Finite Group Databasebeta

← C2×#10594925 #11900334

Subgroups — C2×#10594925 #11900334

Order 1152.

4361 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×C3×#924C212yesmaximal, complemented
4C2×#63982C212yesmaximal, complemented
5C2×#63974C212yesmaximal
6C2×#63900C211yesmaximal, characteristic, complemented
7#10594925C2116yesmaximal, direct product factor
8C2×#63883C212yesmaximal, complemented
9C2×#63871C212yesmaximal, complemented
10C2×#63865C212yesmaximal, complemented
11C2×D3×C22⋊Q8—32nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3—28no—
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2218yes—
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×Dic6C2212yescomplemented
22C22×#627C2212yescomplemented
23C22×#624C2212yes—
24C22×#624C2212yes—
25C2×#3797—28no—
26C2×#3797C2218yescomplemented
27C2×C3×#217C2214yes—
28C2×C3×C4⋊Dic3C2212yescomplemented
29C3×#924C22116yescomplemented
30C2×C3×Dic3⋊C4C2214yescomplemented
31#63982C22116yescomplemented
32#63974C22116yes—
33C2×#3724C2212yescomplemented
34C2×Dic3⋊Dic3C2214yescomplemented
35C2×#3722C2214yes—
36#63900C2218yescomplemented
37#63883C22116yescomplemented
38#63871C22116yescomplemented
39#63865C22116yescomplemented
40C22×D3×Q8—32no—
41C23×C4×D3—32no—
42C23×C4×D3—61no—
43C2×C3×C22⋊Q8—32no—
44C2×#946—32no—
45C2×#924D312yescomplemented
46D3×C22⋊Q8—332no—
47C2×#897—32no—
48C2×#896—34no—
49C2×D3×C4⋊C4—32no—
50C2×D3×C4⋊C4—34no—
51C2×D3×C22⋊C4—34no—
52C2×#878—34no—
53C24×C32C2311yescharacteristic
54C23×C3⋊D3—24no—
55C23×C3⋊D3—24no—
56C23×C3⋊D3Q818yescomplemented
57C23×C3⋊D3C2311yescharacteristic
58C23×C3⋊D3C2314yes—
59C23×C3⋊D3C2311yescharacteristic
60C22×C32×C4—24no—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2314yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3—24no—
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2314yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4×C3⋊D3—24no—
69C2×C4×C3⋊D3—24no—
70C2×C4×C3⋊D3—24no—
71C2×C4×C3⋊D3—232no—
72C2×C4×C3⋊D3D418yes—
73C2×C4×C3⋊D3C2314yes—
74C2×C4×C3⋊D3C2314yes—
75C2×C4×C3⋊D3C2314yes—
76C2×C4×C3⋊D3C2314yes—
77C22×C3×Dic3C2314yes—
78C22×C3×Dic3C2314yes—
79C2×C3×Dic6—28no—
80C2×C3×Dic6C2318yescomplemented
81C2×#627—28no—
82C2×#627C2318yescomplemented
83C2×#624—28no—
84C2×#624—28no—
85C2×#624C2318yes—
86C2×#624C2318yes—
87#3797—232no—
88C3×#217C23116yes—
89C3×C4⋊Dic3C2318yescomplemented
90C3×Dic3⋊C4C23116yescomplemented
91#3724C2318yescomplemented
92Dic3⋊Dic3C23116yescomplemented
93#3722C23116yes—
94C22×C22⋊Q8—91noSylow
95C24×D3—32no—
96C24×D3—61no—
97C22×C3×Q8—32no—
98C23×C3×C4—21no—
99C23×C3×C4C2×D312yes—
100C23×Dic3—32no—
101C23×Dic3—61no—
102C2×D3×Q8—316no—
103C2×D3×Q8—616no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—316no—
109C22×C4×D3—34no—
110C22×C4×D3—34no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C22×C4×D3—61no—
114C22×C4×D3—61no—
115C22×C4×D3—68no—
116C22×C4×D3—616no—
117C22×C4×D3—616no—
118C22×Dic6—34no—
119C22×Dic6C2×D312yescomplemented
120C3×C22⋊Q8—316no—
121C2×C3×C4⋊C4—34no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C22⋊C4—34no—
124C2×#217C2×D314yes—
125#946—316no—
126C2×(C2×D3)⋊C4—34no—
127C2×(C2×D3)⋊C4—34no—
128C2×C4⋊Dic3—34no—
129C2×C4⋊Dic3C2×D312yescomplemented
130#924C2×D3116yescomplemented
131C2×Dic3⋊C4—34no—
132C2×Dic3⋊C4—34no—
133C2×Dic3⋊C4C2×D314yescomplemented
134#897—316no—
135#896—332no—
136D3×C4⋊C4—316no—
137D3×C4⋊C4—332no—
138D3×C22⋊C4—332no—
139#878—332no—
140C23×C32—22no—
141C23×C32—22no—
142C23×C32C2×Q814yescomplemented
143C23×C32C2412yes—
144C23×C32C2411yescharacteristic
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—232no—
148C22×C3⋊D3—28no—
149C22×C3⋊D3—28no—
150C22×C3⋊D3C2×D414yes—
151C22×C3⋊D3C2×Q814yes—
152C22×C3⋊D3C2×Q8116yescomplemented
153C22×C3⋊D3C2×Q814yescomplemented
154C22×C3⋊D3#4114yes—
155C22×C3⋊D3C2412yes—
156C22×C3⋊D3C2412yes—
157C2×C32×C4—22no—
158C2×C32×C4—28no—
159C2×C32×C4C2×D414yes—
160C2×C32×C4C2412yes—
161C2×C32×C4C2412yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—28no—
164C2×C3⋊Dic3C2×D414yes—
165C2×C3⋊Dic3C2412yes—
166C2×C3⋊Dic3C2412yes—
167C4×C3⋊D3—28no—
168C4×C3⋊D3—28no—
169C4×C3⋊D3—28no—
170C4×C3⋊D3C2×D4116yes—
171C2×C3×Dic3—28no—
172C2×C3×Dic3—28no—
173C2×C3×Dic3C2418yes—
174C2×C3×Dic3C2418yes—
175C3×Dic6—216no—
176#627—216no—
177#624—216no—
178#624—216no—
179C23×Q8—91no—
180C24×C4—91no—
181C2×C22⋊Q8—32no—
182C2×C22⋊Q8—92no—
183C2×C22⋊Q8—92no—
184C2×C22⋊Q8—92no—
185C2×C22⋊Q8—916no—
186C22×C4⋊C4—92no—
187C22×C4⋊C4—91no—
188C22×C22⋊C4—92no—
189C24×C3—21no—
190C24×C3C22×D312yes—
191C23×D3—32no—
192C23×D3—316no—
193C23×D3—38no—
194C23×D3—32no—
195C23×D3—68no—
196C23×D3—61no—
197C23×D3—64no—
198C23×D3—61no—
199C23×D3—68no—
200C23×D3—68no—
201C23×D3—68no—
202C23×D3—68no—
203C2×C3×Q8—38no—
204C2×C3×Q8—68no—
205C22×C3×C4—28no—
206C22×C3×C4—28no—
207C22×C3×C4—24no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—34no—
211C22×C3×C4—34no—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D318yes—
214C22×C3×C4C22×D312yes—
215C22×Dic3—32no—
216C22×Dic3—38no—
217C22×Dic3—32no—
218C22×Dic3—61no—
219C22×Dic3—64no—
220C22×Dic3—61no—
221C22×Dic3—68no—
222C22×Dic3—68no—
223C22×Dic3C22×D314yes—
224C22×Dic3C22×D314yes—
225D3×Q8—664no—
226C2×C4×D3—316no—
227C2×C4×D3—38no—
228C2×C4×D3—38no—
229C2×C4×D3—38no—
230C2×C4×D3—38no—
231C2×C4×D3—316no—
232C2×C4×D3—316no—
233C2×C4×D3—68no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—664no—
239C2×C4×D3—616no—
240C2×C4×D3—616no—
241C2×C4×D3—68no—
242C2×C4×D3—68no—
243C2×C4×D3—664no—
244C2×C4×D3—68no—
245C2×C4×D3—68no—
246C2×C4×D3—68no—
247C2×C4×D3—68no—
248C2×Dic6—28no—
249C2×Dic6—316no—
250C2×Dic6—616no—
251C2×Dic6C22×D318yescomplemented
252C3×C4⋊C4—316no—
253C3×C4⋊C4—38no—
254C3×C22⋊C4—316no—
255#217C22×D3116yes—
256(C2×D3)⋊C4—316no—
257(C2×D3)⋊C4—316no—
258C4⋊Dic3—316no—
259C4⋊Dic3C22×D318yescomplemented
260Dic3⋊C4—316no—
261Dic3⋊C4—316no—
262Dic3⋊C4C22×D3116yescomplemented
263C22×C32—28no—
264C22×C32—22no—
265C22×C32—22no—
266C22×C32C22×D412yes—
267C22×C32C22×Q812yes—
268C22×C32C22×Q814yescomplemented
269C22×C32C2×#4112yes—
270C22×C32C2511yescharacteristic
271C2×C3⋊D3—28no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—232no—
275C2×C3⋊D3C22⋊Q8116yescomplemented
276C2×C3⋊D3C22×D414yes—
277C2×C3⋊D3C22×Q814yes—
278C2×C3⋊D3C22×Q814yescomplemented
279C2×C3⋊D3C2×#4114yes—
280C32×C4—22no—
281C32×C4C22×D414yes—
282C3⋊Dic3—22no—
283C3⋊Dic3C22×D414yes—
284C3×Dic3—28no—
285C3×Dic3—28no—
286C25—91no—
287C22×Q8—32no—
288C22×Q8—92no—
289C22×Q8—98no—
290C22×Q8—188no—
291C23×C4—92no—
292C23×C4—92no—
293C23×C4—91no—
294C23×C4—91no—
295C23×C4—91no—
296C23×C4—91no—
297C23×C4—98no—
298C23×C4—91no—
299C23×C4—188no—
300C23×C4D3211yescharacteristic
301C22⋊Q8—316no—
302C22⋊Q8—916no—
303C22⋊Q8—916no—
304C22⋊Q8—916no—
305C2×C4⋊C4—34no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—916no—
308C2×C4⋊C4—98no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—94no—
311C2×C22⋊C4—34no—
312C2×C22⋊C4—916no—
313C2×C22⋊C4—94no—
314C23×C3—24no—
315C23×C3—24no—
316C23×C3—24no—
317C23×C3—24no—
318C23×C3—22no—
319C23×C3—21no—
320C23×C3—24no—
321C23×C3D3×Q818yescomplemented
322C23×C3C23×D314yes—
323C23×C3C23×D312yes—
324C22×D3—38no—
325C22×D3—38no—
326C22×D3—38no—
327C22×D3—34no—
328C22×D3—38no—
329C22×D3—332no—
330C22×D3—34no—
331C22×D3—64no—
332C22×D3—64no—
333C22×D3—64no—
334C22×D3—616no—
335C22×D3—64no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—616no—
339C22×D3—616no—
340C22×D3—664no—
341C22×D3—616no—
342C22×D3—64no—
343C22×D3—664no—
344C22×D3—616no—
345C22×D3—64no—
346C22×D3—64no—
347C22×D3—64no—
348C3×Q8—616no—
349C2×C3×C4—24no—
350C2×C3×C4—216no—
351C2×C3×C4—24no—
352C2×C3×C4—216no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—24no—
356C2×C3×C4—38no—
357C2×C3×C4—38no—
358C2×C3×C4—68no—
359C2×C3×C4—68no—
360C2×C3×C4D3×D418yes—
361C2×C3×C4C23×D314yes—
362C2×C3×C4C23×D314yes—
363C2×Dic3—28no—
364C2×Dic3—28no—
365C2×Dic3—38no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—616no—
372C2×Dic3—616no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3C23×D318yes—
376C2×Dic3C23×D318yes—
377C4×D3—332no—
378C4×D3—616no—
379C4×D3—632no—
380C4×D3—632no—
381C4×D3—616no—
382C4×D3—616no—
383C4×D3—616no—
384C4×D3—616no—
385C4×D3—616no—
386C4×D3—616no—
387Dic6—216no—
388Dic6—632no—
389C2×C32—24no—
390C2×C32C2×C22⋊Q814yescomplemented
391C2×C32C23×D411yescharacteristic
392C2×C32C23×Q811yescharacteristic
393C2×C32C22×#4111yescharacteristic
394C3⋊D3—24no—
395C3⋊D3C2×C22⋊Q818yescomplemented
396C24—91no—
397C24—94no—
398C24—91no—
399C24—98no—
400C24—184no—
401C24—184no—
402C24C2×D3211yescharacteristic
403C2×Q8—38no—
404C2×Q8—68no—
405C2×Q8—98no—
406C2×Q8—188no—
407C2×Q8—1832no—
408C22×C4—24no—
409C22×C4—34no—
410C22×C4—34no—
411C22×C4—98no—
412C22×C4—98no—
413C22×C4—91no—
414C22×C4—94no—
415C22×C4—98no—
416C22×C4—94no—
417C22×C4—91no—
418C22×C4—94no—
419C22×C4—94no—
420C22×C4—94no—
421C22×C4—184no—
422C22×C4—1832no—
423C22×C4—184no—
424C22×C4—188no—
425C22×C4—188no—
426C22×C4—184no—
427C22×C4—184no—
428C22×C4C2×D3214yes—
429C22×C4C2×D3211yescharacteristic
430C22×C4C2×D3211yescharacteristic
431C4⋊C4—316no—
432C4⋊C4—38no—
433C4⋊C4—98no—
434C4⋊C4—916no—
435C22⋊C4—316no—
436C22⋊C4—916no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—216no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—216no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—21no—
448C22×C3C2×D3×D414yes—
449C22×C3C2×D3×Q814yes—
450C22×C3C2×D3×Q818yescomplemented
451C22×C3D3×#4114yes—
452C22×C3C24×D312yes—
453C2×D3—38no—
454C2×D3—38no—
455C2×D3—38no—
456C2×D3—332no—
457C2×D3—38no—
458C2×D3—64no—
459C2×D3—616no—
460C2×D3—64no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—664no—
464C2×D3—64no—
465C2×D3—664no—
466C2×D3—64no—
467C2×D3—616no—
468C2×D3—64no—
469C2×D3—64no—
470C2×D3—616no—
471C3×C4—24no—
472C3×C4—24no—
473C3×C4—24no—
474C3×C4—68no—
475C3×C4—68no—
476C3×C4C2×D3×D418yes—
477Dic3—28no—
478Dic3—28no—
479Dic3—38no—
480Dic3—64no—
481Dic3—64no—
482Dic3—64no—
483C32C22×C22⋊Q811yescharacteristic, complemented, Sylow
484C23—22no—
485C23—22no—
486C23—94no—
487C23—94no—
488C23—94no—
489C23—92no—
490C23—94no—
491C23—916no—
492C23—92no—
493C23—188no—
494C23—188no—
495C23—1832no—
496C23—182no—
497C23—182no—
498C23#379714yescomplemented
499C23C22×D3212yes—
500C23C22×D3211yescharacteristic
501Q8—616no—
502Q8—1816no—
503C2×C4—22no—
504C2×C4—28no—
505C2×C4—38no—
506C2×C4—38no—
507C2×C4—68no—
508C2×C4—68no—
509C2×C4—94no—
510C2×C4—92no—
511C2×C4—916no—
512C2×C4—92no—
513C2×C4—188no—
514C2×C4—188no—
515C2×C4—1816no—
516C2×C4—1816no—
517C2×C4—188no—
518C2×C4—182no—
519C2×C4—188no—
520C2×C4#381114yes—
521C2×C4C22×D3212yes—
522C2×C4C22×D3212yes—
523C2×C3—28no—
524C2×C3—28no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—24no—
529C2×C3D3×C22⋊Q818yescomplemented
530C2×C3C22×D3×D412yes—
531C2×C3C22×D3×Q812yes—
532C2×C3C2×D3×#4112yes—
533D3—316no—
534D3—68no—
535D3—68no—
536D3—68no—
537C22—22no—
538C22—22no—
539C22—28no—
540C22—94no—
541C22—94no—
542C22—94no—
543C22—916no—
544C22—94no—
545C22—1832no—
546C22—182no—
547C22—182no—
548C22—188no—
549C22C2×#379712yes—
550C22C2×#379714yescomplemented
551C22#6430612yes—
552C22C2×#381112yes—
553C22C23×D3211yescharacteristic
554C4—22no—
555C4—68no—
556C4—68no—
557C4—94no—
558C4—182no—
559C4C2×#381114yes—
560C3—21no—
561C3C2×D3×C22⋊Q812yescomplemented
562C2—24no—
563C2—98no—
564C2—184no—
565C2#1059492514yesdirect product factor
566C2C22×#379711yescharacteristic
567C2C2×#6430611yescharacteristic
568C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenterC23×C4D32
hypocenterC32C22×C22⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3797C2semidirect
3. C2×C3×#924C2semidirect
4. C2×#63982C2semidirect
6. C2×#63900C2semidirect
7. #10594925C2direct (N × H)
8. C2×#63883C2semidirect
9. C2×#63871C2semidirect
10. C2×#63865C2semidirect
21. C22×C3×Dic6C22semidirect
22. C22×#627C22semidirect
26. C2×#3797C22semidirect
28. C2×C3×C4⋊Dic3C22semidirect
29. C3×#924C22semidirect
30. C2×C3×Dic3⋊C4C22semidirect
31. #63982C22semidirect
33. C2×#3724C22semidirect
34. C2×Dic3⋊Dic3C22semidirect
36. #63900C22semidirect
37. #63883C22semidirect
38. #63871C22semidirect
39. #63865C22semidirect
45. C2×#924D3semidirect
56. C23×C3⋊D3Q8semidirect
80. C2×C3×Dic6C23semidirect
82. C2×#627C23semidirect
89. C3×C4⋊Dic3C23semidirect
90. C3×Dic3⋊C4C23semidirect
91. #3724C23semidirect
92. Dic3⋊Dic3C23semidirect
119. C22×Dic6C2×D3semidirect
129. C2×C4⋊Dic3C2×D3semidirect
130. #924C2×D3semidirect
133. C2×Dic3⋊C4C2×D3semidirect
142. C23×C32C2×Q8semidirect
152. C22×C3⋊D3C2×Q8semidirect
153. C22×C3⋊D3C2×Q8semidirect
251. C2×Dic6C22×D3semidirect
259. C4⋊Dic3C22×D3semidirect
262. Dic3⋊C4C22×D3semidirect
268. C22×C32C22×Q8semidirect
275. C2×C3⋊D3C22⋊Q8semidirect
278. C2×C3⋊D3C22×Q8semidirect
321. C23×C3D3×Q8semidirect
390. C2×C32C2×C22⋊Q8semidirect
395. C3⋊D3C2×C22⋊Q8semidirect
450. C22×C3C2×D3×Q8semidirect
483. C32C22×C22⋊Q8semidirect
498. C23#3797semidirect
529. C2×C3D3×C22⋊Q8semidirect
550. C22C2×#3797semidirect
561. C3C2×D3×C22⋊Q8semidirect
565. C2#10594925direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C22×#37972
C2×C3×#9242
C2×#639822
C2×#639742
C2×#639002
#105949252
C2×#638832
C2×#638712
C2×#638652
C2×D3×C22⋊Q83