Finite Group Databasebeta

← C2×C3×#5632 #11902643

Subgroups — C2×C3×#5632 #11902643

Order 1152.

3297 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C23×C3×Dic6C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C3×#944C211yesmaximal, characteristic, complemented
5C2×C3×C4×#67C211yesmaximal, characteristic
6C3×#5632C2116yesmaximal, direct product factor
7C2×C3×#897C211yesmaximal, characteristic, complemented
8C2×C3×#896C212yesmaximal, complemented
9C2×C3×#888C212yesmaximal, complemented
10C2×C3×#887C211yesmaximal, characteristic, complemented
11C2×C3×#67⋊C4C212yesmaximal
12C2×C3×#878C212yesmaximal, complemented
13C2×C3×D4×Q8—31nomaximal
14C2×#5632C311yesmaximal, characteristic, direct product factor
15C22×C32×Q8C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C2×C3×D3×Q8—28no—
20C2×C3×D3×Q8C2218yescomplemented
21C22×C3×C4×D3C2212yes—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6—28no—
24C22×C3×Dic6C2212yes—
25C22×C3×Dic6C2212yes—
26C22×C3×Dic6C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic
28C22×C3×Dic6C2218yescomplemented
29C32×C22⋊Q8C2218yescomplemented
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C32×C4⋊C4C2212yes—
32C2×C32×C22⋊C4C2212yes—
33C2×C3×#217C2211yescharacteristic
34C3×#944C2218yescomplemented
35C3×C4×#67C2218yes—
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×C4⋊Dic3C2212yes—
39C2×C3×Dic3⋊C4C2212yes—
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2212yes—
42C2×C3×Dic3⋊C4C2212yes—
43C2×C3×C4×Dic3C2212yes—
44C2×C3×C4×Dic3C2211yescharacteristic
45C3×#897C2218yescomplemented
46C3×#896C22116yescomplemented
47C3×#888C22116yescomplemented
48C3×#887C2218yescomplemented
49C3×#67⋊C4C22116yes—
50C3×#878C22116yescomplemented
51C23×C3×Q8—31no—
52C23×C3×Q8—31no—
53C22×D3×Q8C2×C311yescharacteristic, complemented
54C23×Dic6C2×C311yescharacteristic, complemented
55C3×D4×Q8—316no—
56C2×C3×C4⋊Q8—31no—
57C2×C3×C4⋊Q8—32no—
58C2×C3×C22⋊Q8—21no—
59C2×C3×C22⋊Q8—32no—
60C2×C3×C22⋊Q8—31no—
61C2×C3×C22⋊Q8—32no—
62C2×C3×C22⋊Q8D311yescharacteristic, complemented
63C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
64C2×C3×C4×Q8—31no—
65C2×C3×C4×D4—31no—
66C2×C3×C4×D4—32no—
67C2×#944C2×C311yescharacteristic, complemented
68C2×C4×#67C2×C311yescharacteristic
69#5632C2×C3116yesdirect product factor
70C2×#897C2×C311yescharacteristic, complemented
71C2×#896C2×C312yescomplemented
72C2×#888C2×C312yescomplemented
73C2×#887C2×C311yescharacteristic, complemented
74C2×#67⋊C4C2×C312yes—
75C2×#878C2×C312yescomplemented
76C24×C32C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C2×C32×Q8—24no—
79C2×C32×Q8C2314yes—
80C22×C32×C4—24no—
81C22×C32×C4C2312yes—
82C22×C32×C4C2312yes—
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2314yes—
85C22×C32×C4C2311yescharacteristic
86C2×C3×#67Q818yescomplemented
87C2×C3×#67C2314yes—
88C22×C3×Dic3—28no—
89C22×C3×Dic3C2318yes—
90C22×C3×Dic3C2311yescharacteristic
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C3×D3×Q8—232no—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3—28no—
98C2×C3×C4×D3C2318yes—
99C2×C3×C4×D3C2314yes—
100C2×C3×Dic6—24no—
101C2×C3×Dic6—28no—
102C2×C3×Dic6—28no—
103C2×C3×Dic6—232no—
104C2×C3×Dic6D418yescomplemented
105C2×C3×Dic6C2318yes—
106C2×C3×Dic6C2318yes—
107C2×C3×Dic6C2314yes—
108C2×C3×Dic6C2314yes—
109C32×C4⋊C4C2314yes—
110C32×C4⋊C4C2318yes—
111C32×C22⋊C4C2318yes—
112C3×#217C2314yes—
113C3×(C2×D3)⋊C4C2318yes—
114C3×(C2×D3)⋊C4C2314yes—
115C3×C4⋊Dic3C2318yes—
116C3×Dic3⋊C4C2318yes—
117C3×Dic3⋊C4C2318yes—
118C3×Dic3⋊C4C2318yes—
119C3×Dic3⋊C4C2314yes—
120C3×C4×Dic3C2318yes—
121C3×C4×Dic3C2314yes—
122C2×D4×Q8—31noSylow
123C22×C3×Q8—21no—
124C22×C3×Q8—38no—
125C22×C3×Q8—31no—
126C22×C3×Q8—32no—
127C22×C3×Q8—32no—
128C22×C3×Q8—31no—
129C22×C3×Q8—38no—
130C22×C3×Q8—68no—
131C22×C3×Q8—68no—
132C22×C3×Q8C2×D311yescharacteristic
133C22×C3×Q8C22×C311yescharacteristic
134C22×C3×D4—31no—
135C23×C3×C4—21no—
136C23×C3×C4—32no—
137C23×C3×C4—32no—
138C23×C3×C4—31no—
139C23×C3×C4C2×D311yescharacteristic
140C23×C3×C4C22×C311yescharacteristic
141C22×#67C22×C311yescharacteristic
142C23×Dic3C22×C312yes—
143C2×D3×Q8—28no—
144C2×D3×Q8C22×C318yescomplemented
145C22×C4×D3C22×C312yes—
146C22×C4×D3C22×C311yescharacteristic
147C22×Dic6—28no—
148C22×Dic6C22×C312yes—
149C22×Dic6C22×C311yescharacteristic
150C22×Dic6C22×C312yes—
151C22×Dic6C22×C311yescharacteristic
152C22×Dic6C22×C318yescomplemented
153C3×C4⋊Q8—38no—
154C3×C4⋊Q8—316no—
155C3×C22⋊Q8—28no—
156C3×C22⋊Q8—316no—
157C3×C22⋊Q8—38no—
158C3×C22⋊Q8—316no—
159C3×C22⋊Q8C2×D318yescomplemented
160C3×C22⋊Q8C22×C318yescomplemented
161C3×C4×Q8—38no—
162C3×C4×D4—38no—
163C3×C4×D4—316no—
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4—22no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—32no—
168C2×C3×C4⋊C4—32no—
169C2×C3×C4⋊C4—32no—
170C2×C3×C4⋊C4—32no—
171C2×C3×C4⋊C4C2×D311yescharacteristic
172C2×C3×C4⋊C4C2×D312yes—
173C2×C3×C4⋊C4C22×C311yescharacteristic
174C2×C3×C4⋊C4C22×C312yes—
175C2×C3×C22⋊C4—22no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—32no—
179C2×C3×C22⋊C4C2×D312yes—
180C2×C3×C22⋊C4C22×C312yes—
181C2×C3×C42—32no—
182C2×C3×C42—31no—
183C2×#217C22×C311yescharacteristic
184#944C22×C318yescomplemented
185C4×#67C22×C318yes—
186C2×(C2×D3)⋊C4C22×C312yes—
187C2×(C2×D3)⋊C4C22×C311yescharacteristic
188C2×C4⋊Dic3C22×C312yes—
189C2×Dic3⋊C4C22×C312yes—
190C2×Dic3⋊C4C22×C312yes—
191C2×Dic3⋊C4C22×C312yes—
192C2×Dic3⋊C4C22×C311yescharacteristic
193C2×C4×Dic3C22×C312yes—
194C2×C4×Dic3C22×C311yescharacteristic
195#897C22×C318yescomplemented
196#896C22×C3116yescomplemented
197#888C22×C3116yescomplemented
198#887C22×C318yescomplemented
199#67⋊C4C22×C3116yes—
200#878C22×C3116yescomplemented
201C23×C32—22no—
202C23×C32—22no—
203C23×C32C2×Q814yescomplemented
204C23×C32C2412yes—
205C23×C32C2411yescharacteristic
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3C2×Q814yescomplemented
209C22×C3×D3C2412yes—
210C32×Q8—28no—
211C2×C32×C4—22no—
212C2×C32×C4—24no—
213C2×C32×C4—24no—
214C2×C32×C4—28no—
215C2×C32×C4C2×D414yes—
216C2×C32×C4C2414yes—
217C2×C32×C4C2414yes—
218C2×C32×C4C2412yes—
219C2×C32×C4C2412yes—
220C3×#67C2×Q8116yescomplemented
221C2×C3×Dic3—22no—
222C2×C3×Dic3—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—216no—
225C2×C3×Dic3C2×D418yes—
226C2×C3×Dic3C2×Q814yescomplemented
227C2×C3×Dic3C2412yes—
228C2×C3×Dic3C2414yes—
229C2×C3×Dic3C2412yes—
230C2×C3×Dic3C2414yes—
231C2×C3×Dic3C2412yes—
232C3×C4×D3—28no—
233C3×C4×D3—216no—
234C3×Dic6—28no—
235C3×Dic6—216no—
236C3×Dic6—216no—
237C3×Dic6C2×D4116yescomplemented
238C23×Q8—31no—
239C23×Q8—31no—
240D4×Q8—316no—
241C2×C4⋊Q8—31no—
242C2×C4⋊Q8—32no—
243C2×C22⋊Q8—32no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—32no—
246C2×C22⋊Q8C3×D311yescharacteristic, complemented
247C2×C4×Q8—31no—
248C2×C4×D4—31no—
249C2×C4×D4—32no—
250C24×C3—21no—
251C24×C3—31no—
252C24×C3C22×D311yescharacteristic
253C24×C3C23×C311yescharacteristic
254C23×D3C23×C311yescharacteristic
255C2×C3×Q8—24no—
256C2×C3×Q8—24no—
257C2×C3×Q8—24no—
258C2×C3×Q8—38no—
259C2×C3×Q8—34no—
260C2×C3×Q8—38no—
261C2×C3×Q8—38no—
262C2×C3×Q8—34no—
263C2×C3×Q8—44no—
264C2×C3×Q8—68no—
265C2×C3×Q8—68no—
266C2×C3×Q8—632no—
267C2×C3×Q8—632no—
268C2×C3×Q8—64no—
269C2×C3×Q8C22×D314yes—
270C2×C3×Q8C23×C314yes—
271C2×C3×D4—38no—
272C2×C3×D4—34no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—21no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—21no—
279C22×C3×C4—24no—
280C22×C3×C4—31no—
281C22×C3×C4—32no—
282C22×C3×C4—38no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—32no—
286C22×C3×C4—38no—
287C22×C3×C4—34no—
288C22×C3×C4—44no—
289C22×C3×C4—68no—
290C22×C3×C4—68no—
291C22×C3×C4—64no—
292C22×C3×C4C22×D314yes—
293C22×C3×C4C22×D312yes—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D312yes—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C23×C312yes—
298C22×C3×C4C23×C312yes—
299C22×C3×C4C23×C311yescharacteristic
300C22×C3×C4C23×C314yes—
301C22×C3×C4C23×C311yescharacteristic
302C2×#67C3×Q818yescomplemented
303C2×#67C23×C314yes—
304C22×Dic3—28no—
305C22×Dic3C23×C318yes—
306C22×Dic3C23×C311yescharacteristic
307C22×Dic3C23×C312yes—
308C22×Dic3C23×C311yescharacteristic
309C22×Dic3C23×C312yes—
310C22×Dic3C23×C311yescharacteristic
311D3×Q8—232no—
312C2×C4×D3—24no—
313C2×C4×D3—28no—
314C2×C4×D3C23×C318yes—
315C2×C4×D3C23×C314yes—
316C2×Dic6—24no—
317C2×Dic6—28no—
318C2×Dic6—28no—
319C2×Dic6—232no—
320C2×Dic6C3×D418yescomplemented
321C2×Dic6C23×C318yes—
322C2×Dic6C23×C318yes—
323C2×Dic6C23×C314yes—
324C2×Dic6C23×C314yes—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—28no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—38no—
329C3×C4⋊C4—38no—
330C3×C4⋊C4—38no—
331C3×C4⋊C4—38no—
332C3×C4⋊C4C22×D314yes—
333C3×C4⋊C4C22×D318yes—
334C3×C4⋊C4C23×C314yes—
335C3×C4⋊C4C23×C318yes—
336C3×C22⋊C4—28no—
337C3×C22⋊C4—34no—
338C3×C22⋊C4—34no—
339C3×C22⋊C4—38no—
340C3×C22⋊C4C22×D318yes—
341C3×C22⋊C4C23×C318yes—
342C3×C42—38no—
343C3×C42—34no—
344#217C23×C314yes—
345(C2×D3)⋊C4C23×C318yes—
346(C2×D3)⋊C4C23×C314yes—
347C4⋊Dic3C23×C318yes—
348Dic3⋊C4C23×C318yes—
349Dic3⋊C4C23×C318yes—
350Dic3⋊C4C23×C318yes—
351Dic3⋊C4C23×C314yes—
352C4×Dic3C23×C318yes—
353C4×Dic3C23×C314yes—
354C22×C32—28no—
355C22×C32—22no—
356C22×C32—22no—
357C22×C32C22×D412yes—
358C22×C32C22×Q812yes—
359C22×C32C22×Q814yescomplemented
360C22×C322−1+412yes—
361C22×C32C2511yescharacteristic
362C2×C3×D3—28no—
363C2×C3×D3—22no—
364C2×C3×D3—22no—
365C2×C3×D3C22×Q814yescomplemented
366C32×C4—22no—
367C32×C4—24no—
368C32×C4—24no—
369C32×C4C22×D414yes—
370C3×Dic3—22no—
371C3×Dic3—24no—
372C3×Dic3—22no—
373C3×Dic3C22×D418yes—
374C3×Dic3C22×Q814yescomplemented
375C22×Q8—38no—
376C22×Q8—31no—
377C22×Q8—32no—
378C22×Q8—32no—
379C22×Q8—31no—
380C22×Q8—38no—
381C22×Q8—68no—
382C22×Q8—68no—
383C22×Q8C2×C3×D311yescharacteristic
384C22×D4—31no—
385C23×C4—32no—
386C23×C4—32no—
387C23×C4—31no—
388C23×C4C2×C3×D311yescharacteristic
389C4⋊Q8—38no—
390C4⋊Q8—316no—
391C22⋊Q8—316no—
392C22⋊Q8—38no—
393C22⋊Q8—316no—
394C22⋊Q8C2×C3×D318yescomplemented
395C4×Q8—38no—
396C4×D4—38no—
397C4×D4—316no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4C2×C3×D311yescharacteristic
404C2×C4⋊C4C2×C3×D312yes—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—32no—
408C2×C22⋊C4C2×C3×D312yes—
409C2×C42—32no—
410C2×C42—31no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—22no—
417C23×C3—24no—
418C23×C3—34no—
419C23×C3—32no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—62no—
423C23×C3—62no—
424C23×C3D3×Q814yescomplemented
425C23×C3C2×C3×Q814yescomplemented
426C23×C3C23×D312yes—
427C23×C3C23×D311yescharacteristic
428C23×C3C24×C312yes—
429C23×C3C24×C311yescharacteristic
430C22×D3—22no—
431C22×D3—22no—
432C22×D3C2×C3×Q814yescomplemented
433C22×D3C24×C312yes—
434C3×Q8—28no—
435C3×Q8—28no—
436C3×Q8—316no—
437C3×Q8—48no—
438C3×Q8—616no—
439C3×Q8—616no—
440C3×Q8—68no—
441C3×D4—316no—
442C2×C3×C4—22no—
443C2×C3×C4—24no—
444C2×C3×C4—24no—
445C2×C3×C4—22no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—28no—
449C2×C3×C4—28no—
450C2×C3×C4—22no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—22no—
454C2×C3×C4—24no—
455C2×C3×C4—38no—
456C2×C3×C4—34no—
457C2×C3×C4—32no—
458C2×C3×C4—34no—
459C2×C3×C4—32no—
460C2×C3×C4—34no—
461C2×C3×C4—32no—
462C2×C3×C4—48no—
463C2×C3×C4—44no—
464C2×C3×C4—42no—
465C2×C3×C4—44no—
466C2×C3×C4—616no—
467C2×C3×C4—616no—
468C2×C3×C4—62no—
469C2×C3×C4—64no—
470C2×C3×C4—62no—
471C2×C3×C4—68no—
472C2×C3×C4D3×D414yes—
473C2×C3×C4C2×C3×D414yes—
474C2×C3×C4C23×D314yes—
475C2×C3×C4C23×D312yes—
476C2×C3×C4C23×D314yes—
477C2×C3×C4C23×D312yes—
478C2×C3×C4C24×C314yes—
479C2×C3×C4C24×C314yes—
480C2×C3×C4C24×C312yes—
481C2×C3×C4C24×C312yes—
482#67C2×C3×Q8116yescomplemented
483C2×Dic3—22no—
484C2×Dic3—24no—
485C2×Dic3—22no—
486C2×Dic3—216no—
487C2×Dic3C2×C3×D418yes—
488C2×Dic3C2×C3×Q814yescomplemented
489C2×Dic3C24×C312yes—
490C2×Dic3C24×C314yes—
491C2×Dic3C24×C312yes—
492C2×Dic3C24×C314yes—
493C2×Dic3C24×C312yes—
494C4×D3—28no—
495C4×D3—216no—
496Dic6—28no—
497Dic6—216no—
498Dic6—216no—
499Dic6C2×C3×D4116yescomplemented
500C2×C32—24no—
501C2×C32D4×Q814yescomplemented
502C2×C32C23×D411yescharacteristic
503C2×C32C23×Q811yescharacteristic
504C2×C32C2×2−1+411yescharacteristic
505C3×D3—24no—
506C24—31no—
507C24C22×C3×D311yescharacteristic
508C2×Q8—24no—
509C2×Q8—34no—
510C2×Q8—38no—
511C2×Q8—38no—
512C2×Q8—34no—
513C2×Q8—38no—
514C2×Q8—68no—
515C2×Q8—68no—
516C2×Q8—632no—
517C2×Q8—632no—
518C2×Q8—64no—
519C2×Q8C22×C3×D314yes—
520C2×D4—34no—
521C2×D4—38no—
522C22×C4—24no—
523C22×C4—31no—
524C22×C4—32no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—32no—
528C22×C4—38no—
529C22×C4—38no—
530C22×C4—34no—
531C22×C4—68no—
532C22×C4—68no—
533C22×C4—64no—
534C22×C4C22×C3×D312yes—
535C22×C4C22×C3×D311yescharacteristic
536C22×C4C22×C3×D312yes—
537C22×C4C22×C3×D314yes—
538C22×C4C22×C3×D311yescharacteristic
539C4⋊C4—34no—
540C4⋊C4—38no—
541C4⋊C4—38no—
542C4⋊C4—38no—
543C4⋊C4—38no—
544C4⋊C4C22×C3×D314yes—
545C4⋊C4C22×C3×D318yes—
546C22⋊C4—34no—
547C22⋊C4—34no—
548C22⋊C4—38no—
549C22⋊C4C22×C3×D318yes—
550C42—38no—
551C42—34no—
552C22×C3—28no—
553C22×C3—22no—
554C22×C3—22no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—28no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—24no—
561C22×C3—22no—
562C22×C3—21no—
563C22×C3—34no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—48no—
567C22×C3—68no—
568C22×C3—62no—
569C22×C3—62no—
570C22×C3C2×D3×D412yes—
571C22×C3C2×D3×Q812yes—
572C22×C3C2×D3×Q814yescomplemented
573C22×C3#101012yes—
574C22×C3C22×C3×D412yes—
575C22×C3C22×C3×Q812yes—
576C22×C3C22×C3×Q814yescomplemented
577C22×C3C3×2−1+412yes—
578C22×C3C24×D311yescharacteristic
579C22×C3C25×C311yescharacteristic
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—28no—
583C2×D3C22×C3×Q814yescomplemented
584C3×C4—22no—
585C3×C4—24no—
586C3×C4—24no—
587C3×C4—22no—
588C3×C4—24no—
589C3×C4—24no—
590C3×C4—24no—
591C3×C4—38no—
592C3×C4—34no—
593C3×C4—42no—
594C3×C4—44no—
595C3×C4—44no—
596C3×C4—64no—
597C3×C4—62no—
598C3×C4—62no—
599C3×C4C2×D3×D414yes—
600C3×C4C22×C3×D414yes—
601Dic3—22no—
602Dic3—24no—
603Dic3—22no—
604Dic3C22×C3×D418yes—
605Dic3C22×C3×Q814yescomplemented
606C32C2×D4×Q811yescharacteristic, complemented, Sylow
607C23—22no—
608C23—22no—
609C23—34no—
610C23—32no—
611C23—62no—
612C23—62no—
613C23C3×D3×Q814yescomplemented
614C23C23×C3×D312yes—
615C23C23×C3×D311yescharacteristic
616Q8—28no—
617Q8—316no—
618Q8—616no—
619Q8—616no—
620Q8—68no—
621D4—316no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—28no—
626C2×C4—38no—
627C2×C4—34no—
628C2×C4—32no—
629C2×C4—34no—
630C2×C4—32no—
631C2×C4—32no—
632C2×C4—34no—
633C2×C4—616no—
634C2×C4—616no—
635C2×C4—64no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—68no—
639C2×C4C3×D3×D414yes—
640C2×C4C23×C3×D314yes—
641C2×C4C23×C3×D312yes—
642C2×C4C23×C3×D314yes—
643C2×C4C23×C3×D312yes—
644C2×C3—24no—
645C2×C3—24no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—24no—
650C2×C3—44no—
651C2×C3—64no—
652C2×C3#563214yesdirect product factor
653C2×C3C3×D4×Q814yescomplemented
654C2×C3C22×D3×D411yescharacteristic
655C2×C3C22×D3×Q811yescharacteristic
656C2×C3C2×#101011yescharacteristic
657C2×C3C23×C3×D411yescharacteristic
658C2×C3C23×C3×Q811yescharacteristic
659C2×C3C2×C3×2−1+411yescharacteristic
660D3—24no—
661C22—22no—
662C22—22no—
663C22—28no—
664C22—34no—
665C22—62no—
666C22—62no—
667C22—68no—
668C22C2×C3×D3×D412yes—
669C22C2×C3×D3×Q812yes—
670C22C2×C3×D3×Q814yescomplemented
671C22C3×#101012yes—
672C22C24×C3×D311yescharacteristic
673C4—22no—
674C4—24no—
675C4—24no—
676C4—38no—
677C4—34no—
678C4—64no—
679C4—62no—
680C4—62no—
681C4C2×C3×D3×D414yes—
682C3—21no—
683C3C2×#563211yescharacteristic, direct product factor
684C3C2×C3×D4×Q811yescharacteristic, complemented
685C2—24no—
686C2—64no—
687C2C3×#563214yesdirect product factor
688C2C22×C3×D3×D411yescharacteristic
689C2C22×C3×D3×Q811yescharacteristic
690C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C2×C3×D4×Q8
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×D3×Q8C2semidirect
2. C23×C3×Dic6C2semidirect
3. C2×C32×C22⋊Q8C2semidirect
4. C2×C3×#944C2semidirect
6. C3×#5632C2direct (N × H)
7. C2×C3×#897C2semidirect
8. C2×C3×#896C2semidirect
9. C2×C3×#888C2semidirect
10. C2×C3×#887C2semidirect
12. C2×C3×#878C2semidirect
14. C2×#5632C3direct (N × H)
20. C2×C3×D3×Q8C22semidirect
28. C22×C3×Dic6C22semidirect
29. C32×C22⋊Q8C22semidirect
34. C3×#944C22semidirect
45. C3×#897C22semidirect
46. C3×#896C22semidirect
47. C3×#888C22semidirect
48. C3×#887C22semidirect
50. C3×#878C22semidirect
53. C22×D3×Q8C2×C3semidirect
54. C23×Dic6C2×C3semidirect
62. C2×C3×C22⋊Q8D3semidirect
63. C2×C3×C22⋊Q8C2×C3semidirect
67. C2×#944C2×C3semidirect
69. #5632C2×C3direct (N × H)
70. C2×#897C2×C3semidirect
71. C2×#896C2×C3semidirect
72. C2×#888C2×C3semidirect
73. C2×#887C2×C3semidirect
75. C2×#878C2×C3semidirect
86. C2×C3×#67Q8semidirect
104. C2×C3×Dic6D4semidirect
144. C2×D3×Q8C22×C3semidirect
152. C22×Dic6C22×C3semidirect
159. C3×C22⋊Q8C2×D3semidirect
160. C3×C22⋊Q8C22×C3semidirect
184. #944C22×C3semidirect
195. #897C22×C3semidirect
196. #896C22×C3semidirect
197. #888C22×C3semidirect
198. #887C22×C3semidirect
200. #878C22×C3semidirect
203. C23×C32C2×Q8semidirect
208. C22×C3×D3C2×Q8semidirect
220. C3×#67C2×Q8semidirect
226. C2×C3×Dic3C2×Q8semidirect
237. C3×Dic6C2×D4semidirect
246. C2×C22⋊Q8C3×D3semidirect
302. C2×#67C3×Q8semidirect
320. C2×Dic6C3×D4semidirect
359. C22×C32C22×Q8semidirect
365. C2×C3×D3C22×Q8semidirect
374. C3×Dic3C22×Q8semidirect
394. C22⋊Q8C2×C3×D3semidirect
424. C23×C3D3×Q8semidirect
425. C23×C3C2×C3×Q8semidirect
432. C22×D3C2×C3×Q8semidirect
482. #67C2×C3×Q8semidirect
488. C2×Dic3C2×C3×Q8semidirect
499. Dic6C2×C3×D4semidirect
501. C2×C32D4×Q8semidirect
572. C22×C3C2×D3×Q8semidirect
576. C22×C3C22×C3×Q8semidirect
583. C2×D3C22×C3×Q8semidirect
605. Dic3C22×C3×Q8semidirect
606. C32C2×D4×Q8semidirect
613. C23C3×D3×Q8semidirect
652. C2×C3#5632direct (N × H)
653. C2×C3C3×D4×Q8semidirect
670. C22C2×C3×D3×Q8semidirect
683. C3C2×#5632direct (N × H)
684. C3C2×C3×D4×Q8semidirect
687. C2C3×#5632direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C23×C3×Dic62
C2×C32×C22⋊Q82
C2×C3×#9442
C2×C3×C4×#672
C3×#56322
C2×C3×#8972
C2×C3×#8962
C2×C3×#8882
C2×C3×#8872
C2×C3×#67⋊C42
C2×C3×#8782
C2×C3×D4×Q83
C2×#56323