Finite Group Databasebeta

← C3×#79694 #11870557

Subgroups — C3×#79694 #11870557

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic, complemented
2C3×#5557C211yesmaximal, characteristic, complemented
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5172C211yesmaximal, characteristic
5C3×#5166C211yesmaximal, characteristic, complemented
6C3×C4×#216C211yesmaximal, characteristic, complemented
7C3×C4×#213C211yesmaximal, characteristic, complemented
8C3×#4871C211yesmaximal, characteristic, complemented
9C3×#4868C211yesmaximal, characteristic, complemented
10C3×#4808C211yesmaximal, characteristic, complemented
11C3×#4799C211yesmaximal, characteristic, complemented
12C3×#4787C211yesmaximal, characteristic, complemented
13C3×#4779C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×#4685C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#79694C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C3×#936C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×C4×#67—21no—
28C3×#926—21no—
29C2×C3×#204C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#893—21no—
32C3×#893C2211yescharacteristic
33C3×#892—21no—
34C3×#892C2211yescharacteristic
35C3×#890C2211yescharacteristic
36C3×#883—21no—
37C3×#879—21no—
38C3×C4×D12—21no—
39C3×C4×D12C2211yescharacteristic
40C3×C42×D3—21no—
41C3×C42×D3C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63C4×#239C2×C311yescharacteristic, complemented
64#5557C2×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—21no—
75C3×C4×SD16—31no—
76C3×C4×SD16D311yescharacteristic, complemented
77C3×C4×SD16C2×C311yescharacteristic, complemented
78C3×C4×D8—31no—
79C3×#431—31no—
80#5172C2×C311yescharacteristic
81#5166C2×C311yescharacteristic, complemented
82C4×#216C2×C311yescharacteristic, complemented
83C4×#213C2×C311yescharacteristic, complemented
84#4871C2×C311yescharacteristic, complemented
85#4868C2×C311yescharacteristic, complemented
86#4808C2×C311yescharacteristic, complemented
87#4799C2×C311yescharacteristic, complemented
88#4787C2×C311yescharacteristic, complemented
89#4779C2×C311yescharacteristic, complemented
90C4×#204C2×C311yescharacteristic, complemented
91#4685C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C3×#239—22no—
97C3×#239—22no—
98C2×C3×D12—21no—
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×Dic6C2311yescharacteristic
107C32×SD16—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#216—22no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
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
140C3×#204—22no—
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#239C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—21no—
146C2×C3×SD16—31no—
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×SD16C22×C311yescharacteristic
149C2×C3×D8—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×C4×Q8—21no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×Q8C22×C311yescharacteristic
161C3×C4×D4—21no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×C4×D4—61no—
167C3×C4×D4C2×D311yescharacteristic
168C3×C4×D4C22×C311yescharacteristic
169C3×#117—31no—
170C3×#117—61no—
171C3×#117—61no—
172C2×C3×C42—31no—
173C2×C3×C42—61no—
174Q8×Dic3C22×C311yescharacteristic
175C2×#216C22×C311yescharacteristic
176#938C22×C311yescharacteristic
177#936C22×C311yescharacteristic
178C2×#213C22×C311yescharacteristic
179C4×#67—21no—
180#926—21no—
181C2×#204C22×C311yescharacteristic
182#897C22×C311yescharacteristic
183#893—21no—
184#893C22×C311yescharacteristic
185#892—21no—
186#892C22×C311yescharacteristic
187#890C22×C311yescharacteristic
188#883—21no—
189#879—21no—
190C4×D12—21no—
191C4×D12C22×C311yescharacteristic
192C42×D3—21no—
193C42×D3C22×C311yescharacteristic
194C4×Dic6C22×C311yescharacteristic
195C3×#107—31no—
196C3×#107—31no—
197C3×#106—21no—
198C3×#106—31no—
199C3×#106C2×D311yescharacteristic
200C3×#106C22×C311yescharacteristic
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103C2×D311yescharacteristic
208C3×#103C22×C311yescharacteristic
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102C2×D311yescharacteristic
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#835C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#817C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#807C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4×C3⋊C8C22×C311yescharacteristic
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8#4112yes—
240C32×D4—21no—
241C32×D4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—42no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C3×#67—42no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—24no—
257C3×D12—21no—
258C3×D12#4112yes—
259C3×C4×D3—24no—
260C3×C4×D3—22no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—41no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
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×SD16C3×D311yescharacteristic, complemented
285C4×D8—31no—
286#431—31no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C23×C311yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C23×C311yescharacteristic
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—41no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309#239—22no—
310#239—22no—
311C2×D12—21no—
312C2×D12C23×C311yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3C3×D411yescharacteristic
317C2×C4×D3C3×D411yescharacteristic
318C2×C4×D3C23×C311yescharacteristic
319C2×Dic6C23×C311yescharacteristic
320C3×Q16—62no—
321C3×SD16—24no—
322C3×SD16—22no—
323C3×SD16—22no—
324C3×SD16—62no—
325C3×D8—62no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C23×C311yescharacteristic
333C2×C3×C8C23×C311yescharacteristic
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—41no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—21no—
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—41no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42C22×D311yescharacteristic
371C3×C42C23×C311yescharacteristic
372#217—21no—
373#217—21no—
374#217—21no—
375#216—22no—
376#213—22no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3C23×C311yescharacteristic
385C4⋊Dic3C23×C311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—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
396#204—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—21no—
402C2×C3×D3—22no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C32×C4—22no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4#13512yes—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
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×SD16C2×C3×D311yescharacteristic
424C2×D8—31no—
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×Q8C2×C3×D311yescharacteristic
434C4×D4—31no—
435C4×D4—31no—
436C4×D4—61no—
437C4×D4—61no—
438C4×D4—61no—
439C4×D4C2×C3×D311yescharacteristic
440#117—31no—
441#117—61no—
442#117—61no—
443C2×C42—31no—
444C2×C42—61no—
445#107—31no—
446#107—31no—
447#106—31no—
448#106C2×C3×D311yescharacteristic
449C4⋊C8—31no—
450C4⋊C8—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#103C2×C3×D311yescharacteristic
455#102—31no—
456#102—31no—
457#102—31no—
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—31no—
466C23×C3—41no—
467C23×C3—61no—
468C22×D3—21no—
469C22×D3C2×C3×D411yescharacteristic
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—22no—
473C3×Q8—41no—
474C3×Q8—61no—
475C3×Q8—61no—
476C3×Q8#23512yes—
477C3×Q8C3×#4112yes—
478C3×D4—22no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—32no—
484C3×D4—41no—
485C3×D4—64no—
486C3×D4—61no—
487C3×D4—122no—
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—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—42no—
504C2×C3×C4—42no—
505C2×C3×C4—64no—
506C2×C3×C4—62no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—82no—
513C2×C3×C4—121no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×C3×D411yescharacteristic
519C2×C3×C4C2×C3×D411yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C24×C311yescharacteristic
522#67—42no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3C2×C3×D411yescharacteristic
527C2×Dic3C2×C3×D411yescharacteristic
528C2×Dic3C2×C3×D411yescharacteristic
529D12—24no—
530D12—21no—
531D12C3×#4112yes—
532C4×D3—24no—
533C4×D3—22no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—41no—
537C4×D3—42no—
538C4×D3—42no—
539Dic6—21no—
540Dic6—21no—
541C3×C8—22no—
542C3×C8—21no—
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—41no—
547C3×C8—61no—
548C3×C8—61no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C2×C32—81no—
552C2×C32#52511yescharacteristic
553C2×C32C2×#13511yescharacteristic
554C2×C32#57511yescharacteristic
555C3×D3—41no—
556C3×D3—42no—
557#41—62no—
558#41—62no—
559C2×Q8—31no—
560C2×Q8C22×C3×D311yescharacteristic
561C2×D4—31no—
562C2×D4—61no—
563C2×D4—61no—
564C2×D4C22×C3×D311yescharacteristic
565C22×C4—21no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572Q16—62no—
573SD16—22no—
574SD16—62no—
575D8—62no—
576C2×C8—31no—
577C2×C8—31no—
578C2×C8C22×C3×D311yescharacteristic
579C2×C8C22×C3×D311yescharacteristic
580C4⋊C4—21no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4C22×C3×D311yescharacteristic
589C4⋊C4C22×C3×D311yescharacteristic
590C22⋊C4—21no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C42—21no—
599C42—31no—
600C42—31no—
601C42—31no—
602C42—61no—
603C42—61no—
604C42—61no—
605C42C22×C3×D311yescharacteristic
606C22×C3—21no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—62no—
617C22×C3—61no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C22×C3×D411yescharacteristic
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—22no—
628C2×D3—41no—
629C2×D3—41no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—41no—
638C3×C4—42no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4#91612yes—
652C3×C4C3×#13512yes—
653C3×C4C2×#23511yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4C2×C3×#4111yescharacteristic
656C3×C4C2×C3×#4111yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663C32#310211yescharacteristic, complemented, Sylow
664C23—21no—
665C23—31no—
666C23—61no—
667Q8—21no—
668Q8—61no—
669Q8—61no—
670Q8C3×#23512yes—
671D4—21no—
672D4—21no—
673D4—32no—
674D4—64no—
675D4—61no—
676D4—122no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—42no—
684C2×C4—64no—
685C2×C4—62no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—121no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4C3×D3×D411yescharacteristic
695C2×C4C3×D3×D411yescharacteristic
696C2×C4C23×C3×D311yescharacteristic
697C8—21no—
698C8—21no—
699C8—61no—
700C8—61no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—82no—
705C2×C3—81no—
706C2×C3—81no—
707C2×C3—121no—
708C2×C3—122no—
709C2×C3#554711yescharacteristic
710C2×C3C2×#91611yescharacteristic
711C2×C3#576811yescharacteristic
712C2×C3C3×#52511yescharacteristic
713C2×C3C2×C3×#13511yescharacteristic
714C2×C3C3×#57511yescharacteristic
715D3—41no—
716D3—42no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—61no—
721C22—61no—
722C22—62no—
723C22—61no—
724C22—121no—
725C22—121no—
726C22C2×C3×D3×D411yescharacteristic
727C4—21no—
728C4—22no—
729C4—41no—
730C4—41no—
731C4—61no—
732C4—61no—
733C4—61no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4C3×#91612yes—
738C4C2×C3×#23511yescharacteristic
739C4C3×D3×#4111yescharacteristic
740C3—21no—
741C3#7969411yescharacteristic, direct product factor
742C3C3×#310211yescharacteristic, complemented
743C2—81no—
744C2—121no—
745C2—122no—
746C2C3×#554711yescharacteristic
747C2C2×C3×#91611yescharacteristic
748C2C3×#576811yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5172C2
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×C4×#239C2semidirect
2. C3×#5557C2semidirect
3. C32×C4×SD16C2semidirect
5. C3×#5166C2semidirect
6. C3×C4×#216C2semidirect
7. C3×C4×#213C2semidirect
8. C3×#4871C2semidirect
9. C3×#4868C2semidirect
10. C3×#4808C2semidirect
11. C3×#4799C2semidirect
12. C3×#4787C2semidirect
13. C3×#4779C2semidirect
14. C3×C4×#204C2semidirect
15. C3×#4685C2semidirect
17. #79694C3direct (N × H)
63. C4×#239C2×C3semidirect
64. #5557C2×C3semidirect
76. C3×C4×SD16D3semidirect
77. C3×C4×SD16C2×C3semidirect
81. #5166C2×C3semidirect
82. C4×#216C2×C3semidirect
83. C4×#213C2×C3semidirect
84. #4871C2×C3semidirect
85. #4868C2×C3semidirect
86. #4808C2×C3semidirect
87. #4799C2×C3semidirect
88. #4787C2×C3semidirect
89. #4779C2×C3semidirect
90. C4×#204C2×C3semidirect
91. #4685C2×C3semidirect
284. C4×SD16C3×D3semidirect
663. C32#3102semidirect
741. C3#79694direct (N × H)
742. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
C3×#55572
C32×C4×SD162
C3×#51722
C3×#51662
C3×C4×#2162
C3×C4×#2132
C3×#48712
C3×#48682
C3×#48082
C3×#47992
C3×#47872
C3×#47792
C3×C4×#2042
C3×#46852
C3×#31023
#796943