Finite Group Databasebeta

← C2×C3×#5611 #11902494

Subgroups — C2×C3×#5611 #11902494

Order 1152.

3477 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C212yesmaximal, complemented
2C2×C32×#121C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C2×C3×#935C212yesmaximal, complemented
5C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
6C2×C3×C4×#67C211yesmaximal, characteristic, complemented
7C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#5611C2116yesmaximal, direct product factor
9C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#888C211yesmaximal, characteristic, complemented
11C2×C3×#883C212yesmaximal, complemented
12C2×C3×#878C212yesmaximal, complemented
13C2×C3×#547—31nomaximal
14C2×#5611C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C22×C32×D4C2212yes—
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2212yes—
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2212yes—
21C23×C3×Dic3C2212yes—
22C2×C3×#237—216no—
23C2×C3×#237C22116yescomplemented
24C22×C3×C4×D3C2212yes—
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2212yes—
27C32×#121C2218yescomplemented
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2212yes—
30C2×C3×#217C2212yes—
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2212yes—
33C3×#938C2218yescomplemented
34C3×#935C22116yescomplemented
35C3×D4×Dic3C2218yescomplemented
36C3×C4×#67C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2212yes—
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C2×C3×C4⋊Dic3C2218yescomplemented
42C2×C3×Dic3⋊C4C2212yes—
43C2×C3×Dic3⋊C4C2212yes—
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C3×D3×C4⋊C4C2218yescomplemented
47C3×#888C2218yescomplemented
48C3×#883C22116yescomplemented
49C3×#878C22116yescomplemented
50C22×C3×#41—32no—
51C22×#237C2×C312yescomplemented
52C3×#547—316no—
53C2×C3×C4⋊Q8—31no—
54C2×C3×#123—32no—
55C2×C3×#123—32no—
56C2×C3×C22⋊Q8—32no—
57C2×C3×#121—21no—
58C2×C3×#121—31no—
59C2×C3×#121D311yescharacteristic, complemented
60C2×C3×#121C2×C311yescharacteristic, complemented
61C2×C3×C4×D4—31no—
62C2×C3×C4×D4—31no—
63C22×C3×C4⋊C4—31no—
64C22×C3×C4⋊C4—31no—
65C2×#938C2×C311yescharacteristic, complemented
66C2×#935C2×C312yescomplemented
67C2×D4×Dic3C2×C311yescharacteristic, complemented
68C2×C4×#67C2×C311yescharacteristic, complemented
69C22×C4⋊Dic3C2×C311yescharacteristic, complemented
70#5611C2×C3116yesdirect product factor
71C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
72C2×#888C2×C311yescharacteristic, complemented
73C2×#883C2×C312yescomplemented
74C2×#878C2×C312yescomplemented
75C24×C32C2312yes—
76C24×C32C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C2×C32×D4—28no—
79C2×C32×D4—24no—
80C2×C32×D4C2314yes—
81C2×C32×D4C2318yes—
82C22×C32×C4—24no—
83C22×C32×C4C2312yes—
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2314yes—
86C22×C32×C4C2311yescharacteristic
87C2×C3×#67—28no—
88C2×C3×#67D418yescomplemented
89C2×C3×#67C2318yes—
90C2×C3×#67C2314yes—
91C22×C3×Dic3—28no—
92C22×C3×Dic3—28no—
93C22×C3×Dic3C2318yes—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2318yes—
99C22×C3×Dic3C2311yescharacteristic
100C3×#237—264no—
101C2×C3×C4×D3—28no—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3C2318yes—
104C2×C3×C4×D3C2314yes—
105C2×C3×Dic6—28no—
106C2×C3×Dic6C2318yes—
107C32×C4⋊C4C2314yes—
108C32×C22⋊C4C2318yes—
109C3×#217C2318yes—
110C3×#217C2318yes—
111C3×#217C2314yes—
112C3×(C2×D3)⋊C4C2314yes—
113C3×C4⋊Dic3C2318yes—
114C3×C4⋊Dic3C2314yes—
115C3×C4⋊Dic3C2314yes—
116C3×Dic3⋊C4C2314yes—
117C3×Dic3⋊C4C2318yes—
118C3×Dic3⋊C4C2318yes—
119C3×C4×Dic3C2314yes—
120C2×#547—31noSylow
121C2×C3×#41—316no—
122C2×C3×#41—616no—
123C22×C3×Q8—32no—
124C22×C3×D4—21no—
125C22×C3×D4—22no—
126C22×C3×D4—31no—
127C22×C3×D4—32no—
128C22×C3×D4C2×D312yes—
129C22×C3×D4C2×D311yescharacteristic
130C22×C3×D4C22×C312yes—
131C22×C3×D4C22×C311yescharacteristic
132C23×C3×C4—21no—
133C23×C3×C4—32no—
134C23×C3×C4—32no—
135C23×C3×C4—32no—
136C23×C3×C4—31no—
137C23×C3×C4C2×D311yescharacteristic
138C23×C3×C4C22×C311yescharacteristic
139C22×#67C22×C312yes—
140C22×#67C22×C311yescharacteristic
141C23×Dic3C22×C312yes—
142C23×Dic3C22×C312yes—
143C2×#237—216no—
144C2×#237C22×C3116yescomplemented
145C22×C4×D3C22×C312yes—
146C22×C4×D3C22×C311yescharacteristic
147C22×Dic6C22×C312yes—
148C3×C4⋊Q8—38no—
149C3×#123—316no—
150C3×#123—316no—
151C3×C22⋊Q8—316no—
152C3×#121—28no—
153C3×#121—38no—
154C3×#121C2×D318yescomplemented
155C3×#121C22×C318yescomplemented
156C3×C4×D4—38no—
157C3×C4×D4—38no—
158C2×C3×C4⋊C4—21no—
159C2×C3×C4⋊C4—32no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—32no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—32no—
165C2×C3×C4⋊C4—38no—
166C2×C3×C4⋊C4—38no—
167C2×C3×C4⋊C4C2×D311yescharacteristic
168C2×C3×C4⋊C4C22×C311yescharacteristic
169C2×C3×C22⋊C4—22no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—32no—
172C2×C3×C22⋊C4—32no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4C2×D312yes—
175C2×C3×C22⋊C4C22×C312yes—
176C2×C3×C42—31no—
177C2×#217C22×C312yes—
178C2×#217C22×C312yes—
179C2×#217C22×C311yescharacteristic
180#938C22×C318yescomplemented
181#935C22×C3116yescomplemented
182D4×Dic3C22×C318yescomplemented
183C4×#67C22×C318yescomplemented
184C2×(C2×D3)⋊C4C22×C311yescharacteristic
185C2×C4⋊Dic3C22×C312yes—
186C2×C4⋊Dic3C22×C311yescharacteristic
187C2×C4⋊Dic3C22×C311yescharacteristic
188C2×C4⋊Dic3C22×C318yescomplemented
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×Dic3⋊C4C22×C312yes—
191C2×Dic3⋊C4C22×C312yes—
192C2×C4×Dic3C22×C311yescharacteristic
193D3×C4⋊C4C22×C318yescomplemented
194#888C22×C318yescomplemented
195#883C22×C3116yescomplemented
196#878C22×C3116yescomplemented
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—24no—
200C23×C32—24no—
201C23×C32—24no—
202C23×C32C2×D414yes—
203C23×C32C2414yes—
204C23×C32C2412yes—
205C23×C32C2411yescharacteristic
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3C2×D414yes—
209C22×C3×D3C2412yes—
210C32×D4—216no—
211C32×D4—28no—
212C2×C32×C4—24no—
213C2×C32×C4—22no—
214C2×C32×C4—28no—
215C2×C32×C4#4114yescomplemented
216C2×C32×C4C2414yes—
217C2×C32×C4C2412yes—
218C2×C32×C4C2412yes—
219C3×#67—216no—
220C3×#67C2×D4116yescomplemented
221C2×C3×Dic3—24no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—216no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—216no—
227C2×C3×Dic3C2×D414yes—
228C2×C3×Dic3C2412yes—
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2414yes—
232C2×C3×Dic3C2412yes—
233C3×C4×D3—216no—
234C3×C4×D3—28no—
235C3×Dic6—216no—
236C22×#41—32no—
237#547—316no—
238C2×C4⋊Q8—31no—
239C2×#123—32no—
240C2×#123—32no—
241C2×C22⋊Q8—32no—
242C2×#121—31no—
243C2×#121C3×D311yescharacteristic, complemented
244C2×C4×D4—31no—
245C2×C4×D4—31no—
246C22×C4⋊C4—31no—
247C22×C4⋊C4—31no—
248C24×C3—21no—
249C24×C3—22no—
250C24×C3—31no—
251C24×C3C22×D312yes—
252C24×C3C22×D311yescharacteristic
253C24×C3C23×C312yes—
254C24×C3C23×C311yescharacteristic
255C23×D3C23×C311yescharacteristic
256C3×#41—664no—
257C2×C3×Q8—38no—
258C2×C3×Q8—68no—
259C2×C3×D4—28no—
260C2×C3×D4—28no—
261C2×C3×D4—24no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—28no—
265C2×C3×D4—38no—
266C2×C3×D4—34no—
267C2×C3×D4—38no—
268C2×C3×D4—44no—
269C2×C3×D4—48no—
270C2×C3×D4—68no—
271C2×C3×D4C22×D314yes—
272C2×C3×D4C22×D318yes—
273C2×C3×D4C23×C314yes—
274C2×C3×D4C23×C318yes—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—22no—
280C22×C3×C4—24no—
281C22×C3×C4—31no—
282C22×C3×C4—38no—
283C22×C3×C4—38no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—32no—
287C22×C3×C4—32no—
288C22×C3×C4—34no—
289C22×C3×C4—38no—
290C22×C3×C4—44no—
291C22×C3×C4—68no—
292C22×C3×C4—68no—
293C22×C3×C4—68no—
294C22×C3×C4—64no—
295C22×C3×C4C22×D314yes—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D312yes—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C23×C312yes—
300C22×C3×C4C23×C311yescharacteristic
301C22×C3×C4C23×C314yes—
302C22×C3×C4C23×C311yescharacteristic
303C2×#67—28no—
304C2×#67C3×D418yescomplemented
305C2×#67C23×C318yes—
306C2×#67C23×C314yes—
307C22×Dic3—28no—
308C22×Dic3—28no—
309C22×Dic3C23×C318yes—
310C22×Dic3C23×C311yescharacteristic
311C22×Dic3C23×C311yescharacteristic
312C22×Dic3C23×C312yes—
313C22×Dic3C23×C312yes—
314C22×Dic3C23×C318yes—
315C22×Dic3C23×C311yescharacteristic
316#237—264no—
317C2×C4×D3—28no—
318C2×C4×D3—24no—
319C2×C4×D3C23×C318yes—
320C2×C4×D3C23×C314yes—
321C2×Dic6—28no—
322C2×Dic6C23×C318yes—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—38no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—38no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—34no—
329C3×C4⋊C4—38no—
330C3×C4⋊C4C22×D314yes—
331C3×C4⋊C4C23×C314yes—
332C3×C22⋊C4—28no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4—38no—
335C3×C22⋊C4—38no—
336C3×C22⋊C4—34no—
337C3×C22⋊C4C22×D318yes—
338C3×C22⋊C4C23×C318yes—
339C3×C42—34no—
340#217C23×C318yes—
341#217C23×C318yes—
342#217C23×C314yes—
343(C2×D3)⋊C4C23×C314yes—
344C4⋊Dic3C23×C318yes—
345C4⋊Dic3C23×C314yes—
346C4⋊Dic3C23×C314yes—
347Dic3⋊C4C23×C314yes—
348Dic3⋊C4C23×C318yes—
349Dic3⋊C4C23×C318yes—
350C4×Dic3C23×C314yes—
351C22×C32—28no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—24no—
355C22×C32—24no—
356C22×C32—24no—
357C22×C32—48no—
358C22×C32C22×D414yes—
359C22×C32C22×D412yes—
360C22×C32C2×#4112yes—
361C22×C322−1+412yes—
362C22×C32C2511yescharacteristic
363C2×C3×D3—28no—
364C2×C3×D3—22no—
365C2×C3×D3—22no—
366C2×C3×D3C22×D414yes—
367C32×C4—24no—
368C32×C4—22no—
369C32×C4C2×#4114yescomplemented
370C3×Dic3—24no—
371C3×Dic3—24no—
372C3×Dic3—22no—
373C3×Dic3—22no—
374C3×Dic3C22×D414yes—
375C2×#41—316no—
376C2×#41—616no—
377C22×Q8—32no—
378C22×D4—31no—
379C22×D4—32no—
380C22×D4C2×C3×D311yescharacteristic
381C22×D4C2×C3×D312yes—
382C23×C4—32no—
383C23×C4—32no—
384C23×C4—31no—
385C23×C4—32no—
386C23×C4C2×C3×D311yescharacteristic
387C4⋊Q8—38no—
388#123—316no—
389#123—316no—
390C22⋊Q8—316no—
391#121—38no—
392#121C2×C3×D318yescomplemented
393C4×D4—38no—
394C4×D4—38no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—38no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—38no—
403C2×C4⋊C4C2×C3×D311yescharacteristic
404C2×C22⋊C4—31no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—31no—
408C2×C22⋊C4C2×C3×D312yes—
409C2×C42—31no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—21no—
421C23×C3—22no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—34no—
425C23×C3—32no—
426C23×C3—42no—
427C23×C3—42no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—62no—
432C23×C3—62no—
433C23×C3D3×D414yes—
434C23×C3C2×C3×D414yes—
435C23×C3C23×D314yes—
436C23×C3C23×D312yes—
437C23×C3C23×D311yescharacteristic
438C23×C3C24×C314yes—
439C23×C3C24×C312yes—
440C23×C3C24×C311yescharacteristic
441C22×D3—22no—
442C22×D3—22no—
443C22×D3C2×C3×D414yes—
444C22×D3C24×C312yes—
445C3×Q8—616no—
446C3×D4—216no—
447C3×D4—216no—
448C3×D4—28no—
449C3×D4—28no—
450C3×D4—316no—
451C3×D4—48no—
452C3×D4—416no—
453C3×D4—616no—
454C2×C3×C4—24no—
455C2×C3×C4—22no—
456C2×C3×C4—24no—
457C2×C3×C4—22no—
458C2×C3×C4—28no—
459C2×C3×C4—28no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—34no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—48no—
471C2×C3×C4—42no—
472C2×C3×C4—44no—
473C2×C3×C4—616no—
474C2×C3×C4—616no—
475C2×C3×C4—64no—
476C2×C3×C4—64no—
477C2×C3×C4—616no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—68no—
481C2×C3×C4#23714yescomplemented
482C2×C3×C4C3×#4114yescomplemented
483C2×C3×C4C23×D312yes—
484C2×C3×C4C23×D314yes—
485C2×C3×C4C23×D312yes—
486C2×C3×C4C24×C314yes—
487C2×C3×C4C24×C312yes—
488C2×C3×C4C24×C312yes—
489#67—216no—
490#67C2×C3×D4116yescomplemented
491C2×Dic3—24no—
492C2×Dic3—24no—
493C2×Dic3—216no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—216no—
497C2×Dic3C2×C3×D414yes—
498C2×Dic3C24×C312yes—
499C2×Dic3C24×C312yes—
500C2×Dic3C24×C314yes—
501C2×Dic3C24×C314yes—
502C2×Dic3C24×C312yes—
503C4×D3—216no—
504C4×D3—28no—
505Dic6—216no—
506C2×C32—24no—
507C2×C32—44no—
508C2×C32#54714yescomplemented
509C2×C32C23×D411yescharacteristic
510C2×C32C22×#4111yescharacteristic
511C2×C32C2×2−1+411yescharacteristic
512C3×D3—24no—
513C24—31no—
514C24C22×C3×D312yes—
515C24C22×C3×D311yescharacteristic
516#41—664no—
517C2×Q8—38no—
518C2×Q8—68no—
519C2×D4—28no—
520C2×D4—24no—
521C2×D4—34no—
522C2×D4—38no—
523C2×D4—38no—
524C2×D4—68no—
525C2×D4C22×C3×D314yes—
526C2×D4C22×C3×D318yes—
527C22×C4—24no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—32no—
532C22×C4—32no—
533C22×C4—38no—
534C22×C4—38no—
535C22×C4—34no—
536C22×C4—38no—
537C22×C4—68no—
538C22×C4—68no—
539C22×C4—68no—
540C22×C4—64no—
541C22×C4C22×C3×D311yescharacteristic
542C22×C4C22×C3×D312yes—
543C22×C4C22×C3×D314yes—
544C22×C4C22×C3×D311yescharacteristic
545C4⋊C4—34no—
546C4⋊C4—34no—
547C4⋊C4—38no—
548C4⋊C4—38no—
549C4⋊C4—34no—
550C4⋊C4—38no—
551C4⋊C4C22×C3×D314yes—
552C22⋊C4—34no—
553C22⋊C4—38no—
554C22⋊C4—38no—
555C22⋊C4—34no—
556C22⋊C4C22×C3×D318yes—
557C42—34no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—28no—
563C22×C3—28no—
564C22×C3—24no—
565C22×C3—24no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—22no—
571C22×C3—24no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—21no—
575C22×C3—34no—
576C22×C3—42no—
577C22×C3—48no—
578C22×C3—42no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—44no—
582C22×C3—48no—
583C22×C3—48no—
584C22×C3—62no—
585C22×C3—62no—
586C22×C3—68no—
587C22×C3—88no—
588C22×C3C2×D3×D414yes—
589C22×C3C2×D3×D412yes—
590C22×C3C2×#23712yes—
591C22×C3#101012yes—
592C22×C3C22×C3×D414yes—
593C22×C3C22×C3×D412yes—
594C22×C3C2×C3×#4112yes—
595C22×C3C3×2−1+412yes—
596C22×C3C24×D311yescharacteristic
597C22×C3C25×C311yescharacteristic
598C2×D3—22no—
599C2×D3—22no—
600C2×D3—28no—
601C2×D3C22×C3×D414yes—
602C3×C4—24no—
603C3×C4—22no—
604C3×C4—24no—
605C3×C4—22no—
606C3×C4—24no—
607C3×C4—34no—
608C3×C4—42no—
609C3×C4—44no—
610C3×C4—64no—
611C3×C4—64no—
612C3×C4—62no—
613C3×C4—62no—
614C3×C4C2×#23714yescomplemented
615C3×C4C2×C3×#4114yescomplemented
616Dic3—24no—
617Dic3—24no—
618Dic3—22no—
619Dic3—22no—
620Dic3C22×C3×D414yes—
621C32C2×#54711yescharacteristic, complemented, Sylow
622C23—22no—
623C23—22no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—34no—
628C23—32no—
629C23—62no—
630C23—62no—
631C23C3×D3×D414yes—
632C23C23×C3×D314yes—
633C23C23×C3×D312yes—
634C23C23×C3×D311yescharacteristic
635Q8—616no—
636D4—216no—
637D4—28no—
638D4—316no—
639D4—616no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—28no—
643C2×C4—34no—
644C2×C4—32no—
645C2×C4—32no—
646C2×C4—32no—
647C2×C4—34no—
648C2×C4—34no—
649C2×C4—616no—
650C2×C4—616no—
651C2×C4—64no—
652C2×C4—64no—
653C2×C4—616no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—68no—
657C2×C4C3×#23714yescomplemented
658C2×C4C23×C3×D312yes—
659C2×C4C23×C3×D314yes—
660C2×C4C23×C3×D312yes—
661C2×C3—24no—
662C2×C3—24no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—24no—
666C2×C3—21no—
667C2×C3—44no—
668C2×C3—44no—
669C2×C3—44no—
670C2×C3—64no—
671C2×C3—84no—
672C2×C3#561114yesdirect product factor
673C2×C3C3×#54714yescomplemented
674C2×C3C22×D3×D411yescharacteristic
675C2×C3C22×#23711yescharacteristic
676C2×C3C2×#101011yescharacteristic
677C2×C3C23×C3×D411yescharacteristic
678C2×C3C22×C3×#4111yescharacteristic
679C2×C3C2×C3×2−1+411yescharacteristic
680D3—24no—
681C22—22no—
682C22—28no—
683C22—22no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—34no—
688C22—48no—
689C22—62no—
690C22—68no—
691C22—62no—
692C22C2×C3×D3×D414yes—
693C22C2×C3×D3×D412yes—
694C22C2×C3×#23712yes—
695C22C3×#101012yes—
696C22C24×C3×D311yescharacteristic
697C4—24no—
698C4—22no—
699C4—34no—
700C4—64no—
701C4—64no—
702C4—62no—
703C4—62no—
704C4C2×C3×#23714yescomplemented
705C3—21no—
706C3C2×#561111yescharacteristic, direct product factor
707C3C2×C3×#54711yescharacteristic, complemented
708C2—24no—
709C2—44no—
710C2—64no—
711C2C3×#561114yesdirect product factor
712C2C22×C3×D3×D411yescharacteristic
713C2C22×C3×#23711yescharacteristic
714C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×C32×#121C2semidirect
3. C2×C3×#938C2semidirect
4. C2×C3×#935C2semidirect
5. C2×C3×D4×Dic3C2semidirect
6. C2×C3×C4×#67C2semidirect
7. C22×C3×C4⋊Dic3C2semidirect
8. C3×#5611C2direct (N × H)
9. C2×C3×D3×C4⋊C4C2semidirect
10. C2×C3×#888C2semidirect
11. C2×C3×#883C2semidirect
12. C2×C3×#878C2semidirect
14. C2×#5611C3direct (N × H)
23. C2×C3×#237C22semidirect
27. C32×#121C22semidirect
33. C3×#938C22semidirect
34. C3×#935C22semidirect
35. C3×D4×Dic3C22semidirect
36. C3×C4×#67C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
46. C3×D3×C4⋊C4C22semidirect
47. C3×#888C22semidirect
48. C3×#883C22semidirect
49. C3×#878C22semidirect
51. C22×#237C2×C3semidirect
59. C2×C3×#121D3semidirect
60. C2×C3×#121C2×C3semidirect
65. C2×#938C2×C3semidirect
66. C2×#935C2×C3semidirect
67. C2×D4×Dic3C2×C3semidirect
68. C2×C4×#67C2×C3semidirect
69. C22×C4⋊Dic3C2×C3semidirect
70. #5611C2×C3direct (N × H)
71. C2×D3×C4⋊C4C2×C3semidirect
72. C2×#888C2×C3semidirect
73. C2×#883C2×C3semidirect
74. C2×#878C2×C3semidirect
88. C2×C3×#67D4semidirect
144. C2×#237C22×C3semidirect
154. C3×#121C2×D3semidirect
155. C3×#121C22×C3semidirect
180. #938C22×C3semidirect
181. #935C22×C3semidirect
182. D4×Dic3C22×C3semidirect
183. C4×#67C22×C3semidirect
188. C2×C4⋊Dic3C22×C3semidirect
193. D3×C4⋊C4C22×C3semidirect
194. #888C22×C3semidirect
195. #883C22×C3semidirect
196. #878C22×C3semidirect
215. C2×C32×C4#41semidirect
220. C3×#67C2×D4semidirect
243. C2×#121C3×D3semidirect
304. C2×#67C3×D4semidirect
369. C32×C4C2×#41semidirect
392. #121C2×C3×D3semidirect
481. C2×C3×C4#237semidirect
482. C2×C3×C4C3×#41semidirect
490. #67C2×C3×D4semidirect
508. C2×C32#547semidirect
614. C3×C4C2×#237semidirect
615. C3×C4C2×C3×#41semidirect
621. C32C2×#547semidirect
657. C2×C4C3×#237semidirect
672. C2×C3#5611direct (N × H)
673. C2×C3C3×#547semidirect
704. C4C2×C3×#237semidirect
706. C3C2×#5611direct (N × H)
707. C3C2×C3×#547semidirect
711. C2C3×#5611direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×C32×#1212
C2×C3×#9382
C2×C3×#9352
C2×C3×D4×Dic32
C2×C3×C4×#672
C22×C3×C4⋊Dic32
C3×#56112
C2×C3×D3×C4⋊C42
C2×C3×#8882
C2×C3×#8832
C2×C3×#8782
C2×C3×#5473
C2×#56113