Finite Group Databasebeta

← C2×#10591610 #11874258

Subgroups — C2×#10591610 #11874258

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64156C211yesmaximal, characteristic, complemented
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C22×C3×#215C211yesmaximal, characteristic, complemented
4C2×#63863C211yesmaximal, characteristic, complemented
5C22×#3717C211yesmaximal, characteristic, complemented
6C22×#3714C211yesmaximal, characteristic
7#10591610C218yesmaximal, direct product factor
8C2×#63553C211yesmaximal, characteristic, complemented
9C2×#5191—31nomaximal
10C2×#5168—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64156—22no—
16#64156C2214yescomplemented
17C2×#3752—22no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#216—24no—
20C2×C3×#216C2214yescomplemented
21C2×C3×#215—24no—
22C2×C3×#215C2214yescomplemented
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—22no—
26#63863—22no—
27#63863C2214yescomplemented
28C2×#3717—24no—
29C2×#3717C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yes—
32#63553C2214yescomplemented
33C22×C3×Q16—31no—
34C22×C3×SD16—31no—
35C2×#947—31no—
36C2×#947—31no—
37C2×#947—31no—
38C2×#947—61no—
39C22×#216D311yescharacteristic, complemented
40C22×#215—31no—
41C22×#215D311yescharacteristic, complemented
42C2×#936—31no—
43C22×#213—31no—
44C22×D24—31no—
45C22×#204—31no—
46#5191—38no—
47#5168—38no—
48C2×C8×Dic3—31no—
49C2×C8×Dic3—31no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—22no—
54C2×C32×Q8—22no—
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3D412yes—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2312yes—
63C22×C3×Dic3—21no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—21no—
67C2×C3×D12C2312yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6C2312yes—
72#3752—28no—
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C3×#216—28no—
76C3×#215—28no—
77C2×C3×C3⋊C8D414yes—
78C2×C3×C3⋊C8D414yes—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81(C2×D3)⋊Dic3—28no—
82#3717—28no—
83#3714—28no—
84C2×#495—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8—31no—
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×D4—31no—
90C22×D12—31no—
91C22×D12—31no—
92C22×D12—61no—
93C22×D12C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C2×C3×Q16—34no—
96C2×C3×Q16—64no—
97C2×C3×SD16—34no—
98C2×C3×SD16—64no—
99C22×C3×C8—31no—
100C22×C3×C8—31no—
101C2×#217—62no—
102#947—34no—
103#947—34no—
104#947—34no—
105#947—64no—
106#947—62no—
107#947—62no—
108#947—62no—
109#947—64no—
110C2×#216—24no—
111C2×#216C2×D314yescomplemented
112C2×#215—24no—
113C2×#215—34no—
114C2×#215—64no—
115C2×#215C2×D314yescomplemented
116#936—34no—
117#936—62no—
118C2×#213—34no—
119C2×#213—64no—
120C2×(C2×D3)⋊C4—62no—
121C2×(C2×D3)⋊C4—62no—
122C2×(C2×D3)⋊C4—62no—
123C2×(C2×D3)⋊C4—64no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—61no—
127C22×C3⋊C8C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129C2×D24—34no—
130C2×D24—64no—
131C2×#204—34no—
132C2×#204—64no—
133C8×Dic3—34no—
134C8×Dic3—34no—
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—44no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—44no—
142C32×Q8—22no—
143C32×Q8—22no—
144C32×Q8—42no—
145C2×C32×C4—22no—
146C2×C32×C4—42no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—24no—
152C2×C3⋊Dic3C2×D414yes—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—42no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—42no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—42no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164C3×C3⋊C8C2×D414yes—
165C3×C3⋊C8C2×D414yes—
166C22×Q16—31no—
167C22×SD16—31no—
168C22×SD16—91no—
169C22×D8—91no—
170C2×#124—91no—
171C2×#124—91no—
172#495—98no—
173C2×C4×C8—91no—
174C24×C3—61no—
175C23×D3—21no—
176C23×D3—62no—
177C23×D3—61no—
178C23×D3—61no—
179C2×C3×Q8—22no—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—22no—
186C2×C3×Q8—22no—
187C2×C3×Q8—32no—
188C2×C3×Q8—42no—
189C2×C3×Q8—42no—
190C2×C3×Q8—61no—
191C2×C3×Q8—62no—
192C2×C3×Q8—62no—
193C2×C3×Q8C22×D312yes—
194C2×C3×Q8C22×D312yes—
195C2×C3×D4—32no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C2×C3×D4—62no—
199C22×C3×C4—22no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—61no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—21no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—62no—
210C2×D12—22no—
211C2×D12—22no—
212C2×D12—21no—
213C2×D12—32no—
214C2×D12—32no—
215C2×D12—62no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—62no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—122no—
224C2×D12—122no—
225C2×D12C22×D312yes—
226C2×Dic6—22no—
227C2×Dic6—22no—
228C2×Dic6—21no—
229C2×Dic6C22×D312yes—
230C3×Q16—68no—
231C3×SD16—68no—
232C2×C3×C8—34no—
233C2×C3×C8—34no—
234C2×C3×C8—32no—
235C2×C3×C8—32no—
236#217—68no—
237#216—28no—
238#215—28no—
239#215—68no—
240#213—68no—
241(C2×D3)⋊C4—68no—
242(C2×D3)⋊C4—68no—
243(C2×D3)⋊C4—68no—
244(C2×D3)⋊C4—616no—
245C4×Dic3—32no—
246C4×Dic3—32no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C2×C3⋊C8#6714yes—
252C2×C3⋊C8#6714yes—
253C2×C3⋊C8C22×D312yes—
254C2×C3⋊C8C22×D312yes—
255D24—68no—
256#204—68no—
257C22×C32#12712yes—
258C22×C32#13514yes—
259C22×C32C22×D411yescharacteristic
260C2×C3⋊D3—42no—
261C2×C3⋊D3—44no—
262C2×C3⋊D3—84no—
263C2×C3×D3—42no—
264C2×C3×D3—44no—
265C2×C3×D3—84no—
266C32×C4—42no—
267C32×C4#12712yes—
268C32×C4C22×D411yescharacteristic
269C32×C4C22×D411yescharacteristic
270C3⋊Dic3—24no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×Q8D3211yescharacteristic
274C22×D4—31no—
275C22×D4—91no—
276C2×Q16—34no—
277C2×Q16—64no—
278C2×SD16—34no—
279C2×SD16—64no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—94no—
283C2×D8—184no—
284C22×C8—31no—
285C22×C8—31no—
286#124—94no—
287#124—94no—
288#124—182no—
289#124—182no—
290C2×C22⋊C4—182no—
291C2×C22⋊C4—182no—
292C2×C42—91no—
293C4×C8—94no—
294C23×C3—21no—
295C23×C3—62no—
296C23×C3—124no—
297C23×C3—122no—
298C23×C3D3×D411yescharacteristic
299C23×C3D3×D411yescharacteristic
300C22×D3—22no—
301C22×D3—44no—
302C22×D3—42no—
303C22×D3—64no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—124no—
307C22×D3—128no—
308C22×D3—124no—
309C22×D3—124no—
310C22×D3—122no—
311C22×D3—122no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—42no—
317C3×Q8—42no—
318C3×Q8—44no—
319C3×Q8—42no—
320C3×Q8—42no—
321C3×Q8—62no—
322C3×Q8—62no—
323C3×Q8—122no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—122no—
327C2×C3×C4—24no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—44no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—62no—
338C2×C3×C4—122no—
339C2×C3×C4D3×D412yes—
340C2×C3×C4D3×D412yes—
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—42no—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—124no—
355D12—22no—
356D12—22no—
357D12—42no—
358D12—62no—
359D12—62no—
360D12—62no—
361D12—62no—
362D12—122no—
363D12—122no—
364D12—124no—
365D12—122no—
366D12—122no—
367Dic6—22no—
368Dic6—22no—
369Dic6—42no—
370C3×C8—34no—
371C3×C8—34no—
372C3⋊C8C2×#6714yes—
373C3⋊C8C2×#6714yes—
374C2×C32#49514yescomplemented
375C2×C32C2×#12711yescharacteristic
376C2×C32C2×#13512yes—
377C3⋊D3—82no—
378C3×D3—82no—
379C24—61no—
380C24—181no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—32no—
385C2×Q8—61no—
386C2×Q8—62no—
387C2×Q8—62no—
388C2×Q8C2×D3212yes—
389C2×D4—32no—
390C2×D4—62no—
391C2×D4—62no—
392C2×D4—61no—
393C2×D4—92no—
394C2×D4—182no—
395C2×D4—182no—
396C2×D4—181no—
397C22×C4—21no—
398C22×C4—61no—
399C22×C4—92no—
400C22×C4C2×D3211yescharacteristic
401Q16—68no—
402SD16—68no—
403SD16—188no—
404D8—188no—
405C2×C8—32no—
406C2×C8—32no—
407C2×C8—34no—
408C2×C8—34no—
409C22⋊C4—188no—
410C22⋊C4—188no—
411C42—92no—
412C42—92no—
413C22×C3—21no—
414C22×C3—24no—
415C22×C3—22no—
416C22×C3—124no—
417C22×C3—122no—
418C22×C3—244no—
419C22×C3#91614yes—
420C22×C3#91914yes—
421C22×C3#94012yes—
422C22×C3#94012yes—
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C2×D3×D411yescharacteristic
425C2×D3—44no—
426C2×D3—42no—
427C2×D3—84no—
428C2×D3—124no—
429C2×D3—128no—
430C2×D3—124no—
431C2×D3—124no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—248no—
435C2×D3—244no—
436C2×D3—244no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—44no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—122no—
444C3×C4#94012yes—
445C3×C4#94012yes—
446C3×C4C2×D3×D411yescharacteristic
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C22×#6711yescharacteristic
449C3×C4C22×#6711yescharacteristic
450Dic3—42no—
451Dic3—64no—
452Dic3—64no—
453Dic3—124no—
454C32C2×#49511yescharacteristic, complemented, Sylow
455C23—62no—
456C23—124no—
457C23—122no—
458C23—182no—
459C23—364no—
460C23—362no—
461C23#381111yescharacteristic
462Q8—22no—
463Q8—22no—
464Q8—42no—
465Q8—62no—
466Q8—62no—
467Q8—122no—
468D4—62no—
469D4—62no—
470D4—122no—
471D4—182no—
472D4—182no—
473D4—362no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—62no—
477C2×C4—94no—
478C2×C4—122no—
479C2×C4—184no—
480C2×C4D3×#6712yes—
481C2×C4D3×#6712yes—
482C2×C4#381111yescharacteristic
483C2×C4C22×D3211yescharacteristic
484C8—34no—
485C8—34no—
486C2×C3—22no—
487C2×C3—24no—
488C2×C3—21no—
489C2×C3—242no—
490C2×C3#516814yescomplemented
491C2×C3#519114yescomplemented
492C2×C3C2×#91612yes—
493C2×C3C2×#91912yes—
494C2×C3C2×#94011yescharacteristic
495C2×C3C2×#94011yescharacteristic
496D3—82no—
497D3—244no—
498D3—242no—
499D3—242no—
500C22—124no—
501C22—122no—
502C22—244no—
503C22—364no—
504C22—362no—
505C22—724no—
506C22#6395014yes—
507C22#6397912yes—
508C22C2×#381111yescharacteristic
509C4—42no—
510C4—122no—
511C4—184no—
512C4#6397912yes—
513C4C2×D3×#6711yescharacteristic
514C4C2×D3×#6711yescharacteristic
515C3—21no—
516C3C2×#516811yescharacteristic, complemented
517C3C2×#519111yescharacteristic, complemented
518C2—242no—
519C2—722no—
520C2#1059161014yesdirect product factor
521C2C2×#6395012yes—
522C2C2×#6397911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC22×Q8D32
hypocenterC32C2×#495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64156C2semidirect
2. C22×C3×#216C2semidirect
3. C22×C3×#215C2semidirect
4. C2×#63863C2semidirect
5. C22×#3717C2semidirect
7. #10591610C2direct (N × H)
8. C2×#63553C2semidirect
16. #64156C22semidirect
20. C2×C3×#216C22semidirect
22. C2×C3×#215C22semidirect
27. #63863C22semidirect
29. C2×#3717C22semidirect
32. #63553C22semidirect
39. C22×#216D3semidirect
41. C22×#215D3semidirect
111. C2×#216C2×D3semidirect
115. C2×#215C2×D3semidirect
374. C2×C32#495semidirect
454. C32C2×#495semidirect
490. C2×C3#5168semidirect
491. C2×C3#5191semidirect
516. C3C2×#5168semidirect
517. C3C2×#5191semidirect
520. C2#10591610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C22×C3×#2162
C22×C3×#2152
C2×#638632
C22×#37172
C22×#37142
#105916102
C2×#635532
C2×#51913
C2×#51683