Finite Group Databasebeta

← C3×#80136 #11872105

Subgroups — C3×#80136 #11872105

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic, complemented
2C3×#5643C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5C3×#5165C211yesmaximal, characteristic, complemented
6C3×#5165C211yesmaximal, characteristic, complemented
7C3×#5164C211yesmaximal, characteristic, complemented
8C3×Dic3×SD16C211yesmaximal, characteristic, complemented
9C3×#5045C211yesmaximal, characteristic, complemented
10C3×#4785C211yesmaximal, characteristic, complemented
11C3×#4761C211yesmaximal, characteristic, complemented
12C3×#4759C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4737C211yesmaximal, characteristic, complemented
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3118—31nomaximal
17#80136C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×C3×#217—21no—
23C2×C3×#217—21no—
24C3×#947C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C3×D4×Dic3—21no—
27C3×D4×Dic3—21no—
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic
30C3×D4×Dic3C2211yescharacteristic
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×#930C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C3×#926C2211yescharacteristic
37C3×#898—21no—
38C3×#897—21no—
39C3×#893C2211yescharacteristic, complemented
40C3×#888C2211yescharacteristic, complemented
41C3×#885—21no—
42C3×#883—21no—
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#821C2211yescharacteristic, complemented
52C3×#821C2211yescharacteristic, complemented
53C3×#818C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C8×Dic3C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#542—31no—
62C3×#518—31no—
63#5798C2×C311yescharacteristic, complemented
64#5643C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#476—31no—
68C3×#474—31no—
69C3×#463—31no—
70C3×#463—31no—
71C3×#450—21no—
72C3×#450D311yescharacteristic, complemented
73C3×#450C2×C311yescharacteristic, complemented
74C3×#447—31no—
75C3×#442—31no—
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5217C2×C311yescharacteristic
81#5165C2×C311yescharacteristic, complemented
82#5165C2×C311yescharacteristic, complemented
83#5164C2×C311yescharacteristic, complemented
84Dic3×SD16C2×C311yescharacteristic, complemented
85#5045C2×C311yescharacteristic, complemented
86#4785C2×C311yescharacteristic, complemented
87#4761C2×C311yescharacteristic, complemented
88#4759C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic, complemented
90#4737C2×C311yescharacteristic, complemented
91#4720C2×C311yescharacteristic, complemented
92C24×C32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4—22no—
95C2×C32×D4—22no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×Dic6—21no—
108C32×SD16—22no—
109C32×SD16—22no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#217D411yescharacteristic
122C3×#213—22no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3D411yescharacteristic
130C3×C4⋊Dic3D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3118—31noSylow
142C22×C3×D4—21no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C22×C311yescharacteristic
145C2×C3×SD16—21no—
146C2×C3×SD16—21no—
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×SD16C2×D311yescharacteristic
149C2×C3×SD16C22×C311yescharacteristic
150C2×C3×SD16C22×C311yescharacteristic
151C2×C3×D8—31no—
152C2×C3×D8—31no—
153C3×C4⋊Q8—31no—
154C3×#126—61no—
155C3×#124—31no—
156C3×#124—61no—
157C3×#123—61no—
158C3×C22⋊Q8—21no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C22⋊Q8C22×C311yescharacteristic
162C3×#121—31no—
163C3×C4×Q8—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—61no—
170C3×C4×D4—61no—
171C3×#117—31no—
172C3×#117—31no—
173C2×C3×C22⋊C4—61no—
174C2×C3×C22⋊C4—61no—
175C2×#217—21no—
176C2×#217—21no—
177#947C22×C311yescharacteristic, complemented
178Q8×Dic3C22×C311yescharacteristic, complemented
179D4×Dic3—21no—
180D4×Dic3—21no—
181D4×Dic3C22×C311yescharacteristic
182D4×Dic3C22×C311yescharacteristic
183D4×Dic3C22×C311yescharacteristic
184D4×Dic3C22×C311yescharacteristic
185C2×#213C22×C311yescharacteristic
186C2×#213C22×C311yescharacteristic
187#930C22×C311yescharacteristic
188#926C22×C311yescharacteristic
189#926C22×C311yescharacteristic
190#898—21no—
191#897—21no—
192#893C22×C311yescharacteristic, complemented
193#888C22×C311yescharacteristic, complemented
194#885—21no—
195#883—21no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—21no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102C2×D311yescharacteristic
211C3×#102C2×D311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×C22⋊C8—21no—
215C3×C22⋊C8—31no—
216C3×C22⋊C8C2×D311yescharacteristic
217C3×C22⋊C8C22×C311yescharacteristic
218C3×#97—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic, complemented
221#835C22×C311yescharacteristic, complemented
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224#830C22×C311yescharacteristic
225#821C22×C311yescharacteristic, complemented
226#821C22×C311yescharacteristic, complemented
227#818C22×C311yescharacteristic, complemented
228#817C22×C311yescharacteristic, complemented
229#815C22×C311yescharacteristic, complemented
230Dic3⋊C8C22×C311yescharacteristic, complemented
231Dic3⋊C8C22×C311yescharacteristic, complemented
232C8×Dic3C22×C311yescharacteristic, complemented
233#808C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C23×C32—24no—
236C23×C32—21no—
237C23×C32—21no—
238C23×C32—81no—
239C23×C32—81no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—24no—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4#4112yes—
248C32×D4#4112yes—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—81no—
270C3×Dic6—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—31no—
276#518—31no—
277#485—31no—
278#482—31no—
279#476—31no—
280#474—31no—
281#463—31no—
282#463—31no—
283#450C3×D311yescharacteristic, complemented
284#447—31no—
285#442—31no—
286#440—31no—
287C4×SD16—31no—
288C4×D8—31no—
289#433—31no—
290C24×C3—21no—
291C24×C3—21no—
292C24×C3—41no—
293C2×C3×Q8—21no—
294C2×C3×Q8—61no—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C23×C311yescharacteristic
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4—22no—
300C2×C3×D4—22no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—41no—
307C2×C3×D4—42no—
308C2×C3×D4—42no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C23×C311yescharacteristic
313C2×C3×D4C23×C311yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C2×#67—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C2×D12C23×C311yescharacteristic
328C2×C4×D3—21no—
329C2×Dic6—21no—
330C3×SD16—22no—
331C3×SD16—22no—
332C3×SD16—22no—
333C3×SD16—22no—
334C3×SD16—42no—
335C3×SD16—42no—
336C3×D8—62no—
337C3×D8—62no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C23×C311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C23×C311yescharacteristic
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—31no—
374C3×C42—31no—
375C3×C42—61no—
376C3×C42—61no—
377#217—21no—
378#217—21no—
379#217—21no—
380#217—21no—
381#217—21no—
382#217C3×D411yescharacteristic
383#217C3×D411yescharacteristic
384#213—22no—
385#213—22no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3C3×D411yescharacteristic
392C4⋊Dic3C3×D411yescharacteristic
393C4⋊Dic3C23×C311yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397C4×Dic3—21no—
398C4×Dic3—21no—
399C4×Dic3C23×C311yescharacteristic
400C4×Dic3C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—22no—
406C22×C32—22no—
407C22×C32—21no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—84no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×D4C2×C3×D311yescharacteristic
430C2×SD16C2×C3×D311yescharacteristic
431C2×SD16C2×C3×D311yescharacteristic
432C2×D8—31no—
433C2×D8—31no—
434C4⋊Q8—31no—
435#126—61no—
436#124—31no—
437#124—61no—
438#123—61no—
439C22⋊Q8—61no—
440C22⋊Q8C2×C3×D311yescharacteristic
441#121—31no—
442C4×Q8—31no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450#117—31no—
451#117—31no—
452C2×C22⋊C4—61no—
453C2×C22⋊C4—61no—
454#107—31no—
455#107—31no—
456#106—31no—
457#106—31no—
458C4⋊C8—31no—
459C4⋊C8—31no—
460#103—31no—
461#103—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—31no—
466#102C2×C3×D311yescharacteristic
467#102C2×C3×D311yescharacteristic
468C22⋊C8—31no—
469C22⋊C8C2×C3×D311yescharacteristic
470#97—31no—
471C4×C8—31no—
472C23×C3—24no—
473C23×C3—24no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—44no—
482C23×C3—61no—
483C23×C3—81no—
484C23×C3—81no—
485C23×C3—81no—
486C23×C3—81no—
487C23×C3—82no—
488C23×C3—82no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×C3×D411yescharacteristic
491C22×D3—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—241no—
499C3×D4—24no—
500C3×D4—24no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—44no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—241no—
513C3×D4#23712yes—
514C3×D4#23712yes—
515C3×D4C3×#4112yes—
516C3×D4C3×#4112yes—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—241no—
539C2×C3×C4—241no—
540C2×C3×C4—241no—
541C2×C3×C4—241no—
542C2×C3×C4—241no—
543C2×C3×C4D3×D411yescharacteristic
544C2×C3×C4C2×C3×D411yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C24×C311yescharacteristic
547#67—81no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—81no—
552C2×Dic3—81no—
553C2×Dic3—81no—
554C2×Dic3—81no—
555C2×Dic3C2×C3×D411yescharacteristic
556C2×Dic3C2×C3×D411yescharacteristic
557C2×Dic3C2×C3×D411yescharacteristic
558C2×Dic3C2×C3×D411yescharacteristic
559D12—21no—
560D12—21no—
561C4×D3—81no—
562Dic6—81no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32—42no—
575C2×C32—42no—
576C2×C32#52511yescharacteristic
577C2×C32#57611yescharacteristic
578C2×C32#57711yescharacteristic
579C3×D3—81no—
580C24—21no—
581C2×Q8—61no—
582C2×Q8C22×C3×D311yescharacteristic
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—31no—
587C2×D4—61no—
588C2×D4C22×C3×D311yescharacteristic
589C2×D4C22×C3×D311yescharacteristic
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4C22×C3×D311yescharacteristic
596SD16—22no—
597SD16—22no—
598D8—62no—
599D8—62no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8C22×C3×D311yescharacteristic
603C2×C8C22×C3×D311yescharacteristic
604C4⋊C4—21no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4C22×C3×D311yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—61no—
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—31no—
627C42—61no—
628C42—61no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—22no—
636C22×C3—22no—
637C22×C3—21no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—42no—
644C22×C3—42no—
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—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—84no—
658C22×C3—84no—
659C22×C3—88no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C22×C3×D411yescharacteristic
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
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—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—81no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23711yescharacteristic
687C3×C4C2×#23711yescharacteristic
688C3×C4C2×C3×#4111yescharacteristic
689C3×C4C2×C3×#4111yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697C32#311811yescharacteristic, complemented, Sylow
698C23—24no—
699C23—21no—
700C23—21no—
701C23—61no—
702C23—81no—
703C23—81no—
704C23C3×D3×D411yescharacteristic
705Q8—21no—
706Q8—21no—
707Q8—241no—
708D4—24no—
709D4—21no—
710D4—21no—
711D4—61no—
712D4—61no—
713D4—241no—
714D4C3×#23712yes—
715D4C3×#23712yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—241no—
728C2×C4—241no—
729C2×C4—241no—
730C2×C4—241no—
731C2×C4—241no—
732C2×C4C3×D3×D411yescharacteristic
733C2×C4C23×C3×D311yescharacteristic
734C8—21no—
735C8—21no—
736C8—61no—
737C8—61no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—41no—
743C2×C3—42no—
744C2×C3—42no—
745C2×C3—41no—
746C2×C3—42no—
747C2×C3—42no—
748C2×C3—82no—
749C2×C3—82no—
750C2×C3—241no—
751C2×C3#558611yescharacteristic
752C2×C3#576211yescharacteristic
753C2×C3#577411yescharacteristic
754C2×C3C3×#52511yescharacteristic
755C2×C3C3×#57611yescharacteristic
756C2×C3C3×#57711yescharacteristic
757D3—81no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—84no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22C2×C3×D3×D411yescharacteristic
772C4—21no—
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—61no—
778C4—61no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4C2×C3×#23711yescharacteristic
783C4C2×C3×#23711yescharacteristic
784C3—21no—
785C3#8013611yescharacteristic, direct product factor
786C3C3×#311811yescharacteristic, complemented
787C2—41no—
788C2—42no—
789C2—42no—
790C2—241no—
791C2C3×#558611yescharacteristic
792C2C3×#576211yescharacteristic
793C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC3×#5217C2
hypercenterC3×#450D3
hypocenterC3C3×#3118
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C3×#5798C2semidirect
2. C3×#5643C2semidirect
3. C32×#450C2semidirect
5. C3×#5165C2semidirect
6. C3×#5165C2semidirect
7. C3×#5164C2semidirect
8. C3×Dic3×SD16C2semidirect
9. C3×#5045C2semidirect
10. C3×#4785C2semidirect
11. C3×#4761C2semidirect
12. C3×#4759C2semidirect
13. C3×#4756C2semidirect
14. C3×#4737C2semidirect
15. C3×#4720C2semidirect
17. #80136C3direct (N × H)
24. C3×#947C22semidirect
25. C3×Q8×Dic3C22semidirect
39. C3×#893C22semidirect
40. C3×#888C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
51. C3×#821C22semidirect
52. C3×#821C22semidirect
53. C3×#818C22semidirect
54. C3×#817C22semidirect
55. C3×#815C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C8×Dic3C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
63. #5798C2×C3semidirect
64. #5643C2×C3semidirect
72. C3×#450D3semidirect
73. C3×#450C2×C3semidirect
81. #5165C2×C3semidirect
82. #5165C2×C3semidirect
83. #5164C2×C3semidirect
84. Dic3×SD16C2×C3semidirect
85. #5045C2×C3semidirect
86. #4785C2×C3semidirect
87. #4761C2×C3semidirect
88. #4759C2×C3semidirect
89. #4756C2×C3semidirect
90. #4737C2×C3semidirect
91. #4720C2×C3semidirect
177. #947C22×C3semidirect
178. Q8×Dic3C22×C3semidirect
192. #893C22×C3semidirect
193. #888C22×C3semidirect
220. #835C22×C3semidirect
221. #835C22×C3semidirect
225. #821C22×C3semidirect
226. #821C22×C3semidirect
227. #818C22×C3semidirect
228. #817C22×C3semidirect
229. #815C22×C3semidirect
230. Dic3⋊C8C22×C3semidirect
231. Dic3⋊C8C22×C3semidirect
232. C8×Dic3C22×C3semidirect
233. #808C22×C3semidirect
234. #807C22×C3semidirect
283. #450C3×D3semidirect
697. C32#3118semidirect
785. C3#80136direct (N × H)
786. C3C3×#3118semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C3×#56432
C32×#4502
C3×#52172
C3×#51652
C3×#51642
C3×Dic3×SD162
C3×#50452
C3×#47852
C3×#47612
C3×#47592
C3×#47562
C3×#47372
C3×#47202
C3×#31183
#801363