Finite Group Databasebeta

← C3×#79591 #11870551

Subgroups — C3×#79591 #11870551

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5557C211yesmaximal, characteristic, complemented
2C3×C4×#237C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4C3×#5158C211yesmaximal, characteristic
5C3×#5153C211yesmaximal, characteristic, complemented
6C3×C4×#214C211yesmaximal, characteristic, complemented
7C3×C4×#214C211yesmaximal, characteristic, complemented
8C3×#4888C211yesmaximal, characteristic, complemented
9C3×#4877C211yesmaximal, characteristic, complemented
10C3×#4784C211yesmaximal, characteristic, complemented
11C3×#4783C211yesmaximal, characteristic, complemented
12C3×#4767C211yesmaximal, characteristic, complemented
13C3×#4766C211yesmaximal, characteristic, complemented
14C3×C4×Dic12C211yesmaximal, characteristic, complemented
15C3×#4685C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#79591C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C3×#936C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×C4×#67—21no—
28C3×C4×#67—21no—
29C3×#926—21no—
30C2×C3×C4×Dic3—21no—
31C2×C3×Dic12C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#892C2211yescharacteristic
34C3×#890C2211yescharacteristic
35C3×#887C2211yescharacteristic
36C3×#883—21no—
37C3×#67⋊C4—21no—
38C3×#879—21no—
39C3×#877—21no—
40C3×C42×D3C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5557C2×C311yescharacteristic, complemented
64C4×#237C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#464—31no—
70C3×#463—31no—
71C3×#452—31no—
72C3×#449—31no—
73C3×C4×Q16—31no—
74C3×C4×SD16—31no—
75C3×C4×SD16—31no—
76C3×C4×D8—21no—
77C3×C4×D8D311yescharacteristic, complemented
78C3×C4×D8C2×C311yescharacteristic, complemented
79C3×#431—31no—
80#5158C2×C311yescharacteristic
81#5153C2×C311yescharacteristic, complemented
82C4×#214C2×C311yescharacteristic, complemented
83C4×#214C2×C311yescharacteristic, complemented
84#4888C2×C311yescharacteristic, complemented
85#4877C2×C311yescharacteristic, complemented
86#4784C2×C311yescharacteristic, complemented
87#4783C2×C311yescharacteristic, complemented
88#4767C2×C311yescharacteristic, complemented
89#4766C2×C311yescharacteristic, complemented
90C4×Dic12C2×C311yescharacteristic, complemented
91#4685C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C3×#237—22no—
101C3×#237—22no—
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C32×D8—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#214—22no—
120C3×#214—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—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
140C3×Dic12—22no—
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#237C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—21no—
148C2×C3×D8C2×D311yescharacteristic
149C2×C3×D8C22×C311yescharacteristic
150C3×#126—61no—
151C3×#125—31no—
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×D4—21no—
160C3×C4×D4—21no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163C3×C4×D4—61no—
164C3×C4×D4—61no—
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C2×D311yescharacteristic
167C3×C4×D4C22×C311yescharacteristic
168C3×C4×D4C22×C311yescharacteristic
169C3×#117—31no—
170C3×#117—61no—
171C3×#117—61no—
172C2×C3×C42—31no—
173C2×C3×C42—61no—
174#938C22×C311yescharacteristic
175#936C22×C311yescharacteristic
176D4×Dic3C22×C311yescharacteristic
177C2×#214C22×C311yescharacteristic
178C2×#214C22×C311yescharacteristic
179C4×#67—21no—
180C4×#67—21no—
181#926—21no—
182C2×C4×Dic3—21no—
183C2×Dic12C22×C311yescharacteristic
184#897C22×C311yescharacteristic
185#892C22×C311yescharacteristic
186#890C22×C311yescharacteristic
187#887C22×C311yescharacteristic
188#883—21no—
189#67⋊C4—21no—
190#879—21no—
191#877—21no—
192C42×D3C22×C311yescharacteristic
193C4×Dic6C22×C311yescharacteristic
194C4×Dic6C22×C311yescharacteristic
195C3×#107—21no—
196C3×#107—31no—
197C3×#107C2×D311yescharacteristic
198C3×#107C22×C311yescharacteristic
199C3×#106—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—21no—
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×C4×C8—21no—
218C3×C4×C8—31no—
219C3×C4×C8C2×D311yescharacteristic
220C3×C4×C8C22×C311yescharacteristic
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225#818C22×C311yescharacteristic
226#816C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234C4×C3⋊C8C22×C311yescharacteristic
235C23×C32—21no—
236C23×C32—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×D4—21no—
239C32×D4—21no—
240C32×D4—21no—
241C32×D4#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—42no—
245C2×C32×C4—42no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C3×#67—24no—
250C3×#67—42no—
251C2×C3×Dic3—24no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×C4×D3—22no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—41no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#529—31no—
273C4×#41—31no—
274#485—31no—
275#482—31no—
276#479—31no—
277#478—31no—
278#464—31no—
279#463—31no—
280#452—31no—
281#449—31no—
282C4×Q16—31no—
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8C3×D311yescharacteristic, complemented
286#431—31no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C23×C311yescharacteristic
298C2×C3×D4C23×C311yescharacteristic
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—41no—
307C22×C3×C4—41no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314#237—22no—
315#237—22no—
316C2×C4×D3C3×D411yescharacteristic
317C2×C4×D3C3×D411yescharacteristic
318C2×C4×D3C23×C311yescharacteristic
319C2×Dic6C23×C311yescharacteristic
320C2×Dic6C23×C311yescharacteristic
321C3×Q16—62no—
322C3×SD16—62no—
323C3×SD16—62no—
324C3×D8—24no—
325C3×D8—22no—
326C3×D8—22no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C23×C311yescharacteristic
334C2×C3×C8C23×C311yescharacteristic
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C23×C311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—21no—
362C3×C42—31no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—61no—
366C3×C42—61no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42C22×D311yescharacteristic
370C3×C42C23×C311yescharacteristic
371#217—21no—
372#217—21no—
373#217—21no—
374#217—21no—
375#214—22no—
376#214—22no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C23×C311yescharacteristic
382C4⋊Dic3C23×C311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3C3×D411yescharacteristic
392C4×Dic3C3×D411yescharacteristic
393C4×Dic3C23×C311yescharacteristic
394C2×C3⋊C8C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396Dic12—22no—
397C22×C32—22no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C32×C4—21no—
408C32×C4—41no—
409C32×C4—41no—
410C32×C4#13512yes—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3×Dic3—22no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C2×#41—31no—
421C2×Q16—31no—
422C2×SD16—31no—
423C2×SD16—31no—
424C2×D8C2×C3×D311yescharacteristic
425#126—61no—
426#125—31no—
427#124—31no—
428#123—61no—
429C22⋊Q8—31no—
430#121—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×D4—31no—
435C4×D4—61no—
436C4×D4—61no—
437C4×D4—61no—
438C4×D4C2×C3×D311yescharacteristic
439C4×D4C2×C3×D311yescharacteristic
440#117—31no—
441#117—61no—
442#117—61no—
443C2×C42—31no—
444C2×C42—61no—
445#107—31no—
446#107C2×C3×D311yescharacteristic
447#106—31no—
448#106—31no—
449C4⋊C8—31no—
450C4⋊C8—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#103—31no—
455#102—31no—
456#102—31no—
457#102C2×C3×D311yescharacteristic
458#102C2×C3×D311yescharacteristic
459C22⋊C8—31no—
460C22⋊C8—31no—
461C4×C8—31no—
462C4×C8C2×C3×D311yescharacteristic
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—31no—
468C23×C3—41no—
469C23×C3—41no—
470C22×D3C2×C3×D411yescharacteristic
471C3×Q8—32no—
472C3×Q8—61no—
473C3×Q8—61no—
474C3×Q8—61no—
475C3×D4—22no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—22no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—64no—
486C3×D4—122no—
487C3×D4#23512yes—
488C3×D4C3×#4112yes—
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—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—42no—
502C2×C3×C4—42no—
503C2×C3×C4—42no—
504C2×C3×C4—42no—
505C2×C3×C4—64no—
506C2×C3×C4—61no—
507C2×C3×C4—62no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—82no—
514C2×C3×C4—82no—
515C2×C3×C4—121no—
516C2×C3×C4—122no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4C2×C3×D411yescharacteristic
520C2×C3×C4C2×C3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C24×C311yescharacteristic
523#67—24no—
524#67—42no—
525C2×Dic3—24no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—42no—
531C2×Dic3C2×C3×D411yescharacteristic
532C2×Dic3C2×C3×D411yescharacteristic
533C2×Dic3C2×C3×D411yescharacteristic
534C4×D3—22no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—41no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6C3×#4112yes—
542C3×C8—22no—
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—41no—
548C3×C8—61no—
549C3×C8—61no—
550C3⋊C8—21no—
551C3⋊C8—21no—
552C2×C32—42no—
553C2×C32—81no—
554C2×C32#52511yescharacteristic
555C2×C32C2×#13511yescharacteristic
556C2×C32#57511yescharacteristic
557C3×D3—41no—
558#41—62no—
559#41—62no—
560C2×Q8—31no—
561C2×Q8—31no—
562C2×D4—61no—
563C2×D4—61no—
564C2×D4C22×C3×D311yescharacteristic
565C2×D4C22×C3×D311yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—61no—
572C22×C4—61no—
573Q16—62no—
574SD16—62no—
575SD16—62no—
576D8—22no—
577C2×C8—31no—
578C2×C8—31no—
579C2×C8C22×C3×D311yescharacteristic
580C2×C8C22×C3×D311yescharacteristic
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4C22×C3×D311yescharacteristic
590C4⋊C4C22×C3×D311yescharacteristic
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C42—31no—
600C42—31no—
601C42—31no—
602C42—61no—
603C42—61no—
604C42—61no—
605C42—61no—
606C42C22×C3×D311yescharacteristic
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C22×C3×D411yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—22no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—62no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4#91212yes—
654C3×C4C3×#13512yes—
655C3×C4C2×#23511yescharacteristic
656C3×C4D3×#4111yescharacteristic
657C3×C4C2×C3×#4111yescharacteristic
658C3×C4C2×C3×#4111yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—22no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666C32#310211yescharacteristic, complemented, Sylow
667C23—21no—
668C23—21no—
669C23—31no—
670Q8—32no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674D4—21no—
675D4—21no—
676D4—21no—
677D4—64no—
678D4—122no—
679D4C3×#23512yes—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—64no—
688C2×C4—61no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—121no—
696C2×C4—122no—
697C2×C4C3×D3×D411yescharacteristic
698C2×C4C3×D3×D411yescharacteristic
699C2×C4C23×C3×D311yescharacteristic
700C8—21no—
701C8—21no—
702C8—61no—
703C8—61no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—82no—
710C2×C3—82no—
711C2×C3—81no—
712C2×C3—81no—
713C2×C3—121no—
714C2×C3#554711yescharacteristic
715C2×C3C2×#91211yescharacteristic
716C2×C3#576811yescharacteristic
717C2×C3C3×#52511yescharacteristic
718C2×C3C2×C3×#13511yescharacteristic
719C2×C3C3×#57511yescharacteristic
720D3—41no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22C2×C3×D3×D411yescharacteristic
731C4—21no—
732C4—41no—
733C4—41no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—62no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4C3×#91212yes—
742C4C2×C3×#23511yescharacteristic
743C4C3×D3×#4111yescharacteristic
744C3—21no—
745C3#7959111yescharacteristic, direct product factor
746C3C3×#310211yescharacteristic, complemented
747C2—42no—
748C2—81no—
749C2—121no—
750C2C3×#554711yescharacteristic
751C2C2×C3×#91211yescharacteristic
752C2C3×#576811yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radicalC3×#5158C2
hypercenterC3×C4×D8D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5557C2semidirect
2. C3×C4×#237C2semidirect
3. C32×C4×D8C2semidirect
5. C3×#5153C2semidirect
6. C3×C4×#214C2semidirect
7. C3×C4×#214C2semidirect
8. C3×#4888C2semidirect
9. C3×#4877C2semidirect
10. C3×#4784C2semidirect
11. C3×#4783C2semidirect
12. C3×#4767C2semidirect
13. C3×#4766C2semidirect
14. C3×C4×Dic12C2semidirect
15. C3×#4685C2semidirect
17. #79591C3direct (N × H)
63. #5557C2×C3semidirect
64. C4×#237C2×C3semidirect
77. C3×C4×D8D3semidirect
78. C3×C4×D8C2×C3semidirect
81. #5153C2×C3semidirect
82. C4×#214C2×C3semidirect
83. C4×#214C2×C3semidirect
84. #4888C2×C3semidirect
85. #4877C2×C3semidirect
86. #4784C2×C3semidirect
87. #4783C2×C3semidirect
88. #4767C2×C3semidirect
89. #4766C2×C3semidirect
90. C4×Dic12C2×C3semidirect
91. #4685C2×C3semidirect
285. C4×D8C3×D3semidirect
666. C32#3102semidirect
745. C3#79591direct (N × H)
746. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×#55572
C3×C4×#2372
C32×C4×D82
C3×#51582
C3×#51532
C3×C4×#2142
C3×#48882
C3×#48772
C3×#47842
C3×#47832
C3×#47672
C3×#47662
C3×C4×Dic122
C3×#46852
C3×#31023
#795913