Finite Group Databasebeta

← C3×#79874 #11872712

Subgroups — C3×#79874 #11872712

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5562C211yesmaximal, characteristic, complemented
2C3×#5545C211yesmaximal, characteristic, complemented
3C32×#442C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6C3×C4×#213C211yesmaximal, characteristic, complemented
7C3×C4×#213C211yesmaximal, characteristic, complemented
8C3×#4871C211yesmaximal, characteristic, complemented
9C3×#4866C211yesmaximal, characteristic, complemented
10C3×#4786C211yesmaximal, characteristic, complemented
11C3×#4779C211yesmaximal, characteristic, complemented
12C3×#4773C211yesmaximal, characteristic, complemented
13C3×#4763C211yesmaximal, characteristic, complemented
14C3×#4711C211yesmaximal, characteristic, complemented
15C3×#4709C211yesmaximal, characteristic, complemented
16C3×#3122—31nomaximal
17#79874C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic, complemented
22C3×#940C2211yescharacteristic, complemented
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C3×#929—21no—
29C3×C4×#67—21no—
30C2×C3×(C2×D3)⋊C4—21no—
31C2×C3×D24C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#892C2211yescharacteristic
35C3×#890C2211yescharacteristic, complemented
36C3×#884—21no—
37C3×#883—21no—
38C3×#67⋊C4—21no—
39C3×D3×C22⋊C4—21no—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic, complemented
42C3×#872C2211yescharacteristic
43C32×#106C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic, complemented
46C32×#97C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#817C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4×C3⋊C8C2211yescharacteristic, complemented
61C3×#540—31no—
62C3×#518—31no—
63#5562C2×C311yescharacteristic, complemented
64#5545C2×C311yescharacteristic, complemented
65C3×#482—31no—
66C3×#482—31no—
67C3×#478—31no—
68C3×#478—31no—
69C3×#459—31no—
70C3×#459—31no—
71C3×#447—31no—
72C3×#447—31no—
73C3×#442—21no—
74C3×#442—31no—
75C3×#442D311yescharacteristic, complemented
76C3×#442C2×C311yescharacteristic, complemented
77C3×C4×D8—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5156C2×C311yescharacteristic, complemented
81#5150C2×C311yescharacteristic, complemented
82C4×#213C2×C311yescharacteristic, complemented
83C4×#213C2×C311yescharacteristic, complemented
84#4871C2×C311yescharacteristic, complemented
85#4866C2×C311yescharacteristic, complemented
86#4786C2×C311yescharacteristic, complemented
87#4779C2×C311yescharacteristic, complemented
88#4773C2×C311yescharacteristic, complemented
89#4763C2×C311yescharacteristic, complemented
90#4711C2×C311yescharacteristic, complemented
91#4709C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×D4—22no—
103C3×D3×D4—22no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C32×D8—22no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#213—22no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—22no—
141#3122—31noSylow
142C22×C3×D4—31no—
143C2×D3×D4C22×C311yescharacteristic
144C2×C3×D8—21no—
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C2×C3×D8—31no—
148C2×C3×D8C2×D311yescharacteristic
149C2×C3×D8C22×C311yescharacteristic
150C3×#127—31no—
151C3×#125—31no—
152C3×#123—61no—
153C3×#123—61no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#121—61no—
158C3×C4×D4—21no—
159C3×C4×D4—21no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×C4×D4C2×D311yescharacteristic
167C3×C4×D4C2×D311yescharacteristic, complemented
168C3×C4×D4C22×C311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic, complemented
170C3×#117—31no—
171C3×#117—31no—
172C2×C3×C22⋊C4—61no—
173C2×C3×C22⋊C4—61no—
174#940C22×C311yescharacteristic, complemented
175#938C22×C311yescharacteristic
176D4×Dic3C22×C311yescharacteristic
177C2×#213C22×C311yescharacteristic
178C2×#213C22×C311yescharacteristic
179#930—21no—
180#929—21no—
181C4×#67—21no—
182C2×(C2×D3)⋊C4—21no—
183C2×D24C22×C311yescharacteristic
184#895C22×C311yescharacteristic
185#893C22×C311yescharacteristic
186#892C22×C311yescharacteristic
187#890C22×C311yescharacteristic, complemented
188#884—21no—
189#883—21no—
190#67⋊C4—21no—
191D3×C22⋊C4—21no—
192C4×D12C22×C311yescharacteristic
193C4×D12C22×C311yescharacteristic, complemented
194#872C22×C311yescharacteristic
195C3×#107—31no—
196C3×#107—31no—
197C3×#106—21no—
198C3×#106—31no—
199C3×#106C2×D311yescharacteristic, complemented
200C3×#106C22×C311yescharacteristic, complemented
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#102—21no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic, complemented
213C3×#102C22×C311yescharacteristic
214C3×#102C22×C311yescharacteristic, complemented
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×#97—21no—
218C3×#97C2×D311yescharacteristic, complemented
219C3×#97C22×C311yescharacteristic, complemented
220C3×C4×C8—31no—
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic, complemented
223#821C22×C311yescharacteristic
224#821C22×C311yescharacteristic, complemented
225(C2×D3)⋊C8C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227#817C22×C311yescharacteristic, complemented
228Dic3⋊C8C22×C311yescharacteristic, complemented
229Dic3⋊C8C22×C311yescharacteristic, complemented
230#809C22×C311yescharacteristic
231#809C22×C311yescharacteristic, complemented
232#807C22×C311yescharacteristic, complemented
233#807C22×C311yescharacteristic, complemented
234C4×C3⋊C8C22×C311yescharacteristic, complemented
235C23×C32—21no—
236C23×C32—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—81no—
250C2×C32×C4—81no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—24no—
255C3×#67—81no—
256C3×#67—81no—
257C3×#67—81no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—81no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×C4×D3—81no—
273C3×C4×D3—81no—
274C32×C8—21no—
275C32×C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—31no—
279#518—31no—
280#482—31no—
281#482—31no—
282#478—31no—
283#478—31no—
284#459—31no—
285#459—31no—
286#447—31no—
287#447—31no—
288#442—31no—
289#442C3×D311yescharacteristic, complemented
290C4×D8—31no—
291C4×D8—31no—
292#433—31no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4—62no—
304C2×C3×D4—62no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C23×C311yescharacteristic
309C2×C3×D4C23×C311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—41no—
316C22×C3×C4—41no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C2×#67—21no—
322C2×#67—21no—
323C2×#67—21no—
324C2×#67—21no—
325C22×Dic3—21no—
326D3×D4—22no—
327D3×D4—22no—
328C2×D12—21no—
329C2×D12C23×C311yescharacteristic
330C2×D12C23×C311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3C23×C311yescharacteristic
335C3×D8—24no—
336C3×D8—22no—
337C3×D8—22no—
338C3×D8—62no—
339C3×D8—62no—
340C3×D8—62no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C42—21no—
377C3×C42—31no—
378C3×C42—61no—
379C3×C42C22×D311yescharacteristic
380C3×C42C23×C311yescharacteristic
381#217—21no—
382#217—21no—
383#213—22no—
384#213—22no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4C3×D411yescharacteristic
391(C2×D3)⋊C4C3×D411yescharacteristic
392C4⋊Dic3—21no—
393C4⋊Dic3C23×C311yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4C3×D411yescharacteristic
397Dic3⋊C4C3×D411yescharacteristic
398C4×Dic3—21no—
399C4×Dic3C23×C311yescharacteristic
400C2×C3⋊C8C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402D24—22no—
403C22×C32—22no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—22no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—84no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C22×D4—31no—
432C2×D8—31no—
433C2×D8—31no—
434C2×D8—31no—
435C2×D8C2×C3×D311yescharacteristic
436#127—31no—
437#125—31no—
438#123—61no—
439#123—61no—
440#121—31no—
441#121—31no—
442#121—61no—
443#121—61no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4C2×C3×D311yescharacteristic
451C4×D4C2×C3×D311yescharacteristic, complemented
452#117—31no—
453#117—31no—
454C2×C22⋊C4—61no—
455C2×C22⋊C4—61no—
456#107—31no—
457#107—31no—
458#106—31no—
459#106C2×C3×D311yescharacteristic, complemented
460C4⋊C8—31no—
461C4⋊C8—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102—31no—
468#102C2×C3×D311yescharacteristic
469#102C2×C3×D311yescharacteristic, complemented
470C22⋊C8—31no—
471C22⋊C8—31no—
472#97C2×C3×D311yescharacteristic, complemented
473C4×C8—31no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—64no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—241no—
485C23×C3—241no—
486C22×D3—21no—
487C22×D3—24no—
488C22×D3—21no—
489C22×D3—81no—
490C22×D3—81no—
491C22×D3C2×C3×D411yescharacteristic
492C3×D4—22no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—32no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—64no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—241no—
508C3×D4—241no—
509C3×D4—241no—
510C3×D4—241no—
511C3×D4#23512yes—
512C3×D4C3×#4112yes—
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—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—81no—
530C2×C3×C4—81no—
531C2×C3×C4—81no—
532C2×C3×C4—81no—
533C2×C3×C4—82no—
534C2×C3×C4—82no—
535C2×C3×C4—241no—
536C2×C3×C4—241no—
537C2×C3×C4—241no—
538C2×C3×C4—241no—
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4C2×C3×D411yescharacteristic
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C24×C311yescharacteristic
545#67—24no—
546#67—81no—
547#67—81no—
548#67—81no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—81no—
552C2×Dic3C2×C3×D411yescharacteristic
553C2×Dic3C2×C3×D411yescharacteristic
554C2×Dic3C2×C3×D411yescharacteristic
555D12—21no—
556D12—21no—
557D12—21no—
558D12—81no—
559D12C3×#4112yes—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—81no—
563C4×D3—81no—
564C4×D3—81no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C2×C32—42no—
576C2×C32—81no—
577C2×C32#52511yescharacteristic
578C2×C32#57611yescharacteristic
579C2×C32#57611yescharacteristic
580C3×D3—41no—
581C3×D3—42no—
582C3×D3—81no—
583C24—61no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—62no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4C22×C3×D311yescharacteristic
594C2×D4C22×C3×D311yescharacteristic
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602D8—22no—
603D8—62no—
604D8—62no—
605D8—62no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8C22×C3×D311yescharacteristic
609C2×C8C22×C3×D311yescharacteristic
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4C22×C3×D311yescharacteristic
617C4⋊C4C22×C3×D311yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C42—31no—
630C42—61no—
631C42C22×C3×D311yescharacteristic
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—244no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C22×C3×D411yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—84no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—81no—
689C3×C4—81no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4C2×#23511yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4C2×C3×#4111yescharacteristic
695C3×C4C2×C3×#4111yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701C32#312211yescharacteristic, complemented, Sylow
702C23—21no—
703C23—21no—
704C23—31no—
705C23—64no—
706C23—61no—
707C23—61no—
708C23—241no—
709C23—241no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—32no—
714D4—64no—
715D4—61no—
716D4—61no—
717D4—61no—
718D4—241no—
719D4—241no—
720D4—241no—
721D4—241no—
722D4C3×#23512yes—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—241no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4—241no—
738C2×C4C3×D3×D411yescharacteristic
739C2×C4C3×D3×D411yescharacteristic
740C2×C4C23×C3×D311yescharacteristic
741C8—21no—
742C8—21no—
743C8—61no—
744C8—61no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—42no—
749C2×C3—42no—
750C2×C3—82no—
751C2×C3—82no—
752C2×C3—81no—
753C2×C3—81no—
754C2×C3—121no—
755C2×C3—122no—
756C2×C3—241no—
757C2×C3#554711yescharacteristic
758C2×C3#577411yescharacteristic
759C2×C3#577411yescharacteristic
760C2×C3C3×#52511yescharacteristic
761C2×C3C3×#57611yescharacteristic
762C2×C3C3×#57611yescharacteristic
763D3—41no—
764D3—42no—
765D3—81no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—62no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—244no—
782C22C2×C3×D3×D411yescharacteristic
783C4—21no—
784C4—21no—
785C4—41no—
786C4—41no—
787C4—61no—
788C4—61no—
789C4—61no—
790C4—121no—
791C4—121no—
792C4C2×C3×#23511yescharacteristic
793C4C3×D3×#4111yescharacteristic
794C3—21no—
795C3#7987411yescharacteristic, direct product factor
796C3C3×#312211yescharacteristic, complemented
797C2—42no—
798C2—81no—
799C2—121no—
800C2—122no—
801C2—241no—
802C2C3×#554711yescharacteristic
803C2C3×#577411yescharacteristic
804C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#442C2
socleC22×C32C22×D4
hypercenterC3×#442D3
hypocenterC3C3×#3122
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
1. C3×#5562C2semidirect
2. C3×#5545C2semidirect
3. C32×#442C2semidirect
4. C3×#5156C2semidirect
5. C3×#5150C2semidirect
6. C3×C4×#213C2semidirect
7. C3×C4×#213C2semidirect
8. C3×#4871C2semidirect
9. C3×#4866C2semidirect
10. C3×#4786C2semidirect
11. C3×#4779C2semidirect
12. C3×#4773C2semidirect
13. C3×#4763C2semidirect
14. C3×#4711C2semidirect
15. C3×#4709C2semidirect
17. #79874C3direct (N × H)
21. C32×C4×D4C22semidirect
22. C3×#940C22semidirect
35. C3×#890C22semidirect
41. C3×C4×D12C22semidirect
43. C32×#106C22semidirect
45. C32×#102C22semidirect
46. C32×#97C22semidirect
48. C3×#832C22semidirect
50. C3×#821C22semidirect
53. C3×#817C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
57. C3×#809C22semidirect
58. C3×#807C22semidirect
59. C3×#807C22semidirect
60. C3×C4×C3⋊C8C22semidirect
63. #5562C2×C3semidirect
64. #5545C2×C3semidirect
75. C3×#442D3semidirect
76. C3×#442C2×C3semidirect
80. #5156C2×C3semidirect
81. #5150C2×C3semidirect
82. C4×#213C2×C3semidirect
83. C4×#213C2×C3semidirect
84. #4871C2×C3semidirect
85. #4866C2×C3semidirect
86. #4786C2×C3semidirect
87. #4779C2×C3semidirect
88. #4773C2×C3semidirect
89. #4763C2×C3semidirect
90. #4711C2×C3semidirect
91. #4709C2×C3semidirect
167. C3×C4×D4C2×D3semidirect
169. C3×C4×D4C22×C3semidirect
174. #940C22×C3semidirect
187. #890C22×C3semidirect
193. C4×D12C22×C3semidirect
199. C3×#106C2×D3semidirect
200. C3×#106C22×C3semidirect
212. C3×#102C2×D3semidirect
214. C3×#102C22×C3semidirect
218. C3×#97C2×D3semidirect
219. C3×#97C22×C3semidirect
222. #832C22×C3semidirect
224. #821C22×C3semidirect
227. #817C22×C3semidirect
228. Dic3⋊C8C22×C3semidirect
229. Dic3⋊C8C22×C3semidirect
231. #809C22×C3semidirect
232. #807C22×C3semidirect
233. #807C22×C3semidirect
234. C4×C3⋊C8C22×C3semidirect
289. #442C3×D3semidirect
451. C4×D4C2×C3×D3semidirect
459. #106C2×C3×D3semidirect
469. #102C2×C3×D3semidirect
472. #97C2×C3×D3semidirect
701. C32#3122semidirect
795. C3#79874direct (N × H)
796. C3C3×#3122semidirect

Maximal subgroups

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

subgroupindex
C3×#55622
C3×#55452
C32×#4422
C3×#51562
C3×#51502
C3×C4×#2132
C3×#48712
C3×#48662
C3×#47862
C3×#47792
C3×#47732
C3×#47632
C3×#47112
C3×#47092
C3×#31223
#798743