Finite Group Databasebeta

← C2×C3×D3×C22⋊Q8 #11900310

Subgroups — C2×C3×D3×C22⋊Q8 #11900310

Order 1152.

3841 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C23×C3×C4×D3C211yesmaximal, characteristic
3C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C3×#946C211yesmaximal, characteristic, complemented
5C2×C3×#924C211yesmaximal, characteristic, complemented
6C3×D3×C22⋊Q8C2116yesmaximal, direct product factor
7C2×C3×#897C211yesmaximal, characteristic, complemented
8C2×C3×#896C212yesmaximal, complemented
9C2×C3×D3×C4⋊C4C212yesmaximal, complemented
10C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
11C2×C3×D3×C22⋊C4C212yesmaximal
12C2×C3×#878C212yesmaximal, complemented
13C22×C3×C22⋊Q8—31nomaximal
14C2×D3×C22⋊Q8C311yesmaximal, characteristic, direct product factor
15C24×C3×D3C2211yescharacteristic
16C22×C32×Q8C2211yescharacteristic, complemented
17C23×C32×C4C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C2×C3×D3×Q8—28no—
20C2×C3×D3×Q8C2218yescomplemented
21C22×C3×C4×D3—28no—
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2212yes—
24C22×C3×C4×D3C2212yes—
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2218yes—
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×Dic6C2212yescomplemented
30C22×C3×Dic6C2211yescharacteristic, complemented
31C32×C22⋊Q8C2218yescomplemented
32C2×C32×C4⋊C4C2212yescomplemented
33C2×C32×C4⋊C4C2211yescharacteristic, complemented
34C2×C32×C22⋊C4C2212yes—
35C2×C3×#217C2212yes—
36C3×#946C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×(C2×D3)⋊C4C2212yes—
39C2×C3×C4⋊Dic3C2212yescomplemented
40C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
41C3×#924C2218yescomplemented
42C2×C3×Dic3⋊C4C2212yescomplemented
43C2×C3×Dic3⋊C4C2212yescomplemented
44C2×C3×Dic3⋊C4C2212yescomplemented
45C3×#897C2218yescomplemented
46C3×#896C22116yescomplemented
47C3×D3×C4⋊C4C2218yescomplemented
48C3×D3×C4⋊C4C22116yescomplemented
49C3×D3×C22⋊C4C22116yes—
50C3×#878C22116yescomplemented
51C23×C3×Q8—31no—
52C24×C3×C4—31no—
53C22×D3×Q8C2×C311yescharacteristic, complemented
54C23×C4×D3C2×C311yescharacteristic
55C2×C3×C22⋊Q8—21no—
56C2×C3×C22⋊Q8—31no—
57C2×C3×C22⋊Q8—31no—
58C2×C3×C22⋊Q8—316no—
59C2×C3×C22⋊Q8—32no—
60C2×C3×C22⋊Q8—31no—
61C2×C3×C22⋊Q8—32no—
62C2×C3×C22⋊Q8D311yescharacteristic, direct product factor
63C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
64C22×C3×C4⋊C4—31no—
65C22×C3×C4⋊C4—32no—
66C22×C3×C22⋊C4—32no—
67C2×#946C2×C311yescharacteristic, complemented
68C2×#924C2×C311yescharacteristic, complemented
69D3×C22⋊Q8C2×C3116yesdirect product factor
70C2×#897C2×C311yescharacteristic, complemented
71C2×#896C2×C312yescomplemented
72C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
73C2×D3×C4⋊C4C2×C312yescomplemented
74C2×D3×C22⋊C4C2×C312yes—
75C2×#878C2×C312yescomplemented
76C24×C32C2311yescharacteristic
77C23×C3×D3—24no—
78C23×C3×D3—24no—
79C23×C3×D3Q818yescomplemented
80C23×C3×D3C2314yes—
81C23×C3×D3C2311yescharacteristic
82C23×C3×D3C2311yescharacteristic
83C2×C32×Q8—24no—
84C2×C32×Q8C2314yescomplemented
85C22×C32×C4—24no—
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2312yes—
88C22×C32×C4C2312yes—
89C22×C32×C4C2314yes—
90C22×C32×C4C2311yescharacteristic
91C22×C3×Dic3—24no—
92C22×C3×Dic3C2314yes—
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2312yes—
96C22×C3×Dic3C2311yescharacteristic
97C3×D3×Q8—232no—
98C2×C3×C4×D3—24no—
99C2×C3×C4×D3—28no—
100C2×C3×C4×D3—28no—
101C2×C3×C4×D3—24no—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3—232no—
104C2×C3×C4×D3D418yes—
105C2×C3×C4×D3C2318yes—
106C2×C3×C4×D3C2318yes—
107C2×C3×C4×D3C2314yes—
108C2×C3×C4×D3C2314yes—
109C2×C3×C4×D3C2314yes—
110C2×C3×C4×D3C2314yes—
111C2×C3×Dic6—24no—
112C2×C3×Dic6—28no—
113C2×C3×Dic6C2318yescomplemented
114C2×C3×Dic6C2314yescomplemented
115C32×C4⋊C4C2318yescomplemented
116C32×C4⋊C4C2314yescomplemented
117C32×C22⋊C4C2318yes—
118C3×#217C2318yes—
119C3×(C2×D3)⋊C4C2318yes—
120C3×(C2×D3)⋊C4C2318yes—
121C3×C4⋊Dic3C2318yescomplemented
122C3×C4⋊Dic3C2314yescomplemented
123C3×Dic3⋊C4C2318yescomplemented
124C3×Dic3⋊C4C2318yescomplemented
125C3×Dic3⋊C4C2318yescomplemented
126C22×C22⋊Q8—31noSylow
127C25×C3—31no—
128C24×D3C22×C311yescharacteristic
129C22×C3×Q8—21no—
130C22×C3×Q8—38no—
131C22×C3×Q8—32no—
132C22×C3×Q8—31no—
133C22×C3×Q8—68no—
134C22×C3×Q8C2×D311yescharacteristic, complemented
135C22×C3×Q8C22×C311yescharacteristic, complemented
136C23×C3×C4—21no—
137C23×C3×C4—31no—
138C23×C3×C4—31no—
139C23×C3×C4—31no—
140C23×C3×C4—31no—
141C23×C3×C4—38no—
142C23×C3×C4—31no—
143C23×C3×C4—32no—
144C23×C3×C4—32no—
145C23×C3×C4—68no—
146C23×C3×C4C2×D311yescharacteristic
147C23×C3×C4C22×C311yescharacteristic
148C23×Dic3C22×C311yescharacteristic
149C2×D3×Q8—28no—
150C2×D3×Q8C22×C318yescomplemented
151C22×C4×D3—28no—
152C22×C4×D3C22×C311yescharacteristic
153C22×C4×D3C22×C311yescharacteristic
154C22×C4×D3C22×C311yescharacteristic
155C22×C4×D3C22×C318yes—
156C22×C4×D3C22×C312yes—
157C22×C4×D3C22×C312yes—
158C22×C4×D3C22×C311yescharacteristic
159C22×Dic6C22×C312yescomplemented
160C22×Dic6C22×C311yescharacteristic, complemented
161C3×C22⋊Q8—28no—
162C3×C22⋊Q8—38no—
163C3×C22⋊Q8—38no—
164C3×C22⋊Q8—316no—
165C3×C22⋊Q8—38no—
166C3×C22⋊Q8—316no—
167C3×C22⋊Q8C2×D318yesdirect product factor
168C3×C22⋊Q8C22×C318yescomplemented
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4—22no—
171C2×C3×C4⋊C4—32no—
172C2×C3×C4⋊C4—32no—
173C2×C3×C4⋊C4—32no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—32no—
176C2×C3×C4⋊C4—38no—
177C2×C3×C4⋊C4—316no—
178C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
179C2×C3×C4⋊C4C2×D312yescomplemented
180C2×C3×C4⋊C4C22×C312yescomplemented
181C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
182C2×C3×C22⋊C4—22no—
183C2×C3×C22⋊C4—32no—
184C2×C3×C22⋊C4—32no—
185C2×C3×C22⋊C4—32no—
186C2×C3×C22⋊C4—316no—
187C2×C3×C22⋊C4C2×D312yes—
188C2×C3×C22⋊C4C22×C312yes—
189C2×#217C22×C312yes—
190#946C22×C318yescomplemented
191C2×(C2×D3)⋊C4C22×C312yes—
192C2×(C2×D3)⋊C4C22×C312yes—
193C2×C4⋊Dic3C22×C312yescomplemented
194C2×C4⋊Dic3C22×C311yescharacteristic, complemented
195#924C22×C318yescomplemented
196C2×Dic3⋊C4C22×C312yescomplemented
197C2×Dic3⋊C4C22×C312yescomplemented
198C2×Dic3⋊C4C22×C312yescomplemented
199#897C22×C318yescomplemented
200#896C22×C3116yescomplemented
201D3×C4⋊C4C22×C318yescomplemented
202D3×C4⋊C4C22×C3116yescomplemented
203D3×C22⋊C4C22×C3116yes—
204#878C22×C3116yescomplemented
205C23×C32—22no—
206C23×C32—22no—
207C23×C32C2×Q814yescomplemented
208C23×C32C2412yes—
209C23×C32C2411yescharacteristic
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3—232no—
213C22×C3×D3—28no—
214C22×C3×D3—28no—
215C22×C3×D3C2×D414yes—
216C22×C3×D3C2×Q814yes—
217C22×C3×D3C2×Q8116yescomplemented
218C22×C3×D3C2×Q814yescomplemented
219C22×C3×D3#4114yes—
220C22×C3×D3C2412yes—
221C22×C3×D3C2412yes—
222C32×Q8—28no—
223C2×C32×C4—24no—
224C2×C32×C4—22no—
225C2×C32×C4—24no—
226C2×C32×C4—28no—
227C2×C32×C4C2×D414yes—
228C2×C32×C4C2412yes—
229C2×C32×C4C2414yes—
230C2×C32×C4C2414yes—
231C2×C32×C4C2412yes—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—24no—
235C2×C3×Dic3—28no—
236C2×C3×Dic3C2×D414yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C3×C4×D3—28no—
242C3×C4×D3—216no—
243C3×C4×D3—216no—
244C3×C4×D3—28no—
245C3×C4×D3—28no—
246C3×C4×D3C2×D4116yes—
247C3×Dic6—28no—
248C3×Dic6—216no—
249C23×Q8—31no—
250C24×C4—31no—
251C2×C22⋊Q8—31no—
252C2×C22⋊Q8—31no—
253C2×C22⋊Q8—316no—
254C2×C22⋊Q8—32no—
255C2×C22⋊Q8—31no—
256C2×C22⋊Q8—32no—
257C2×C22⋊Q8C3×D311yescharacteristic, direct product factor
258C22×C4⋊C4—31no—
259C22×C4⋊C4—32no—
260C22×C22⋊C4—32no—
261C24×C3—21no—
262C24×C3—31no—
263C24×C3—38no—
264C24×C3—34no—
265C24×C3—31no—
266C24×C3—64no—
267C24×C3—64no—
268C24×C3C22×D311yescharacteristic
269C24×C3C23×C311yescharacteristic
270C23×D3—24no—
271C23×D3—24no—
272C23×D3C3×Q818yescomplemented
273C23×D3C23×C314yes—
274C23×D3C23×C311yescharacteristic
275C23×D3C23×C311yescharacteristic
276C2×C3×Q8—24no—
277C2×C3×Q8—24no—
278C2×C3×Q8—24no—
279C2×C3×Q8—38no—
280C2×C3×Q8—34no—
281C2×C3×Q8—44no—
282C2×C3×Q8—68no—
283C2×C3×Q8—632no—
284C2×C3×Q8—64no—
285C2×C3×Q8C22×D314yescomplemented
286C2×C3×Q8C23×C314yescomplemented
287C22×C3×C4—24no—
288C22×C3×C4—24no—
289C22×C3×C4—21no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—21no—
293C22×C3×C4—24no—
294C22×C3×C4—31no—
295C22×C3×C4—38no—
296C22×C3×C4—34no—
297C22×C3×C4—34no—
298C22×C3×C4—32no—
299C22×C3×C4—32no—
300C22×C3×C4—31no—
301C22×C3×C4—38no—
302C22×C3×C4—38no—
303C22×C3×C4—34no—
304C22×C3×C4—34no—
305C22×C3×C4—34no—
306C22×C3×C4—44no—
307C22×C3×C4—64no—
308C22×C3×C4—632no—
309C22×C3×C4—68no—
310C22×C3×C4—64no—
311C22×C3×C4—68no—
312C22×C3×C4—64no—
313C22×C3×C4—64no—
314C22×C3×C4C22×D314yes—
315C22×C3×C4C22×D312yes—
316C22×C3×C4C22×D312yes—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C22×C3×C4C23×C312yes—
321C22×C3×C4C23×C312yes—
322C22×C3×C4C23×C314yes—
323C22×C3×C4C23×C311yescharacteristic
324C22×Dic3—24no—
325C22×Dic3C23×C314yes—
326C22×Dic3C23×C312yes—
327C22×Dic3C23×C311yescharacteristic
328C22×Dic3C23×C312yes—
329C22×Dic3C23×C311yescharacteristic
330D3×Q8—232no—
331C2×C4×D3—24no—
332C2×C4×D3—28no—
333C2×C4×D3—28no—
334C2×C4×D3—24no—
335C2×C4×D3—24no—
336C2×C4×D3—232no—
337C2×C4×D3C3×D418yes—
338C2×C4×D3C23×C318yes—
339C2×C4×D3C23×C318yes—
340C2×C4×D3C23×C314yes—
341C2×C4×D3C23×C314yes—
342C2×C4×D3C23×C314yes—
343C2×C4×D3C23×C314yes—
344C2×Dic6—24no—
345C2×Dic6—28no—
346C2×Dic6C23×C318yescomplemented
347C2×Dic6C23×C314yescomplemented
348C3×C4⋊C4—24no—
349C3×C4⋊C4—28no—
350C3×C4⋊C4—38no—
351C3×C4⋊C4—38no—
352C3×C4⋊C4—38no—
353C3×C4⋊C4—34no—
354C3×C4⋊C4—38no—
355C3×C4⋊C4C22×D314yescomplemented
356C3×C4⋊C4C22×D318yescomplemented
357C3×C4⋊C4C23×C318yescomplemented
358C3×C4⋊C4C23×C314yescomplemented
359C3×C22⋊C4—28no—
360C3×C22⋊C4—38no—
361C3×C22⋊C4—38no—
362C3×C22⋊C4—38no—
363C3×C22⋊C4C22×D318yes—
364C3×C22⋊C4C23×C318yes—
365#217C23×C318yes—
366(C2×D3)⋊C4C23×C318yes—
367(C2×D3)⋊C4C23×C318yes—
368C4⋊Dic3C23×C318yescomplemented
369C4⋊Dic3C23×C314yescomplemented
370Dic3⋊C4C23×C318yescomplemented
371Dic3⋊C4C23×C318yescomplemented
372Dic3⋊C4C23×C318yescomplemented
373C22×C32—28no—
374C22×C32—22no—
375C22×C32—22no—
376C22×C32C22×D412yes—
377C22×C32C22×Q812yes—
378C22×C32C22×Q814yescomplemented
379C22×C32C2×#4112yes—
380C22×C32C2511yescharacteristic
381C2×C3×D3—28no—
382C2×C3×D3—22no—
383C2×C3×D3—22no—
384C2×C3×D3—232no—
385C2×C3×D3C22⋊Q8116yesdirect product factor
386C2×C3×D3C22×D414yes—
387C2×C3×D3C22×Q814yes—
388C2×C3×D3C22×Q814yescomplemented
389C2×C3×D3C2×#4114yes—
390C32×C4—24no—
391C32×C4—22no—
392C32×C4—24no—
393C32×C4C22×D414yes—
394C3×Dic3—24no—
395C3×Dic3—22no—
396C3×Dic3—24no—
397C3×Dic3C22×D414yes—
398C25—31no—
399C22×Q8—38no—
400C22×Q8—32no—
401C22×Q8—31no—
402C22×Q8—68no—
403C22×Q8C2×C3×D311yescharacteristic, complemented
404C23×C4—31no—
405C23×C4—31no—
406C23×C4—32no—
407C23×C4—32no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—38no—
411C23×C4—31no—
412C23×C4—68no—
413C23×C4C2×C3×D311yescharacteristic
414C22⋊Q8—38no—
415C22⋊Q8—38no—
416C22⋊Q8—316no—
417C22⋊Q8—38no—
418C22⋊Q8—316no—
419C22⋊Q8C2×C3×D318yesdirect product factor
420C2×C4⋊C4—32no—
421C2×C4⋊C4—32no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—38no—
426C2×C4⋊C4—316no—
427C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
428C2×C4⋊C4C2×C3×D312yescomplemented
429C2×C22⋊C4—32no—
430C2×C22⋊C4—32no—
431C2×C22⋊C4—32no—
432C2×C22⋊C4—316no—
433C2×C22⋊C4C2×C3×D312yes—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—22no—
440C23×C3—24no—
441C23×C3—34no—
442C23×C3—34no—
443C23×C3—34no—
444C23×C3—32no—
445C23×C3—34no—
446C23×C3—316no—
447C23×C3—32no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—68no—
451C23×C3—68no—
452C23×C3—632no—
453C23×C3—62no—
454C23×C3—62no—
455C23×C3D3×Q814yescomplemented
456C23×C3C2×C3×Q814yescomplemented
457C23×C3C23×D312yes—
458C23×C3C23×D311yescharacteristic
459C23×C3C24×C312yes—
460C23×C3C24×C311yescharacteristic
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—232no—
464C22×D3—28no—
465C22×D3—28no—
466C22×D3C2×C3×D414yes—
467C22×D3C2×C3×Q814yes—
468C22×D3C2×C3×Q8116yescomplemented
469C22×D3C2×C3×Q814yescomplemented
470C22×D3C3×#4114yes—
471C22×D3C24×C312yes—
472C22×D3C24×C312yes—
473C3×Q8—28no—
474C3×Q8—28no—
475C3×Q8—48no—
476C3×Q8—616no—
477C3×Q8—68no—
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—22no—
483C2×C3×C4—24no—
484C2×C3×C4—28no—
485C2×C3×C4—28no—
486C2×C3×C4—22no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—22no—
490C2×C3×C4—24no—
491C2×C3×C4—34no—
492C2×C3×C4—32no—
493C2×C3×C4—316no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—32no—
497C2×C3×C4—48no—
498C2×C3×C4—44no—
499C2×C3×C4—42no—
500C2×C3×C4—44no—
501C2×C3×C4—68no—
502C2×C3×C4—616no—
503C2×C3×C4—68no—
504C2×C3×C4—616no—
505C2×C3×C4—68no—
506C2×C3×C4—62no—
507C2×C3×C4—64no—
508C2×C3×C4—64no—
509C2×C3×C4—68no—
510C2×C3×C4D3×D414yes—
511C2×C3×C4C2×C3×D414yes—
512C2×C3×C4C23×D314yes—
513C2×C3×C4C23×D314yes—
514C2×C3×C4C23×D312yes—
515C2×C3×C4C23×D312yes—
516C2×C3×C4C24×C312yes—
517C2×C3×C4C24×C314yes—
518C2×C3×C4C24×C314yes—
519C2×C3×C4C24×C312yes—
520C2×Dic3—24no—
521C2×Dic3—22no—
522C2×Dic3—24no—
523C2×Dic3—28no—
524C2×Dic3C2×C3×D414yes—
525C2×Dic3C24×C314yes—
526C2×Dic3C24×C312yes—
527C2×Dic3C24×C314yes—
528C2×Dic3C24×C312yes—
529C4×D3—28no—
530C4×D3—216no—
531C4×D3—216no—
532C4×D3—28no—
533C4×D3—28no—
534C4×D3C2×C3×D4116yes—
535Dic6—28no—
536Dic6—216no—
537C2×C32—24no—
538C2×C32C2×C22⋊Q814yescomplemented
539C2×C32C23×D411yescharacteristic
540C2×C32C23×Q811yescharacteristic
541C2×C32C22×#4111yescharacteristic
542C3×D3—24no—
543C3×D3C2×C22⋊Q818yesdirect product factor
544C24—31no—
545C24—34no—
546C24—31no—
547C24—38no—
548C24—64no—
549C24—64no—
550C24C22×C3×D311yescharacteristic
551C2×Q8—24no—
552C2×Q8—38no—
553C2×Q8—34no—
554C2×Q8—68no—
555C2×Q8—632no—
556C2×Q8—64no—
557C2×Q8C22×C3×D314yescomplemented
558C22×C4—24no—
559C22×C4—31no—
560C22×C4—34no—
561C22×C4—38no—
562C22×C4—32no—
563C22×C4—32no—
564C22×C4—31no—
565C22×C4—34no—
566C22×C4—38no—
567C22×C4—38no—
568C22×C4—34no—
569C22×C4—34no—
570C22×C4—34no—
571C22×C4—64no—
572C22×C4—632no—
573C22×C4—64no—
574C22×C4—68no—
575C22×C4—68no—
576C22×C4—64no—
577C22×C4—64no—
578C22×C4C22×C3×D312yes—
579C22×C4C22×C3×D312yes—
580C22×C4C22×C3×D311yescharacteristic
581C22×C4C22×C3×D314yes—
582C22×C4C22×C3×D311yescharacteristic
583C4⋊C4—38no—
584C4⋊C4—38no—
585C4⋊C4—38no—
586C4⋊C4—34no—
587C4⋊C4—38no—
588C4⋊C4C22×C3×D314yescomplemented
589C4⋊C4C22×C3×D318yescomplemented
590C22⋊C4—38no—
591C22⋊C4—38no—
592C22⋊C4—38no—
593C22⋊C4C22×C3×D318yes—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—28no—
599C22×C3—28no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—24no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—34no—
606C22×C3—34no—
607C22×C3—34no—
608C22×C3—316no—
609C22×C3—34no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—48no—
613C22×C3—632no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—68no—
617C22×C3C2×D3×D412yes—
618C22×C3C2×D3×Q812yes—
619C22×C3C2×D3×Q814yescomplemented
620C22×C3D3×#4112yes—
621C22×C3C22×C3×D412yes—
622C22×C3C22×C3×Q812yes—
623C22×C3C22×C3×Q814yescomplemented
624C22×C3C2×C3×#4112yes—
625C22×C3C24×D311yescharacteristic
626C22×C3C25×C311yescharacteristic
627C2×D3—22no—
628C2×D3—22no—
629C2×D3—28no—
630C2×D3—232no—
631C2×D3C3×C22⋊Q8116yesdirect product factor
632C2×D3C22×C3×D414yes—
633C2×D3C22×C3×Q814yes—
634C2×D3C22×C3×Q814yescomplemented
635C2×D3C2×C3×#4114yes—
636C3×C4—22no—
637C3×C4—24no—
638C3×C4—24no—
639C3×C4—24no—
640C3×C4—22no—
641C3×C4—24no—
642C3×C4—24no—
643C3×C4—34no—
644C3×C4—42no—
645C3×C4—44no—
646C3×C4—44no—
647C3×C4—62no—
648C3×C4—64no—
649C3×C4—64no—
650C3×C4C2×D3×D414yes—
651C3×C4C22×C3×D414yes—
652Dic3—24no—
653Dic3—22no—
654Dic3—24no—
655Dic3C22×C3×D414yes—
656C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
657C23—22no—
658C23—22no—
659C23—34no—
660C23—34no—
661C23—34no—
662C23—32no—
663C23—34no—
664C23—316no—
665C23—32no—
666C23—68no—
667C23—68no—
668C23—632no—
669C23—62no—
670C23—62no—
671C23C3×D3×Q814yescomplemented
672C23C23×C3×D312yes—
673C23C23×C3×D311yescharacteristic
674Q8—28no—
675Q8—616no—
676Q8—68no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—28no—
681C2×C4—34no—
682C2×C4—32no—
683C2×C4—316no—
684C2×C4—34no—
685C2×C4—34no—
686C2×C4—32no—
687C2×C4—68no—
688C2×C4—68no—
689C2×C4—616no—
690C2×C4—616no—
691C2×C4—68no—
692C2×C4—62no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—68no—
696C2×C4C3×D3×D414yes—
697C2×C4C23×C3×D314yes—
698C2×C4C23×C3×D314yes—
699C2×C4C23×C3×D312yes—
700C2×C4C23×C3×D312yes—
701C2×C3—24no—
702C2×C3—24no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—24no—
707C2×C3—38no—
708C2×C3—44no—
709C2×C3—64no—
710C2×C3D3×C22⋊Q814yesdirect product factor
711C2×C3C2×C3×C22⋊Q814yescomplemented
712C2×C3C22×D3×D411yescharacteristic
713C2×C3C22×D3×Q811yescharacteristic
714C2×C3C2×D3×#4111yescharacteristic
715C2×C3C23×C3×D411yescharacteristic
716C2×C3C23×C3×Q811yescharacteristic
717C2×C3C22×C3×#4111yescharacteristic
718D3—24no—
719D3C2×C3×C22⋊Q818yesdirect product factor
720C22—22no—
721C22—22no—
722C22—28no—
723C22—34no—
724C22—34no—
725C22—34no—
726C22—316no—
727C22—34no—
728C22—632no—
729C22—62no—
730C22—62no—
731C22—68no—
732C22C2×C3×D3×D412yes—
733C22C2×C3×D3×Q812yes—
734C22C2×C3×D3×Q814yescomplemented
735C22C3×D3×#4112yes—
736C22C24×C3×D311yescharacteristic
737C4—22no—
738C4—24no—
739C4—24no—
740C4—34no—
741C4—62no—
742C4—64no—
743C4—64no—
744C4C2×C3×D3×D414yes—
745C3—21no—
746C3C2×D3×C22⋊Q811yescharacteristic, direct product factor
747C3C22×C3×C22⋊Q811yescharacteristic, complemented
748C2—24no—
749C2—38no—
750C2—64no—
751C2C3×D3×C22⋊Q814yesdirect product factor
752C2C22×C3×D3×D411yescharacteristic
753C2C22×C3×D3×Q811yescharacteristic
754C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C22×C3×C22⋊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
3. C2×C32×C22⋊Q8C2semidirect
4. C2×C3×#946C2semidirect
5. C2×C3×#924C2semidirect
6. C3×D3×C22⋊Q8C2direct (N × H)
7. C2×C3×#897C2semidirect
8. C2×C3×#896C2semidirect
9. C2×C3×D3×C4⋊C4C2semidirect
10. C2×C3×D3×C4⋊C4C2semidirect
12. C2×C3×#878C2semidirect
14. C2×D3×C22⋊Q8C3direct (N × H)
16. C22×C32×Q8C22semidirect
20. C2×C3×D3×Q8C22semidirect
29. C22×C3×Dic6C22semidirect
30. C22×C3×Dic6C22semidirect
31. C32×C22⋊Q8C22semidirect
32. C2×C32×C4⋊C4C22semidirect
33. C2×C32×C4⋊C4C22semidirect
36. C3×#946C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
41. C3×#924C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C3×#897C22semidirect
46. C3×#896C22semidirect
47. C3×D3×C4⋊C4C22semidirect
48. C3×D3×C4⋊C4C22semidirect
50. C3×#878C22semidirect
53. C22×D3×Q8C2×C3semidirect
62. C2×C3×C22⋊Q8D3direct (N × H)
63. C2×C3×C22⋊Q8C2×C3semidirect
67. C2×#946C2×C3semidirect
68. C2×#924C2×C3semidirect
69. D3×C22⋊Q8C2×C3direct (N × H)
70. C2×#897C2×C3semidirect
71. C2×#896C2×C3semidirect
72. C2×D3×C4⋊C4C2×C3semidirect
73. C2×D3×C4⋊C4C2×C3semidirect
75. C2×#878C2×C3semidirect
79. C23×C3×D3Q8semidirect
84. C2×C32×Q8C23semidirect
113. C2×C3×Dic6C23semidirect
114. C2×C3×Dic6C23semidirect
115. C32×C4⋊C4C23semidirect
116. C32×C4⋊C4C23semidirect
121. C3×C4⋊Dic3C23semidirect
122. C3×C4⋊Dic3C23semidirect
123. C3×Dic3⋊C4C23semidirect
124. C3×Dic3⋊C4C23semidirect
125. C3×Dic3⋊C4C23semidirect
134. C22×C3×Q8C2×D3semidirect
135. C22×C3×Q8C22×C3semidirect
150. C2×D3×Q8C22×C3semidirect
159. C22×Dic6C22×C3semidirect
160. C22×Dic6C22×C3semidirect
167. C3×C22⋊Q8C2×D3direct (N × H)
168. C3×C22⋊Q8C22×C3semidirect
178. C2×C3×C4⋊C4C2×D3semidirect
179. C2×C3×C4⋊C4C2×D3semidirect
180. C2×C3×C4⋊C4C22×C3semidirect
181. C2×C3×C4⋊C4C22×C3semidirect
190. #946C22×C3semidirect
193. C2×C4⋊Dic3C22×C3semidirect
194. C2×C4⋊Dic3C22×C3semidirect
195. #924C22×C3semidirect
196. C2×Dic3⋊C4C22×C3semidirect
197. C2×Dic3⋊C4C22×C3semidirect
198. C2×Dic3⋊C4C22×C3semidirect
199. #897C22×C3semidirect
200. #896C22×C3semidirect
201. D3×C4⋊C4C22×C3semidirect
202. D3×C4⋊C4C22×C3semidirect
204. #878C22×C3semidirect
207. C23×C32C2×Q8semidirect
217. C22×C3×D3C2×Q8semidirect
218. C22×C3×D3C2×Q8semidirect
257. C2×C22⋊Q8C3×D3direct (N × H)
272. C23×D3C3×Q8semidirect
285. C2×C3×Q8C22×D3semidirect
286. C2×C3×Q8C23×C3semidirect
346. C2×Dic6C23×C3semidirect
347. C2×Dic6C23×C3semidirect
355. C3×C4⋊C4C22×D3semidirect
356. C3×C4⋊C4C22×D3semidirect
357. C3×C4⋊C4C23×C3semidirect
358. C3×C4⋊C4C23×C3semidirect
368. C4⋊Dic3C23×C3semidirect
369. C4⋊Dic3C23×C3semidirect
370. Dic3⋊C4C23×C3semidirect
371. Dic3⋊C4C23×C3semidirect
372. Dic3⋊C4C23×C3semidirect
378. C22×C32C22×Q8semidirect
385. C2×C3×D3C22⋊Q8direct (N × H)
388. C2×C3×D3C22×Q8semidirect
403. C22×Q8C2×C3×D3semidirect
419. C22⋊Q8C2×C3×D3direct (N × H)
427. C2×C4⋊C4C2×C3×D3semidirect
428. C2×C4⋊C4C2×C3×D3semidirect
455. C23×C3D3×Q8semidirect
456. C23×C3C2×C3×Q8semidirect
468. C22×D3C2×C3×Q8semidirect
469. C22×D3C2×C3×Q8semidirect
538. C2×C32C2×C22⋊Q8semidirect
543. C3×D3C2×C22⋊Q8direct (N × H)
557. C2×Q8C22×C3×D3semidirect
588. C4⋊C4C22×C3×D3semidirect
589. C4⋊C4C22×C3×D3semidirect
619. C22×C3C2×D3×Q8semidirect
623. C22×C3C22×C3×Q8semidirect
631. C2×D3C3×C22⋊Q8direct (N × H)
634. C2×D3C22×C3×Q8semidirect
656. C32C22×C22⋊Q8semidirect
671. C23C3×D3×Q8semidirect
710. C2×C3D3×C22⋊Q8direct (N × H)
711. C2×C3C2×C3×C22⋊Q8semidirect
719. D3C2×C3×C22⋊Q8direct (N × H)
734. C22C2×C3×D3×Q8semidirect
746. C3C2×D3×C22⋊Q8direct (N × H)
747. C3C22×C3×C22⋊Q8semidirect
751. C2C3×D3×C22⋊Q8direct (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×C4×D32
C2×C32×C22⋊Q82
C2×C3×#9462
C2×C3×#9242
C3×D3×C22⋊Q82
C2×C3×#8972
C2×C3×#8962
C2×C3×D3×C4⋊C42
C2×C3×D3×C22⋊C42
C2×C3×#8782
C22×C3×C22⋊Q83
C2×D3×C22⋊Q83