Finite Group Databasebeta

← C3×#79185 #11869651

Subgroups — C3×#79185 #11869651

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5524C211yesmaximal, characteristic
2C3×D3×#117C211yesmaximal, characteristic, complemented
3C32×#427C211yesmaximal, characteristic, complemented
4C3×#5113C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7C3×#4998C211yesmaximal, characteristic, complemented
8C3×#4888C211yesmaximal, characteristic, complemented
9C3×#4885C211yesmaximal, characteristic, complemented
10C3×#4884C211yesmaximal, characteristic, complemented
11C3×#4882C211yesmaximal, characteristic, complemented
12C3×#4868C211yesmaximal, characteristic, complemented
13C3×#4866C211yesmaximal, characteristic, complemented
14C3×#4863C211yesmaximal, characteristic, complemented
15C3×#4862C211yesmaximal, characteristic, complemented
16C3×#3091—31nomaximal
17#79185C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C32×#117C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×#897C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×#895C2211yescharacteristic
29C3×#892C2211yescharacteristic
30C3×#892C2211yescharacteristic
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×D3×C4⋊C4C2211yescharacteristic
33C3×#886—21no—
34C3×#882—21no—
35C3×D3×C22⋊C4—21no—
36C3×#877—21no—
37C3×C4×D12—21no—
38C3×C4×D12—21no—
39C3×#872—21no—
40C3×C42×D3—21no—
41C32×#107C2211yescharacteristic, complemented
42C32×#107C2211yescharacteristic, complemented
43C32×#106C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C3×#821C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic, complemented
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#525—31no—
62C2×C3×#117—31no—
63#5524C2×C311yescharacteristic
64D3×#117C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#485—31no—
67C3×#484—31no—
68C3×#483—31no—
69C3×#482—31no—
70C3×#482—31no—
71C3×#481—31no—
72C3×#480—31no—
73C3×#427—21no—
74C3×#427—31no—
75C3×#427D311yescharacteristic, complemented
76C3×#427C2×C311yescharacteristic, complemented
77C3×#416—31no—
78C3×#416—31no—
79C2×C3×C22⋊C8—31no—
80#5113C2×C311yescharacteristic, complemented
81C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
82#5002C2×C311yescharacteristic, complemented
83#4998C2×C311yescharacteristic, complemented
84#4888C2×C311yescharacteristic, complemented
85#4885C2×C311yescharacteristic, complemented
86#4884C2×C311yescharacteristic, complemented
87#4882C2×C311yescharacteristic, complemented
88#4868C2×C311yescharacteristic, complemented
89#4866C2×C311yescharacteristic, complemented
90#4863C2×C311yescharacteristic, complemented
91#4862C2×C311yescharacteristic, complemented
92C23×C3×D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C22×C3×Dic3D411yescharacteristic
96C3×#235—22no—
97C3×#235—22no—
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C32×C8—22no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C32×C42—21no—
121C32×C42—21no—
122C3×#217—21no—
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×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C2×C3×C3⋊C8—22no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3091—31noSylow
142C2×C3×#41—31no—
143C23×C3×C4—31no—
144C2×#235C22×C311yescharacteristic
145C22×C4×D3C22×C311yescharacteristic
146C22×C3×C8—21no—
147C22×C3×C8—31no—
148C22×C3×C8C2×D311yescharacteristic
149C22×C3×C8C22×C311yescharacteristic
150C3×#123—61no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C3×#121—31no—
154C3×#121—31no—
155C3×#120—61no—
156C3×C4×D4—61no—
157C3×C4×D4—61no—
158C3×#117—21no—
159C3×#117—21no—
160C3×#117—31no—
161C3×#117—31no—
162C3×#117—31no—
163C3×#117—61no—
164C3×#117—61no—
165C3×#117C2×D311yescharacteristic
166C3×#117C2×D311yescharacteristic
167C3×#117C22×C311yescharacteristic
168C3×#117C22×C311yescharacteristic
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C22⋊C4—61no—
172C2×C3×C42—61no—
173#926C22×C311yescharacteristic
174C22×C3⋊C8C22×C311yescharacteristic
175#897C22×C311yescharacteristic
176#897C22×C311yescharacteristic
177#895C22×C311yescharacteristic
178#895C22×C311yescharacteristic
179#892C22×C311yescharacteristic
180#892C22×C311yescharacteristic
181D3×C4⋊C4C22×C311yescharacteristic
182D3×C4⋊C4C22×C311yescharacteristic
183#886—21no—
184#882—21no—
185D3×C22⋊C4—21no—
186#877—21no—
187C4×D12—21no—
188C4×D12—21no—
189#872—21no—
190C42×D3—21no—
191C3×#107—21no—
192C3×#107—21no—
193C3×#107—31no—
194C3×#107—31no—
195C3×#107C2×D311yescharacteristic, complemented
196C3×#107C2×D311yescharacteristic, complemented
197C3×#107C22×C311yescharacteristic, complemented
198C3×#107C22×C311yescharacteristic, complemented
199C3×#106—21no—
200C3×#106—21no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#106C2×D311yescharacteristic, complemented
204C3×#106C2×D311yescharacteristic, complemented
205C3×#106C22×C311yescharacteristic, complemented
206C3×#106C22×C311yescharacteristic, complemented
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8—31no—
219#821C22×C311yescharacteristic, complemented
220#821C22×C311yescharacteristic, complemented
221(C2×D3)⋊C8C22×C311yescharacteristic
222(C2×D3)⋊C8C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225#816C22×C311yescharacteristic, complemented
226#816C22×C311yescharacteristic, complemented
227#810C22×C311yescharacteristic, complemented
228#810C22×C311yescharacteristic, complemented
229#809C22×C311yescharacteristic, complemented
230#809C22×C311yescharacteristic, complemented
231#808C22×C311yescharacteristic, complemented
232#808C22×C311yescharacteristic, complemented
233#807C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—22no—
237C22×C3×D3—22no—
238C22×C3×D3—21no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4#4112yes—
248C2×C32×C4#4112yes—
249C2×C32×C4C2411yescharacteristic
250C3×#67—42no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—42no—
260C3×D12—42no—
261C3×C4×D3—22no—
262C3×C4×D3—22no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—31no—
277C2×#117—31no—
278#485—31no—
279#485—31no—
280#484—31no—
281#483—31no—
282#482—31no—
283#482—31no—
284#481—31no—
285#480—31no—
286#427—31no—
287#427C3×D311yescharacteristic, complemented
288#416—31no—
289#416—31no—
290C2×C22⋊C8—31no—
291C24×C3—31no—
292C23×D3C3×D411yescharacteristic
293C3×#41—62no—
294C3×#41—62no—
295C2×C3×Q8—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—62no—
309C22×C3×C4—62no—
310C22×C3×C4—61no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C23×C311yescharacteristic
313C2×#67—21no—
314C22×Dic3C3×D411yescharacteristic
315#235—22no—
316#235—22no—
317C2×D12—21no—
318C2×D12—21no—
319C2×D12C23×C311yescharacteristic
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3C3×D411yescharacteristic
326C2×C4×D3C3×D411yescharacteristic
327C2×C4×D3C23×C311yescharacteristic
328C2×C4×D3C23×C311yescharacteristic
329C2×Dic6C23×C311yescharacteristic
330C2×C3×C8—24no—
331C2×C3×C8—22no—
332C2×C3×C8—22no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—62no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C2×C3×C8C23×C311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C23×C311yescharacteristic
357C3×C4⋊C4C23×C311yescharacteristic
358C3×C4⋊C4C23×C311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—41no—
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—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—41no—
378C3×C42—41no—
379C3×C42—61no—
380C3×C42—61no—
381C3×C42—61no—
382#217—21no—
383(C2×D3)⋊C4—21no—
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—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3C23×C311yescharacteristic
392C4⋊Dic3C23×C311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395C4×Dic3—21no—
396C4×Dic3—21no—
397C4×Dic3—21no—
398C2×C3⋊C8—22no—
399C2×C3⋊C8C23×C311yescharacteristic
400C2×C3⋊C8C23×C311yescharacteristic
401C22×C32—21no—
402C22×C32—21no—
403C22×C32#12312yes—
404C22×C32C22×D411yescharacteristic
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—44no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3#13512yes—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4#12312yes—
420C32×C4C2×#4111yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C2×#41—31no—
428C23×C4—31no—
429C22×C8—31no—
430C22×C8C2×C3×D311yescharacteristic
431#123—61no—
432C22⋊Q8—31no—
433C22⋊Q8—31no—
434#121—31no—
435#121—31no—
436#120—61no—
437C4×D4—61no—
438C4×D4—61no—
439#117—31no—
440#117—31no—
441#117—31no—
442#117—61no—
443#117—61no—
444#117C2×C3×D311yescharacteristic
445#117C2×C3×D311yescharacteristic
446C2×C4⋊C4—31no—
447C2×C4⋊C4—31no—
448C2×C22⋊C4—61no—
449C2×C42—61no—
450#107—31no—
451#107—31no—
452#107C2×C3×D311yescharacteristic, complemented
453#107C2×C3×D311yescharacteristic, complemented
454#106—31no—
455#106—31no—
456#106C2×C3×D311yescharacteristic, complemented
457#106C2×C3×D311yescharacteristic, complemented
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—31no—
466C22⋊C8—31no—
467C22⋊C8—31no—
468C22⋊C8—31no—
469C22⋊C8—31no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—31no—
473C23×C3—62no—
474C23×C3—62no—
475C23×C3—61no—
476C23×C3—121no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×C3×D411yescharacteristic
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—21no—
482C22×D3—41no—
483C22×D3C2×C3×D411yescharacteristic
484C22×D3C2×C3×D411yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—122no—
490C3×D4—122no—
491C3×D4—122no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4—122no—
522C2×C3×C4—122no—
523C2×C3×C4#23512yes—
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4#23912yes—
526C2×C3×C4C2×C3×D411yescharacteristic
527C2×C3×C4C3×#4112yes—
528C2×C3×C4C3×#4112yes—
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C24×C311yescharacteristic
531#67—42no—
532C2×Dic3—22no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3C2×C3×D411yescharacteristic
537C2×Dic3C2×C3×D411yescharacteristic
538D12—21no—
539D12—21no—
540D12—42no—
541D12—42no—
542C4×D3—22no—
543C4×D3—22no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549C4×D3—42no—
550C4×D3—42no—
551Dic6—21no—
552Dic6—21no—
553C3×C8—22no—
554C3×C8—22no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32—22no—
564C2×C32C2×#12311yescharacteristic
565C2×C32C2×#13511yescharacteristic
566C2×C32#57511yescharacteristic
567C3×D3—22no—
568C3×D3—41no—
569C3×D3—81no—
570C24—31no—
571#41—62no—
572#41—62no—
573C2×Q8—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—61no—
588C22×C4C22×C3×D311yescharacteristic
589C2×C8—22no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—62no—
593C2×C8C22×C3×D311yescharacteristic
594C2×C8C22×C3×D311yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4C22×C3×D311yescharacteristic
602C4⋊C4C22×C3×D311yescharacteristic
603C4⋊C4C22×C3×D311yescharacteristic
604C4⋊C4C22×C3×D311yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C42—21no—
615C42—21no—
616C42—61no—
617C42—61no—
618C42—61no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—32no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—124no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3#89412yes—
638C22×C3C3×#12312yes—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×C3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—44no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3C3×#13512yes—
651C3×C4—22no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4—81no—
667C3×C4—81no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4#89412yes—
672C3×C4C3×#12312yes—
673C3×C4C2×#23511yescharacteristic
674C3×C4C2×#23911yescharacteristic
675C3×C4C2×C3×#4111yescharacteristic
676C3×C4C2×C3×#4111yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682C32#309111yescharacteristic, complemented, Sylow
683C23—31no—
684C23—31no—
685C23—62no—
686C23—62no—
687C23—61no—
688C23—121no—
689C23C3×D3×D411yescharacteristic
690Q8—61no—
691Q8—61no—
692D4—61no—
693D4—61no—
694D4—122no—
695D4—122no—
696D4—122no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4C3×#23512yes—
717C2×C4C3×D3×D411yescharacteristic
718C2×C4C3×#23912yes—
719C2×C4C23×C3×D311yescharacteristic
720C8—21no—
721C8—21no—
722C8—61no—
723C8—61no—
724C2×C3—22no—
725C2×C3—22no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—62no—
731C2×C3—121no—
732C2×C3—241no—
733C2×C3C2×#89411yescharacteristic
734C2×C3D3×#13511yescharacteristic
735C2×C3#576811yescharacteristic
736C2×C3C2×C3×#12311yescharacteristic
737C2×C3C2×C3×#13511yescharacteristic
738C2×C3C3×#57511yescharacteristic
739D3—22no—
740D3—41no—
741D3—81no—
742C22—21no—
743C22—21no—
744C22—32no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—61no—
750C22—124no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22C3×#89412yes—
755C22C2×C3×D3×D411yescharacteristic
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—61no—
761C4—61no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4C3×#89412yes—
766C4C2×C3×#23511yescharacteristic
767C4C2×C3×#23911yescharacteristic
768C3—21no—
769C3#7918511yescharacteristic, direct product factor
770C3C3×#309111yescharacteristic, complemented
771C2—22no—
772C2—62no—
773C2—121no—
774C2—241no—
775C2C2×C3×#89411yescharacteristic
776C2C3×D3×#13511yescharacteristic
777C2C3×#576811yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#427C2
socleC22×C32C22×D4
prime radicalC3×#5524C2
hypercenterC3×#427D3
hypocenterC3C3×#3091
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#427

Complements

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

NH ≅ G/Ntype
2. C3×D3×#117C2semidirect
3. C32×#427C2semidirect
4. C3×#5113C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C3×#5002C2semidirect
7. C3×#4998C2semidirect
8. C3×#4888C2semidirect
9. C3×#4885C2semidirect
10. C3×#4884C2semidirect
11. C3×#4882C2semidirect
12. C3×#4868C2semidirect
13. C3×#4866C2semidirect
14. C3×#4863C2semidirect
15. C3×#4862C2semidirect
17. #79185C3direct (N × H)
41. C32×#107C22semidirect
42. C32×#107C22semidirect
43. C32×#106C22semidirect
44. C32×#106C22semidirect
45. C3×#821C22semidirect
46. C3×#821C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. C3×#810C22semidirect
54. C3×#810C22semidirect
55. C3×#809C22semidirect
56. C3×#809C22semidirect
57. C3×#808C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×#807C22semidirect
64. D3×#117C2×C3semidirect
75. C3×#427D3semidirect
76. C3×#427C2×C3semidirect
80. #5113C2×C3semidirect
81. C2×(C2×D3)⋊C8C2×C3semidirect
82. #5002C2×C3semidirect
83. #4998C2×C3semidirect
84. #4888C2×C3semidirect
85. #4885C2×C3semidirect
86. #4884C2×C3semidirect
87. #4882C2×C3semidirect
88. #4868C2×C3semidirect
89. #4866C2×C3semidirect
90. #4863C2×C3semidirect
91. #4862C2×C3semidirect
195. C3×#107C2×D3semidirect
196. C3×#107C2×D3semidirect
197. C3×#107C22×C3semidirect
198. C3×#107C22×C3semidirect
203. C3×#106C2×D3semidirect
204. C3×#106C2×D3semidirect
205. C3×#106C22×C3semidirect
206. C3×#106C22×C3semidirect
219. #821C22×C3semidirect
220. #821C22×C3semidirect
225. #816C22×C3semidirect
226. #816C22×C3semidirect
227. #810C22×C3semidirect
228. #810C22×C3semidirect
229. #809C22×C3semidirect
230. #809C22×C3semidirect
231. #808C22×C3semidirect
232. #808C22×C3semidirect
233. #807C22×C3semidirect
234. #807C22×C3semidirect
287. #427C3×D3semidirect
452. #107C2×C3×D3semidirect
453. #107C2×C3×D3semidirect
456. #106C2×C3×D3semidirect
457. #106C2×C3×D3semidirect
682. C32#3091semidirect
769. C3#79185direct (N × H)
770. C3C3×#3091semidirect

Maximal subgroups

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

subgroupindex
C3×#55242
C3×D3×#1172
C32×#4272
C3×#51132
C2×C3×(C2×D3)⋊C82
C3×#50022
C3×#49982
C3×#48882
C3×#48852
C3×#48842
C3×#48822
C3×#48682
C3×#48662
C3×#48632
C3×#48622
C3×#30913
#791853