Finite Group Databasebeta

← C2×D3×#878 #11900331

Subgroups — C2×D3×#878 #11900331

Order 1152.

3841 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64087C211yesmaximal, characteristic, complemented
4C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
5C2×C3×#878C211yesmaximal, characteristic, complemented
6C2×#63982C211yesmaximal, characteristic, complemented
7C2×D3×#217C211yesmaximal, characteristic
8C2×#63964C211yesmaximal, characteristic, complemented
9C2×#63899C211yesmaximal, characteristic, complemented
10C2×#63896C211yesmaximal, characteristic, complemented
11C2×#63893C211yesmaximal, characteristic, complemented
12C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
13C2×#63887C211yesmaximal, characteristic, complemented
14C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16D3×#878C2116yesmaximal, direct product factor
17C2×D3×C22⋊Q8—31nomaximal
18C22×#878—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic, complemented
26C22×#627C2211yescharacteristic, complemented
27C22×#627C2211yescharacteristic, complemented
28C22×D3×Dic3—28no—
29C22×D3×Dic3C2218yes—
30C22×D3×Dic3C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic
32C22×D3×Dic3C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic
35C22×D3×Dic3C2211yescharacteristic
36C2×D3×Dic6—28no—
37C2×D3×Dic6C2218yescomplemented
38C2×C32×C22⋊C4C2211yescharacteristic
39C2×#3757C2211yescharacteristic
40C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C2×#3750C2211yescharacteristic, complemented
42C2×#3750C2211yescharacteristic, complemented
43#64087C2218yescomplemented
44C2×C3×#217C2211yescharacteristic
45C2×C3×#217C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
49C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C3×D3×C22⋊C4C2218yes—
52C3×#878C2218yescomplemented
53#63982C2218yescomplemented
54D3×#217C2218yes—
55C2×#3724C2211yescharacteristic, complemented
56C2×#3724C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60C2×Dic3⋊Dic3C2211yescharacteristic, complemented
61#63964C2218yescomplemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic
63C2×(C2×D3)⋊Dic3C2211yescharacteristic
64#63899C2218yescomplemented
65#63896C2218yescomplemented
66#63893C2218yescomplemented
67D3×C4⋊Dic3C2218yescomplemented
68#63887C2218yescomplemented
69D3×Dic3⋊C4C2218yescomplemented
70D3×Dic3⋊C4C2218yescomplemented
71C24×Dic3—31no—
72C22×D3×Q8—31no—
73C23×C4×D3—31no—
74C23×Dic6—31no—
75C2×C3×C22⋊Q8—31no—
76C22×C3×C22⋊C4—31no—
77C22×#217—31no—
78C2×#946—31no—
79C22×C4⋊Dic3—31no—
80C2×#924—31no—
81C22×Dic3⋊C4—31no—
82C22×Dic3⋊C4—31no—
83D3×C22⋊Q8—316no—
84C2×#897—31no—
85C2×#896—31no—
86C2×#896—31no—
87C2×D3×C4⋊C4—31no—
88C2×D3×C4⋊C4—31no—
89C2×D3×C4⋊C4—31no—
90C2×D3×C22⋊C4—31no—
91C2×D3×C22⋊C4D311yescharacteristic
92C2×#878—31no—
93C2×#878—31no—
94C2×#878—31no—
95C2×#878—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#878—31no—
101C2×#878—316no—
102C2×#878—61no—
103C2×#878D311yescharacteristic, direct product factor
104C24×C32C2311yescharacteristic
105C23×C3×D3—24no—
106C23×C3×D3—24no—
107C23×C3×D3Q818yescomplemented
108C23×C3×D3C2314yes—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C3⋊Dic3—24no—
114C22×C3⋊Dic3C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C2×#634—24no—
120C2×#634C2314yescomplemented
121C22×C3×Dic3—24no—
122C22×C3×Dic3C2314yes—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—24no—
130C2×C3×C4×D3—24no—
131C2×C3×C4×D3C2314yes—
132C2×C3×C4×D3C2314yes—
133C2×C3×Dic6—24no—
134C2×C3×Dic6C2314yescomplemented
135C2×#627—24no—
136C2×#627—24no—
137C2×#627C2314yescomplemented
138C2×#627C2314yescomplemented
139C2×D3×Dic3—24no—
140C2×D3×Dic3—24no—
141C2×D3×Dic3—24no—
142C2×D3×Dic3—24no—
143C2×D3×Dic3—24no—
144C2×D3×Dic3—232no—
145C2×D3×Dic3D418yes—
146C2×D3×Dic3C2314yes—
147C2×D3×Dic3C2314yes—
148C2×D3×Dic3C2314yes—
149C2×D3×Dic3C2314yes—
150C2×D3×Dic3C2314yes—
151C2×D3×Dic3C2314yes—
152D3×Dic6—232no—
153C32×C22⋊C4C2314yes—
154#3757C2314yes—
155C4⋊(C3⋊Dic3)C2314yescomplemented
156#3750C2314yescomplemented
157#3750C2314yescomplemented
158C3×#217C2314yes—
159C3×#217C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×C4⋊Dic3C2314yescomplemented
163C3×Dic3⋊C4C2314yescomplemented
164C3×Dic3⋊C4C2314yescomplemented
165#3724C2314yescomplemented
166#3724C2314yescomplemented
167Dic3⋊Dic3C2314yescomplemented
168Dic3⋊Dic3C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173C22×C22⋊Q8—91noSylow
174C25×C3—31no—
175C24×D3C2×D311yescharacteristic
176C22×C3×Q8—31no—
177C23×C3×C4—31no—
178C23×C3×C4—31no—
179C23×C3×C4—31no—
180C23×Dic3—31no—
181C23×Dic3—31no—
182C23×Dic3—31no—
183C23×Dic3—31no—
184C23×Dic3—31no—
185C23×Dic3—38no—
186C23×Dic3—31no—
187C23×Dic3—31no—
188C23×Dic3—31no—
189C23×Dic3—61no—
190C23×Dic3—68no—
191C23×Dic3C2×D311yescharacteristic
192C2×D3×Q8—38no—
193C2×D3×Q8—68no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—31no—
198C22×C4×D3—38no—
199C22×C4×D3—31no—
200C22×C4×D3—31no—
201C22×C4×D3—68no—
202C22×C4×D3C2×D311yescharacteristic
203C22×C4×D3C2×D311yescharacteristic
204C22×Dic6—31no—
205C22×Dic6—31no—
206C22×Dic6—31no—
207C22×Dic6—31no—
208C22×Dic6—31no—
209C22×Dic6—31no—
210C22×Dic6—38no—
211C22×Dic6—61no—
212C22×Dic6—68no—
213C22×Dic6C2×D311yescharacteristic, complemented
214C3×C22⋊Q8—38no—
215C2×C3×C4⋊C4—31no—
216C2×C3×C4⋊C4—31no—
217C2×C3×C4⋊C4—31no—
218C2×C3×C22⋊C4—21no—
219C2×C3×C22⋊C4—31no—
220C2×C3×C22⋊C4—31no—
221C2×C3×C22⋊C4—31no—
222C2×C3×C22⋊C4—31no—
223C2×C3×C22⋊C4—38no—
224C2×C3×C22⋊C4C2×D311yescharacteristic
225C2×C3×C22⋊C4C2×D311yescharacteristic
226C2×#217—31no—
227C2×#217—31no—
228C2×#217—31no—
229C2×#217—31no—
230C2×#217—38no—
231C2×#217—61no—
232C2×#217C2×D311yescharacteristic
233C2×#217C2×D311yescharacteristic
234#946—38no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239C2×C4⋊Dic3—31no—
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3—31no—
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3—38no—
246C2×C4⋊Dic3—61no—
247C2×C4⋊Dic3C2×D311yescharacteristic, complemented
248#924—38no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—38no—
262C2×Dic3⋊C4—38no—
263C2×Dic3⋊C4—61no—
264C2×Dic3⋊C4—61no—
265C2×Dic3⋊C4C2×D311yescharacteristic, complemented
266C2×Dic3⋊C4C2×D311yescharacteristic, complemented
267#897—38no—
268#896—38no—
269#896—38no—
270D3×C4⋊C4—38no—
271D3×C4⋊C4—38no—
272D3×C4⋊C4—38no—
273D3×C22⋊C4—38no—
274D3×C22⋊C4C2×D318yes—
275#878—38no—
276#878—38no—
277#878—38no—
278#878—38no—
279#878—38no—
280#878—38no—
281#878—38no—
282#878—38no—
283#878—38no—
284#878—68no—
285#878C2×D318yesdirect product factor
286C23×C32—22no—
287C23×C32—22no—
288C23×C32C2×Q814yescomplemented
289C23×C32C2412yes—
290C23×C32C2411yescharacteristic
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—232no—
294C22×C3×D3—28no—
295C22×C3×D3—28no—
296C22×C3×D3C2×D414yes—
297C22×C3×D3C2×Q814yes—
298C22×C3×D3C2×Q8116yescomplemented
299C22×C3×D3C2×Q814yescomplemented
300C22×C3×D3#4114yes—
301C22×C3×D3C2412yes—
302C22×C3×D3C2412yes—
303C2×C32×C4—22no—
304C2×C32×C4—22no—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3—28no—
311C2×C3⋊Dic3C2×D414yes—
312C2×C3⋊Dic3C2412yes—
313C2×C3⋊Dic3C2412yes—
314C2×C3⋊Dic3C2412yes—
315C2×C3⋊Dic3C2412yes—
316#634—28no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—28no—
323C2×C3×Dic3C2×D414yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C3×C4×D3—28no—
331C3×C4×D3—28no—
332C3×Dic6—28no—
333#627—28no—
334#627—28no—
335D3×Dic3—28no—
336D3×Dic3—28no—
337D3×Dic3—28no—
338D3×Dic3—28no—
339D3×Dic3—28no—
340D3×Dic3C2×D4116yes—
341C23×Q8—91no—
342C24×C4—91no—
343C2×C22⋊Q8—31no—
344C2×C22⋊Q8—91no—
345C2×C22⋊Q8—91no—
346C2×C22⋊Q8—91no—
347C2×C22⋊Q8—91no—
348C2×C22⋊Q8—916no—
349C2×C22⋊Q8—91no—
350C2×C22⋊Q8—91no—
351C2×C22⋊Q8—91no—
352C22×C4⋊C4—91no—
353C22×C4⋊C4—91no—
354C22×C4⋊C4—91no—
355C22×C22⋊C4—31no—
356C22×C22⋊C4—91no—
357C24×C3—21no—
358C24×C3—31no—
359C24×C3—38no—
360C24×C3—34no—
361C24×C3—31no—
362C24×C3—64no—
363C24×C3—64no—
364C24×C3C22×D311yescharacteristic
365C24×C3C22×D311yescharacteristic
366C23×D3—24no—
367C23×D3—24no—
368C23×D3Dic618yescomplemented
369C23×D3C22×D314yes—
370C23×D3C22×D311yescharacteristic
371C23×D3C22×D311yescharacteristic
372C2×C3×Q8—34no—
373C2×C3×Q8—64no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—34no—
383C22×C3×C4—34no—
384C22×C3×C4—34no—
385C22×C3×C4—64no—
386C22×C3×C4—64no—
387C22×C3×C4—64no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×Dic3—24no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—38no—
396C22×Dic3—34no—
397C22×Dic3—34no—
398C22×Dic3—34no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—34no—
406C22×Dic3—34no—
407C22×Dic3—34no—
408C22×Dic3—34no—
409C22×Dic3—34no—
410C22×Dic3—61no—
411C22×Dic3—64no—
412C22×Dic3—61no—
413C22×Dic3—61no—
414C22×Dic3—61no—
415C22×Dic3—64no—
416C22×Dic3—632no—
417C22×Dic3—64no—
418C22×Dic3—64no—
419C22×Dic3—64no—
420C22×Dic3—64no—
421C22×Dic3—64no—
422C22×Dic3—64no—
423C22×Dic3—124no—
424C22×Dic3C22×D314yes—
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D311yescharacteristic
428C22×Dic3C22×D311yescharacteristic
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431D3×Q8—632no—
432C2×C4×D3—24no—
433C2×C4×D3—24no—
434C2×C4×D3—38no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—632no—
442C2×C4×D3—64no—
443C2×C4×D3—64no—
444C2×C4×D3—64no—
445C2×C4×D3—64no—
446C2×C4×D3—64no—
447C2×C4×D3C22×D314yes—
448C2×C4×D3C22×D314yes—
449C2×Dic6—24no—
450C2×Dic6—34no—
451C2×Dic6—34no—
452C2×Dic6—34no—
453C2×Dic6—34no—
454C2×Dic6—34no—
455C2×Dic6—34no—
456C2×Dic6—64no—
457C2×Dic6—632no—
458C2×Dic6—64no—
459C2×Dic6—64no—
460C2×Dic6—64no—
461C2×Dic6—64no—
462C2×Dic6—64no—
463C2×Dic6—64no—
464C2×Dic6—124no—
465C2×Dic6C22×D314yescomplemented
466C3×C4⋊C4—34no—
467C3×C4⋊C4—34no—
468C3×C4⋊C4—34no—
469C3×C22⋊C4—24no—
470C3×C22⋊C4—34no—
471C3×C22⋊C4—34no—
472C3×C22⋊C4—34no—
473C3×C22⋊C4—34no—
474C3×C22⋊C4C22×D314yes—
475C3×C22⋊C4C22×D314yes—
476#217—34no—
477#217—34no—
478#217—34no—
479#217—34no—
480#217—64no—
481#217C22×D314yes—
482#217C22×D314yes—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4C22×D314yes—
486(C2×D3)⋊C4C22×D314yes—
487C4⋊Dic3—34no—
488C4⋊Dic3—34no—
489C4⋊Dic3—34no—
490C4⋊Dic3—34no—
491C4⋊Dic3—34no—
492C4⋊Dic3—34no—
493C4⋊Dic3—64no—
494C4⋊Dic3C22×D314yescomplemented
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—64no—
508Dic3⋊C4—64no—
509Dic3⋊C4C22×D314yescomplemented
510Dic3⋊C4C22×D314yescomplemented
511C22×C32—28no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32C22×D412yes—
515C22×C32C22×Q812yes—
516C22×C32C22×Q814yescomplemented
517C22×C32C2×#4112yes—
518C22×C32C2511yescharacteristic
519C2×C3×D3—28no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—232no—
523C2×C3×D3C22⋊Q8116yescomplemented
524C2×C3×D3C22×D414yes—
525C2×C3×D3C22×Q814yes—
526C2×C3×D3C22×Q814yescomplemented
527C2×C3×D3C2×#4114yes—
528C32×C4—22no—
529C32×C4—22no—
530C3⋊Dic3—22no—
531C3⋊Dic3—22no—
532C3⋊Dic3—22no—
533C3⋊Dic3C22×D414yes—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3—22no—
538C3×Dic3—22no—
539C3×Dic3C22×D414yes—
540C25—31no—
541C22×Q8—31no—
542C22×Q8—91no—
543C22×Q8—91no—
544C22×Q8—98no—
545C22×Q8—91no—
546C22×Q8—188no—
547C23×C4—31no—
548C23×C4—31no—
549C23×C4—31no—
550C23×C4—91no—
551C23×C4—91no—
552C23×C4—91no—
553C23×C4—91no—
554C23×C4—91no—
555C23×C4—98no—
556C23×C4—91no—
557C23×C4—91no—
558C23×C4—188no—
559C22⋊Q8—38no—
560C22⋊Q8—98no—
561C22⋊Q8—98no—
562C22⋊Q8—98no—
563C22⋊Q8—98no—
564C22⋊Q8—98no—
565C22⋊Q8—98no—
566C22⋊Q8—98no—
567C2×C4⋊C4—31no—
568C2×C4⋊C4—31no—
569C2×C4⋊C4—31no—
570C2×C4⋊C4—98no—
571C2×C4⋊C4—98no—
572C2×C4⋊C4—98no—
573C2×C4⋊C4—91no—
574C2×C4⋊C4—91no—
575C2×C4⋊C4—91no—
576C2×C4⋊C4—91no—
577C2×C4⋊C4—91no—
578C2×C4⋊C4—91no—
579C2×C4⋊C4—91no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4—91no—
582C2×C22⋊C4—31no—
583C2×C22⋊C4—31no—
584C2×C22⋊C4—31no—
585C2×C22⋊C4—31no—
586C2×C22⋊C4—38no—
587C2×C22⋊C4—98no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—91no—
590C2×C22⋊C4—91no—
591C2×C22⋊C4D3211yescharacteristic
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—21no—
598C23×C3—24no—
599C23×C3—34no—
600C23×C3—34no—
601C23×C3—34no—
602C23×C3—32no—
603C23×C3—34no—
604C23×C3—316no—
605C23×C3—32no—
606C23×C3—42no—
607C23×C3—42no—
608C23×C3—68no—
609C23×C3—68no—
610C23×C3—632no—
611C23×C3—62no—
612C23×C3—62no—
613C23×C3C2×Dic614yescomplemented
614C23×C3D3×Q814yescomplemented
615C23×C3C23×D312yes—
616C23×C3C23×D312yes—
617C23×C3C23×D311yescharacteristic
618C23×C3C23×D311yescharacteristic
619C22×D3—22no—
620C22×D3—22no—
621C22×D3—232no—
622C22×D3—28no—
623C22×D3—28no—
624C22×D3C2×Dic614yes—
625C22×D3C2×Dic6116yescomplemented
626C22×D3C2×Dic614yescomplemented
627C22×D3D3×D414yes—
628C22×D3#23714yes—
629C22×D3C23×D312yes—
630C22×D3C23×D312yes—
631C3×Q8—68no—
632C2×C3×C4—22no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—34no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—42no—
646C2×C3×C4—42no—
647C2×C3×C4—68no—
648C2×C3×C4—68no—
649C2×C3×C4—68no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—62no—
655C2×C3×C4C23×D312yes—
656C2×C3×C4C23×D312yes—
657C2×C3×C4C23×D312yes—
658C2×C3×C4C23×D312yes—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—28no—
665C2×Dic3—34no—
666C2×Dic3—34no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—316no—
670C2×Dic3—32no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—64no—
677C2×Dic3—62no—
678C2×Dic3—62no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—68no—
682C2×Dic3—68no—
683C2×Dic3—68no—
684C2×Dic3—68no—
685C2×Dic3—68no—
686C2×Dic3—68no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—68no—
694C2×Dic3—128no—
695C2×Dic3—122no—
696C2×Dic3—122no—
697C2×Dic3—122no—
698C2×Dic3D3×D414yes—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D312yes—
701C2×Dic3C23×D312yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C4×D3—28no—
706C4×D3—28no—
707C4×D3—316no—
708C4×D3—68no—
709C4×D3—68no—
710C4×D3—68no—
711C4×D3—68no—
712C4×D3—68no—
713Dic6—28no—
714Dic6—68no—
715Dic6—68no—
716Dic6—68no—
717Dic6—68no—
718Dic6—68no—
719Dic6—68no—
720Dic6—128no—
721C2×C32—24no—
722C2×C32C2×C22⋊Q814yescomplemented
723C2×C32C23×D411yescharacteristic
724C2×C32C23×Q811yescharacteristic
725C2×C32C22×#4111yescharacteristic
726C3×D3—24no—
727C3×D3C2×C22⋊Q818yescomplemented
728C24—31no—
729C24—34no—
730C24—31no—
731C24—38no—
732C24—64no—
733C24—64no—
734C24C2×D3211yescharacteristic
735C2×Q8—34no—
736C2×Q8—64no—
737C2×Q8—94no—
738C2×Q8—94no—
739C2×Q8—94no—
740C2×Q8—184no—
741C2×Q8—184no—
742C2×Q8—184no—
743C2×Q8—1832no—
744C22×C4—31no—
745C22×C4—34no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—34no—
752C22×C4—34no—
753C22×C4—64no—
754C22×C4—64no—
755C22×C4—64no—
756C22×C4—94no—
757C22×C4—98no—
758C22×C4—94no—
759C22×C4—94no—
760C22×C4—94no—
761C22×C4—94no—
762C22×C4—94no—
763C22×C4—91no—
764C22×C4—94no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—91no—
768C22×C4—184no—
769C22×C4—1832no—
770C22×C4—184no—
771C22×C4—184no—
772C22×C4—184no—
773C22×C4—184no—
774C22×C4—184no—
775C22×C4C2×D3211yescharacteristic
776C22×C4C2×D3211yescharacteristic
777C4⋊C4—34no—
778C4⋊C4—34no—
779C4⋊C4—34no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C4⋊C4—94no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—94no—
787C4⋊C4—94no—
788C4⋊C4—94no—
789C22⋊C4—34no—
790C22⋊C4—34no—
791C22⋊C4—34no—
792C22⋊C4—34no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4C2×D3214yes—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—28no—
802C22×C3—28no—
803C22×C3—22no—
804C22×C3—24no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—21no—
808C22×C3—34no—
809C22×C3—34no—
810C22×C3—34no—
811C22×C3—316no—
812C22×C3—34no—
813C22×C3—42no—
814C22×C3—48no—
815C22×C3—42no—
816C22×C3—632no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—68no—
820C22×C3C22×Dic612yes—
821C22×C3C22×Dic614yescomplemented
822C22×C3C2×D3×D412yes—
823C22×C3C2×D3×D412yes—
824C22×C3C2×#23712yes—
825C22×C3C2×D3×Q812yes—
826C22×C3C2×D3×Q814yescomplemented
827C22×C3D3×#4112yes—
828C22×C3C24×D311yescharacteristic
829C22×C3C24×D311yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—28no—
833C2×D3—232no—
834C2×D3#878116yesdirect product factor
835C2×D3C22×Dic614yes—
836C2×D3C22×Dic614yescomplemented
837C2×D3C2×D3×D414yes—
838C2×D3C2×#23714yes—
839C3×C4—22no—
840C3×C4—22no—
841C3×C4—22no—
842C3×C4—22no—
843C3×C4—34no—
844C3×C4—42no—
845C3×C4—42no—
846C3×C4—62no—
847C3×C4—62no—
848C3×C4—62no—
849C3×C4—62no—
850C3×C4—62no—
851Dic3—22no—
852Dic3—22no—
853Dic3—22no—
854Dic3—22no—
855Dic3—22no—
856Dic3—34no—
857Dic3—34no—
858Dic3—64no—
859Dic3—62no—
860Dic3—62no—
861Dic3—62no—
862Dic3—62no—
863Dic3—62no—
864Dic3—62no—
865Dic3—122no—
866Dic3—122no—
867Dic3—122no—
868Dic3C2×D3×D414yes—
869C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
870C23—22no—
871C23—22no—
872C23—34no—
873C23—34no—
874C23—34no—
875C23—32no—
876C23—34no—
877C23—316no—
878C23—32no—
879C23—68no—
880C23—632no—
881C23—68no—
882C23—62no—
883C23—62no—
884C23D3×Dic614yescomplemented
885C23C22×D3212yes—
886C23C22×D3211yescharacteristic
887Q8—68no—
888Q8—188no—
889Q8—188no—
890Q8—188no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—34no—
894C2×C4—32no—
895C2×C4—32no—
896C2×C4—32no—
897C2×C4—32no—
898C2×C4—32no—
899C2×C4—32no—
900C2×C4—68no—
901C2×C4—68no—
902C2×C4—68no—
903C2×C4—62no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—62no—
908C2×C4—916no—
909C2×C4—94no—
910C2×C4—92no—
911C2×C4—92no—
912C2×C4—92no—
913C2×C4—92no—
914C2×C4—188no—
915C2×C4—188no—
916C2×C4—188no—
917C2×C4—188no—
918C2×C4—188no—
919C2×C4—188no—
920C2×C4—182no—
921C2×C4—182no—
922C2×C4—182no—
923C2×C4C22×D3212yes—
924C2×C4C22×D3212yes—
925C2×C3—24no—
926C2×C3—24no—
927C2×C3—24no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—38no—
932C2×C3—44no—
933C2×C3—64no—
934C2×C3C2×#87814yescomplemented
935C2×C3D3×C22⋊Q814yescomplemented
936C2×C3C23×Dic611yescharacteristic
937C2×C3C22×D3×D411yescharacteristic
938C2×C3C22×D3×D411yescharacteristic
939C2×C3C22×#23711yescharacteristic
940C2×C3C22×D3×Q811yescharacteristic
941C2×C3C2×D3×#4111yescharacteristic
942D3—24no—
943D3C2×#87818yesdirect product factor
944C22—28no—
945C22—22no—
946C22—22no—
947C22—316no—
948C22—34no—
949C22—34no—
950C22—34no—
951C22—34no—
952C22—632no—
953C22—68no—
954C22—62no—
955C22—62no—
956C22C2×D3×Dic612yes—
957C22C2×D3×Dic614yescomplemented
958C22D32×D412yes—
959C22D3×#23712yes—
960C22C23×D3211yescharacteristic
961C4—22no—
962C4—22no—
963C4—34no—
964C4—62no—
965C4—62no—
966C4—62no—
967C4—62no—
968C4—62no—
969C4—94no—
970C4—182no—
971C4—182no—
972C4—182no—
973C3—21no—
974C3C22×#87811yescharacteristic, complemented
975C3C2×D3×C22⋊Q811yescharacteristic, complemented
976C2—24no—
977C2—38no—
978C2—64no—
979C2D3×#87814yesdirect product factor
980C2C22×D3×Dic611yescharacteristic
981C2C2×D32×D411yescharacteristic
982C2C2×D3×#23711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32C22×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic6C2semidirect
3. C2×#64087C2semidirect
5. C2×C3×#878C2semidirect
6. C2×#63982C2semidirect
8. C2×#63964C2semidirect
9. C2×#63899C2semidirect
10. C2×#63896C2semidirect
11. C2×#63893C2semidirect
12. C2×D3×C4⋊Dic3C2semidirect
13. C2×#63887C2semidirect
14. C2×D3×Dic3⋊C4C2semidirect
15. C2×D3×Dic3⋊C4C2semidirect
16. D3×#878C2direct (N × H)
21. C22×#634C22semidirect
25. C22×C3×Dic6C22semidirect
26. C22×#627C22semidirect
27. C22×#627C22semidirect
37. C2×D3×Dic6C22semidirect
40. C2×C4⋊(C3⋊Dic3)C22semidirect
41. C2×#3750C22semidirect
42. C2×#3750C22semidirect
43. #64087C22semidirect
48. C2×C3×C4⋊Dic3C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
52. C3×#878C22semidirect
53. #63982C22semidirect
55. C2×#3724C22semidirect
56. C2×#3724C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. C2×Dic3⋊Dic3C22semidirect
61. #63964C22semidirect
64. #63899C22semidirect
65. #63896C22semidirect
66. #63893C22semidirect
67. D3×C4⋊Dic3C22semidirect
68. #63887C22semidirect
69. D3×Dic3⋊C4C22semidirect
70. D3×Dic3⋊C4C22semidirect
103. C2×#878D3direct (N × H)
107. C23×C3×D3Q8semidirect
120. C2×#634C23semidirect
134. C2×C3×Dic6C23semidirect
137. C2×#627C23semidirect
138. C2×#627C23semidirect
155. C4⋊(C3⋊Dic3)C23semidirect
156. #3750C23semidirect
157. #3750C23semidirect
162. C3×C4⋊Dic3C23semidirect
163. C3×Dic3⋊C4C23semidirect
164. C3×Dic3⋊C4C23semidirect
165. #3724C23semidirect
166. #3724C23semidirect
167. Dic3⋊Dic3C23semidirect
168. Dic3⋊Dic3C23semidirect
169. Dic3⋊Dic3C23semidirect
170. Dic3⋊Dic3C23semidirect
213. C22×Dic6C2×D3semidirect
247. C2×C4⋊Dic3C2×D3semidirect
265. C2×Dic3⋊C4C2×D3semidirect
266. C2×Dic3⋊C4C2×D3semidirect
285. #878C2×D3direct (N × H)
288. C23×C32C2×Q8semidirect
298. C22×C3×D3C2×Q8semidirect
299. C22×C3×D3C2×Q8semidirect
368. C23×D3Dic6semidirect
465. C2×Dic6C22×D3semidirect
494. C4⋊Dic3C22×D3semidirect
509. Dic3⋊C4C22×D3semidirect
510. Dic3⋊C4C22×D3semidirect
516. C22×C32C22×Q8semidirect
523. C2×C3×D3C22⋊Q8semidirect
526. C2×C3×D3C22×Q8semidirect
613. C23×C3C2×Dic6semidirect
614. C23×C3D3×Q8semidirect
625. C22×D3C2×Dic6semidirect
626. C22×D3C2×Dic6semidirect
722. C2×C32C2×C22⋊Q8semidirect
727. C3×D3C2×C22⋊Q8semidirect
821. C22×C3C22×Dic6semidirect
826. C22×C3C2×D3×Q8semidirect
834. C2×D3#878direct (N × H)
836. C2×D3C22×Dic6semidirect
869. C32C22×C22⋊Q8semidirect
884. C23D3×Dic6semidirect
934. C2×C3C2×#878semidirect
935. C2×C3D3×C22⋊Q8semidirect
943. D3C2×#878direct (N × H)
957. C22C2×D3×Dic6semidirect
974. C3C22×#878semidirect
975. C3C2×D3×C22⋊Q8semidirect
979. C2D3×#878direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C22×D3×Dic62
C2×#640872
C2×C3×D3×C22⋊C42
C2×C3×#8782
C2×#639822
C2×D3×#2172
C2×#639642
C2×#638992
C2×#638962
C2×#638932
C2×D3×C4⋊Dic32
C2×#638872
C2×D3×Dic3⋊C42
D3×#8782
C2×D3×C22⋊Q83
C22×#8783