Finite Group Databasebeta

← C2×C3×#5507 #11902497

Subgroups — C2×C3×#5507 #11902497

Order 1152.

3473 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C212yesmaximal, complemented
2C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C2×C3×#929C212yesmaximal, complemented
5C2×C3×C4×#67C211yesmaximal, characteristic, complemented
6C2×C3×#896C212yesmaximal, complemented
7C3×#5507C2116yesmaximal, direct product factor
8C2×C3×#895C211yesmaximal, characteristic, complemented
9C2×C3×#894C212yesmaximal, complemented
10C2×C3×#893C211yesmaximal, characteristic, complemented
11C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C3×#888C211yesmaximal, characteristic, complemented
13C2×C3×#547—31nomaximal
14C2×#5507C311yesmaximal, characteristic, direct product factor
15C23×C32×C4C2211yescharacteristic
16C23×C32×C4C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2211yescharacteristic
19C2×C3×#235—216no—
20C2×C3×#235C22116yescomplemented
21C22×C3×D12C2211yescharacteristic
22C22×C3×D12C2212yes—
23C22×C3×C4×D3C2212yes—
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2212yes—
26C22×C3×Dic6C2212yes—
27C2×C32×C4⋊C4C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C32×C4⋊C4C2212yes—
30C2×C32×C4⋊C4C2218yescomplemented
31C2×C3×#217C2211yescharacteristic
32C3×#930C2218yescomplemented
33C3×#929C22116yescomplemented
34C3×C4×#67C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×(C2×D3)⋊C4C2212yes—
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2212yes—
41C2×C3×Dic3⋊C4C2212yes—
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#896C22116yescomplemented
45C3×#895C2218yescomplemented
46C3×#894C22116yescomplemented
47C3×#893C2218yescomplemented
48C3×D3×C4⋊C4C2218yescomplemented
49C3×#888C2218yescomplemented
50C22×C3×#41—32no—
51C22×#235C2×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—31no—
58C2×C3×#121—31no—
59C2×C3×C4×D4—31no—
60C2×C3×C4×D4—31no—
61C22×C3×C4⋊C4—21no—
62C22×C3×C4⋊C4—31no—
63C22×C3×C4⋊C4D311yescharacteristic, complemented
64C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
65C2×#930C2×C311yescharacteristic, complemented
66C2×#929C2×C312yescomplemented
67C2×C4×#67C2×C311yescharacteristic, complemented
68C2×#896C2×C312yescomplemented
69#5507C2×C3116yesdirect product factor
70C2×#895C2×C311yescharacteristic, complemented
71C2×#894C2×C312yescomplemented
72C2×#893C2×C311yescharacteristic, complemented
73C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
74C2×#888C2×C311yescharacteristic, complemented
75C24×C32C2311yescharacteristic
76C23×C3×D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C22×C32×C4—28no—
79C22×C32×C4—24no—
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2312yes—
82C22×C32×C4C2312yes—
83C22×C32×C4C2314yes—
84C22×C32×C4C2318yes—
85C22×C32×C4C2311yescharacteristic
86C2×C3×#67—28no—
87C2×C3×#67D418yescomplemented
88C2×C3×#67C2318yes—
89C2×C3×#67C2314yes—
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2311yescharacteristic
94C3×#235—264no—
95C2×C3×D12—28no—
96C2×C3×D12—24no—
97C2×C3×D12C2314yes—
98C2×C3×D12C2318yes—
99C2×C3×C4×D3—28no—
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3—28no—
102C2×C3×C4×D3C2318yes—
103C2×C3×C4×D3C2314yes—
104C2×C3×C4×D3C2318yes—
105C2×C3×Dic6—28no—
106C2×C3×Dic6C2318yes—
107C32×C4⋊C4C2314yes—
108C32×C4⋊C4C2314yes—
109C32×C4⋊C4C2318yes—
110C3×#217C2314yes—
111C3×(C2×D3)⋊C4C2318yes—
112C3×(C2×D3)⋊C4C2314yes—
113C3×(C2×D3)⋊C4C2318yes—
114C3×(C2×D3)⋊C4C2318yes—
115C3×C4⋊Dic3C2314yes—
116C3×Dic3⋊C4C2318yes—
117C3×Dic3⋊C4C2318yes—
118C3×Dic3⋊C4C2314yes—
119C3×C4×Dic3C2314yes—
120C2×#547—31noSylow
121C2×C3×#41—316no—
122C2×C3×#41—616no—
123C22×C3×Q8—32no—
124C22×C3×D4—31no—
125C22×C3×D4—32no—
126C22×C3×D4—32no—
127C22×C3×D4—31no—
128C23×C3×C4—21no—
129C23×C3×C4—22no—
130C23×C3×C4—32no—
131C23×C3×C4—32no—
132C23×C3×C4—31no—
133C23×C3×C4C2×D312yes—
134C23×C3×C4C2×D311yescharacteristic
135C23×C3×C4C22×C312yes—
136C23×C3×C4C22×C311yescharacteristic
137C22×#67C22×C312yes—
138C22×#67C22×C311yescharacteristic
139C2×#235—216no—
140C2×#235C22×C3116yescomplemented
141C22×D12C22×C312yes—
142C22×D12C22×C311yescharacteristic
143C22×C4×D3C22×C312yes—
144C22×C4×D3C22×C312yes—
145C22×C4×D3C22×C311yescharacteristic
146C22×Dic6C22×C312yes—
147C3×C4⋊Q8—38no—
148C3×#123—316no—
149C3×#123—316no—
150C3×C22⋊Q8—316no—
151C3×#121—38no—
152C3×#121—38no—
153C3×C4×D4—38no—
154C3×C4×D4—38no—
155C2×C3×C4⋊C4—21no—
156C2×C3×C4⋊C4—21no—
157C2×C3×C4⋊C4—22no—
158C2×C3×C4⋊C4—28no—
159C2×C3×C4⋊C4—32no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—32no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—38no—
164C2×C3×C4⋊C4C2×D311yescharacteristic
165C2×C3×C4⋊C4C2×D311yescharacteristic
166C2×C3×C4⋊C4C2×D312yes—
167C2×C3×C4⋊C4C2×D318yescomplemented
168C2×C3×C4⋊C4C22×C311yescharacteristic
169C2×C3×C4⋊C4C22×C311yescharacteristic
170C2×C3×C4⋊C4C22×C312yes—
171C2×C3×C4⋊C4C22×C318yescomplemented
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—32no—
175C2×C3×C22⋊C4—32no—
176C2×C3×C22⋊C4—32no—
177C2×C3×C42—31no—
178C2×#217C22×C311yescharacteristic
179#930C22×C318yescomplemented
180#929C22×C3116yescomplemented
181C4×#67C22×C318yescomplemented
182C2×(C2×D3)⋊C4C22×C312yes—
183C2×(C2×D3)⋊C4C22×C311yescharacteristic
184C2×(C2×D3)⋊C4C22×C312yes—
185C2×(C2×D3)⋊C4C22×C312yes—
186C2×C4⋊Dic3C22×C311yescharacteristic
187C2×Dic3⋊C4C22×C312yes—
188C2×Dic3⋊C4C22×C312yes—
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×C4×Dic3C22×C311yescharacteristic
191#896C22×C3116yescomplemented
192#895C22×C318yescomplemented
193#894C22×C3116yescomplemented
194#893C22×C318yescomplemented
195D3×C4⋊C4C22×C318yescomplemented
196#888C22×C318yescomplemented
197C23×C32—22no—
198C23×C32—22no—
199C23×C32C2×D414yes—
200C23×C32C2412yes—
201C23×C32C2411yescharacteristic
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—24no—
205C22×C3×D3—24no—
206C22×C3×D3—24no—
207C22×C3×D3C2×D414yes—
208C22×C3×D3C2414yes—
209C22×C3×D3C2412yes—
210C2×C32×C4—22no—
211C2×C32×C4—28no—
212C2×C32×C4—24no—
213C2×C32×C4—24no—
214C2×C32×C4—216no—
215C2×C32×C4#4114yescomplemented
216C2×C32×C4C2412yes—
217C2×C32×C4C2414yes—
218C2×C32×C4C2414yes—
219C2×C32×C4C2412yes—
220C3×#67—216no—
221C3×#67C2×D4116yescomplemented
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3C2×D414yes—
226C2×C3×Dic3C2412yes—
227C2×C3×Dic3C2412yes—
228C2×C3×Dic3C2414yes—
229C2×C3×Dic3C2412yes—
230C3×D12—216no—
231C3×D12—28no—
232C3×C4×D3—216no—
233C3×C4×D3—28no—
234C3×C4×D3—216no—
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×#121—31no—
244C2×C4×D4—31no—
245C2×C4×D4—31no—
246C22×C4⋊C4—31no—
247C22×C4⋊C4C3×D311yescharacteristic, complemented
248C24×C3—21no—
249C24×C3—31no—
250C24×C3—32no—
251C24×C3C22×D311yescharacteristic
252C24×C3C23×C311yescharacteristic
253C23×D3C23×C312yes—
254C23×D3C23×C311yescharacteristic
255C3×#41—664no—
256C2×C3×Q8—38no—
257C2×C3×Q8—68no—
258C2×C3×D4—38no—
259C2×C3×D4—34no—
260C2×C3×D4—38no—
261C2×C3×D4—34no—
262C2×C3×D4—38no—
263C2×C3×D4—68no—
264C2×C3×D4—68no—
265C2×C3×D4—64no—
266C22×C3×C4—28no—
267C22×C3×C4—28no—
268C22×C3×C4—28no—
269C22×C3×C4—24no—
270C22×C3×C4—24no—
271C22×C3×C4—21no—
272C22×C3×C4—24no—
273C22×C3×C4—21no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—28no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—32no—
281C22×C3×C4—34no—
282C22×C3×C4—38no—
283C22×C3×C4—38no—
284C22×C3×C4—48no—
285C22×C3×C4—68no—
286C22×C3×C4—68no—
287C22×C3×C4—64no—
288C22×C3×C4C22×D314yes—
289C22×C3×C4C22×D318yes—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D312yes—
292C22×C3×C4C22×D312yes—
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C23×C311yescharacteristic
295C22×C3×C4C23×C312yes—
296C22×C3×C4C23×C312yes—
297C22×C3×C4C23×C314yes—
298C22×C3×C4C23×C318yes—
299C22×C3×C4C23×C311yescharacteristic
300C2×#67—28no—
301C2×#67C3×D418yescomplemented
302C2×#67C23×C318yes—
303C2×#67C23×C314yes—
304C22×Dic3C23×C311yescharacteristic
305C22×Dic3C23×C311yescharacteristic
306C22×Dic3C23×C312yes—
307C22×Dic3C23×C311yescharacteristic
308#235—264no—
309C2×D12—28no—
310C2×D12—24no—
311C2×D12C23×C314yes—
312C2×D12C23×C318yes—
313C2×C4×D3—28no—
314C2×C4×D3—24no—
315C2×C4×D3—28no—
316C2×C4×D3C23×C318yes—
317C2×C4×D3C23×C314yes—
318C2×C4×D3C23×C318yes—
319C2×Dic6—28no—
320C2×Dic6C23×C318yes—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—24no—
323C3×C4⋊C4—28no—
324C3×C4⋊C4—38no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—38no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4C22×D314yes—
329C3×C4⋊C4C22×D314yes—
330C3×C4⋊C4C22×D318yes—
331C3×C4⋊C4C23×C314yes—
332C3×C4⋊C4C23×C314yes—
333C3×C4⋊C4C23×C318yes—
334C3×C22⋊C4—34no—
335C3×C22⋊C4—34no—
336C3×C22⋊C4—38no—
337C3×C22⋊C4—38no—
338C3×C22⋊C4—38no—
339C3×C42—34no—
340#217C23×C314yes—
341(C2×D3)⋊C4C23×C318yes—
342(C2×D3)⋊C4C23×C314yes—
343(C2×D3)⋊C4C23×C318yes—
344(C2×D3)⋊C4C23×C318yes—
345C4⋊Dic3C23×C314yes—
346Dic3⋊C4C23×C318yes—
347Dic3⋊C4C23×C318yes—
348Dic3⋊C4C23×C314yes—
349C4×Dic3C23×C314yes—
350C22×C32—28no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32C22×D414yes—
354C22×C32C22×D412yes—
355C22×C32C2×#4112yes—
356C22×C322−1+412yes—
357C22×C32C2511yescharacteristic
358C2×C3×D3—28no—
359C2×C3×D3—22no—
360C2×C3×D3—22no—
361C2×C3×D3—24no—
362C2×C3×D3—24no—
363C2×C3×D3—24no—
364C2×C3×D3—48no—
365C2×C3×D3C22×D414yes—
366C32×C4—22no—
367C32×C4—24no—
368C32×C4—24no—
369C32×C4C2×#4114yescomplemented
370C3×Dic3—24no—
371C3×Dic3—22no—
372C3×Dic3—22no—
373C3×Dic3C22×D414yes—
374C2×#41—316no—
375C2×#41—616no—
376C22×Q8—32no—
377C22×D4—31no—
378C22×D4—32no—
379C22×D4—31no—
380C22×D4—32no—
381C23×C4—31no—
382C23×C4—32no—
383C23×C4—32no—
384C23×C4C2×C3×D311yescharacteristic
385C23×C4C2×C3×D312yes—
386C4⋊Q8—38no—
387#123—316no—
388#123—316no—
389C22⋊Q8—316no—
390#121—38no—
391#121—38no—
392C4×D4—38no—
393C4×D4—38no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—38no—
399C2×C4⋊C4C2×C3×D311yescharacteristic
400C2×C4⋊C4C2×C3×D311yescharacteristic
401C2×C4⋊C4C2×C3×D312yes—
402C2×C4⋊C4C2×C3×D318yescomplemented
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—32no—
408C2×C42—31no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—22no—
416C23×C3—21no—
417C23×C3—24no—
418C23×C3—34no—
419C23×C3—32no—
420C23×C3—34no—
421C23×C3—62no—
422C23×C3—62no—
423C23×C3—64no—
424C23×C3—64no—
425C23×C3—64no—
426C23×C3D3×D414yes—
427C23×C3C2×C3×D414yes—
428C23×C3C23×D312yes—
429C23×C3C23×D311yescharacteristic
430C23×C3C24×C312yes—
431C23×C3C24×C311yescharacteristic
432C22×D3—22no—
433C22×D3—22no—
434C22×D3—24no—
435C22×D3—24no—
436C22×D3—24no—
437C22×D3C2×C3×D414yes—
438C22×D3C24×C314yes—
439C22×D3C24×C312yes—
440C3×Q8—616no—
441C3×D4—316no—
442C3×D4—616no—
443C3×D4—616no—
444C3×D4—68no—
445C2×C3×C4—24no—
446C2×C3×C4—216no—
447C2×C3×C4—22no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—216no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—216no—
454C2×C3×C4—22no—
455C2×C3×C4—28no—
456C2×C3×C4—28no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—34no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—34no—
467C2×C3×C4—44no—
468C2×C3×C4—44no—
469C2×C3×C4—416no—
470C2×C3×C4—616no—
471C2×C3×C4—616no—
472C2×C3×C4—62no—
473C2×C3×C4—64no—
474C2×C3×C4—62no—
475C2×C3×C4—68no—
476C2×C3×C4#23514yescomplemented
477C2×C3×C4C3×#4114yescomplemented
478C2×C3×C4C23×D312yes—
479C2×C3×C4C23×D314yes—
480C2×C3×C4C23×D314yes—
481C2×C3×C4C23×D312yes—
482C2×C3×C4C24×C312yes—
483C2×C3×C4C24×C314yes—
484C2×C3×C4C24×C314yes—
485C2×C3×C4C24×C312yes—
486#67—216no—
487#67C2×C3×D4116yescomplemented
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3C2×C3×D414yes—
492C2×Dic3C24×C312yes—
493C2×Dic3C24×C312yes—
494C2×Dic3C24×C314yes—
495C2×Dic3C24×C312yes—
496D12—216no—
497D12—28no—
498C4×D3—216no—
499C4×D3—28no—
500C4×D3—216no—
501Dic6—216no—
502C2×C32—24no—
503C2×C32#54714yescomplemented
504C2×C32C23×D411yescharacteristic
505C2×C32C22×#4111yescharacteristic
506C2×C32C2×2−1+411yescharacteristic
507C3×D3—24no—
508C3×D3—44no—
509C24—31no—
510C24—32no—
511C24C22×C3×D311yescharacteristic
512#41—664no—
513C2×Q8—38no—
514C2×Q8—68no—
515C2×D4—34no—
516C2×D4—38no—
517C2×D4—38no—
518C2×D4—34no—
519C2×D4—38no—
520C2×D4—68no—
521C2×D4—68no—
522C2×D4—64no—
523C22×C4—28no—
524C22×C4—24no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—32no—
529C22×C4—34no—
530C22×C4—38no—
531C22×C4—38no—
532C22×C4—68no—
533C22×C4—68no—
534C22×C4—64no—
535C22×C4C22×C3×D311yescharacteristic
536C22×C4C22×C3×D312yes—
537C22×C4C22×C3×D312yes—
538C22×C4C22×C3×D314yes—
539C22×C4C22×C3×D318yes—
540C22×C4C22×C3×D311yescharacteristic
541C4⋊C4—34no—
542C4⋊C4—38no—
543C4⋊C4—34no—
544C4⋊C4—38no—
545C4⋊C4C22×C3×D314yes—
546C4⋊C4C22×C3×D314yes—
547C4⋊C4C22×C3×D318yes—
548C22⋊C4—34no—
549C22⋊C4—34no—
550C22⋊C4—38no—
551C22⋊C4—38no—
552C22⋊C4—38no—
553C42—34no—
554C22×C3—24no—
555C22×C3—216no—
556C22×C3—24no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—28no—
562C22×C3—28no—
563C22×C3—22no—
564C22×C3—24no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—21no—
568C22×C3—34no—
569C22×C3—62no—
570C22×C3—62no—
571C22×C3—68no—
572C22×C3—64no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—128no—
576C22×C3C2×#23512yes—
577C22×C3C2×D3×D414yes—
578C22×C3C2×D3×D412yes—
579C22×C3#100712yes—
580C22×C3C22×C3×D414yes—
581C22×C3C22×C3×D412yes—
582C22×C3C2×C3×#4112yes—
583C22×C3C3×2−1+412yes—
584C22×C3C24×D311yescharacteristic
585C22×C3C25×C311yescharacteristic
586C2×D3—22no—
587C2×D3—22no—
588C2×D3—28no—
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—48no—
593C2×D3C22×C3×D414yes—
594C3×C4—24no—
595C3×C4—22no—
596C3×C4—24no—
597C3×C4—24no—
598C3×C4—24no—
599C3×C4—24no—
600C3×C4—22no—
601C3×C4—24no—
602C3×C4—34no—
603C3×C4—44no—
604C3×C4—44no—
605C3×C4—62no—
606C3×C4—64no—
607C3×C4—62no—
608C3×C4C2×#23514yescomplemented
609C3×C4C2×C3×#4114yescomplemented
610Dic3—24no—
611Dic3—22no—
612Dic3—22no—
613Dic3C22×C3×D414yes—
614C32C2×#54711yescharacteristic, complemented, Sylow
615C23—22no—
616C23—22no—
617C23—34no—
618C23—32no—
619C23—34no—
620C23—62no—
621C23—62no—
622C23—64no—
623C23—64no—
624C23—64no—
625C23C3×D3×D414yes—
626C23C23×C3×D312yes—
627C23C23×C3×D311yescharacteristic
628Q8—616no—
629D4—316no—
630D4—616no—
631D4—616no—
632D4—68no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—216no—
637C2×C4—28no—
638C2×C4—34no—
639C2×C4—32no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—34no—
643C2×C4—616no—
644C2×C4—616no—
645C2×C4—62no—
646C2×C4—64no—
647C2×C4—62no—
648C2×C4—68no—
649C2×C4C3×#23514yescomplemented
650C2×C4C23×C3×D312yes—
651C2×C4C23×C3×D314yes—
652C2×C4C23×C3×D314yes—
653C2×C4C23×C3×D312yes—
654C2×C3—28no—
655C2×C3—24no—
656C2×C3—24no—
657C2×C3—24no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—64no—
662C2×C3—124no—
663C2×C3#550714yesdirect product factor
664C2×C3C3×#54714yescomplemented
665C2×C3C22×#23511yescharacteristic
666C2×C3C22×D3×D411yescharacteristic
667C2×C3C2×#100711yescharacteristic
668C2×C3C23×C3×D411yescharacteristic
669C2×C3C22×C3×#4111yescharacteristic
670C2×C3C2×C3×2−1+411yescharacteristic
671D3—24no—
672D3—44no—
673C22—28no—
674C22—22no—
675C22—22no—
676C22—34no—
677C22—68no—
678C22—62no—
679C22—62no—
680C22—64no—
681C22—64no—
682C22—64no—
683C22—128no—
684C22C2×C3×#23512yes—
685C22C2×C3×D3×D414yes—
686C22C2×C3×D3×D412yes—
687C22C3×#100712yes—
688C22C24×C3×D311yescharacteristic
689C4—22no—
690C4—24no—
691C4—24no—
692C4—34no—
693C4—62no—
694C4—64no—
695C4—62no—
696C4C2×C3×#23514yescomplemented
697C3—21no—
698C3C2×#550711yescharacteristic, direct product factor
699C3C2×C3×#54711yescharacteristic, complemented
700C2—24no—
701C2—64no—
702C2—124no—
703C2C3×#550714yesdirect product factor
704C2C22×C3×#23511yescharacteristic
705C2C22×C3×D3×D411yescharacteristic
706C2C2×C3×#100711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C24
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×C32×C4⋊C4C2semidirect
3. C2×C3×#930C2semidirect
4. C2×C3×#929C2semidirect
5. C2×C3×C4×#67C2semidirect
6. C2×C3×#896C2semidirect
7. C3×#5507C2direct (N × H)
8. C2×C3×#895C2semidirect
9. C2×C3×#894C2semidirect
10. C2×C3×#893C2semidirect
11. C2×C3×D3×C4⋊C4C2semidirect
12. C2×C3×#888C2semidirect
14. C2×#5507C3direct (N × H)
20. C2×C3×#235C22semidirect
30. C2×C32×C4⋊C4C22semidirect
32. C3×#930C22semidirect
33. C3×#929C22semidirect
34. C3×C4×#67C22semidirect
44. C3×#896C22semidirect
45. C3×#895C22semidirect
46. C3×#894C22semidirect
47. C3×#893C22semidirect
48. C3×D3×C4⋊C4C22semidirect
49. C3×#888C22semidirect
51. C22×#235C2×C3semidirect
63. C22×C3×C4⋊C4D3semidirect
64. C22×C3×C4⋊C4C2×C3semidirect
65. C2×#930C2×C3semidirect
66. C2×#929C2×C3semidirect
67. C2×C4×#67C2×C3semidirect
68. C2×#896C2×C3semidirect
69. #5507C2×C3direct (N × H)
70. C2×#895C2×C3semidirect
71. C2×#894C2×C3semidirect
72. C2×#893C2×C3semidirect
73. C2×D3×C4⋊C4C2×C3semidirect
74. C2×#888C2×C3semidirect
87. C2×C3×#67D4semidirect
140. C2×#235C22×C3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
171. C2×C3×C4⋊C4C22×C3semidirect
179. #930C22×C3semidirect
180. #929C22×C3semidirect
181. C4×#67C22×C3semidirect
191. #896C22×C3semidirect
192. #895C22×C3semidirect
193. #894C22×C3semidirect
194. #893C22×C3semidirect
195. D3×C4⋊C4C22×C3semidirect
196. #888C22×C3semidirect
215. C2×C32×C4#41semidirect
221. C3×#67C2×D4semidirect
247. C22×C4⋊C4C3×D3semidirect
301. C2×#67C3×D4semidirect
369. C32×C4C2×#41semidirect
402. C2×C4⋊C4C2×C3×D3semidirect
476. C2×C3×C4#235semidirect
477. C2×C3×C4C3×#41semidirect
487. #67C2×C3×D4semidirect
503. C2×C32#547semidirect
608. C3×C4C2×#235semidirect
609. C3×C4C2×C3×#41semidirect
614. C32C2×#547semidirect
649. C2×C4C3×#235semidirect
663. C2×C3#5507direct (N × H)
664. C2×C3C3×#547semidirect
696. C4C2×C3×#235semidirect
698. C3C2×#5507direct (N × H)
699. C3C2×C3×#547semidirect
703. C2C3×#5507direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×C32×C4⋊C42
C2×C3×#9302
C2×C3×#9292
C2×C3×C4×#672
C2×C3×#8962
C3×#55072
C2×C3×#8952
C2×C3×#8942
C2×C3×#8932
C2×C3×D3×C4⋊C42
C2×C3×#8882
C2×C3×#5473
C2×#55073