Finite Group Databasebeta

← C2×C3×#5596 #11900740

Subgroups — C2×C3×#5596 #11900740

Order 1152.

3669 conjugacy classes of subgroups.

The subgroup lattice has 732 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×#940C211yesmaximal, characteristic, complemented
4C2×C3×#939C212yesmaximal, complemented
5C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
6C2×C3×#930C211yesmaximal, characteristic, complemented
7C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
8C3×#5596C2116yesmaximal, direct product factor
9C2×C3×#893C211yesmaximal, characteristic, complemented
10C2×C3×#888C211yesmaximal, characteristic, complemented
11C2×C3×#885C212yesmaximal, complemented
12C2×C3×#67⋊C4C212yesmaximal, complemented
13C2×C3×#532—31nomaximal
14C2×#5596C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C22×C32×D4C2212yes—
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C22×C3×#67C2212yes—
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2212yes—
23C23×C3×Dic3C2211yescharacteristic
24C2×C3×#237—216no—
25C2×C3×#237C22116yescomplemented
26C22×C3×D12C2211yescharacteristic
27C22×C3×C4×D3C2212yes—
28C22×C3×Dic6C2212yes—
29C32×#121C2218yescomplemented
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C22⋊C4C2212yes—
32C2×C3×#217C2212yes—
33C3×#940C2218yescomplemented
34C3×#939C22116yescomplemented
35C3×D4×Dic3C2218yescomplemented
36C3×#930C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×(C2×D3)⋊C4C2212yes—
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2212yes—
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C2×C3×C4×Dic3C2218yescomplemented
46C3×#893C2218yescomplemented
47C3×#888C2218yescomplemented
48C3×#885C22116yescomplemented
49C3×#67⋊C4C22116yescomplemented
50C22×C3×#41—32no—
51C22×#237C2×C312yescomplemented
52C3×#532—316no—
53C2×C3×C4⋊Q8—31no—
54C2×C3×#127—31no—
55C2×C3×#124—32no—
56C2×C3×#121—21no—
57C2×C3×#121—32no—
58C2×C3×#121—31no—
59C2×C3×#121D311yescharacteristic, complemented
60C2×C3×#121C2×C311yescharacteristic, complemented
61C2×C3×C4×D4—31no—
62C2×C3×C4×D4—31no—
63C2×C3×C4×D4—32no—
64C22×C3×C42—31no—
65C2×#940C2×C311yescharacteristic, complemented
66C2×#939C2×C312yescomplemented
67C2×D4×Dic3C2×C311yescharacteristic, complemented
68C2×#930C2×C311yescharacteristic, complemented
69C22×C4×Dic3C2×C311yescharacteristic, complemented
70#5596C2×C3116yesdirect product factor
71C2×#893C2×C311yescharacteristic, complemented
72C2×#888C2×C311yescharacteristic, complemented
73C2×#885C2×C312yescomplemented
74C2×#67⋊C4C2×C312yescomplemented
75C24×C32C2312yes—
76C24×C32C2311yescharacteristic
77C23×C3×D3C2312yes—
78C2×C32×D4—28no—
79C2×C32×D4—24no—
80C2×C32×D4C2314yes—
81C2×C32×D4C2318yes—
82C22×C32×C4—24no—
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2314yes—
85C22×C32×C4C2312yes—
86C22×C32×C4C2311yescharacteristic
87C2×C3×#67—28no—
88C2×C3×#67—28no—
89C2×C3×#67—28no—
90C2×C3×#67C2318yes—
91C2×C3×#67C2318yes—
92C2×C3×#67C2318yes—
93C22×C3×Dic3—28no—
94C22×C3×Dic3—24no—
95C22×C3×Dic3D418yescomplemented
96C22×C3×Dic3C2318yes—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2314yes—
99C22×C3×Dic3C2312yes—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2314yes—
103C22×C3×Dic3C2311yescharacteristic
104C3×#237—264no—
105C2×C3×D12—24no—
106C2×C3×D12C2314yes—
107C2×C3×C4×D3—28no—
108C2×C3×C4×D3C2318yes—
109C2×C3×Dic6—28no—
110C2×C3×Dic6C2318yes—
111C32×C4⋊C4C2314yes—
112C32×C22⋊C4C2318yes—
113C3×#217C2318yes—
114C3×(C2×D3)⋊C4C2318yes—
115C3×(C2×D3)⋊C4C2318yes—
116C3×C4⋊Dic3C2314yes—
117C3×Dic3⋊C4C2318yes—
118C3×C4×Dic3C2314yes—
119C3×C4×Dic3C2314yes—
120C3×C4×Dic3C2314yes—
121C3×C4×Dic3C2314yes—
122C2×#532—31noSylow
123C2×C3×#41—316no—
124C2×C3×#41—616no—
125C22×C3×Q8—32no—
126C22×C3×D4—21no—
127C22×C3×D4—22no—
128C22×C3×D4—32no—
129C22×C3×D4—32no—
130C22×C3×D4—32no—
131C22×C3×D4—31no—
132C22×C3×D4C2×D312yes—
133C22×C3×D4C2×D311yescharacteristic
134C22×C3×D4C22×C312yes—
135C22×C3×D4C22×C311yescharacteristic
136C23×C3×C4—21no—
137C23×C3×C4—31no—
138C23×C3×C4—32no—
139C23×C3×C4—31no—
140C23×C3×C4—32no—
141C23×C3×C4C2×D311yescharacteristic
142C23×C3×C4C22×C311yescharacteristic
143C22×#67C22×C312yes—
144C22×#67C22×C312yes—
145C22×#67C22×C312yes—
146C23×Dic3C22×C312yes—
147C23×Dic3C22×C311yescharacteristic
148C23×Dic3C22×C311yescharacteristic
149C2×#237—216no—
150C2×#237C22×C3116yescomplemented
151C22×D12C22×C311yescharacteristic
152C22×C4×D3C22×C312yes—
153C22×Dic6C22×C312yes—
154C3×C4⋊Q8—38no—
155C3×#127—38no—
156C3×#124—316no—
157C3×#121—28no—
158C3×#121—316no—
159C3×#121—38no—
160C3×#121C2×D318yescomplemented
161C3×#121C22×C318yescomplemented
162C3×C4×D4—38no—
163C3×C4×D4—38no—
164C3×C4×D4—316no—
165C2×C3×C4⋊C4—21no—
166C2×C3×C4⋊C4—32no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4C2×D311yescharacteristic
169C2×C3×C4⋊C4C22×C311yescharacteristic
170C2×C3×C22⋊C4—22no—
171C2×C3×C22⋊C4—32no—
172C2×C3×C22⋊C4—32no—
173C2×C3×C22⋊C4—32no—
174C2×C3×C22⋊C4C2×D312yes—
175C2×C3×C22⋊C4C22×C312yes—
176C2×C3×C42—31no—
177C2×C3×C42—31no—
178C2×C3×C42—31no—
179C2×C3×C42—31no—
180C2×C3×C42—38no—
181C2×#217C22×C312yes—
182#940C22×C318yescomplemented
183#939C22×C3116yescomplemented
184D4×Dic3C22×C318yescomplemented
185#930C22×C318yescomplemented
186C2×(C2×D3)⋊C4C22×C312yes—
187C2×(C2×D3)⋊C4C22×C312yes—
188C2×C4⋊Dic3C22×C311yescharacteristic
189C2×Dic3⋊C4C22×C312yes—
190C2×C4×Dic3C22×C311yescharacteristic
191C2×C4×Dic3C22×C311yescharacteristic
192C2×C4×Dic3C22×C311yescharacteristic
193C2×C4×Dic3C22×C311yescharacteristic
194C2×C4×Dic3C22×C318yescomplemented
195#893C22×C318yescomplemented
196#888C22×C318yescomplemented
197#885C22×C3116yescomplemented
198#67⋊C4C22×C3116yescomplemented
199C23×C32—22no—
200C23×C32—22no—
201C23×C32—24no—
202C23×C32—24no—
203C23×C32—24no—
204C23×C32C2×D414yes—
205C23×C32C2414yes—
206C23×C32C2412yes—
207C23×C32C2411yescharacteristic
208C22×C3×D3—24no—
209C22×C3×D3—24no—
210C22×C3×D3—24no—
211C22×C3×D3C2414yes—
212C32×D4—216no—
213C32×D4—28no—
214C2×C32×C4—24no—
215C2×C32×C4—22no—
216C2×C32×C4—28no—
217C2×C32×C4#4114yescomplemented
218C2×C32×C4C2412yes—
219C2×C32×C4C2414yes—
220C2×C32×C4C2412yes—
221C3×#67—216no—
222C3×#67—216no—
223C3×#67—216no—
224C2×C3×Dic3—24no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—216no—
227C2×C3×Dic3—28no—
228C2×C3×Dic3C2×D414yes—
229C2×C3×Dic3C2×D414yes—
230C2×C3×Dic3C2×D4116yescomplemented
231C2×C3×Dic3#4114yescomplemented
232C2×C3×Dic3C2412yes—
233C2×C3×Dic3C2414yes—
234C2×C3×Dic3C2412yes—
235C2×C3×Dic3C2412yes—
236C2×C3×Dic3C2412yes—
237C3×D12—28no—
238C3×C4×D3—216no—
239C3×Dic6—216no—
240C22×#41—32no—
241#532—316no—
242C2×C4⋊Q8—31no—
243C2×#127—31no—
244C2×#124—32no—
245C2×#121—32no—
246C2×#121—31no—
247C2×#121C3×D311yescharacteristic, complemented
248C2×C4×D4—31no—
249C2×C4×D4—31no—
250C2×C4×D4—32no—
251C22×C42—31no—
252C24×C3—21no—
253C24×C3—22no—
254C24×C3—32no—
255C24×C3C22×D312yes—
256C24×C3C22×D311yescharacteristic
257C24×C3C23×C312yes—
258C24×C3C23×C311yescharacteristic
259C23×D3C23×C312yes—
260C3×#41—664no—
261C2×C3×Q8—38no—
262C2×C3×Q8—68no—
263C2×C3×D4—28no—
264C2×C3×D4—28no—
265C2×C3×D4—24no—
266C2×C3×D4—24no—
267C2×C3×D4—24no—
268C2×C3×D4—28no—
269C2×C3×D4—38no—
270C2×C3×D4—38no—
271C2×C3×D4—38no—
272C2×C3×D4—34no—
273C2×C3×D4—44no—
274C2×C3×D4—48no—
275C2×C3×D4—68no—
276C2×C3×D4—68no—
277C2×C3×D4—68no—
278C2×C3×D4—64no—
279C2×C3×D4C22×D314yes—
280C2×C3×D4C22×D318yes—
281C2×C3×D4C23×C314yes—
282C2×C3×D4C23×C318yes—
283C22×C3×C4—24no—
284C22×C3×C4—24no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—22no—
288C22×C3×C4—24no—
289C22×C3×C4—38no—
290C22×C3×C4—34no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—34no—
295C22×C3×C4—38no—
296C22×C3×C4—31no—
297C22×C3×C4—32no—
298C22×C3×C4—38no—
299C22×C3×C4—44no—
300C22×C3×C4—68no—
301C22×C3×C4—64no—
302C22×C3×C4—68no—
303C22×C3×C4C22×D314yes—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D312yes—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C23×C311yescharacteristic
308C22×C3×C4C23×C314yes—
309C22×C3×C4C23×C312yes—
310C22×C3×C4C23×C311yescharacteristic
311C2×#67—28no—
312C2×#67—28no—
313C2×#67—28no—
314C2×#67C23×C318yes—
315C2×#67C23×C318yes—
316C2×#67C23×C318yes—
317C22×Dic3—28no—
318C22×Dic3—24no—
319C22×Dic3C3×D418yescomplemented
320C22×Dic3C23×C318yes—
321C22×Dic3C23×C311yescharacteristic
322C22×Dic3C23×C314yes—
323C22×Dic3C23×C312yes—
324C22×Dic3C23×C311yescharacteristic
325C22×Dic3C23×C311yescharacteristic
326C22×Dic3C23×C314yes—
327C22×Dic3C23×C311yescharacteristic
328#237—264no—
329C2×D12—24no—
330C2×D12C23×C314yes—
331C2×C4×D3—28no—
332C2×C4×D3C23×C318yes—
333C2×Dic6—28no—
334C2×Dic6C23×C318yes—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—38no—
337C3×C4⋊C4—34no—
338C3×C4⋊C4C22×D314yes—
339C3×C4⋊C4C23×C314yes—
340C3×C22⋊C4—28no—
341C3×C22⋊C4—38no—
342C3×C22⋊C4—38no—
343C3×C22⋊C4—38no—
344C3×C22⋊C4C22×D318yes—
345C3×C22⋊C4C23×C318yes—
346C3×C42—34no—
347C3×C42—34no—
348C3×C42—34no—
349C3×C42—34no—
350#217C23×C318yes—
351(C2×D3)⋊C4C23×C318yes—
352(C2×D3)⋊C4C23×C318yes—
353C4⋊Dic3C23×C314yes—
354Dic3⋊C4C23×C318yes—
355C4×Dic3C23×C314yes—
356C4×Dic3C23×C314yes—
357C4×Dic3C23×C314yes—
358C4×Dic3C23×C314yes—
359C22×C32—28no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—24no—
363C22×C32—24no—
364C22×C32—24no—
365C22×C32—48no—
366C22×C32C22×D414yes—
367C22×C32C22×D412yes—
368C22×C32C2×#4112yes—
369C22×C32C2×#4112yes—
370C22×C32C2511yescharacteristic
371C2×C3×D3—24no—
372C2×C3×D3—24no—
373C2×C3×D3—24no—
374C2×C3×D3—48no—
375C32×C4—24no—
376C32×C4—22no—
377C32×C4C2×#4114yescomplemented
378C3×Dic3—24no—
379C3×Dic3—22no—
380C3×Dic3C22×D414yes—
381C3×Dic3C22×D414yes—
382C3×Dic3C2×#4114yescomplemented
383C2×#41—316no—
384C2×#41—616no—
385C22×Q8—32no—
386C22×D4—32no—
387C22×D4—32no—
388C22×D4—32no—
389C22×D4—31no—
390C22×D4C2×C3×D311yescharacteristic
391C22×D4C2×C3×D312yes—
392C23×C4—31no—
393C23×C4—32no—
394C23×C4—31no—
395C23×C4—32no—
396C23×C4C2×C3×D311yescharacteristic
397C4⋊Q8—38no—
398#127—38no—
399#124—316no—
400#121—316no—
401#121—38no—
402#121C2×C3×D318yescomplemented
403C4×D4—38no—
404C4×D4—38no—
405C4×D4—316no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4C2×C3×D311yescharacteristic
409C2×C22⋊C4—32no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—32no—
412C2×C22⋊C4C2×C3×D312yes—
413C2×C42—31no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—31no—
417C2×C42—38no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—24no—
423C23×C3—24no—
424C23×C3—24no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—21no—
429C23×C3—22no—
430C23×C3—24no—
431C23×C3—24no—
432C23×C3—34no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—44no—
436C23×C3—44no—
437C23×C3—44no—
438C23×C3—64no—
439C23×C3—64no—
440C23×C3—64no—
441C23×C3D3×D414yes—
442C23×C3C2×C3×D414yes—
443C23×C3C23×D314yes—
444C23×C3C23×D312yes—
445C23×C3C23×D311yescharacteristic
446C23×C3C24×C314yes—
447C23×C3C24×C312yes—
448C23×C3C24×C311yescharacteristic
449C22×D3—24no—
450C22×D3—24no—
451C22×D3—24no—
452C22×D3C24×C314yes—
453C3×Q8—616no—
454C3×D4—216no—
455C3×D4—216no—
456C3×D4—28no—
457C3×D4—28no—
458C3×D4—48no—
459C3×D4—416no—
460C3×D4—616no—
461C3×D4—616no—
462C3×D4—616no—
463C3×D4—68no—
464C2×C3×C4—24no—
465C2×C3×C4—22no—
466C2×C3×C4—24no—
467C2×C3×C4—22no—
468C2×C3×C4—28no—
469C2×C3×C4—28no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—34no—
475C2×C3×C4—34no—
476C2×C3×C4—316no—
477C2×C3×C4—34no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—34no—
483C2×C3×C4—48no—
484C2×C3×C4—42no—
485C2×C3×C4—44no—
486C2×C3×C4—616no—
487C2×C3×C4—68no—
488C2×C3×C4—616no—
489C2×C3×C4—64no—
490C2×C3×C4—62no—
491C2×C3×C4#23714yescomplemented
492C2×C3×C4C3×#4114yescomplemented
493C2×C3×C4C23×D312yes—
494C2×C3×C4C23×D314yes—
495C2×C3×C4C23×D312yes—
496C2×C3×C4C24×C312yes—
497C2×C3×C4C24×C314yes—
498C2×C3×C4C24×C312yes—
499#67—216no—
500#67—216no—
501#67—216no—
502C2×Dic3—24no—
503C2×Dic3—22no—
504C2×Dic3—216no—
505C2×Dic3—28no—
506C2×Dic3C2×C3×D414yes—
507C2×Dic3C2×C3×D414yes—
508C2×Dic3C2×C3×D4116yescomplemented
509C2×Dic3C3×#4114yescomplemented
510C2×Dic3C24×C312yes—
511C2×Dic3C24×C314yes—
512C2×Dic3C24×C312yes—
513C2×Dic3C24×C312yes—
514C2×Dic3C24×C312yes—
515D12—28no—
516C4×D3—216no—
517Dic6—216no—
518C2×C32—24no—
519C2×C32—44no—
520C2×C32#53214yescomplemented
521C2×C32C23×D411yescharacteristic
522C2×C32C22×#4111yescharacteristic
523C2×C32C22×#4111yescharacteristic
524C3×D3—44no—
525C24—32no—
526C24C22×C3×D312yes—
527C24C22×C3×D311yescharacteristic
528#41—664no—
529C2×Q8—38no—
530C2×Q8—68no—
531C2×D4—28no—
532C2×D4—24no—
533C2×D4—38no—
534C2×D4—38no—
535C2×D4—38no—
536C2×D4—34no—
537C2×D4—68no—
538C2×D4—68no—
539C2×D4—68no—
540C2×D4—64no—
541C2×D4C22×C3×D314yes—
542C2×D4C22×C3×D318yes—
543C22×C4—24no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—34no—
548C22×C4—38no—
549C22×C4—31no—
550C22×C4—34no—
551C22×C4—32no—
552C22×C4—38no—
553C22×C4—38no—
554C22×C4—68no—
555C22×C4—68no—
556C22×C4—64no—
557C22×C4C22×C3×D311yescharacteristic
558C22×C4C22×C3×D314yes—
559C22×C4C22×C3×D312yes—
560C22×C4C22×C3×D311yescharacteristic
561C4⋊C4—38no—
562C4⋊C4—34no—
563C4⋊C4C22×C3×D314yes—
564C22⋊C4—38no—
565C22⋊C4—38no—
566C22⋊C4—38no—
567C22⋊C4C22×C3×D318yes—
568C42—34no—
569C42—34no—
570C42—34no—
571C42—34no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—28no—
577C22×C3—28no—
578C22×C3—24no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—24no—
584C22×C3—22no—
585C22×C3—24no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—21no—
589C22×C3—42no—
590C22×C3—48no—
591C22×C3—42no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—48no—
596C22×C3—48no—
597C22×C3—64no—
598C22×C3—64no—
599C22×C3—64no—
600C22×C3—88no—
601C22×C3—128no—
602C22×C3C2×D3×D414yes—
603C22×C3C2×D3×D412yes—
604C22×C3C2×#23712yes—
605C22×C3D3×#4112yes—
606C22×C3C22×C3×D414yes—
607C22×C3C22×C3×D412yes—
608C22×C3C2×C3×#4112yes—
609C22×C3C2×C3×#4112yes—
610C22×C3C24×D311yescharacteristic
611C22×C3C25×C311yescharacteristic
612C2×D3—24no—
613C2×D3—24no—
614C2×D3—24no—
615C2×D3—48no—
616C3×C4—24no—
617C3×C4—22no—
618C3×C4—24no—
619C3×C4—22no—
620C3×C4—24no—
621C3×C4—34no—
622C3×C4—34no—
623C3×C4—34no—
624C3×C4—42no—
625C3×C4—44no—
626C3×C4—64no—
627C3×C4—62no—
628C3×C4C2×#23714yescomplemented
629C3×C4C2×C3×#4114yescomplemented
630Dic3—24no—
631Dic3—22no—
632Dic3C22×C3×D414yes—
633Dic3C22×C3×D414yes—
634Dic3C2×C3×#4114yescomplemented
635C32C2×#53211yescharacteristic, complemented, Sylow
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—34no—
642C23—64no—
643C23—64no—
644C23—64no—
645C23C3×D3×D414yes—
646C23C23×C3×D314yes—
647C23C23×C3×D312yes—
648C23C23×C3×D311yescharacteristic
649Q8—616no—
650D4—216no—
651D4—28no—
652D4—616no—
653D4—616no—
654D4—616no—
655D4—68no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—28no—
659C2×C4—34no—
660C2×C4—34no—
661C2×C4—316no—
662C2×C4—34no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—34no—
668C2×C4—616no—
669C2×C4—616no—
670C2×C4—68no—
671C2×C4—64no—
672C2×C4—62no—
673C2×C4C3×#23714yescomplemented
674C2×C4C23×C3×D312yes—
675C2×C4C23×C3×D314yes—
676C2×C4C23×C3×D312yes—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—24no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—44no—
684C2×C3—44no—
685C2×C3—44no—
686C2×C3—84no—
687C2×C3—124no—
688C2×C3#559614yesdirect product factor
689C2×C3C3×#53214yescomplemented
690C2×C3C22×D3×D411yescharacteristic
691C2×C3C22×#23711yescharacteristic
692C2×C3C2×D3×#4111yescharacteristic
693C2×C3C23×C3×D411yescharacteristic
694C2×C3C22×C3×#4111yescharacteristic
695C2×C3C22×C3×#4111yescharacteristic
696D3—44no—
697C22—28no—
698C22—22no—
699C22—22no—
700C22—24no—
701C22—24no—
702C22—24no—
703C22—48no—
704C22—64no—
705C22—64no—
706C22—64no—
707C22—128no—
708C22C2×C3×D3×D414yes—
709C22C2×C3×D3×D412yes—
710C22C2×C3×#23712yes—
711C22C3×D3×#4112yes—
712C22C24×C3×D311yescharacteristic
713C4—24no—
714C4—22no—
715C4—34no—
716C4—34no—
717C4—34no—
718C4—64no—
719C4—62no—
720C4C2×C3×#23714yescomplemented
721C3—21no—
722C3C2×#559611yescharacteristic, direct product factor
723C3C2×C3×#53211yescharacteristic, complemented
724C2—24no—
725C2—44no—
726C2—124no—
727C2C3×#559614yesdirect product factor
728C2C22×C3×D3×D411yescharacteristic
729C2C22×C3×#23711yescharacteristic
730C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#532
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×#940C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×D4×Dic3C2semidirect
6. C2×C3×#930C2semidirect
7. C22×C3×C4×Dic3C2semidirect
8. C3×#5596C2direct (N × H)
9. C2×C3×#893C2semidirect
10. C2×C3×#888C2semidirect
11. C2×C3×#885C2semidirect
12. C2×C3×#67⋊C4C2semidirect
14. C2×#5596C3direct (N × H)
25. C2×C3×#237C22semidirect
29. C32×#121C22semidirect
33. C3×#940C22semidirect
34. C3×#939C22semidirect
35. C3×D4×Dic3C22semidirect
36. C3×#930C22semidirect
45. C2×C3×C4×Dic3C22semidirect
46. C3×#893C22semidirect
47. C3×#888C22semidirect
48. C3×#885C22semidirect
49. C3×#67⋊C4C22semidirect
51. C22×#237C2×C3semidirect
59. C2×C3×#121D3semidirect
60. C2×C3×#121C2×C3semidirect
65. C2×#940C2×C3semidirect
66. C2×#939C2×C3semidirect
67. C2×D4×Dic3C2×C3semidirect
68. C2×#930C2×C3semidirect
69. C22×C4×Dic3C2×C3semidirect
70. #5596C2×C3direct (N × H)
71. C2×#893C2×C3semidirect
72. C2×#888C2×C3semidirect
73. C2×#885C2×C3semidirect
74. C2×#67⋊C4C2×C3semidirect
95. C22×C3×Dic3D4semidirect
150. C2×#237C22×C3semidirect
160. C3×#121C2×D3semidirect
161. C3×#121C22×C3semidirect
182. #940C22×C3semidirect
183. #939C22×C3semidirect
184. D4×Dic3C22×C3semidirect
185. #930C22×C3semidirect
194. C2×C4×Dic3C22×C3semidirect
195. #893C22×C3semidirect
196. #888C22×C3semidirect
197. #885C22×C3semidirect
198. #67⋊C4C22×C3semidirect
217. C2×C32×C4#41semidirect
230. C2×C3×Dic3C2×D4semidirect
231. C2×C3×Dic3#41semidirect
247. C2×#121C3×D3semidirect
319. C22×Dic3C3×D4semidirect
377. C32×C4C2×#41semidirect
382. C3×Dic3C2×#41semidirect
402. #121C2×C3×D3semidirect
491. C2×C3×C4#237semidirect
492. C2×C3×C4C3×#41semidirect
508. C2×Dic3C2×C3×D4semidirect
509. C2×Dic3C3×#41semidirect
520. C2×C32#532semidirect
628. C3×C4C2×#237semidirect
629. C3×C4C2×C3×#41semidirect
634. Dic3C2×C3×#41semidirect
635. C32C2×#532semidirect
673. C2×C4C3×#237semidirect
688. C2×C3#5596direct (N × H)
689. C2×C3C3×#532semidirect
720. C4C2×C3×#237semidirect
722. C3C2×#5596direct (N × H)
723. C3C2×C3×#532semidirect
727. C2C3×#5596direct (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×#9402
C2×C3×#9392
C2×C3×D4×Dic32
C2×C3×#9302
C22×C3×C4×Dic32
C3×#55962
C2×C3×#8932
C2×C3×#8882
C2×C3×#8852
C2×C3×#67⋊C42
C2×C3×#5323
C2×#55963