Finite Group Databasebeta

← C2×#10594033 #11901923

Subgroups — C2×#10594033 #11901923

Order 1152.

2325 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C2×C3×#878C212yesmaximal
3C22×#3724C211yesmaximal, characteristic
4C2×#63964C212yesmaximal
5C2×#63957C211yesmaximal, characteristic
6C2×#63919C211yesmaximal, characteristic, complemented
7C2×#63873C211yesmaximal, characteristic, complemented
8C2×#63870C211yesmaximal, characteristic, complemented
9C2×#63870C211yesmaximal, characteristic, complemented
10C2×#63847C212yesmaximal, complemented
11C2×#63839C212yesmaximal, complemented
12#10594033C2116yesmaximal, direct product factor
13C2×#5623—32nomaximal
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C22×C3×Dic6C2212yes—
17C22×#627C2212yes—
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24#64086C2218yes—
25C2×C3×#217C2212yes—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C3×#878C22116yes—
30C2×#3724C2212yes—
31C2×#3724C2212yes—
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2218yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39#63964C22116yes—
40#63957C2218yes—
41C2×Dic32C2212yes—
42#63919C2218yescomplemented
43#63873C2218yescomplemented
44#63870C2218yescomplemented
45#63870C2218yescomplemented
46#63847C22116yescomplemented
47#63839C22116yescomplemented
48C2×C3×C22⋊Q8—32no—
49C2×#944—32no—
50C2×#944—32no—
51C2×#924—32no—
52C22×Dic3⋊C4—32no—
53#5623—332no—
54C2×#889—32no—
55C2×#889—32no—
56C2×#889—32no—
57C2×#889—32no—
58C2×#888—32no—
59C2×#888—32no—
60C2×#878—32no—
61C2×#878D312yes—
62C2×#877—32no—
63C2×#877—32no—
64C2×#877—61no—
65C24×C32C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3Q818yescomplemented
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2314yes—
74C22×C3×Dic3—44no—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2318yes—
80C2×C3×Dic6—44no—
81C2×C3×Dic6C2318yes—
82C2×#627—44no—
83C2×#627C2318yes—
84C32×C22⋊C4C2314yes—
85#3757C2314yes—
86#3750C2314yes—
87#3750C2314yes—
88C4×C3⋊Dic3C2314yes—
89C4×C3⋊Dic3C2314yes—
90C3×#217C2318yes—
91C3×C4⋊Dic3C2318yes—
92C3×Dic3⋊C4C2318yes—
93C3×Dic3⋊C4C2318yes—
94#3724C2318yes—
95#3724C2318yes—
96#3724C2314yes—
97#3724C2314yes—
98#3724C2314yes—
99#3724C2314yes—
100Dic3⋊Dic3C2318yes—
101Dic3⋊Dic3C2318yes—
102Dic32C2318yes—
103C2×#544—91noSylow
104C22×C3×Q8—32no—
105C23×C3×C4—32no—
106C23×Dic3—32no—
107C23×Dic3—61no—
108C23×Dic3C2×D312yes—
109C22×Dic6—32no—
110C22×Dic6—32no—
111C22×Dic6C2×D312yes—
112C3×C22⋊Q8—316no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4C2×D312yes—
119C2×#217—32no—
120C2×#217—61no—
121C2×#217C2×D312yes—
122#944—316no—
123#944—316no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3C2×D312yes—
127#924—316no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—316no—
141C2×Dic3⋊C4—61no—
142C2×Dic3⋊C4—61no—
143C2×Dic3⋊C4C2×D312yes—
144C2×Dic3⋊C4C2×D312yes—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—61no—
150C2×C4×Dic3—61no—
151#889—316no—
152#889—316no—
153#889—316no—
154#889—316no—
155#888—316no—
156#888—316no—
157#878—316no—
158#878C2×D3116yes—
159#877—316no—
160#877—316no—
161#877—68no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32C2×Q814yes—
165C23×C32C2412yes—
166C23×C32C2411yescharacteristic
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4C2412yes—
170C2×C32×C4C2412yes—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C2×Q814yes—
174C2×C3⋊Dic3C2×Q814yes—
175C2×C3⋊Dic3C2×Q8116yescomplemented
176C2×C3⋊Dic3C2412yes—
177C2×C3⋊Dic3C2412yes—
178C2×C3⋊Dic3C2412yes—
179C2×C3⋊Dic3C2412yes—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—48no—
185C2×C3×Dic3C2414yes—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C2×C3×Dic3C2414yes—
189C3×Dic6—48no—
190#627—48no—
191#544—916no—
192C2×C4⋊Q8—91no—
193C2×C4⋊Q8—92no—
194C2×C4⋊Q8—91no—
195C2×#125—92no—
196C2×#125—91no—
197C2×#125—91no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—92no—
200C2×#117—91no—
201C2×#117—91no—
202C22×C4⋊C4—91no—
203C24×C3—21no—
204C24×C3C22×D312yes—
205C2×C3×Q8—38no—
206C2×C3×Q8—124no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—38no—
214C22×C3×C4—124no—
215C22×C3×C4C22×D312yes—
216C22×C3×C4C22×D312yes—
217C22×Dic3—316no—
218C22×Dic3—38no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—32no—
223C22×Dic3—44no—
224C22×Dic3—64no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—68no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D318yes—
235C2×Dic6—38no—
236C2×Dic6—38no—
237C2×Dic6—44no—
238C2×Dic6—124no—
239C2×Dic6—124no—
240C2×Dic6C22×D318yes—
241C3×C4⋊C4—38no—
242C3×C4⋊C4—38no—
243C3×C4⋊C4—38no—
244C3×C22⋊C4—24no—
245C3×C22⋊C4—38no—
246C3×C22⋊C4C22×D318yes—
247#217—38no—
248#217—64no—
249#217C22×D318yes—
250C4⋊Dic3—38no—
251C4⋊Dic3—38no—
252C4⋊Dic3C22×D318yes—
253Dic3⋊C4—38no—
254Dic3⋊C4—38no—
255Dic3⋊C4—38no—
256Dic3⋊C4—38no—
257Dic3⋊C4—38no—
258Dic3⋊C4—38no—
259Dic3⋊C4—38no—
260Dic3⋊C4—38no—
261Dic3⋊C4—38no—
262Dic3⋊C4—38no—
263Dic3⋊C4—38no—
264Dic3⋊C4—38no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4C22×D318yes—
268Dic3⋊C4C22×D318yes—
269C4×Dic3—38no—
270C4×Dic3—38no—
271C4×Dic3—38no—
272C4×Dic3—38no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C22×C32—28no—
276C22×C32—22no—
277C22×C32—22no—
278C22×C32C22×Q814yes—
279C22×C32C22×Q812yes—
280C22×C32H(5,𝔽2)12yes—
281C22×C322−1+412yes—
282C22×C32C2511yescharacteristic
283C32×C4—22no—
284C32×C4—22no—
285C3⋊Dic3—22no—
286C3⋊Dic3—22no—
287C3⋊Dic3C22×Q814yes—
288C3⋊Dic3C22×Q814yes—
289C3×Dic3—24no—
290C3×Dic3—24no—
291C3×Dic3—24no—
292C3×Dic3—24no—
293C22×Q8—32no—
294C22×Q8—92no—
295C23×C4—32no—
296C23×C4—91no—
297C4⋊Q8—98no—
298C4⋊Q8—916no—
299C4⋊Q8—98no—
300#125—916no—
301#125—98no—
302#125—98no—
303C22⋊Q8—316no—
304C22⋊Q8—916no—
305#117—98no—
306#117—98no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—32no—
309C2×C4⋊C4—32no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—92no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—98no—
314C2×C4⋊C4—91no—
315C2×C4⋊C4—91no—
316C2×C4⋊C4—92no—
317C2×C4⋊C4—92no—
318C2×C4⋊C4—92no—
319C2×C4⋊C4—91no—
320C2×C4⋊C4—91no—
321C2×C22⋊C4—32no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4D3211yescharacteristic
324C2×C42—92no—
325C2×C42—91no—
326C2×C42—91no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—22no—
330C23×C3—21no—
331C23×C3—24no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3D3×Q818yes—
335C23×C3C23×D314yes—
336C23×C3C23×D312yes—
337C3×Q8—128no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—34no—
343C2×C3×C4—34no—
344C2×C3×C4—34no—
345C2×C3×C4—34no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—64no—
349C2×C3×C4—64no—
350C2×C3×C4—64no—
351C2×C3×C4—64no—
352C2×C3×C4—128no—
353C2×C3×C4C23×D314yes—
354C2×C3×C4C23×D314yes—
355C2×Dic3—24no—
356C2×Dic3—24no—
357C2×Dic3—24no—
358C2×Dic3—24no—
359C2×Dic3—38no—
360C2×Dic3—38no—
361C2×Dic3—332no—
362C2×Dic3—34no—
363C2×Dic3—34no—
364C2×Dic3—34no—
365C2×Dic3—34no—
366C2×Dic3—48no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C2×Dic3—616no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3C23×D314yes—
379C2×Dic3C23×D314yes—
380C2×Dic3C23×D314yes—
381C2×Dic3C23×D314yes—
382Dic6—48no—
383Dic6—128no—
384Dic6—128no—
385C2×C32—24no—
386C2×C32#54414yescomplemented
387C2×C32C23×Q811yescharacteristic
388C2×C32C2×H(5,𝔽2)11yescharacteristic
389C2×C32C2×2−1+411yescharacteristic
390C24C2×D3211yescharacteristic
391C2×Q8—38no—
392C2×Q8—98no—
393C2×Q8—124no—
394C2×Q8—364no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—38no—
400C22×C4—94no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4—98no—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—124no—
407C22×C4C2×D3211yescharacteristic
408C22×C4C2×D3211yescharacteristic
409C4⋊C4—38no—
410C4⋊C4—38no—
411C4⋊C4—38no—
412C4⋊C4—94no—
413C4⋊C4—98no—
414C4⋊C4—94no—
415C4⋊C4—94no—
416C4⋊C4—94no—
417C4⋊C4—98no—
418C4⋊C4—98no—
419C4⋊C4—98no—
420C4⋊C4—94no—
421C4⋊C4—94no—
422C22⋊C4—38no—
423C22⋊C4—94no—
424C22⋊C4C2×D3214yes—
425C42—98no—
426C42—94no—
427C42—94no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—216no—
431C22×C3—22no—
432C22×C3—24no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—21no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—48no—
439C22×C3#100414yes—
440C22×C3C2×D3×Q818yes—
441C22×C3C2×D3×Q814yes—
442C22×C3#101014yes—
443C22×C3C24×D312yes—
444C3×C4—24no—
445C3×C4—24no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—64no—
449C3×C4—64no—
450C3×C4—64no—
451C3×C4—64no—
452Dic3—24no—
453Dic3—24no—
454Dic3—24no—
455Dic3—24no—
456Dic3—38no—
457Dic3—38no—
458Dic3—64no—
459Dic3—64no—
460Dic3—64no—
461Dic3—64no—
462Dic3—122no—
463Dic3—122no—
464C32C2×#54411yescharacteristic, complemented, Sylow
465C23—22no—
466C23—22no—
467C23#379714yes—
468C23C22×D3212yes—
469C23C22×D3211yescharacteristic
470Q8—128no—
471Q8—368no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—34no—
475C2×C4—34no—
476C2×C4—34no—
477C2×C4—34no—
478C2×C4—64no—
479C2×C4—64no—
480C2×C4—64no—
481C2×C4—64no—
482C2×C4—916no—
483C2×C4—94no—
484C2×C4—94no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—128no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4C22×D3212yes—
493C2×C4C22×D3212yes—
494C2×C3—28no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—24no—
499C2×C3—44no—
500C2×C3#562318yescomplemented
501C2×C3C2×#100412yes—
502C2×C3C22×D3×Q812yes—
503C2×C3C2×#101012yes—
504C22—22no—
505C22—22no—
506C22—28no—
507C22C2×#379714yes—
508C22C2×#379712yes—
509C22#6430912yes—
510C22#6431312yes—
511C22C23×D3211yescharacteristic
512C4—22no—
513C4—22no—
514C4—64no—
515C4—64no—
516C4—64no—
517C4—64no—
518C4—94no—
519C4—94no—
520C4—182no—
521C4—182no—
522C3—21no—
523C3C2×#562312yescomplemented
524C2—24no—
525C2#1059403314yesdirect product factor
526C2C22×#379711yescharacteristic
527C2C2×#6430911yescharacteristic
528C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C2×#63919C2semidirect
7. C2×#63873C2semidirect
8. C2×#63870C2semidirect
9. C2×#63870C2semidirect
10. C2×#63847C2semidirect
11. C2×#63839C2semidirect
12. #10594033C2direct (N × H)
42. #63919C22semidirect
43. #63873C22semidirect
44. #63870C22semidirect
45. #63870C22semidirect
46. #63847C22semidirect
47. #63839C22semidirect
68. C22×C3⋊Dic3Q8semidirect
175. C2×C3⋊Dic3C2×Q8semidirect
386. C2×C32#544semidirect
464. C32C2×#544semidirect
500. C2×C3#5623semidirect
523. C3C2×#5623semidirect
525. C2#10594033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640862
C2×C3×#8782
C22×#37242
C2×#639642
C2×#639572
C2×#639192
C2×#638732
C2×#638702
C2×#638472
C2×#638392
#105940332
C2×#56233