Finite Group Databasebeta

← C3×#79746 #11870581

Subgroups — C3×#79746 #11870581

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5580C211yesmaximal, characteristic, complemented
2C3×C4×#239C211yesmaximal, characteristic, complemented
3C32×C4×Q16C211yesmaximal, characteristic, complemented
4C3×#5187C211yesmaximal, characteristic, complemented
5C3×#5185C211yesmaximal, characteristic, complemented
6C3×C4×#215C211yesmaximal, characteristic, complemented
7C3×C4×#215C211yesmaximal, characteristic, complemented
8C3×#4891C211yesmaximal, characteristic, complemented
9C3×#4885C211yesmaximal, characteristic, complemented
10C3×#4819C211yesmaximal, characteristic, complemented
11C3×#4814C211yesmaximal, characteristic, complemented
12C3×#4810C211yesmaximal, characteristic
13C3×#4796C211yesmaximal, characteristic, complemented
14C3×C4×D24C211yesmaximal, characteristic, complemented
15C3×#4685C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#79746C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C32×Q16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28C3×#898—21no—
29C3×#895C2211yescharacteristic
30C3×#894—21no—
31C3×#893—21no—
32C3×#893C2211yescharacteristic
33C3×#892—21no—
34C3×#892C2211yescharacteristic
35C3×#890C2211yescharacteristic
36C3×C4×D12—21no—
37C3×C4×D12—21no—
38C3×C4×D12C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×#872—21no—
41C3×C42×D3—21no—
42C3×C42×D3C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×C4×C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5580C2×C311yescharacteristic, complemented
64C4×#239C2×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—21no—
74C3×C4×Q16D311yescharacteristic, complemented
75C3×C4×Q16C2×C311yescharacteristic, complemented
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#431—31no—
80#5187C2×C311yescharacteristic, complemented
81#5185C2×C311yescharacteristic, complemented
82C4×#215C2×C311yescharacteristic, complemented
83C4×#215C2×C311yescharacteristic, complemented
84#4891C2×C311yescharacteristic, complemented
85#4885C2×C311yescharacteristic, complemented
86#4819C2×C311yescharacteristic, complemented
87#4814C2×C311yescharacteristic, complemented
88#4810C2×C311yescharacteristic
89#4796C2×C311yescharacteristic, complemented
90C4×D24C2×C311yescharacteristic, complemented
91#4685C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C3×#239—22no—
95C3×#239—22no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C32×Q16—22no—
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42—21no—
116C32×C42C2311yescharacteristic
117C3×#215—22no—
118C3×#215—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—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×D24—22no—
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#239C22×C311yescharacteristic
144C2×C3×Q16—21no—
145C2×C3×Q16C2×D311yescharacteristic
146C2×C3×Q16C22×C311yescharacteristic
147C2×C3×SD16—31no—
148C2×C3×SD16—31no—
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—21no—
158C3×C4×Q8—31no—
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×Q8C2×D311yescharacteristic
161C3×C4×Q8C22×C311yescharacteristic
162C3×C4×Q8C22×C311yescharacteristic
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C3×C4×D4—61no—
168C3×C4×D4—61no—
169C3×#117—31no—
170C3×#117—61no—
171C3×#117—61no—
172C2×C3×C42—31no—
173C2×C3×C42—61no—
174#947C22×C311yescharacteristic
175#946C22×C311yescharacteristic
176Q8×Dic3C22×C311yescharacteristic
177C2×#215C22×C311yescharacteristic
178C2×#215C22×C311yescharacteristic
179C2×D24C22×C311yescharacteristic
180#898—21no—
181#895C22×C311yescharacteristic
182#894—21no—
183#893—21no—
184#893C22×C311yescharacteristic
185#892—21no—
186#892C22×C311yescharacteristic
187#890C22×C311yescharacteristic
188C4×D12—21no—
189C4×D12—21no—
190C4×D12C22×C311yescharacteristic
191C4×D12C22×C311yescharacteristic
192#872—21no—
193C42×D3—21no—
194C42×D3C22×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—21no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103C2×D311yescharacteristic
208C3×#103C2×D311yescharacteristic
209C3×#103C22×C311yescharacteristic
210C3×#103C22×C311yescharacteristic
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
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#835C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227#818C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234C4×C3⋊C8C22×C311yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8—21no—
240C32×Q8—21no—
241C32×Q8#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—24no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—42no—
259C3×D12#4112yes—
260C3×C4×D3—24no—
261C3×C4×D3—22no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—41no—
265C3×C4×D3—42no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
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×Q16C3×D311yescharacteristic, complemented
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8—31no—
286#431—31no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—21no—
290C2×C3×Q8—21no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×Q8C23×C311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306#239—22no—
307#239—22no—
308C2×D12—21no—
309C2×D12—21no—
310C2×D12C23×C311yescharacteristic
311C2×D12C23×C311yescharacteristic
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3C3×D411yescharacteristic
317C2×C4×D3C3×D411yescharacteristic
318C2×C4×D3C23×C311yescharacteristic
319C3×Q16—24no—
320C3×Q16—22no—
321C3×Q16—22no—
322C3×SD16—62no—
323C3×SD16—62no—
324C3×D8—62no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C23×C311yescharacteristic
332C2×C3×C8C23×C311yescharacteristic
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C4⋊C4C23×C311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
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×C42—21no—
360C3×C42—21no—
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—41no—
368C3×C42—41no—
369C3×C42—61no—
370C3×C42—61no—
371C3×C42C22×D311yescharacteristic
372C3×C42C23×C311yescharacteristic
373#215—22no—
374#215—22no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3—21no—
385C4⋊Dic3C23×C311yescharacteristic
386C4⋊Dic3C23×C311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3C3×D411yescharacteristic
392C4×Dic3C3×D411yescharacteristic
393C4×Dic3C23×C311yescharacteristic
394C2×C3⋊C8C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396D24—22no—
397C22×C32C22×D411yescharacteristic
398C2×C3×D3—21no—
399C2×C3×D3—22no—
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C32×C4—22no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4#13512yes—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C2×#41—31no—
421C2×Q16C2×C3×D311yescharacteristic
422C2×SD16—31no—
423C2×SD16—31no—
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×Q8C2×C3×D311yescharacteristic
433C4×Q8C2×C3×D311yescharacteristic
434C4×D4—31no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—61no—
438C4×D4—61no—
439C4×D4—61no—
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#103C2×C3×D311yescharacteristic
454#103C2×C3×D311yescharacteristic
455#102—31no—
456#102—31no—
457#102—31no—
458#102—31no—
459C22⋊C8—31no—
460C22⋊C8—31no—
461C4×C8—31no—
462C4×C8C2×C3×D311yescharacteristic
463C23×C3—31no—
464C23×C3—61no—
465C23×C3—61no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3C2×C3×D411yescharacteristic
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—22no—
472C3×Q8—21no—
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—22no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8#23512yes—
480C3×Q8C3×#4112yes—
481C3×D4—32no—
482C3×D4—64no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—122no—
487C2×C3×C4—21no—
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—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
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—121no—
512C2×C3×C4—122no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×C3×D411yescharacteristic
518C2×C3×C4C2×C3×D411yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C24×C311yescharacteristic
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3C2×C3×D411yescharacteristic
524C2×Dic3C2×C3×D411yescharacteristic
525C2×Dic3C2×C3×D411yescharacteristic
526D12—24no—
527D12—21no—
528D12—21no—
529D12—21no—
530D12—42no—
531D12C3×#4112yes—
532C4×D3—24no—
533C4×D3—22no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—41no—
537C4×D3—42no—
538C4×D3—42no—
539C4×D3—42no—
540C3×C8—22no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—21no—
544C3×C8—21no—
545C3×C8—41no—
546C3×C8—61no—
547C3×C8—61no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C2×C32#52511yescharacteristic
551C2×C32C2×#13511yescharacteristic
552C2×C32#57511yescharacteristic
553C3×D3—41no—
554C3×D3—42no—
555C3×D3—81no—
556#41—62no—
557#41—62no—
558C2×Q8C22×C3×D311yescharacteristic
559C2×Q8C22×C3×D311yescharacteristic
560C2×D4—31no—
561C2×D4—31no—
562C2×D4—61no—
563C2×D4—61no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571Q16—22no—
572SD16—62no—
573SD16—62no—
574D8—62no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8C22×C3×D311yescharacteristic
578C2×C8C22×C3×D311yescharacteristic
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4C22×C3×D311yescharacteristic
588C4⋊C4C22×C3×D311yescharacteristic
589C22⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C42—21no—
598C42—21no—
599C42—31no—
600C42—31no—
601C42—31no—
602C42—61no—
603C42—61no—
604C42C22×C3×D311yescharacteristic
605C22×C3—21no—
606C22×C3—61no—
607C22×C3—61no—
608C22×C3—62no—
609C22×C3—61no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3C2×D3×D411yescharacteristic
616C22×C3C22×C3×D411yescharacteristic
617C2×D3—21no—
618C2×D3—21no—
619C2×D3—21no—
620C2×D3—22no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—41no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—41no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4#91912yes—
650C3×C4C3×#13512yes—
651C3×C4C2×#23511yescharacteristic
652C3×C4D3×#4111yescharacteristic
653C3×C4C2×C3×#4111yescharacteristic
654C3×C4C2×C3×#4111yescharacteristic
655Dic3—21no—
656Dic3—21no—
657Dic3—21no—
658Dic3—41no—
659Dic3—41no—
660C32#310211yescharacteristic, complemented, Sylow
661C23—31no—
662C23—61no—
663C23—61no—
664Q8—21no—
665Q8—21no—
666Q8—21no—
667Q8C3×#23512yes—
668D4—32no—
669D4—64no—
670D4—61no—
671D4—61no—
672D4—61no—
673D4—122no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—64no—
682C2×C4—62no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—121no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—122no—
691C2×C4C3×D3×D411yescharacteristic
692C2×C4C3×D3×D411yescharacteristic
693C2×C4C23×C3×D311yescharacteristic
694C8—21no—
695C8—21no—
696C8—61no—
697C8—61no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—121no—
702C2×C3—122no—
703C2×C3—241no—
704C2×C3#554711yescharacteristic
705C2×C3C2×#91911yescharacteristic
706C2×C3#576811yescharacteristic
707C2×C3C3×#52511yescharacteristic
708C2×C3C2×C3×#13511yescharacteristic
709C2×C3C3×#57511yescharacteristic
710D3—41no—
711D3—42no—
712D3—81no—
713C22—61no—
714C22—61no—
715C22—62no—
716C22—61no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22C2×C3×D3×D411yescharacteristic
723C4—21no—
724C4—22no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—61no—
729C4—61no—
730C4—61no—
731C4—121no—
732C4—121no—
733C4C3×#91912yes—
734C4C2×C3×#23511yescharacteristic
735C4C3×D3×#4111yescharacteristic
736C3—21no—
737C3#7974611yescharacteristic, direct product factor
738C3C3×#310211yescharacteristic, complemented
739C2—121no—
740C2—122no—
741C2—241no—
742C2C3×#554711yescharacteristic
743C2C2×C3×#91911yescharacteristic
744C2C3×#576811yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC3×#4810C2
hypercenterC3×C4×Q16D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C3×#5580C2semidirect
2. C3×C4×#239C2semidirect
3. C32×C4×Q16C2semidirect
4. C3×#5187C2semidirect
5. C3×#5185C2semidirect
6. C3×C4×#215C2semidirect
7. C3×C4×#215C2semidirect
8. C3×#4891C2semidirect
9. C3×#4885C2semidirect
10. C3×#4819C2semidirect
11. C3×#4814C2semidirect
13. C3×#4796C2semidirect
14. C3×C4×D24C2semidirect
15. C3×#4685C2semidirect
17. #79746C3direct (N × H)
63. #5580C2×C3semidirect
64. C4×#239C2×C3semidirect
74. C3×C4×Q16D3semidirect
75. C3×C4×Q16C2×C3semidirect
80. #5187C2×C3semidirect
81. #5185C2×C3semidirect
82. C4×#215C2×C3semidirect
83. C4×#215C2×C3semidirect
84. #4891C2×C3semidirect
85. #4885C2×C3semidirect
86. #4819C2×C3semidirect
87. #4814C2×C3semidirect
89. #4796C2×C3semidirect
90. C4×D24C2×C3semidirect
91. #4685C2×C3semidirect
282. C4×Q16C3×D3semidirect
660. C32#3102semidirect
737. C3#79746direct (N × H)
738. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×#55802
C3×C4×#2392
C32×C4×Q162
C3×#51872
C3×#51852
C3×C4×#2152
C3×#48912
C3×#48852
C3×#48192
C3×#48142
C3×#48102
C3×#47962
C3×C4×D242
C3×#46852
C3×#31023
#797463