Finite Group Databasebeta

← C3×#81146 #11872721

Subgroups — C3×#81146 #11872721

Order 1152.

887 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5697C211yesmaximal, characteristic, complemented
2C3×#5545C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5015C211yesmaximal, characteristic, complemented
6C3×#4885C211yesmaximal, characteristic, complemented
7C3×#4872C211yesmaximal, characteristic, complemented
8C3×#4869C211yesmaximal, characteristic, complemented
9C3×#4866C211yesmaximal, characteristic, complemented
10C3×#4843C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic, complemented
13C3×#4773C211yesmaximal, characteristic, complemented
14C3×#4773C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3122—31nomaximal
17#81146C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C32×#125C2211yescharacteristic, complemented
20C32×C4×D4C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C2×C3×D24C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28C3×#895—21no—
29C3×#895—21no—
30C3×#895C2211yescharacteristic
31C3×#895C2211yescharacteristic
32C3×#894—21no—
33C3×#894—21no—
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic, complemented
36C3×#893C2211yescharacteristic, complemented
37C3×#892C2211yescharacteristic
38C3×#67⋊C4—21no—
39C3×D3×C22⋊C4—21no—
40C3×#874C2211yescharacteristic, complemented
41C3×C4×D12C2211yescharacteristic
42C3×#872C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×C4⋊C8C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#540—31no—
62C3×#518—31no—
63#5697C2×C311yescharacteristic, complemented
64#5545C2×C311yescharacteristic, complemented
65C3×#482—31no—
66C3×#482—31no—
67C3×#478—21no—
68C3×#478—31no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#459—31no—
72C3×#459—31no—
73C3×#447—31no—
74C3×#447—31no—
75C3×#442—31no—
76C3×#442—31no—
77C3×C4×D8—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5066C2×C311yescharacteristic, complemented
81#5015C2×C311yescharacteristic, complemented
82#4885C2×C311yescharacteristic, complemented
83#4872C2×C311yescharacteristic, complemented
84#4869C2×C311yescharacteristic, complemented
85#4866C2×C311yescharacteristic, complemented
86#4843C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4785C2×C311yescharacteristic, complemented
89#4773C2×C311yescharacteristic, complemented
90#4773C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4—22no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42C2311yescharacteristic
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)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×D24—22no—
141#3122—31noSylow
142C22×C3×D4—31no—
143C2×D3×D4C22×C311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C2×C3×D8—31no—
148C3×#127—31no—
149C3×#125—21no—
150C3×#125C2×D311yescharacteristic, complemented
151C3×#125C22×C311yescharacteristic, complemented
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—31no—
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×D4C22×C311yescharacteristic
168C3×#117—31no—
169C3×#117—31no—
170C2×C3×C22⋊C4—61no—
171C2×C3×C22⋊C4—61no—
172D4×Dic3C22×C311yescharacteristic
173C2×#213C22×C311yescharacteristic
174C2×#213C22×C311yescharacteristic
175C4×#67—21no—
176C2×(C2×D3)⋊C4—21no—
177C2×D24C22×C311yescharacteristic
178C2×D24C22×C311yescharacteristic
179#895—21no—
180#895—21no—
181#895C22×C311yescharacteristic
182#895C22×C311yescharacteristic
183#894—21no—
184#894—21no—
185#893C22×C311yescharacteristic
186#893C22×C311yescharacteristic, complemented
187#893C22×C311yescharacteristic, complemented
188#892C22×C311yescharacteristic
189#67⋊C4—21no—
190D3×C22⋊C4—21no—
191#874C22×C311yescharacteristic, complemented
192C4×D12C22×C311yescharacteristic
193#872C22×C311yescharacteristic
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic, complemented
197C3×#107C22×C311yescharacteristic, complemented
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic, complemented
201C3×#106C22×C311yescharacteristic, complemented
202C3×C4⋊C8—21no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8C2×D311yescharacteristic, complemented
205C3×C4⋊C8C22×C311yescharacteristic, complemented
206C3×#102—21no—
207C3×#102—21no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C2×D311yescharacteristic
216C3×#102C22×C311yescharacteristic
217C3×#102C22×C311yescharacteristic
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#821C22×C311yescharacteristic, complemented
223#821C22×C311yescharacteristic, complemented
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#815C22×C311yescharacteristic, complemented
227C8×Dic3C22×C311yescharacteristic, complemented
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#809C22×C311yescharacteristic, complemented
231#809C22×C311yescharacteristic, complemented
232#808C22×C311yescharacteristic, complemented
233#807C22×C311yescharacteristic, complemented
234C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—81no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
264C3×D12—81no—
265C3×D12—81no—
266C3×D12—81no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—81no—
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#478C3×D311yescharacteristic, complemented
284#459—31no—
285#459—31no—
286#447—31no—
287#447—31no—
288#442—31no—
289#442—31no—
290C4×D8—31no—
291C4×D8—31no—
292#433—31no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C23×C311yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4—21no—
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—61no—
317C2×#67—21no—
318C22×Dic3—21no—
319D3×D4—22no—
320D3×D4—22no—
321C2×D12—21no—
322C2×D12—21no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12C23×C311yescharacteristic
326C2×D12C23×C311yescharacteristic
327C2×D12C23×C311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3C23×C311yescharacteristic
333C3×D8—62no—
334C3×D8—62no—
335C3×D8—62no—
336C3×D8—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—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4—41no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—61no—
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#213—22no—
383#213—22no—
384(C2×D3)⋊C4—21no—
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)⋊C4—21no—
391(C2×D3)⋊C4C3×D411yescharacteristic
392(C2×D3)⋊C4C3×D411yescharacteristic
393C4⋊Dic3C23×C311yescharacteristic
394Dic3⋊C4C3×D411yescharacteristic
395Dic3⋊C4C3×D411yescharacteristic
396C4×Dic3—21no—
397C4×Dic3C23×C311yescharacteristic
398C2×C3⋊C8C23×C311yescharacteristic
399C2×C3⋊C8C23×C311yescharacteristic
400D24—22no—
401D24—22no—
402C22×C32—22no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—21no—
407C2×C3×D3—22no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—84no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—31no—
431C2×D8—31no—
432C2×D8—31no—
433C2×D8—31no—
434C2×D8—31no—
435#127—31no—
436#125C2×C3×D311yescharacteristic, complemented
437#123—61no—
438#123—61no—
439#121—31no—
440#121—31no—
441#121—61no—
442#121—61no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4C2×C3×D311yescharacteristic
451#117—31no—
452#117—31no—
453C2×C22⋊C4—61no—
454C2×C22⋊C4—61no—
455#107—31no—
456#107C2×C3×D311yescharacteristic, complemented
457#106—31no—
458#106C2×C3×D311yescharacteristic, complemented
459C4⋊C8—31no—
460C4⋊C8C2×C3×D311yescharacteristic, complemented
461#102—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102C2×C3×D311yescharacteristic
468#102C2×C3×D311yescharacteristic
469C22⋊C8—31no—
470C22⋊C8—31no—
471#97—31no—
472C4×C8—31no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—41no—
477C23×C3—64no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—241no—
482C23×C3—241no—
483C22×D3—21no—
484C22×D3—24no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—81no—
488C22×D3—81no—
489C22×D3C2×C3×D411yescharacteristic
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—241no—
502C3×D4—241no—
503C3×D4—241no—
504C3×D4—241no—
505C3×D4#23912yes—
506C3×D4C3×#4112yes—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—81no—
526C2×C3×C4—81no—
527C2×C3×C4—82no—
528C2×C3×C4—241no—
529C2×C3×C4—241no—
530C2×C3×C4—241no—
531C2×C3×C4—241no—
532C2×C3×C4—241no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×C3×D411yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C24×C311yescharacteristic
539#67—24no—
540C2×Dic3—21no—
541C2×Dic3—81no—
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544C2×Dic3C2×C3×D411yescharacteristic
545D12—21no—
546D12—21no—
547D12—21no—
548D12—21no—
549D12—21no—
550D12—81no—
551D12—81no—
552D12—81no—
553D12—81no—
554D12C3×#4112yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—81no—
558C4×D3—81no—
559C4×D3—81no—
560C4×D3—81no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C2×C32—42no—
572C2×C32#52511yescharacteristic
573C2×C32#57611yescharacteristic
574C2×C32#57611yescharacteristic
575C3×D3—41no—
576C3×D3—42no—
577C3×D3—81no—
578C3×D3—81no—
579C24—61no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—61no—
586C2×D4—62no—
587C2×D4—62no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4C22×C3×D311yescharacteristic
591C22×C4—21no—
592C22×C4—31no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598D8—62no—
599D8—62no—
600D8—62no—
601D8—62no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8C22×C3×D311yescharacteristic
605C2×C8C22×C3×D311yescharacteristic
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4C22×C3×D311yescharacteristic
612C4⋊C4C22×C3×D311yescharacteristic
613C4⋊C4C22×C3×D311yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—31no—
616C22⋊C4—31no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C42—31no—
626C42—61no—
627C42C22×C3×D311yescharacteristic
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—42no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—62no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—244no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C22×C3×D411yescharacteristic
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—22no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—84no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4C2×#23911yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4C2×C3×#4111yescharacteristic
690C3×C4C2×C3×#4111yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695C32#312211yescharacteristic, complemented, Sylow
696C23—21no—
697C23—31no—
698C23—64no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—241no—
703C23—241no—
704D4—21no—
705D4—32no—
706D4—64no—
707D4—61no—
708D4—61no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—241no—
713D4—241no—
714D4—241no—
715D4—241no—
716D4C3×#23912yes—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—81no—
727C2×C4—241no—
728C2×C4—241no—
729C2×C4—241no—
730C2×C4—241no—
731C2×C4—241no—
732C2×C4C3×D3×D411yescharacteristic
733C2×C4C3×D3×D411yescharacteristic
734C2×C4C23×C3×D311yescharacteristic
735C8—21no—
736C8—21no—
737C8—61no—
738C8—61no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3—121no—
746C2×C3—122no—
747C2×C3—241no—
748C2×C3—241no—
749C2×C3#562711yescharacteristic
750C2×C3#576911yescharacteristic
751C2×C3#577411yescharacteristic
752C2×C3C3×#52511yescharacteristic
753C2×C3C3×#57611yescharacteristic
754C2×C3C3×#57611yescharacteristic
755D3—41no—
756D3—42no—
757D3—81no—
758D3—81no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—244no—
775C22C2×C3×D3×D411yescharacteristic
776C4—21no—
777C4—21no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—61no—
782C4—61no—
783C4—61no—
784C4—121no—
785C4C2×C3×#23911yescharacteristic
786C4C3×D3×#4111yescharacteristic
787C3—21no—
788C3#8114611yescharacteristic, direct product factor
789C3C3×#312211yescharacteristic, complemented
790C2—42no—
791C2—121no—
792C2—122no—
793C2—241no—
794C2—241no—
795C2C3×#562711yescharacteristic
796C2C3×#576911yescharacteristic
797C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
hypercenterC3×#478D3
hypocenterC3C3×#3122
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5697C2semidirect
2. C3×#5545C2semidirect
3. C32×#478C2semidirect
4. C3×#5066C2semidirect
5. C3×#5015C2semidirect
6. C3×#4885C2semidirect
7. C3×#4872C2semidirect
8. C3×#4869C2semidirect
9. C3×#4866C2semidirect
10. C3×#4843C2semidirect
11. C3×#4840C2semidirect
12. C3×#4785C2semidirect
13. C3×#4773C2semidirect
14. C3×#4773C2semidirect
15. C3×#4756C2semidirect
17. #81146C3direct (N × H)
19. C32×#125C22semidirect
35. C3×#893C22semidirect
36. C3×#893C22semidirect
40. C3×#874C22semidirect
43. C32×#107C22semidirect
44. C32×#106C22semidirect
45. C32×C4⋊C8C22semidirect
48. C3×#821C22semidirect
49. C3×#821C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
56. C3×#809C22semidirect
57. C3×#809C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5697C2×C3semidirect
64. #5545C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5066C2×C3semidirect
81. #5015C2×C3semidirect
82. #4885C2×C3semidirect
83. #4872C2×C3semidirect
84. #4869C2×C3semidirect
85. #4866C2×C3semidirect
86. #4843C2×C3semidirect
87. #4840C2×C3semidirect
88. #4785C2×C3semidirect
89. #4773C2×C3semidirect
90. #4773C2×C3semidirect
91. #4756C2×C3semidirect
150. C3×#125C2×D3semidirect
151. C3×#125C22×C3semidirect
186. #893C22×C3semidirect
187. #893C22×C3semidirect
191. #874C22×C3semidirect
196. C3×#107C2×D3semidirect
197. C3×#107C22×C3semidirect
200. C3×#106C2×D3semidirect
201. C3×#106C22×C3semidirect
204. C3×C4⋊C8C2×D3semidirect
205. C3×C4⋊C8C22×C3semidirect
222. #821C22×C3semidirect
223. #821C22×C3semidirect
226. #815C22×C3semidirect
227. C8×Dic3C22×C3semidirect
230. #809C22×C3semidirect
231. #809C22×C3semidirect
232. #808C22×C3semidirect
233. #807C22×C3semidirect
234. C4⋊(C3⋊C8)C22×C3semidirect
283. #478C3×D3semidirect
436. #125C2×C3×D3semidirect
456. #107C2×C3×D3semidirect
458. #106C2×C3×D3semidirect
460. C4⋊C8C2×C3×D3semidirect
695. C32#3122semidirect
788. C3#81146direct (N × H)
789. C3C3×#3122semidirect

Maximal subgroups

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

subgroupindex
C3×#56972
C3×#55452
C32×#4782
C3×#50662
C3×#50152
C3×#48852
C3×#48722
C3×#48692
C3×#48662
C3×#48432
C3×#48402
C3×#47852
C3×#47732
C3×#47562
C3×#31223
#811463