311yescharacteristic
233#807C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235#803C22×C311yescharacteristic, complemented
236C23×C32—21no—
237C22×C3×D3—24no—
238C22×C3×D3—21no—
239C22×C3×D3—42no—
240C22×C3×D3—42no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4#4112yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—42no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C3×#67—24no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—22no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—22no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—42no—
273C32×C8—21no—
274C32×C8—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#533—31no—
278C2×C4×D4—31no—
279#484—31no—
280#484—31no—
281#474—31no—
282#474—31no—
283#461—31no—
284#461—31no—
285#450—31no—
286#450—31no—
287#440—31no—
288#440—31no—
289#440—31no—
290#440C3×D311yescharacteristic, complemented
291#432—31no—
292C24×C3—61no—
293C23×D3—21no—
294C2×C3×Q8—21no—
295C2×C3×Q8—31no—
296C2×C3×Q8—61no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C23×C311yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C23×C311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—41no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—124no—
317C2×#67—21no—
318C22×Dic3—21no—
319D3×D4—22no—
320D3×D4—22no—
321C2×D12C23×C311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—44no—
326C2×C4×D3C3×D411yescharacteristic
327C2×C4×D3C3×D411yescharacteristic
328C2×C4×D3C23×C311yescharacteristic
329C2×Dic6—21no—
330C2×Dic6C23×C311yescharacteristic
331C3×SD16—24no—
332C3×SD16—22no—
333C3×SD16—22no—
334C3×SD16—62no—
335C3×SD16—62no—
336C3×SD16—62no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C2×C3×C8C23×C311yescharacteristic
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—41no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—31no—
375C3×C42—31no—
376C3×C42—31no—
377C3×C42—41no—
378C3×C42—61no—
379C3×C42C22×D311yescharacteristic
380C3×C42C23×C311yescharacteristic
381#217—21no—
382#215—22no—
383#214—22no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3C23×C311yescharacteristic
390C4⋊Dic3C23×C311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397C4×Dic3—21no—
398C4×Dic3C3×D411yescharacteristic
399C4×Dic3C3×D411yescharacteristic
400C4×Dic3C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403#204—22no—
404C22×C32—22no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—22no—
411C2×C3×D3—48no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3#13712yes—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3AGL(1,ℤ/8)12yes—
428C22×D4—31no—
429C23×C4—61no—
430C2×SD16—31no—
431C2×SD16—31no—
432C2×SD16—31no—
433C2×SD16C2×C3×D311yescharacteristic
434C4⋊Q8—31no—
435C4⋊Q8—31no—
436#125—61no—
437C22⋊Q8—31no—
438C22⋊Q8—31no—
439C22⋊Q8—61no—
440C4×Q8—31no—
441C4×Q8—61no—
442C4×Q8C2×C3×D311yescharacteristic, complemented
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—61no—
447C4×D4—61no—
448C4×D4C2×C3×D311yescharacteristic
449#117—61no—
450C2×C4⋊C4—31no—
451C2×C22⋊C4—61no—
452C2×C42—31no—
453#107—31no—
454#107—31no—
455#107—31no—
456#107C2×C3×D311yescharacteristic, complemented
457C4⋊C8—31no—
458C4⋊C8—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103C2×C3×D311yescharacteristic, complemented
463#102—31no—
464#102—31no—
465#102—31no—
466#102C2×C3×D311yescharacteristic
467C22⋊C8—31no—
468C22⋊C8—31no—
469#97—31no—
470#97C2×C3×D311yescharacteristic, complemented
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—41no—
475C23×C3—64no—
476C23×C3—61no—
477C23×C3—122no—
478C23×C3—122no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3C2×C3×D411yescharacteristic
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—122no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—22no—
496C3×D4—32no—
497C3×D4—41no—
498C3×D4—64no—
499C3×D4—61no—
500C3×D4#23512yes—
501C3×D4C3×#4112yes—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—42no—
518C2×C3×C4—42no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—82no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C2×C3×D411yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C24×C311yescharacteristic
537#67—24no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—42no—
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544C2×Dic3C2×C3×D411yescharacteristic
545D12—21no—
546D12C3×#4112yes—
547C4×D3—22no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—22no—
551C4×D3—42no—
552C4×D3—42no—
553C4×D3—42no—
554Dic6—21no—
555Dic6—21no—
556Dic6—42no—
557C3×C8—22no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—41no—
563C3×C8—61no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—21no—
567C2×C32—42no—
568C2×C32#52511yescharacteristic
569C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
570C2×C32C2×#13711yescharacteristic
571C3×D3—22no—
572C3×D3—42no—
573C24—61no—
574C2×Q8—31no—
575C2×Q8—61no—
576C2×Q8C22×C3×D311yescharacteristic
577C2×D4—31no—
578C2×D4—61no—
579C2×D4—62no—
580C2×D4—62no—
581C2×D4C22×C3×D311yescharacteristic
582C22×C4—21no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—124no—
591SD16—22no—
592SD16—62no—
593SD16—62no—
594SD16—62no—
595C2×C8—31no—
596C2×C8—31no—
597C2×C8C22×C3×D311yescharacteristic
598C2×C8C22×C3×D311yescharacteristic
599C4⋊C4—21no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4C22×C3×D311yescharacteristic
610C4⋊C4C22×C3×D311yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C42—21no—
618C42—31no—
619C42—31no—
620C42—31no—
621C42—61no—
622C42C22×C3×D311yescharacteristic
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—42no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—62no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—128no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×C3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—48no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3C3×#13712yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—42no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C2×#23511yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4C2×C3×#4111yescharacteristic
675C3×C4C2×C3×#4111yescharacteristic
676Dic3—21no—
677Dic3—21no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3C3×AGL(1,ℤ/8)12yes—
682C32#311011yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—64no—
686C23—61no—
687C23—122no—
688C23—122no—
689Q8—21no—
690Q8—21no—
691Q8—61no—
692Q8—61no—
693Q8—122no—
694D4—21no—
695D4—32no—
696D4—64no—
697D4—61no—
698D4C3×#23512yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—42no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4C3×D3×D411yescharacteristic
718C2×C4C3×D3×D411yescharacteristic
719C2×C4C23×C3×D311yescharacteristic
720C8—21no—
721C8—21no—
722C8—61no—
723C8—61no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—62no—
730C2×C3—82no—
731C2×C3—122no—
732C2×C3#554711yescharacteristic
733C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
734C2×C3D3×#13711yescharacteristic
735C2×C3C3×#52511yescharacteristic
736C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
737C2×C3C2×C3×#13711yescharacteristic
738D3—22no—
739D3—42no—
740C22—22no—
741C22—32no—
742C22—41no—
743C22—41no—
744C22—61no—
745C22—61no—
746C22—62no—
747C22—128no—
748C22—121no—
749C22—121no—
750C22C2×C3×D3×D411yescharacteristic
751C4—21no—
752C4—21no—
753C4—32no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—61no—
758C4—61no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4C2×C3×#23511yescharacteristic
763C4C3×D3×#4111yescharacteristic
764C3—21no—
765C3#7977911yescharacteristic, direct product factor
766C3C3×#311011yescharacteristic, complemented
767C2—42no—
768C2—62no—
769C2—122no—
770C2C3×#554711yescharacteristic
771C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
772C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC3×#440D3
hypocenterC3C3×#3110
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C3×#5578C2semidirect
3. C32×#440C2semidirect
5. C3×#5162C2semidirect
6. C3×#5026C2semidirect
7. C3×#5018C2semidirect
8. C3×#4890C2semidirect
9. C3×#4884C2semidirect
10. C3×#4818C2semidirect
11. C3×#4811C2semidirect
13. C3×#4759C2semidirect
14. C3×#4710C2semidirect
15. C3×#4705C2semidirect
17. #79779C3direct (N × H)
21. C32×C4×Q8C22semidirect
24. C3×#944C22semidirect
35. C3×#888C22semidirect
42. C3×C4×Dic6C22semidirect
43. C32×#107C22semidirect
44. C32×#103C22semidirect
46. C32×#97C22semidirect
47. C3×#835C22semidirect
52. C3×#818C22semidirect
53. C3×#816C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×#810C22semidirect
58. C3×#807C22semidirect
59. C3×#807C22semidirect
60. C3×#803C22semidirect
63. #5578C2×C3semidirect
77. C3×#440D3semidirect
78. C3×#440C2×C3semidirect
81. #5162C2×C3semidirect
82. #5026C2×C3semidirect
83. #5018C2×C3semidirect
84. #4890C2×C3semidirect
85. #4884C2×C3semidirect
86. #4818C2×C3semidirect
87. #4811C2×C3semidirect
89. #4759C2×C3semidirect
90. #4710C2×C3semidirect
91. #4705C2×C3semidirect
162. C3×C4×Q8C2×D3semidirect
163. C3×C4×Q8C22×C3semidirect
177. #944C22×C3semidirect
188. #888C22×C3semidirect
195. C4×Dic6C22×C3semidirect
200. C3×#107C2×D3semidirect
201. C3×#107C22×C3semidirect
208. C3×#103C2×D3semidirect
209. C3×#103C22×C3semidirect
220. C3×#97C2×D3semidirect
221. C3×#97C22×C3semidirect
222. #835C22×C3semidirect
227. #818C22×C3semidirect
228. #816C22×C3semidirect
229. Dic3⋊C8C22×C3semidirect
230. Dic3⋊C8C22×C3semidirect
231. #810C22×C3semidirect
233. #807C22×C3semidirect
234. #807C22×C3semidirect
235. #803C22×C3semidirect
290. #440C3×D3semidirect
442. C4×Q8C2×C3×D3semidirect
456. #107C2×C3×D3semidirect
462. #103C2×C3×D3semidirect
470. #97C2×C3×D3semidirect
682. C32#3110semidirect
765. C3#79779direct (N × H)
766. C3C3×#3110semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
C3×C4×D3×D42
C32×#4402
C3×#51692
C3×#51622
C3×#50262
C3×#50182
C3×#48902
C3×#48842
C3×#48182
C3×#48112
C3×#47762
C3×#47592
C3×#47102
C3×#47052
C3×#31103
#797793