Finite Group Databasebeta

← C2×D3×#897 #11900329

Subgroups — C2×D3×#897 #11900329

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×C4×D32C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64106C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
6C2×D3×(C2×D3)⋊C4C212yesmaximal
7C2×#63895C212yesmaximal, complemented
8C2×#63893C212yesmaximal, complemented
9C2×D3×C4⋊Dic3C212yesmaximal, complemented
10C2×#63871C211yesmaximal, characteristic, complemented
11C2×#63857C211yesmaximal, characteristic, complemented
12D3×#897C2116yesmaximal, direct product factor
13C2×D3×C22⋊Q8—31nomaximal
14C22×#897—31nomaximal
15C23×D32C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C22×C3×C4×D3C2212yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C22×#627C2212yescomplemented
23C22×#624C2211yescharacteristic
24C22×D3×Dic3C2212yes—
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C2×C4×D32—28no—
28C2×C4×D32C2218yes—
29C2×D3×Dic6—28no—
30C2×D3×Dic6C2218yescomplemented
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C2×#3752C2212yes—
33C2×C4⋊(C3⋊Dic3)C2212yescomplemented
34#64106C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2212yes—
36C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
37C2×C3×C4⋊Dic3C2212yescomplemented
38C2×C3×Dic3⋊C4C2212yescomplemented
39C3×#897C2218yescomplemented
40C3×D3×C4⋊C4C2218yescomplemented
41C2×Dic3⋊Dic3C2212yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43C2×#3722C2212yes—
44C2×(C2×D3)⋊Dic3C2212yes—
45D3×(C2×D3)⋊C4C22116yes—
46#63895C22116yescomplemented
47#63893C22116yescomplemented
48D3×C4⋊Dic3C22116yescomplemented
49#63871C2218yescomplemented
50#63857C2218yescomplemented
51C22×D3×Q8—31no—
52C23×C4×D3—31no—
53C23×C4×D3—31no—
54C23×Dic6—31no—
55C2×C3×C22⋊Q8—31no—
56C22×C3×C4⋊C4—31no—
57C2×#946—31no—
58C22×(C2×D3)⋊C4—32no—
59C22×C4⋊Dic3—32no—
60C2×#924—31no—
61D3×C22⋊Q8—316no—
62C2×#897—31no—
63C2×#897—31no—
64C2×#897—31no—
65C2×#897—31no—
66C2×#897—32no—
67C2×#897—32no—
68C2×#897—316no—
69C2×#897—61no—
70C2×#897D311yescharacteristic, direct product factor
71C2×#896—32no—
72C2×D3×C4⋊C4—32no—
73C2×D3×C4⋊C4D311yescharacteristic, complemented
74C2×D3×C22⋊C4—32no—
75C2×#878—32no—
76C23×C3⋊D3C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C22×D32—24no—
80C22×D32—24no—
81C22×D32Q818yescomplemented
82C22×D32C2314yes—
83C22×C32×C4C2312yes—
84C22×C32×C4C2311yescharacteristic
85C22×C3⋊Dic3C2311yescharacteristic
86C22×C3⋊Dic3C2312yes—
87C2×C4×C3⋊D3—24no—
88C2×C4×C3⋊D3C2314yes—
89C2×#634—24no—
90C2×#634C2314yescomplemented
91C22×C3×Dic3C2312yes—
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2312yes—
94C22×C3×Dic3C2311yescharacteristic
95C2×C3×C4×D3—28no—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3D418yes—
98C2×C3×C4×D3C2318yes—
99C2×C3×C4×D3C2314yes—
100C2×C3×C4×D3C2314yes—
101C2×C3×Dic6—24no—
102C2×C3×Dic6C2314yescomplemented
103C2×#627—28no—
104C2×#627C2318yescomplemented
105C2×#624—24no—
106C2×#624C2314yes—
107C2×D3×Dic3—28no—
108C2×D3×Dic3—24no—
109C2×D3×Dic3—24no—
110C2×D3×Dic3C2318yes—
111C2×D3×Dic3C2314yes—
112C2×D3×Dic3C2314yes—
113C4×D32—232no—
114D3×Dic6—232no—
115C32×C4⋊C4C2314yescomplemented
116#3752C2318yes—
117C4⋊(C3⋊Dic3)C2318yescomplemented
118C3×(C2×D3)⋊C4C2318yes—
119C3×C4⋊Dic3C2314yescomplemented
120C3×C4⋊Dic3C2318yescomplemented
121C3×Dic3⋊C4C2318yescomplemented
122Dic3⋊Dic3C2318yescomplemented
123Dic3⋊Dic3C2318yescomplemented
124#3722C2318yes—
125(C2×D3)⋊Dic3C2318yes—
126C22×C22⋊Q8—91noSylow
127C24×D3—31no—
128C24×D3—31no—
129C22×C3×Q8—31no—
130C23×C3×C4—31no—
131C23×C3×C4—31no—
132C23×C3×C4—32no—
133C23×Dic3—32no—
134C23×Dic3—31no—
135C23×Dic3—31no—
136C2×D3×Q8—38no—
137C2×D3×Q8—68no—
138C22×C4×D3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—32no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—38no—
146C22×C4×D3—38no—
147C22×C4×D3—61no—
148C22×C4×D3—68no—
149C22×C4×D3—68no—
150C22×C4×D3C2×D311yescharacteristic
151C22×C4×D3C2×D312yes—
152C22×C4×D3C2×D311yescharacteristic
153C22×Dic6—31no—
154C22×Dic6—31no—
155C22×Dic6—32no—
156C22×Dic6—32no—
157C22×Dic6—38no—
158C22×Dic6—61no—
159C22×Dic6—68no—
160C22×Dic6C2×D311yescharacteristic, complemented
161C3×C22⋊Q8—38no—
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4—32no—
164C2×C3×C4⋊C4—32no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—38no—
167C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
168C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
169C2×C3×C22⋊C4—32no—
170C2×#217—32no—
171#946—38no—
172C2×(C2×D3)⋊C4—32no—
173C2×(C2×D3)⋊C4—32no—
174C2×(C2×D3)⋊C4—32no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—316no—
178C2×(C2×D3)⋊C4—62no—
179C2×(C2×D3)⋊C4C2×D312yes—
180C2×C4⋊Dic3—32no—
181C2×C4⋊Dic3—32no—
182C2×C4⋊Dic3—32no—
183C2×C4⋊Dic3—32no—
184C2×C4⋊Dic3—316no—
185C2×C4⋊Dic3—62no—
186C2×C4⋊Dic3C2×D311yescharacteristic, complemented
187C2×C4⋊Dic3C2×D312yescomplemented
188#924—38no—
189C2×Dic3⋊C4—32no—
190C2×Dic3⋊C4—32no—
191C2×Dic3⋊C4C2×D312yescomplemented
192#897—38no—
193#897—38no—
194#897—38no—
195#897—38no—
196#897—316no—
197#897—316no—
198#897—68no—
199#897C2×D318yesdirect product factor
200#896—316no—
201D3×C4⋊C4—316no—
202D3×C4⋊C4C2×D318yescomplemented
203D3×C22⋊C4—316no—
204#878—316no—
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—22no—
207C22×C3⋊D3—22no—
208C22×C3⋊D3C2×Q814yescomplemented
209C22×C3⋊D3C2412yes—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3C2×D414yes—
213C22×C3×D3C2×Q814yes—
214C22×C3×D3C2×Q814yescomplemented
215C22×C3×D3#4114yes—
216C22×C3×D3C2412yes—
217C22×C3×D3C2412yes—
218C2×D32—232no—
219C2×D32—28no—
220C2×D32—28no—
221C2×D32C2×Q8116yescomplemented
222C2×C32×C4—24no—
223C2×C32×C4C2×D414yes—
224C2×C32×C4C2414yes—
225C2×C32×C4C2412yes—
226C2×C3⋊Dic3—22no—
227C2×C3⋊Dic3—24no—
228C2×C3⋊Dic3C2414yes—
229C2×C3⋊Dic3C2412yes—
230C4×C3⋊D3—28no—
231#634—28no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—24no—
235C2×C3×Dic3C2×D414yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2412yes—
240C3×C4×D3—216no—
241C3×C4×D3—28no—
242C3×C4×D3C2×D4116yes—
243C3×Dic6—28no—
244#627—216no—
245#624—28no—
246D3×Dic3—216no—
247D3×Dic3—28no—
248D3×Dic3—28no—
249C23×Q8—91no—
250C24×C4—91no—
251C2×C22⋊Q8—31no—
252C2×C22⋊Q8—92no—
253C2×C22⋊Q8—92no—
254C2×C22⋊Q8—916no—
255C2×C22⋊Q8—91no—
256C2×C22⋊Q8—91no—
257C2×C22⋊Q8—91no—
258C22×C4⋊C4—31no—
259C22×C4⋊C4—92no—
260C22×C22⋊C4—92no—
261C24×C3—31no—
262C24×C3—31no—
263C23×D3—31no—
264C23×D3—31no—
265C23×D3—38no—
266C23×D3—38no—
267C23×D3—34no—
268C23×D3—34no—
269C23×D3—61no—
270C23×D3—64no—
271C23×D3—64no—
272C23×D3—64no—
273C23×D3—64no—
274C23×D3C22×D311yescharacteristic
275C23×D3C22×D311yescharacteristic
276C2×C3×Q8—34no—
277C2×C3×Q8—64no—
278C22×C3×C4—21no—
279C22×C3×C4—22no—
280C22×C3×C4—31no—
281C22×C3×C4—38no—
282C22×C3×C4—34no—
283C22×C3×C4—31no—
284C22×C3×C4—32no—
285C22×C3×C4—32no—
286C22×C3×C4—34no—
287C22×C3×C4—38no—
288C22×C3×C4—68no—
289C22×C3×C4—64no—
290C22×C3×C4C22×D312yes—
291C22×C3×C4C22×D312yes—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×Dic3—31no—
295C22×Dic3—32no—
296C22×Dic3—31no—
297C22×Dic3—32no—
298C22×Dic3—34no—
299C22×Dic3—34no—
300C22×Dic3—38no—
301C22×Dic3—61no—
302C22×Dic3—62no—
303C22×Dic3—68no—
304C22×Dic3—64no—
305C22×Dic3—64no—
306C22×Dic3C22×D312yes—
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D312yes—
309C22×Dic3C22×D311yescharacteristic
310D3×Q8—632no—
311C2×C4×D3—28no—
312C2×C4×D3—24no—
313C2×C4×D3—38no—
314C2×C4×D3—34no—
315C2×C4×D3—34no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—34no—
319C2×C4×D3—34no—
320C2×C4×D3—64no—
321C2×C4×D3—632no—
322C2×C4×D3—64no—
323C2×C4×D3—64no—
324C2×C4×D3—64no—
325C2×C4×D3—68no—
326C2×C4×D3—64no—
327C2×C4×D3—64no—
328C2×C4×D3—64no—
329C2×C4×D3—632no—
330C2×C4×D3—124no—
331C2×C4×D3D1218yes—
332C2×C4×D3C22×D318yes—
333C2×C4×D3C22×D314yes—
334C2×C4×D3C22×D314yes—
335C2×Dic6—24no—
336C2×Dic6—34no—
337C2×Dic6—34no—
338C2×Dic6—38no—
339C2×Dic6—38no—
340C2×Dic6—64no—
341C2×Dic6—632no—
342C2×Dic6—68no—
343C2×Dic6—64no—
344C2×Dic6—64no—
345C2×Dic6—68no—
346C2×Dic6—124no—
347C2×Dic6C22×D314yescomplemented
348C3×C4⋊C4—24no—
349C3×C4⋊C4—38no—
350C3×C4⋊C4—38no—
351C3×C4⋊C4—34no—
352C3×C4⋊C4C22×D314yescomplemented
353C3×C4⋊C4C22×D314yescomplemented
354C3×C22⋊C4—38no—
355#217—38no—
356(C2×D3)⋊C4—38no—
357(C2×D3)⋊C4—38no—
358(C2×D3)⋊C4—38no—
359(C2×D3)⋊C4—38no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—68no—
362(C2×D3)⋊C4C22×D318yes—
363C4⋊Dic3—38no—
364C4⋊Dic3—38no—
365C4⋊Dic3—38no—
366C4⋊Dic3—38no—
367C4⋊Dic3—68no—
368C4⋊Dic3C22×D314yescomplemented
369C4⋊Dic3C22×D318yescomplemented
370Dic3⋊C4—38no—
371Dic3⋊C4—38no—
372Dic3⋊C4C22×D318yescomplemented
373C22×C32C22×D412yes—
374C22×C32C22×Q812yes—
375C22×C32C2×#4112yes—
376C22×C32C2511yescharacteristic
377C2×C3⋊D3—28no—
378C2×C3⋊D3—22no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3C22×Q814yescomplemented
381C2×C3×D3—28no—
382C2×C3×D3—22no—
383C2×C3×D3—22no—
384C2×C3×D3C22⋊Q8116yescomplemented
385C2×C3×D3C22×D414yes—
386C2×C3×D3C22×Q814yes—
387C2×C3×D3C22×Q814yescomplemented
388C2×C3×D3C2×#4114yes—
389D32—232no—
390C32×C4—24no—
391C32×C4C22×D414yes—
392C3⋊Dic3—22no—
393C3⋊Dic3—24no—
394C3×Dic3—22no—
395C3×Dic3—24no—
396C3×Dic3—24no—
397C3×Dic3C22×D414yes—
398C25—91no—
399C22×Q8—31no—
400C22×Q8—92no—
401C22×Q8—98no—
402C22×Q8—91no—
403C22×Q8—188no—
404C23×C4—31no—
405C23×C4—32no—
406C23×C4—31no—
407C23×C4—91no—
408C23×C4—98no—
409C23×C4—92no—
410C23×C4—91no—
411C23×C4—91no—
412C23×C4—91no—
413C23×C4—188no—
414C22⋊Q8—38no—
415C22⋊Q8—916no—
416C22⋊Q8—916no—
417C22⋊Q8—98no—
418C22⋊Q8—98no—
419C22⋊Q8—98no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—31no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—38no—
424C2×C4⋊C4—916no—
425C2×C4⋊C4—92no—
426C2×C4⋊C4—92no—
427C2×C4⋊C4—92no—
428C2×C4⋊C4D3211yescharacteristic, complemented
429C2×C22⋊C4—32no—
430C2×C22⋊C4—916no—
431C2×C22⋊C4—92no—
432C2×C22⋊C4—92no—
433C2×C22⋊C4—92no—
434C23×C3—21no—
435C23×C3—34no—
436C23×C3—34no—
437C23×C3—34no—
438C23×C3—32no—
439C23×C3—34no—
440C23×C3—32no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3C23×D311yescharacteristic
444C23×C3C23×D311yescharacteristic
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—34no—
448C22×D3—34no—
449C22×D3—32no—
450C22×D3—32no—
451C22×D3—316no—
452C22×D3—316no—
453C22×D3—64no—
454C22×D3—62no—
455C22×D3—68no—
456C22×D3—68no—
457C22×D3—632no—
458C22×D3—62no—
459C22×D3—62no—
460C22×D3—62no—
461C22×D3—62no—
462C22×D3—632no—
463C22×D3—68no—
464C22×D3—68no—
465C22×D3—122no—
466C22×D3—122no—
467C22×D3C2×D1214yes—
468C22×D3#23714yes—
469C22×D3D3×Q814yes—
470C22×D3D3×Q814yescomplemented
471C22×D3C23×D312yes—
472C22×D3C23×D312yes—
473C3×Q8—68no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—24no—
478C2×C3×C4—24no—
479C2×C3×C4—34no—
480C2×C3×C4—32no—
481C2×C3×C4—316no—
482C2×C3×C4—32no—
483C2×C3×C4—34no—
484C2×C3×C4—34no—
485C2×C3×C4—44no—
486C2×C3×C4—616no—
487C2×C3×C4—64no—
488C2×C3×C4—62no—
489C2×C3×C4—64no—
490C2×C3×C4—68no—
491C2×C3×C4C2×D1214yes—
492C2×C3×C4D3×D414yes—
493C2×C3×C4C23×D314yes—
494C2×C3×C4C23×D314yes—
495C2×C3×C4C23×D312yes—
496C2×C3×C4C23×D312yes—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—24no—
500C2×Dic3—32no—
501C2×Dic3—34no—
502C2×Dic3—32no—
503C2×Dic3—34no—
504C2×Dic3—62no—
505C2×Dic3—64no—
506C2×Dic3—616no—
507C2×Dic3—68no—
508C2×Dic3—64no—
509C2×Dic3—62no—
510C2×Dic3—64no—
511C2×Dic3—62no—
512C2×Dic3—68no—
513C2×Dic3—124no—
514C2×Dic3—122no—
515C2×Dic3C2×D1214yes—
516C2×Dic3C23×D314yes—
517C2×Dic3C23×D312yes—
518C2×Dic3C23×D314yes—
519C2×Dic3C23×D312yes—
520C4×D3—216no—
521C4×D3—28no—
522C4×D3—68no—
523C4×D3—68no—
524C4×D3—68no—
525C4×D3—616no—
526C4×D3—68no—
527C4×D3—68no—
528C4×D3—68no—
529C4×D3—128no—
530C4×D3C2×D12116yes—
531Dic6—28no—
532Dic6—616no—
533Dic6—68no—
534Dic6—68no—
535Dic6—616no—
536Dic6—128no—
537C2×C32C2×C22⋊Q814yescomplemented
538C2×C32C23×D411yescharacteristic
539C2×C32C23×Q811yescharacteristic
540C2×C32C22×#4111yescharacteristic
541C3⋊D3—24no—
542C3×D3—24no—
543C3×D3C2×C22⋊Q818yescomplemented
544C24—31no—
545C24—31no—
546C24—94no—
547C24—98no—
548C24—91no—
549C24—184no—
550C24—184no—
551C2×Q8—34no—
552C2×Q8—64no—
553C2×Q8—98no—
554C2×Q8—94no—
555C2×Q8—188no—
556C2×Q8—1832no—
557C2×Q8—184no—
558C22×C4—31no—
559C22×C4—34no—
560C22×C4—38no—
561C22×C4—32no—
562C22×C4—32no—
563C22×C4—31no—
564C22×C4—38no—
565C22×C4—34no—
566C22×C4—68no—
567C22×C4—64no—
568C22×C4—94no—
569C22×C4—98no—
570C22×C4—94no—
571C22×C4—94no—
572C22×C4—92no—
573C22×C4—91no—
574C22×C4—94no—
575C22×C4—184no—
576C22×C4—1832no—
577C22×C4—184no—
578C22×C4—184no—
579C22×C4—188no—
580C22×C4—184no—
581C22×C4C2×D3212yes—
582C22×C4C2×D3211yescharacteristic
583C4⋊C4—38no—
584C4⋊C4—34no—
585C4⋊C4—38no—
586C4⋊C4—98no—
587C4⋊C4—98no—
588C4⋊C4—98no—
589C4⋊C4C2×D3214yescomplemented
590C22⋊C4—38no—
591C22⋊C4—98no—
592C22⋊C4—98no—
593C22⋊C4—98no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—21no—
598C22×C3—34no—
599C22×C3—34no—
600C22×C3—34no—
601C22×C3—316no—
602C22×C3—34no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—68no—
606C22×C3C22×D1212yes—
607C22×C3C2×D3×D412yes—
608C22×C3C2×#23712yes—
609C22×C3C2×D3×Q812yes—
610C22×C3C2×D3×Q812yes—
611C22×C3D3×#4112yes—
612C22×C3C24×D311yescharacteristic
613C22×C3C24×D311yescharacteristic
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—28no—
617C2×D3—34no—
618C2×D3—34no—
619C2×D3—64no—
620C2×D3—632no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—62no—
625C2×D3—68no—
626C2×D3—68no—
627C2×D3—632no—
628C2×D3—122no—
629C2×D3—122no—
630C2×D3—128no—
631C2×D3#897116yesdirect product factor
632C2×D3C22×D1214yes—
633C2×D3C2×#23714yes—
634C2×D3C2×D3×Q814yes—
635C2×D3C2×D3×Q814yescomplemented
636C3×C4—24no—
637C3×C4—24no—
638C3×C4—24no—
639C3×C4—34no—
640C3×C4—44no—
641C3×C4—64no—
642C3×C4—62no—
643C3×C4—64no—
644C3×C4C22×D1214yes—
645C3×C4C2×D3×D414yes—
646Dic3—24no—
647Dic3—22no—
648Dic3—24no—
649Dic3—64no—
650Dic3—62no—
651Dic3—64no—
652Dic3—62no—
653Dic3—124no—
654Dic3—122no—
655Dic3C22×D1214yes—
656C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
657C23—34no—
658C23—34no—
659C23—34no—
660C23—32no—
661C23—34no—
662C23—32no—
663C23—62no—
664C23—62no—
665C23—916no—
666C23—94no—
667C23—92no—
668C23—188no—
669C23—188no—
670C23—1832no—
671C23—182no—
672C23—182no—
673C23C22×D3211yescharacteristic
674Q8—68no—
675Q8—1816no—
676Q8—188no—
677C2×C4—24no—
678C2×C4—34no—
679C2×C4—32no—
680C2×C4—316no—
681C2×C4—34no—
682C2×C4—34no—
683C2×C4—32no—
684C2×C4—616no—
685C2×C4—62no—
686C2×C4—64no—
687C2×C4—64no—
688C2×C4—68no—
689C2×C4—94no—
690C2×C4—92no—
691C2×C4—188no—
692C2×C4—188no—
693C2×C4—188no—
694C2×C4—1816no—
695C2×C4—182no—
696C2×C4—184no—
697C2×C4—188no—
698C2×C4D3×D1214yes—
699C2×C4C22×D3214yes—
700C2×C4C22×D3212yes—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—24no—
704C2×C3—21no—
705C2×C3—38no—
706C2×C3—64no—
707C2×C3C2×#89714yescomplemented
708C2×C3D3×C22⋊Q814yescomplemented
709C2×C3C23×D1211yescharacteristic
710C2×C3C22×D3×D411yescharacteristic
711C2×C3C22×#23711yescharacteristic
712C2×C3C22×D3×Q811yescharacteristic
713C2×C3C22×D3×Q811yescharacteristic
714C2×C3C2×D3×#4111yescharacteristic
715D3—24no—
716D3—64no—
717D3—64no—
718D3—124no—
719D3C2×#89718yesdirect product factor
720C22—34no—
721C22—34no—
722C22—316no—
723C22—34no—
724C22—34no—
725C22—62no—
726C22—62no—
727C22—68no—
728C22—94no—
729C22—1832no—
730C22—182no—
731C22—182no—
732C22—188no—
733C22C2×D3×D1212yes—
734C22D3×#23712yes—
735C22D32×Q812yes—
736C22C23×D3211yescharacteristic
737C4—24no—
738C4—34no—
739C4—62no—
740C4—64no—
741C4—64no—
742C4—182no—
743C4—184no—
744C4C2×D3×D1214yes—
745C3—21no—
746C3C22×#89711yescharacteristic, complemented
747C3C2×D3×C22⋊Q811yescharacteristic, complemented
748C2—38no—
749C2—64no—
750C2—184no—
751C2D3×#89714yesdirect product factor
752C2C22×D3×D1211yescharacteristic
753C2C2×D3×#23711yescharacteristic
754C2C2×D32×Q811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32C22×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic6C2semidirect
3. C2×#64106C2semidirect
4. C2×C3×#897C2semidirect
5. C2×C3×D3×C4⋊C4C2semidirect
7. C2×#63895C2semidirect
8. C2×#63893C2semidirect
9. C2×D3×C4⋊Dic3C2semidirect
10. C2×#63871C2semidirect
11. C2×#63857C2semidirect
12. D3×#897C2direct (N × H)
17. C22×#634C22semidirect
21. C22×C3×Dic6C22semidirect
22. C22×#627C22semidirect
30. C2×D3×Dic6C22semidirect
31. C2×C32×C4⋊C4C22semidirect
33. C2×C4⋊(C3⋊Dic3)C22semidirect
34. #64106C22semidirect
36. C2×C3×C4⋊Dic3C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C3×#897C22semidirect
40. C3×D3×C4⋊C4C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
46. #63895C22semidirect
47. #63893C22semidirect
48. D3×C4⋊Dic3C22semidirect
49. #63871C22semidirect
50. #63857C22semidirect
70. C2×#897D3direct (N × H)
73. C2×D3×C4⋊C4D3semidirect
81. C22×D32Q8semidirect
90. C2×#634C23semidirect
102. C2×C3×Dic6C23semidirect
104. C2×#627C23semidirect
115. C32×C4⋊C4C23semidirect
117. C4⋊(C3⋊Dic3)C23semidirect
119. C3×C4⋊Dic3C23semidirect
120. C3×C4⋊Dic3C23semidirect
121. C3×Dic3⋊C4C23semidirect
122. Dic3⋊Dic3C23semidirect
123. Dic3⋊Dic3C23semidirect
160. C22×Dic6C2×D3semidirect
167. C2×C3×C4⋊C4C2×D3semidirect
168. C2×C3×C4⋊C4C2×D3semidirect
186. C2×C4⋊Dic3C2×D3semidirect
187. C2×C4⋊Dic3C2×D3semidirect
191. C2×Dic3⋊C4C2×D3semidirect
199. #897C2×D3direct (N × H)
202. D3×C4⋊C4C2×D3semidirect
208. C22×C3⋊D3C2×Q8semidirect
214. C22×C3×D3C2×Q8semidirect
221. C2×D32C2×Q8semidirect
347. C2×Dic6C22×D3semidirect
352. C3×C4⋊C4C22×D3semidirect
353. C3×C4⋊C4C22×D3semidirect
368. C4⋊Dic3C22×D3semidirect
369. C4⋊Dic3C22×D3semidirect
372. Dic3⋊C4C22×D3semidirect
380. C2×C3⋊D3C22×Q8semidirect
384. C2×C3×D3C22⋊Q8semidirect
387. C2×C3×D3C22×Q8semidirect
428. C2×C4⋊C4D32semidirect
470. C22×D3D3×Q8semidirect
537. C2×C32C2×C22⋊Q8semidirect
543. C3×D3C2×C22⋊Q8semidirect
589. C4⋊C4C2×D32semidirect
631. C2×D3#897direct (N × H)
635. C2×D3C2×D3×Q8semidirect
656. C32C22×C22⋊Q8semidirect
707. C2×C3C2×#897semidirect
708. C2×C3D3×C22⋊Q8semidirect
719. D3C2×#897direct (N × H)
746. C3C22×#897semidirect
747. C3C2×D3×C22⋊Q8semidirect
751. C2D3×#897direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D322
C22×D3×Dic62
C2×#641062
C2×C3×#8972
C2×C3×D3×C4⋊C42
C2×D3×(C2×D3)⋊C42
C2×#638952
C2×#638932
C2×D3×C4⋊Dic32
C2×#638712
C2×#638572
D3×#8972
C2×D3×C22⋊Q83
C22×#8973