Finite Group Databasebeta

← C3×D3×#537 #11901120

Subgroups — C3×D3×#537 #11901120

Order 1152.

3427 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C212yesmaximal, complemented
2C32×#537C211yesmaximal, characteristic, complemented
3C3×#5833C212yesmaximal, complemented
4C3×#5629C214yesmaximal, complemented
5C3×D3×C22⋊Q8C214yesmaximal, complemented
6C3×#5608C214yesmaximal, complemented
7C3×D3×#121C214yesmaximal, complemented
8C3×D3×#121C214yesmaximal, complemented
9C3×#5597C214yesmaximal, complemented
10C3×#5510C211yesmaximal, characteristic, complemented
11C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C3×#537—31nomaximal
13D3×#537C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2212yescomplemented
15C3×D3×#41—216no—
16C2×C3×#239C2212yescomplemented
17C2×C3×D3×Q8C2212yes—
18C2×C3×#237C2214yescomplemented
19C2×C3×#237C2212yescomplemented
20C2×C3×D3×D4C2212yes—
21C2×C3×D3×D4C2214yes—
22C2×C3×D3×D4C2214yes—
23C2×C3×#235C2212yescomplemented
24C2×C3×#235C2214yescomplemented
25C22×C3×C4×D3C2214yes—
26C22×C3×C4×D3C2212yes—
27C22×C3×C4×D3C2211yescharacteristic
28C32×C22⋊Q8C2214yescomplemented
29C32×#121C2214yescomplemented
30C32×#121C2214yescomplemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C3×#946C2214yescomplemented
33C3×#939C2218yescomplemented
34C3×#939C2218yescomplemented
35C3×#938C2214yescomplemented
36C3×#938C2214yescomplemented
37C3×#930C2214yescomplemented
38C3×#930C2214yescomplemented
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C3×#924C2214yescomplemented
41C2×C3×Dic3⋊C4C2212yescomplemented
42C3×#897C2214yescomplemented
43C3×#896C2218yescomplemented
44C3×#895C2214yescomplemented
45C3×#895C2214yescomplemented
46C3×D3×C4⋊C4C2214yes—
47C3×D3×C4⋊C4C2214yes—
48C3×D3×C4⋊C4C2214yescomplemented
49C3×#884C2218yescomplemented
50C3×#884C2218yescomplemented
51C3×D3×C22⋊C4C2218yes—
52C3×#878C2218yescomplemented
53C22×C3×#41—32no—
54C2×D3×#41C2×C312yescomplemented
55C3×#537—21no—
56C3×#537—32no—
57C3×#537—34no—
58C3×#537—34no—
59C3×#537—34no—
60C3×#537—31no—
61C3×#537D311yescharacteristic, direct product factor
62C3×#537C2×C311yescharacteristic, complemented
63C2×C3×C22⋊Q8—34no—
64C2×C3×#121—34no—
65C2×C3×#121—34no—
66C22×C3×C4⋊C4—31no—
67#5833C2×C312yescomplemented
68#5629C2×C314yescomplemented
69D3×C22⋊Q8C2×C314yescomplemented
70#5608C2×C314yescomplemented
71D3×#121C2×C314yescomplemented
72D3×#121C2×C314yescomplemented
73#5597C2×C314yescomplemented
74#5510C2×C311yescharacteristic, complemented
75C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
76C23×C3×D3C2314yes—
77C23×C3×D3C2311yescharacteristic
78C32×#41—28no—
79C2×C32×Q8C2312yes—
80C2×C32×D4C2312yes—
81C2×C32×D4C2314yes—
82C2×C32×D4C2314yes—
83C22×C32×C4C2314yes—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C2×C3×#67C2314yes—
87C2×C3×#67C2314yes—
88C2×C3×#67C2314yes—
89C2×C3×#67C2318yes—
90C22×C3×Dic3C2314yes—
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C3×#239—28no—
94C3×D3×Q8—28no—
95C3×#237—216no—
96C3×#237—28no—
97C3×D3×D4—216no—
98C3×D3×D4—28no—
99C3×D3×D4—48no—
100C3×#235—28no—
101C3×#235—216no—
102C2×C3×D12C2314yes—
103C2×C3×D12C2312yes—
104C2×C3×D12C2314yes—
105C2×C3×C4×D3—216no—
106C2×C3×C4×D3—44no—
107C2×C3×C4×D3D418yescomplemented
108C2×C3×C4×D3C2314yes—
109C2×C3×C4×D3C2314yes—
110C2×C3×C4×D3C2314yes—
111C2×C3×C4×D3C2314yes—
112C2×C3×C4×D3C2314yes—
113C2×C3×C4×D3C2312yes—
114C2×C3×C4×D3C2312yes—
115C2×C3×Dic6C2314yes—
116C2×C3×Dic6C2312yes—
117C32×C4⋊C4C2314yes—
118C32×C4⋊C4C2314yes—
119C32×C22⋊C4C2318yes—
120C3×#217C2318yes—
121C3×(C2×D3)⋊C4C2318yes—
122C3×(C2×D3)⋊C4C2318yes—
123C3×C4⋊Dic3C2314yes—
124C3×C4⋊Dic3C2314yes—
125C3×Dic3⋊C4C2318yes—
126C3×Dic3⋊C4C2318yes—
127C2×#537—31noSylow
128C2×C3×#41—22no—
129C2×C3×#41—32no—
130C2×C3×#41—34no—
131C2×C3×#41—32no—
132C2×C3×#41—34no—
133C2×C3×#41—32no—
134C2×C3×#41—616no—
135C2×C3×#41C2×D312yescomplemented
136C2×C3×#41C22×C312yescomplemented
137C22×C3×Q8—32no—
138C22×C3×D4—32no—
139C22×C3×D4—34no—
140C22×C3×D4—34no—
141C23×C3×C4—31no—
142C23×C3×C4—34no—
143C23×C3×C4—32no—
144D3×#41—216no—
145C2×#239C22×C312yescomplemented
146C2×D3×Q8C22×C312yes—
147C2×#237C22×C314yescomplemented
148C2×#237C22×C312yescomplemented
149C2×D3×D4C22×C314yes—
150C2×D3×D4C22×C312yes—
151C2×D3×D4C22×C314yes—
152C2×#235C22×C312yescomplemented
153C2×#235C22×C314yescomplemented
154C22×C4×D3C22×C314yes—
155C22×C4×D3C22×C312yes—
156C22×C4×D3C22×C311yescharacteristic
157C3×C22⋊Q8—24no—
158C3×C22⋊Q8—34no—
159C3×C22⋊Q8—34no—
160C3×C22⋊Q8—38no—
161C3×C22⋊Q8—34no—
162C3×C22⋊Q8—38no—
163C3×C22⋊Q8C2×D314yescomplemented
164C3×C22⋊Q8C22×C314yescomplemented
165C3×#121—24no—
166C3×#121—24no—
167C3×#121—34no—
168C3×#121—34no—
169C3×#121—38no—
170C3×#121—38no—
171C3×#121—34no—
172C3×#121—34no—
173C3×#121—34no—
174C3×#121—34no—
175C3×#121—38no—
176C3×#121—38no—
177C3×#121C2×D314yescomplemented
178C3×#121C2×D314yescomplemented
179C3×#121C22×C314yescomplemented
180C3×#121C22×C314yescomplemented
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—32no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—34no—
185C2×C3×C4⋊C4—34no—
186C2×C3×C4⋊C4—34no—
187C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
188C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
189C2×C3×C22⋊C4—38no—
190#946C22×C314yescomplemented
191#939C22×C318yescomplemented
192#939C22×C318yescomplemented
193#938C22×C314yescomplemented
194#938C22×C314yescomplemented
195#930C22×C314yescomplemented
196#930C22×C314yescomplemented
197C2×C4⋊Dic3C22×C311yescharacteristic, complemented
198#924C22×C314yescomplemented
199C2×Dic3⋊C4C22×C312yescomplemented
200#897C22×C314yescomplemented
201#896C22×C318yescomplemented
202#895C22×C314yescomplemented
203#895C22×C314yescomplemented
204D3×C4⋊C4C22×C314yes—
205D3×C4⋊C4C22×C314yes—
206D3×C4⋊C4C22×C314yescomplemented
207#884C22×C318yescomplemented
208#884C22×C318yescomplemented
209D3×C22⋊C4C22×C318yes—
210#878C22×C318yescomplemented
211C23×C32C2414yes—
212C23×C32C2411yescharacteristic
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—28no—
216C22×C3×D3—28no—
217C22×C3×D3—28no—
218C22×C3×D3C2×D414yes—
219C22×C3×D3C2414yes—
220C22×C3×D3C2411yescharacteristic
221C22×C3×D3C2411yescharacteristic
222C32×Q8—24no—
223C32×D4—28no—
224C32×D4—24no—
225C32×D4—44no—
226C2×C32×C4—28no—
227C2×C32×C4—42no—
228C2×C32×C4C2×D414yescomplemented
229C2×C32×C4C2414yes—
230C2×C32×C4C2414yes—
231C2×C32×C4C2412yes—
232C3×#67—28no—
233C3×#67—28no—
234C3×#67—28no—
235C3×#67—48no—
236C2×C3×Dic3—28no—
237C2×C3×Dic3—42no—
238C2×C3×Dic3C2×D414yescomplemented
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2414yes—
241C2×C3×Dic3C2412yes—
242C3×D12—28no—
243C3×D12—24no—
244C3×D12—44no—
245C3×C4×D3—28no—
246C3×C4×D3—28no—
247C3×C4×D3—28no—
248C3×C4×D3—28no—
249C3×C4×D3—44no—
250C3×C4×D3C2×D418yes—
251C3×C4×D3C2×D418yescomplemented
252C3×Dic6—24no—
253C3×Dic6—28no—
254C22×#41—32no—
255#537—32no—
256#537—34no—
257#537—34no—
258#537—34no—
259#537—31no—
260#537C3×D311yescharacteristic, direct product factor
261C2×C22⋊Q8—34no—
262C2×#121—34no—
263C2×#121—34no—
264C22×C4⋊C4—31no—
265C24×C3—31no—
266C24×C3—34no—
267C23×D3C23×C314yes—
268C23×D3C23×C311yescharacteristic
269C3×#41—28no—
270C3×#41—28no—
271C3×#41—48no—
272C3×#41—616no—
273C3×#41—616no—
274C3×#41—68no—
275C3×#41—68no—
276C3×#41—68no—
277C2×C3×Q8—22no—
278C2×C3×Q8—34no—
279C2×C3×Q8—32no—
280C2×C3×Q8—68no—
281C2×C3×Q8C22×D312yes—
282C2×C3×Q8C23×C312yes—
283C2×C3×D4—22no—
284C2×C3×D4—24no—
285C2×C3×D4—24no—
286C2×C3×D4—34no—
287C2×C3×D4—34no—
288C2×C3×D4—34no—
289C2×C3×D4—38no—
290C2×C3×D4—34no—
291C2×C3×D4—32no—
292C2×C3×D4—34no—
293C2×C3×D4—68no—
294C2×C3×D4—616no—
295C2×C3×D4—128no—
296C2×C3×D4C22×D314yes—
297C2×C3×D4C22×D312yes—
298C2×C3×D4C22×D314yes—
299C2×C3×D4C23×C312yes—
300C2×C3×D4C23×C314yes—
301C2×C3×D4C23×C314yes—
302C22×C3×C4—21no—
303C22×C3×C4—24no—
304C22×C3×C4—22no—
305C22×C3×C4—31no—
306C22×C3×C4—38no—
307C22×C3×C4—32no—
308C22×C3×C4—32no—
309C22×C3×C4—34no—
310C22×C3×C4—32no—
311C22×C3×C4—34no—
312C22×C3×C4—34no—
313C22×C3×C4—34no—
314C22×C3×C4—34no—
315C22×C3×C4—34no—
316C22×C3×C4—616no—
317C22×C3×C4—124no—
318C22×C3×C4C22×D314yes—
319C22×C3×C4C22×D312yes—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C23×C314yes—
322C22×C3×C4C23×C312yes—
323C22×C3×C4C23×C311yescharacteristic
324C2×#67C23×C314yes—
325C2×#67C23×C314yes—
326C2×#67C23×C314yes—
327C2×#67C23×C318yes—
328C22×Dic3C23×C314yes—
329C22×Dic3C23×C312yes—
330C22×Dic3C23×C311yescharacteristic
331#239—28no—
332D3×Q8—28no—
333#237—216no—
334#237—28no—
335D3×D4—216no—
336D3×D4—28no—
337D3×D4—48no—
338#235—28no—
339#235—216no—
340C2×D12C23×C314yes—
341C2×D12C23×C312yes—
342C2×D12C23×C314yes—
343C2×C4×D3—216no—
344C2×C4×D3—44no—
345C2×C4×D3C3×D418yescomplemented
346C2×C4×D3C23×C314yes—
347C2×C4×D3C23×C314yes—
348C2×C4×D3C23×C314yes—
349C2×C4×D3C23×C314yes—
350C2×C4×D3C23×C314yes—
351C2×C4×D3C23×C312yes—
352C2×C4×D3C23×C312yes—
353C2×Dic6C23×C314yes—
354C2×Dic6C23×C312yes—
355C3×C4⋊C4—24no—
356C3×C4⋊C4—24no—
357C3×C4⋊C4—38no—
358C3×C4⋊C4—38no—
359C3×C4⋊C4—34no—
360C3×C4⋊C4—34no—
361C3×C4⋊C4C22×D314yes—
362C3×C4⋊C4C22×D314yes—
363C3×C4⋊C4C23×C314yes—
364C3×C4⋊C4C23×C314yes—
365C3×C22⋊C4—28no—
366C3×C22⋊C4—38no—
367C3×C22⋊C4—38no—
368C3×C22⋊C4—38no—
369C3×C22⋊C4C22×D318yes—
370C3×C22⋊C4C23×C318yes—
371#217C23×C318yes—
372(C2×D3)⋊C4C23×C318yes—
373(C2×D3)⋊C4C23×C318yes—
374C4⋊Dic3C23×C314yes—
375C4⋊Dic3C23×C314yes—
376Dic3⋊C4C23×C318yes—
377Dic3⋊C4C23×C318yes—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—24no—
381C22×C32—24no—
382C22×C32—24no—
383C22×C32C22×D412yes—
384C22×C32C2511yescharacteristic
385C2×C3×D3—21no—
386C2×C3×D3—21no—
387C2×C3×D3—28no—
388C2×C3×D3—24no—
389C2×C3×D3—24no—
390C2×C3×D3—24no—
391C2×C3×D3—416no—
392C2×C3×D3C22×D412yes—
393C2×C3×D3C22×D412yes—
394C2×C3×D3H(5,𝔽2)12yes—
395C2×C3×D32−1+412yes—
396C32×C4—24no—
397C32×C4—24no—
398C32×C4C22×D414yes—
399C3×Dic3—24no—
400C3×Dic3—24no—
401C3×Dic3C22×D414yes—
402C2×#41—32no—
403C2×#41—34no—
404C2×#41—32no—
405C2×#41—34no—
406C2×#41—32no—
407C2×#41—616no—
408C2×#41C2×C3×D312yescomplemented
409C22×Q8—32no—
410C22×D4—32no—
411C22×D4—34no—
412C22×D4—34no—
413C23×C4—31no—
414C23×C4—34no—
415C23×C4—32no—
416C22⋊Q8—34no—
417C22⋊Q8—34no—
418C22⋊Q8—38no—
419C22⋊Q8—34no—
420C22⋊Q8—38no—
421C22⋊Q8C2×C3×D314yescomplemented
422#121—34no—
423#121—34no—
424#121—38no—
425#121—38no—
426#121—34no—
427#121—34no—
428#121—34no—
429#121—34no—
430#121—38no—
431#121—38no—
432#121C2×C3×D314yescomplemented
433#121C2×C3×D314yescomplemented
434C2×C4⋊C4—32no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—34no—
437C2×C4⋊C4—34no—
438C2×C4⋊C4—34no—
439C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
440C2×C22⋊C4—38no—
441C23×C3—21no—
442C23×C3—24no—
443C23×C3—31no—
444C23×C3—34no—
445C23×C3—31no—
446C23×C3—34no—
447C23×C3—62no—
448C23×C3—62no—
449C23×C3—68no—
450C23×C3—68no—
451C23×C3—68no—
452C23×C3C23×D314yes—
453C23×C3C23×D311yescharacteristic
454C23×C3C24×C314yes—
455C23×C3C24×C311yescharacteristic
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—28no—
459C22×D3—28no—
460C22×D3—28no—
461C22×D3C2×C3×D414yes—
462C22×D3C24×C314yes—
463C22×D3C24×C311yescharacteristic
464C22×D3C24×C311yescharacteristic
465C3×Q8—24no—
466C3×Q8—24no—
467C3×Q8—44no—
468C3×Q8—68no—
469C3×Q8—64no—
470C3×D4—28no—
471C3×D4—28no—
472C3×D4—24no—
473C3×D4—24no—
474C3×D4—44no—
475C3×D4—48no—
476C3×D4—44no—
477C3×D4—44no—
478C3×D4—68no—
479C3×D4—68no—
480C3×D4—68no—
481C3×D4—68no—
482C3×D4—64no—
483C3×D4—84no—
484C3×D4—124no—
485C3×D4—128no—
486C2×C3×C4—28no—
487C2×C3×C4—28no—
488C2×C3×C4—22no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—34no—
493C2×C3×C4—32no—
494C2×C3×C4—38no—
495C2×C3×C4—38no—
496C2×C3×C4—34no—
497C2×C3×C4—34no—
498C2×C3×C4—48no—
499C2×C3×C4—42no—
500C2×C3×C4—42no—
501C2×C3×C4—68no—
502C2×C3×C4—68no—
503C2×C3×C4—68no—
504C2×C3×C4—68no—
505C2×C3×C4—68no—
506C2×C3×C4—82no—
507C2×C3×C4—124no—
508C2×C3×C4—122no—
509C2×C3×C4D3×D414yescomplemented
510C2×C3×C4C2×C3×D414yescomplemented
511C2×C3×C4C23×D314yes—
512C2×C3×C4C23×D314yes—
513C2×C3×C4C23×D312yes—
514C2×C3×C4C24×C314yes—
515C2×C3×C4C24×C314yes—
516C2×C3×C4C24×C312yes—
517#67—28no—
518#67—28no—
519#67—28no—
520#67—48no—
521C2×Dic3—28no—
522C2×Dic3—42no—
523C2×Dic3C2×C3×D414yescomplemented
524C2×Dic3C24×C314yes—
525C2×Dic3C24×C314yes—
526C2×Dic3C24×C312yes—
527D12—28no—
528D12—24no—
529D12—44no—
530C4×D3—28no—
531C4×D3—28no—
532C4×D3—28no—
533C4×D3—28no—
534C4×D3—44no—
535C4×D3C2×C3×D418yes—
536C4×D3C2×C3×D418yescomplemented
537Dic6—24no—
538Dic6—28no—
539C2×C32—22no—
540C2×C32—44no—
541C2×C32C23×D411yescharacteristic
542C2×C32C2×H(5,𝔽2)11yescharacteristic
543C2×C32C2×2−1+411yescharacteristic
544C3×D3—22no—
545C3×D3—44no—
546C3×D3#53714yesdirect product factor
547C24—31no—
548C24—34no—
549#41—28no—
550#41—616no—
551#41—616no—
552#41—68no—
553#41—68no—
554#41—68no—
555C2×Q8—34no—
556C2×Q8—32no—
557C2×Q8—68no—
558C2×Q8C22×C3×D312yes—
559C2×D4—34no—
560C2×D4—34no—
561C2×D4—34no—
562C2×D4—38no—
563C2×D4—34no—
564C2×D4—32no—
565C2×D4—34no—
566C2×D4—68no—
567C2×D4—616no—
568C2×D4—128no—
569C2×D4C22×C3×D314yes—
570C2×D4C22×C3×D312yes—
571C2×D4C22×C3×D314yes—
572C22×C4—31no—
573C22×C4—32no—
574C22×C4—32no—
575C22×C4—38no—
576C22×C4—34no—
577C22×C4—32no—
578C22×C4—34no—
579C22×C4—34no—
580C22×C4—34no—
581C22×C4—34no—
582C22×C4—34no—
583C22×C4—616no—
584C22×C4—124no—
585C22×C4C22×C3×D314yes—
586C22×C4C22×C3×D312yes—
587C22×C4C22×C3×D311yescharacteristic
588C4⋊C4—38no—
589C4⋊C4—34no—
590C4⋊C4—38no—
591C4⋊C4—34no—
592C4⋊C4C22×C3×D314yes—
593C4⋊C4C22×C3×D314yes—
594C22⋊C4—38no—
595C22⋊C4—38no—
596C22⋊C4—38no—
597C22⋊C4C22×C3×D318yes—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—24no—
603C22×C3—24no—
604C22×C3—24no—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—32no—
611C22×C3—32no—
612C22×C3—32no—
613C22×C3—32no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—44no—
617C22×C3—44no—
618C22×C3—44no—
619C22×C3—68no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—64no—
623C22×C3—64no—
624C22×C3—64no—
625C22×C3—1216no—
626C22×C3C2×D3×D412yes—
627C22×C3C22×C3×D412yes—
628C22×C3C24×D311yescharacteristic
629C22×C3C25×C311yescharacteristic
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—28no—
633C2×D3—24no—
634C2×D3—24no—
635C2×D3—24no—
636C2×D3—416no—
637C2×D3C22×C3×D412yes—
638C2×D3C22×C3×D412yes—
639C2×D3C3×H(5,𝔽2)12yes—
640C2×D3C3×2−1+412yes—
641C3×C4—24no—
642C3×C4—24no—
643C3×C4—24no—
644C3×C4—24no—
645C3×C4—24no—
646C3×C4—34no—
647C3×C4—44no—
648C3×C4—44no—
649C3×C4—64no—
650C3×C4—64no—
651C3×C4C2×D3×D414yes—
652C3×C4C22×C3×D414yes—
653Dic3—24no—
654Dic3—24no—
655Dic3C22×C3×D414yes—
656C32C2×#53711yescharacteristic, complemented, Sylow
657C23—31no—
658C23—34no—
659C23—31no—
660C23—34no—
661C23—62no—
662C23—62no—
663C23—68no—
664C23—68no—
665C23—68no—
666C23C23×C3×D314yes—
667C23C23×C3×D311yescharacteristic
668Q8—24no—
669Q8—68no—
670Q8—64no—
671D4—28no—
672D4—24no—
673D4—44no—
674D4—68no—
675D4—68no—
676D4—68no—
677D4—68no—
678D4—64no—
679D4—124no—
680D4—128no—
681C2×C4—28no—
682C2×C4—34no—
683C2×C4—32no—
684C2×C4—38no—
685C2×C4—38no—
686C2×C4—34no—
687C2×C4—34no—
688C2×C4—42no—
689C2×C4—68no—
690C2×C4—68no—
691C2×C4—68no—
692C2×C4—68no—
693C2×C4—68no—
694C2×C4—124no—
695C2×C4—122no—
696C2×C4C3×D3×D414yescomplemented
697C2×C4C23×C3×D314yes—
698C2×C4C23×C3×D314yes—
699C2×C4C23×C3×D312yes—
700C2×C3—22no—
701C2×C3—22no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—34no—
706C2×C3—42no—
707C2×C3—44no—
708C2×C3—44no—
709C2×C3—62no—
710C2×C3—84no—
711C2×C3—124no—
712C2×C3C22×D3×D411yescharacteristic
713C2×C3D3×H(5,𝔽2)11yescharacteristic
714C2×C3D3×2−1+411yescharacteristic
715C2×C3C23×C3×D411yescharacteristic
716C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
717C2×C3C2×C3×2−1+411yescharacteristic
718D3—22no—
719D3—44no—
720D3C3×#53714yesdirect product factor
721C22—21no—
722C22—21no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—32no—
727C22—32no—
728C22—32no—
729C22—32no—
730C22—68no—
731C22—61no—
732C22—61no—
733C22—64no—
734C22—64no—
735C22—64no—
736C22—1216no—
737C22C2×C3×D3×D412yes—
738C22C24×C3×D311yescharacteristic
739C4—24no—
740C4—24no—
741C4—34no—
742C4—64no—
743C4—64no—
744C4C2×C3×D3×D414yes—
745C3—21no—
746C3D3×#53711yescharacteristic, direct product factor
747C3C2×C3×#53711yescharacteristic, complemented
748C2—22no—
749C2—34no—
750C2—44no—
751C2—62no—
752C2—124no—
753C2C22×C3×D3×D411yescharacteristic
754C2C3×D3×H(5,𝔽2)11yescharacteristic
755C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#537C2
socleC22×C32C25
hypercenterC3×#537D3
hypocenterC3C2×C3×#537
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#537

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C32×#537C2semidirect
3. C3×#5833C2semidirect
4. C3×#5629C2semidirect
5. C3×D3×C22⋊Q8C2semidirect
6. C3×#5608C2semidirect
7. C3×D3×#121C2semidirect
8. C3×D3×#121C2semidirect
9. C3×#5597C2semidirect
10. C3×#5510C2semidirect
11. C2×C3×D3×C4⋊C4C2semidirect
13. D3×#537C3direct (N × H)
14. C2×C32×#41C22semidirect
16. C2×C3×#239C22semidirect
18. C2×C3×#237C22semidirect
19. C2×C3×#237C22semidirect
23. C2×C3×#235C22semidirect
24. C2×C3×#235C22semidirect
28. C32×C22⋊Q8C22semidirect
29. C32×#121C22semidirect
30. C32×#121C22semidirect
31. C2×C32×C4⋊C4C22semidirect
32. C3×#946C22semidirect
33. C3×#939C22semidirect
34. C3×#939C22semidirect
35. C3×#938C22semidirect
36. C3×#938C22semidirect
37. C3×#930C22semidirect
38. C3×#930C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C3×#924C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C3×#897C22semidirect
43. C3×#896C22semidirect
44. C3×#895C22semidirect
45. C3×#895C22semidirect
48. C3×D3×C4⋊C4C22semidirect
49. C3×#884C22semidirect
50. C3×#884C22semidirect
52. C3×#878C22semidirect
54. C2×D3×#41C2×C3semidirect
61. C3×#537D3direct (N × H)
62. C3×#537C2×C3semidirect
67. #5833C2×C3semidirect
68. #5629C2×C3semidirect
69. D3×C22⋊Q8C2×C3semidirect
70. #5608C2×C3semidirect
71. D3×#121C2×C3semidirect
72. D3×#121C2×C3semidirect
73. #5597C2×C3semidirect
74. #5510C2×C3semidirect
75. C2×D3×C4⋊C4C2×C3semidirect
107. C2×C3×C4×D3D4semidirect
135. C2×C3×#41C2×D3semidirect
136. C2×C3×#41C22×C3semidirect
145. C2×#239C22×C3semidirect
147. C2×#237C22×C3semidirect
148. C2×#237C22×C3semidirect
152. C2×#235C22×C3semidirect
153. C2×#235C22×C3semidirect
163. C3×C22⋊Q8C2×D3semidirect
164. C3×C22⋊Q8C22×C3semidirect
177. C3×#121C2×D3semidirect
178. C3×#121C2×D3semidirect
179. C3×#121C22×C3semidirect
180. C3×#121C22×C3semidirect
187. C2×C3×C4⋊C4C2×D3semidirect
188. C2×C3×C4⋊C4C22×C3semidirect
190. #946C22×C3semidirect
191. #939C22×C3semidirect
192. #939C22×C3semidirect
193. #938C22×C3semidirect
194. #938C22×C3semidirect
195. #930C22×C3semidirect
196. #930C22×C3semidirect
197. C2×C4⋊Dic3C22×C3semidirect
198. #924C22×C3semidirect
199. C2×Dic3⋊C4C22×C3semidirect
200. #897C22×C3semidirect
201. #896C22×C3semidirect
202. #895C22×C3semidirect
203. #895C22×C3semidirect
206. D3×C4⋊C4C22×C3semidirect
207. #884C22×C3semidirect
208. #884C22×C3semidirect
210. #878C22×C3semidirect
228. C2×C32×C4C2×D4semidirect
238. C2×C3×Dic3C2×D4semidirect
251. C3×C4×D3C2×D4semidirect
260. #537C3×D3direct (N × H)
345. C2×C4×D3C3×D4semidirect
408. C2×#41C2×C3×D3semidirect
421. C22⋊Q8C2×C3×D3semidirect
432. #121C2×C3×D3semidirect
433. #121C2×C3×D3semidirect
439. C2×C4⋊C4C2×C3×D3semidirect
509. C2×C3×C4D3×D4semidirect
510. C2×C3×C4C2×C3×D4semidirect
523. C2×Dic3C2×C3×D4semidirect
536. C4×D3C2×C3×D4semidirect
546. C3×D3#537direct (N × H)
656. C32C2×#537semidirect
696. C2×C4C3×D3×D4semidirect
720. D3C3×#537direct (N × H)
746. C3D3×#537direct (N × H)
747. C3C2×C3×#537semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C32×#5372
C3×#58332
C3×#56292
C3×D3×C22⋊Q82
C3×#56082
C3×D3×#1212
C3×#55972
C3×#55102
C2×C3×D3×C4⋊C42
C2×C3×#5373
D3×#5373