Finite Group Databasebeta

← C3×#81186 #11887190

Subgroups — C3×#81186 #11887190

Order 1152.

867 conjugacy classes of subgroups.

The subgroup lattice has 791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic, complemented
2C3×#5554C211yesmaximal, characteristic
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5068C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6C3×#4887C211yesmaximal, characteristic, complemented
7C3×#4885C211yesmaximal, characteristic, complemented
8C3×#4864C211yesmaximal, characteristic, complemented
9C3×#4862C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4834C211yesmaximal, characteristic, complemented
12C3×#4783C211yesmaximal, characteristic, complemented
13C3×#4776C211yesmaximal, characteristic, complemented
14C3×#4772C211yesmaximal, characteristic, complemented
15C3×D3×#102C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#81186C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C32×#125C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#930—21no—
24C2×C3×(C2×D3)⋊C4—21no—
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic, complemented
29C3×#898—21no—
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#897C2211yescharacteristic, complemented
33C3×#895C2211yescharacteristic
34C3×#894—21no—
35C3×#892—21no—
36C3×#892C2211yescharacteristic, complemented
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#890—21no—
39C3×#886—21no—
40C3×#882—21no—
41C3×#875C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45C32×#106C2211yescharacteristic, complemented
46C32×C4⋊C8C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic, complemented
60C3×C4×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5694C2×C311yescharacteristic, complemented
64#5554C2×C311yescharacteristic
65C3×#488—31no—
66C3×#483—31no—
67C3×#482—31no—
68C3×#478—21no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#467—31no—
72C3×#465—31no—
73C3×#464—31no—
74C3×#452—31no—
75C3×#450—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80#5068C2×C311yescharacteristic, complemented
81C4×#214C2×C311yescharacteristic, complemented
82#4887C2×C311yescharacteristic, complemented
83#4885C2×C311yescharacteristic, complemented
84#4864C2×C311yescharacteristic, complemented
85#4862C2×C311yescharacteristic, complemented
86#4845C2×C311yescharacteristic, complemented
87#4834C2×C311yescharacteristic, complemented
88#4783C2×C311yescharacteristic, complemented
89#4776C2×C311yescharacteristic, complemented
90#4772C2×C311yescharacteristic, complemented
91D3×#102C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—41no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C2×C3×D12—21no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119C3×#214—22no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×Dic12—41no—
141C3×#204—41no—
142C3×D3×C8—41no—
143C3×D3×C8—41no—
144#3296—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C22×C311yescharacteristic
148C2×D3×D4C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×#126—61no—
155C3×#125—21no—
156C3×#125—61no—
157C3×#125C2×D311yescharacteristic, complemented
158C3×#125C22×C311yescharacteristic, complemented
159C3×#124—31no—
160C3×#123—61no—
161C3×#123—61no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×#121—31no—
166C3×#121—61no—
167C3×#120—61no—
168C3×C4×Q8—31no—
169C3×C4×D4—21no—
170C3×C4×D4—31no—
171C3×C4×D4C2×D311yescharacteristic
172C3×C4×D4C22×C311yescharacteristic
173C3×#117—31no—
174C3×#117—61no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—61no—
177C2×#214C22×C311yescharacteristic
178#930—21no—
179C2×(C2×D3)⋊C4—21no—
180C2×Dic12C22×C311yescharacteristic, complemented
181C2×#204C22×C311yescharacteristic
182C2×D3×C8C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic, complemented
184#898—21no—
185#897C22×C311yescharacteristic
186#897C22×C311yescharacteristic
187#897C22×C311yescharacteristic, complemented
188#895C22×C311yescharacteristic
189#894—21no—
190#892—21no—
191#892C22×C311yescharacteristic, complemented
192D3×C4⋊C4C22×C311yescharacteristic
193#890—21no—
194#886—21no—
195#882—21no—
196#875C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C4×Dic6C22×C311yescharacteristic, complemented
199C3×#107—21no—
200C3×#107C2×D311yescharacteristic, complemented
201C3×#107C22×C311yescharacteristic, complemented
202C3×#106—21no—
203C3×#106—31no—
204C3×#106C2×D311yescharacteristic, complemented
205C3×#106C22×C311yescharacteristic, complemented
206C3×C4⋊C8—21no—
207C3×C4⋊C8C2×D311yescharacteristic, complemented
208C3×C4⋊C8C22×C311yescharacteristic, complemented
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#102—21no—
214C3×#102—21no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102C2×D311yescharacteristic
220C3×#102C2×D311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×#102C22×C311yescharacteristic
223C3×C22⋊C8—31no—
224C3×C22⋊C8—31no—
225C3×C4×C8—31no—
226#832C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic, complemented
230#816C22×C311yescharacteristic, complemented
231#810C22×C311yescharacteristic, complemented
232#810C22×C311yescharacteristic, complemented
233#810C22×C311yescharacteristic, complemented
234#809C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#808C22×C311yescharacteristic, complemented
237C4×C3⋊C8C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3—81no—
243C22×C3×D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
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—42no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—81no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—31no—
281#488—31no—
282#483—31no—
283#482—31no—
284#478C3×D311yescharacteristic, complemented
285#467—31no—
286#465—31no—
287#464—31no—
288#452—31no—
289#450—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C23×C311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C2×#67—21no—
318C2×#67—21no—
319C22×Dic3—21no—
320#237—22no—
321#237—41no—
322D3×D4—22no—
323D3×D4—41no—
324C2×D12—21no—
325C2×D12C3×D411yescharacteristic
326C2×D12C23×C311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3C23×C311yescharacteristic
329C2×C4×D3C23×C311yescharacteristic
330C2×Dic6C23×C311yescharacteristic
331C2×Dic6C23×C311yescharacteristic
332C3×Q16—121no—
333C3×SD16—62no—
334C3×SD16—121no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—121no—
340C2×C3×C8—121no—
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—41no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C23×C311yescharacteristic
365C3×C4⋊C4C23×C311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—41no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C42—21no—
380C3×C42—61no—
381C3×C42—61no—
382C3×C42C22×D311yescharacteristic
383C3×C42C23×C311yescharacteristic
384#214—22no—
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)⋊C4—21no—
392(C2×D3)⋊C4C3×D411yescharacteristic
393(C2×D3)⋊C4C3×D411yescharacteristic
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3—21no—
397C4⋊Dic3C3×D411yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C2×C3⋊C8C23×C311yescharacteristic
404C2×C3⋊C8C23×C311yescharacteristic
405Dic12—41no—
406#204—41no—
407D3×C8—41no—
408D3×C8—41no—
409C22×C32—22no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—84no—
422C2×C3×D3#13512yes—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—31no—
440C22×C8—31no—
441C22×C8—31no—
442#126—61no—
443#125—61no—
444#125C2×C3×D311yescharacteristic, complemented
445#124—31no—
446#123—61no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451#121—31no—
452#121—61no—
453#120—61no—
454C4×Q8—31no—
455C4×D4—31no—
456C4×D4C2×C3×D311yescharacteristic
457#117—31no—
458#117—61no—
459C2×C4⋊C4—31no—
460C2×C22⋊C4—61no—
461#107C2×C3×D311yescharacteristic, complemented
462#106—31no—
463#106C2×C3×D311yescharacteristic, complemented
464C4⋊C8C2×C3×D311yescharacteristic, complemented
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#102—31no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102C2×C3×D311yescharacteristic
474#102C2×C3×D311yescharacteristic
475C22⋊C8—31no—
476C22⋊C8—31no—
477C4×C8—31no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C22×D3—21no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3—81no—
491C22×D3C2×C3×D411yescharacteristic
492C22×D3C2×C3×D411yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—62no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—122no—
505C3×D4—122no—
506C3×D4—241no—
507C3×D4#23912yes—
508C3×D4C3×#4112yes—
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—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—81no—
531C2×C3×C4—81no—
532C2×C3×C4—82no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C2×C3×D411yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C24×C311yescharacteristic
541#67—42no—
542#67—42no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—42no—
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549D12—22no—
550D12—21no—
551D12—21no—
552D12—81no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C2×C32—42no—
573C2×C32#54611yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—22no—
577C3×D3—41no—
578C3×D3—81no—
579C24—61no—
580#41—62no—
581#41—121no—
582C2×Q8—31no—
583C2×Q8—31no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—62no—
589C2×D4—61no—
590C2×D4—121no—
591C2×D4C22×C3×D311yescharacteristic
592C22×C4—21no—
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—61no—
597Q16—121no—
598SD16—62no—
599SD16—121no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—121no—
603C2×C8—121no—
604C2×C8C22×C3×D311yescharacteristic
605C2×C8C22×C3×D311yescharacteristic
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4C22×C3×D311yescharacteristic
616C4⋊C4C22×C3×D311yescharacteristic
617C4⋊C4C22×C3×D311yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C42—61no—
629C42—61no—
630C42C22×C3×D311yescharacteristic
631C22×C3—22no—
632C22×C3—22no—
633C22×C3—21no—
634C22×C3—32no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—81no—
646C22×C3—81no—
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—21no—
657C2×D3—21no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—84no—
662C2×D3C3×#13512yes—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4C2×#23911yescharacteristic
686C3×C4#100911yescharacteristic
687C3×C4C2×C3×#4111yescharacteristic
688C3×C4C3×H(5,𝔽2)11yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694C32#329611yescharacteristic, complemented, Sylow
695C23—21no—
696C23—31no—
697C23—31no—
698C23—61no—
699C23—122no—
700C23—122no—
701C23—241no—
702Q8—61no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706D4—21no—
707D4—62no—
708D4—61no—
709D4—61no—
710D4—122no—
711D4—122no—
712D4—241no—
713D4C3×#23912yes—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—81no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4C3×D3×D411yescharacteristic
730C2×C4C3×D3×D411yescharacteristic
731C2×C4C23×C3×D311yescharacteristic
732C8—21no—
733C8—21no—
734C8—61no—
735C8—61no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—42no—
741C2×C3—62no—
742C2×C3—82no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3#563011yescharacteristic
746C2×C3D3×#13511yescharacteristic
747C2×C3#577511yescharacteristic
748C2×C3C3×#54611yescharacteristic
749C2×C3C2×C3×#13511yescharacteristic
750C2×C3C3×#57711yescharacteristic
751D3—22no—
752D3—41no—
753D3—81no—
754C22—22no—
755C22—32no—
756C22—41no—
757C22—41no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—244no—
767C22C2×C3×D3×D411yescharacteristic
768C4—21no—
769C4—21no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4C2×C3×#23911yescharacteristic
779C4C3×#100911yescharacteristic
780C3—21no—
781C3#8118611yescharacteristic, direct product factor
782C3C3×#329611yescharacteristic, complemented
783C2—42no—
784C2—62no—
785C2—121no—
786C2—241no—
787C2C3×#563011yescharacteristic
788C2C3×D3×#13511yescharacteristic
789C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC3×#5554C2
hypercenterC3×#478D3
hypocenterC3C3×#3296
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×#5694C2semidirect
3. C32×#478C2semidirect
4. C3×#5068C2semidirect
5. C3×C4×#214C2semidirect
6. C3×#4887C2semidirect
7. C3×#4885C2semidirect
8. C3×#4864C2semidirect
9. C3×#4862C2semidirect
10. C3×#4845C2semidirect
11. C3×#4834C2semidirect
12. C3×#4783C2semidirect
13. C3×#4776C2semidirect
14. C3×#4772C2semidirect
15. C3×D3×#102C2semidirect
17. #81186C3direct (N × H)
20. C32×#125C22semidirect
25. C2×C3×Dic12C22semidirect
28. C2×C3×D3×C8C22semidirect
32. C3×#897C22semidirect
36. C3×#892C22semidirect
43. C3×C4×Dic6C22semidirect
44. C32×#107C22semidirect
45. C32×#106C22semidirect
46. C32×C4⋊C8C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#816C22semidirect
54. C3×#810C22semidirect
55. C3×#810C22semidirect
56. C3×#810C22semidirect
59. C3×#808C22semidirect
60. C3×C4×C3⋊C8C22semidirect
63. #5694C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5068C2×C3semidirect
81. C4×#214C2×C3semidirect
82. #4887C2×C3semidirect
83. #4885C2×C3semidirect
84. #4864C2×C3semidirect
85. #4862C2×C3semidirect
86. #4845C2×C3semidirect
87. #4834C2×C3semidirect
88. #4783C2×C3semidirect
89. #4776C2×C3semidirect
90. #4772C2×C3semidirect
91. D3×#102C2×C3semidirect
157. C3×#125C2×D3semidirect
158. C3×#125C22×C3semidirect
180. C2×Dic12C22×C3semidirect
183. C2×D3×C8C22×C3semidirect
187. #897C22×C3semidirect
191. #892C22×C3semidirect
198. C4×Dic6C22×C3semidirect
200. C3×#107C2×D3semidirect
201. C3×#107C22×C3semidirect
204. C3×#106C2×D3semidirect
205. C3×#106C22×C3semidirect
207. C3×C4⋊C8C2×D3semidirect
208. C3×C4⋊C8C22×C3semidirect
229. (C2×D3)⋊C8C22×C3semidirect
230. #816C22×C3semidirect
231. #810C22×C3semidirect
232. #810C22×C3semidirect
233. #810C22×C3semidirect
236. #808C22×C3semidirect
237. C4×C3⋊C8C22×C3semidirect
284. #478C3×D3semidirect
444. #125C2×C3×D3semidirect
461. #107C2×C3×D3semidirect
463. #106C2×C3×D3semidirect
464. C4⋊C8C2×C3×D3semidirect
694. C32#3296semidirect
781. C3#81186direct (N × H)
782. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
C3×#55542
C32×#4782
C3×#50682
C3×C4×#2142
C3×#48872
C3×#48852
C3×#48642
C3×#48622
C3×#48452
C3×#48342
C3×#47832
C3×#47762
C3×#47722
C3×D3×#1022
C3×#32963
#811863