Finite Group Databasebeta

← C2×C3×#5629 #11901132

Subgroups — C2×C3×#5629 #11901132

Order 1152.

3441 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5C2×C3×#930C211yesmaximal, characteristic, complemented
6C3×#5629C2116yesmaximal, direct product factor
7C2×C3×#896C212yesmaximal, complemented
8C2×C3×#895C211yesmaximal, characteristic, complemented
9C2×C3×#895C212yesmaximal, complemented
10C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
11C2×C3×#884C212yesmaximal, complemented
12C2×C3×#884C212yesmaximal, complemented
13C2×C3×#537—31nomaximal
14C2×#5629C311yesmaximal, characteristic, direct product factor
15C22×C32×Q8C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2212yes—
20C2×C3×#239—28no—
21C2×C3×#239C2218yescomplemented
22C2×C3×#235—28no—
23C2×C3×#235C2218yescomplemented
24C22×C3×D12C2212yes—
25C22×C3×D12C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C22×C3×D12C2212yes—
28C22×C3×C4×D3C2212yes—
29C22×C3×C4×D3C2211yescharacteristic
30C22×C3×C4×D3C2212yes—
31C22×C3×C4×D3C2211yescharacteristic
32C22×C3×Dic6C2211yescharacteristic
33C32×C22⋊Q8C2218yescomplemented
34C2×C32×C4⋊C4C2211yescharacteristic
35C2×C32×C4⋊C4C2212yes—
36C2×C32×C22⋊C4C2212yes—
37C3×#946C2218yescomplemented
38C3×#930C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2212yes—
40C2×C3×(C2×D3)⋊C4C2212yes—
41C2×C3×(C2×D3)⋊C4C2212yes—
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C2×C3×Dic3⋊C4C2212yes—
44C2×C3×Dic3⋊C4C2212yes—
45C3×#896C22116yescomplemented
46C3×#895C2218yescomplemented
47C3×#895C22116yescomplemented
48C3×D3×C4⋊C4C2218yescomplemented
49C3×#884C22116yescomplemented
50C3×#884C22116yescomplemented
51C22×C3×#41—31no—
52C22×C3×#41—31no—
53C22×#239C2×C311yescharacteristic, complemented
54C22×#235C2×C311yescharacteristic, complemented
55C3×#537—316no—
56C2×C3×C22⋊Q8—21no—
57C2×C3×C22⋊Q8—31no—
58C2×C3×C22⋊Q8—32no—
59C2×C3×C22⋊Q8D311yescharacteristic, complemented
60C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
61C2×C3×#121—31no—
62C2×C3×#121—31no—
63C2×C3×#121—32no—
64C2×C3×#121—32no—
65C2×C3×#121—32no—
66C22×C3×C4⋊C4—31no—
67C2×#946C2×C311yescharacteristic, complemented
68C2×#930C2×C311yescharacteristic, complemented
69#5629C2×C3116yesdirect product factor
70C2×#896C2×C312yescomplemented
71C2×#895C2×C311yescharacteristic, complemented
72C2×#895C2×C312yescomplemented
73C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
74C2×#884C2×C312yescomplemented
75C2×#884C2×C312yescomplemented
76C24×C32C2311yescharacteristic
77C23×C3×D3C2312yes—
78C23×C3×D3C2311yescharacteristic
79C23×C3×D3C2311yescharacteristic
80C2×C32×Q8—24no—
81C2×C32×Q8C2314yes—
82C22×C32×C4—24no—
83C22×C32×C4C2312yes—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C2×C3×#67—24no—
89C2×C3×#67—24no—
90C2×C3×#67—44no—
91C2×C3×#67C2314yes—
92C2×C3×#67C2314yes—
93C2×C3×#67C2318yes—
94C22×C3×Dic3C2312yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C3×#239—232no—
98C3×#235—232no—
99C2×C3×D12—24no—
100C2×C3×D12—28no—
101C2×C3×D12—24no—
102C2×C3×D12—44no—
103C2×C3×D12C2318yes—
104C2×C3×D12C2314yes—
105C2×C3×D12C2314yes—
106C2×C3×D12C2318yes—
107C2×C3×C4×D3—24no—
108C2×C3×C4×D3—28no—
109C2×C3×C4×D3—44no—
110C2×C3×C4×D3D418yescomplemented
111C2×C3×C4×D3C2318yes—
112C2×C3×C4×D3C2314yes—
113C2×C3×C4×D3C2318yes—
114C2×C3×C4×D3C2314yes—
115C2×C3×Dic6—24no—
116C2×C3×Dic6C2314yes—
117C32×C4⋊C4C2314yes—
118C32×C4⋊C4C2318yes—
119C32×C22⋊C4C2318yes—
120C3×(C2×D3)⋊C4C2318yes—
121C3×(C2×D3)⋊C4C2318yes—
122C3×(C2×D3)⋊C4C2318yes—
123C3×C4⋊Dic3C2314yes—
124C3×Dic3⋊C4C2318yes—
125C3×Dic3⋊C4C2318yes—
126C2×#537—31noSylow
127C2×C3×#41—38no—
128C2×C3×#41—38no—
129C2×C3×#41—68no—
130C2×C3×#41—68no—
131C22×C3×Q8—21no—
132C22×C3×Q8—31no—
133C22×C3×Q8C2×D311yescharacteristic
134C22×C3×Q8C22×C311yescharacteristic
135C22×C3×D4—31no—
136C22×C3×D4—31no—
137C22×C3×D4—32no—
138C22×C3×D4—31no—
139C22×C3×D4—32no—
140C22×C3×D4—31no—
141C22×C3×D4—32no—
142C23×C3×C4—21no—
143C23×C3×C4—31no—
144C23×C3×C4—32no—
145C23×C3×C4—31no—
146C23×C3×C4—32no—
147C23×C3×C4C2×D311yescharacteristic
148C23×C3×C4C22×C311yescharacteristic
149C22×#67C22×C311yescharacteristic
150C22×#67C22×C311yescharacteristic
151C22×#67C22×C312yes—
152C2×#239—28no—
153C2×#239C22×C318yescomplemented
154C2×#235—28no—
155C2×#235C22×C318yescomplemented
156C22×D12C22×C311yescharacteristic
157C22×D12C22×C312yes—
158C22×D12C22×C311yescharacteristic
159C22×D12C22×C312yes—
160C22×C4×D3C22×C311yescharacteristic
161C22×C4×D3C22×C312yes—
162C22×C4×D3C22×C312yes—
163C22×C4×D3C22×C311yescharacteristic
164C22×Dic6C22×C311yescharacteristic
165C3×C22⋊Q8—28no—
166C3×C22⋊Q8—38no—
167C3×C22⋊Q8—316no—
168C3×C22⋊Q8C2×D318yescomplemented
169C3×C22⋊Q8C22×C318yescomplemented
170C3×#121—38no—
171C3×#121—38no—
172C3×#121—316no—
173C3×#121—316no—
174C3×#121—316no—
175C2×C3×C4⋊C4—21no—
176C2×C3×C4⋊C4—22no—
177C2×C3×C4⋊C4—32no—
178C2×C3×C4⋊C4—32no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—38no—
181C2×C3×C4⋊C4C2×D311yescharacteristic
182C2×C3×C4⋊C4C2×D312yes—
183C2×C3×C4⋊C4C22×C311yescharacteristic
184C2×C3×C4⋊C4C22×C312yes—
185C2×C3×C22⋊C4—22no—
186C2×C3×C22⋊C4—32no—
187C2×C3×C22⋊C4—32no—
188C2×C3×C22⋊C4—32no—
189C2×C3×C22⋊C4C2×D312yes—
190C2×C3×C22⋊C4C22×C312yes—
191#946C22×C318yescomplemented
192#930C22×C318yescomplemented
193C2×(C2×D3)⋊C4C22×C312yes—
194C2×(C2×D3)⋊C4C22×C312yes—
195C2×(C2×D3)⋊C4C22×C312yes—
196C2×C4⋊Dic3C22×C311yescharacteristic
197C2×Dic3⋊C4C22×C312yes—
198C2×Dic3⋊C4C22×C312yes—
199#896C22×C3116yescomplemented
200#895C22×C318yescomplemented
201#895C22×C3116yescomplemented
202D3×C4⋊C4C22×C318yescomplemented
203#884C22×C3116yescomplemented
204#884C22×C3116yescomplemented
205C23×C32—22no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32C2412yes—
209C23×C32C2411yescharacteristic
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—24no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—24no—
216C22×C3×D3—24no—
217C22×C3×D3—22no—
218C22×C3×D3C2×D414yes—
219C22×C3×D3C2414yes—
220C22×C3×D3C2412yes—
221C22×C3×D3C2412yes—
222C32×Q8—28no—
223C2×C32×C4—22no—
224C2×C32×C4—24no—
225C2×C32×C4—24no—
226C2×C32×C4—28no—
227C2×C32×C4C2×D414yes—
228C2×C32×C4C2414yes—
229C2×C32×C4C2414yes—
230C2×C32×C4C2412yes—
231C2×C32×C4C2412yes—
232C3×#67—28no—
233C3×#67—28no—
234C3×#67—48no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—24no—
237C2×C3×Dic3C2×D414yes—
238C2×C3×Dic3C2414yes—
239C2×C3×Dic3C2412yes—
240C2×C3×Dic3C2412yes—
241C3×D12—28no—
242C3×D12—216no—
243C3×D12—28no—
244C3×D12—48no—
245C3×C4×D3—28no—
246C3×C4×D3—216no—
247C3×C4×D3—48no—
248C3×C4×D3C2×D4116yescomplemented
249C3×Dic6—28no—
250C22×#41—31no—
251C22×#41—31no—
252#537—316no—
253C2×C22⋊Q8—31no—
254C2×C22⋊Q8—32no—
255C2×C22⋊Q8C3×D311yescharacteristic, complemented
256C2×#121—31no—
257C2×#121—31no—
258C2×#121—32no—
259C2×#121—32no—
260C2×#121—32no—
261C22×C4⋊C4—31no—
262C24×C3—21no—
263C24×C3—31no—
264C24×C3—31no—
265C24×C3—32no—
266C24×C3C22×D311yescharacteristic
267C24×C3C23×C311yescharacteristic
268C23×D3C23×C312yes—
269C23×D3C23×C311yescharacteristic
270C23×D3C23×C311yescharacteristic
271C3×#41—632no—
272C3×#41—632no—
273C2×C3×Q8—24no—
274C2×C3×Q8—24no—
275C2×C3×Q8—24no—
276C2×C3×Q8—34no—
277C2×C3×Q8—44no—
278C2×C3×Q8—64no—
279C2×C3×Q8C22×D314yes—
280C2×C3×Q8C23×C314yes—
281C2×C3×D4—34no—
282C2×C3×D4—34no—
283C2×C3×D4—38no—
284C2×C3×D4—34no—
285C2×C3×D4—38no—
286C2×C3×D4—34no—
287C2×C3×D4—38no—
288C2×C3×D4—64no—
289C2×C3×D4—68no—
290C2×C3×D4—64no—
291C2×C3×D4—64no—
292C2×C3×D4—64no—
293C2×C3×D4—124no—
294C2×C3×D4—124no—
295C22×C3×C4—24no—
296C22×C3×C4—24no—
297C22×C3×C4—21no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—21no—
301C22×C3×C4—24no—
302C22×C3×C4—31no—
303C22×C3×C4—38no—
304C22×C3×C4—34no—
305C22×C3×C4—32no—
306C22×C3×C4—31no—
307C22×C3×C4—38no—
308C22×C3×C4—34no—
309C22×C3×C4—38no—
310C22×C3×C4—44no—
311C22×C3×C4—68no—
312C22×C3×C4—64no—
313C22×C3×C4—124no—
314C22×C3×C4C22×D314yes—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D312yes—
317C22×C3×C4C22×D312yes—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C23×C312yes—
320C22×C3×C4C23×C312yes—
321C22×C3×C4C23×C311yescharacteristic
322C22×C3×C4C23×C314yes—
323C22×C3×C4C23×C311yescharacteristic
324C2×#67—24no—
325C2×#67—24no—
326C2×#67—44no—
327C2×#67C23×C314yes—
328C2×#67C23×C314yes—
329C2×#67C23×C318yes—
330C22×Dic3C23×C312yes—
331C22×Dic3C23×C311yescharacteristic
332C22×Dic3C23×C311yescharacteristic
333#239—232no—
334#235—232no—
335C2×D12—24no—
336C2×D12—28no—
337C2×D12—24no—
338C2×D12—44no—
339C2×D12C23×C318yes—
340C2×D12C23×C314yes—
341C2×D12C23×C314yes—
342C2×D12C23×C318yes—
343C2×C4×D3—24no—
344C2×C4×D3—28no—
345C2×C4×D3—44no—
346C2×C4×D3C3×D418yescomplemented
347C2×C4×D3C23×C318yes—
348C2×C4×D3C23×C314yes—
349C2×C4×D3C23×C318yes—
350C2×C4×D3C23×C314yes—
351C2×Dic6—24no—
352C2×Dic6C23×C314yes—
353C3×C4⋊C4—24no—
354C3×C4⋊C4—28no—
355C3×C4⋊C4—38no—
356C3×C4⋊C4—38no—
357C3×C4⋊C4—34no—
358C3×C4⋊C4C22×D314yes—
359C3×C4⋊C4C22×D318yes—
360C3×C4⋊C4C23×C314yes—
361C3×C4⋊C4C23×C318yes—
362C3×C22⋊C4—28no—
363C3×C22⋊C4—38no—
364C3×C22⋊C4—38no—
365C3×C22⋊C4—38no—
366C3×C22⋊C4C22×D318yes—
367C3×C22⋊C4C23×C318yes—
368(C2×D3)⋊C4C23×C318yes—
369(C2×D3)⋊C4C23×C318yes—
370(C2×D3)⋊C4C23×C318yes—
371C4⋊Dic3C23×C314yes—
372Dic3⋊C4C23×C318yes—
373Dic3⋊C4C23×C318yes—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32—22no—
377C22×C32—44no—
378C22×C32C22×D412yes—
379C22×C32H(5,𝔽2)12yes—
380C22×C322−1+412yes—
381C22×C32C2511yescharacteristic
382C2×C3×D3—28no—
383C2×C3×D3—22no—
384C2×C3×D3—22no—
385C2×C3×D3—24no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—24no—
389C2×C3×D3—24no—
390C2×C3×D3—22no—
391C2×C3×D3—48no—
392C2×C3×D3—44no—
393C2×C3×D3C22×D414yes—
394C32×C4—22no—
395C32×C4—24no—
396C32×C4—24no—
397C32×C4C22×D414yes—
398C3×Dic3—22no—
399C3×Dic3—24no—
400C3×Dic3C22×D414yes—
401C2×#41—38no—
402C2×#41—38no—
403C2×#41—68no—
404C2×#41—68no—
405C22×Q8—31no—
406C22×Q8C2×C3×D311yescharacteristic
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—32no—
410C22×D4—31no—
411C22×D4—32no—
412C22×D4—31no—
413C22×D4—32no—
414C23×C4—31no—
415C23×C4—32no—
416C23×C4—31no—
417C23×C4—32no—
418C23×C4C2×C3×D311yescharacteristic
419C22⋊Q8—38no—
420C22⋊Q8—316no—
421C22⋊Q8C2×C3×D318yescomplemented
422#121—38no—
423#121—38no—
424#121—316no—
425#121—316no—
426#121—316no—
427C2×C4⋊C4—32no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—32no—
430C2×C4⋊C4—38no—
431C2×C4⋊C4C2×C3×D311yescharacteristic
432C2×C4⋊C4C2×C3×D312yes—
433C2×C22⋊C4—32no—
434C2×C22⋊C4—32no—
435C2×C22⋊C4—32no—
436C2×C22⋊C4C2×C3×D312yes—
437C23×C3—24no—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—21no—
445C23×C3—22no—
446C23×C3—34no—
447C23×C3—32no—
448C23×C3—32no—
449C23×C3—34no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—62no—
453C23×C3—62no—
454C23×C3—64no—
455C23×C3—62no—
456C23×C3—62no—
457C23×C3—64no—
458C23×C3—62no—
459C23×C3—64no—
460C23×C3C23×D312yes—
461C23×C3C23×D311yescharacteristic
462C23×C3C24×C312yes—
463C23×C3C24×C311yescharacteristic
464C22×D3—22no—
465C22×D3—22no—
466C22×D3—24no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—24no—
470C22×D3—24no—
471C22×D3—22no—
472C22×D3C2×C3×D414yes—
473C22×D3C24×C314yes—
474C22×D3C24×C312yes—
475C22×D3C24×C312yes—
476C3×Q8—28no—
477C3×Q8—28no—
478C3×Q8—48no—
479C3×Q8—68no—
480C3×D4—68no—
481C3×D4—616no—
482C3×D4—68no—
483C3×D4—68no—
484C3×D4—68no—
485C3×D4—128no—
486C3×D4—128no—
487C2×C3×C4—22no—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—22no—
491C2×C3×C4—24no—
492C2×C3×C4—24no—
493C2×C3×C4—28no—
494C2×C3×C4—28no—
495C2×C3×C4—22no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—22no—
499C2×C3×C4—24no—
500C2×C3×C4—34no—
501C2×C3×C4—32no—
502C2×C3×C4—316no—
503C2×C3×C4—34no—
504C2×C3×C4—32no—
505C2×C3×C4—48no—
506C2×C3×C4—44no—
507C2×C3×C4—42no—
508C2×C3×C4—44no—
509C2×C3×C4—616no—
510C2×C3×C4—62no—
511C2×C3×C4—64no—
512C2×C3×C4—68no—
513C2×C3×C4—128no—
514C2×C3×C4D3×D414yes—
515C2×C3×C4C2×C3×D414yes—
516C2×C3×C4C23×D312yes—
517C2×C3×C4C23×D314yes—
518C2×C3×C4C23×D314yes—
519C2×C3×C4C23×D312yes—
520C2×C3×C4C24×C314yes—
521C2×C3×C4C24×C314yes—
522C2×C3×C4C24×C312yes—
523C2×C3×C4C24×C312yes—
524#67—28no—
525#67—28no—
526#67—48no—
527C2×Dic3—22no—
528C2×Dic3—24no—
529C2×Dic3C2×C3×D414yes—
530C2×Dic3C24×C314yes—
531C2×Dic3C24×C312yes—
532C2×Dic3C24×C312yes—
533D12—28no—
534D12—216no—
535D12—28no—
536D12—48no—
537C4×D3—28no—
538C4×D3—216no—
539C4×D3—48no—
540C4×D3C2×C3×D4116yescomplemented
541Dic6—28no—
542C2×C32—42no—
543C2×C32#53714yescomplemented
544C2×C32C23×D411yescharacteristic
545C2×C32C2×H(5,𝔽2)11yescharacteristic
546C2×C32C2×2−1+411yescharacteristic
547C3×D3—24no—
548C3×D3—44no—
549C3×D3—42no—
550C24—31no—
551C24—31no—
552C24—32no—
553C24C22×C3×D311yescharacteristic
554#41—632no—
555#41—632no—
556C2×Q8—24no—
557C2×Q8—34no—
558C2×Q8—64no—
559C2×Q8C22×C3×D314yes—
560C2×D4—34no—
561C2×D4—34no—
562C2×D4—38no—
563C2×D4—34no—
564C2×D4—38no—
565C2×D4—34no—
566C2×D4—38no—
567C2×D4—64no—
568C2×D4—68no—
569C2×D4—64no—
570C2×D4—64no—
571C2×D4—64no—
572C2×D4—124no—
573C2×D4—124no—
574C22×C4—24no—
575C22×C4—31no—
576C22×C4—34no—
577C22×C4—38no—
578C22×C4—32no—
579C22×C4—31no—
580C22×C4—38no—
581C22×C4—34no—
582C22×C4—38no—
583C22×C4—68no—
584C22×C4—64no—
585C22×C4—124no—
586C22×C4C22×C3×D311yescharacteristic
587C22×C4C22×C3×D312yes—
588C22×C4C22×C3×D312yes—
589C22×C4C22×C3×D314yes—
590C22×C4C22×C3×D311yescharacteristic
591C4⋊C4—38no—
592C4⋊C4—34no—
593C4⋊C4—38no—
594C4⋊C4C22×C3×D314yes—
595C4⋊C4C22×C3×D318yes—
596C22⋊C4—38no—
597C22⋊C4—38no—
598C22⋊C4—38no—
599C22⋊C4C22×C3×D318yes—
600C22×C3—24no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—21no—
611C22×C3—34no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—48no—
615C22×C3—44no—
616C22×C3—44no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—68no—
620C22×C3—64no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—64no—
624C22×C3—62no—
625C22×C3—64no—
626C22×C3—128no—
627C22×C3—124no—
628C22×C3C2×D3×D412yes—
629C22×C3#100712yes—
630C22×C3#100912yes—
631C22×C3C22×C3×D412yes—
632C22×C3C3×H(5,𝔽2)12yes—
633C22×C3C3×2−1+412yes—
634C22×C3C24×D311yescharacteristic
635C22×C3C25×C311yescharacteristic
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—28no—
639C2×D3—24no—
640C2×D3—22no—
641C2×D3—22no—
642C2×D3—24no—
643C2×D3—24no—
644C2×D3—22no—
645C2×D3—48no—
646C2×D3—44no—
647C2×D3C22×C3×D414yes—
648C3×C4—22no—
649C3×C4—24no—
650C3×C4—24no—
651C3×C4—22no—
652C3×C4—24no—
653C3×C4—24no—
654C3×C4—24no—
655C3×C4—34no—
656C3×C4—42no—
657C3×C4—44no—
658C3×C4—44no—
659C3×C4—62no—
660C3×C4—64no—
661C3×C4C2×D3×D414yes—
662C3×C4C22×C3×D414yes—
663Dic3—22no—
664Dic3—24no—
665Dic3C22×C3×D414yes—
666C32C2×#53711yescharacteristic, complemented, Sylow
667C23—22no—
668C23—22no—
669C23—22no—
670C23—34no—
671C23—32no—
672C23—32no—
673C23—34no—
674C23—62no—
675C23—62no—
676C23—64no—
677C23—62no—
678C23—62no—
679C23—64no—
680C23—62no—
681C23—64no—
682C23C23×C3×D312yes—
683C23C23×C3×D311yescharacteristic
684Q8—28no—
685Q8—68no—
686D4—68no—
687D4—616no—
688D4—68no—
689D4—68no—
690D4—68no—
691D4—128no—
692D4—128no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—34no—
698C2×C4—32no—
699C2×C4—316no—
700C2×C4—34no—
701C2×C4—32no—
702C2×C4—616no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—68no—
706C2×C4—128no—
707C2×C4C3×D3×D414yes—
708C2×C4C23×C3×D312yes—
709C2×C4C23×C3×D314yes—
710C2×C4C23×C3×D314yes—
711C2×C4C23×C3×D312yes—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—24no—
716C2×C3—44no—
717C2×C3—42no—
718C2×C3—42no—
719C2×C3—64no—
720C2×C3—124no—
721C2×C3—122no—
722C2×C3#562914yesdirect product factor
723C2×C3C3×#53714yescomplemented
724C2×C3C22×D3×D411yescharacteristic
725C2×C3C2×#100711yescharacteristic
726C2×C3C2×#100911yescharacteristic
727C2×C3C23×C3×D411yescharacteristic
728C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
729C2×C3C2×C3×2−1+411yescharacteristic
730D3—24no—
731D3—44no—
732D3—42no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—34no—
737C22—44no—
738C22—62no—
739C22—62no—
740C22—68no—
741C22—64no—
742C22—62no—
743C22—62no—
744C22—64no—
745C22—62no—
746C22—64no—
747C22—128no—
748C22—124no—
749C22C2×C3×D3×D412yes—
750C22C3×#100712yes—
751C22C3×#100912yes—
752C22C24×C3×D311yescharacteristic
753C4—22no—
754C4—24no—
755C4—24no—
756C4—34no—
757C4—62no—
758C4—64no—
759C4C2×C3×D3×D414yes—
760C3—21no—
761C3C2×#562911yescharacteristic, direct product factor
762C3C2×C3×#53711yescharacteristic, complemented
763C2—42no—
764C2—64no—
765C2—124no—
766C2—122no—
767C2C3×#562914yesdirect product factor
768C2C22×C3×D3×D411yescharacteristic
769C2C2×C3×#100711yescharacteristic
770C2C2×C3×#100911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C2×C3×#537
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C22×C3×#235C2semidirect
3. C2×C32×C22⋊Q8C2semidirect
4. C2×C3×#946C2semidirect
5. C2×C3×#930C2semidirect
6. C3×#5629C2direct (N × H)
7. C2×C3×#896C2semidirect
8. C2×C3×#895C2semidirect
9. C2×C3×#895C2semidirect
10. C2×C3×D3×C4⋊C4C2semidirect
11. C2×C3×#884C2semidirect
12. C2×C3×#884C2semidirect
14. C2×#5629C3direct (N × H)
21. C2×C3×#239C22semidirect
23. C2×C3×#235C22semidirect
33. C32×C22⋊Q8C22semidirect
37. C3×#946C22semidirect
38. C3×#930C22semidirect
45. C3×#896C22semidirect
46. C3×#895C22semidirect
47. C3×#895C22semidirect
48. C3×D3×C4⋊C4C22semidirect
49. C3×#884C22semidirect
50. C3×#884C22semidirect
53. C22×#239C2×C3semidirect
54. C22×#235C2×C3semidirect
59. C2×C3×C22⋊Q8D3semidirect
60. C2×C3×C22⋊Q8C2×C3semidirect
67. C2×#946C2×C3semidirect
68. C2×#930C2×C3semidirect
69. #5629C2×C3direct (N × H)
70. C2×#896C2×C3semidirect
71. C2×#895C2×C3semidirect
72. C2×#895C2×C3semidirect
73. C2×D3×C4⋊C4C2×C3semidirect
74. C2×#884C2×C3semidirect
75. C2×#884C2×C3semidirect
110. C2×C3×C4×D3D4semidirect
153. C2×#239C22×C3semidirect
155. C2×#235C22×C3semidirect
168. C3×C22⋊Q8C2×D3semidirect
169. C3×C22⋊Q8C22×C3semidirect
191. #946C22×C3semidirect
192. #930C22×C3semidirect
199. #896C22×C3semidirect
200. #895C22×C3semidirect
201. #895C22×C3semidirect
202. D3×C4⋊C4C22×C3semidirect
203. #884C22×C3semidirect
204. #884C22×C3semidirect
248. C3×C4×D3C2×D4semidirect
255. C2×C22⋊Q8C3×D3semidirect
346. C2×C4×D3C3×D4semidirect
421. C22⋊Q8C2×C3×D3semidirect
540. C4×D3C2×C3×D4semidirect
543. C2×C32#537semidirect
666. C32C2×#537semidirect
722. C2×C3#5629direct (N × H)
723. C2×C3C3×#537semidirect
761. C3C2×#5629direct (N × H)
762. C3C2×C3×#537semidirect
767. C2C3×#5629direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×C3×#2352
C2×C32×C22⋊Q82
C2×C3×#9462
C2×C3×#9302
C3×#56292
C2×C3×#8962
C2×C3×#8952
C2×C3×D3×C4⋊C42
C2×C3×#8842
C2×C3×#5373
C2×#56293