Finite Group Databasebeta

← C3×#80413 #11872795

Subgroups — C3×#80413 #11872795

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5731C211yesmaximal, characteristic, complemented
2C3×#5545C211yesmaximal, characteristic
3C32×#461C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic
5C3×#5169C211yesmaximal, characteristic
6C3×#5164C211yesmaximal, characteristic, complemented
7C3×Dic3×SD16C211yesmaximal, characteristic, complemented
8C3×#5083C211yesmaximal, characteristic, complemented
9C3×#5009C211yesmaximal, characteristic, complemented
10C3×#4847C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4817C211yesmaximal, characteristic, complemented
13C3×#4815C211yesmaximal, characteristic, complemented
14C3×#4814C211yesmaximal, characteristic, complemented
15C3×#4788C211yesmaximal, characteristic, complemented
16C3×#3123—31nomaximal
17#80413C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C4⋊Q8C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C3×C4×#67—21no—
31C2×C3×(C2×D3)⋊C4—21no—
32C3×#898—21no—
33C3×#898—21no—
34C3×#893C2211yescharacteristic
35C3×#892C2211yescharacteristic
36C3×#889—21no—
37C3×#889—21no—
38C3×#67⋊C4—21no—
39C3×D3×C22⋊C4—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#872C2211yescharacteristic
42C3×#870C2211yescharacteristic, complemented
43C32×C4⋊C8C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
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×#541—31no—
62C3×#518—31no—
63#5731C2×C311yescharacteristic, complemented
64#5545C2×C311yescharacteristic
65C3×#485—31no—
66C3×#485—31no—
67C3×#478—31no—
68C3×#478—31no—
69C3×#461—21no—
70C3×#461—31no—
71C3×#461D311yescharacteristic, complemented
72C3×#461C2×C311yescharacteristic, complemented
73C3×#450—31no—
74C3×#450—31no—
75C3×#440—31no—
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5169C2×C311yescharacteristic
81#5169C2×C311yescharacteristic
82#5164C2×C311yescharacteristic, complemented
83Dic3×SD16C2×C311yescharacteristic, complemented
84#5083C2×C311yescharacteristic, complemented
85#5009C2×C311yescharacteristic, complemented
86#4847C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4817C2×C311yescharacteristic, complemented
89#4815C2×C311yescharacteristic, complemented
90#4814C2×C311yescharacteristic, complemented
91#4788C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C32×SD16—22no—
106C32×SD16—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#215—22no—
116C3×#215—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3123—31noSylow
142C22×C3×D4—31no—
143C2×D3×D4C22×C311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16—21no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C2×C3×SD16C2×D311yescharacteristic
149C2×C3×SD16C2×D311yescharacteristic
150C2×C3×SD16C22×C311yescharacteristic
151C2×C3×SD16C22×C311yescharacteristic
152C3×C4⋊Q8—21no—
153C3×C4⋊Q8C2×D311yescharacteristic, complemented
154C3×C4⋊Q8C22×C311yescharacteristic, complemented
155C3×#126—61no—
156C3×#126—61no—
157C3×#125—31no—
158C3×#125—61no—
159C3×#125—61no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×D4—21no—
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#946C22×C311yescharacteristic
177#946C22×C311yescharacteristic
178Q8×Dic3C22×C311yescharacteristic, complemented
179Q8×Dic3C22×C311yescharacteristic, complemented
180C2×#215C22×C311yescharacteristic
181C2×#215C22×C311yescharacteristic
182D4×Dic3C22×C311yescharacteristic
183C4×#67—21no—
184C2×(C2×D3)⋊C4—21no—
185#898—21no—
186#898—21no—
187#893C22×C311yescharacteristic
188#892C22×C311yescharacteristic
189#889—21no—
190#889—21no—
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×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic, complemented
209C3×#103C2×D311yescharacteristic, complemented
210C3×#103C22×C311yescharacteristic, complemented
211C3×#103C22×C311yescharacteristic, complemented
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×#97—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic, complemented
221#835C22×C311yescharacteristic, complemented
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic
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—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—81no—
239C22×C3×D3—81no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—81no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—24no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—31no—
273#518—31no—
274#485—31no—
275#485—31no—
276#478—31no—
277#478—31no—
278#461—31no—
279#461C3×D311yescharacteristic, complemented
280#450—31no—
281#450—31no—
282#440—31no—
283#440—31no—
284C4×SD16—31no—
285C4×SD16—31no—
286#433—31no—
287C24×C3—61no—
288C23×D3—21no—
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—21no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C23×C311yescharacteristic
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—41no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C22×Dic3—21no—
311D3×D4—22no—
312D3×D4—22no—
313C2×D12C23×C311yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3C23×C311yescharacteristic
317C3×SD16—22no—
318C3×SD16—22no—
319C3×SD16—22no—
320C3×SD16—22no—
321C3×SD16—42no—
322C3×SD16—42no—
323C3×SD16—62no—
324C3×SD16—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—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C23×C311yescharacteristic
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—41no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—21no—
365C3×C42—31no—
366C3×C42—61no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42C22×D311yescharacteristic
370C3×C42C23×C311yescharacteristic
371#217—21no—
372#215—22no—
373#215—22no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4C3×D411yescharacteristic
380(C2×D3)⋊C4C3×D411yescharacteristic
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3C23×C311yescharacteristic
384C4⋊Dic3C23×C311yescharacteristic
385C4⋊Dic3C23×C311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4C3×D411yescharacteristic
391Dic3⋊C4C3×D411yescharacteristic
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397C2×C3⋊C8C23×C311yescharacteristic
398C22×C32—22no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C2×C3×D3—21no—
403C2×C3×D3—22no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—84no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—41no—
412C32×C4—41no—
413C32×C4—41no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C22×D4—31no—
423C2×SD16—31no—
424C2×SD16—31no—
425C2×SD16C2×C3×D311yescharacteristic
426C2×SD16C2×C3×D311yescharacteristic
427C4⋊Q8C2×C3×D311yescharacteristic, complemented
428#126—61no—
429#126—61no—
430#125—31no—
431#125—61no—
432#125—61no—
433C22⋊Q8—31no—
434C22⋊Q8—31no—
435C4×Q8—31no—
436C4×Q8—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—31no—
440C4×D4—61no—
441C4×D4—61no—
442C4×D4C2×C3×D311yescharacteristic
443#117—31no—
444#117—31no—
445C2×C22⋊C4—61no—
446C2×C22⋊C4—61no—
447#107—31no—
448#107—31no—
449#106—31no—
450#106—31no—
451C4⋊C8—31no—
452C4⋊C8C2×C3×D311yescharacteristic, complemented
453#103—31no—
454#103—31no—
455#103C2×C3×D311yescharacteristic, complemented
456#103C2×C3×D311yescharacteristic, complemented
457#102—31no—
458#102—31no—
459#102—31no—
460#102—31no—
461C22⋊C8—31no—
462C22⋊C8—31no—
463#97—31no—
464C4×C8—31no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—31no—
468C23×C3—41no—
469C23×C3—64no—
470C23×C3—61no—
471C23×C3—241no—
472C23×C3—241no—
473C22×D3—21no—
474C22×D3—24no—
475C22×D3—81no—
476C22×D3—81no—
477C22×D3C2×C3×D411yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4#23712yes—
498C3×D4C3×#4112yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—81no—
520C2×C3×C4—81no—
521C2×C3×C4—82no—
522C2×C3×C4—241no—
523C2×C3×C4—241no—
524C2×C3×C4—241no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C2×C3×D411yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C24×C311yescharacteristic
531#67—24no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—81no—
536C2×Dic3C2×C3×D411yescharacteristic
537C2×Dic3C2×C3×D411yescharacteristic
538C2×Dic3C2×C3×D411yescharacteristic
539D12—21no—
540D12C3×#4112yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—81no—
544C4×D3—81no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—41no—
550C3×C8—41no—
551C3×C8—61no—
552C3×C8—61no—
553C3⋊C8—21no—
554C3⋊C8—21no—
555C2×C32—42no—
556C2×C32#52511yescharacteristic
557C2×C32#57711yescharacteristic
558C2×C32#57711yescharacteristic
559C3×D3—41no—
560C3×D3—42no—
561C24—61no—
562C2×Q8C22×C3×D311yescharacteristic
563C2×Q8C22×C3×D311yescharacteristic
564C2×D4—31no—
565C2×D4—61no—
566C2×D4—62no—
567C2×D4—62no—
568C2×D4C22×C3×D311yescharacteristic
569C22×C4—21no—
570C22×C4—31no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574SD16—22no—
575SD16—22no—
576SD16—62no—
577SD16—62no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8C22×C3×D311yescharacteristic
581C2×C8C22×C3×D311yescharacteristic
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—31no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4C22×C3×D311yescharacteristic
596C22⋊C4—21no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—61no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C42—31no—
606C42—61no—
607C42—61no—
608C42—61no—
609C42C22×C3×D311yescharacteristic
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—42no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—62no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—244no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C22×C3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—22no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—84no—
636C3×C4—22no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—81no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C2×#23711yescharacteristic
660C3×C4D3×#4111yescharacteristic
661C3×C4C2×C3×#4111yescharacteristic
662C3×C4C2×C3×#4111yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669C32#312311yescharacteristic, complemented, Sylow
670C23—21no—
671C23—31no—
672C23—64no—
673C23—61no—
674C23—241no—
675C23—241no—
676Q8—21no—
677Q8—21no—
678Q8—21no—
679Q8—21no—
680D4—21no—
681D4—32no—
682D4—64no—
683D4—61no—
684D4C3×#23712yes—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—81no—
697C2×C4—241no—
698C2×C4—241no—
699C2×C4—241no—
700C2×C4C3×D3×D411yescharacteristic
701C2×C4C3×D3×D411yescharacteristic
702C2×C4C23×C3×D311yescharacteristic
703C8—21no—
704C8—21no—
705C8—61no—
706C8—61no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—42no—
711C2×C3—42no—
712C2×C3—82no—
713C2×C3—121no—
714C2×C3—122no—
715C2×C3#560611yescharacteristic
716C2×C3#576211yescharacteristic
717C2×C3#577811yescharacteristic
718C2×C3C3×#52511yescharacteristic
719C2×C3C3×#57711yescharacteristic
720C2×C3C3×#57711yescharacteristic
721D3—41no—
722D3—42no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—62no—
730C22—121no—
731C22—121no—
732C22—244no—
733C22C2×C3×D3×D411yescharacteristic
734C4—21no—
735C4—21no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—61no—
740C4—61no—
741C4—61no—
742C4—121no—
743C4—121no—
744C4—121no—
745C4C2×C3×#23711yescharacteristic
746C4C3×D3×#4111yescharacteristic
747C3—21no—
748C3#8041311yescharacteristic, direct product factor
749C3C3×#312311yescharacteristic, complemented
750C2—42no—
751C2—121no—
752C2—122no—
753C2C3×#560611yescharacteristic
754C2C3×#576211yescharacteristic
755C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC3×#461D3
hypocenterC3C3×#3123
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C3×#5731C2semidirect
3. C32×#461C2semidirect
6. C3×#5164C2semidirect
7. C3×Dic3×SD16C2semidirect
8. C3×#5083C2semidirect
9. C3×#5009C2semidirect
10. C3×#4847C2semidirect
11. C3×#4840C2semidirect
12. C3×#4817C2semidirect
13. C3×#4815C2semidirect
14. C3×#4814C2semidirect
15. C3×#4788C2semidirect
17. #80413C3direct (N × H)
21. C32×C4⋊Q8C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C3×Q8×Dic3C22semidirect
42. C3×#870C22semidirect
43. C32×C4⋊C8C22semidirect
44. C32×#103C22semidirect
45. C32×#103C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
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. #5731C2×C3semidirect
71. C3×#461D3semidirect
72. C3×#461C2×C3semidirect
82. #5164C2×C3semidirect
83. Dic3×SD16C2×C3semidirect
84. #5083C2×C3semidirect
85. #5009C2×C3semidirect
86. #4847C2×C3semidirect
87. #4840C2×C3semidirect
88. #4817C2×C3semidirect
89. #4815C2×C3semidirect
90. #4814C2×C3semidirect
91. #4788C2×C3semidirect
153. C3×C4⋊Q8C2×D3semidirect
154. C3×C4⋊Q8C22×C3semidirect
178. Q8×Dic3C22×C3semidirect
179. Q8×Dic3C22×C3semidirect
195. #870C22×C3semidirect
202. C3×C4⋊C8C2×D3semidirect
203. C3×C4⋊C8C22×C3semidirect
208. C3×#103C2×D3semidirect
209. C3×#103C2×D3semidirect
210. C3×#103C22×C3semidirect
211. C3×#103C22×C3semidirect
220. #835C22×C3semidirect
221. #835C22×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
279. #461C3×D3semidirect
427. C4⋊Q8C2×C3×D3semidirect
452. C4⋊C8C2×C3×D3semidirect
455. #103C2×C3×D3semidirect
456. #103C2×C3×D3semidirect
669. C32#3123semidirect
748. C3#80413direct (N × H)
749. C3C3×#3123semidirect

Maximal subgroups

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

subgroupindex
C3×#57312
C3×#55452
C32×#4612
C3×#51692
C3×#51642
C3×Dic3×SD162
C3×#50832
C3×#50092
C3×#48472
C3×#48402
C3×#48172
C3×#48152
C3×#48142
C3×#47882
C3×#31233
#804133