Finite Group Databasebeta

← C3×#76202 #11805422

Subgroups — C3×#76202 #11805422

Order 1152.

1637 conjugacy classes of subgroups.

The subgroup lattice has 659 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C2×C3×#893C211yesmaximal, characteristic
3C2×C3×D3×C4⋊C4C212yesmaximal, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic
5C32×#389C211yesmaximal, characteristic, complemented
6C3×#4989C212yesmaximal, complemented
7C3×#4984C211yesmaximal, characteristic, complemented
8C3×#4975C211yesmaximal, characteristic, complemented
9C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
10C3×#4668C212yesmaximal, complemented
11C3×#4667C212yesmaximal, complemented
12C3×D4×C4⋊C4—31nomaximal
13#76202C311yesmaximal, characteristic, direct product factor
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2212yes—
18C2×C32×C4⋊C4C2212yes—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#893—24no—
34C3×#893C418yescomplemented
35C3×D3×C4⋊C4—28no—
36C3×C4×D12—24no—
37C32×#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C2×C3×C4×D4—31no—
42C2×C3×C4×D4—31no—
43C2×C3×C4×D4—31no—
44C22×C3×C4⋊C4—32no—
45C2×#893C2×C311yescharacteristic
46C2×#893C2×C311yescharacteristic
47C2×D3×C4⋊C4C2×C312yescomplemented
48C2×C4×D12C2×C311yescharacteristic
49C3×#389—21no—
50C3×#389—31no—
51C3×#389D311yescharacteristic, complemented
52C3×#389C2×C311yescharacteristic, complemented
53C3×#385—32no—
54C3×#385—32no—
55C3×#384—31no—
56C3×#380—32no—
57C3×C4×C4⋊C4—31no—
58#4989C2×C312yescomplemented
59#4984C2×C311yescharacteristic, complemented
60#4975C2×C311yescharacteristic, complemented
61C4×Dic3⋊C4C2×C311yescharacteristic, complemented
62#4668C2×C312yescomplemented
63#4667C2×C312yescomplemented
64C23×C3×D3C2312yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×C3×D12C2×C414yes—
76C2×C3×D12D414yes—
77C2×C3×D12Q814yes—
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3—24no—
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3—42no—
85C2×C3×C4×D3—42no—
86C2×C3×C4×D3C2×C418yescomplemented
87C32×C4⋊C4—24no—
88C32×C4⋊C4—22no—
89C32×C4⋊C4C2×C414yescomplemented
90C32×C42—22no—
91C3×(C2×D3)⋊C4—24no—
92C3×(C2×D3)⋊C4—24no—
93C3×(C2×D3)⋊C4C2×C418yescomplemented
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3—24no—
96C3×Dic3⋊C4—24no—
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—42no—
99C3×Dic3⋊C4D414yescomplemented
100C3×C4×Dic3—22no—
101C3×C4×Dic3C2×C414yescomplemented
102D4×C4⋊C4—31noSylow
103C22×C3×D4—31no—
104C23×C3×C4—32no—
105C23×C3×C4—32no—
106C23×C3×C4—32no—
107C22×D12C22×C311yescharacteristic
108C22×C4×D3C22×C312yes—
109C22×C4×D3C22×C312yes—
110C22×C4×D3C22×C312yes—
111C3×C4×D4—38no—
112C3×C4×D4—64no—
113C3×C4×D4—64no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—32no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4—68no—
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C4⋊C4C2×D312yes—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C22×C311yescharacteristic
128C2×C3×C4⋊C4C22×C312yes—
129C2×C3×C4⋊C4C22×C311yescharacteristic
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—21no—
134C2×C3×C42—31no—
135C2×C3×C42—31no—
136C2×C3×C42C2×D311yescharacteristic
137C2×C3×C42C22×C311yescharacteristic
138C2×(C2×D3)⋊C4C22×C312yes—
139C2×(C2×D3)⋊C4C22×C312yes—
140C2×(C2×D3)⋊C4C22×C312yes—
141C2×C4⋊Dic3C22×C312yes—
142C2×C4⋊Dic3C22×C311yescharacteristic
143C2×Dic3⋊C4C22×C311yescharacteristic
144C2×Dic3⋊C4C22×C312yes—
145C2×Dic3⋊C4C22×C312yes—
146C2×Dic3⋊C4C22×C311yescharacteristic
147C2×C4×Dic3C22×C311yescharacteristic
148C2×C4×Dic3C22×C311yescharacteristic
149#893—24no—
150#893C3×C418yescomplemented
151D3×C4⋊C4—28no—
152C4×D12—24no—
153C3×#95—22no—
154C3×#95—31no—
155C3×#95—31no—
156C3×#95—32no—
157C3×#95C2×D312yes—
158C3×#95C22×C312yes—
159C3⋊#95C22×C312yes—
160C3⋊#95C22×C311yescharacteristic
161C3⋊#95C22×C311yescharacteristic
162C23×C32C2411yescharacteristic
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—22no—
167C22×C3×D3C22×C414yes—
168C22×C3×D3C2×D414yes—
169C22×C3×D3C2×Q814yes—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4—21no—
173C2×C32×C4—22no—
174C2×C32×C4—21no—
175C2×C32×C4—22no—
176C2×C32×C4—21no—
177C2×C32×C4—22no—
178C2×C32×C4—21no—
179C2×C32×C4—22no—
180C2×C32×C4C22×C414yes—
181C2×C32×C4C22×C412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2×Q812yes—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3C22×C412yes—
196C2×C3×Dic3C22×C412yes—
197C2×C3×Dic3C2×D412yes—
198C2×C3×Dic3C2×D412yes—
199C2×C3×Dic3#4112yes—
200C3×D12C4⋊C4116yescomplemented
201C3×C4×D3—216no—
202C3×C4×D3—48no—
203C3×C4×D3—48no—
204C2×C4×D4—31no—
205C2×C4×D4—31no—
206C2×C4×D4—31no—
207C22×C4⋊C4—32no—
208#389—31no—
209#389C3×D311yescharacteristic, complemented
210#385—32no—
211#385—32no—
212#384—31no—
213#380—32no—
214C4×C4⋊C4—31no—
215C24×C3—32no—
216C23×D3C23×C312yes—
217C2×C3×D4—34no—
218C2×C3×D4—34no—
219C2×C3×D4—34no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—38no—
229C22×C3×C4—31no—
230C22×C3×C4—32no—
231C22×C3×C4—64no—
232C22×C3×C4—64no—
233C22×C3×C4—64no—
234C22×C3×C4—64no—
235C22×C3×C4—64no—
236C22×C3×C4—64no—
237C22×C3×C4—122no—
238C22×C3×C4—122no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D312yes—
241C22×C3×C4C22×D312yes—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C23×C311yescharacteristic
245C22×C3×C4C23×C312yes—
246C22×C3×C4C23×C312yes—
247C22×C3×C4C23×C311yescharacteristic
248C22×C3×C4C23×C311yescharacteristic
249C22×Dic3C23×C311yescharacteristic
250C22×Dic3C23×C312yes—
251C22×Dic3C23×C311yescharacteristic
252C22×Dic3C23×C311yescharacteristic
253C22×Dic3C23×C311yescharacteristic
254C2×D12C2×C3×C414yes—
255C2×D12C3×D414yes—
256C2×D12C3×Q814yes—
257C2×C4×D3—24no—
258C2×C4×D3—24no—
259C2×C4×D3—24no—
260C2×C4×D3—24no—
261C2×C4×D3—24no—
262C2×C4×D3—24no—
263C2×C4×D3—42no—
264C2×C4×D3—42no—
265C2×C4×D3C2×C3×C418yescomplemented
266C3×C4⋊C4—24no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—24no—
271C3×C4⋊C4—34no—
272C3×C4⋊C4—44no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4—64no—
276C3×C4⋊C4—64no—
277C3×C4⋊C4—62no—
278C3×C4⋊C4—122no—
279C3×C4⋊C4C4×D314yescomplemented
280C3×C4⋊C4C2×C3×C414yescomplemented
281C3×C22⋊C4—38no—
282C3×C22⋊C4—64no—
283C3×C22⋊C4—64no—
284C3×C42—22no—
285C3×C42—22no—
286C3×C42—34no—
287C3×C42—42no—
288C3×C42—62no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4C2×C3×C418yescomplemented
292C4⋊Dic3—22no—
293C4⋊Dic3—24no—
294Dic3⋊C4—24no—
295Dic3⋊C4—22no—
296Dic3⋊C4—42no—
297Dic3⋊C4C3×D414yescomplemented
298C4×Dic3—22no—
299C4×Dic3C2×C3×C414yescomplemented
300C22×C32C23×C411yescharacteristic
301C22×C32C22×D411yescharacteristic
302C22×C32C22×D411yescharacteristic
303C22×C32C22×Q811yescharacteristic
304C22×C32C2×#4111yescharacteristic
305C22×C32H(5,𝔽2)11yescharacteristic
306C22×C322−1+411yescharacteristic
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—24no—
310C2×C3×D3—24no—
311C2×C3×D3—24no—
312C2×C3×D3—24no—
313C2×C3×D3C2×C4⋊C418yescomplemented
314C32×C4—24no—
315C32×C4—22no—
316C32×C4—41no—
317C32×C4—42no—
318C32×C4C2×C4⋊C414yescomplemented
319C3×Dic3—22no—
320C3×Dic3—22no—
321C3×Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3C4×D414yescomplemented
324C22×D4—31no—
325C23×C4—32no—
326C23×C4—32no—
327C23×C4—32no—
328C4×D4—38no—
329C4×D4—64no—
330C4×D4—64no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—32no—
333C2×C4⋊C4—32no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—32no—
337C2×C4⋊C4—68no—
338C2×C4⋊C4C2×C3×D312yes—
339C2×C4⋊C4C2×C3×D311yescharacteristic
340C2×C4⋊C4C2×C3×D311yescharacteristic
341C2×C22⋊C4—32no—
342C2×C22⋊C4—32no—
343C2×C22⋊C4—32no—
344C2×C42—31no—
345C2×C42—31no—
346C2×C42C2×C3×D311yescharacteristic
347#95—31no—
348#95—31no—
349#95—32no—
350#95C2×C3×D312yes—
351C23×C3—21no—
352C23×C3—34no—
353C23×C3—34no—
354C23×C3—34no—
355C23×C3—62no—
356C23×C3—62no—
357C23×C3—62no—
358C23×C3—62no—
359C23×C3C23×D311yescharacteristic
360C23×C3C24×C311yescharacteristic
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3C22×C3×C414yes—
366C22×D3C2×C3×D414yes—
367C22×D3C2×C3×Q814yes—
368C3×D4—316no—
369C2×C3×C4—21no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—24no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—616no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—61no—
413C2×C3×C4—61no—
414C2×C3×C4—61no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—62no—
420C2×C3×C4—128no—
421C2×C3×C4—128no—
422C2×C3×C4C2×C4×D314yes—
423C2×C3×C4C2×C4×D312yes—
424C2×C3×C4D3×D412yes—
425C2×C3×C4D3×D412yes—
426C2×C3×C4D3×Q812yes—
427C2×C3×C4C22×C3×C414yes—
428C2×C3×C4C22×C3×C412yes—
429C2×C3×C4C2×C3×D412yes—
430C2×C3×C4C2×C3×D412yes—
431C2×C3×C4C2×C3×Q812yes—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3C22×C3×C412yes—
443C2×Dic3C22×C3×C412yes—
444C2×Dic3C2×C3×D412yes—
445C2×Dic3C2×C3×D412yes—
446C2×Dic3C3×#4112yes—
447D12C3×C4⋊C4116yescomplemented
448C4×D3—216no—
449C4×D3—48no—
450C4×D3—48no—
451C2×C32C22×C4⋊C411yescharacteristic
452C2×C32C2×C4×D411yescharacteristic
453C2×C32#52011yescharacteristic
454C2×C32D4211yescharacteristic
455C2×C32#54711yescharacteristic
456C2×C32D4×Q811yescharacteristic
457C2×C32#55411yescharacteristic
458C3×D3—28no—
459C24—32no—
460C2×D4—34no—
461C2×D4—34no—
462C2×D4—34no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—31no—
466C22×C4—38no—
467C22×C4—31no—
468C22×C4—32no—
469C22×C4—64no—
470C22×C4—64no—
471C22×C4—64no—
472C22×C4—64no—
473C22×C4—64no—
474C22×C4—64no—
475C22×C4—122no—
476C22×C4—122no—
477C22×C4C22×C3×D311yescharacteristic
478C22×C4C22×C3×D312yes—
479C22×C4C22×C3×D312yes—
480C22×C4C22×C3×D311yescharacteristic
481C22×C4C22×C3×D311yescharacteristic
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—34no—
485C4⋊C4—64no—
486C4⋊C4—64no—
487C4⋊C4—62no—
488C4⋊C4—62no—
489C4⋊C4—122no—
490C4⋊C4C3×C4×D314yescomplemented
491C22⋊C4—38no—
492C22⋊C4—64no—
493C22⋊C4—64no—
494C42—22no—
495C42—34no—
496C42—62no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—38no—
505C22×C3—64no—
506C22×C3—64no—
507C22×C3—64no—
508C22×C3—64no—
509C22×C3—64no—
510C22×C3—64no—
511C22×C3C22×C4×D311yescharacteristic
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C2×D3×D411yescharacteristic
514C22×C3C2×D3×Q811yescharacteristic
515C22×C3#100711yescharacteristic
516C22×C3D3×#4111yescharacteristic
517C22×C3#100911yescharacteristic
518C22×C3C23×C3×C411yescharacteristic
519C22×C3C22×C3×D411yescharacteristic
520C22×C3C22×C3×D411yescharacteristic
521C22×C3C22×C3×Q811yescharacteristic
522C22×C3C2×C3×#4111yescharacteristic
523C22×C3C3×H(5,𝔽2)11yescharacteristic
524C22×C3C3×2−1+411yescharacteristic
525C2×D3—24no—
526C2×D3—24no—
527C2×D3—24no—
528C2×D3—24no—
529C2×D3—24no—
530C2×D3—24no—
531C2×D3C2×C3×C4⋊C418yescomplemented
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—24no—
537C3×C4—34no—
538C3×C4—44no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—42no—
542C3×C4—42no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—62no—
546C3×C4—62no—
547C3×C4—82no—
548C3×C4—122no—
549C3×C4—121no—
550C3×C4D3×C4⋊C414yescomplemented
551C3×C4C2×C3×C4⋊C414yescomplemented
552Dic3—22no—
553Dic3—22no—
554Dic3—42no—
555Dic3—41no—
556Dic3C3×C4×D414yescomplemented
557C32D4×C4⋊C411yescharacteristic, complemented, Sylow
558C23—34no—
559C23—34no—
560C23—34no—
561C23—62no—
562C23—62no—
563C23—62no—
564C23—62no—
565C23C23×C3×D311yescharacteristic
566D4—316no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—32no—
580C2×C4—32no—
581C2×C4—32no—
582C2×C4—616no—
583C2×C4—61no—
584C2×C4—61no—
585C2×C4—61no—
586C2×C4—61no—
587C2×C4—61no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—62no—
593C2×C4—128no—
594C2×C4—128no—
595C2×C4C2×C3×C4×D314yes—
596C2×C4C2×C3×C4×D312yes—
597C2×C4C3×D3×D412yes—
598C2×C4C3×D3×D412yes—
599C2×C4C3×D3×Q812yes—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—68no—
608C2×C3C2×D3×C4⋊C411yescharacteristic
609C2×C3C4×D3×D411yescharacteristic
610C2×C3#557411yescharacteristic
611C2×C3#560911yescharacteristic
612C2×C3#563111yescharacteristic
613C2×C3#569011yescharacteristic
614C2×C3#572711yescharacteristic
615C2×C3C22×C3×C4⋊C411yescharacteristic
616C2×C3C2×C3×C4×D411yescharacteristic
617C2×C3C3×#52011yescharacteristic
618C2×C3C3×D4211yescharacteristic
619C2×C3C3×#54711yescharacteristic
620C2×C3C3×D4×Q811yescharacteristic
621C2×C3C3×#55411yescharacteristic
622D3—28no—
623C22—38no—
624C22—64no—
625C22—64no—
626C22—64no—
627C22—64no—
628C22—64no—
629C22—64no—
630C22C22×C3×C4×D311yescharacteristic
631C22C2×C3×D3×D411yescharacteristic
632C22C2×C3×D3×D411yescharacteristic
633C22C2×C3×D3×Q811yescharacteristic
634C22C3×#100711yescharacteristic
635C22C3×D3×#4111yescharacteristic
636C22C3×#100911yescharacteristic
637C4—24no—
638C4—22no—
639C4—34no—
640C4—42no—
641C4—41no—
642C4—62no—
643C4—62no—
644C4—122no—
645C4—121no—
646C4C3×D3×C4⋊C414yescomplemented
647C3—21no—
648C3#7620211yescharacteristic, direct product factor
649C3C3×D4×C4⋊C411yescharacteristic, complemented
650C2—68no—
651C2C2×C3×D3×C4⋊C411yescharacteristic
652C2C3×C4×D3×D411yescharacteristic
653C2C3×#557411yescharacteristic
654C2C3×#560911yescharacteristic
655C2C3×#563111yescharacteristic
656C2C3×#569011yescharacteristic
657C2C3×#572711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#389C2
socleC23×C32C24
prime radicalC22×C3×D12C22
cosocleC23×C3C24×C3
hypercenterC3×#389D3
hypocenterC3C3×D4×C4⋊C4
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
3. C2×C3×D3×C4⋊C4C2semidirect
5. C32×#389C2semidirect
6. C3×#4989C2semidirect
7. C3×#4984C2semidirect
8. C3×#4975C2semidirect
9. C3×C4×Dic3⋊C4C2semidirect
10. C3×#4668C2semidirect
11. C3×#4667C2semidirect
13. #76202C3direct (N × H)
34. C3×#893C4semidirect
47. C2×D3×C4⋊C4C2×C3semidirect
51. C3×#389D3semidirect
52. C3×#389C2×C3semidirect
58. #4989C2×C3semidirect
59. #4984C2×C3semidirect
60. #4975C2×C3semidirect
61. C4×Dic3⋊C4C2×C3semidirect
62. #4668C2×C3semidirect
63. #4667C2×C3semidirect
86. C2×C3×C4×D3C2×C4semidirect
89. C32×C4⋊C4C2×C4semidirect
93. C3×(C2×D3)⋊C4C2×C4semidirect
99. C3×Dic3⋊C4D4semidirect
101. C3×C4×Dic3C2×C4semidirect
150. #893C3×C4semidirect
200. C3×D12C4⋊C4semidirect
209. #389C3×D3semidirect
265. C2×C4×D3C2×C3×C4semidirect
279. C3×C4⋊C4C4×D3semidirect
280. C3×C4⋊C4C2×C3×C4semidirect
291. (C2×D3)⋊C4C2×C3×C4semidirect
297. Dic3⋊C4C3×D4semidirect
299. C4×Dic3C2×C3×C4semidirect
313. C2×C3×D3C2×C4⋊C4semidirect
318. C32×C4C2×C4⋊C4semidirect
323. C3×Dic3C4×D4semidirect
447. D12C3×C4⋊C4semidirect
490. C4⋊C4C3×C4×D3semidirect
531. C2×D3C2×C3×C4⋊C4semidirect
550. C3×C4D3×C4⋊C4semidirect
551. C3×C4C2×C3×C4⋊C4semidirect
556. Dic3C3×C4×D4semidirect
557. C32D4×C4⋊C4semidirect
646. C4C3×D3×C4⋊C4semidirect
648. C3#76202direct (N × H)
649. C3C3×D4×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×D3×C4⋊C42
C2×C3×C4×D122
C32×#3892
C3×#49892
C3×#49842
C3×#49752
C3×C4×Dic3⋊C42
C3×#46682
C3×#46672
C3×D4×C4⋊C43
#762023