Finite Group Databasebeta

← C2×#10594072 #11902678

Subgroups — C2×#10594072 #11902678

Order 1152.

3349 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#627C211yesmaximal, characteristic, complemented
2C22×#3797C211yesmaximal, characteristic, complemented
3C2×#64090C211yesmaximal, characteristic
4C2×C3×#878C212yesmaximal, complemented
5C2×#63982C211yesmaximal, characteristic, complemented
6C2×#63952C212yesmaximal
7C2×#63919C211yesmaximal, characteristic, complemented
8C2×#63895C212yesmaximal, complemented
9C2×#63865C211yesmaximal, characteristic, complemented
10C2×#63839C212yesmaximal, complemented
11C2×#63838C211yesmaximal, characteristic, complemented
12#10594072C2116yesmaximal, direct product factor
13C2×#5632—32nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C22×C3×Dic6C2212yes—
19C22×#627—28no—
20C22×#627C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×#627C2212yes—
23C22×#627C2211yescharacteristic
24C22×#627C2218yescomplemented
25C22×#624C2212yes—
26C2×#3797—28no—
27C2×#3797C2218yescomplemented
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32#64090C2218yes—
33C2×C3×#217C2212yes—
34C2×C3×C4⋊Dic3C2212yes—
35C2×C3×Dic3⋊C4C2212yes—
36C2×C3×Dic3⋊C4C2212yes—
37C3×#878C22116yescomplemented
38#63982C2218yescomplemented
39C2×#3724C2211yescharacteristic
40C2×#3724C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42C2×#3722C2212yes—
43C2×Dic32C2212yes—
44#63952C22116yes—
45#63919C2218yescomplemented
46#63895C22116yescomplemented
47#63865C2218yescomplemented
48#63839C22116yescomplemented
49#63838C2218yescomplemented
50C22×D3×Q8—32no—
51C23×Dic6—32no—
52C2×C3×C22⋊Q8—32no—
53C2×#944—32no—
54C2×C4×#67—32no—
55#5632—332no—
56C2×#897—32no—
57C2×#896—32no—
58C2×#896—32no—
59C2×#888—32no—
60C2×#888—32no—
61C2×#887—32no—
62C2×#67⋊C4—32no—
63C2×#67⋊C4—32no—
64C2×#67⋊C4—61no—
65C2×#878—32no—
66C2×#878D312yescomplemented
67C24×C32C2311yescharacteristic
68C23×C3⋊D3C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×#638Q818yescomplemented
72C2×#638C2314yes—
73C22×C3⋊Dic3—24no—
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2314yes—
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3C2314yes—
80C22×C3×Dic3—28no—
81C22×C3×Dic3C2318yes—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C2×C3×Dic6—28no—
87C2×C3×Dic6C2318yes—
88C2×#627—24no—
89C2×#627—24no—
90C2×#627—28no—
91C2×#627—232no—
92C2×#627D418yescomplemented
93C2×#627C2314yes—
94C2×#627C2318yes—
95C2×#627C2314yes—
96C2×#627C2314yes—
97C2×#624—28no—
98C2×#624C2318yes—
99#3797—232no—
100C32×C22⋊C4C2314yes—
101#3752C2314yes—
102#3750C2314yes—
103C4×C3⋊Dic3C2314yes—
104C3×#217C2318yes—
105C3×C4⋊Dic3C2318yes—
106C3×Dic3⋊C4C2318yes—
107C3×Dic3⋊C4C2318yes—
108#3724C2314yes—
109#3724C2318yes—
110Dic3⋊Dic3C2318yes—
111#3722C2318yes—
112Dic32C2318yes—
113C2×D4×Q8—91noSylow
114C22×C3×Q8—32no—
115C23×C3×C4—32no—
116C22×#67—32no—
117C22×#67—61no—
118C23×Dic3—32no—
119C23×Dic3—61no—
120C23×Dic3C2×D312yes—
121C2×D3×Q8—316no—
122C2×D3×Q8—616no—
123C22×C4×D3—32no—
124C22×C4×D3—32no—
125C22×C4×D3—32no—
126C22×C4×D3—61no—
127C22×Dic6—32no—
128C22×Dic6—316no—
129C22×Dic6—32no—
130C22×Dic6—32no—
131C22×Dic6—32no—
132C22×Dic6—32no—
133C22×Dic6—616no—
134C22×Dic6C2×D312yes—
135C3×C22⋊Q8—316no—
136C2×C3×C4⋊C4—32no—
137C2×C3×C4⋊C4—32no—
138C2×C3×C4⋊C4—32no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C22⋊C4C2×D312yes—
142C2×#217C2×D312yes—
143#944—316no—
144C4×#67—316no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—61no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3C2×D312yes—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—61no—
157C2×Dic3⋊C4C2×D312yes—
158C2×Dic3⋊C4C2×D312yes—
159C2×C4×Dic3—32no—
160C2×C4×Dic3—32no—
161C2×C4×Dic3—32no—
162C2×C4×Dic3—61no—
163#897—316no—
164#896—316no—
165#896—316no—
166#888—316no—
167#888—316no—
168#887—316no—
169#67⋊C4—316no—
170#67⋊C4—316no—
171#67⋊C4—68no—
172#878—316no—
173#878C2×D3116yescomplemented
174C23×C32—22no—
175C23×C32—22no—
176C23×C32C2×Q814yescomplemented
177C23×C32C2412yes—
178C23×C32C2411yescharacteristic
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3C2×Q814yescomplemented
182C22×C3⋊D3C2412yes—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4C2412yes—
186C2×C32×C4C2412yes—
187#638C2×Q8116yescomplemented
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—28no—
190C2×C3⋊Dic3C2×D414yes—
191C2×C3⋊Dic3C2×Q814yescomplemented
192C2×C3⋊Dic3C2412yes—
193C2×C3⋊Dic3C2412yes—
194C2×C3⋊Dic3C2412yes—
195C4×C3⋊D3—28no—
196C2×C3×Dic3—24no—
197C2×C3×Dic3—24no—
198C2×C3×Dic3—24no—
199C2×C3×Dic3—216no—
200C2×C3×Dic3C2×D418yes—
201C2×C3×Dic3C2414yes—
202C2×C3×Dic3C2414yes—
203C2×C3×Dic3C2414yes—
204C2×C3×Dic3C2414yes—
205C3×Dic6—216no—
206#627—28no—
207#627—28no—
208#627—216no—
209#627C2×D4116yescomplemented
210#624—216no—
211C23×Q8—91no—
212C23×Q8—91no—
213D4×Q8—916no—
214C2×C4⋊Q8—91no—
215C2×C4⋊Q8—92no—
216C2×C22⋊Q8—32no—
217C2×C22⋊Q8—91no—
218C2×C22⋊Q8—91no—
219C2×C22⋊Q8—92no—
220C2×C4×Q8—91no—
221C2×C4×D4—92no—
222C2×C4×D4—91no—
223C24×C3—21no—
224C24×C3C22×D312yes—
225C23×D3—32no—
226C23×D3—61no—
227C2×C3×Q8—38no—
228C2×C3×Q8—68no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—32no—
234C22×C3×C4—32no—
235C22×C3×C4—38no—
236C22×C3×C4—68no—
237C22×C3×C4C22×D312yes—
238C22×C3×C4C22×D312yes—
239C2×#67—316no—
240C2×#67—38no—
241C2×#67—64no—
242C2×#67—68no—
243C22×Dic3—28no—
244C22×Dic3—32no—
245C22×Dic3—32no—
246C22×Dic3—38no—
247C22×Dic3—32no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—64no—
251C22×Dic3—61no—
252C22×Dic3—68no—
253C22×Dic3—124no—
254C22×Dic3C22×D318yes—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D312yes—
259D3×Q8—664no—
260C2×C4×D3—38no—
261C2×C4×D3—38no—
262C2×C4×D3—38no—
263C2×C4×D3—64no—
264C2×C4×D3—68no—
265C2×C4×D3—68no—
266C2×C4×D3—68no—
267C2×C4×D3—124no—
268C2×Dic6—28no—
269C2×Dic6—316no—
270C2×Dic6—38no—
271C2×Dic6—38no—
272C2×Dic6—38no—
273C2×Dic6—38no—
274C2×Dic6—38no—
275C2×Dic6—664no—
276C2×Dic6—68no—
277C2×Dic6—68no—
278C2×Dic6—68no—
279C2×Dic6—68no—
280C2×Dic6C22×D318yes—
281C3×C4⋊C4—38no—
282C3×C4⋊C4—38no—
283C3×C4⋊C4—38no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—38no—
286C3×C22⋊C4C22×D318yes—
287#217C22×D318yes—
288(C2×D3)⋊C4—38no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—38no—
291(C2×D3)⋊C4—64no—
292C4⋊Dic3—38no—
293C4⋊Dic3C22×D318yes—
294Dic3⋊C4—38no—
295Dic3⋊C4—38no—
296Dic3⋊C4—38no—
297Dic3⋊C4—38no—
298Dic3⋊C4—38no—
299Dic3⋊C4—64no—
300Dic3⋊C4C22×D318yes—
301Dic3⋊C4C22×D318yes—
302C4×Dic3—38no—
303C4×Dic3—38no—
304C4×Dic3—38no—
305C4×Dic3—64no—
306C22×C32—28no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32C22×D412yes—
310C22×C32C22×Q812yes—
311C22×C32C22×Q814yescomplemented
312C22×C322−1+412yes—
313C22×C32C2511yescharacteristic
314C2×C3⋊D3—28no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3—22no—
317C2×C3⋊D3C22×Q814yescomplemented
318C32×C4—22no—
319C32×C4—22no—
320C3⋊Dic3—22no—
321C3⋊Dic3C22×D414yes—
322C3⋊Dic3C22×Q814yescomplemented
323C3×Dic3—24no—
324C3×Dic3—24no—
325C3×Dic3—24no—
326C3×Dic3C22×D418yes—
327C22×Q8—32no—
328C22×Q8—91no—
329C22×Q8—92no—
330C22×Q8—91no—
331C22×Q8—91no—
332C22×Q8—98no—
333C22×Q8—98no—
334C22×Q8—188no—
335C22×Q8—188no—
336C22×D4—91no—
337C23×C4—32no—
338C23×C4—92no—
339C23×C4—91no—
340C23×C4—91no—
341C4⋊Q8—98no—
342C4⋊Q8—916no—
343C22⋊Q8—316no—
344C22⋊Q8—98no—
345C22⋊Q8—98no—
346C22⋊Q8—916no—
347C4×Q8—98no—
348C4×D4—916no—
349C4×D4—98no—
350C2×C4⋊C4—32no—
351C2×C4⋊C4—32no—
352C2×C4⋊C4—32no—
353C2×C4⋊C4—92no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—92no—
356C2×C4⋊C4—91no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—92no—
359C2×C22⋊C4—91no—
360C2×C22⋊C4D3211yescharacteristic
361C2×C42—92no—
362C2×C42—91no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—22no—
366C23×C3—21no—
367C23×C3—24no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3D3×Q818yescomplemented
371C23×C3C23×D314yes—
372C23×C3C23×D312yes—
373C22×D3—38no—
374C22×D3—34no—
375C22×D3—64no—
376C22×D3—62no—
377C22×D3—64no—
378C22×D3—64no—
379C22×D3—122no—
380C22×D3—122no—
381C3×Q8—616no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—38no—
387C2×C3×C4—34no—
388C2×C3×C4—34no—
389C2×C3×C4—34no—
390C2×C3×C4—34no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—616no—
394C2×C3×C4—64no—
395C2×C3×C4—64no—
396C2×C3×C4—64no—
397C2×C3×C4C23×D314yes—
398C2×C3×C4C23×D314yes—
399#67—332no—
400#67—616no—
401C2×Dic3—24no—
402C2×Dic3—24no—
403C2×Dic3—24no—
404C2×Dic3—216no—
405C2×Dic3—38no—
406C2×Dic3—38no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—34no—
410C2×Dic3—64no—
411C2×Dic3—64no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—616no—
416C2×Dic3—64no—
417C2×Dic3—128no—
418C2×Dic3—122no—
419C2×Dic3D3×D418yes—
420C2×Dic3C23×D314yes—
421C2×Dic3C23×D314yes—
422C2×Dic3C23×D314yes—
423C2×Dic3C23×D314yes—
424C4×D3—616no—
425C4×D3—616no—
426C4×D3—616no—
427C4×D3—128no—
428Dic6—216no—
429Dic6—332no—
430Dic6—616no—
431Dic6—616no—
432Dic6—616no—
433Dic6—616no—
434C2×C32—24no—
435C2×C32D4×Q814yescomplemented
436C2×C32C23×D411yescharacteristic
437C2×C32C23×Q811yescharacteristic
438C2×C32C2×2−1+411yescharacteristic
439C3⋊D3—24no—
440C24—91no—
441C24C2×D3211yescharacteristic
442C2×Q8—38no—
443C2×Q8—68no—
444C2×Q8—94no—
445C2×Q8—98no—
446C2×Q8—98no—
447C2×Q8—94no—
448C2×Q8—94no—
449C2×Q8—188no—
450C2×Q8—184no—
451C2×Q8—184no—
452C2×Q8—1832no—
453C2×Q8—1832no—
454C2×D4—94no—
455C2×D4—98no—
456C22×C4—32no—
457C22×C4—38no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—68no—
462C22×C4—98no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—94no—
466C22×C4—91no—
467C22×C4—94no—
468C22×C4—184no—
469C22×C4—188no—
470C22×C4—184no—
471C22×C4C2×D3211yescharacteristic
472C22×C4C2×D3211yescharacteristic
473C4⋊C4—38no—
474C4⋊C4—38no—
475C4⋊C4—38no—
476C4⋊C4—98no—
477C4⋊C4—94no—
478C4⋊C4—98no—
479C4⋊C4—94no—
480C22⋊C4—38no—
481C22⋊C4—98no—
482C22⋊C4—94no—
483C22⋊C4C2×D3214yes—
484C42—98no—
485C42—94no—
486C22×C3—216no—
487C22×C3—24no—
488C22×C3—24no—
489C22×C3—22no—
490C22×C3—24no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—42no—
495C22×C3—48no—
496C22×C3—42no—
497C22×C3C2×D3×D414yes—
498C22×C3C2×D3×Q814yes—
499C22×C3C2×D3×Q818yescomplemented
500C22×C3#101014yes—
501C22×C3C24×D312yes—
502C2×D3—38no—
503C2×D3—64no—
504C2×D3—616no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—122no—
508C2×D3—128no—
509C2×D3—122no—
510C3×C4—24no—
511C3×C4—24no—
512C3×C4—38no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—64no—
516C3×C4—64no—
517C3×C4—64no—
518Dic3—24no—
519Dic3—24no—
520Dic3—24no—
521Dic3—38no—
522Dic3—38no—
523Dic3—64no—
524Dic3—64no—
525Dic3—64no—
526Dic3—122no—
527Dic3C2×D3×D418yes—
528C32C2×D4×Q811yescharacteristic, complemented, Sylow
529C23—22no—
530C23—22no—
531C23—94no—
532C23—92no—
533C23—182no—
534C23—182no—
535C23#379714yescomplemented
536C23C22×D3212yes—
537C23C22×D3211yescharacteristic
538Q8—616no—
539Q8—916no—
540Q8—1816no—
541Q8—188no—
542Q8—188no—
543D4—916no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—38no—
547C2×C4—34no—
548C2×C4—34no—
549C2×C4—34no—
550C2×C4—34no—
551C2×C4—616no—
552C2×C4—64no—
553C2×C4—64no—
554C2×C4—64no—
555C2×C4—94no—
556C2×C4—94no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—188no—
561C2×C4—1816no—
562C2×C4—188no—
563C2×C4—182no—
564C2×C4C22×D3212yes—
565C2×C4C22×D3212yes—
566C2×C3—28no—
567C2×C3—24no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—44no—
572C2×C3#563218yescomplemented
573C2×C3C22×D3×D412yes—
574C2×C3C22×D3×Q812yes—
575C2×C3C2×#101012yes—
576D3—68no—
577D3—124no—
578C22—28no—
579C22—22no—
580C22—22no—
581C22—94no—
582C22—188no—
583C22—182no—
584C22—182no—
585C22C2×#379712yes—
586C22C2×#379714yescomplemented
587C22#6430912yes—
588C22D32×D412yes—
589C22C23×D3211yescharacteristic
590C4—22no—
591C4—22no—
592C4—38no—
593C4—64no—
594C4—64no—
595C4—64no—
596C4—94no—
597C4—94no—
598C4—182no—
599C3—21no—
600C3C2×#563212yescomplemented
601C2—24no—
602C2—184no—
603C2#1059407214yesdirect product factor
604C2C22×#379711yescharacteristic
605C2C2×#6430911yescharacteristic
606C2C2×D32×D411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#627C2semidirect
2. C22×#3797C2semidirect
4. C2×C3×#878C2semidirect
5. C2×#63982C2semidirect
7. C2×#63919C2semidirect
8. C2×#63895C2semidirect
9. C2×#63865C2semidirect
10. C2×#63839C2semidirect
11. C2×#63838C2semidirect
12. #10594072C2direct (N × H)
24. C22×#627C22semidirect
27. C2×#3797C22semidirect
37. C3×#878C22semidirect
38. #63982C22semidirect
45. #63919C22semidirect
46. #63895C22semidirect
47. #63865C22semidirect
48. #63839C22semidirect
49. #63838C22semidirect
66. C2×#878D3semidirect
71. C2×#638Q8semidirect
92. C2×#627D4semidirect
173. #878C2×D3semidirect
176. C23×C32C2×Q8semidirect
181. C22×C3⋊D3C2×Q8semidirect
187. #638C2×Q8semidirect
191. C2×C3⋊Dic3C2×Q8semidirect
209. #627C2×D4semidirect
311. C22×C32C22×Q8semidirect
317. C2×C3⋊D3C22×Q8semidirect
322. C3⋊Dic3C22×Q8semidirect
370. C23×C3D3×Q8semidirect
435. C2×C32D4×Q8semidirect
499. C22×C3C2×D3×Q8semidirect
528. C32C2×D4×Q8semidirect
535. C23#3797semidirect
572. C2×C3#5632semidirect
586. C22C2×#3797semidirect
600. C3C2×#5632semidirect
603. C2#10594072direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6272
C22×#37972
C2×#640902
C2×C3×#8782
C2×#639822
C2×#639522
C2×#639192
C2×#638952
C2×#638652
C2×#638392
C2×#638382
#105940722
C2×#56323