Finite Group Databasebeta

← C3×#80317 #11872709

Subgroups — C3×#80317 #11872709

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5719C211yesmaximal, characteristic, complemented
2C3×#5545C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5156C211yesmaximal, characteristic, complemented
6C3×#5152C211yesmaximal, characteristic, complemented
7C3×Dic3×D8C211yesmaximal, characteristic, complemented
8C3×#5072C211yesmaximal, characteristic, complemented
9C3×#5009C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic, complemented
13C3×#4784C211yesmaximal, characteristic, complemented
14C3×#4779C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3122—31nomaximal
17#80317C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×#127C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C3×#939—21no—
24C3×#939—21no—
25C3×#938C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×#935—21no—
28C3×#935—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic, complemented
31C3×D4×Dic3C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×C4×#67—21no—
35C2×C3×(C2×D3)⋊C4—21no—
36C3×#893C2211yescharacteristic
37C3×#892C2211yescharacteristic
38C3×#67⋊C4—21no—
39C3×D3×C22⋊C4—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#872C2211yescharacteristic
42C3×#870C2211yescharacteristic, complemented
43C32×C4⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#818C2211yescharacteristic, complemented
55C3×#817C2211yescharacteristic, complemented
56C3×#815C2211yescharacteristic, complemented
57C3×C8×Dic3C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#540—31no—
62C3×#518—31no—
63#5719C2×C311yescharacteristic, complemented
64#5545C2×C311yescharacteristic, complemented
65C3×#482—31no—
66C3×#482—31no—
67C3×#478—31no—
68C3×#478—31no—
69C3×#459—21no—
70C3×#459—31no—
71C3×#459D311yescharacteristic, complemented
72C3×#459C2×C311yescharacteristic, complemented
73C3×#447—31no—
74C3×#447—31no—
75C3×#442—31no—
76C3×#442—31no—
77C3×C4×D8—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5156C2×C311yescharacteristic, complemented
81#5156C2×C311yescharacteristic, complemented
82#5152C2×C311yescharacteristic, complemented
83Dic3×D8C2×C311yescharacteristic, complemented
84#5072C2×C311yescharacteristic, complemented
85#5009C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4785C2×C311yescharacteristic, complemented
89#4784C2×C311yescharacteristic, complemented
90#4779C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C32×D8—22no—
112C32×D8—22no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C42C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#213—22no—
124C3×#213—22no—
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⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4D411yescharacteristic
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3122—31noSylow
142C22×C3×D4—31no—
143C2×D3×D4C22×C311yescharacteristic
144C2×C3×D8—21no—
145C2×C3×D8—21no—
146C2×C3×D8—31no—
147C2×C3×D8—31no—
148C2×C3×D8C2×D311yescharacteristic
149C2×C3×D8C2×D311yescharacteristic
150C2×C3×D8C22×C311yescharacteristic
151C2×C3×D8C22×C311yescharacteristic
152C3×#127—21no—
153C3×#127C2×D311yescharacteristic, complemented
154C3×#127C22×C311yescharacteristic, complemented
155C3×#125—31no—
156C3×#123—61no—
157C3×#123—61no—
158C3×#121—31no—
159C3×#121—31no—
160C3×#121—61no—
161C3×#121—61no—
162C3×C4×D4—21no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—61no—
169C3×C4×D4—61no—
170C3×C4×D4C2×D311yescharacteristic
171C3×C4×D4C22×C311yescharacteristic
172C3×#117—31no—
173C3×#117—31no—
174C2×C3×C22⋊C4—61no—
175C2×C3×C22⋊C4—61no—
176#939—21no—
177#939—21no—
178#938C22×C311yescharacteristic
179#938C22×C311yescharacteristic
180#935—21no—
181#935—21no—
182D4×Dic3C22×C311yescharacteristic
183D4×Dic3C22×C311yescharacteristic, complemented
184D4×Dic3C22×C311yescharacteristic, complemented
185C2×#213C22×C311yescharacteristic
186C2×#213C22×C311yescharacteristic
187C4×#67—21no—
188C2×(C2×D3)⋊C4—21no—
189#893C22×C311yescharacteristic
190#892C22×C311yescharacteristic
191#67⋊C4—21no—
192D3×C22⋊C4—21no—
193C4×D12C22×C311yescharacteristic
194#872C22×C311yescharacteristic
195#870C22×C311yescharacteristic, complemented
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—21no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8C2×D311yescharacteristic, complemented
203C3×C4⋊C8C22×C311yescharacteristic, complemented
204C3×#102—21no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic, complemented
213C3×#102C2×D311yescharacteristic, complemented
214C3×#102C22×C311yescharacteristic, complemented
215C3×#102C22×C311yescharacteristic, complemented
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×#97—31no—
219C3×C4×C8—31no—
220#832C22×C311yescharacteristic
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic, complemented
223#832C22×C311yescharacteristic, complemented
224#821C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228#818C22×C311yescharacteristic, complemented
229#817C22×C311yescharacteristic, complemented
230#815C22×C311yescharacteristic, complemented
231C8×Dic3C22×C311yescharacteristic, complemented
232#808C22×C311yescharacteristic, complemented
233#807C22×C311yescharacteristic, complemented
234C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
235C23×C32—21no—
236C23×C32—21no—
237C23×C32—21no—
238C22×C3×D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—81no—
249C32×D4—81no—
250C32×D4#4112yes—
251C2×C32×C4—21no—
252C2×C32×C4—81no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—24no—
257C3×#67—81no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12#4112yes—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
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#459C3×D311yescharacteristic, complemented
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—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—41no—
304C2×C3×D4—41no—
305C2×C3×D4—61no—
306C2×C3×D4—62no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C23×C311yescharacteristic
314C2×C3×D4C23×C311yescharacteristic
315C2×C3×D4C23×C311yescharacteristic
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—41no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C2×#67—21no—
326C2×#67—21no—
327C2×#67—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331D3×D4—22no—
332D3×D4—22no—
333C2×D12C23×C311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3C23×C311yescharacteristic
337C3×D8—22no—
338C3×D8—22no—
339C3×D8—22no—
340C3×D8—22no—
341C3×D8—42no—
342C3×D8—42no—
343C3×D8—62no—
344C3×D8—62no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C23×C311yescharacteristic
352C2×C3×C8C23×C311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
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#217—21no—
383#217—21no—
384#217—21no—
385#217—21no—
386#213—22no—
387#213—22no—
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
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4C3×D411yescharacteristic
399Dic3⋊C4C3×D411yescharacteristic
400C4×Dic3—21no—
401C4×Dic3C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403C2×C3⋊C8C23×C311yescharacteristic
404C22×C32—22no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—84no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C22×D4—31no—
433C2×D8—31no—
434C2×D8—31no—
435C2×D8C2×C3×D311yescharacteristic
436C2×D8C2×C3×D311yescharacteristic
437#127C2×C3×D311yescharacteristic, complemented
438#125—31no—
439#123—61no—
440#123—61no—
441#121—31no—
442#121—31no—
443#121—61no—
444#121—61no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—31no—
449C4×D4—31no—
450C4×D4—61no—
451C4×D4—61no—
452C4×D4C2×C3×D311yescharacteristic
453#117—31no—
454#117—31no—
455C2×C22⋊C4—61no—
456C2×C22⋊C4—61no—
457#107—31no—
458#107—31no—
459#106—31no—
460#106—31no—
461C4⋊C8—31no—
462C4⋊C8C2×C3×D311yescharacteristic, complemented
463#102—31no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102—31no—
468#102—31no—
469#102C2×C3×D311yescharacteristic, complemented
470#102C2×C3×D311yescharacteristic, complemented
471C22⋊C8—31no—
472C22⋊C8—31no—
473#97—31no—
474C4×C8—31no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—64no—
486C23×C3—61no—
487C23×C3—241no—
488C23×C3—241no—
489C22×D3—21no—
490C22×D3—24no—
491C22×D3—81no—
492C22×D3—81no—
493C22×D3C2×C3×D411yescharacteristic
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—22no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—64no—
512C3×D4—61no—
513C3×D4—81no—
514C3×D4—81no—
515C3×D4—81no—
516C3×D4—81no—
517C3×D4—82no—
518C3×D4—82no—
519C3×D4—241no—
520C3×D4—241no—
521C3×D4#23712yes—
522C3×D4C3×#4112yes—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—81no—
538C2×C3×C4—81no—
539C2×C3×C4—82no—
540C2×C3×C4—241no—
541C2×C3×C4—241no—
542C2×C3×C4—241no—
543C2×C3×C4—241no—
544C2×C3×C4—241no—
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4C2×C3×D411yescharacteristic
548C2×C3×C4C2×C3×D411yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C24×C311yescharacteristic
551#67—24no—
552#67—81no—
553#67—81no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—81no—
558C2×Dic3—81no—
559C2×Dic3—81no—
560C2×Dic3C2×C3×D411yescharacteristic
561C2×Dic3C2×C3×D411yescharacteristic
562C2×Dic3C2×C3×D411yescharacteristic
563D12—21no—
564D12C3×#4112yes—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—81no—
568C4×D3—81no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—41no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C2×C32—42no—
580C2×C32—81no—
581C2×C32—81no—
582C2×C32#52511yescharacteristic
583C2×C32#57611yescharacteristic
584C2×C32#57611yescharacteristic
585C3×D3—41no—
586C3×D3—42no—
587C24—61no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—62no—
593C2×D4—62no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4C22×C3×D311yescharacteristic
597C2×D4C22×C3×D311yescharacteristic
598C2×D4C22×C3×D311yescharacteristic
599C22×C4—21no—
600C22×C4—31no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606D8—22no—
607D8—22no—
608D8—62no—
609D8—62no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8C22×C3×D311yescharacteristic
613C2×C8C22×C3×D311yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4C22×C3×D311yescharacteristic
622C22⋊C4—21no—
623C22⋊C4—31no—
624C22⋊C4—31no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C42—31no—
634C42—61no—
635C42C22×C3×D311yescharacteristic
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—42no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—62no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—244no—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C22×C3×D411yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—22no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—84no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4C2×#23711yescharacteristic
698C3×C4D3×#4111yescharacteristic
699C3×C4C2×C3×#4111yescharacteristic
700C3×C4C2×C3×#4111yescharacteristic
701Dic3—21no—
702Dic3—21no—
703Dic3—21no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707C32#312211yescharacteristic, complemented, Sylow
708C23—21no—
709C23—21no—
710C23—21no—
711C23—31no—
712C23—64no—
713C23—61no—
714C23—241no—
715C23—241no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—32no—
722D4—64no—
723D4—61no—
724D4—81no—
725D4—81no—
726D4—241no—
727D4—241no—
728D4C3×#23712yes—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—81no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—241no—
743C2×C4—241no—
744C2×C4C3×D3×D411yescharacteristic
745C2×C4C3×D3×D411yescharacteristic
746C2×C4C23×C3×D311yescharacteristic
747C8—21no—
748C8—21no—
749C8—61no—
750C8—61no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—42no—
756C2×C3—82no—
757C2×C3—81no—
758C2×C3—81no—
759C2×C3—81no—
760C2×C3—81no—
761C2×C3—121no—
762C2×C3—122no—
763C2×C3—161no—
764C2×C3—161no—
765C2×C3#560611yescharacteristic
766C2×C3#575711yescharacteristic
767C2×C3#577411yescharacteristic
768C2×C3C3×#52511yescharacteristic
769C2×C3C3×#57611yescharacteristic
770C2×C3C3×#57611yescharacteristic
771D3—41no—
772D3—42no—
773C22—22no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—61no—
783C22—61no—
784C22—61no—
785C22—62no—
786C22—121no—
787C22—121no—
788C22—244no—
789C22C2×C3×D3×D411yescharacteristic
790C4—21no—
791C4—21no—
792C4—41no—
793C4—61no—
794C4—61no—
795C4—61no—
796C4—121no—
797C4—121no—
798C4—121no—
799C4C2×C3×#23711yescharacteristic
800C4C3×D3×#4111yescharacteristic
801C3—21no—
802C3#8031711yescharacteristic, direct product factor
803C3C3×#312211yescharacteristic, complemented
804C2—42no—
805C2—81no—
806C2—81no—
807C2—121no—
808C2—122no—
809C2C3×#560611yescharacteristic
810C2C3×#575711yescharacteristic
811C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenterC3×#459D3
hypocenterC3C3×#3122
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C3×#5719C2semidirect
2. C3×#5545C2semidirect
3. C32×#459C2semidirect
4. C3×#5156C2semidirect
5. C3×#5156C2semidirect
6. C3×#5152C2semidirect
7. C3×Dic3×D8C2semidirect
8. C3×#5072C2semidirect
9. C3×#5009C2semidirect
10. C3×#4847C2semidirect
11. C3×#4840C2semidirect
12. C3×#4785C2semidirect
13. C3×#4784C2semidirect
14. C3×#4779C2semidirect
15. C3×#4756C2semidirect
17. #80317C3direct (N × H)
21. C32×#127C22semidirect
30. C3×D4×Dic3C22semidirect
31. C3×D4×Dic3C22semidirect
42. C3×#870C22semidirect
43. C32×C4⋊C8C22semidirect
44. C32×#102C22semidirect
45. C32×#102C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
54. C3×#818C22semidirect
55. C3×#817C22semidirect
56. C3×#815C22semidirect
57. C3×C8×Dic3C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5719C2×C3semidirect
64. #5545C2×C3semidirect
71. C3×#459D3semidirect
72. C3×#459C2×C3semidirect
80. #5156C2×C3semidirect
81. #5156C2×C3semidirect
82. #5152C2×C3semidirect
83. Dic3×D8C2×C3semidirect
84. #5072C2×C3semidirect
85. #5009C2×C3semidirect
86. #4847C2×C3semidirect
87. #4840C2×C3semidirect
88. #4785C2×C3semidirect
89. #4784C2×C3semidirect
90. #4779C2×C3semidirect
91. #4756C2×C3semidirect
153. C3×#127C2×D3semidirect
154. C3×#127C22×C3semidirect
183. D4×Dic3C22×C3semidirect
184. D4×Dic3C22×C3semidirect
195. #870C22×C3semidirect
202. C3×C4⋊C8C2×D3semidirect
203. C3×C4⋊C8C22×C3semidirect
212. C3×#102C2×D3semidirect
213. C3×#102C2×D3semidirect
214. C3×#102C22×C3semidirect
215. C3×#102C22×C3semidirect
222. #832C22×C3semidirect
223. #832C22×C3semidirect
228. #818C22×C3semidirect
229. #817C22×C3semidirect
230. #815C22×C3semidirect
231. C8×Dic3C22×C3semidirect
232. #808C22×C3semidirect
233. #807C22×C3semidirect
234. C4⋊(C3⋊C8)C22×C3semidirect
285. #459C3×D3semidirect
437. #127C2×C3×D3semidirect
462. C4⋊C8C2×C3×D3semidirect
469. #102C2×C3×D3semidirect
470. #102C2×C3×D3semidirect
707. C32#3122semidirect
802. C3#80317direct (N × H)
803. C3C3×#3122semidirect

Maximal subgroups

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

subgroupindex
C3×#57192
C3×#55452
C32×#4592
C3×#51562
C3×#51522
C3×Dic3×D82
C3×#50722
C3×#50092
C3×#48472
C3×#48402
C3×#47852
C3×#47842
C3×#47792
C3×#47562
C3×#31223
#803173