Finite Group Databasebeta

← C2×#10591464 #11866916

Subgroups — C2×#10591464 #11866916

Order 1152.

1301 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
1C2×#64147C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×#63871C211yesmaximal, characteristic, complemented
4C22×#3712C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591464C218yesmaximal, direct product factor
7C2×#63575C211yesmaximal, characteristic, complemented
8C2×#63566C211yesmaximal, characteristic, complemented
9C2×#5174—31nomaximal
10C2×#4780—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#638—21no—
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3757—21no—
16#64147—22no—
17#64147C2214yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×#214—24no—
20C2×C3×#214C2214yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×#3722—21no—
26#63871—22no—
27#63871C2214yescomplemented
28C2×#3712—24no—
29C2×#3712C2214yescomplemented
30C3×#832C2214yescomplemented
31#63575C2214yescomplemented
32#63566C2214yescomplemented
33C22×C3×SD16—31no—
34C2×#946—31no—
35C2×#938—31no—
36C2×#938—31no—
37C2×#938—61no—
38C22×#214D311yescharacteristic, complemented
39C22×ΓL(1,𝔽25)—31no—
40C22×ΓL(1,𝔽25)—31no—
41C2×#897—31no—
42C2×C3×#102—31no—
43C2×#835—31no—
44C2×#832D311yescharacteristic, complemented
45#5174—38no—
46C2×#818—31no—
47C2×#816—31no—
48C2×#807—31no—
49#4780—38no—
50C24×C32—21no—
51C23×C3⋊D3D411yescharacteristic
52C2×C32×D4—22no—
53C2×C32×D4—21no—
54C2×C32×D4—22no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C2×#638—24no—
58C2×#638—44no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3D411yescharacteristic
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3D412yes—
64C2×C4×C3⋊D3C2312yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71#3757—24no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C3×#214—28no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8D414yescomplemented
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81Dic3⋊Dic3—24no—
82#3722—24no—
83#3712—28no—
84C2×#468—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×#67—61no—
90C22×#67—61no—
91C22×#67—62no—
92C22×C4×D3—31no—
93C22×C4×D3—31no—
94C22×C4×D3—61no—
95C22×Dic6C2×D311yescharacteristic
96C2×C3×SD16—34no—
97C2×C3×SD16—64no—
98C22×C3×C8—31no—
99C22×C3×C8—31no—
100C2×C3×C4⋊C4—31no—
101C2×#217—61no—
102C2×#217—61no—
103C2×#217—62no—
104#946—34no—
105#946—62no—
106#938—34no—
107#938—34no—
108#938—64no—
109#938—62no—
110#938—62no—
111#938—64no—
112C2×#214—24no—
113C2×#214C2×D314yescomplemented
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—61no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×Dic3⋊C4—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123C22×C3⋊C8C2×D311yescharacteristic
124C2×ΓL(1,𝔽25)—34no—
125C2×ΓL(1,𝔽25)—34no—
126C2×ΓL(1,𝔽25)—64no—
127C2×ΓL(1,𝔽25)—64no—
128#897—34no—
129#897—62no—
130C3×#102—34no—
131#835—34no—
132#832C2×D314yescomplemented
133#818—34no—
134#816—34no—
135#807—34no—
136C23×C32—22no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32—42no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3C2×D412yes—
145C32×D4—22no—
146C32×D4—22no—
147C32×D4—42no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152#638—48no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—42no—
156C2×C3⋊Dic3C2×D412yes—
157C4×C3⋊D3—24no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3—42no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8C2×D414yescomplemented
169C22×SD16—31no—
170C22×M16—91no—
171C2×C22⋊Q8—91no—
172C2×#121—91no—
173#468—98no—
174C2×#107—91no—
175C2×#103—91no—
176C2×#102—31no—
177C24×C3—22no—
178C24×C3—21no—
179C24×C3—21no—
180C23×D3—31no—
181C23×D3—31no—
182C23×D3—61no—
183C2×C3×Q8—32no—
184C2×C3×Q8—61no—
185C2×C3×Q8—62no—
186C2×C3×Q8—62no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—22no—
195C2×C3×D4—42no—
196C2×C3×D4—42no—
197C2×C3×D4C22×D312yes—
198C2×C3×D4C22×D312yes—
199C22×C3×C4—21no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67—64no—
205C2×#67—64no—
206C2×#67—68no—
207C2×#67—128no—
208C2×#67—124no—
209C2×#67—124no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—61no—
215C22×Dic3—62no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C2×C4×D3—32no—
219C2×C4×D3—32no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—122no—
229C2×C4×D3—122no—
230C2×Dic6—22no—
231C2×Dic6—22no—
232C2×Dic6—21no—
233C2×Dic6C22×D312yes—
234C3×SD16—68no—
235C2×C3×C8—34no—
236C2×C3×C8—32no—
237C2×C3×C8—32no—
238C2×C3×C8—62no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—61no—
241#217—64no—
242#217—64no—
243#217—68no—
244#214—28no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—21no—
248C4⋊Dic3—32no—
249C4⋊Dic3—32no—
250C4⋊Dic3—62no—
251C4⋊Dic3—64no—
252C4⋊Dic3—62no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4—64no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8#6714yescomplemented
259C2×C3⋊C8C22×D312yes—
260C2×C3⋊C8C22×D312yes—
261ΓL(1,𝔽25)—68no—
262ΓL(1,𝔽25)—68no—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32—84no—
267C22×C32#12112yes—
268C22×C32AGL(1,ℤ/8)12yes—
269C22×C32#13712yes—
270C22×C32C22×D411yescharacteristic
271C2×C3⋊D3—22no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—44no—
275C32×C4#12112yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C2×#4111yescharacteristic
278C3⋊Dic3—22no—
279C3⋊Dic3—42no—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C22×Q8—31no—
283C22×D4—181no—
284C22×D4D3211yescharacteristic
285C23×C4—91no—
286C2×SD16—34no—
287C2×SD16—64no—
288C2×M16—94no—
289C2×M16—184no—
290C22×C8—31no—
291C22×C8—31no—
292C22⋊Q8—94no—
293C22⋊Q8—182no—
294#121—94no—
295#121—182no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—181no—
299C2×C22⋊C4—181no—
300C2×C22⋊C4—181no—
301#107—94no—
302#103—94no—
303#102—34no—
304C23×C3—24no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—21no—
308C23×C3—44no—
309C23×C3—44no—
310C23×C3—44no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3D3×D411yescharacteristic
318C23×C3D3×D411yescharacteristic
319C22×D3—32no—
320C22×D3—32no—
321C22×D3—62no—
322C22×D3—64no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—122no—
330C22×D3—122no—
331C3×Q8—62no—
332C3×Q8—62no—
333C3×Q8—122no—
334C3×D4—22no—
335C3×D4—22no—
336C3×D4—22no—
337C3×D4—22no—
338C3×D4—42no—
339C3×D4—42no—
340C3×D4—44no—
341C3×D4—42no—
342C3×D4—42no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—122no—
350C2×C3×C4—122no—
351C2×C3×C4#23512yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4#23712yes—
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—1216no—
360#67—128no—
361#67—128no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—42no—
367C2×Dic3—42no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—122no—
375C2×Dic3—124no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C4×D3—64no—
379C4×D3—64no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—122no—
385C4×D3—122no—
386C4×D3—124no—
387Dic6—22no—
388Dic6—22no—
389Dic6—42no—
390C3×C8—34no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8C2×#6714yescomplemented
394C2×C32—82no—
395C2×C32#46814yescomplemented
396C2×C32C2×#12111yescharacteristic
397C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
398C2×C32C2×#13711yescharacteristic
399C3⋊D3—42no—
400C24—21no—
401C24—91no—
402C2×Q8—32no—
403C2×Q8—61no—
404C2×Q8—62no—
405C2×Q8—62no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—184no—
410C2×D4—364no—
411C2×D4C2×D3212yes—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—91no—
415C22×C4—92no—
416C22×C4—92no—
417C22×C4—182no—
418C22×C4—182no—
419C22×C4—181no—
420C22×C4C2×D3211yescharacteristic
421SD16—68no—
422M16—188no—
423C2×C8—32no—
424C2×C8—34no—
425C2×C8—32no—
426C2×C8—62no—
427C4⋊C4—32no—
428C4⋊C4—61no—
429C4⋊C4—92no—
430C4⋊C4—184no—
431C4⋊C4—181no—
432C22⋊C4—184no—
433C22⋊C4—184no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—44no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—88no—
448C22×C3—84no—
449C22×C3—84no—
450C22×C3#88412yes—
451C22×C3#91112yes—
452C22×C3#91412yes—
453C22×C3#91512yes—
454C22×C3#91512yes—
455C22×C3#93812yes—
456C22×C3C2×D3×D411yescharacteristic
457C22×C3C2×D3×D411yescharacteristic
458C2×D3—64no—
459C2×D3—62no—
460C2×D3—62no—
461C2×D3—62no—
462C2×D3—62no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—128no—
468C2×D3—124no—
469C2×D3—124no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—122no—
474C3×C4—122no—
475C3×C4#88412yes—
476C3×C4#93812yes—
477C3×C4C2×#23511yescharacteristic
478C3×C4C2×D3×D411yescharacteristic
479C3×C4C2×#23711yescharacteristic
480C3×C4C22×#6711yescharacteristic
481Dic3—42no—
482Dic3—42no—
483Dic3—62no—
484Dic3—62no—
485Dic3—122no—
486Dic3—124no—
487Dic3—122no—
488Dic3—122no—
489C32C2×#46811yescharacteristic, complemented, Sylow
490C23—22no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—92no—
495C23—182no—
496C23—182no—
497C23—182no—
498C23#381111yescharacteristic
499Q8—62no—
500Q8—62no—
501Q8—122no—
502D4—22no—
503D4—22no—
504D4—42no—
505D4—368no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—92no—
509C2×C4—122no—
510C2×C4—122no—
511C2×C4—182no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—184no—
515C2×C4—182no—
516C2×C4—362no—
517C2×C4#380412yes—
518C2×C4D3×#6712yes—
519C2×C4#381111yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—34no—
522C8—62no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—24no—
527C2×C3—84no—
528C2×C3—82no—
529C2×C3—82no—
530C2×C3#478014yescomplemented
531C2×C3#517414yescomplemented
532C2×C3C2×#88411yescharacteristic
533C2×C3C2×#91111yescharacteristic
534C2×C3C2×#91411yescharacteristic
535C2×C3C2×#91511yescharacteristic
536C2×C3C2×#91511yescharacteristic
537C2×C3C2×#93811yescharacteristic
538D3—124no—
539D3—122no—
540D3—122no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—84no—
545C22—182no—
546C22—182no—
547C22—182no—
548C22—364no—
549C22#6393112yes—
550C22#6393712yes—
551C22#6395812yes—
552C22C2×#381111yescharacteristic
553C4—122no—
554C4—122no—
555C4—182no—
556C4—362no—
557C4#6395812yes—
558C4C2×#380411yescharacteristic
559C4C2×D3×#6711yescharacteristic
560C3—21no—
561C3C2×#478011yescharacteristic, complemented
562C3C2×#517411yescharacteristic, complemented
563C2—82no—
564C2—362no—
565C2#1059146414yesdirect product factor
566C2C2×#6393111yescharacteristic
567C2C2×#6393711yescharacteristic
568C2C2×#6395811yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×#64147C2
hypercenterC22×D4D32
hypocenterC32C2×#468
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C2×#63871C2semidirect
4. C22×#3712C2semidirect
5. C2×C3×#832C2semidirect
6. #10591464C2direct (N × H)
7. C2×#63575C2semidirect
8. C2×#63566C2semidirect
20. C2×C3×#214C22semidirect
27. #63871C22semidirect
29. C2×#3712C22semidirect
30. C3×#832C22semidirect
31. #63575C22semidirect
32. #63566C22semidirect
38. C22×#214D3semidirect
44. C2×#832D3semidirect
78. C2×C3×C3⋊C8D4semidirect
113. C2×#214C2×D3semidirect
132. #832C2×D3semidirect
168. C3×C3⋊C8C2×D4semidirect
258. C2×C3⋊C8#67semidirect
393. C3⋊C8C2×#67semidirect
395. C2×C32#468semidirect
489. C32C2×#468semidirect
530. C2×C3#4780semidirect
531. C2×C3#5174semidirect
561. C3C2×#4780semidirect
562. C3C2×#5174semidirect
565. C2#10591464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641472
C22×C3×#2142
C2×#638712
C22×#37122
C2×C3×#8322
#105914642
C2×#635752
C2×#635662
C2×#51743
C2×#47803